Kenneth J. Metcalf

Boeing Corporation, Canoga Park, California

Power Management and Distribution (PMAD)

Model Development

Final Report

NASA/CR—2011-217268

November 2011
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Kenneth J. Metcalf

Boeing Corporation, Canoga Park, California

Power Management and Distribution (PMAD)

Model Development

Final Report

NASA/CR—2011-217268

November 2011

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared under Contract NAS3–01140
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TABLE OF CONTENTS 

Paragraph Page

1.0 SUMMARY .................................................................................................................................................... 1 

2.0 INTRODUCTION........................................................................................................................................... 3 

3.0 POWER CONDITIONING MODEL DEVELOPMENT ................................................................................. 5 

3.1 Power Conditioning Stages Approach ............................................................................................... 6 

3.2 Chopper Stage Model ........................................................................................................................ 7 

3.3 Inverter and Standard Transformer Models ..................................................................................... 18 

3.3.1 Inverter Transformer Stage Model ................................................................................................. 18 

3.3.2 Standard Transformer Stage Model .............................................................................................. 26 

3.4 Rectifier Stage Model ....................................................................................................................... 30 

3.5 DC Filter Stage Model ...................................................................................................................... 35 

3.6 AC Filter Stage Model ...................................................................................................................... 42 

3.7 DC RBI Model ................................................................................................................................... 47 

3.8 AC RBI Model ................................................................................................................................... 51 

3.9 DC RPC Model ................................................................................................................................. 56 

3.10 AC RPC Model ............................................................................................................................... 60 

3.11 Ancillary Hardware Equations ........................................................................................................ 65 

3.11.1 Conductor and Connector Equations .......................................................................................... 65 

3.11.2 Control and Monitoring Subsystem Mass and Parasitic Power Equations ................................. 68 

3.11.3 Component Volume, Dimension, and Enclosure Equations ....................................................... 70 

3.11.4 Radiator Area and Mass Equations ............................................................................................ 75 

4.0 POWER CONDITIONING MODELS .......................................................................................................... 77 

4.1 Frequency Considerations ............................................................................................................... 77 

4.2 Low Voltage Design Adjustments .................................................................................................... 79 

4.3 Enclosure/Baseplate Type Selection Considerations ...................................................................... 79 

4.4 Enclosure/Baseplate and Coldplate/Radiator Material Options ....................................................... 79 

4.5 Control and Monitoring Harness Material Considerations ............................................................... 80 

4.6 Filter Frequency and Ripple Factor Considerations ......................................................................... 80 

4.7 DC/DC Converter Model .................................................................................................................. 81 

4.8 AC/AC Frequency Converter Model ................................................................................................. 83 

4.9 AC/DC Static Rectifier Model ........................................................................................................... 85 

4.10 Transformer Unit Model .................................................................................................................. 87 

4.11 DC RBI Switchgear Model .............................................................................................................. 89 

4.12 AC RBI Switchgear Model .............................................................................................................. 91 

4.13 DC RPCM Rack Model ................................................................................................................... 93 

4.14 AC RPCM Rack Model ................................................................................................................... 95 

4.15 Solar Array Shunt Regulator Model ............................................................................................... 97 

4.16 Battery Charge Discharge Unit Model ............................................................................................ 99 

4.17 DC Insulated Transmission Line Model ....................................................................................... 102 

4.18 Single and 3-Phase AC Insulated Transmission Line Model ....................................................... 103 

5.0 CONCLUSIONS AND RECOMMENDATIONS ....................................................................................... 105 

References ....................................................................................................................................................... 106 

NASA/CR—2011-217268 iii
LIST OF TABLES 

Table No. Page

TABLE 1: 1 KWE SWITCH MODULE MASS BREAKDOWN ................................................................................................ 7 

TABLE 2: KEY POWER MOSFET SWITCH CHARACTERISTICS – 1992 ............................................................................ 8 

TABLE 3: KEY POWER MOSFET SWITCH CHARACTERISTICS – 2002 ............................................................................ 8 

TABLE 4: COMPARISON OF 1992 AND 2002 MOSFET POWER LOSSES .......................................................................... 8 

TABLE 5: COMPARISON OF RESONANT AND WEINBERG CONVERTER MASSES .............................................................. 9 

TABLE 6: CHOPPER MODEL VARIABLE DEFINITIONS ................................................................................................... 10 

TABLE 7: EFFICIENCY CORRECTIONS FOR LOW VOLTAGE CHOPPER MASS ESTIMATES ............................................... 13 

TABLE 8: CONVERTER FREQUENCY INPUT GUIDE ....................................................................................................... 17 

TABLE 9: INVERTER TRANSFORMER MODEL VARIABLE DEFINITIONS ......................................................................... 18 

TABLE 10: TRANSFORMER STEP RATIO GUIDELINES ................................................................................................... 25 

TABLE 11: STANDARD TRANSFORMER MODEL VARIABLE DEFINITIONS ..................................................................... 28 

TABLE 12: 1 KWE DIODE MODULE MASS BREAKDOWN .............................................................................................. 29 

TABLE 13: RECTIFIER STAGE MODEL VARIABLE DEFINITIONS .................................................................................... 30 

TABLE 14: EFFICIENCY CORRECTIONS FOR LOWER VOLTAGE RECTIFIER MASS ESTIMATES ....................................... 33 

TABLE 15: DC FILTER MODEL VARIABLE DEFINITIONS .............................................................................................. 34 

TABLE 16: AC FILTER MODEL VARIABLE DEFINITIONS .............................................................................................. 42 

TABLE 17: DC RBI MODEL VARIABLE DEFINITIONS ................................................................................................... 47 

TABLE 18: AC RBI MODEL VARIABLE DEFINITIONS ................................................................................................... 51 

TABLE 19: DC RPC MODEL VARIABLE DEFINITIONS .................................................................................................. 56 

TABLE 20: AC RPC MODEL VARIABLE DEFINITIONS .................................................................................................. 60 

TABLE 21: CONDUCTOR AND CONNECTOR EQUATION VARIABLE DEFINITIONS .......................................................... 65 

TABLE 22: CONTROL AND MONITORING EQUATION VARIABLE DEFINITIONS .............................................................. 69 

TABLE 23: COMPARISON OF SSF AND ISS POWER CONDITIONING COMPONENT DENSITIES ......................................... 71 

TABLE 24: FINNED HEAT EXCHANGER BOX ASPECT RATIOS ...................................................................................... 72 

TABLE 25: FINNED HEAT EXCHANGER BOX MASS BREAKDOWN ............................................................................... 72 

TABLE 26: FINNED HEAT EXCHANGER BOX MASS PER SURFACE AREA .................................................................... 73 

TABLE 27: COLDPLATE BOX MASS BREAKDOWN ....................................................................................................... 73 

TABLE 28: CARBON-CARBON FINNED HEAT EXCHANGER BOX MASS BREAKDOWNS ................................................. 74 

TABLE 29: CARBON-CARBON COLDPLATE BOX MASS BREAKDOWNS ........................................................................ 74 

TABLE 30: SUGGESTED CONVERTER / INVERTER SWITCHING FREQUENCY MAXIMUMS .............................................. 78 

TABLE 31: SUGGESTED BCDU SWITCHING FREQUENCY MAXIMUMS ......................................................................... 78 

TABLE 32: SUGGESTED ARRAY SHUNT REGULATOR SWITCHING FREQUENCY MAXIMUMS ........................................ 78 

TABLE 33: MODEL EFFICIENCY VALUES FOR LOW VOLTAGE COMPONENT DESIGNS .................................................. 79 

TABLE 34: DC/DC CONVERTER MODEL INPUT PARAMETER RANGES ......................................................................... 82 

TABLE 35: AC/AC FREQUENCY CONVERTER MODEL INPUT PARAMETER RANGES ..................................................... 84 

TABLE 36: AC/DC STATIC RECTIFIER MODEL INPUT PARAMETER RANGES ................................................................ 86 

TABLE 37: AC/AC TRANSFORMER UNIT MODEL INPUT PARAMETER RANGES ............................................................ 88 

TABLE 38: DC RBI SWITCHGEAR UNIT MODEL INPUT PARAMETER RANGES .............................................................. 90 

TABLE 39: AC RBI SWITCHGEAR UNIT MODEL INPUT PARAMETER RANGES .............................................................. 92 

TABLE 40: DC REMOTE POWER CONTROL MODULE RACK MODEL INPUT PARAMETER RANGES ................................. 94 

TABLE 41: AC REMOTE POWER CONTROL MODULE RACK MODEL INPUT PARAMETER RANGES ................................. 96 

TABLE 42: SOLAR ARRAY SHUNT REGULATOR MODEL INPUT PARAMETER RANGES................................................... 98 

TABLE 43: BATTERY CHARGE DISCHARGE UNIT MODEL INPUT PARAMETER RANGES .............................................. 100 

TABLE 44: DC INSULATED TRANSMISSION LINE MODEL INPUT PARAMETER RANGES ............................................... 102 

TABLE 45: SINGLE- AND 3-PHASE AC INSULATED TRANSMISSION LINE MODEL INPUT PARAMETER RANGES ........... 104 

NASA/CR—2011-217268 iv
LIST OF FIGURES 

Figure No. Page

FIGURE 1: CHOPPER SPWT VS EFFICIENCY ................................................................................................................. 11 

FIGURE 2: CHOPPER SPWT VS POWER LEVEL ............................................................................................................. 13 

FIGURE 3: CHOPPER SPWT VS POWER LEVEL - 1 PHASE AND 3 PHASE ....................................................................... 13 

FIGURE 4: CHOPPER SPWT VS VOLTAGE – LOW VOLTAGE REGION ........................................................................... 15 

FIGURE 5: CHOPPER SPWT VS VOLTAGE – HIGH VOLTAGE REGION ........................................................................... 16 

FIGURE 6: CHOPPER SPWT VS FREQUENCY – SINGLE & 3 PHASE DESIGNS ................................................................ 17 

FIGURE 7: CHOPPER SPWT VS FREQUENCY – SINGLE PHASE DESIGNS ....................................................................... 18 

FIGURE 8: INVERTER TRANSFORMER SPWT VS EFFICIENCY ....................................................................................... 21 

FIGURE 9: INVERTER TRANSFORMER SPWT – 1 PHASE VS 3 PHASE ............................................................................ 23 

FIGURE 10: INVERTER TRANSFORMER SPWT VS POWER (WIDE RANGE) .................................................................... 24 

FIGURE 11: INVERTER TRANSFORMER SPWT VS POWER (NARROW RANGE) .............................................................. 24 

FIGURE 12: INVERTER TRANSFORMER SPWT VS VOLTAGE ........................................................................................ 25 

FIGURE 13: INVERTER TRANSFORMER SPWT VS FREQUENCY (WIDE RANGE) ............................................................ 28 

FIGURE 14: INVERTER TRANSFORMER SPWT VS FREQUENCY (NARROW RANGE) ...................................................... 29 

FIGURE 15: RECTIFIER SPWT – 1 PHASE VS 3 PHASE .................................................................................................. 31 

FIGURE 16: RECTIFIER SPWT VS EFFICIENCY ............................................................................................................. 32 

FIGURE 17: RECTIFIER SPWT VS LOW VOLTAGES ...................................................................................................... 34 

FIGURE 18: DC FILTER SPWT VS RIPPLE FACTOR ...................................................................................................... 37 

FIGURE 19: DC FILTER SPWT VS EFFICIENCY ............................................................................................................ 38 

FIGURE 20: DC FILTER SPWT VS POWER – SINGLE–PHASE AND 3-PHASE ................................................................ 39 

FIGURE 21: DC FILTER SPWT VS VOLTAGE – LOW VOLTAGE REGION ..................................................................... 40 

FIGURE 22: DC FILTER SPWT VS VOLTAGE – HIGH VOLTAGE REGION .................................................................... 41 

FIGURE 23: DC FILTER SPWT VS FREQUENCY ............................................................................................................ 42 

FIGURE 24: AC FILTER SPWT VS POWER - SINGLE PHASE & 3 PHASE ...................................................................... 44 

FIGURE 25: AC FILTER SPWT VS EFFICIENCY ............................................................................................................ 44 

FIGURE 26: AC FILTER SPWT VS POWER .................................................................................................................... 46 

FIGURE 27: AC FILTER SPWT VS FREQUENCY ............................................................................................................ 47 

FIGURE 28: DC RBI SPWT VS EFFICIENCY ................................................................................................................. 49 

FIGURE 29: DC RBI SPWT VS POWER LEVEL ............................................................................................................. 50 

FIGURE 30: DC RBI SPWT VS VOLTAGE .................................................................................................................... 51 

FIGURE 31: AC RBI SPWT - 1 PHASE VS 3 PHASE ..................................................................................................... 53 

FIGURE 32: AC RBI SPWT VS EFFICIENCY ................................................................................................................. 54 

FIGURE 33: AC RBI SPWT VS POWER LEVEL ............................................................................................................. 55 

FIGURE 34: AC RBI SPWT VS VOLTAGE .................................................................................................................... 56 

FIGURE 35: DC RPC SPWT VS EFFICIENCY ................................................................................................................ 58 

FIGURE 36: DC RPC SPWT VS POWER LEVEL ............................................................................................................ 59 

FIGURE 37: DC RPC SPWT VS VOLTAGE ................................................................................................................... 60 

FIGURE 38: AC RPC SPWT - 1 PHASE VS 3-PHASE ................................................................................................... 62 

FIGURE 39: AC RPC SPWT VS EFFICIENCY ................................................................................................................ 63 

FIGURE 40: AC RPC SPWT VS POWER LEVEL ............................................................................................................ 64 

FIGURE 41: AC RPC SPWT VS VOLTAGE ................................................................................................................... 65 

NASA/CR—2011-217268 v

1.0 SUMMARY

Power management and distribution (PMAD) models were developed in the early 1990’s to model candidate 

architectures for various Space Exploration Initiative (SEI) missions. They were used to generate "ballpark" 

component mass estimates to support conceptual PMAD system design studies. The initial set of models 

was provided to NASA Lewis Research Center (since renamed Glenn Research Center) in 1992 [Ref. 1]. 

They were developed to estimate the characteristics of power conditioning components predicted to be 

available in the 2005 timeframe. Early 90’s component and device designs and material technologies were 

projected forward to the 2005 timeframe, and algorithms reflecting those design and material improvements 

were incorporated into the models to generate mass, volume, and efficiency estimates for circa 2005 

components.

The models are about ten years old now and NASA GRC requested a review of them to determine if they 

should be updated to bring them into agreement with current performance projections or to incorporate 

unforeseen design or technology advances. This report documents the results of this review and the 

updated power conditioning models and new transmission line models generated to estimate post 2005 

PMAD system masses and sizes. This effort continues the expansion and enhancement of a library of 

PMAD models developed to allow system designers to assess future power system architectures and distribution techniques quickly and consistently.

These models are designed primarily for space missions that require continuous power for long periods and 

are capable of supporting manned operations. Model development is based on the premise that a power 

conditioning unit can be broken down into its major stages and elements, and that by developing mass trends 

as a function of power, voltage, and frequency for the basic devices and components within them, trends can 

be derived for the larger assemblies. The mass of a complete component is determined by summing the 

masses of the power conditioning stages and adding on the mass of the control and monitoring, enclosure, 

and thermal management subsystems. The thermal management algorithms are based on passive thermal 

control (heat pipe radiator) and calculate the associated coldplate and radiator mass. The model 

documentation explains the component equations, including their coefficients and exponents; identifies 

model limitations; specifies valid input ranges; and discusses methods for applying the component models.

The review indicated some of the technology and design advancement projections built into the models were 

too aggressive and significant modifications were made to the box (enclosure and baseplate) and thermal 

management (coldplate and radiator) equations. The as-built space station component boxes were 

substantially larger and heavier than originally estimated. Unanticipated structural panels, smaller boxes, 

were also installed in them. The original box algorithms were largely based on those designs and they were 

revised to agree with the as-built masses. The packaging density, which determines the box size, was also 

reduced, resulting in larger calculated box sizes. The original radiator equations were generated from a lunar 

base thermal management analysis. The DC to DC Converter Unit (DDCU) coldplate and heat pipe radiator 

design is more relevant to most space missions, so the coldplate and radiator size and mass equations were 

modified to agree with it. And finally, to support mass versus cost trades in the design of these elements, 

aluminum and carbon-carbon material options were incorporated into the box and radiator algorithms.

The model calculated too low of a mass for the converter electronics, even after its efficiency inputs were 

increased to agree with on-orbit DDCU efficiencies. Electronics mass can be traded against efficiency, and 

the algorithms contain equations to model this trade. The efficiency calculations were revised to reflect these 

improvements, and a Weinberg converter algorithm was added to better model this part of the DDCU. This 

algorithm and the previously developed resonant converter algorithm were modified to incorporate higher 

switch and diode masses, because previous estimates were judged too optimistic after a review of these 

devices. The transformer and dc filter mass estimation equations were changed to reflect improved 

performance at higher operating frequencies. A measure of the combined changes can be obtained by 

looking at the range of mass outputs the DDCU model can predict for the International Space Station (ISS) 

DDCU. The revised model predicts the mass of the ISS DDCU would be about 6% less if minimal advances 

were to occur, essentially today’s technology, but if all the advances projected to be available in the 2005 to 

2010 timeframe were incorporated, it predicts its mass could be reduced as much as 53%.

NASA/CR—2011-217268 1
2.0 INTRODUCTION

This effort was initiated to update several PMAD models previously provided to NASA GRC in 1992 and to 

provide two new component and two new transmission line models. The predecessors of these models were 

originally developed to evaluate centralized versus decentralized lunar base power system architectures and 

to conduct voltage and frequency trade studies [Ref. 2]. When NASA GRC received the results of these 

early studies they had questions about the development, applications, and capabilities of the models that 

were used. It was decided these models needed to be documented to define their capabilities and 

limitations, and to allow critical review by experts in the field. Additional models were also required to allow a 

wider variety of power systems to be evaluated. This lead to the creation of the original Task Order 15 report,

which documented the development and capabilities of ten of the most essential models [Ref. 1]. It was 

understood this was only the beginning and that subsequent reports would be required to add to this set of 

models and to periodically update previously provided models to incorporate technology advances. Later 

reports provided power processing unit models for electric propulsion system assessments and new power 

conditioning and transmission line models. Gradually a library of PMAD models was formed. This report 

continues that development.

The models contained in this report are intended to be simple to use and yield useful results. While these 

objectives are desirable, the simplicity of the models themselves may lead individuals not familiar with PMAD 

systems to assume the components are easy to design and the technology is mature. This is not the case. 

The size and complexity of the models is kept down by identifying the basic stages within components and 

developing generalized mass relationships for these stages from component designs presented in papers 

and employed on similar programs. Designers are constantly developing new design approaches and 

incorporating new technologies to achieve better performance and reduce mass. Consequently, to develop 

representative PMAD models of future components it was necessary to review emerging technologies and 

evaluate these against proposed space applications. The objective was to formulate a set of component 

characteristics and operating conditions that would be consistent with future PMAD designs.

This power conditioning model update was begun by reviewing many of the component designs and device 

technologies used as the starting point for the original models. The previous performance and technology 

advances incorporated into the models were then assessed against present designs, device capabilities, and 

material properties to evaluate the level of actual advancement against the original projections. Then using 

this power element technology assessment, the amount of advancement expected over the next five years 

was gauged to obtain device characteristics and material properties consistent with post 2005 technologies. 

The resulting values were compared against the original values used to generate the stage mass algorithms 

that are combined to form the various component models. The mass values generated by the updated 

models were compared against other component mass projections to validate their accuracy. The overall 

model estimates were then validated against other design projections to served as benchmarks, and they 

were the basis for mass breakdowns generated at other operating points. Equations representing the various component stages were developed from these data points using curve fitting techniques. The final step 

was to assimilate selected equations into a spreadsheet to form a complete component model.

Anticipated improvements in PMAD components are reflected in the models and discussed in the sections 

dedicated to those devices. Although a concentrated development effort is necessary to achieve many of 

these performance levels, this report does not propose methods for realizing them or identify critical technology areas. This is not its intent. Technology projections are addressed on a case by case basis, but in 

general they are based on information obtained from related power system studies and designs, and discussions with experts in the PMAD field. The purpose of this report is not to supply component design 

information, but to present models representative of future PMAD components and explain the rationale 

behind their development. Future studies are planned by NASA to generate technology road maps that will 

identify the critical technologies that must be developed to fabricate and deploy advanced power systems.

Every space application will have different operating requirements, many of which are not even envisioned at 

the present time. Although the models in this report are designed to accept a wide range of operating 

parameters, they are not capable of addressing all aspects of a particular application. It was necessary to 

NASA/CR—2011-217268 2
assume typical values for some parameters. This naturally introduces a certain amount of error and it is one 

reason model outputs should be compared with other sources of information.

These models also address a specific type of power system operation. They are designed to support 

assessments of long life, high reliability power systems supplying continuous power. Continuous power 

systems are designed for steady state operation and they typically operate for years. A PMAD system 

designed for long term operation requires radiators and passive and/or active thermal management techniques. Components in a passive system contain internal heat sinks and thermal paths that conduct 

generated heat to a coldplate. The hardware necessary to passively cool a device may account for 80 to 

90% of its total mass. Heat pipes routed through the coldplate then transport this heat out to a radiator for 

dissipation. An active cooling system employing a coldplate would use a pumped loop containing a liquid 

to carry heat from the coldplate to a radiator surface.

These models should not be used for burst power applications because the thermal management 

approach employed with this type of system is very different. Burst power systems are designed for short 

term operation, generally less than fifteen minutes. This short operating life allows the use of adiabatic or 

cryogenic cooling techniques. Adiabatic cooling relies on the heat capacity of the component and 

adjacent structure to absorb generated heat. Mass constraints essentially limit adiabatic cooling times to 

under 120 seconds. Cryogenic cooling normally uses liquid hydrogen or nitrogen to cool the power conditioning components to near cryogenic temperatures. The cryogenic liquid and its tankage can be quite 

heavy; hence, the operating life of these systems is limited. Cryogenic cooling is typically used only when 

the cryogenic liquid has other uses, such as for a propellant. A person who incorrectly uses these models 

to estimate masses in burst power applications will obtain power conditioning mass estimates that are 

much too heavy. In some cases, the estimates may be ten times the actual values.

Another factor affecting PMAD mass is whether the platform is manned or unmanned. Man critical systems 

have higher reliability, availability, and maintainability requirements. Consequently, a more conservative 

design approach is usually employed. Components are operated at lower power densities and temperatures. 

This increases PMAD mass because added thermal management hardware is required and larger power 

devices are used throughout the system. The components in a manned system may also need to be 

designed for easy removal and maintenance. This also drives up PMAD mass because components will 

need to be equipped with electrical connectors, mechanical disconnects, and heat exchangers or fluid couplings to provide detachable heat transfer paths.

Since many proposed space missions are manned or support manned expeditions, reliability considerations 

influenced the model development. A detailed reliability analysis was not conducted during this study, 

therefore it was necessary to make some basic assumptions. It is anticipated that most missions will require 

the power conditioning components to achieve at least a ten year operating life. Because many of the 

present Space Station components are designed to meet a fifteen-year mean time between failure (MTBF), 

this data was relied on heavily during the model development. Reliability is normally improved in two ways: 

(1) key elements within a component can be made redundant, and (2) multiple smaller units, each sized to 

handle a percentage of the power, can replace a single large unit. Unfortunately, reliability considerations 

typically increase power system mass and place added demands on the instrumentation and control 

subsystem. Incorporating internal redundancy into a component increases its mass since additional

elements are required. Replacing a single power conditioning unit with multiple smaller units increases mass 

because some economies of scale are sacrificed and ancillary hardware such as the enclosure, and control 

and monitoring now occupy a larger percentage of the total component mass. The size and complexity of the

instrumentation and control (I&C) subsystem that oversees the entire power system is also expanded since it 

must monitor a larger number of units and coordinate their operation. The mass impacts associated with an 

enlarged I&C subsystem are not addressed by these models since they only pertain to individual power 

conditioning components.

NASA/CR—2011-217268 3
3.0 POWER CONDITIONING MODEL DEVELOPMENT 

Before the original power conditioning model development was begun in 1992, a power element technology 

assessment was conducted to determine the amount of advancement one could reasonably expect by the 

year 2000. This study was conducted in 1991 [Ref. 3] and examined the key power element technologies, 

switching devices, magnetic materials, and capacitors expected to be used in high power systems. The 

current and potential capabilities of existing elements were determined as well as the projected 

capabilities of advanced alternatives. After considering anticipated technology advances in the context of 

proposed SEI missions, general conclusions were reached. Numerous improvements were projected for 

converter elements, thermal management subsystems and packaging techniques. It was anticipated that 

carbon-carbon would be used extensively for enclosures and heat pipes, replacing aluminum in many 

applications. Component radiators would also utilize carbon-carbon extensively. Improvements in the 

magnetic materials area were expected to be fairly minor and occur mainly in the high frequency region. 

High frequency transformer and inductor core masses and losses were expected to decline modestly as a 

result. Incremental improvements in capacitors were also expected to yield modest gains in energy density 

and efficiency. At the time, most semiconductor switches were limited to operating voltages below 500 V 

[Ref. 4]. The exception was silicon controlled rectifiers (SCRs), one of the switch types within the thyristor 

family, were available at voltages up to 5000 V, but their turn off requirements limited their applications1 [Ref. 

5]. Anticipated advances in metal-oxide-semiconductor field-effect-transistors (MOSFETs) and MOS controlled thyristors (MCTs) indicated much higher voltage devices could be developed by the year 2000, 

possibly as high as 5000 V [Ref. 6, 7, 8). The development of high voltage, high current density semiconductor switches was expected to make higher voltage, higher power converters more practical. 

Improvements in MOSFET construction, particularly changes that that lowered their losses, were expected to 

reduce the mass of converters and improve their efficiency. However, these predicted technology advances 

were highly speculative because a key driver would be development funding and it could vary considerably.

Since these projections were for post 2000 semiconductor switches and its 2002, the capabilities of current 

switches can be reviewed to see if the original projections panned out. The on-resistance of MOSFETs has 

declined substantially, but not at much as was projected, necessitating an increase in the reference switch 

module mass (this is addressed in detail in section 3.1.1). Their voltage rating has also been increased, but 

they have only reached 1200 V [Ref. 9], well below the original 5000 V projection. This is may be partially 

due to the progress that has occurred in insulated gate bipolar transistors (IGBTs). IGBTs are available at 

voltages up to 4500 V [Ref. 10], with on-resistance and turn-on, turn-off times close to those of MOSFETs 

[Ref. 11]. The development of MCTs has also been slower than projected, which may again be partially due 

to the progress in high voltage IGBTs. Presently, 1400 V rated MCTs are available [Ref. 12]. Higher voltage 

MCTs can be manufactured, but the allowable conduction current density falls off rapidly at voltages above 

2000 V. Thyristors with ratings up to 12,000 V are available [Ref. 13], but as noted previously their turn-off 

characteristics limit their use to rectifiers and ac switches, and their relatively slow turn-on time further limits 

them to low frequency applications. So in summary, the development of high voltage MOSFETs and MCTs 

has been slower than projected, but IGBTs have largely filled this gap. MOSFET losses have declined, but 

not as much as projected. The conclusion is the originally generated equations for the chopper and rectifier 

stages, which were partially based on the properties of these switches and diodes, must be changed to 

reflect less semiconductor switch development and reduced performance capabilities.

Based on the original technology assessment and this review, device characteristics were defined that were 

deemed to be consistent with future PMAD designs. This data served as a foundation for the actual component model development. Models were generated using a six step process: (1) the specific stages in a 

component were identified; (2) mass breakdowns for these stages were obtained by studying component 

designs or hardware; (3) projected technology advances were considered and used to adjust these mass 

 

 1 An SCR cannot be turned off by simply removing the gate signal, the current flow must either be interrupted or forced to flow in the opposite direction. For ac switching or rectification, these turn-off 

requirements may be acceptable because the current naturally crosses through zero each half cycle. 

However in a DC application, such as an inverter switch, they aren't usually acceptable.

NASA/CR—2011-217268 4
breakdowns to yield mass values consistent with the 2005 to 2010 time period; (4) these adjusted mass 

breakdowns were used as benchmarks and they were extrapolated from to generate mass tabulations at 

other operating points; (5) equations were generated to fit these points using curve fitting techniques; and (6) 

selected equations were assimilated to form a complete model. This entire process is based on the theory 

that the mass of a power conditioning component can be estimated by summing the masses of its power 

processing stages and associated hardware (this approach is treated in detail in the next section).

The original stage equations contained in the models were developed and validated by comparing the mass 

breakdowns used for equation development and the resulting model generated mass estimates with existing 

designs [Ref. 1, Appendix A]. The original mass breakdowns were derived from Rocketdyne and Ford 

Aerospace SSF and TRW 20 kHz component mass breakdowns [Ref. 14, 15, 16], after they were modified 

to incorporate projected technology advances. To assess the accuracy of these original breakdowns against 

present designs, the masses of several of the ISS flight components were obtained [Ref. 17]. Unfortunately, 

it wasn’t possible to obtain mass breakdowns of these components, but by obtaining the shipping masses of 

their enclosures and baseplates, and factoring known component design modifications into the original 

breakdowns, it was possible to develop reasonably accurate mass breakdowns of the current components. 

These derived mass breakdowns served as the new benchmarks for subsequent extrapolations. Because it 

was easier to project the improvements for a single item, each element in a stage was evaluated individually. 

To generate mass breakdowns at other operating points, the impact on mass as power, voltage, efficiency, 

and frequency are changed were considered separately. The individual element mass impacts were then 

summed to obtain an estimate of the total mass impact of a change in an operating parameter. This approach simplified the extrapolation process and resulted in greater confidence in the values.

3.1 POWER CONDITIONING STAGES APPROACH

Power conditioning components tend to have common stages. For example, the dc/dc converter, the dc/ac 

inverter and the ac/ac frequency converter, each have a chopper stage. The interconnection and control of

these stages determine the function and operation of the total converter. Hence, one can define the stages 

contained in a specified converter, calculate their individual masses, and then add these values to the control 

and monitoring hardware mass, the enclosure mass and the thermal management and radiator subsystem 

mass to determine the total mass of a complete converter.

The masses of power conditioning components were estimated by defining the stages in a component and 

generating mass equations for them using the previously described six step process. Much of the information used to develop these equations was obtained from SSF and ISS documentation. These designs were 

considered to best typify future space based components because the space station power levels and 

component life times are approaching those planned for future space missions. Because the intent is to 

model future systems, these mass figures were adjusted to incorporate projected technology advances. 

Equations were then developed to estimate the mass of ancillary hardware such as controllers, data interface 

modules and monitoring sensors. The masses of the individual stages and ancillary hardware are summed 

to obtain the total electronics mass. Based on this mass and a factor computed for the density of electronics, 

the enclosure and baseplate masses were estimated. These values are then summed to obtain the component mass. Finally, a mass is computed for the radiator and added to this component mass to obtain the 

total mass of a power conditioning component subsystem, including its thermal management hardware.

Because the PMAD component models contain interconnected stages, the best way to explain their 

development is to individually address the development of the component stage equations. To better present 

the supporting rationale, these equations will be further broken down and their parts discussed separately. 

Because many effects can’t be easily explained mathematically, graphs will be used liberally to display the 

mass effects projected to occur as an operating point is varied over the range of interest. The equations 

incorporate information obtained from technical reports, program documentation, textbooks, design manuals, 

and vendor catalogues. These sources will be identified during the model discussions.

NASA/CR—2011-217268 5
3.2 CHOPPER STAGE MODEL

The chopper stage converts dc into ac, and its included in the inverter, dc/dc converter and frequency 

converter models. The design of a chopper can follow one of several different topologies, depending on the 

design requirements. The chopper stage equations provided in this report are based on Weinberg converter 

and parallel resonant converter circuit topologies. They were developed from simplified representations of 

these topologies, though, and are only intended to provide rough mass estimates for comparing components. 

To obtain more accurate mass estimates, specific designs should be generated by a circuit designer.

The chopper section has switch modules, diodes, inductors and capacitors. Each switch module contains a 

semiconductor switch and is supported by a snubber circuit to dampen voltage spikes occurring during 

switching, a heat sink for thermal management, gate drive circuitry to turn it on and off, switch control logic to 

implement the selected switching scheme (e.g., pulse-width-modulation) and packing and mounting 

hardware. Estimated mass breakdowns for circa 1992, present 2002, and projected post 2005 1 kWe switch 

modules, including support hardware, are shown in Table 1. A 1 kWe power level was selected to provide a 

per unit basis for later mass extrapolations. The 1992 mass values were originally estimated from briefing 

packages prepared by TRW, Ford Aerospace, and Rocketdyne in support of SSF, and a power MOSFET 

catalogue [Ref. 14, 15, 16, 4). The 2002 mass breakdown was developed from a comparison of present 

power MOSFET characteristics (obtained from ST Microelectronics data sheets dated 1998 through 2001) 

with 1992 power MOSFET characteristics (obtained from a 1992 Harris Semiconductor power MOSFET 

catalogue) [Ref. 18, 19]. These results are discussed later. The projected 2005 mass breakdown originates 

from articles discussing future power conditioning component developments, discussions with experts in the 

field of power conditioning [Ref. 20, 21, 22, 23], and an extrapolation from the 1992 and 2002 data. The 

projected 2005 mass breakdown was used as a basis for the subsequent equation development.

Table 1: 1 kWe Switch Module Mass Breakdown

Projected

Circa 1992 Present 2002 Post 2005

Hardware Element Mass (grams) Mass (grams) Mass (grams)

Active Switch Element 7 6 5 

Snubber Circuitry 20 18 17

Heat Sink, Thermal Management 48 40 37

Gate Drive Circuitry 25 20 18

Switch Control Logic 20 15 13

Packaging and Mounting 40 33 30

 Total Switch Module 160 132 120

When this model development effort was initiated in 1992, advances in switch fabrication techniques, better 

switch geometries, and continuing size reductions in integrated circuits were expected to reduce the mass of 

switch elements. Much of the power semiconductor development was expected to be aimed at improving 

their efficiency because the main limiting factor in electronics mass reduction was and still is the inability to 

remove waste heat [Ref. 23]. For this reason, the best method of evaluating semiconductor development 

was considered to be an assessment of the reduction in switch losses. In general switch losses are of two 

types, conduction losses and switching (or edge) losses occurring during switch turn-on and turn-off. 

Conduction losses can best be evaluated by comparing the on-resistance of the switch, while switching 

losses are best assessed by comparing the rise time when the switch is turned-on (tr) and the fall time when 

the switch is turned-off (tf). A better performing switch will have a lower on-resistance and shorter rise and 

fall times. MOSFETs were selected for this evaluation because they tend to be the most widely used type of 

power switch because of their good conduction and excellent gate turn-on, turn-off characteristics. The 

performance characteristics of power MOSFETs circa 1992 are presented in Table 2, while comparable 

power MOSFET characteristics are provided in Table 3. The worst case losses for the two sets of switches 

are also provided for 20 and 40 kHz switching frequencies, typical of what might be obtained under worst 

NASA/CR—2011-217268 6
case switching conditions with pulse-width-modulation (PWM). Table 4 compares the two sets of loss 

values, and shows how much these losses have been reduced from about 1992 to 2002.

Table 2: Key Power MOSFET Switch Characteristics – 1992

Table 3: Key Power MOSFET Switch Characteristics – 2002

Table 4: Comparison of 1992 and 2002 MOSFET Power Losses

1992 MOSFET 

Harris P/N

VDSS 

(volts)

IDS 

(amps)

RDS 

(ohms)

tr 

(nsec)

tf 

(nsec)

20 kHz 

Losses 

(watts)

40 kHz 

Losses 

(watts)

RFP40N10 100 40 0.04 30 20 68.0 72.0

IRF251R 150 30 0.085 120 80 94.5 112.5

IRF640R 200 18 0.14 50 35 51.5 57.6

IRF740R 400 10 0.47 25 25 51.0 55.0

IRFP460 500 20 0.27 81 65 137.2 166.4

IRFPC40R 600 8 1 18 20 67.6 71.3

IRFPG40R 1000 4.3 3.5 50 50 73.3 81.9

Harris - Harris Semiconductor

2002 MOSFET 

STM P/N

VDSS 

(volts)

IDS 

(amps)

RDS 

(ohms)

tr 

(nsec)

tf 

(nsec)

20 kHz 

Losses 

(watts)

40 kHz 

Losses 

(watts)

STP40NF10L 100 40 0.028 82 24 61.8

STB40NS15 150 30 0.065 45 35 65.7 72.9

IRF640MFP 200 18 0.15 27 25 52.3 56.1

IRF740 400 10 0.48 10 10 49.6 51.2

STW20NM50FD 500 20 0.22 20 15 95.0 102.0

STP8NM60FP 600 8 0.9 10 10 59.5 61.4

STW5NB100 1000 4.3 2.9 11 22 56.5 59.3

STM - STMicroelectronics

2002 MOSFETs 1992 MOSFETs 2002 / 1992 Losses

VDSS 

(volts)

IDS 

(amps)

20 kHz 

Losses 

(watts)

40 kHz 

Losses 

(watts)

20 kHz 

Losses 

(watts)

40 kHz 

Losses 

(watts)

20 kHz 

Losses 

(watts)

40 kHz 

Losses 

(watts)

100 40 53.3 61.8 68.0 72.0 78.4% 85.8%

150 30 65.7 72.9 94.5 112.5 69.5% 64.8%

200 18 52.3 56.1 51.5 57.6 101.7% 97.4%

400 10 49.6 51.2 51.0 55.0 97.3% 93.1%

500 20 95.0 102.0 137.2 166.4 69.2% 61.3%

600 8 59.5 61.4 67.6 71.3 88.0% 86.2%

1000 4.3 56.5 59.3 73.3 81.9 77.0% 72.4%

Average 83.0% 80.1%

NASA/CR—2011-217268 7
Table 4 indicates power MOSFET losses have declined about 20% since 1992, which should allow the 

mass of their associated heat sinks to be reduced a similar amount. The estimated heat sink mass in 

1992 for a 1 kWe switch was 48 grams. Based on this reduction in losses, this value is now estimated to 

be 40 grams, and assuming similar efficiency improvements in the future its projected to be 37 grams post 

2005. The expected introduction of graphite based fibers in heat sinks to facilitate heat removal should also 

allow heat sink mass reductions because graphite has superior heat transfer characteristics and its specific 

weight is about two-thirds that of aluminum. During the course of this investigation it was noted that the 

semiconductor manufacturers also claim the switch die size has been reduced 10%, while achieving these 

performance gains. These statements support the currently estimated and projected reduction in active 

switch element size shown in Table 1. The snubber and gate drive circuit masses are also assumed to 

decline, but at a slower rate. Continuing size reductions in integrated circuits, particularly in electrically 

erasable programmable read only memory (EEPROMs) and programmable logic arrays (PLAs), support the 

size reductions shown for switch control logic circuits. The packaging and mounting mass should decline in 

proportion to the mass reductions obtained in the other elements. The total projected mass of a 1 kWe 

switch assembly post 2005 is now projected to be 120 grams. When the original post 2005 estimate was 

made in 1992 the total mass of a 1 kWe switch module was estimated to be 100 grams. This now appears 

to have been slightly too optimistic, and the mass algorithms for the stages containing switch modules have 

been adjusted to reflect the new post 2005 projected 1 kWe switch module mass of 120 grams.

In addition to switch module mass, ancillary hardware is required in the chopper circuit to manage internal 

energy flows and to supply current during switch off periods. A parallel resonant topology has a tank circuit 

consisting of an inductor and capacitor that stores energy to facilitate current circulation and switching; a 

Weinberg converter topology requires an input inductor to maintain a constant current supply. In 1992 when 

these models were developed, inductor and capacitor masses were projected to decline about 10% by 2005, 

and most of this mass gain was expected to occur at higher frequencies. Research continues to develop 

alternate magnetic materials, but there haven’t been any new materials introduced in the past ten years. The 

most recently developed materials, metglas and ferrites, were available in 1992. Long term, proven materials 

such as supermalloy and orthonal are still widely used, and are expected to continue to be widely used. The 

main change in magnetic materials has been a reduction in losses at higher frequencies, accomplished 

through thinner laminations or improved manufacturing capabilities. This has resulted in mass reductions in 

high frequency applications and enabled higher switching speeds in resonant and switch mode converters. 

Capacitor development has enabled improvements in energy storage density, particularly with 

aerocapacitors, but their application is limited by their voltage capabilities. Because aerocapacitor cells can 

only withstand a few volts, several must be stacked to reach the voltage levels required for high power 

circuits. This has sharply limited their use. Overall the mass of the tank hardware in a chopper circuit was 

expected to decline about 10% from 1995 to 2005, and this still seems to be reasonably valid. Consequently 

the inductor and capacitor mass equations weren’t changed. Table 5 shows mass breakdowns for 1 kWe, 

40 kHz, post 2005 resonant and Weinberg converters. These breakdowns were generated from information 

obtained from Rocketdyne, NASA LeRC, General Dynamics, and TRW [Ref. 14, 15, 23, 24, 25]. They don’t 

include the transformer and rectifier diode masses, which are addressed in subsequent sections. 

Table 5: Comparison of Resonant and Weinberg Converter Masses

Element or Device Post 2005 1 kWe

Resonant Converter

Post 2005 1 kWe

Weinberg Converter

Switch Modules 285 grams 240

Diode Modules 130 grams 164

Inductor 182 grams 265

Capacitor 118 grams -----

 Total 715 grams 669 grams

NASA/CR—2011-217268 8
Using these mass breakdowns, algorithms were developed for Weinberg and resonant converter topologies. 

The Weinberg converter equations are incorporated into the DC to DC Converter model, while the resonant 

converter equations are contained in the DC to AC Inverter and Frequency Converter models. The 

subsequent paragraphs explain the development of the single-phase and 3-phase chopper stage equations 

in detail. The variables that will be used during this discussion are shown in Table 6. When a factor is being 

discussed it will be underlined. Graphs accompany each section to illustrate the parameters that have been 

incorporated into the equations. Only the Weinberg converter graphs are shown, the ones for the resonant 

converter would look very similar.

Table 6: Chopper Model Variable Definitions

1CSM Single-Phase Chopper Stage Mass

3CSM 3-Phase Chopper Stage Mass

CSE Chopper Stage Efficiency (97.6%)

CSAM Chopper Stage Available Modules

CSRM Chopper Stage Required Modules

CSPO Chopper Stage Power Output (kWe)

CSVI Chopper Stage Voltage Input (Vdc)

CSF Chopper Stage Frequency (kHz)

Mass Coefficient

1CSM=0.645*((EXP0.01/(1-CSE)))/1.5169)*(CSAM/CSRM)*CSPO*((CSPO/CSRM)-0.065

 *(CSVI/(CSVI-2))7

*EXP(CSVI/40000)*(20/CSF)0.45*EXP(CSPO

0.1*CSF/200))

3CSM=0.685*((EXP0.01/(1-CSE)))/1.5169)*(CSAM/CSRM)*CSPO*((CSPO/CSRM)-0.07

 *(CSVI/(CSVI-2))7

*EXP(CSVI/40000)*(20/CSF)0.45*EXP(CSPO

0.1*CSF/200))

The chopper stage mass coefficients in these equations were calibrated to yield values consistent with the 

post 2005 1 kWe switch mass breakdown and actual component designs [Ref. 14, 15, 16, 17, 26].

Efficiency Factor

1CSM=0.645*((EXP0.01/(1-CSE)))/1.5169)*(CSAM/CSRM)*CSPO*((CSPO/CSRM)-0.065

 *(CSVI/(CSVI-2))7

*EXP(CSVI/40000)*(20/CSF)0.45*EXP(CSPO

0.1*CSF/200))

3CSM=0.685*((EXP0.01/(1-CSE)))/1.5169)*(CSAM/CSRM)*CSPO*((CSPO/CSRM)-0.07

 *(CSVI/(CSVI-2))7

*EXP(CSVI/40000)*(20/CSF)0.45*EXP(CSPO

0.1*CSF/200))

The factors underlined above estimate the changes in specific weight that occur over a range of chopper 

efficiencies. Within reason, the interconnecting wiring and ancillary hardware resistive losses, and the switch 

conduction losses can be reduced by increasing the size of the wiring and ancillary hardware, and the active 

switch element area and snubber component ratings. If the switch losses are always less over the full 

operating range, it should be possible to reduce the heat sink mass. It was previously noted that power 

MOSFET improvements have enabled their losses to be reduced 20% and continuing research is expected 

to reduce their losses another 10 to 15%. Furthermore, the space station dc/dc converter, on which much of 

this model development is based, is exhibiting an on-orbit efficiency of about 94% at full load, a substantial 

improvement over the specified 92% efficiency on which these models were originally based. These factors 

NASA/CR—2011-217268 9
enabled the nominal chopper efficiency to be increased from 96% to 97.6%. By gauging the effect of power 

losses on individual elements within a switching module, chopper mass estimates were developed for efficiencies ranging from 96.8 to 98.4%. An efficiency factor was then calculated and incorporated into the 

chopper mass equation. Figure 1 shows a graph of the resulting specific weight versus efficiency values that 

were developed with this approach. Note that the depicted chopper efficiency range is relatively narrow.

Chopper efficiencies higher than about 98.5% aren’t considered practical due to limitations in circuit topology 

designs and switch fabrication techniques. Lower efficiencies are undesirable because of the increased 

thermal management and radiator mass. However, low operating voltages cause addition losses and result 

in efficiencies poorer than those shown. This will be explained further in the discussion of voltage factors.

Figure 1: Chopper SPWT vs Efficiency

Redundancy Factor

1CSM=0.645*((EXP0.01/(1-CSE)))/1.5169)*(CSAM/CSRM)*CSPO*((CSPO/CSRM)-0.065

 *(CSVI/(CSVI-2))7

*EXP(CSVI/40000)*(20/CSF)0.45*EXP(CSPO

0.1*CSF/200))

3CSM=0.685*((EXP0.01/(1-CSE)))/1.5169)*(CSAM/CSRM)*CSPO*((CSPO/CSRM)-0.07

 *(CSVI/(CSVI-2))7

*EXP(CSVI/40000)*(20/CSF)0.45*EXP(CSPO

0.1*CSF/200))

The redundancy mass impacts that will occur for this stage when modules are added to enhance reliability 

are reflected in the above factor. This redundancy factor does not include the increased system control and 

monitoring requirements and their associated mass. The "available modules" value is the actual number of 

modules present in the component; the "required modules" number is the actual number of modules required 

to achieve full output power. If a design requires 4/3 redundancy to meet the reliability requirements, each 

channel will be rated to carry 33% of the power. 4 channels are available, but only 3 channels are needed to 

supply full power. The fourth channel represents the mass penalty incurred in this particular stage to achieve 

a higher reliability.

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

96.80% 97.00% 97.20% 97.40% 97.60% 97.80% 98.00% 98.20% 98.40%

Efficiency (%)

k

g

/

k

W

e

1 kWe

10 kWe

100 kWe

NASA/CR—2011-217268 10
Power Level Multiplier

1CSM=0.645*((EXP0.01/(1-CSE)))/1.5169)*(CSAM/CSRM)*CSPO*((CSPO/CSRM)-0.065

 *(CSVI/(CSVI-2))7

*EXP(CSVI/40000)*(20/CSF)0.45*EXP(CSPO

0.1*CSF/200))

3CSM=0.685*((EXP0.01/(1-CSE)))/1.5169)*(CSAM/CSRM)*CSPO*((CSPO/CSRM)-0.07

 *(CSVI/(CSVI-2))7

*EXP(CSVI/40000)*(20/CSF)0.45*EXP(CSPO

0.1*CSF/200))

The equations can be used to calculate the mass or specific weight of the chopper. When the above 

multiplier is included, the value that results is a chopper mass estimate. To obtain the specific weight of the 

chopper, remove this multiplier.

Power Level Factor

1CSM=0.645*((EXP0.01/(1-CSE)))/1.5169)*(CSAM/CSRM)*CSPO*((CSPO/CSRM)-0.065

 *(CSVI/(CSVI-2))7

*EXP(CSVI/40000)*(20/CSF)0.45*EXP(CSPO

0.1*CSF/200))

3CSM=0.685*((EXP0.01/(1-CSE)))/1.5169)*(CSAM/CSRM)*CSPO*((CSPO/CSRM)-0.07

 *(CSVI/(CSVI-2))7

*EXP(CSVI/40000)*(20/CSF)0.45*EXP(CSPO

0.1*CSF/200))

As the power level of the chopper increases, certain economies of scale present themselves and allow a 

reduction in specific weight. Although, the active switch element, snubber circuitry, and thermal management 

hardware sizes will increase nearly linearly with power level, the mass of the gate drive circuitry and switch 

control logic will rise at a much slower rate. This causes switch module specific weights to decline as power 

levels rise. The specific weight of the tank hardware also declines slowly as the power level rises because 

the inductors, capacitors, diodes, resistors and interconnecting wiring forming this subsystem can be fabricated and configured more efficiently. Components can also be packaged more effectively at higher power 

levels, further reducing the packaging volume and mounting mass.

The masses of individual elements of a single-phase chopper were extrapolated to generate mass estimates 

for a complete unit at power levels ranging from 0.5 to 100 kWe. Based on these mass estimates, it was 

concluded that the specific weight of a single-phase chopper would decline at the 0.065 power as power level 

rose. The results of this evaluation are illustrated in Figure 2.

A 3-phase chopper has three single-phase choppers operating in unison. Regardless of whether a resonant 

or Weinberg converter is employed, each phase will require its own ancilliary hardware. This is necessary to 

generate three separate waveforms, each offset 120 degrees from the other. Power handling devices can 

not be shared between phases, only the control hardware is common. 3-phase chopper mass estimates 

were calculated by summing the masses of three single-phase choppers, each assumed to be processing 

exactly one-third of the power. Separate gate drive circuitry was assumed for each switch, but the switch 

control logic was integrated into a single unit to ensure synchronized operation and facilitate voltage regulation and frequency control. 3-phase chopper mass estimates were generated for power levels ranging from 

10 to 250 kWe. These estimates indicated the specific weights of 3-phase choppers also decline at the 0.07 

power as power levels increase. The specific weights of 10 to 250 kWe single- and 3-phase choppers are 

compared in Figure 3 at two resonant frequencies.

NASA/CR—2011-217268 11
Figure 2: Chopper SPWT vs Power Level

0.50

0.55

0.60

0.65

0.70

0.75

10 15 20 25 30 40 50 60 80 100 150 200 250

Power (kWe)

k

g

/

k

W

e

1 Ph, 20 kHz

3 Ph, 20 kHz

1 Ph, 40 kHz

3 Ph, 40 kHz

Figure 3: Chopper SPWT vs Power Level - 1 Phase and 3 Phase

The required number of modules is also included in this equation segment. A modular design approach 

with multiple power modules could be used to enhance reliability. If this approach is used each module 

would process a percentage of the total assembly output power, and the specific weight of each chopper 

must be calculated at this power level to obtain an accurate electrical system mass estimate. The masses 

of the separate choppers are then added together to obtain the mass of the complete assembly.

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

1.10

0.5 1 5 10 15 20 25 30 40 50 60 80 100 150 200 250

Power (kWe)

k

g

/

k

W

e

10 kHz

20 kHz

40 kHz

NASA/CR—2011-217268 12
Voltage Level Factors

1CSM=0.645*((EXP0.01/(1-CSE)))/1.5169)*(CSAM/CSRM)*CSPO*((CSPO/CSRM)-0.065

 *(CSVI/(CSVI-2))7

*EXP(CSVI/40000)*(20/CSF)0.45*EXP(CSPO

0.1*CSF/200))

3CSM=0.685*((EXP0.01/(1-CSE)))/1.5169)*(CSAM/CSRM)*CSPO*((CSPO/CSRM)-0.07

 *(CSVI/(CSVI-2))7

*EXP(CSVI/40000)*(20/CSF)0.45*EXP(CSPO

0.1*CSF/200))

It was necessary to include two factors to cover the full voltage range that will be encountered by a chopper. 

The first, "(CSVI/(CSVI-2))7

", addresses the influences on power conductor and switch mass as the voltage 

level declines. The second, "EXP(CSVI/40000)", covers the mass increases occurring as voltages increase.

Since conduction losses are calculated with the equation I2

R, and current levels rise as voltage declines, the 

chopper efficiency will be poorer at lower voltage levels2

. In most designs, these higher losses are partially 

offset by lowering the resistances of circuit elements. To accomplish this the cross sectional areas of the 

conductors and switches must be increased, which causes their mass to increase. To obtain proper mass 

estimates for low voltage choppers, the efficiency parameter that is input into the chopper module should be 

decreased in accordance with Table 7. Using the values shown here, smooth specific weight versus input 

voltage curves will be generated for the Weinberg and resonant converter chopper designs. These values 

reflect the increase in mass and reduction in efficiency that occurs at lower voltages. The specific weight 

curves generated with these values are shown in Figure 4 for 0.5 and 1 kWe power levels.

Table 7: Efficiency Corrections for Low Voltage Chopper Mass Estimates

Input Resonant Chopper

Voltage Input Efficiency

(Vdc) (percent) 

120 97.60

110 97.60

100 97.57

90 97.53

80 97.47

70 97.36

60 97.23

50 97.00

40 96.67

30 96.00

20 93.60

High voltage chopper designs will require alternate design approaches. Currently MOSFETs are used most 

often for chopper switches, although MCTs may become more prominent in the future if their potentially lower 

forward voltage drop and higher voltage and power capabilities are realized [Ref. 21, 22, 27]. To switch very 

high voltages, it may be necessary to connect the switch modules in series. Theoretically, since the voltage 

across a single module is not increased, the insulating requirements and mass of the individual modules are 

unchanged. In practice, this probably will not be true. Added hardware will be needed to force the switch 

modules to voltage share and limit parasitic capacitance. Even with this added hardware, the insulation and 

 

 2 The equation I2

R also applies in high frequency applications, but the skin effect drives the effective 

resistance of the conductors up. This increased resistance can be partially offset by employing alternate conductor constructions such as Litz wire, but mass and thermal conduction penalties are incurred. 

For 20 kHz designs a guideline is a conductor’s ac resistance is 1.3 times its dc resistance.

NASA/CR—2011-217268 13
switch ratings may need to be increased to tolerate uneven or improperly applied voltages. It is expected that 

the switch synchronization problems that are a concern in any chopper design will be exacerbated in a high 

voltage design. Unfortunately, little information is available on actual design techniques since there is not 

much demand for a high voltage chopper at the present time and very little space suitable hardware is rated 

for high voltage applications.

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

20 30 40 50 60 70 80 90 100 110 120

Input Voltage (Vdc)

k

g

/

k

W

e

0.5 kWe

1 kWe

Figure 4: Chopper SPWT vs Voltage – Low Voltage Region

General Electric evaluated a 1 MWe inverter design for NASA [Ref. 28]. It used a module containing four 

parallel strings, each containing 100 amp MCTs. This module is rated for 200 amps total. Each string was 

composed of ten 1000 volt MCTs stacked in series to provide a 5000 volt switching potential. Based on the 

design results, the operating limits of the composite assembly were lower than the sum of the individual 

parts. Topology and component design modifications are necessary to insure proper voltage and current 

sharing between MCTs. These constraints result in size, mass, and loss penalties. It will also be challenging 

to achieve synchronized switching with these 40 MCTs at high frequencies. Poor synchronization will lead to 

excessive losses in the snubber circuits and result in a low switching efficiency.

Based on the items previously discussed, the following observations were made about high voltage chopper 

designs and masses. The data obtained to date from the high power inverter study indicates high voltage 

designs will incur mass penalties to insure voltage sharing and limit parasitic capacitance. The switch ratings 

and insulation levels will probably need to be increased to guard against potential voltage imbalances. Even 

power conditioning devices as rugged as transformers rise in mass as voltage levels increase. It is expected 

that the mass of a chopper will rise at a faster rate with voltage than a transformer since its components tend 

to be much more sensitive to over voltage conditions and voltage spikes. Based on this reasoning, the factor 

underlined in the above equation was developed. Specific weight curves for high voltage chopper designs 

obtained from this equation are shown in Figure 5 at 10, 100, and 250 kWe power levels.

NASA/CR—2011-217268 14
0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

160 250 500 750 1000 1500 2000 2500 3000 4000 5000 6000 7000 8000 9000 10000

Input Voltage (Vdc)

k

g

/

k

W

e

10 kWe

100 kWe

250 kWe

Figure 5: Chopper SPWT vs Voltage – High Voltage Region

Frequency Factors

1CSM=0.645*((EXP0.01/(1-CSE)))/1.5169)*(CSAM/CSRM)*CSPO*((CSPO/CSRM)-0.065

 *(CSVI/(CSVI-2))7

*EXP(CSVI/40000)*(20/CSF)0.45*EXP(CSPO

0.1*CSF/200)) 

3CSM=0.685*((EXP0.01/(1-CSE)))/1.5169)*(CSAM/CSRM)*CSPO*((CSPO/CSRM)-0.07

 *(CSVI/(CSVI-2))7

*EXP(CSVI/40000)*(20/CSF)0.45*EXP(CSPO

0.1*CSF/200)) 

The masses of the chopper switches are largely unaffected by changes in frequency. But, the masses of the 

current feed inductor in the Weinberg converter and the resonant converter tank inductor and capacitor are 

impacted by frequency. The critical inductance in the Weinberg converter is directly proportional to the 

switching frequency. The resonant frequency of a resonant circuit is calculated by the equation:

2πf=1/(L*C)0.5

Where: f = the resonant frequency in hertz

L = the circuit inductance in henries

C = the circuit capacitance in farads

From this equation one can see that the inductor and capacitor values, and their associated masses, are a 

function of frequency. While this equation is correct, it does not convey all the factors that must be 

considered in a converter design. It indicates the mass of the tank hardware will change linearly in a direction 

opposite to the frequency change. This is not entirely true. Other factors such as parasitic reactances in the 

circuit and hysteresis and eddy current losses must be considered. Depending on the switching or resonant 

frequency, they may have a strong influence on the converter design.

At low frequencies, parasitic reactances are small and hysteresis and eddy current effects are minor. This 

allows more common, often lighter weight component types and materials to be employed. Other converter 

topologies may also be used because the mass increases occurring in the Weinberg converter inductor or 

NASA/CR—2011-217268 15
the tank hardware of a resonant converter may be unacceptable at low frequencies. A PWM converter 

topology may be better. Assuming a designer selects the topology that minimizes mass and considering the 

effects of frequency and circuit parasitics, chopper mass estimates were generated at several frequencies. 

These estimates were extrapolated from detailed design estimates and existing designs [Ref. 14, 15, 17, 23, 

24, 26]. They were utilized to develop the frequency factors contained in the chopper mass equations. 

Figure 6 compares the specific weights obtained with these equations for single- and 3-phase designs at 10 

and 100 kWe power levels for frequencies ranging from 1 to 50 kHz. Note that the 3-phase design is slightly 

heavier over the full frequency range due to its higher parts count.

As the switching or resonant frequency rises, the effects of parasitic reactances and hysteresis and eddy 

current losses become more pronounced and strongly influence the converter design. Its anticipated they will 

largely offset supposed improvements and cause the design to reach a point where its difficult to obtain 

further mass reductions by increasing the switching frequency. The product of power and frequency approaches a constant value. This is the reason the mass of the chopper circuit levels out above 60 kHz and 

may actually begin to rise at frequencies beyond this point. Since most of the available design information 

was based on 20 kHz and 40 kHz inversion frequencies, the equations were calibrated to yield good results 

at these frequencies. The single-phase Weinberg converter topology specific weight curves shown in Figure 

7 depict the strong influence frequency has on chopper mass and show the specific weight of a chopper 

approaches a constant value of about 0.55 kg/kWe as the frequency and power level rises.

Figure 6: Chopper SPWT vs Frequency – Single & 3 Phase Designs

Before leaving this subject, it should be noted that at high power and frequency levels fewer switching 

devices are available. Therefore, even if there isn’t a circuit limitation that precludes using a high resonant 

frequency, the availability of suitable parts may force the designer to settle for a lower frequency design. 

To make higher operating frequencies practical, high power switching devices with faster switching 

speeds are under development. For example, the 0.1-0.2 μsec switching times being projected for MCTs 

represent a significant improvement in high power switching. Parasitic inductive and capacitive reactances

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

10 15 20 25 30 35 40 45 50 60 70

Frequency (kHz)

k

g

/

k

W

e

1 Ph, 10 kWe

1 Ph, 100 kWe

3 Ph, 10 kWe

3 Ph, 100 kWe

NASA/CR—2011-217268 16
0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.05

10 15 20 25 30 35 40 45 50 60 70

Frequency (kHz)

k

g

/

k

W

e

1 Ph, 1 kWe

1 Ph, 10 kWe

1 Ph, 100 kWe

Figure 7: Chopper SPWT vs Frequency – Single Phase Designs

though, will still drive the allowable switching frequency downward as power levels rise. The point is 

although the model will generate a mass estimate for a high power chopper operating at a high frequency, 

one must consider whether the design is really practical. Table 8 is offered as a guide to assist the model 

user in selecting inversion frequencies appropriate for future component power levels.

Table 8: Converter Frequency Input Guide

Converter Suggested Inversion

Power Level Frequency Limit 

500 Watts to 1 kWe 100 kHz

1 to 5 kWe 80 kHz

5 to 20 kWe 55 kHz

20 to 40 kWe 50 kHz

40 to 80 kWe 40 kHz

80 to 150 kWe 35 kHz

Greater than 150 kWe 30 kHz

3.3 INVERTER AND STANDARD TRANSFORMER MODELS

Two types of transformers may be used in a PMAD system depending on the architecture and user needs: 

inverter transformers that are an integral part of a converter circuit, and standard transformers. These 

transformers will be significantly different because the operating frequencies, and waveform harmonic 

content are different for the two applications. For this reason, it was necessary to create two model types 

to address the characteristics of the two designs. The inverter transformer design will be presented first 

because it tends to be more involved and cover a wider range of design considerations. The standard 

transformer discussion will rely heavily on the information and rationale presented in the inverter 

transformer section. The equations previously developed for the two types of transformers in 1992 still 

NASA/CR—2011-217268 17
generate masses consistent with projected transformer designs, but minor changes were made in the 

efficiency and frequency sections to reflect the improved efficiencies possible at high frequencies due to 

thinner laminations and improvements in magnetic material fabrication processes.

3.3.1 Inverter Transformer Stage Model

The inverter transformer stage is contained in the inverter, dc/dc converter, and frequency converter 

models. An inverter transformer follows or precedes a chopper section. It is used to step up or down the 

input voltage, and/or to provide isolation between the input and output.

Although transformer design guidelines have been established to deal with most operating requirements; 

there are many practical design and materials limitations that continue to hinder transformer fabrication. 

These design difficulties are more pronounced at high frequencies, and high frequency designs proposed 

for high power and/or high voltage levels are particularly complicated. However, established transformer 

design principles can provide insight into how these problems might be solved and in turn the evolution of 

transformer design. For this reason, design manuals and technical bulletins were frequently referred to to 

guide the equation development [Ref. 29, 30, 31, 32, 33]. The variables that will be used in the inverter 

transformer stage model discussion are shown in Table 9.

Table 9: Inverter Transformer Model Variable Definitions

1ITSM Single-Phase Inverter Transformer Stage Mass

3ITSM 3-Phase Inverter Transformer Stage Mass

ITSE Inverter Transformer Stage Efficiency (99.2%)

ITSAM Inverter Transformer Stage Available Modules

ITSRM Inverter Transformer Stage Required Modules

ITSPO Inverter Transformer Stage Power Output (kWe)

ITSVI Inverter Transformer Stage Voltage Input (Vrms)

ITSVO Inverter Transformer Stage Voltage Output (Vrms)

ITSF Inverter Transformer Stage Frequency (kHz)

The equations used to estimate the mass of single-phase and 3-phase transformers are shown below. 

Sections of these equations will be discussed individually to identify the parts that correspond to specific 

parameters. The subsequent paragraphs will explain the development of the factors and constants 

contained in these equations. The factor being discussed will be underlined and accompanying graphs 

will be used to illustrate results and trends determined during this study.

Mass Coefficient

1ITSM=1.27*((EXP(0.0048/(1-ITSE)))/1.8221)*(ITSAM/ITSRM)*ITSPO*((ITSPO/ITSRM)-0.08

 *EXP(ITSVI/200000)*EXP(ITSVO/200000)*ITSF-0.47+(ITSF/300)1.4-(200/ITSPO)

0.03* 

 ((MAX(0,ITSF-30))/300)1.7) 

3ITSM=2.75*((EXP(0.0048/(1-ITSE)))/1.8221)*(ITSAM/ITSRM)*ITSPO*((ITSPO/ITSRM)-0.25

 *EXP(ITSVI/200000)*EXP(ITSVO/200000)*ITSF-0.47+(ITSF/300)1.4-(200/ITSPO)

0.03* 

 ((MAX(0,ITSF-30))/300)1.7) 

The constants, "1.27" and "2.75", were determined by calibrating these mass equations against the 

masses of known inverter transformer designs. They are designed to yield acceptable mass estimates 

NASA/CR—2011-217268 18
over the ranges specified for each of the input parameters. These constants are partially determined by 

the wave form factor3 and are 10% larger than the corresponding constants contained in the standard 

transformer equation. Because the chopper rapidly switches a dc input to fabricate an ac output, the 

inverter transformer input is not a smooth sinusoid and it exhibits many square wave characteristics. 

Square waves have a high harmonic content; consequently, they generate higher losses in the transformer core. Calculations and design procedures contained in design manuals indicate an inverter transformer core must be sized 10% larger to lower the core flux density and manage the added losses resulting from the square wave harmonics [Ref. 29, 30, 31].

Efficiency Factor

1ITSM=1.27*((EXP(0.0048/(1-ITSE)))/1.8221)*(ITSAM/ITSRM)*ITSPO*((ITSPO/ITSRM)-0.08

 *EXP(ITSVI/200000)*EXP(ITSVO/200000)*ITSF-0.47+(ITSF/300)1.4-(200/ITSPO)

0.03* 

 ((MAX(0,ITSF-30))/300)1.7) 

3ITSM=2.75*((EXP(0.0048/(1-ITSE)))/1.8221)*(ITSAM/ITSRM)*ITSPO*((ITSPO/ITSRM)-0.25

 *EXP(ITSVI/200000)*EXP(ITSVO/200000)*ITSF-0.47+(ITSF/300)1.4-(200/ITSPO)

0.03* 

 ((MAX(0,ITSF-30))/300)1.7) 

The factor underlined above is used to estimate the mass effects that will occur when the transformer 

efficiency is changed. To reduce losses and increase transformer efficiency, the flux density in the core is 

lowered and the resistance of the windings is reduced. A lower core flux density will reduce core losses; 

however, Faraday's law shows the core effective cross sectional area must be increased to compensate.

E=4BmAcNfx10-5 (square wave)

where: E = applied voltage (rms)

 4 = square wave form factor

 Bm = flux density in gauss

 Ac = core effective cross sectional area in cm2

 N = number of primary turns

 f = frequency in kHz

This naturally increases core mass. To reduce winding resistance and losses, the winding conductor area 

must be increased. This can be seen from the equation used to calculate conductor electrical resistivity.

R=ρl/A

where: R = conductor resistance

ρ = volume resistivity (μΩ×cm)

l = length in cm

A = cross sectional area in cm2

To raise the transformer efficiency from 99.2% to 99.6%, the transformer losses need to be cut in half. 

Core loss versus flux density tables contained in transformer design manuals indicated a 25% reduction in 

flux density would reduce losses 50%. To achieve this the core cross sectional area and associated mass 

would increase 33%. To cut the winding losses in half, the conductor area would need to double. This 

doubles the conductor mass. Summing only these two effects and using a ratio of about 2:1 for winding 

mass to core mass with a 20 kHz transformer results in a transformer mass increase of about 75%. 

However, increasing the core size further increases in the conductor mass due to the added length of the 

turns; and the larger winding size will enlarge the core window. Clearly the core and winding dimensions 

 

 3 The form factor is the ratio of the root-mean-square value to the average absolute value, averaged 

over a full period of the waveform.

NASA/CR—2011-217268 19
are interrelated. After including estimates for these interdependent influences, a mass increase of 85% 

was obtained. The trends reflected by the resulting efficiency factor are shown in Figure 8 for 10 and 20 

kHz frequencies and 10 and 100 kWe transformer power levels.

Figure 8: Inverter Transformer SPWT vs Efficiency

Redundancy Factor

1ITSM=1.27*((EXP(0.0048/(1-ITSE)))/1.8221)*(ITSAM/ITSRM)*ITSPO*((ITSPO/ITSRM)-0.08

 *EXP(ITSVI/200000)*EXP(ITSVO/200000)*ITSF-0.47+(ITSF/300)1.4-(200/ITSPO)

0.03* 

 ((MAX(0,ITSF-30))/300)1.7) 

3ITSM=2.75*((EXP(0.0048/(1-ITSE)))/1.8221)*(ITSAM/ITSRM)*ITSPO*((ITSPO/ITSRM)-0.25

 *EXP(ITSVI/200000)*EXP(ITSVO/200000)*ITSF-0.47+(ITSF/300)1.4-(200/ITSPO)

0.03* 

 ((MAX(0,ITSF-30))/300)1.7) 

The above factor addresses the mass impacts resulting from the use of a modular design to enhance reliability. The available modules is the actual number of modules present in the component; the required 

modules is the actual number of modules required to achieve full output power. For example, assume a 

design requires 4/3 redundancy to meet the reliability requirements. Each channel is rated to handle 33% 

of the power, but 4 channels are available. This factor shows a 4/3 redundancy design will be 33% 

heavier. Only 3 channels are needed to supply full power; the fourth channel represents the mass penalty 

incurred to enhance reliability.

Power Level Multiplier

1ITSM=1.27*((EXP(0.0048/(1-ITSE)))/1.8221)*(ITSAM/ITSRM)*ITSPO*((ITSPO/ITSRM)-0.08

 *EXP(ITSVI/200000)*EXP(ITSVO/200000)*ITSF-0.47+(ITSF/300)1.4-(200/ITSPO)

0.03* 

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

98.6% 98.7% 98.8% 98.9% 99.0% 99.1% 99.2% 99.3% 99.4% 99.5% 99.6%

Efficiency (%)

k

g

/

k

W

e

10 kWe, 10 kHz

100 kWe, 10 kHz

10 kWe, 20 kHz

100 kWe, 20 kHz

NASA/CR—2011-217268 20
 ((MAX(0,ITSF-30))/300)1.7) 

3ITSM=2.75*((EXP(0.0048/(1-ITSE)))/1.8221)*(ITSAM/ITSRM)*ITSPO*((ITSPO/ITSRM)-0.25

 *EXP(ITSVI/200000)*EXP(ITSVO/200000)*ITSF-0.47+(ITSF/300)1.4-(200/ITSPO)

0.03* 

 ((MAX(0,ITSF-30))/300)1.7) 

The equations can be used to calculate either transformer mass or transformer specific weight. When the 

above multiplier is included, the calculations will yield the transformer mass. To obtain the transformer 

specific weight, simply remove this multiplier.

Power Level Factor

1ITSM=1.27*((EXP(0.0048/(1-ITSE)))/1.8221)*(ITSAM/ITSRM)*ITSPO*((ITSPO/ITSRM)-0.08

 *EXP(ITSVI/200000)*EXP(ITSVO/200000)*ITSF-0.47+(ITSF/300)1.4-(200/ITSPO)

0.03* 

 ((MAX(0,ITSF-30))/300)1.7) 

3ITSM=2.75*((EXP(0.0048/(1-ITSE)))/1.8221)*(ITSAM/ITSRM)*ITSPO*((ITSPO/ITSRM)-0.25

 *EXP(ITSVI/200000)*EXP(ITSVO/200000)*ITSF-0.47+(ITSF/300)1.4-(200/ITSPO)

0.03* 

 ((MAX(0,ITSF-30))/300)1.7) 

As transformer size increases, the core can be better utilized, and the current density increased in the 

windings to reduce their cross sectional area. These economies of scale result in a transformer specific 

weight reduction at higher power levels. The "Standard Handbook for Electrical Engineers" indicated the 

specific weight of a 3-phase transformer would decline by the 0.25 power with power level [Ref. 34]. This 

was verified for 60 Hz transformers by referring to the transformer masses contained in a vendor 

catalogue [Ref. 35]. This factor was also assumed to hold for high frequency 3-phase transformer designs, but there wasn’t any mass information available to confirm it. The same vendor catalogue showed 

the specific weight of a low frequency single-phase transformer would decline by the 0.08 power with 

power level. Mass figures obtained from another source indicated this factor also held true for high 

frequency single-phase transformer designs [Ref. 29]. The specific weights of single- and 3-phase 

transformer designs are compared in Figure 9. This figure shows a 1 kHz single-phase transformer will 

weigh less than a 3-phase one until a power level of about 100 kWe is reached. This value was projected 

from information contained in a vendor catalogue and a transformer design handbook [Ref. 35, 36]. The 

mass cross over point for high frequency single- and 3-phase transformers occurs at a higher power level. 

The mass gains achievable with a change from a single- to 3-phase design occur mainly in the core. 

These gains are expected to be less at higher frequencies because the core mass occupies a smaller 

percentage of the transformer mass. With this assumption incorporated into the equations, Figure 9 

shows that a single-phase 20 kHz transformer design is more weight efficient below 250 kWe. Figure 10 

shows only single-phase transformer designs and allows specific weight comparisons at several 

frequencies over a wide power range. Figure 11 also depicts single-phase designs, but it concentrates on 

the power levels and frequencies expected to be used most often in inverter transformer designs.

Voltage Level Factors

1ITSM=1.27*((EXP(0.0048/(1-ITSE)))/1.8221)*(ITSAM/ITSRM)*ITSPO*((ITSPO/ITSRM)-0.08

 *EXP(ITSVI/200000)*EXP(ITSVO/200000)*ITSF-0.47+(ITSF/300)1.4-(200/ITSPO)

0.03* 

 ((MAX(0,ITSF-30))/300)

1.7) 

3ITSM=2.75*((EXP(0.0048/(1-ITSE)))/1.8221)*(ITSAM/ITSRM)*ITSPO*((ITSPO/ITSRM)-0.25

 *EXP(ITSVI/200000)*EXP(ITSVO/200000)*ITSF-0.47+(ITSF/300)1.4-(200/ITSPo)0.03* 

NASA/CR—2011-217268 21
 ((MAX(0,ITSF-30))/300)1.7) 

0.20

0.30

0.40

0.50

0.60

10 15 20 25 30 40 50 60 80 100 150 200 250

Output Power (kWe)

k

g

/

k

W

e

1 Ph, 10 kHz

3 Ph, 10 kHz

1 Ph, 20 kHz

3 Ph, 20 kHz

1 Ph, 40 kHz

3 Ph, 40 kHz

Figure 9: Inverter Transformer SPWT – 1 Phase vs 3 Phase

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

0.5 1 5 10 15 20 25 30 40 50 60 80 100 150 200 250

Output Power (kWe)

k

g

/

k

W

e

1 kHz

5 kHz

10 kHz

20 kHz

40 kHz

Figure 10: Inverter Transformer SPWT vs Power (Wide Range)

NASA/CR—2011-217268 22
0.23

0.25

0.27

0.29

0.31

0.33

0.35

1 5 10 15 20 25 30 40 50

Output Power (kWe)

k

g

/

k

W

e

20 kHz

30 kHz

40 kHz

50 kHz

Figure 11: Inverter Transformer SPWT vs Power (Narrow Range)

The voltage factor development had to consider two factors, the influence of insulation stress on transformer mass as voltage rises, and high voltage transformer design limitations occurring as frequency 

rises. Only the insulation stress effects will be addressed initially. It is mainly the volts per turn not the 

terminal voltage that determines the stress placed on the insulation and consequently its thickness. The 

thickness of the insulation can be calculated from its dielectric strength, usually expressed in volts per mil. 

For typical operating ranges, the dielectric strength of most insulating materials is reasonably constant 

regardless of the transformer frequency. This information indicates the voltage mass effects occurring at 

low frequency also apply at higher frequencies.

This observation is important since the information on high voltage transformers is limited to low frequency 

designs. Low frequency, commercial transformer data showed transformer specific weight rose slowly 

until voltage levels approached 20 kV. This is well above the 10 kV voltage level expected to be used in 

most space applications. The minor increase in specific weight was attributed to the additional insulation 

needed to prevent insulation breakdown between windings, and the need for high voltage terminations. 

This added winding insulation will increase the winding cross sectional area and necessitate a slightly 

larger core window area. However, the impact is minor. In addition, the insulation mass is a very small 

percentage of the total transformer mass, so it can increase substantially and the transformer mass will 

only change slightly. The information obtained from this analysis was sufficient to develop a transformer 

voltage factor, but it was not enough to know how to properly apply it. The voltage factor determined at 

this point is shown for different transformer power levels in Figure 12. It shows transformer mass will only 

rise about 5% when the primary or secondary voltage is increased from 20 to 10,000 Vrms.

It was previously stated that the volts per turn determined the insulation thickness and that the dielectric 

strength of an insulating material is basically independent of frequency. However, frequency does 

influence the calculated volts per turn and this ultimately impacts the voltage characteristics of the comNASA/CR—2011-217268 23
plete transformer. Referring back to Faraday's law and rearranging the terms, one can see that the volts 

per turn is a function of frequency.

Figure 12: Inverter Transformer SPWT vs Voltage

E/N= (K,Bm,Ac,f)

where: E = applied voltage (rms)

K = form factor constant

 Bm = flux density

 Ac = core effective cross sectional area

N = number of primary turns

f = frequency

Because of nonlinearities in transformer design, particularly in core material characteristics, the product of 

core cross sectional area and flux density can not be linearly changed to accommodate an increasing 

frequency. This situation indicates a designer will encounter voltage restraints as frequency rises. To 

verify this conclusion, a transformer design analysis was conducted and transformer point designs were 

evaluated. They showed that the volts per turn will increase significantly when moving from 60 Hz to 20 

kHz, possibly enough to increase the insulation level on the turns. Thicker insulation will lead to greater 

separation distances between the primary and secondary windings, and reduce transformer coupling. 

This results in higher leakage flux. Because leakage flux increases if additional winding insulation is 

needed and the effects attributable to turn-to-turn capacitance rise with frequency, a high frequency transformer tends to have more reactance. High voltage transformers have more turns, which increases the 

total turn-to-turn or winding capacitance. Although these effects are compounding, they are not enough to 

preclude the design of a high voltage, high frequency transformer. But they do complicate its design and 

emphasize the need to minimize turn-to-turn capacitance.

It was already mentioned that a high voltage transformer has a higher winding capacitance; and 

transformer coupling is poorer if thicker winding insulation is required. Leakage inductance also rises as 

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

0.36

0.38

0.40

20 100 250 500 750 1000 1500 2000 2500 3000 4000 5000 6000 7000 8000 9000 10000

Input or Output Voltage Level (Vrms)

k

g

/

k

W

e

1 kWe 10 kWe

50 kWe 100 kWe

250 kWe

NASA/CR—2011-217268 24
the distance between the windings increases. To maximize transformer coupling and minimize leakage 

inductance, the primary and secondary windings must be in close proximity. However, this is difficult to 

accomplish in a transformer that has a high voltage ratio because thick insulation levels are required to 

prevent primary to secondary voltage breakdown. Most loads require a relatively low voltage; therefore, 

the voltage will need to be stepped down further in a system that uses high voltage transmission. This 

forces the distribution transformers to utilize higher voltage ratios and leads to higher leakage inductance.

Oscillations in the power system, a phenomenon known as ringing, may result from the leakage capacitance and inductance present in high voltage transformers. Ringing occurs because the parasitic capacitive and inductive reactances transfer energy back and forth during operation and after turn off until it is 

damped out by element resistances. This increases transformer losses and may cause damage if high 

voltage spikes result. Ringing is frequency related because the effects attributable to parasitic capacitive 

and inductive reactances grow as frequency rises. Power may also be a factor because it may make it 

more difficult to limit stray capacitance and inductance due to fabrication constraints resulting from the 

transformer's larger physical size.

Ringing limits the acceptable voltage ratio of the transformer. In a discussion with John Beiss, he 

indicated the step ratio of a present 20 kHz transformer is probably limited to about 6 or 7 due to ringing. 

However, a transformer design generated by Space Power Incorporated exhibited a voltage ratio of 10, 

180 divided by 18 Vrms. Its demonstrated efficiency of 99.1% indicates this step ratio is feasible, although 

it will be harder to achieve good operating characteristics at higher voltages [Ref. 37]. Commercial 

transformer data indicates a step ratio of 145 is obtainable with a 60 Hz transformer. Using these two 

values, an empirical relationship was developed to estimate reasonable step ratios for transformers at 

several different frequencies. This relationship is shown below and it was used to generate the values 

shown in Table 10. This table is only offered as a guide; its main intent is to point out the need to include 

step ratio effects when evaluating a high voltage power transmission design. It shows that it may be 

necessary to connect transformers in series to utilize a high voltage transmission system with input or 

output components that require fairly low voltages, especially if high frequency distribution is employed.

SR=39.7*f-0.46

where: SR = acceptable step ratio

 f = frequency in kHz

Table 10: Transformer Step Ratio Guidelines

Transformer Suggested

Frequency Step Ratio

 (kHz) Limit 

0.060 145

0.070 135

0.400 60

1 40

5 19

10 14

15 11

20 10

25 9 

30 8 

35 8 

40 7 

45 7 

50 7 

NASA/CR—2011-217268 25
Frequency Factors

1ITSM=1.27*((EXP(0.0048/(1-ITSE)))/1.8221)*(ITSAM/ITSRM)*ITSPO*((ITSPO/ITSRM)-0.08

 *EXP(ITSVI/200000)*EXP(ITSVO/200000)*ITSF-0.47+(ITSF/300)1.4-(200/ITSPO)

0.03*

 ((MAX(0,ITSF-30))/300)1.7)

3ITSM=2.75*((EXP(0.0048/(1-ITSE)))/1.8221)*(ITSAM/ITSRM)*ITSPO*((ITSPO/ITSRM)-0.25

 *EXP(ITSVI/200000)*EXP(ITSVO/200000)*ITSF-0.47+(ITSF/300)1.4

-(200/ITSPO)

0.03*

 ((MAX(0,ITSF-30))/300)1.7)

Transformer core mass declines with increasing frequency. Faraday's law shows the flux density required 

to generate a voltage is lower at a higher frequency. Because the flux density is lower, the transformer 

core volume and mass are reduced. Winding mass also declines because the mean length of the turns is 

less. However, core mass does not decrease linearly with frequency as Faraday's law appears to 

indicate. Alternate core materials must be employed at higher frequencies to hold down losses. While 

these materials are more efficient, they must be operated at lower flux densities. For transformer 

operating frequencies ranging from 10 to 60 kHz, the selected core materials might progress from 50-50 

Ni-Fe, to Permalloy, to Supermalloy, to Metglas. During this materials progression, the allowable flux 

density will roughly decline from about 10,000 to 2,000 Gauss.

In addition to material limitations, other factors must be addressed during a transformer design. Thermal 

management considerations may limit how much the core size can be reduced. The surface area of a 

transformer must be sufficient to allow internally generated heat to be conducted away. At high frequencies, roughly above 60 kHz, another set of effects begins to dictate the size of a power transformer core. 

The eddy current and hysteresis losses become high enough to actually drive the core volume and mass 

upward. This seems to be where the greatest advancement has been in recent years and it has allowed 

circuit designers to use higher switching frequencies to lower transformer mass. This has enabled higher 

power inverter transformer frequencies to increase from 20 to 50 kHz, to 30 to 60 kHz. At high power 

levels, 50 kWe and above for example, the preferred frequency is probably in the range of 30 to 40 kHz. 

For power levels below 20 kWe, the optimum frequency can range from 40 kHz all the way up to 80 kHz 

for a 1 to 2 kWe transformer.

To determine how transformer mass declines as frequency is increased, inverter transformer mass 

estimates were examined at 1, 2, 5, 10, 20, 40, and 60 kHz [Ref. 14, 17, 29, 30, 31, 32]. Based on these 

designs, the mass gains occurring as frequency is increased are shown in Figure 13 for several power levels. Figure 14 concentrates on the frequencies envisioned to be used for most spaced based inverter 

transformer designs. It shows the optimum design frequency shifts downward as the transformer power 

level rises. This reflects a feature that has been incorporated into the transformer mass equations.

3.3.2 Standard Transformer Stage Model

The standard transformer stage is contained in the transformer, and transformer/static rectifier models. 

Standard ac transformers will be used in ac power transmission systems primarily at the user end to step 

down a high transmission voltage to a level suitable for secondary distribution. Standard ac transformers 

may also follow an alternator or inverter output in certain cases. However, this will not be as common 

because alternators can provide nearly any voltage desired and inverters and frequency converters will 

probably contain their own integral inverter transformer stage. Transformers following an alternator will 

experience frequencies less than 5 kHz. If the system utilizes inverters or frequency converters to change 

the characteristics of the power source, the transformers will probably be designed for frequencies 

between 20 and 50 kHz. The type of ac waveform encountered should be a smooth sinusoid with a low 

harmonic content. A pure sinusoid minimizes transformer core losses because the added eddy current 

and hysteresis losses resulting from high frequency harmonics are not present.

NASA/CR—2011-217268 26
Figure 13: Inverter Transformer SPWT vs Frequency (Wide Range)

Figure 14: Inverter Transformer SPWT vs Frequency (Narrow Range)

0.100

0.300

0.500

0.700

0.900

1.100

1.300

1 2 5 10 15 20 25 30 35 40 45 50 55 60 70 80 90 100

Frequency (kHz)

k

g

/

k

W

e

1 kWe

10 kWe

50 kWe

100 kWe

250 kWe

0.200

0.220

0.240

0.260

0.280

0.300

0.320

0.340

0.360

0.380

0.400

15 20 25 30 35 40 45 50 55 60 70 80

Frequency (kHz)

k

g

/

k

W

e

1 kWe

10 kWe

20 kWe

50 kWe

NASA/CR—2011-217268 27
Because a fine transformer design manual existed, especially for low frequency transformer designs, it 

was frequently referred to assist in the equation development [Ref. 36]. The variables used in the 

standard transformer stage model discussion are shown in Table 11. 

Table 11: Standard Transformer Model Variable Definitions

1STSM Single-Phase Standard Transformer Stage Mass

3STSM 3-Phase Standard Transformer Stage Mass

STSE Standard Transformer Stage Efficiency (98%)

STSAM Standard Transformer Stage Available Modules

STSRM Standard Transformer Stage Required Modules

STSPO Standard Transformer Stage Power Output (kWe)

STSVI Standard Transformer Stage Voltage Input (Vrms)

STSVO Standard Transformer Stage Voltage Output (Vrms)

STSF Standard Transformer Stage Frequency (kHz)

The equations used to estimate the mass of single-phase and 3-phase standard transformers are shown 

below. Only the mass coefficient will be discussed here since the rest of the factors are identical to those 

contained in the section on inverter transformers. To see how the specific weight or mass of a standard 

transformer changes with efficiency, power level, voltage, and frequency refer to the graphs contained in 

the inverter transformer section and subtract 10% from each value. The shape of the curves will be 

identical for both designs, the standard transformer curves are simply shifted downward a slight amount.

Mass Coefficient

1STSM=1.15*((EXP(0.0048/(1-STSE)))/1.8221)*(STSAM/STSRM)*STSPO*((STSPO/STSRM)-0.08

 *EXP(STSVI/200000)*EXP(STSVO/200000)*STSF-0.47+(STSF/300)1.4-(200/STSPO)

0.03* 

 ((MAX(0,STSF-30))/300)1.7) 

3STSM=2.5*((EXP(0.003/(1-STSE)))/1.35)*(STSAM/STSRM)*STSPO*((STSPO/STSRM)-0.25

 *EXP(STSVI/200000)*EXP(STSVO/200000)*STSF-0.47+(STSF/300)1.4-(200/STSPO)

0.03* 

 ((MAX(0,STSF-30))/300)1.7) 

The constants, "1.15" and "2.5", were determined by calibrating these mass equations against the masses 

of standard transformer designs--minus their enclosures--contained in vendor catalogues [Ref. 35]. 

Initially, an individual might feel the mass of a terrestrial transformer would be heavier than a space-based 

transformer. However, the masses of low frequency commercial and space-based transformers were felt 

to be comparable. Most of the transformer mass is concentrated in the transformer core and windings, 

and this will be nearly equivalent in both designs. Because the space-based transformer mounting hardware needs to be stronger than similar earth-based mounting hardware to withstand the launch 

environment, the mass reductions possible by using alternate materials and space type packaging 

approaches will be largely offset. Terrestrial transformers mainly rely on convection for cooling, a spacebased unit must include thermal management hardware and use conduction. Finally, the enclosure mass 

is calculated by a separate algorithm and not included in this equation.

These constants are designed to produce reasonably accurate mass estimates for the specified input 

parameters contained in the component models. They are 10% less than those shown in the inverter 

transformer section because the wave form factors of the power inputs differ. The waveform encountered 

by a standard transformer is a smooth sinusoid with a low harmonic content. A pure sinusoid minimizes 

NASA/CR—2011-217268 28
transformer core losses because the added eddy current and hysteresis losses resulting from high 

frequency harmonics are not present. The square wave input of an inverter transformer has a high 

harmonic content; consequently, it generates higher losses in the transformer core. The design equations 

contained in design manuals indicate a standard transformer core can be 10% smaller due to these 

improved waveform characteristics [Ref. 29, 32].

3.4 RECTIFIER STAGE MODEL

The rectifier stage converts ac into dc. It is contained in the rectifier, transformer/rectifier, dc/dc converter, 

and frequency converter models. Two basic operating types of rectifiers are available, diode and switching. 

The diode rectifier is a static device that simply converts ac into dc. The switching rectifier is essentially a 

simplified chopper operating in reverse. Since it uses active switching devices such as SCRs or MOSFETs it 

can regulate the output voltage. This is done by adjusting the commutation angle, the point at which the 

switch is turned on to allow conduction. The equations presented here are for diode rectifiers.

The rectification stage consists of a diode network. Mass breakdowns for a circa 1992, present 2002 and 

projected post 2005 diodes capable of handling 1 kWe are shown in Table 12. Note this breakdown is similar to the previous switch module breakdown contained in the chopper section. The main differences are the 

snubber circuitry, gate drive circuitry, and switch control logic have been removed because diodes aren’t 

active switching devices and the mass of the packaging and mounting hardware has been reduced because 

there are fewer parts. The original mass values were estimated from briefing packages prepared by 

Rocketdyne, Ford Aerospace, and TRW in support of SSF [Ref. 14, 15, 16]. Projected mass improvements 

were obtained from by comparing 1992 diode characteristics with present diode characteristics and 

extrapolating to post 2005 [Ref. 38].

Table 12: 1 kWe Diode Module Mass Breakdown

Projected

Circa 1992 Present 2002 Post 2005

Hardware Element Mass (grams) Mass (grams) Mass (grams)

Diode Element 7 6 5 

Heat Sink, Thermal Management 48 40 35

Packaging and Mounting 40 30 25

 Total Switch Module 95 76 65

Two full wave rectifier configurations are available, a center-tapped full-wave rectifier, or a bridge rectifier 

circuit. The center-tapped rectifier construction is simpler, but bridge rectifiers appear to be more attractive 

for high voltage applications because the peak inverse voltage imposed across each diode is half the centertapped case. Bridge rectifiers also make better use of transformers. A center-tapped rectifier requires two 1 

kWe diodes, each weighing 65 grams; a bridge rectifier uses four 500 watt diodes, each weighing 33 grams. 

The total mass in each case is 130 grams. Based on this assessment, the total mass of a future 1 kWe 

rectifier is projected to be about 130 grams.

The subsequent paragraphs will explain the development of the single-phase and 3-phase rectifier stage 

equations in detail. These sections will use the format presented earlier in the chopper stage discussion 

since the items are comparable in many respects. The variables that will be used during this discussion are 

shown in Table 13.

NASA/CR—2011-217268 29
Table 13: Rectifier Stage Model Variable Definitions

1RSM Single-Phase Rectifier Stage Mass

3RSM Three-Phase Rectifier Stage Mass

RSE Rectifier Stage Efficiency (98.7%)

RSAM Rectifier Stage Available Modules

RSRM Rectifier Stage Required Modules

RSPO Rectifier Stage Power Output (kWe)

RSVI Rectifier Stage Voltage Input (Vrms)

Mass Coefficient

1RSM=0.1175*((EXP(0.005/(1-RSE)))/1.469)*(RSAM/RSRM)*RSPO*(RSVI/(RSVI-2))6

3RSM=0.12*((EXP(0.005/(1-RSE)))/1.469)*(RSAM/RSRM)*RSPO*(RSVI/(RSVI-2))6

To calculate the rectifier stage mass coefficients, the equations were calibrated to yield values consistent with 

the above 1 kWe mass breakdown and actual component designs [Ref. 14, 15, 17].

The diodes comprising three single-phase full wave rectifiers are interconnected to form a 3-phase full wave 

rectifier. Six diodes are required and each processes a third of the power. The 3-phase rectifier design was 

judged to be slightly heavier because of the added number of diodes. This would probably enlarge the 

mounting area and increase the interconnecting wiring weight. Figure 15 compares the specific weights of 

single- and 3-phase rectifiers.

0.120

0.125

0.130

0.135

0.140

0.145

10 15 20 25 30 40 50 60 80 100 150 200 250

Power (kWe)

k

g

/

k

W

e

1 Ph

3 Ph

Figure 15: Rectifier SPWT – 1 Phase vs 3 Phase

NASA/CR—2011-217268 30
Efficiency Factor

1RSM=0.1175*((EXP(0.005/(1-RSE)))/1.469)*(RSAM/RSRM)*RSPO*(RSVI/(RSVI-2))6

3RSM=0.12*((EXP(0.005/(1-RSE)))/1.469)*(RSAM/RSRM)*RSPO*(RSVI/(RSVI-2))6

The factor underlined above estimates the specific weight values associated with a range of rectifier 

efficiencies. Within reason, the interconnecting wiring and the diode conduction losses can be reduced by 

increasing the size of the wiring and the diode die area. An improved efficiency allows a reduction in the heat 

sink mass. The effect of power losses on individual elements within a diode module were assessed to 

develop rectifier mass estimates for efficiencies ranging from 98.3 to 99.1%. From this analysis, an efficiency factor was calculated and incorporated into the rectifier mass equation. Figure 16 shows a graph of 

the resulting specific weight versus efficiency values that were developed with this approach. Note that the 

depicted rectifier efficiency range is relatively narrow. Rectifier efficiencies higher than about 99.5% are not 

considered practical due to diode fabrication limitations. Lower efficiencies are undesirable because of the 

additional radiator mass. Because silicon diodes require a forward bias voltage of about 0.7 V before they 

will conduct, their efficiency is considerably less at lower operating voltages. This will be addressed later in 

the section on voltage factors.

0.110

0.115

0.120

0.125

0.130

0.135

0.140

0.145

0.150

0.155

0.160

98.3% 98.4% 98.5% 98.6% 98.7% 98.8% 98.9% 99.0% 99.1%

Efficiency (%)

k

g

/

k

W

e

Figure 16: Rectifier SPWT vs Efficiency

Redundancy Factor

1RSM=0.1175*((EXP(0.005/(1-RSE)))/1.469)*(RSAM/RSRM)*RSPO*(RSVI/(RSVI-2))6

3RSM=0.12*((EXP(0.005/(1-RSE)))/1.469)*(RSAM/RSRM)*RSPO*(RSVI/(RSVI-2))6

The above factor computes the redundancy mass impacts occurring when a modular design approach is 

used to improve reliability. The "available modules" number is the actual number of modules present in the 

NASA/CR—2011-217268 31
component; the "required modules" value is the actual number of modules required to achieve full output 

power. If a design requires 4/3 redundancy to meet the reliability requirements, each channel will be rated to 

carry 33% of the power. 4 channels are available, but only 3 channels are needed to supply full power. The 

mass of the fourth channel is the penalty paid to obtain a higher reliability.

Power Level Multiplier

1RSM=0.1175*((EXP(0.005/(1-RSE)))/1.469)*(RSAM/RSRM)*RSPO*(RSVI/(RSVI-2))6

3RSM=0.12*((EXP(0.005/(1-RSE)))/1.469)*(RSAM/RSRM)*RSPO*(RSVI/(RSVI-2))6

The equations can be used to calculate the mass or specific weight of the rectifier. When the above 

multiplier is included, the value that results is a rectifier mass estimate. To obtain the specific weight of the 

rectifier, remove this multiplier.

A power factor was not included in the rectifier equation to improve the specific weight at higher power levels. 

As the rectifier power level increases, a slight reduction in specific weight may occur because it is possible to 

package larger sized units more compactly; however, this minor effect was considered to be to small to 

warrant the inclusion of an additional factor.

Frequency Factor

Although it may be necessary to incorporate fast recovery diodes in a high frequency design, the effect of 

frequency on rectifier mass was considered to be minor. In fact it may even be desirable to incorporate fast 

recovery diodes in lower frequency designs to gain an improvement in efficiency. For these reasons, it was 

not considered necessary to include a frequency factor in the equations.

Voltage Level Factors

1RSM=0.1175*((EXP(0.005/(1-RSE)))/1.469)*(RSAM/RSRM)*RSPO*(RSVI/(RSVI-2))6

3RSM=0.12*((EXP(0.005/(1-RSE)))/1.469)*(RSAM/RSRM)*RSPO*(RSVI/(RSVI-2))6

The low voltage impacts on rectifier and chopper mass were judged to be similar; therefore, the approaches 

used to define the low voltage factor are comparable. Two primary effects cause the rectifier efficiency to 

decline as the voltage level is reduced: the bias voltage imparted across the diode, and the conduction 

losses. Silicon diodes require a forward bias voltage of about 0.7 V before they will conduct. At lower voltage 

levels this bias voltage is a larger percentage of the device voltage; therefore, the efficiency is reduced. 

Conduction losses are calculated with the equation I2

R. Since current levels rise as voltage declines, the 

rectifier efficiency is poorer at lower voltage levels. Methods are available to partially offset these losses, but 

they have associated mass penalties. The resistances of circuit elements can be lowered by increasing the 

cross sectional areas of the conductors and leads, but it causes their mass to increase. Increasing the diode 

die area and reducing its current density will lower the conduction losses, but a heavy mass penalty can be 

incurred. An alternate approach is to replace these standard diodes with Schottky diodes or germanium 

rectifiers [Ref. 39]. Schottky rectifiers have a lower forward voltage drop, but they generally are not as rugged. The bias voltage of a germanium rectifier is about 0.3 V, but it is more limited in temperature and has a 

lower breakdown voltage.

Because of these factors, the efficiency parameter input for rectifier stage calculations should be decreased 

in accordance with Table 14. These values reflect the increase in mass and reduction in efficiency that 

occurs at lower voltages. These values will yield a smoothly increasing mass curve. The rectifier specific 

weight curve generated with these values is shown in Figure 17.

NASA/CR—2011-217268 32
Table 14: Efficiency Corrections for Lower Voltage Rectifier Mass Estimates

Input Voltage (Vrms) Input Rectifier Efficiency (percent) 

120 98.70

110 98.70

100 98.68

90 98.66

80 98.62

70 98.56

60 98.50

50 98.38

40 98.20

30 97.95

20 96.70

Presently, diodes are available that can withstand reverse voltages up to 24000 V and are rated for ac supply 

voltages up to 9000 Vrms [Ref. 38]. This should be adequate for most space based power conditioning 

needs and further improvements are likely over the next few years. Because of the availability of these 

extremely high voltage diodes it isn’t necessary to use a pancake configuration consisting of diodes stacked 

in series to achieve high voltage capabilities. As a result the mass penalties associated with maintaining 

proper voltage sharing across the diodes in these stacks don’t have to be incurred and the previously 

included high voltage segment of these equations was removed.

0.12

0.13

0.14

0.15

0.16

0.17

0.18

20 30 40 50 60 70 80 90 100 110 120

Input Voltage (Vrms)

k

g

/

k

W

e

Figure 17: Rectifier SPWT vs Low Voltages

NASA/CR—2011-217268 33
3.5 DC FILTER STAGE MODEL

The dc filter stage conditions the dc voltage to obtain the power quality required by the system. Two dc 

filters may be required for a component, one on the input and another on the output. Most components 

containing a chopper or rectifier will require dc filtering; therefore, dc filter stages are contained in the 

rectifier, dc/dc converter, and inverter models. Filtering mass is difficult to estimate. The power quality requirements for future applications are vague or nonexistent, and the design of a filter is a complex process 

that is heavily influenced by the circuit topology. The filter stage equations presented here are generalized 

and only intended to provide rough mass estimates to facilitate component comparisons. For more accurate mass estimates, power quality requirements must be defined and specific filter designs generated.

A single-stage filter design was assumed to precede the chopper and follow the rectifier. This 

configuration is relatively simple, consisting of a series inductor and a parallel capacitor. Since the input to 

a chopper and the output from a rectifier are periodically discontinuous and they have a high ripple content, filtering is needed to smooth the dc level and suppress voltage and current spikes. The masses of 

the filter hardware elements preceding the chopper and following the rectifier were assumed to be 

comparable because they are both performing similar functions, providing energy to smooth the dc level 

during discontinuous conduction periods. Due to the approximations and inaccuracies already inherent in 

these models, it was not considered practical to identify differences in the two filter designs and develop 

alternate equations for both applications.

Based on space station documentation [Ref. 14, 17], the mass of a dc filter following a 1 kWe, 120 Vdc 

single-phase rectifier, designed to reduce the output ripple content to 0.4%, was estimated to be 470 

grams. This rectifier was assumed to follow a Weinberg converter operating at 40 kHz. The ripple frequency of a 3-phase rectifier is three times higher than a single-phase design. This decreases the energy 

that must be stored in the filter hardware to one-third of the single phase value and proportionally reduces 

the filter mass. Consequently, the mass of a dc filter following a 3-phase rectifier also designed to reduce 

the output ripple to 0.4% is 157 grams. Filter inductor and capacitor masses aren’t projected to decline 

significantly, but gradual improvements in their manufacture and materials are expected to allow them to 

operate at higher frequencies without exhibiting higher losses. This capability will lower filter mass.

Internal model development studies conducted after the delivery of the original Task Order 15 report [Ref. 

1] showed the mass per farad of a capacitor rises as the voltage level it is designed for is increased [Ref. 

40, 41, 42, 43, 44]. Both the dielectric thickness and capacitor plate area must be increased at higher 

voltages. This effect partially offsets the reduction in filter mass that occurs because of the ability to use a 

smaller capacitor value and it was incorporated into the dc filter equations presented in this report.

To develop the dc filter stage mass equations, power conditioning model analyses by Gilmour, Moriarty, 

and TRW were referred to for guidance [Ref. 45, 46, 47). The equations developed by TRW under 

contract NAS3-19690 were especially valuable since they allowed dc filter masses to be calculated for numerous conditions. The variables contained in the dc filter stage equations are shown in Table 15.

Table 15: DC Filter Model Variable Definitions

1FSM Single-Phase Dc Filter Stage Mass

3FSM 3-Phase Dc Filter Stage Mass

FSRF Dc Filter Stage Ripple Factor (0.1 to 5%)

FSE Dc Filter Stage Efficiency (99.8%)

FSAM Dc Filter Stage Available Modules

FSRM Dc Filter Stage Required Modules

FSPO Dc Filter Stage Power Output (kWe)

FSVO Dc Filter Stage Voltage Output (Vdc)

FSF Dc Filter Stage Frequency (kHz)

NASA/CR—2011-217268 34
The equations developed for the single-phase and 3-phase dc filter mass estimates are shown below. 

Each factor in the equations will be discussed separately. The factor being discussed will be underlined 

and accompanying graphs will be used to display the values generated by the equations.

Mass Coefficient

1FSM=22.05*(1/(FSRF/0.01)0.5)*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO* 

 (FSVO

-0.9+0.000015)*(40/FSF)

3FSM=22.05*(1/(FSRF/0.01)0.5)*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO* 

 (FSVO

-0.9+0.000015)*(13.33/FSF)

A four step process was used to calculate the mass coefficient contained in the above dc filter equations. 

First, masses of actual LC filter designs were located in technical reports [Ref. 14, 15, 17, 48]. Because 

the filter masses identified in these reports were under widely varying conditions, it allowed the later 

developed filter equations to be verified in different applications. The next step was to calculate filter 

masses using equations developed by TRW during a component mass optimization study [Ref. 47]. The 

parameters input into these filter mass equations were obtained from values contained in the reference 

reports. The third step compared the calculated filter masses with masses listed in reports. Finally, discrepancies were noted and investigated.

The TRW equations generally appeared to be quite accurate and seemed to correctly reflect the dc filter 

mass trends associated with voltage, frequency, and efficiency. Using a mass coefficient value of "22.05" 

yielded good dc filter mass estimates for filters preceding a Weinberg converter and following a static 

rectifier. However, because a resonant converter switches at the zero current crossing point, it doesn’t 

generate as much electromagnetic interference during switching. This translates into a lower filter mass, 

but there wasn’t enough information available to calculate the mass of a filter for a resonant converter 

designed to meet the same requirements as a Weinberg converter filter. Conservatively, it was estimated 

this filter would be 5% lighter than the filters used with a Weinberg converter and a static rectifier, which 

resulted in a mass coefficient of "20.9". Since this is the only difference in the filter equations, only the 

filter equation designed for a Weinberg converter will be displayed throughout the filter discussion.

Ripple Factor

1FSM=22.05*(1/(FSRF/0.01)0.5)*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO* 

 (FSVO

-0.9+0.000015)*(40/FSF)

3FSM=22.05*(1/(FSRF/0.01)0.5)*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO* 

 (FSVO

-0.9+0.000015)*(13.33/FSF)

The ripple factor measures the amount of ripple existing on the dc waveform. It is calculated with the 

following equation:

RF=(VR)/Vdc

where: RF is the ripple factor expressed as a percentage

 VR is the ripple voltage level expressed as a rms value

 Vdc is the dc voltage level.

The dc filter mass will increase as the ripple requirements get more demanding. Equations derived by 

Gilmore and later verified by the TRW calculations showed that the mass would change by the reciprocal 

of the square root of the increase in the ripple factor. This led to the factor underlined above. Figure 18 

shows the rise in dc filter mass occurring as the ripple factor is reduced. To obtain filter masses 

consistent with the ISS DDCU design requirements, set the ripple factor to 0.4%. For utility power 

applications, such as following a large alternator based power source or feeding drive motors, a value of 

NASA/CR—2011-217268 35
5% is suggested. The subsequent graphs on filter characteristics use a ripple factor of 0.4% unless 

otherwise noted.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

0.1% 0.2% 0.3% 0.4% 0.5% 0.6% 0.7% 0.8% 0.9% 1.0% 1.1% 1.2% 1.3% 1.4% 1.5% 1.6% 1.7% 1.8% 1.9% 2.0%

Required Ripple Factor Percentage

kg/kWe

20 kHz

40 kHz

Figure 18: DC Filter SPWT vs Ripple Factor

Efficiency Factor

1FSM=22.05*(1/(FSRF/0.01)0.5)*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO* 

 (FSVO

-0.9+0.000015)*(40/FSF)

3FSM=22.05*(1/(FSRF/0.01)0.5)*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO* 

 (FSVO

-0.9+0.000015)*(13.33/FSF)

The efficiency of an LC filter network is determined by the equivalent series resistance (ESR) of the 

inductor and capacitor. To reduce the ESRs of these devices the inductor winding and core size, and the 

capacitor dielectric cross sectional area must be increased. This increases filter mass. The TRW equations were used to calculate filter masses for efficiency values ranging from 99.7 to 99.9%. An equation 

based curve was then matched to those data points. The equation segment underlined above was

computed during that exercise and used to generate Figure 19. It shows the change in dc filter specific 

weight occurring with a change in efficiency.

Redundancy Factor

1FSM=22.05*(1/(FSRF/0.01)0.5)*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO* 

 (FSVO

-0.9+0.000015)*(40/FSF)

3FSM=22.05*(1/(FSRF/0.01)0.5)*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO* 

 (FSVO

-0.9+0.000015)*(13.33/FSF)

NASA/CR—2011-217268 36
The redundancy factor underlined above addresses the mass penalty associated with a more reliable 

system. The actual number of modules in the assembly is defined by the "available modules" value. The 

number of modules needed to provide full power is defined by the "required modules" value. If a design 

requires 4/3 redundancy to meet the reliability requirements, four 33% rated channels will be used. This 

increases the mass of the assembly at least 33%. The mass of the fourth channel is the penalty incurred 

to achieve a higher reliability.

Figure 19: DC Filter SPWT vs Efficiency

Power Level Multiplier

1FSM=22.05*(1/(FSRF/0.01)0.5)*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO* 

 (FSVO

-0.9+0.000015)*(40/FSF)

3FSM=22.05*(1/(FSRF/0.01)0.5)*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO* 

 (FSVO

-0.9+0.000015)*(13.33/FSF)

The equations can calculate filter mass or specific weight. When the power level multiplier is included, the 

equations determine the mass of the dc filter. Remove this multiplier to obtain the dc filter specific weight.

A power level factor is not included in the dc filter mass equations because the TRW equations indicated 

the filter specific weight remained constant with power level. This is shown in Figure 20 for single- and 3-

phase filter designs. Because the energy density of the capacitors and inductors in the filter network 

remains constant regardless of the power level, the filter specific weight does not change. The gains that 

might be realized in packaging density as the size of the filter element was increased were considered to 

be minor. After some consideration it was decided a power level factor wasn’t necessary.

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

99.70% 99.72% 99.74% 99.76% 99.78% 99.80% 99.82% 99.84% 99.86% 99.88% 99.90%

Efficiency (%)

kg/kWe

NASA/CR—2011-217268 37
0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

10 15 20 25 30 40 50 60 80 100 150 200 250

Power (kWe)

kg/kWe

1 Phase, 20 kHz

3 Phase, 20 kHz

1 Phase, 40 kHz

3 Phase, 40 kHz

Figure 20: DC Filter SPWT vs Power – Single–Phase and 3-Phase

Voltage Level Factors

1FSM=22.05*(1/(FSRF/0.01)0.5)*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO* 

 (FSVO

-0.9+0.000015)*(40/FSF)

3FSM=22.05*(1/(FSRF/0.01)0.5)*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO* 

 (FSVO

-0.9+0.000015)*(13.33/FSF)

In most LC filter designs, the mass of the capacitor is the largest portion of the filter mass. To determine 

the changes that will occur in filter mass as the voltage level rises, the changes occurring in capacitor 

mass must be identified. For a given power level and frequency, the energy that must be stored in the 

filter is constant regardless of the voltage level, but filter capacitance is not. The energy stored in a 

capacitor is defined by the equation:

E=1⁄2CV2

where: C is the capacitance in farads

 V is the voltage level in volts.

By inspection, one can see that the energy stored in a capacitor rises with the voltage squared. If the 

voltage level is doubled, the capacitance can be reduced to one-fourth of its previous value and the 

amount of energy that is stored will remain the same. If one could assume a constant mass per farad, the 

capacitor mass would drop to one-fourth of its previous value. However, an increase in voltage will 

necessitate a thicker dielectric to withstand the electric field being imparted between the plates. 

Furthermore, the following equation shows that the capacitor plate area must also be increased to maintain the same level of capacitance.

NASA/CR—2011-217268 38
C=εoεA/t

where: C is the capacitance in farads

εo is the dielectric constant of a vacuum (0.0884 x10-12 F/cm)

ε is the relative dielectric constant of the dielectric material

A is the capacitor plate area in cm2

t is the thickness of the dielectric material in cm

The fact that both the dielectric thickness and capacitor plate area must be increased at higher voltages 

causes the mass per farad to rise as the voltage level is increased. This partially offsets the reduction in 

filter mass that occurs because of the ability to use a lower capacitor rating. Mass versus voltage data 

was obtained for high voltage tantalum capacitors, ceramic surface mount, disc and multilayer capacitors, 

and two types of polyester/polypropylene dielectric capacitors [Ref. 41, 42, 43, 44]. This data showed 

capacitor mass rises at an exponential rate of 0.3 for ceramic disc capacitors and up to 1.1 for 

polyester/polypropylene capacitors. Ceramic disc capacitors are only available in picofarad sizes, too 

small for high power filters. The ceramic surface mount and polyester/polypropylene capacitors, with 

exponents of 0.9 and 1.1, were judged the best for this application. The types reviewed are specifically 

designed for dc filtering applications and they have the high voltage capability and are available in the 

range of sizes required for this application. Based on this analysis an exponent of 1.1 was used to 

calculate the change in capacitor mass as a function of voltage. Since the capacitance in a dc filter 

declines according to the voltage squared (-2 exponent), while per this analysis its mass is rising at an 

exponential rate of 1.1, the two factors must be multiplied together to obtain the total effect. Adding the 

two exponents together (the exponents are added when two factors are multiplied) resulted in the final 

exponent value of -0.9. Because the mass of the capacitor dominates the filter mass over the voltages of 

interest, almost all of the change in filter mass results from a change in capacitor mass. At lower voltages 

this correlation appears quite accurate. Figure 21 shows the relationship between filter mass and voltage 

for voltage levels below 120 Vdc.

Figure 21: DC Filter SPWT vs Voltage – Low Voltage Region

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

20 30 40 50 60 70 80 90 100 110 120

Output Voltage (Vdc)

kg/kWe

NASA/CR—2011-217268 39
Because capacitor mass declines with voltage, the inductor mass becomes a noticeable fraction of the 

filter mass at higher voltages. This is the reason for the constant “0.000015”. For voltages above a 

approximately 5000 Vdc, the reduction in capacitor mass that occurs with a rising voltage is largely offset 

by the capacitor's rising mass per farad and a larger percentage of inductor mass in the filter. This causes 

the filter specific weight to approach a constant value, as shown in Figure 22. The voltage factor underlined above is designed to cover a voltage range of 20 to 10000 Vdc, and it was developed by integrating 

the data from these analyses.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

120 160 250 500 750 1000 1500 2000 2500 3000 4000 5000 6000 7000 8000 9000 10000

Output Voltage (Vdc)

kg/kWe

Figure 22: DC Filter SPWT vs Voltage – High Voltage Region

Frequency Factor

1FSM=22.05*(1/(FSRF/0.01)0.5)*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO* 

 (FSVO

-0.9+0.000015)*(40/FSF)

3FSM=22.05*(1/(FSRF/0.01)0.5)*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO* 

 (FSVO

-0.9+0.000015)*(13.33/FSF)

The mass of a dc filter is primarily determined by the amount of energy it must store. The energy storage 

requirements are in turn proportional to the ripple frequency. The further apart the wavecrests of the 

ripple voltage are, the more energy a filter must provide to the system to maintain a smooth dc output. 

The ripple frequency of a full wave rectified single-phase waveform is twice the input frequency. Because 

the three phases of a 3-phase system are superimposed after rectification, the output ripple frequency is 

six times the operating frequency. This is why the factor “13.33” in the 3-Phase filter equation is one-third 

the size of the single-phase value, “40”. Because the best mass data available was for the ISS DDCU, 

which has a 40 kHz switching frequency, the filter masses were referenced to a 40 kHz frequency. Figure 

43 shows how much the filter mass declines as the switching frequency of a dc/dc converter is increased. 

These masses are consistent with filters following single-phase rectifiers that are designed to meet a 

ripple requirement of 0.4%.

NASA/CR—2011-217268 40
Figure 23: DC Filter SPWT vs Frequency

3.6 AC FILTER STAGE MODEL

Resonant converters can typically achieve less than 5% total harmonic distortion without filtering. This is 

adequate for most PMAD applications; however, a series harmonic trap is required to prevent external 

harmonics from being amplified within the converter. The mass of a harmonic filter is difficult to estimate. 

In discussions held with converter designers familiar with the design of harmonic filters, they indicated 

present harmonic filter designs are not optimized and quite a bit of improvement is expected. Many articles discuss harmonic distortion, but none were found that described a method for calculating the mass of 

a harmonic filter. Consequently, the following equations are approximate since there is very little concrete 

data. It is recommended that further work be done in this area when additional information becomes 

available. If more accurate mass estimates are required, it will be necessary to define power quality requirements and have a knowledgeable designer generate a specific filter design.

A harmonic filter is located before the converter input or after its output, and it is connected in series with 

the source or load. The equations in this report are based on a series resonant circuit tuned to the inversion frequency of the converter. The filter configuration itself consists of a current transformer that is 

connected in parallel with a resistor, and a series connected inductor and capacitor combination [Ref. 49]. 

The current transformer is required to obtain reasonable values for the inductor and capacitor and to 

reflect adequate resistance into the line to inhibit harmonics [Ref. 23]. Much of the filter mass is 

concentrated in this current transformer and it can not be eliminated.

A technical presentation compiled by TRW indicated the mass of a harmonic filter placed on the output of 

a 5 kWe, 20 kHz inverter would weigh 1071 grams [Ref. 15]. The specific weight of this filter is about 0.21 

kg/kWe. In a discussion held at the "High Frequency Power Distribution and Controls Technology 

Conference" in June 1991, John Biess indicated it might be possible to reduce this filter design to onethird of its present weight with extensive analysis and optimization. This would result in a specific weight 

of about 0.07 kg/kWe [Ref. 23]. However, he also indicated this value might be optimistic. Based on this 

discussion, it was decided to use a value of 0.1 kg/kWe for a harmonic filter following a single-phase 1 

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

3.6

3.8

4.0

5 10 15 20 25 30 35 40 45 50 60 70 80 90 100

Frequency (kHz)

kg/kWe

NASA/CR—2011-217268 41
kWe, 20 kHz inverter. The harmonic filter used for a 3-phase inverter was assumed to consist of three 

single-phase inverter filters each rated to carry one-third of the power. Its mass would be just slightly 

heavier due to economies of scale. The estimated masses of filters following single-phase and 3-phase, 1 

kWe inverters was estimated to be 100 and 105 grams respectively.

The variables used in the ac filter stage equations are shown in Table 16.

Table 16: AC Filter Model Variable Definitions

1FSM Single-Phase Ac Filter Stage Mass

3FSM 3-Phase Ac Filter Stage Mass

FSE Ac Filter Stage Efficiency (99.5%)

FSAM Ac Filter Stage Available Modules

FSRM Ac Filter Stage Required Modules

FSPO Ac Filter Stage Power Output (kWe)

FSF Ac Filter Stage Frequency (kHz)

The equations generated to estimate the masses of single-phase and 3-phase ac filters follow. The 

factors in the equations will be discussed separately and underlined. Graphs will be used to depict the 

effects calculated by the equations.

Mass Coefficient

1FSM=0.1*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO*(FSPO/FSRM)-0.03*(FSF/20)-0.6

3FSM=0.105*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO*(FSPO/FSRM)-0.03*(FSF/20)-0.6

The single- and 3-phase ac filter stage mass coefficients were calibrated to yield specific weights of 0.1 

and 0.105 kg/kWe respectively, when placed after a 1 kWe, 20 kHz inverter. The inverter filter specific 

weights are based on the previously discussed conversation with John Biess [Ref. 23]. The mass coefficient for the 3-phase design is larger because it consists of three single-phase filters, each carrying onethird of the power. Economies of scale are lost in the current transformer as the filter power level 

declines. This causes the mass of the 3-phase filter to be slightly greater. The difference in masses of 

single- and 3-phase ac filters is illustrated in Figure 24. This figure compares the specific weights of 

inverter filter designs at 20 and 40 kHz resonant frequencies.

Efficiency Factor

1FSM=0.1*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO*(FSPO/FSRM)-0.03*(FSF/20)-0.6

3FSM=0.105*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO*(FSPO/FSRM)-0.03*(FSF/20)-0.6

The ac filter design presented in this study uses a series resonant circuit. This circuit has the largest 

influence on filter efficiency and its efficiency is determined by the ESRs of the inductor and capacitor 

composing it. These ESRs can only be decreased by enlarging the inductor winding and core, the capacitor dielectric area, and the interconnecting lead wires. A larger filter mass will result. Since this same 

process occurred in the dc filter case, the efficiency factors were assumed to be the same. This factor 

lead to the relationship for ac filter efficiency shown graphically in Figure 25.

NASA/CR—2011-217268 42
Figure 24: AC Filter SPWT vs Power - Single Phase & 3 Phase

Figure 25: AC Filter SPWT vs Efficiency

0.05

0.06

0.07

0.08

0.09

0.10

0.11

10 15 20 25 30 40 50 60 80 100 150 200 250

Power (kWe)

k

g

/

k

W

e

Single-Phase, 20 kHz

3-Phase, 20 kHz

Single-Phase, 40 kHz

3-Phase, 40 kHz

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

99.70% 99.72% 99.74% 99.76% 99.78% 99.80% 99.82% 99.84% 99.86% 99.88% 99.90%

Efficiency (%)

k

g

/

k

W

e

NASA/CR—2011-217268 43
Redundancy Factor

1FSM=0.1*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO*(FSPO/FSRM)-0.03*(FSF/20)-0.6

3FSM=0.105*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO*(FSPO/FSRM)-0.03*(FSF/20)-0.6

A redundancy factor accounts for the additional mass needed to realize a more reliable system. The 

actual number of modules in the assembly is defined by the "available modules" value. The number of 

modules needed to provide full power is defined by the "required modules" value. A design requiring 4/3 

redundancy has four 33% rated channels. The mass of this assembly will be at least 33% heavier and the 

mass of the fourth channel is part of the penalty associated with this higher reliability requirement.

Power Level Multiplier

1FSM=0.1*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO*(FSPO/FSRM)-0.03*(FSF/20)-0.6

3FSM=0.105*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO*(FSPO/FSRM)-0.03*(FSF/20)-0.6

These equations can calculate the mass or specific weight of the ac filter. If the power level multiplier is 

included, the mass of the ac filter will be calculated; removing it produces the filter's specific weight.

Power Level Factor

1FSM=0.1*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO*(FSPO/FSRM)-0.03*(FSF/20)-0.6

3FSM=0.105*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO*(FSPO/FSRM)-0.03*(FSF/20)-0.6

The heaviest element in the ac filter is the current transformer. As the filter power level increases and the 

size of this transformer grows, its core is better utilized, and the winding current density increases slightly. 

These economies of scale reduce the current transformer specific weight by the 0.08 power as the filter 

power level rises. Similar evaluations of the inductor, capacitor, and resistor specific weights indicated 

they did not change with power level. Combining the specific weight contributions of all the elements in 

the ac filter indicated the specific weight of the complete filter declined at the 0.03 power as the ac filter 

power level grew. This effect is shown in Figure 26 for 10, 20, and 40 kHz single-phase ac filter designs.

The "required modules" figure is included in this factor to address the use of a modular design approach. 

The total output power of the assembly must be divided by the required number of modules since each 

module processes just a portion of this power. Because the specific weight of an ac filter changes with 

power, its mass must be calculated at the power level of the individual modules and not the power level of 

the complete assembly.

Frequency Factor

1FSM=0.1*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO*(FSPO/FSRM)-0.03*(FSF/20)-0.6

3FSM=0.105*((1-0.998)/(1-FSE))*(FSAM/FSRM)*FSPO*(FSPO/FSRM)-0.03*(FSF/20)-0.6

The combined impact of frequency on ac filter mass was determined by evaluating the influence 

frequency had on the current transformer, the series resonant circuit, and the resistor masses. The mass 

of the current transformer core will decline with increasing frequency because the flux density needed to 

generate a given voltage declines as frequency rises. This lower flux density reduces the transformer 

core volume and mass. A smaller core means less winding mass because the mean length of the turns is

NASA/CR—2011-217268 44
0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.5 1 5 10 15 20 25 30 40 50 60 80 100 150 200 250

Power (kWe)

k

g

/

k

W

e

10 kHz

20 kHz

40 kHz

Figure 26: AC Filter SPWT vs Power

less. By totaling the overall effect, it was determined that the current transformer specific weight declined 

at the 0.47 power as frequency rose. 

The resonant frequency of the series resonant circuit is calculated with the following equation.

FR=1/(LC)0.5

Where: FR is the resonant frequency,

L is the circuit inductance in Henries,

C is the circuit capacitance in Farads.

By inspection one can see the circuit inductance and capacitance must double if the resonant frequency is 

cut in half. This causes the inductor and capacitor mass to double and shows that the mass of a series 

resonant circuit is inversely proportional to frequency. The final element in the filter, the resistor, is 

unaffected by frequency. By adding these individual frequency effects together, a frequency factor was 

generated for the complete ac filter. This calculation indicated the specific weight of an ac filter would 

decline at the 0.6 power as its resonant frequency rose. The combined influence of frequency on filter 

mass is shown in Figure 27 for 1 and 100 kWe single-phase ac filter designs.

Voltage Factor

The current transformer contained in the ac filter is necessary to obtain reasonable values for the inductor 

and capacitor and to reflect adequate resistance into the line to inhibit harmonics. Consequently, the 

effects of different operating voltages on the resonant circuit elements and the resistor can be offset by 

selecting the proper turns ratio for this transformer. This means the only item that will be impacted by 

varying the voltage level is the current transformer itself. The effect of voltage on a transformer was previously investigated in section 3.1.2.1 and it was shown to be fairly minor. Since the transformer is only 

one element in the filter, the cumulative effect will be even less. After a short analysis, it was considered 

negligible and a factor was not included in the equations.

NASA/CR—2011-217268 45
0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

10 15 20 25 30 35 40 45 50 55 60

Frequency (kHz)

k

g

/

k

W

e

1 kWe

100 kWe

Figure 27: AC Filter SPWT vs Frequency

3.7 DC RBI MODEL

Dc remote bus isolators (RBIs) are smart circuit protection devices that incorporate current sensors and 

are used to switch dc power and interrupt fault currents. They are located in dc switchgear units. This 

section discusses the equations developed to estimate their masses as a function of power, efficiency, 

and voltage.

The latest dc RBI switchgear design uses a channelized approach because the card cage assembly that 

controls and monitors the dc RBI operation can be shared among several units. Three basic design 

approaches are available for a single RBI channel, a mechanical relay, a hybrid arrangement consisting of 

a mechanical relay paralleled with a semiconductor switch, or a semiconductor switch. The ISS RBIs use 

a mechanical relay and add a snubber circuit to suppress voltage transients occurring during opening and 

closing periods. A hybrid arrangement has certain advantages because the relay and semiconductor 

switch can function together to improve the operating characteristics of the RBI switch. The relay carries 

the bulk of the current during normal operation; this results in a high efficiency switch. The main need for 

the semiconductor switch is during opening and closing times. It closes immediately before relay closing 

to quell relay chatter transients, and it opens after the relay to suppress opening transients. The opening 

rate of the semiconductor can be varied to obtain the best opening characteristics. A design that only 

uses a semiconductor switch exhibits very good opening and closing characteristics. However, the conduction resistance of a semiconductor is much higher than a relay contact; therefore, the switch losses are 

significantly higher during normal operating periods.

The dc RBI model described in this report is based on a hybrid switch configuration. This design was 

considered to provide the best combination of mass, efficiency, and switching characteristics. However, 

as the RBI voltage rises the switch design will probably change from a relay in parallel with a single semiconductor to a vacuum switch in parallel with a number of series connected semiconductors. At the 

present time, the semiconductor devices in a dc RBI would likely be MOSFETs or insulated gate bipolar 

transistors (IGBTs). Future RBI designs will probably use MCTs. Mass breakdowns were generated for 

two sizes of dc RBIs. These mass estimates were derived from a SSF RBI mass breakdown that was 

NASA/CR—2011-217268 46
adjusted to be consistent with the as-built flight DC Switching Unit (DCSU) and information obtained from 

a Ford Aerospace briefing package [Ref. 14, 17, 50]. The original RBI efficiency was calculated from RBI 

loss information contained in a Rocketdyne SSF document [Ref. 51]. During this review, the previously 

calculated efficiency value determined for the dc RBIs was checked against the Electrical Power System 

On-Orbit Performance (EPSOP) Modeling Data report, which showed the original efficiency value, 

99.85%, was consistent with the flight design [Ref. 52]. These mass and efficiency values were utilized as 

a basis for the subsequent equation development.

The following paragraphs explain the dc RBI equation development. Graphs are used in conjunction with 

technical descriptions to explain the equation rationale. The variables used in this discussion are shown in

Table 17.

Table 17: DC RBI Model Variable Definitions

DRBM Dc RBI Mass

DRBE Dc RBI Efficiency (99.85%)

DRBAM Dc RBI Available Modules

DRBRM Dc RBI Required Modules

DRBPO Dc RBI Power Output (kWe)

DRBVO Dc RBI Voltage Output (Vdc)

Mass Coefficient

DRBM=0.12*((EXP(0.0008/(1-DRBE)))/1.7)*(DRBAM/DRBRM)*DRBPO*(DRBPO/DRBRM)-0.15* 

 (DRBVO/200)0.13

The dc RBI mass coefficient was developed from SSF DC RBI mass breakdowns. To be consistent with 

the previously discussed future design, the design of the SSF dc RBI was revised to include a 

semiconductor switch in parallel with the mechanical relay, the snubber circuitry was removed since it was 

no longer required, and mass benefits obtained from minor hardware advancements were incorporated. 

The mass coefficient was calibrated to yield values consistent with these mass breakdowns.

Efficiency Factor

DRBM=0.12*((EXP(0.0008/(1-DRBE)))/1.7)*(DRBAM/DRBRM)*DRBPO*(DRBPO/DRBRM)-0.15* 

 (DRBVO/200)0.13

The above underlined factor estimates the change in specific weight occurring with a change in dc RBI 

efficiency. The efficiency of an RBI is quite high and it does not appear practical to change it much. 

However, it can be increased by reducing the resistances of the relay contacts and semiconductor. To 

accomplish this, the conduction areas of these elements must be enlarged. Basically, doubling the 

masses of the relay contacts and semiconductor switch will cut their losses in half. Since the losses are 

cut in half, the thermal management hardware changes likewise. The rest of the RBI elements will also 

change slightly to conform to the new relay, semiconductor, and thermal management hardware designs. 

The variation in RBI mass was estimated for efficiencies ranging from 99.8 to 99.9% and it was used to 

generate the above efficiency factor. A graph of RBI specific weights that shows the results of this 

analysis is contained in Figure 28. Note that the depicted dc RBI efficiency range is relatively narrow. Efficiencies higher than about 99.9% are not considered viable because the relay contact and semiconductor 

switch size will become impractical. It is not feasible to cut the RBI mass below a certain level because 

the relay contacts, semiconductor switch, and structural hardware simply will not be strong enough to 

withstand the stresses encountered while interrupting a fault current.

NASA/CR—2011-217268 47
0.05

0.06

0.07

0.08

0.09

0.10

0.11

99.80% 99.81% 99.82% 99.83% 99.84% 99.85% 99.86% 99.87% 99.88% 99.89% 99.90%

Efficiency (%)

k

g

/

k

W

e

Figure 28: DC RBI SPWT vs Efficiency

Redundancy Factor

DRBM=0.12*((EXP(0.0008/(1-DRBE)))/1.7)*(DRBAM/DRBRM)*DRBPO*(DRBPO/DRBRM)-0.15* 

 (DRBVO/200)0.13

The mass of a dc RBI network will rise if a modular design approach is used to enhance reliability. The 

mass increase is estimated by the factor above. The "available modules" number is the actual number of 

modules present in the component; the "required modules" value is the actual number of modules required to provide the full output power level. If the reliability requirements of a system force a design to 

use 4/3 redundancy, each channel is designed to carry 33% of the power. Although 4 channels are available, only 3 channels are needed to supply full power. The mass of the fourth channel is the penalty paid 

to obtain the higher specified reliability.

Power Level Multiplier

DRBM=0.12*((EXP(0.0008/(1-DRBE)))/1.7)*(DRBAM/DRBRM)*DRBPO*(DRBPO/DRBRM)-0.15* 

 (DRBVO/200)0.13

The equation can be used to calculate the mass or specific weight of the dc RBI. When the above 

multiplier is included, the value that results estimates the RBI mass. To obtain the specific weight of the 

RBI, remove this multiplier.

Power Level Factor

DRBM=0.12*((EXP(0.0008/(1-DRBE)))/1.7)*(DRBAM/DRBRM)*DRBPO*(DRBPO/DRBRM)-0.15* 

 (DRBVO/200)0.13

NASA/CR—2011-217268 48
The masses of the power conducting parts of the dc RBI, which are the relay contacts and the semiconductor switch, will increase nearly linearly with a rise in power. However, the mass of supporting hardware 

elements, such as driver modules, sensors, and control logic devices, grows at a slower rate. This results 

in some economies of scale as the dc RBI power level rises and causes its specific weight to decline. The 

change in the specific weight of a dc RBI as the power level rises is shown in Figure 29.

Figure 29: DC RBI SPWT vs Power Level

Voltage Level Factor

DRBM=0.12*((EXP(0.0008/(1-DRBE)))/1.7)*(DRBAM/DRBRM)*DRBPO*(DRBPO/DRBRM)-0.15* 

 (DRBVO/200)0.13

As the voltage across a dc RBI increases, its mass was expected to rise at a slightly higher rate. This is 

because the elements in the RBI must be further isolated, more insulation is required, and the stresses 

are higher. The separation distance between the relay contacts in a dc RBI will need to increase as the 

voltage level rises to prevent vacuum breakdown and arcing. The mass of the semiconductor switch in 

parallel with the relay is also expected to rise. The semiconductor devices will need to be connected in 

series to handle higher voltages; however, series connected semiconductors do not inherently share 

voltages evenly. Additional hardware is needed to make them voltage share and protect them in case 

they do not. Finally, dc systems normally require capacitors to maintain voltage stability. Unfortunately, 

the capacitors will discharge into a fault and greatly increase the initial fault current. The RBI must be 

structurally strong enough to withstand the added stress of this discharge. Each of these factors 

increases the mass of the complete RBI. By referring to terrestrial RBI designs, an estimate of this mass 

increase was developed and it was utilized to generate the factor shown above. The results of this 

exercise are shown in Figure 30.

0.04

0.05

0.06

0.07

0.08

0.09

0.10

5 10 15 20 25 30 40 50 60 80 100 150 200 250

Power (kWe)

k

g

/

k

W

e

NASA/CR—2011-217268 49
0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

0.14

100 200 400 700 1000 1500 2000 3000 4000 5000 6000 7000 8000 9000 10000

Voltage (Vdc)

k

g

/

k

W

e

Figure 30: DC RBI SPWT vs Voltage

3.8 AC RBI MODEL

Ac RBIs are smart circuit protection switches with current sensors. They are used to switch major ac 

power feeds and interrupt faults. They are located in ac switchgear units. The equations developed to 

estimate ac RBI mass as it varies with power and voltage are discussed in this section.

The ac RBI design will be similar in many respects to the dc RBI design. An ac RBI switchgear unit will 

also use a channelized approach because the card cage assembly that controls and monitors ac RBI 

operation can be shared between several RBIs. Two configurations are practical for an ac RBI channel, a 

hybrid arrangement consisting of a fast acting mechanical relay that is paralleled with a back-to-back pair 

of semiconductor switches, or just a back-to-back pair of semiconductor switches. A solitary mechanical 

relay is not fast enough to open during the zero current crossing; consequently, this configuration is not 

practical.

The hybrid arrangement is preferred because the relay and semiconductor switch can work together to 

improve the operating characteristics of the RBI switch. During normal power delivery periods, the relay 

carries the bulk of the current. The mechanical relay contacts greatly reduce conduction losses and allow 

high efficiency operation. The semiconductor switches are primarily required during opening and closing 

times. Only semiconductor switches can operate fast enough to close or open within the zero current 

crossing point limits. The semiconductor switches are closed immediately before relay closing to quell 

relay chatter transients, and opened after the relay to suppress opening transients. An RBI design using 

just semiconductor switches exhibits very good opening and closing characteristics; however, its conduction losses are much higher than a hybrid design with a relay. Consequently, the efficiency of this ac 

RBI design would be much poorer.

The ac RBI model described in this report is based on a hybrid switch configuration. This design was 

considered to provide the best combination of mass, efficiency, and switching characteristics. However, 

as the RBI voltage rises the RBI switch design will probably change from a relay in parallel with a single 

NASA/CR—2011-217268 50
semiconductor to a vacuum switch in parallel with a number of series connected semiconductors. At the 

present time, the semiconductor devices in an ac RBI would probably be SCRs. Future RBI designs may 

use MCTs. In a telephone conversation with Dave Fox of Westinghouse, he indicated that ac and dc RBIs 

rated to conduct the same amount of power would have similar masses (Ref. 53). The data bus interface 

and control elements in the ac RBIs would probably be the same as those in the dc units. The relay in an 

ac RBI would be lighter because the existence of a zero current crossing point eases fault current 

interruption; however, the mass of the ac RBI must include the mass of a back-to-back pair of semiconductor switches and their drivers. Based on this discussion the masses of many of the elements in an ac 

RBI were obtained from the SSF dc RBI mass breakdown [Ref. 14].

The ensuing paragraphs explain the development of single-phase and 3-phase ac RBI equations in detail. 

The equation formulation is explained via technical descriptions and graphs. The variables used in 

succeeding discussions are listed in Table 18.

Table 18: AC RBI Model Variable Definitions

1ARB Single-Phase ac RBI Mass

3ARB Three-Phase ac RBI Mass

ARBE Ac RBI Efficiency (99.85%)

ARBAM Ac RBI Available Modules

ARBRM Ac RBI Required Modules

ARBPO Ac RBI Power Output (kWe)

ARBVO Ac RBI Voltage Output (Vrms)

Mass Coefficient

1ARB=0.1*((EXP(0.0008/(1-ARBE)))/1.7)*(ARBAM/ARBRM)*ARBPO*(ARBPO/ARBRM)-0.13* 

 (ARBVO/200)0.05

3ARB=0.135*((EXP(0.0008/(1-ARBE)))/1.7)*(ARBAM/ARBRM)*ARBPO*(ARBPO/ARBRM)-0.15* 

 (ARBVO/200)0.05

The SSF dc RBI mass breakdowns were used as a starting point to generate mass breakdowns for ac 

RBIs. The resulting ac RBI mass breakdowns were then used to determine the mass coefficients 

underlined above. Many elements in dc and ac RBIs will be equivalent; therefore, the masses of these dc 

RBI elements were also used in the ac RBI case. The size of the relay in an ac RBI is smaller, but an ac 

RBI requires a back-to-back pair of semiconductor switches. The reduced relay mass and the mass of 

these semiconductor switches and their drivers was included in the ac RBI mass breakdowns. The ac 

RBI mass breakdown was completed by removing the snubber circuitry included in the SSF dc RBI design 

and incorporating the mass gains resulting from minor hardware advancements expected over the next 

ten years. The mass breakdowns generated for future ac RBIs are located in Appendix A on pages A-8 

and A-9. The mass coefficients contained in the ac RBI mass equations were calculated to yield values 

consistent with these mass breakdowns.

The mass of the relay in a 3-phase ac RBI design was estimated to be about 50% heavier due to the need 

for two additional contact and semiconductor switch pairs. However, because the mass of the control 

logic and thermal management hardware is similar in both designs and the packaging weight difference 

becomes less as the RBI size grows, the relative difference in mass between the two designs also 

declines as the power level rises. The specific weights of single- and 3-phase ac RBI designs are

compared in Figure 31.

NASA/CR—2011-217268 51
0.04

0.05

0.06

0.07

0.08

0.09

0.10

0.11

0.12

5 10 15 20 25 30 40 50 60 80 100 150 200 250

Power (kWe)

k

g

/

k

W

e

Single-Phase AC RBI

3-Phase AC RBI

Figure 31: AC RBI SPWT - 1 Phase vs 3 Phase

Efficiency Factor

1ARB=0.1*((EXP(0.0008/(1-ARBE)))/1.7)*(ARBAM/ARBRM)*ARBPO*(ARBPO/ARBRM)-0.13* 

 (ARBVO/200)0.05

3ARB=0.135*((EXP(0.0008/(1-ARBE)))/1.7)*(ARBAM/ARBRM)*ARBPO*(ARBPO/ARBRM)-0.15* 

 (ARBVO/200)0.05

The efficiency of an ac RBI was expected to be the same as a dc RBI; the reactive parasitics associated 

with ac operation were expected to be negligible. The efficiency of an ac RBI can be increased by 

enlarging the conduction area of the relay contacts and semiconductor switches to reduce their resistance. 

Doubling the mass of the relay contacts and semiconductor switches should cut conduction losses in half. 

The mass of the thermal management hardware should decline proportionally. Other RBI elements will 

change slightly to conform to the new relay, semiconductor, and thermal management hardware designs. 

Changes in RBI mass were estimated for efficiencies ranging from 99.8 to 99.9%. Efficiencies higher than 

99.9% are not considered practical because the relay contact and semiconductor switch sizes would 

become too large. Below an efficiency of 99.8% the structural integrity of the RBI, and the strength of its 

relay contacts and semiconductor switches would be suspect. RBI mass breakdowns generated during 

this process were used to create the above efficiency factor. A graph of ac RBI specific weights as a 

function of efficiency is shown in Figure 32.

NASA/CR—2011-217268 52
0.04

0.05

0.06

0.07

0.08

0.09

0.10

99.80% 99.81% 99.82% 99.83% 99.84% 99.85% 99.86% 99.87% 99.88% 99.89% 99.90%

Efficiency (%)

k

g

/

k

W

e

Figure 32: AC RBI SPWT vs Efficiency

Redundancy Factor

1ARB=0.1*((EXP(0.0008/(1-ARBE)))/1.7)*(ARBAM/ARBRM)*ARBPO*(ARBPO/ARBRM)-0.13* 

 (ARBVO/200)0.05

3ARB=0.135*((EXP(0.0008/(1-ARBE)))/1.7)*(ARBAM/ARBRM)*ARBPO*(ARBPO/ARBRM)-0.15* 

 (ARBVO/200)0.05

If a modular design approach is used to enhance reliability, the total mass of the ac RBI units will rise. 

The above factor estimates this mass increase. The actual number of modules present in the system is 

defined by the "available modules" number; the number of modules required to deliver full power is specified by the "required modules" value. If a system is designed with 4/3 redundancy, each channel is 

capable of carrying 33% of the power. The fourth channel is not required to provide full power and its 

mass is the penalty paid to obtain a higher reliability.

Power Level Multiplier

1ARB=0.1*((EXP(0.0008/(1-ARBE)))/1.7)*(ARBAM/ARBRM)*ARBPO*(ARBPO/ARBRM)-0.13* 

 (ARBVO/200)0.05

3ARB=0.135*((EXP(0.0008/(1-ARBE)))/1.7)*(ARBAM/ARBRM)*ARBPO*(ARBPO/ARBRM)-0.15* 

 (ARBVO/200)0.05

The equations can be used to calculate the mass or specific weight of the ac RBI. When the above 

multiplier is included, the value that results is an estimate of the RBI mass. To obtain the specific weight 

of the RBI, remove this multiplier.

NASA/CR—2011-217268 53
Power Level Factor

1ARB=0.1*((EXP(0.0008/(1-ARBE)))/1.7)*(ARBAM/ARBRM)*ARBPO*(ARBPO/ARBRM)-0.13* 

 (ARBVO/200)0.05

3ARB=0.135*((EXP(0.0008/(1-ARBE)))/1.7)*(ARBAM/ARBRM)*ARBPO*(ARBPO/ARBRM)-0.15* 

 (ARBVO/200)0.05

The mass of the relay contacts and semiconductor switches will rise nearly linearly with an increase in 

power because they are the power conducting elements in the ac RBI. However, the masses of the 

drivers, sensors, and logic devices do not rise as fast. These trends result in some economies of scale as 

ac RBI power levels rise and they cause specific weights to decline. Because the mass of the ancillary 

hardware in a 3-phase ac RBI occupies a larger percentage of its total mass, the gains in specific weight 

that occur with power are greater in this RBI design than in the single-phase RBI design. This explains the

difference between the single- and 3-phase power level multiplier exponents, -0.18 and -0.21. The 

difference in mass growth rates between single- and 3-phase ac RBIs can be seen by referring back to 

Figure 31. An expanded view of only the single-phase ac RBI is shown in Figure 33.

Figure 33: AC RBI SPWT vs Power Level

Voltage Level Factor

1ARB=0.1*((EXP(0.0008/(1-ARBE)))/1.7)*(ARBAM/ARBRM)*ARBPO*(ARBPO/ARBRM)-0.13* 

 (ARBVO/200)0.05

3ARB=0.135*((EXP(0.0008/(1-ARBE)))/1.7)*(ARBAM/ARBRM)*ARBPO*(ARBPO/ARBRM)-0.15* 

 (ARBVO/200)0.05

0.040

0.045

0.050

0.055

0.060

0.065

0.070

0.075

0.080

0.085

0.090

5 10 15 20 25 30 40 50 60 80 100 150 200 250

Power (kWe)

k

g

/

k

W

e

NASA/CR—2011-217268 54
A number of effects, some of them offsetting, occur as the voltage across an ac RBI increases. The 

internal RBI wiring and its devices will require more insulation to withstand the added voltage stresses. 

The relay contacts will need to be separated further to prevent vacuum breakdown. These effects tend to 

increase the RBI mass, especially the relay mass. However, assuming the RBI power level remains the 

same, the current conducted by the contacts will decline as the voltage rises. This reduces the mass of 

the relay contacts and the relay driver. Since the mechanical parts of the relay are heavier than insulation, 

the overall effect should be a slight reduction in relay mass as the ac RBI voltage increases. The mass of 

the semiconductor switches in parallel with the relay, however, is expected to rise as voltage increases. 

Semiconductor devices must be connected in series to switch higher voltages; however, series connected 

semiconductors will not naturally share voltages evenly. Additional hardware is needed to make them 

voltage share and protect them in case they do not. These factors increase the mass of the RBI. After 

weighing the increase in semiconductor mass against the reduction in relay mass, it appears the mass of 

a complete ac RBI will slowly rise as voltage levels rise. Figure 34 displays the results of this evaluation.

Figure 34: AC RBI SPWT vs Voltage

3.9 DC RPC MODEL

Dc remote power controllers (RPCs) are used to switch and monitor individual dc load circuits and provide 

circuit protection. These devices will be located in dc power distribution racks. This section explains the 

equation developed to estimate their masses as a function of power, efficiency, and voltage. This 

equation provides rough mass estimates for component comparison purposes. For more accurate mass 

estimates specific component designs must be developed.

The present ISS dc RPC module design uses a channelized approach similar to the dc RBI configuration 

since the card cage assembly that controls and monitors the operation of a dc RPC can be shared among 

several units. Two types of RPCs are employed depending on the current rating. The 65 amp rated RPC 

uses a relay, while the 25 amp and lower rated RPCs utilize semiconductor switches. An alternative would

be an RPC channel with a hybrid arrangement consisting of a mechanical relay paralleled with a semiconductor switch. A hybrid arrangement is attractive because the relay and semiconductor switch can 

function together to yield a high efficiency switch that also exhibits good opening and closing characteristics. However, because the semiconductor only switch design is lighter and semiconductor switches, 

0.050

0.055

0.060

0.065

0.070

0.075

0.080

0.085

0.090

0.095

0.100

100 200 400 700 1000 1500 2000 3000 4000 5000 6000 7000 8000 9000 10000

Voltage (Vrms)

k

g

/

k

W

e

NASA/CR—2011-217268 55
especially MOSFETs, have lower “on” resistances then past generations of semiconductor switches the 

dc RPC equation described in this section is based on a semiconductor only switch configuration. Since a 

dc RPC is essentially a lower power dc RBI in many respects and most of their characteristics are similar, 

the paragraphs describing the RPC equation development and rationale will rely heavily on the previous 

dc RBI discussion. Explanations will be succinct to reduce the amount of repetition. If additional information is desired please refer back to the dc RBI discussion.

It was mentioned that the dc RBI and RPC configurations are similar; however, there are some differences 

that cause their specific weights to vary. The mass of the thermal management hardware occupies a 

larger percentage of the RPC mass. This is partially because an RPC is less efficient, but mainly because 

thermal management hardware does not scale linearly down to these smaller power levels. The mass of 

the housing and structure of an RPC also assumes a greater portion of the total mass for the same 

reason. The effect of these two items causes the specific weight of an RPC to be considerably higher 

than a RBI. Dc RPC mass breakdowns are contained in Appendix A on page A-10 and A-11. They were 

derived from SSF RPC mass breakdowns, adjusted to reflect the flight unit masses [Ref. 14, 17]. The 

efficiency of the dc RPC was calculated using the ISS RPC Interface Control Document (ICD), which 

indicated the value previously calculated during Task Order 15, 99.85%, was too high and it was reduced 

to 99.7% [Ref. 54]. These values were used as a basis for the subsequent equation development.

The dc RPC equation development is explained in the following paragraphs. Graphs are used in 

conjunction with technical descriptions to explain the equation rationale. Variables used in this discussion 

are shown in Table 19.

Table 19: DC RPC Model Variable Definitions

DRPM Dc RPC Mass

DRPE Dc RPC Efficiency (99.7%)

DRPAM Dc RPC Available Modules

DRPRM Dc RPC Required Modules

DRPPO Dc RPC Power Output (kWe)

DRPVO Dc RPC Voltage Output (Vdc)

Mass Coefficient

DRPM=0.135*((EXP(0.0006/(1-DRPE)))/1.2214)*(DRPAM/DRPRM)*DRPPO*(DRPPO/DRPRM)-0.12* 

 (DRPVO/120)0.04

The dc RPC mass breakdowns located in Appendix A were derived from SSF dc RPC mass breakdowns. 

The mass totals obtained from these breakdowns were checked against the latest flight unit masses and 

were found to be in close agreement. The SSF RPC mass breakdowns and those used for this equation 

development are based on a semiconductor switch configuration. Mass gains originating from technology 

improvements are incorporated into the dc RPCM rack model and the breakdowns in Appendix A and they 

reflect a 2 to 3% reduction in total RPC mass depending on its configuration. An RPC with more channels, 

16 channels versus one for instance, tends to be slightly heavier due to the mass overhead for more 

switch gate drives, sensors, and additional control elements. The above mass coefficient was calculated 

to yield values consistent with these mass breakdowns.

Efficiency Factor

DRPM=0.135*((EXP(0.0006/(1-DRPE)))/1.2214)*(DRPAM/DRPRM)*DRPPO*(DRPPO/DRPRM)-0.12* 

 (DRPVO/120)0.04

NASA/CR—2011-217268 56
The above underlined factor estimates the change in specific weight occurring with a change in dc RPC 

efficiency. The efficiency of an RPC can be raised by enlarging the contact and semiconductor conduction area to reduce their resistance. The mass of the semiconductor switch will increase, but the sensor, 

control logic and gate drive circuitry mass doesn’t change significantly, and the thermal management 

hardware mass will decline slightly. RPC mass estimates were generated for efficiencies ranging from 

99.65 to 99.75% and they were used to generate the above efficiency factor. A graph of these RPC 

specific weights is shown in Figure 35.

Figure 35: DC RPC SPWT vs Efficiency

Redundancy Factor

DRPM=0.135*((EXP(0.0006/(1-DRPE)))/1.2214)*(DRPAM/DRPRM)*DRPPO*(DRPPO/DRPRM)-0.12* 

 (DRPVO/120)0.04

The mass of a dc RPC network rises if a modular design approach is used to enhance reliability. The 

factor underlined above estimates this mass increase. The "available modules" number is the actual 

number of modules present in the component; the "required modules" number is the actual number of 

modules required to provide full output power. Assume the system reliability requirements necessitate the 

use of 4/3 redundancy. Each channel will be designed to carry 33% of the power. 4 channels will be 

available, but only 3 are needed to supply full power. The mass of the fourth channel is the penalty paid to 

obtain the higher specified reliability.

Power Level Multiplier

DRPM=0.135*((EXP(0.0006/(1-DRPE)))/1.2214)*(DRPAM/DRPRM)*DRPPO*(DRPPO/DRPRM)-0.12* 

 (DRPVO/120)0.04

0.112

0.114

0.116

0.118

0.120

0.122

0.124

0.126

99.65% 99.66% 99.67% 99.68% 99.69% 99.70% 99.71% 99.72% 99.73% 99.74% 99.75%

Efficiency (%)

k

g

/

k

W

e

NASA/CR—2011-217268 57
The equation can be used to calculate the mass or specific weight of the dc RPC. When the above 

multiplier is included, the RPC mass is estimated. To obtain the specific weight of the RPC, remove this 

multiplier.

Power Level Factor

DRPM=0.135*((EXP(0.0006/(1-DRPE)))/1.2214)*(DRPAM/DRPRM)*DRPPO*(DRPPO/DRPRM)-0.12* 

 (DRPVO/120)0.04

The mass of the dc RPC semiconductor switch will increase proportionally with a rise in power. However, 

the masses of supporting hardware elements, such as gate drive circuits, sensors, and control logic 

devices, will grow at a slower rate. This results in some economies of scale as the RPC power level rises 

and causes its specific weight to decline. The change in the specific weight of a dc RPC as the power 

level rises is shown in Figure 36.

Figure 36: DC RPC SPWT vs Power Level

Voltage Level Factor

DRPM=0.135*((EXP(0.0006/(1-DRPE)))/1.2214)*(DRPAM/DRPRM)*DRPPO*(DRPPO/DRPRM)-0.12* 

 (DRPVO/120)0.04

The mass of an RPC was expected to rise slowly as the voltage across it was increased. However, RPCs 

are located near the loads and experience voltages that are much lower than RBIs. Consequently, many 

effects identified with high voltage operation, such as vacuum relay breakdown, presumably will not be a 

factor. RPC voltages also are not high enough to warrant connecting semiconductor switches in series. 

This means the problems associated with this form of operation will not occur and the mass of the 

semiconductor switches should not rise much with voltage. Finally, the largest capacitors contained in dc 

systems are normally located in the primary power distribution components near the power source.

0.06

0.07

0.08

0.09

0.10

0.11

0.12

0.13

0.14

0.15

0.16

1 2 3 4 5 6 7 8 9 10 12 16 20

Power (kWe)

k

g

/

k

W

e

NASA/CR—2011-217268 58
These capacitors will be isolated from the RPCs by dc/dc converters that are likely equipped with current 

limiting. This will greatly reduce the effects of capacitor discharge into a load fault and mitigate the stress 

imposed on the RPC. The main item that will increase the mass of the RPC is added insulation. This is 

needed to withstand higher voltages, but its effect on RPC mass should be minor. Figure 37 displays the 

results of this analysis.

Figure 37: DC RPC SPWT vs Voltage

3.10 AC RPC MODEL

Ac RPCs are used to switch and monitor individual ac load circuits and provide circuit protection. These 

devices will be located in ac power distribution racks. The following paragraphs explain the equations 

generated to estimate the masses of single- and 3-phase RPCs as a function of power, efficiency, and 

voltage. These equations generate rough mass estimates for component comparison purposes. Specific 

component designs must be developed for more accurate mass estimates.

It is anticipated the ac RPC module design will use a channelized approach like the ac RBI configuration. 

This allows the card cage assembly that controls and monitors ac RPC operation to be shared among 

several units. The ac RPC equations described here are based on switch configurations consisting of 

back-to-back semiconductor switch pairs. This design is lighter and semiconductor switches, especially 

MOSFETs, have lower “on” resistances then previous devices. This enables high efficiency operation 

without the use of a parallel relay contact. Since an ac RPC is basically a low power ac RBI in many 

respects and most features are similar, the information presented in the ac RBI section will be relied on 

while describing the RPC equation development. The ac RPC discussion is shortened to reduce the 

amount of repetition. If additional information is desired please refer back to the ac RBI discussion.

The ac RPC and RBI configurations are similar; however, certain differences will cause their specific 

weights to differ considerably. The mass of the thermal management hardware, housing, and structure 

will assume a greater percentage of the RPC mass because it does not scale linearly down to the smaller 

RPC power levels. This results in the specific weight of an RPC being much higher than a RBI. In a telephone conversation with Dave Fox of Westinghouse, he indicated that comparably rated ac and dc RPCs 

0.100

0.105

0.110

0.115

0.120

0.125

0.130

0.135

20 40 60 80 100 120 140 160 180 200 250 300 400 500

Voltage (Vdc)

k

g

/

k

W

e

NASA/CR—2011-217268 59
should have similar masses [Ref. 53]. The data bus interface and control elements in the ac RPCs would 

probably be like those in the dc units. However, the mass of the ac RPC must include the masses of two 

gate drives for the back-to-back semiconductor switch pairs, and additional logic to control and coordinate 

the operation of the two devices. The masses of many of the elements in an ac RPC were obtained from 

the SSF dc RPC mass breakdowns that were adjusted to reflect the flight unit masses [Ref. 14, 17]. 

These masses were used as a basis for the following equation development.

The following paragraphs explain the development of the single-phase and 3-phase ac RPC equations. 

The variables used in these discussions are listed in Table 20.

Table 20: AC RPC Model Variable Definitions

1ARP Ac RPC Mass

3ARP Ac RPC Mass

ARPE Ac RPC Efficiency (99.7%)

ARPAM Ac RPC Available Modules

ARPRM Ac RPC Required Modules

ARPPO Ac RPC Power Output (kWe)

ARPVO Ac RPC Voltage Output (Vrms)

Mass Coefficient

1ARP=0.15*((EXP(0.0007/(1-ARPE)))/1.2628)*(ARPAM/ARPRM)*ARPPO*(ARPPO/ARPRM)-0.14* 

 (ARPVO/120)0.03

3ARP=0.21*((EXP(0.0007/(1-ARPE)))/1.2628)*(ARPAM/ARPRM)*ARPPO*(ARPPO/ARPRM)-0.22* 

 (ARPVO/120)0.03

The ac RPC mass breakdowns used the SSF dc RPC mass breakdowns as a starting point. Many items 

in dc and ac RPCs will be the same, so dc RPC component masses were also used for the ac RPC case. 

The ac RPC requires a back-to-back pair of semiconductor switches to conduct an alternating current. 

The mass effects resulting from this design difference were incorporated into the ac RPC mass breakdowns. To complete the ac RPC mass breakdowns, mass gains occurring as a result of minor hardware 

advancements were also included. The above mass coefficients were determined from these ac RPC 

mass breakdowns.

The mass of a 3-phase ac RPC will be higher than a single-phase RPC because the 3-phase design 

requires two more back-to-back pairs of semiconductor switches with gate drive circuits and two additional 

sets of sensors. However, the control logic and thermal management hardware masses are similar in 

both designs and the packaging weight difference becomes less as the RPC size grows, so the relative 

difference in mass becomes less as the power level rises. Single- and 3-phase RPC specific weights are 

compared in Figure 38.

NASA/CR—2011-217268 60
0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

1 2 3 4 5 6 7 8 9 10 12 16 20

Power (kWe)

k

g

/

k

W

e

Single-Phase AC RPC

3-Phase AC RPC

Figure 38: AC RPC SPWT - 1 Phase vs 3-Phase

Efficiency Factor

1ARP=0.15*((EXP(0.0007/(1-ARPE)))/1.2628)*(ARPAM/ARPRM)*ARPPO*(ARPPO/ARPRM)-0.14* 

 (ARPVO/120)0.03

3ARP=0.21*((EXP(0.0007/(1-ARPE)))/1.2628)*(ARPAM/ARPRM)*ARPPO*(ARPPO/ARPRM)-0.22* 

 (ARPVO/120)0.03

The factor underlined above estimates the change in specific weight occurring with a change in ac RPC 

efficiency. The efficiency of an ac RPC was assumed to be the same as a dc RPC; the reactive parasitics 

associated with ac operation were expected to be negligible. Because the efficiency of the dc RPC was 

lowered to agree with an efficiency of 99.7%, derived from the RPC ICD, the nominal efficiency of the ac 

RPC was also correspondingly lowered. The efficiency of an ac RPC can be increased by enlarging the 

conduction area of the semiconductor switches. This will reduce their resistance. The mass of the 

semiconductor switches will increase, but the sensor, control logic and gate drive circuitry mass doesn’t 

change significantly, and the thermal management hardware mass will decline slightly. RPC mass 

estimates were generated for efficiencies ranging from 99.65 to 99.75%. They were used to calculate the 

efficiency equation element. A graph showing how RPC specific weights vary with efficiency is shown in 

Figure 39.

NASA/CR—2011-217268 61
0.120

0.122

0.124

0.126

0.128

0.130

0.132

0.134

0.136

0.138

0.140

99.65% 99.66% 99.67% 99.68% 99.69% 99.70% 99.71% 99.72% 99.73% 99.74% 99.75%

Efficiency (%)

k

g

/

k

W

e

Figure 39: AC RPC SPWT vs Efficiency

Redundancy Factor

1ARP=0.15*((EXP(0.0007/(1-ARPE)))/1.2628)*(ARPAM/ARPRM)*ARPPO*(ARPPO/ARPRM)-0.14* 

 (ARPVO/120)0.03

3ARP=0.21*((EXP(0.0007/(1-ARPE)))/1.2628)*(ARPAM/ARPRM)*ARPPO*(ARPPO/ARPRM)-0.22* 

 (ARPVO/120)0.03

A modular design approach used to improve reliability will cause the total mass of an ac RPC assembly to 

rise. This mass increase is estimated by the above factor. The actual number of modules present in the 

assembly is specified by the "available modules" number; the number of modules required to deliver full 

power is defined by the "required modules" value. If a system is designed with 4/3 redundancy, each 

channel can carry up to 33% of the power. The fourth channel is included solely to improve reliability and 

its mass is the penalty paid to obtain the higher reliability.

Power Level Multiplier

1ARP=0.15*((EXP(0.0007/(1-ARPE)))/1.2628)*(ARPAM/ARPRM)*ARPPO*(ARPPO/ARPRM)-0.14* 

 (ARPVO/120)0.03

3ARP=0.21*((EXP(0.0007/(1-ARPE)))/1.2628)*(ARPAM/ARPRM)*ARPPO*(ARPPO/ARPRM)-0.22* 

 (ARPVO/120)0.03

NASA/CR—2011-217268 62
The equations can be used to calculate the mass or specific weight of the ac RPC. When the above 

multiplier is included, the value that results estimates the RPC mass. To obtain the specific weight of the 

RPC, remove this multiplier.

Power Level Factor

1ARP=0.15*((EXP(0.0007/(1-ARPE)))/1.2628)*(ARPAM/ARPRM)*ARPPO*(ARPPO/ARPRM)-0.14* 

 (ARPVO/120)0.03

3ARP=0.21*((EXP(0.0007/(1-ARPE)))/1.2628)*(ARPAM/ARPRM)*ARPPO*(ARPPO/ARPRM)-0.22* 

 (ARPVO/120)0.03

The masses of the semiconductor switches in an ac RPC increase fairly linearly with a rise in power. 

However, the masses of supporting hardware elements, such as driver modules, sensors, and control 

logic devices, grow at a much slower rate. This results in some economies of scale as the RPC power 

level rises and it causes its specific weight to decline. Because the mass of the control logic and gate 

drive circuits, and the sensors in a 3-phase ac RPC occupies a greater portion of its total mass, the 

reductions in specific weight occurring with power are greater in this RPC design than in the single-phase 

design. This causes the difference in the single- and 3-phase power level multiplier exponents, -0.14 and 

-0.22. The difference in mass growth rates between single- and 3-phase ac RPCs can be seen by 

referring back to Figure 38. An expanded view of only the single-phase ac RPC is shown in Figure 40.

Figure 40: AC RPC SPWT vs Power Level

Voltage Level Factor

1ARP=0.15*((EXP(0.0007/(1-ARPE)))/1.2628)*(ARPAM/ARPRM)*ARPPO*(ARPPO/ARPRM)-0.14* 

 (ARPVO/120)0.03

0.08

0.09

0.10

0.11

0.12

0.13

0.14

0.15

0.16

1 2 3 4 5 6 7 8 9 10 12 16 20

Power (kWe)

k

g

/

k

W

e

NASA/CR—2011-217268 63
3ARP=0.21*((EXP(0.0007/(1-ARPE)))/1.2628)*(ARPAM/ARPRM)*ARPPO*(ARPPO/ARPRM)-0.22* 

 (ARPVO/120)0.03

The ac RPCs will be located near the loads; consequently, the voltages they will experience will be lower 

than RBIs. This means that many effects associated with high voltage operation, such as vacuum relay 

breakdown, presumably will not occur. The RPC devices and internal wiring will require additional insulation to withstand the higher voltage stresses. While the RPC voltages are not high enough to warrant connecting the semiconductor switches in series, their masses will probably rise slowly to maintain adequate 

operating margins at higher voltages. The combined effects of additional insulation, conformal coatings, 

and other voltage related design features will cause the mass of the RPC to rise slightly as voltage levels 

rise. The results of this evaluation are displayed in Figure 41.

Figure 41: AC RPC SPWT vs Voltage

3.11 ANCILLARY HARDWARE EQUATIONS

Every power conditioning component requires additional ancillary hardware to enable it to perform its 

functions, protect it from the environment, dissipate excess generated heat, and mount and support the 

internal circuit elements and devices. In this report, the component ancillary hardware is considered to 

consist of the following items: conductors and connectors, a control and monitoring subsystem, an 

enclosure and baseplate collectively called a box, and a thermal management system consisting of a 

coldplate and radiator. These items are addressed separately in the following sections.

0.110

0.115

0.120

0.125

0.130

0.135

0.140

0.145

20 40 60 80 100 120 140 160 180 200 250 300 400 500

Voltage (Vrms)

k

g

/

k

W

e

NASA/CR—2011-217268 64
3.11.1 Conductor and Connector Equations

Within a power conditioning component, conductors are required for internal power distribution and the 

transmission of control and monitoring commands and data. This section establishes a mass for the input 

and output power conductors, the conductors that transfer power from one stage to the next, the control 

and monitoring harnesses, and the power and control and monitoring connectors. This conductor mass 

doesn’t include the wiring within a particular stage, for example the wiring in the chopper stage that connects its switches and tank hardware. This wiring is included as part of the stages ancillary hardware.

The information used to develop the following equations was obtained from SSF documentation (Ref. 14, 

16, 17, 50). Table 21 defines the variables used in the equations. These equations are based on copper 

power conductors because copper is more ductile and occupies a smaller volume than aluminum. 

However, the model allows the selection of copper or fiber optic conductors within the control and 

monitoring cable harnesses. Separate equations are provided for single- and 3-phase systems because 

the conductor sizes and control and monitoring harness masses are calculated differently.

Table 21: Conductor and Connector Equation Variable Definitions

1CCM Single-Phase Conductor and Connector Mass

3CCM 3-Phase Conductor and Connector Mass

CE Component Efficiency

AM Available Modules

RM Required Modules

PO Power Output (kWe)

VI Voltage Input (VrmsL-L or Vdc)

VO Voltage Output (VrmsL-L or Vdc)

EL Packaged Electronics Length (meters)

EW Packaged Electronics Width (meters)

EH Packaged Electronics Width (meters)

Finned Heat Exchanger Box with Copper Control & Monitoring Conductors

Single-Phase, 1 Voltage: 1CCM=(AM/RM)*58.6*(0.5*(EL+EW)+EH)*(PO/VO) 

+AM*(5.22*(0.5*(EL+EW)+EH)+0.238*(PO/RM)0.1+0.2667*(PO/RM)0.5)

Single-Phase, 2 Voltages: 1CCM=(AM/RM)*29.3*(0.5*(EL+EW)+EH)*((PO/CE/VI)+(PO/VO))

+AM*(5.22*(0.5*(EL+EW)+EH)+0.238*(PO/RM)0.1+0.2667*(PO/RM)0.5)

 3-Phase, 1 Voltage: 3CCM=(AM/RM)*58.6*(30.5/2)*(0.5*(EL+EW)+EH)*(PO/VO) 

+AM*(5.22*1.5*(0.5*(EL+EW)+EH)+1.5*0.238*(PO/RM)0.1+0.2667*(PO/RM)0.5)

 3-Phase, 2 Voltages: 3CCM=(AM/RM)*29.3*(30.5/2)*(0.5*(EL+EW)+EH)*((PO/CE/VI)+(PO/VO))

+AM*(5.22*1.5*(0.5*(EL+EW)+EH)+1.5*0.238*(PO/RM)0.1+0.2667*(PO/RM)0.5)

NASA/CR—2011-217268 65
Finned Heat Exchanger Box with Fiber Optic Control & Monitoring Conductors

Single-Phase, 1 Voltage: 1CCM=(AM/RM)*58.6*(0.5*(EL+EW)+EH)*(PO/VO) 

+AM*(2.61*(0.5*(EL+EW)+EH)+0.238*(PO/RM)0.1+0.2667*(PO/RM)0.5)

Single-Phase, 2 Voltages: 1CCM=(AM/RM)*29.3*(0.5*(EL+EW)+EH)*((PO/CE/VI)+(PO/VO))

+AM*(2.61*(0.5*(EL+EW)+EH)+0.238*(PO/RM)0.1+0.2667*(PO/RM)0.5)

 3-Phase, 1 Voltage: 3CCM=(AM/RM)*58.6*(30.5/2)*(0.5*(EL+EW)+EH)*(PO/VO) 

+AM*(2.61*1.5*(0.5*(EL+EW)+EH)+1.5*0.238*(PO/RM)0.1+0.2667*(PO/RM)0.5)

 3-Phase, 2 Voltages: 3CCM=(AM/RM)*29.3*(30.5/2)*(0.5*(EL+EW)+EH)*((PO/CE/VI)+(PO/VO))

+AM*(2.61*1.5*(0.5*(EL+EW)+EH)+1.5*0.238*(PO/RM)0.1+0.2667*(PO/RM)0.5)

Coldplate Box with Copper Control & Monitoring Conductors

Single-Phase, 1 Voltage: 1CCM=(AM/RM)*58.6*(0.5*(EL+EW)+0.75*EH)*(PO/VO) 

+AM*(5.22*(0.5*(EL+EW)+0.75*EH)+0.238*(PO/RM)0.1+0.2667*(PO/RM)0.5)

Single-Phase, 2 Voltages: 1CCM=(AM/RM)*29.3*(0.5*(EL+EW)+0.75*EH)*((PO/CE/VI)+(PO/VO))

+AM*(5.22*(0.5*(EL+EW)+0.75*EH)+0.238*(PO/RM)0.1+0.2667*(PO/RM)0.5)

 3-Phase, 1 Voltage: 3CCM=(AM/RM)*58.6*(30.5/2)*(0.5*(EL+EW)+0.75*EH)*(PO/VO) 

+AM*(5.22*1.5*(0.5*(EL+EW)+0.75*EH)+1.5*0.238*(PO/RM)0.1+0.2667*(PO/RM)0.5)

 3-Phase, 2 Voltages: CCM=(AM/RM)*29.3*(30.5/2)*(0.5*(EL+EW)+0.75*EH)*((PO/CE/VI)+(PO/VO))

+AM*(5.22*1.5*(0.5*(EL+EW)+0.75*EH)+1.5*0.238*(PO/RM)0.1+0.2667*(PO/RM)0.5)

Coldplate Box with Fiber Optic Control & Monitoring Conductors

Single-Phase, 1 Voltage: 1CCM=(AM/RM)*58.6*(0.5*(EL+EW)+0.75*EH)*(PO/VO) 

+AM*(2.61*(0.5*(EL+EW)+0.75*EH)+0.238*(PO/RM)0.1+0.2667*(PO/RM)0.5)

Single-Phase, 2 Voltages: 1CCM=(AM/RM)*29.3*(0.5*(EL+EW)+0.75*EH)*((PO/CE/VI)+(PO/VO))

+AM*(2.61*(0.5*(EL+EW)+0.75*EH)+0.238*(PO/RM)0.1+0.2667*(PO/RM)0.5)

 3-Phase, 1 Voltage: 3CCM=(AM/RM)*58.6*(30.5/2)*(0.5*(EL+EW)+0.75*EH)*(PO/VO) 

+AM*(2.61*1.5*(0.5*(EL+EW)+0.75*EH)+1.5*0.238*(PO/RM)0.1+0.2667*(PO/RM)0.5)

 3-Phase, 2 Voltages: CCM=(AM/RM)*29.3*(30.5/2)*(0.5*(EL+EW)+0.75*EH)*((PO/CE/VI)+(PO/VO))

+AM*(2.61*1.5*(0.5*(EL+EW)+0.75*EH)+1.5*0.238*(PO/RM)0.1+0.2667*(PO/RM)0.5)

Power Conductor Equation Segment

Single-Phase, 2 Voltages: 1CCM=(AM/RM)*29.3*(0.5*(EL+EW)+EH)*((PO/CE/VI)+(PO/VO))

+AM*(5.22*(0.5*(EL+EW)+EH)+0.238*(PO/RM)0.1+0.2667*(PO/RM)0.5)

 3-Phase, 2 Voltages: 3CCM=(AM/RM)*29.3*(30.5/2)*(0.5*(EL+EW)+EH)*((PO/CE/VI)+(PO/VO))

+AM*(5.22*1.5*(0.5*(EL+EW)+EH)+1.5*0.238*(PO/RM)0.1+0.2667*(PO/RM)0.5)

NASA/CR—2011-217268 66
Power conductors are primarily sized on the basis of current; therefore, the conductor mass is a function 

of the maximum steady state current levels within a component. If a voltage transformation occurs in the 

component, it is necessary to include separate factors for the input and output current levels. The length 

of the power conductors was estimated to be proportional to half the length plus width plus the full height 

of the box in the case of the finned heat exchanger (FH) box. The power cables and control and 

monitoring harnesses are typically run near the top of the box, above the circuit boards and devices, and 

are brought out by connectors located in the top half of the box. This cable routing design is indicative of 

a coldplate (CP) style box. However, in the case of the FH box the cables exit the main box through a 

cutout and are routed down the side of it, within an electrical box add-on, to connectors located on a plate 

approximately half way down the side of the box. This design feature is present to allow robotic 

replacement of the component, but it adds to the length and mass of the cables. For this reason the CP 

box power cable segment equation reduces this to 75% of the full height. The coefficient “29.3” was 

determined to yield a power conductor mass consistent with the ISS DDCU conductor mass. With the 

exception of the Sequential Shunt Unit (SSU), a value of “58.6” is used for the boxes that operate at a 

single voltage level and the factor input power divided by efficiency divided by the input voltage is 

removed. A value of “51.3” is used for the SSU because approximately one-third of its internal power 

conductors are aluminum instead of copper. For an equivalent transmission efficiency, aluminum reduces 

the mass of the conductors 52.5%, but at the expense of increased conductor size. The factor “30.5/2” 

was included for the 3-phase component conductor mass because 3-phase power distribution is more 

efficient for transmitting power than single phase [Power System Analysis textbook]. Further information 

is provided on the design and modeling differences between the FH and CP box in section 3.1.10.3.

Control and Monitoring Cable Harness Equation Segment

Single-Phase, 2 Voltages: 1CCM=(AM/RM)*29.3*(0.5*(EL+EW)+EH)*((PO/CE/VI)+(PO/VO))

+AM*(5.22*(0.5*(EL+EW)+EH)+0.238*(PO/RM)0.1+0.2667*(PO/RM)0.5)

 3-Phase, 2 Voltages: 3CCM=(AM/RM)*29.3*(30.5/2)*(0.5*(L+W)+H)*((PO/CE/VI)+(PO/VO))

+AM*(5.22*1.5*(0.5*(L+W)+H)+1.5*0.238*(PO/RM)0.1+0.2667*(PO/RM)0.5)

From SSF component mass breakdowns, the average mass of a control and monitoring wiring harness for a 

5 to 10 kWe rated component was estimated to be 3.6 kg. Based on discussions with component designers, 

this mass was estimated to drop about 50% with the use of fiber optics [Ref. 23], although the sensitivity of 

fiber optic cables to radiation may preclude their use in some environments. For this reason, and possible 

technology maturity reasons, copper or fiber optic conductors are offered as a choice in defining the control 

and monitoring harness mass. Replacing most of the copper wiring with fiber optic cables reduces the mass 

of the control and monitoring wiring to 1.8 kg. The length of the control and monitoring harness was again 

estimated to be proportional to half the length plus width plus height of the box in the case of the finned 

heat exchanger (FH) box. As before the height is removed from this equation for the CP box. The value 

“5.22” was chosen to provide a control and monitoring harness mass that matched the mass of the DDCU 

harness. This value is reduced to “2.61” for a fiber optic harness. Because the SSU has more sensors, 

its control and monitoring harness copper and fiber optic masses are “7.8” and “3.9”, respectively.

The delta mass of the control and monitoring harness in a 3 phase component was estimated by dividing the 

harness into command and data/sensor cable portions and assessing how these portions would change with 

a move from a single-phase to 3-phase component. Lacking a breakdown, it was assumed half the harness 

was dedicated to commands and half for data/sensors. It was assumed the command cable mass would be 

the same, regardless of whether the component was single- or 3-phase. The effect on the data/sensor half 

was estimated by counting the number of sensors in the DDCU, 7, and dividing them into two categories, 

voltage and current sensors, 4, and other sensors, 3. A single phase ac to ac converter would probably still 

have a voltage and current sensor on the input and a set on the output, so these sensor quantities wouldn’t 

change. However, a 3 phase component would likely have a voltage and current sensor per phase, or six on 

the input and six on the output. This would bring the total to 15 sensors. A 3 phase dc to ac inverter or ac to 

dc rectifier would probably have four less sensors, or 11 total. A rough average of these two values, 14, or 

twice the number in a single phase component, was used as an estimate of the sensor quantity in a 3 phase 

component. So based on this assessment, the data/sensor harness mass was assumed to be twice as 

NASA/CR—2011-217268 67
heavy in a 3-phase component. Since the data/sensor harness mass was previously assumed to be half the 

mass of the total control and monitoring harness, and it doubles with a change from single-phase to 3-phase, 

the result is the total control and monitoring wiring mass is 50% heavier in a 3 phase component.

Power and Control and Monitoring Connector Equation Segments

Single-Phase, 2 Voltages: 1CCM=(AM/RM)*29.3*(0.5*(EL+EW)+EH)*((PO/CE/VI)+(PO/VO))

+AM*(5.22*(0.5*(EL+EW)+EH)+0.238*(PO/RM)0.1+0.2667*(PO/RM)0.5)

 3-Phase, 2 Voltages: 3CCM=(AM/RM)*29.3*(30.5/2)*(0.5*(EL+EW)+EH)*((PO/CE/VI)+(PO/VO))

+AM*(5.22*1.5*(0.5*(EL+EW)+EH)+1.5*0.238*(PO/RM)0.1+0.2667*(PO/RM)0.5) 

Based on a survey of ISS components, DDCU, DCSU, Battery Charge/Discharge Unit (BCDU), and SSU, 

and an evaluation of their connector masses [Ref. 55], it was concluded about 70% of the connector mass is 

dedicated to the input/output power cables and the remaining 30% is used for the control and monitoring 

cables. The factors “0.238” and “0.2667” generate the correct connector masses for the DDCU at its 6.25 

kWe full power rating. The power connector mass was estimated to increase at an exponential rate of 0.5, 

causing the connector mass to increase about 41% if the power level is doubled. The mass of the 

connectors used for the control and monitoring cables was assumed to increase at an exponential rate of 0.1 

because a few more sensors, to monitor temperature for example, may be used in a higher power 

component because of its larger size. But, the mass increase was assumed to be very slight with an 

increase in power. The factor, “1.5” is added for a 3-phase component because it was previously assumed 

50% more signals would be required with a 3-phase component, and the connector mass would increase 

correspondingly. For 3-phase components that accept 3-phase power and provide it, a factor of “1.5” will 

also be included in the power connector equation segment. The AC to AC frequency changer is an example 

of this type of component. However, if the component uses 3-phase power distribution internally, but accepts 

and provides dc power externally, its power connector mass was assumed to be the same as for a singlephase component. The DDCU is the best example of this type of component.

3.11.2 Control and Monitoring Subsystem Mass and Parasitic Power Equations

Each of the power conditioning components will have some type of control and monitoring subsystem. This 

subsystem was assumed to consist of a controller card, a data interface module, various voltage, current, 

and temperature sensors, and a housekeeping power supply. A component controller card responds to 

higher level commands and controls the minute steps necessary to implement these commands. The 

monitoring system queries the internal sensors and provides data on the component operating status to the 

internal controller or higher level computers. A data interface module, containing numerous analog to digital 

conversion circuits, is required to convert the sensor signals into the proper form for data bus transmission. 

The power supply provides the low voltage power outputs, usually +/-15 and 5 Vdc, required by these units.

SSF component documentation was utilized to formulate the control and monitoring mass equations [Ref. 14, 

16, 17, 50]. Table 22 defines the variables used in these equations. Because a 3-phase system was 

assumed to have nearly twice as much monitoring data to collect and process, separate equations are 

provided for single- and 3-phase systems. The equations are broken into three parts, the controller card and 

data interface module, the sensors, and the housekeeping power supply.

NASA/CR—2011-217268 68
Table 22: Control and Monitoring Equation Variable Definitions

1CMM Single-Phase Control and Monitoring Mass

3CMM 3-Phase Control and Monitoring Mass

1CMP Single-Phase Control and Monitoring Power

3CMP 3-Phase Control and Monitoring Power

AM Available Modules

RM Required Modules

PO Power Output (kWe)

Single-Phase Mass: 1CMM=AM*(1.2+0.158*(PO/RM)0.5)+70*0.75*1.1*1CMP

3-Phase Mass: 3CMM=AM*(1.6+0.316*(PO/RM)0.5)+70*0.75*1.1*3CMP

Single-Phase Power: 1CMP=AM*43.3*(PO/RM)0.1

3-Phase Power: 3CMP=AM*57.4*(PO/RM)0.1

The estimated mass of a SSF controller card and data interface module for a converter or switchgear unit 

was 2.8 kg. During ISS design and development, control and data processing advancements allowed the 

mass of the controller and data interface cards to decline to an estimated 1.8 kg. With continuing progress 

according to Moore’s Law (computing power doubles every 2 years for the same size processor), it was felt 

this value would decrease a third to a mass of 1.2 kg after 2005. A value of 1.6 kg was assumed for a 3-

phase component due to the additional data handling requirements. In support of this estimate, Texas 

Instruments already manufactures a Processor Interface Controller and Communication Module that has a 

MIL-STD-1750A processor, 256-K of EEPROM memory, and a MIL-STD-1553 data bus interface on a single 

card that weighs 0.6 kg. The ISS SSU control and data processing is considerably heavier because 88 array 

strings must be monitored, and a ramp generator and multiple comparator circuits are required to generate 

the signals that are used to control individual shunting of the array strings. Based on combined SSF and ISS 

SSU mass estimates, this assembly was estimated to weigh about 6.4 kg. It was assumed with advances it 

would be possible to reduce its mass to 5.4 kg. The BCDU controller and data module weighs 5.0 kg. The 

battery monitor weighs an estimated 5.4 kg. With advancements it was assumed these masses would 

decline to 4.0 kg and 4.9 kg respectively. A combined mass savings of 1.5 kg, approximately 15%.

Again using SSF component mass breakdowns, except for the SSU, a value of 0.6 kg was estimated for the 

mass of the monitoring sensors in a typical 10 kWe component. Anticipating technology improvements by the 

year 2005, the 0.6 value was reduced to 0.5 kg. Per the previous explanation in section 3.1.10.1, a 3-phase 

system was estimated to have about twice as many sensors, so a value of 1.0 kg was used for it. The mass 

of the sensors will increase as the component power level rises. A potential transformer used to measure 

high voltages will weigh considerably more than one that measures low voltages. It was estimated the mass 

of a potential transformer would nearly double if the voltage it was measuring was doubled. A similar 

estimate was made for a current transformer. To obtain this level of sensor mass gain as the power level is 

increased, an exponent of 0.5 was included in the sensor mass factor. The sensor mass factors were calibrated to yield 0.5 and 1.0 kg respectively for single- and 3-phase 10 kWe components. The SSU sensor 

mass was estimated to be 2.6 kg because of the need to monitor the individual array strings.

Power must be obtained from the component input to operate the control and monitoring subsystem, the 

semiconductor switch gate drive circuitry and control logic, data signal converters, relay coils, etc. The 

sum of these power demands represents the component’s parasitic power requirement. The 6.25 kWe 

DDCU standby power demand is 85 watts [Ref. 56]. This value reflects the converter on, ready to deliver 

power. Its power supply is 65% efficient, leaving 55 watts for the actual control and monitoring elements. 

Most of this control and monitoring power is consumed in the processor, the gate drives, and data 

input/output signal conditioning cards. It was assumed their power demand would decline about 30% by 

NASA/CR—2011-217268 69
2005 with the introduction of lower voltage digital chips (5 volt to 3 volt), enabling lower power consuming 

processors and input/output cards. This lowered the control and monitoring power to 39 watts. Dividing 

this by the power supply efficiency, assumed to improve from 65% to 75%, a final value of 52 watts is 

obtained for a 6.25 kWe, single phase component. 3-phase components have more gate drive circuits 

and data input/output channels to account for the additional sensors, but the processor would probably be 

the same as in a single phase component. The power demand of its control and monitoring elements was 

estimated to be 33% higher, or 52 watts. Dividing this by power supply efficiency, a value of 69 watts is 

obtained for the control and monitoring power consumption of a 6.25 kWe, 3 phase component. It is 

expected that parasitic power demands will rise slowly as component power levels increase, because 

certain control and monitoring devices will need more power to perform their functions. The exponent 0.1 

was included in the factor to account for these gradual power increases. The control and monitoring power 

demand equation coefficients were calculated to yield control and monitoring power consumption values of 

52 watts for a single phase, 6.25 kWe component, and 69 watts for a 3 phase component.

The SSU, BCDU and switchgear parasitic power demands are different than those for a converter. The ISS 

SSU parasitic power requirements are more because of the need to individually control and monitor the array 

strings and power the ramp generator and comparator circuits. Currently, the SSU parasitic power demand 

is 91.5 watts [Ref. 56]. Of this, 24 watts are consumed in the power supply resulting in an efficiency of 

73.8%. It was assumed the remaining 67.5 watts could be reduced to 57.8 watts. Dividing this by 0.75, the 

efficiency of the power supply is assumed to improve, results in an estimated parasitic power demand of 76.8 

watts. The BCDU parasitic power demand is 94 watts [Ref. 56]. It was assumed its parasitic power demand 

could be reduced 20% through the use of lower power consuming chips and an improved power supply 

efficiency, resulting in a new value of 75 watts. The parasitic power demand of the switchgear units includes 

the power demanded by the switchgear control assembly (SCA) and the power required to hold in the RBI 

relay coils. The SCA requires 15 watts and each of the RBIs also needs 15 watts for their hold-in coil.

The control and monitoring system normally receives its power from a dedicated housekeeping power 

supply. The mass of this power supply was assumed directly proportional to its output power level, and its 

mass was computed using the previously derived control and monitoring subsystem power consumption 

values. The DDCU power supply is rated for 65 watts and weighs 4.8 kg. Its specific power was expected to 

improve 5% to about 70 kg/kWe with improved power supply topologies, switches, and higher packaging 

densities. The 6.25 kWe control and monitoring power demand values for the single and 3 phase units, 52 

and 69 watts, were multiplied by the assumed power supply efficiency of 75%, a 1.1 factor reflecting a 10% 

power rating margin, and 70 kg/kWe, yielding 3.0 kg and 4.0 kg respectively. A higher power supply margin, 

1.6, was incorporated into the switchgear control and monitoring algorithm to account for the high, but short 

term relay coil pickup power demand. Because this power demand is transitory its not included in the 

algorithm that estimates the switchgear units steady state parasitic power level. This value is used in the 

switchgear unit’s efficiency calculations. The SSU mass breakdowns indicate it’s power supply has a higher 

power density and a value of 65 kg/kWe was used for it. Although the BCDU parasitics included the power 

required for battery monitoring, the SSF BCDU mass breakdown did not include the two power supplies 

added to feed power to the cell monitor multiplexors housed in the batteries. However, using a power supply 

specific power of 70 kg/kWe, consistent with the DDCU, increased the SSF estimated BCDU power supply 

mass 2 kg, sufficient to cover the mass of the omitted battery multiplexor power supplies. The net effect of 

these adjustments was the stated SSF BCDU control and monitoring mass was increased 0.5 kg.

3.11.3 Component Volume, Dimension, and Enclosure Equations

Regardless of the power level, the density of the packaged electronics in power conditioning components 

operating under similar conditions will normally be similar. To determine appropriate component electronics densities for two types of enclosure/baseplate designs, the packaged electronics densities of five 

SSF components were computed using their projected weights and compared with the as-built ISS 

component densities. The packaged electronics density values were assumed to include all the 

electronics devices and hardware, plus everything they require for operation and support, cabling, circuit 

boards, card cages, and structural panels. This information is presented in Table 23.

NASA/CR—2011-217268 70
Table 23: Comparison of SSF and ISS Power Conditioning Component Densities

Projected SSF As-Built ISS

Packaged Packaged

Electronics Density Electronics Density

(grams/cubic cm) (grams/cubic cm)

Component CP FH CP FH

DC/DC Converter Unit-Internal 0.404(1) N/A 0.382(1) N/A

DC/DC Converter Unit-External N/A 0.250 N/A 0.197

Battery Charge/Discharge Unit N/A 0.283 0.449(2) 0.250

DC Switching Unit N/A 0.333 0.364(2) 0.203

Main Bus Switching Unit N/A 0.339 0.428(2) 0.239

 Average 0.404 0.301 0.249 0.222

(1): The DDCU-I box design is consistent with a coldplate box design but it is mounted in an internal location. Because an external box 

requires a more robust enclosure to withstand the external environment, the coldplate box design employed in this report is based on 

the DDCU-I box dimensions but with external box wall thicknesses.

(2): The coldplate electronics densities were estimated for the BCDU, DCSU, and MBSU by comparing the differences in dimensions 

between the DDCU-I and DDCU-E boxes, and subtracting equal amounts from the BCDU, DCSU, and MBSU Type I box dimensions.

A component requires an enclosure and baseplate to provide protection from the environment, and as a 

means of providing structural attachment and thermal management. Enclosure and baseplate types vary 

depending on the application. Two baseplate/enclosure types, finned heat exchanger (FH) and coldplate 

(CP), and two material options, aluminum (Al) and carbon-carbon (CC), are discussed here and offered as 

enclosure/baseplate design and material choices in the models.

The FH enclosure/baseplate design uses a finned heat exchanger to transfer heat from the component to a 

similarly finned coldplate. This concept is relatively heavy and has a higher temperature drop than other approaches, but it was selected for the ISS to allow replacement of the power conditioning units. Its electrical 

connectors are mounted on an external plate, pins pointing downward, to allow them to be mated to installed 

cable box connectors by means of robotically manipulated ACME screws that draw the component down and 

hold it in place. Pressure pads are present to maintain the correct tension on the ACME screws, both onorbit and more importantly during launch. Because the FH box has an electrical connector box on its end to 

route the power and control cables down to the connectors and the ACME screw hardware protrudes through 

the box, its packaged electronics density relative to the size of its enclosure is much lower.

The coldplate enclosure/baseplate design doesn’t allow on-orbit replacement, because the component’s 

baseplate is tightly bolted to the coldplate. It also doesn’t have an electrical connector box, ACME screws, or 

pressure pads. These items are all present to support the orbital replacement unit (ORU) removal and 

replacement requirements of the ISS FH design, and aren’t required with the CP design. The result is a 

smaller, lighter box, but one that can’t be replaced on-orbit. The CP design is fairly representative of a typical 

satellite box, while the FH design is presently unique to ISS.

The DDCU packaged electronics density values were used for all converter, inverter, rectifier and transformer

type component models. The BCDU values were used for the BCDU model. The MBSU values were used 

for the switchgear models. It was assumed a 5% improvement in packaging densities would be realized by 

the year 2005 for all component types and both box types, FH and CP. Using these densities, the component volume can be calculated for either the FH or CP box using the following formula:

CV=CEM/(PED*1000)

where: CV = Component Volume in cubic meters

CEM = Component Electronics Mass in kilograms

PED = Packaged Electronics Density for Selected Box Type in g/cm3

NASA/CR—2011-217268 71
Knowing the component volume, it is possible to generate dimensions for the component. Using ISS box 

dimensions as a guide, per unit aspect ratios were defined for the FH and CP style boxes for the component 

types. These aspect ratios are shown in Table 24. Using these aspect ratios and computing the cube root of 

the volume, the component height, width, and length can be calculated for the two types of boxes. An 

example of the equations is shown below for the DDCU / converter box designs.

Table 24: Finned Heat Exchanger Box Aspect Ratios

Component Length Aspect Ratio Width Aspect Ratio Height Aspect Ratio

FH Box (BCDU, MBSU) 1.626 1.150 0.535

FH Box (DDCU-E) 1.351 1.148 0.646

CP Box (Est. BCDU, MBSU) 1.916 1.084 0.482

CP Box (DDCU-I) 1.610 1.043 0.596

CP Length=1.610*CV0.3333 or FH Length=1.351*CV0.3333

CP Width=1.043*CV0.3333 or FH Width=1.148*CV0.3333

CP Height=0.596*CV0.3333 or FH Height=0.646*CV0.3333

The equations that were developed to define component enclosure masses are based on the masses of two 

space station ORU box styles, Type I and Type IV. Both box styles are constructed from aluminum and use 

the FH design. The ORU box mass breakdowns shown in Table 24 were generated from a combination of 

SSF documentation [Ref. 14] and enclosure and baseplate delivery inspection and receiving records.

Table 25: Finned Heat Exchanger Box Mass Breakdown

Box Subassembly Type I BCDU Type I MBSU Type IV DDCU

Enclosure 14.1 14.1 10.9

Connector Structure 0.6 0.6 0.6

Mounting hardware 5.3 5.3 5.3

Radiant Fin Baseplate 19.7 24.0 19.5

 Total 39.7 44.0 36.3

Type I ORU Box dimensions: 104.1 cm length, 73.7 cm width, and 34.3 cm height

Type IV ORU Box dimensions: 71.8 cm length, 61.0 cm width, and 34.3 cm height

Knowing the sizes of the two box types the mass per surface area of the enclosure and baseplate can be 

calculated. These values are required to calculate the masses of different sized FH boxes and it is provided 

in Table 26. These values were also used to generate enclosure and baseplate masses for the smaller size 

CP style boxes.

NASA/CR—2011-217268 72
Table 26: Finned Heat Exchanger Box Mass per Surface Area

Box Subassembly Type I BCDU Type I MBSU Type IV DDCU

Enclosure Mass per Surface 

Area (kg/m2)

7.1 7.1 8.1

Radiant Fin Baseplate Mass 

per Surface Area (kg/m2)

25.7 31.3 44.6

The mass of the radiant fins is about 25% of the radiant fin baseplate mass. The remaining portion provides 

structural support for the attachment of the fins and the internal mounting of the component hardware and 

devices. The mounting plate portion of the radiant fin baseplate is the part that would serve as the coldplate 

if the component was enclosed by a CP type box. The electronics would be mounted directly on this coldplate 

and a coolant would be pumped through the heat exchanger piping contained in it to remove excess heat. 

The baseplate for a CP style box then has exactly one-half the mass per unit area as the FH style boxes. 

The FH design has hardware to allow robotic removal and replacement of the ORUs, but this hardware isn’t 

required with the CP design and it was removed from the mass summary for it. Using the previously 

calculated per unit masses for the FH enclosure and the CP baseplate and applying them to an equivalently 

sized CP box the values shown in Table 27 are obtained. Comparing these with the value in Table 25, one 

can see that a CP style box is significantly lighter. Furthermore, because the packaged electronics density in 

a CP box is much higher, its size can be reduced lowering these masses even further.

Table 27: Coldplate Box Mass Breakdown

Box Subassembly BCDU MBSU DDCU

Enclosure 14.1 14.1 10.9

Connector Structure 0.6 0.6 0.6

Baseplate 14.8 18.0 14.6

 Total 29.5 32.7 26.1

Two material options offered in the models, aluminum and carbon-carbon. Aluminum’s main advantage is its 

much less expensive than carbon-carbon. Carbon-carbon is fairly new, and it has only recently become 

widely available. Carbon-carbon has several advantages over aluminum: (1) its lighter 1.65 g/cm3 versus 

2.7 g/cm3 for aluminum, (2) it provides better shielding effectiveness against radiated electromagnetic 

interference (EMI) at lower frequencies (< 100 MHz) and is comparable at higher frequencies (> 100 MHz), 

(3) its more resistant to atomic oxygen degradation, and (4) it doesn’t exhibit RF pitting (corrosion), a 

phenomena in which radio frequency power erodes the surface of a material. Finally, carbon-carbon’s 

shielding effectiveness against ionizing radiation is comparable to aluminum.

Because of its advantages, its expected carbon-carbon will replace much of the aluminum in future boxes. 

The density of aluminum is 2.7 g/cm3

, carbon-carbon is 1.65 g/cm3. A mass reduction of about 39%. It will 

probably be impractical to replace the connector structure and mounting hardware materials with carboncarbon, but it should be fine for the enclosure and baseplate. Tables 28 and 29 list projected mass 

breakdowns for the FH and CP box designs after the aluminum in the enclosure and baseplate has been 

replaced with carbon-carbon. These masses and the associated mass per unit area values were used to 

calculate the masses of varying sizes of carbon-carbon FH and CP style boxes.

NASA/CR—2011-217268 73
Table 28: Carbon-Carbon Finned Heat Exchanger Box Mass Breakdowns

Box Subassembly Type I BCDU Type I MBSU Type IV DDCU

Enclosure 8.6 8.6 6.7

Connector Structure 0.6 0.6 0.6

Mounting hardware 5.3 5.3 5.3

Radiant Fin Baseplate 12.0 14.7 11.9

 Total 26.5 29.2 24.5

Table 29: Carbon-Carbon Coldplate Box Mass Breakdowns

Box Subassembly BCDU MBSU DDCU

Enclosure 8.6 8.6 6.7

Connector Structure 0.6 0.6 0.6

Baseplate 9.0 11.0 8.9

 Total 18.2 20.2 16.2

Using these mass per unit area values, its now fairly easy to develop generalized equations to calculate the 

masses of different sized aluminum and carbon-carbon FH and CP style box masses. The equations for the 

DDCU type components are shown below. The BCDU and switchgear style equations are the same, except 

they use different mass per unit area values for the coefficients. The connector and mounting hardware mass 

was assumed to double with a factor of 10 power increase, the reason for the 0.3 exponent, and was 

calibrated to yield 5.9 kg and 0.6 kg at 6.25 kWe for the FH and CP boxes respectively.

ALFHBM=3.4*(PO/RM)^0.3+8.1*((L*W)+2*(L*H)+2*(W*H))+44.6*(L*W)

ALCPBM=0.35*(PO/RM)^0.3+8.1*((L*W)+2*(L*H)+2*(W*H))+33.45*(L*W)

CCFHBM =3.4*(PO/RM)^0.3+5.0*((L*W)+2*(L*H)+2*(W*H))+27.3*(L*W)

CCCPBM =0.35*(PO/RM)^0.3+5.0*((L*W)+2*(L*H)+2*(W*H))+20.44*(L*W)

where: ALFHBM = Aluminum Finned Heat Exchanger Box Mass in kilograms

ALCPBM = Aluminum Coldplate Based Box Mass in kilograms

CCFHBM = Carbon-Carbon Finned Heat Exchanger Box Mass in kilograms

CCCPBM = Carbon-Carbon Coldplate Based Box Mass in kilograms

CV = Component Volume in cubic meters

L = Length in meters

W = Width in meters

H = Height in meters

 PO = Power Output (kWe)

RM = Required Modules

A generalized reference cable run length and internal packaging box mass estimate were developed from 

an estimate of the DDCU’s elemental electronics density and its weight. For this estimate of electronics 

density the mass of the cabling and structural boxes was removed. The DDCU’s electronics weighs about 

23 kg, and its density was estimated to be 0.45 g/cm3

. These values were used to estimate the volume of

the electronics using the following formula:

NASA/CR—2011-217268 74
EV = 1.25 * EM / (ED * 1000)

where: EV is the volume of the elemental electronics

EM is the mass of the electronics

ED is the density of the electronics

The factor “1.25” was added to account for the volume occupied by structural hardware supporting the 

electronics such as card cages and circuit boards, and to provide routing areas for board to board wiring. 

With this definition of the electronics volume, a rough estimate of the length, width, and height of the 

electronics was made using the previously derived FH and CP box aspect ratios. These electronics 

length, width, height values were used to compute reference cable run lengths for the FH and CP boxes 

and to scale the mass of the internal packaging boxes.

The mass of the internal packaging or support boxes wasn’t included in the previous version of models 

because of the difficulty in defining and estimating this hardware. Looking at a picture of the DDCU, its 

clear it occupies a significant portion of the DDCU’s mass. The DDCU has four internal boxes to hold the 

input and output filters, direct current element (Weinberg converter chopper, transformer, and rectifier), 

and the control and monitoring card cage and circuit boards. There is also the hardware that holds the 

boards, inductors, transformers, capacitors in place, and mounting hardware such as and screws, bolts 

and nuts. Lacking mass information on this hardware, its mass was crudely estimated by adding all the 

masses of all the identified elements, and subtracting this subtotal from the total mass of the component. 

After identified component advancements were considered, an estimated mass of 5.35 kg was computed 

for the DDCU. Since most of this mass is concentrated in the four internal support boxes, its mass was 

referenced to and will scale with the computed end and side areas of the electronics volume. A similar 

approach and the same mass coefficients (13.12 and 8.02) were used for the other components except 

the array shunt regulator model. The values computed for this model were 11.1 and 6.78.

3.11.4 Radiator Area and Mass Equations

A radiator is needed to dissipate the waste heat a power conditioning component generates. The DDCU 

heat pipe (HP) radiator design was used to develop the radiator equations in these models. The models 

allow the selection of either a single or two sided radiator, both of which are developed from the single sided 

DDCU radiator design. The DDCU HP radiator is required to dissipate at least 290 watts at EOL, and it is 

172.7 cm long, 59.0 cm wide, and 2.0 cm thick. It has two parts, a coldplate section on which the DDCU 

mounts, and a radiator section. The coldplate part is 59.1 cm by 59.0 cm, and weighs 7.8 kg. The radiator 

section is 113.7 cm by 59.0 cm, and weighs 14.9 kg. The total mass of the HP radiator is 22.7 kg.

The thermal analysis of the DDCU-HP was consulted to obtain sink and baseplate temperatures, and to 

determine an appropriate temperature drop from the baseplate to the radiator for the CP box design [Ref. 

57]. The radiator equations were developed to size the component coldplate and radiator for the conditions 

experienced by the DDCU-HP in its worst case hot environment. Consistent with this analysis, the sink 

temperature default was set at 294 K and the maximum baseplate temperature was set at 63 °C. The 4° C 

temperature delta present between the electronics baseplate and the radiator surface [Ref. 57] was used for 

the CP box design and based on a discussion with an ISS thermal analyst an 11° C temperature delta was 

set as the default for the FH box design. The radiator area was computed using a standard radiator thermal 

dissipation formula, and the coefficient (1.0823E+10) was calibrated to calculate a radiator area of 0.3354 m2

(half of the DDCU HP radiator area for the two-sided radiator case) at a heat dissipation level of 290 watts 

using the previously defined worst case conditions. The coefficient, 22.26, in the radiator mass equation 

generates masses for the coldplate and radiator equivalent to the DDCU HP’s aluminum coldplate and 

radiator mass. These coefficients were multiplied by (1.65 g/cm2 / 2.7 g/cm2

) to obtain the mass of a carboncarbon radiator and its coldplate under the same conditions.

RA=(1.0823E+10/RS*Q)/((CPT+273-TD)4

-TS

4

) 

ALRM= 22.26*(L*W)+22.26*RA

CCRM= 13.6*(L*W)+13.6*RA

NASA/CR—2011-217268 75
where: RA = Radiator Area in square meters

RS = Number of Radiator Sides (1 or 2)

ALRM = Aluminum Radiator Mass in kilograms

CCRM = Carbon-Carbon Radiator Mass in kilograms

Q = Heat to be Dissipated in kWt

CPT = Coldplate Temperature in °C

TD = Temperature Delta from Coldplate to Radiator Surface in °C

TS = Radiator Sink Temperature in Kelvin (294 K is recommended default)

NASA/CR—2011-217268 76
4.0 POWER CONDITIONING COMPONENT MODELS

A complete power conditioning component model is created by linking individual stages and combining 

these with ancillary component hardware. The equations must undergo a few changes to integrate them 

into a component model. The power and voltage levels for each stage must be computed within their 

respective equations to obtain the most accurate mass estimates. These values are calculated by 

inserting the efficiencies of the subsequent stages and including the voltage coefficients associated with 

inversion and rectification. The equations that define the voltage relationships for single- and 3-phase 

rectification are shown below. These equations are simply reversed to obtain the corresponding relationships for inversion.

Single-Phase: Vdc=0.9*Vrms

3-Phase: Vdc=1.35*Vrms

where: Vdc = the output dc voltage from a rectifier or the input dc voltage to a chopper

Vrms = the line-to-line ac voltage from a chopper or the input line-to-line ac voltage 

fed to a rectifier

The component mass equations include these voltage factors and the efficiencies of the interconnected 

stages. They also include factors to calculate the mass impacts incurred in the devices that process the 

component’s parasitic power.

The component models are designed to cover a range of applications, from PMAD systems that use high 

frequency inverters and converters to lower frequency rotary or linear alternator based power systems. To 

evaluate these systems they can be configured to model combinations of dc and single and 3-phase ac 

components. Other input options are available to allow the user to select design features and assess 

potential improvements such as higher frequency operation or the use of carbon-carbon for the enclosure 

and baseplate. The models are designed to be user friendly, but the user is responsible for inputting valid 

values. To assist the user in defining the models to match their application, key inputs such as frequency,

filtering, and material options will be considered further. Although the models are best suited to high 

power applications with voltage levels above 120 volts, they can be used to assess low voltage systems if

the default efficiency and ripple factor values are changed. This will also be addressed further.

4.1 FREQUENCY CONSIDERATIONS

The operating frequency of a rectifier or transformer or the switching frequency chosen for an inverter or 

converter is a strong determinant of component mass. Increasing the frequency generally reduces the 

masses of magnetic components such as inductors or transformers, and the sizes of filter elements, such 

as the input or output capacitor in a dc filter. The model algorithms calculate a reduction in component 

mass as a function of frequency, but they aren’t able to reflect the increasing losses that will occur in 

switches, magnetic cores, capacitors, even conductors as frequency rises. The rationale built into the 

models is as technology advances in switches, magnetic materials, etc., it will be possible to move to 

higher frequencies and obtain the mass benefits without incurring higher losses. This means there is a 

time element to the use of higher switching frequencies. The power level also has an impact. It becomes 

increasingly difficult to control reactive power losses and extract internally generated heat as devices 

increase in size. To assist the user in selecting an appropriate switching frequency to match their 

application and time frame, Tables 30, 31, and 32 are offered as guides. These values are estimates 

intended to reflect projected switching capabilities, but there are many technical challenges to solve before 

these higher frequencies can be utilized in future component designs. The user is again cautioned to keep 

in mind that these models are only designed to generate ballpark component mass estimates.

NASA/CR—2011-217268 77
Table 30: Suggested Converter / Inverter Switching Frequency Maximums

Inverter or Converter

Power Level

2002 to 2004 

Frequency (kHz)

2005 to 2007 

Frequency (kHz)

2007 to 2010 

Frequency (kHz)

500 Watts to 1 kWe 70 85 100

1 to 5 kWe 60 70 80

5 to 20 kWe 40 48 55

20 to 40 kWe 35 42 50

40 to 80 kWe 30 35 40

80 to 150 kWe 25 30 35

Greater than 150 kWe 20 25 30

The ISS BCDU is able to use a higher switching frequency, 80 kHz, because it can use a bi-directional 

buck / boost regulator topology that isn’t required to provide isolation between the input and output. This 

design is expected to be typical of future BCDU designs. The following table is offered as guide in 

selecting switching frequencies for these units.

Table 31: Suggested BCDU Switching Frequency Maximums

BCDU 

Power Level

2002 to 2004 

Frequency (kHz)

2005 to 2007 

Frequency (kHz)

2007 to 2010 

Frequency (kHz)

500 Watts to 1 kWe 100 110 120

1 to 5 kWe 90 100 110

5 to 10 kWe 80 90 100

10 to 20 kWe 60 70 80

The ISS SSU uses a pulse width modulation frequency (PWM) of 20 kHz to provide fine voltage control 

between the voltage steps resulting from switching on or off an array string. The model indicates a higher 

PWM frequency would save mass in the array string EMI filters. The following is offered as a guide for 

this unit, but the user should evaluate these suggested inputs further.

Table 32: Suggested Array Shunt Regulator Switching Frequency Maximums

Shunt Regulator

Power Level

2002 to 2004 

Frequency (kHz)

2005 to 2007 

Frequency (kHz)

2007 to 2010 

Frequency (kHz)

500 Watts to 1 kWe 50 60 70

1 to 5 kWe 40 50 60

5 to 20 kWe 30 40 50

20 to 100 kWe 20 25 30

A few applications will require a large transformation in the voltage level. Its desirable to use high 

frequency transformers, either stand alone or within a converter, for this function. However, because 

parasitic effects become more troublesome at higher frequencies, there are limits on how large of a step 

ratio a transformer can achieve. A more detailed discussion of the effects and guidelines for selecting an 

appropriate voltage step ratio as a function of frequency are discussed in section 3.1.2.1, Inverter 

Transformer Stage Model, under the heading Voltage Level Factors and are provided in Table 10, 

Transformer Step Ratio Guidelines.

Other frequency effects are addressed under Filter Frequency and Ripple Factor Considerations.

NASA/CR—2011-217268 78
4.2 LOW VOLTAGE DESIGN ADJUSTMENTS

The models are primary designed to assess future power systems that are expected to provide more 

power and use higher voltage levels to meet their requirements. However, they can be used to assess 

lower power, low voltage designs if some of the default efficiencies are changed. As component designs 

decline in voltage, the current levels in conductors, switches, diodes, and numerous other devices 

increases, causing I2

R losses to increase. It becomes more difficult to obtain high operating efficiencies, 

and the normal trade is to accept some reduction in efficiency to avoid a heavy mass penalty. The default 

efficiencies in the models for the chopper and rectifier stages should be changed to reflect this decline as 

the voltage level is decreased, and the following table is offered as a guide in making these adjustments.

Table 33: Model Efficiency Values for Low Voltage Component Designs

Voltage Level (volts)

Chopper

Efficiency (%)

Rectifier

Efficiency (%)

120 97.60 98.70

110 97.60 98.70

100 95.57 98.68

90 97.53 98.66

80 97.47 98.62

70 97.36 98.56

60 97.23 98.50

50 97.00 98.38

40 96.67 98.20

30 96.00 97.95

20 93.60 96.70

4.3 ENCLOSURE/BASEPLATE TYPE SELECTION CONSIDERATIONS

The component models allow either a Finned Heat Exchanger (FH) or Coldplate (CP) box type to be 

selected. The FH enclosure/baseplate design uses a finned heat exchanger to transfer heat from the 

component to a similarly finned coldplate. The main advantage of this design is it allows on-orbit, in space 

replacement of the power conditioning units. Its finned heat exchanger is fairly heavy and exhibits a higher 

temperature drop from baseplate to coldplate than direct contact thermal transfer designs. The electrical 

connectors are mounted on an external plate, pins pointing downward, to allow them to be mated to installed 

cable box connectors by means of robotically manipulated ACME screws that draw the component down and 

hold it in place. Pressure pads are present to maintain the correct tension on the ACME screws, both onorbit and more importantly during launch. Because the FH box has an electrical connector box on its end to 

route the power and control cables down to the connectors and the ACME screw hardware protrudes through 

the box, its packaged electronics density relative to the size of its enclosure is much lower. Presently, this 

box design is only used on the ISS.

The CP enclosure/baseplate design is more typical of satellite component boxes. It doesn’t permit on-orbit 

replacement because the component’s baseplate is bolted directly to a coldplate. The baseplate fins are 

eliminated, reducing its mass. The electrical connector box, ACME screws, and pressure pads aren’t 

required either and they’re also eliminated. These items are all present to support the removal and 

replacement requirements of the ISS orbital replacement units (ORUs). Eliminating the ACME screws also 

makes available the interior volume that had been lost with their protrusions through the box. This allows 

much higher packaging densities with the CP box. The result is a smaller, lighter box.

4.4 ENCLOSURE / BASEPLATE AND COLDPLATE / RADIATOR MATERIAL OPTIONS

The component models give the user the option of selecting aluminum or carbon-carbon enclosures, 

baseplates, and internal structural members such as panels, braces, and card cages. Aluminum’s main 

NASA/CR—2011-217268 79
advantage is its much less expensive than carbon-carbon. Carbon-carbon is fairly new, and it has only 

recently become widely available. As a box material, carbon-carbon has several advantages over aluminum: 

(1) its lighter 1.65 g/cm3 versus 2.7 g/cm3 for aluminum, (2) it provides better shielding effectiveness against 

radiated electromagnetic interference (EMI) at lower frequencies (< 100 MHz) and is comparable at higher 

frequencies (> 100 MHz), (3) its more resistant to atomic oxygen degradation, and (4) it doesn’t exhibit RF 

pitting (corrosion), a phenomena in which radio frequency power erodes the surface of a material. Finally, 

carbon-carbon’s shielding effectiveness against ionizing radiation is comparable to aluminum.

4.5 CONTROL AND MONITORING HARNESS MATERIAL CONSIDERATIONS

The models estimate the use of fiber optic lines instead of copper wires will reduce the mass of the control 

and monitoring harness 50%. The main concern with this substitution is the sensitivity of the fiber optic 

lines and optical couplers to radiation. The effects of ionizing radiation on optical fiber, both from Gamma 

sources and the space environment, has been studied extensively. Optical fiber will darken when exposed 

to ionizing radiation creating centers of absorption where unwanted elements and other optical defects 

were present. A fiber’s performance in a radiation environment depends on the materials used to make 

the glass, the processes used, coatings used, dose type and rate and total dose. Manufacturers supplying 

the space flight market are aware of these dependencies and have developed manufacturing processes to

produce products capable of withstanding tens to hundreds of kRads(Si) total dose with less than one dB 

increase in loss per kilometer of fiber. If the planned mission will experience total integrated dose levels of 

radiation in excess of hundreds of kRads(Si), the user should evaluate the impact of this on fiber optic 

lines and devices before selecting this option in the models. Further information on this subject is 

available on-line [Ref. 58, 59].

4.6 FILTER FREQUENCY AND RIPPLE FACTOR CONSIDERATIONS

The mass of the component filters strongly depends on the source or switching frequency and the voltage 

level. The mass of a dc filter following a rectifier stage increases rapidly at lower frequencies because its 

filter capacitor must store more energy to bridge the span between rectifier pulses. Filter mass also rises 

at lower voltages because the amount of energy the filtering capacitors can store declines with voltage 

and the size of the capacitor must be increased to compensate. A component designer is usually free to 

choose the switching frequency, and its one of the main reasons inverters and converters are moving to 

higher frequency operation. However, the designer is often required to accept the characteristics of the 

power source. Low frequency power sources pose special challenges for the development of lightweight 

PMAD systems. Linear alternator waveforms are particularly difficult to process because their output is 

single phase, low frequency ac, less than 80 Hz, and its limited to voltage levels under 500 Vrms. One 

approach is to rectify the output and distribute the power as dc or alternately follow the rectifier with an 

inverter to step-up the voltage level. The ac to ac frequency converter model combines the rectifier and 

inverter stages. The output from a rotary alternator is less difficult to process because its typically higher 

in frequency, several hundred hertz to a few kilohertz, and can be provided over a wider voltage range. 

But, its main advantage in this context is its 3-phase output triples the number of rectifier pulses, reducing 

the filter mass to one-third of the value required with a single-phase machine.

The component model filter equations reflect these effects and they will calculate much higher masses for 

low frequency, low voltage filters. To lower this mass, the first step is for the designer to determine if an 

alternate power source is available or if the source can provide a higher frequency and/or higher voltage 

output. If this isn’t possible there are a couple of other steps the user can take to reduce these masses. 

One is to reduce the ripple factor. Its not practical to provide the same level of filtering in a low frequency 

application as in a high frequency one because the filter mass penalties become prohibitive. System 

designers must be willing to accept a poorer power quality, which translates into a higher ripple factor. 

The dc to dc converter operates at 40 kHz and its filters are required to limit the ripple content to less than 

0.4%. Conversely, the ripple content provided by a filter following a 70 Hz linear alternator probably can’t 

be any lower than 5%, and may need to go as high as 20%, to obtain a reasonable mass. The efficiency 

of this filter will probably also have to be reduced to lower its mass. The nominal efficiency of a high 

frequency filter is estimated to be 99.8%, but it may be necessary to reduce the efficiency of a low 

frequency filter to as low as 95% to obtain an acceptable mass.

NASA/CR—2011-217268 80
4.7 DC/DC CONVERTER MODEL

The dc/dc converter model combines the chopper, inverter transformer, and rectifier stage equations. It is 

completed with the addition of input and output dc filtering and equations to calculate the control and 

monitoring, conductor and connector, and box and radiator masses. It is only capable of generating ballpark component mass estimates. For more accurate mass values, a circuit designer should be consulted. 

Application Notes: Dc/dc converters are used to change a dc voltage to a higher or lower level. They also 

provide isolation between the input and output to reduce transmitted interference. The dc/dc converter 

models can be used to estimate the masses of converters that follow a dc power source or those located 

near the loads. In the two applications, the main difference is expected to be the filtering demands. The 

filter requirements will be determined by the particular applications, but a ripple factor as high as 5% may 

be acceptable for converters that follow sources and feed industrial power devices such as heaters, while 

a ripple factor less than 1% is recommended for converters that supply sensitive loads. The ISS dc/dc 

converter is limited to +/-0.5 volts ripple on its ~120 Vdc output, a ripple factor of 0.4%

Model Input Parameter Ranges: The spreadsheet is designed to cover a specific range of input 

parameters. Using input parameters outside of these ranges could result in inaccurate mass estimates 

and it is not recommended. Table 34 lists appropriate input ranges and the values recommended to yield 

the best results. It also identifies the sources that should be consulted for certain items. It is considered 

to be the users responsibility to select compatible input parameters that are suitable for the application 

and operating conditions.

Model Validation: The dc/dc converter model was validated against the ISS flight DDCU. The model 

calculates a mass of 62.0 kg (136.7 lbs) for a DDCU manufactured to conform to the ISS DDCU design 

specifications. The ISS flight DDCU weighs 65.8 kg (145 lbs) [Ref. 17]. The ISS mass properties group 

estimated the dc converter element (DCE) within the DDCU would weigh 9.2 kg (20.3 lbs) [Ref. 14]. The 

model predicts the DCE would weigh 8.9 kg (19.7 lbs). The lower mass is attributable to semiconductor 

switch and diode improvements incorporated into the model. The DCE is composed of the chopper, 

transformer, and rectifier stages, which are common stages in several of the other models. The mass 

properties group estimated the DDCU filters would weigh 7.35 kg (16.2 lbs). The model is calibrated to 

also calculate a filter mass of 7.35 (16.2 lbs). The model is configured to calculate a combined mass 

reduction of 1.4 kg (3.1 lbs) in the controller, data module and power supply due to improvements. The 

total mass reduction calculated by the model in the electronics is then 1.7 kg (4.0 lbs). With these 

incorporated electronics improvements and a higher electronics packaging density, the model calculates 

the box mass would decline 2.1 kg (4.6 lbs). The overall mass reduction of 3.8 kg (8.4 lbs) matches the 

difference in mass between the ISS flight DDCU and the model calculated mass.

NASA/CR—2011-217268 81
Table 34: DC/DC Converter Model Input Parameter Ranges

DC/DC Converter

Input Parameter

Recommended

Input Range

Default 

Value Comments

Output Power Level 0.5 to 250 kWe 

Input Voltage Level(1) 20 to 10,000 Vdc See par 4.2, Low Voltage Design 

Adjustments, for voltages below 120 Vdc

Output Voltage Level(1) 20 to 10,000 Vdc See par 4.2, Low Voltage Design 

Adjustments, for voltages below 120 Vdc

Number of Phases 1 or 3 1 

Inversion Frequency 10 to 100 kHz 40 kHz See par 4.1, Frequency Considerations

Ripple Factor Percentage 0.1 to 5% 0.4% See par 4.6, Filter Frequency and Ripple 

Factor Considerations

Available Modules 1-5 1 Must be equal to or greater than the number 

of Required Modules

Required Modules 1-5 1 

Enclosure/Baseplate Type FH or CP FH See par 4.3, Enclosure/Baseplate Type 

Selection Considerations

Enclosure/Baseplate 

Material

Al or CC Al See par 4.4, Enclosure / Baseplate and 

Coldplate / Radiator Material Options

Control & Monitoring 

Harness Material

Cu or FO Cu See par 4.5, Control and Monitoring 

Harness Material Considerations

Coldplate and Radiator 

Material

Al or CC Al See par 4.4, Enclosure / Baseplate and 

Coldplate / Radiator Material Options

Single or Two Sided 

Radiator

1 or 2 2 

Maximum Radiator

Sink Temperature

200 to 300 K 294 K 

Maximum Baseplate

Temperature

-30 to 65° C 63° C 

Maximum Baseplate to

Radiator Delta 

Temperature

3 to 20° C 11° C

4° C

11° C Delta T for Finned Heat Exchanger 

4° C Delta T for Coldplate Baseplate

Chopper Efficiency 96.8 to 98.4% 97.6% Reduce efficiency for low voltages, see par 

4.2, Low Voltage Design Adjustments

Transformer Efficiency 98.6 to 99.6% 99.2% 

Rectifier Efficiency 98.3 to 99.1% 98.7% Reduce efficiency for low voltages, see par 

4.2, Low Voltage Design Adjustments

DC Filter Efficiency 99.7 to 99.9% 99.8% 

NASA/CR—2011-217268 82
4.8 AC/AC FREQUENCY CONVERTER MODEL

The ac/ac frequency converter model is based on a dc link frequency converter design. The ac input is 

rectified and lightly filtered to obtain dc. This dc is then fed to an inverter to obtain a new ac frequency 

output. It contains the same stages as a dc/dc converter with the addition of an intermediate dc bus filter, 

but the sequence of the stages is rearranged to obtain an alternate function. With the addition of output 

filtering and ancillary hardware, the model is completed. This model is only able to generate ballpark 

component mass estimates. For more accurate mass values, a circuit designer should be consulted.

Application Notes: Ac/ac frequency converters are used to change an incoming ac frequency to a higher 

or lower value. The internal transformer also isolates the input and output, thus reducing transmitted 

interference. The frequency converter model described here is best suited for estimating the masses of 

converters directly following an alternator power source. In this application, the alternator's low frequency 

output is typically stepped up to a higher frequency for transmission. The primary purpose of this 

frequency conversion is to reduce the mass of subsequent distribution transformers. This frequency 

converter model can also be used at the load end if the input frequency is relatively low, 5 kHz or less, and 

the waveform has a low harmonic content. These models are not suitable for high frequency inputs. High 

frequency conversions are typically performed by ac receivers or pulse density modulation motor drives. 

They require different models.

Model Input Parameter Ranges: The results generated by this spreadsheet are only valid for a certain 

range of input parameters. Inaccurate mass estimates may result if input parameters outside of the 

ranges defined in Table 35 are used and it is not recommended. Table 35 also identifies the values that 

should yield the best results, and lists sources that should be consulted in certain cases. The user is 

responsible for selecting input parameters that do not conflict and are reasonable for the application and 

operating conditions.

Model Validation: Because there haven’t been any ac power systems flown or even developed to a high 

level, its not possible to validate the ac/ac frequency converter model against a flight unit. However, the 

ac/ac frequency converter model does have several stages in common with the dc/dc converter, rectifier, 

dc filter, chopper, and transformer, and it was validated against the flight ISS DDCU. See the dc/dc 

converter model validation paragraph.

NASA/CR—2011-217268 83
Table 35: AC/AC Frequency Converter Model Input Parameter Ranges

AC/AC Frequency 

Converter

Input Parameter

Recommended

Input Range

Default 

Value

Comments

Output Power Level 0.5 to 250 kWe 

Input Voltage Level(1) 20 to 10,000 

Vdc

See par 4.2, Low Voltage Design Adjustments, 

for voltages below 120 Vdc

Output Voltage Level

(1) 20 to 10,000 

Vdc

See par 4.2, Low Voltage Design Adjustments, 

for voltages below 120 Vdc

Number of Input Phases 1 or 3 

Number of Output Phases 1 or 3 

Input Frequency 60 Hz to 5 kHz See par 4.1, Frequency Considerations

Output or Inversion 

Frequency

10 to 100 kHz 20 kHz See par 4.1, Frequency Considerations

DC Bus Ripple Factor 

Percentage

1 to 20% 5% See par 4.6, Filter Frequency and Ripple Factor 

Considerations

Available Modules 1-5 1 Must be equal to or greater than the number of 

Required Modules

Required Modules 1-5 1 

Enclosure/Baseplate Type FH or CP FH See par 4.3, Enclosure/Baseplate Type 

Selection Considerations

Enclosure/Baseplate 

Material

Al or CC Al See par 4.4, Enclosure / Baseplate and 

Coldplate / Radiator Material Options

Control & Monitoring 

Harness Material

Cu or FO Cu See par 4.5, Control and Monitoring Harness 

Material Considerations

Coldplate and Radiator 

Material

Al or CC Al See par 4.4, Enclosure / Baseplate and 

Coldplate / Radiator Material Options

Single or Two Sided 

Radiator

1 or 2 2 

Maximum Radiator

Sink Temperature

200 to 300 K 294 K 

Maximum Baseplate

Temperature

-30 to 65° C 63° C 

Maximum Baseplate to

Radiator Delta 

Temperature

3 to 20° C 11° C

4° C

11° C Delta T for Finned Heat Exchanger 

4° C Delta T for Coldplate Baseplate

Chopper Efficiency 96.8 to 98.4% 97.6% Reduce efficiency for low voltages, see par 4.2, 

Low Voltage Design Adjustments

Transformer Efficiency 98.6 to 99.6% 99.2% 

Rectifier Efficiency 98.3 to 99.1% 98.7% Reduce efficiency for low voltages, see par 4.2, 

Low Voltage Design Adjustments

DC Bus Filter Efficiency 95 to 99.8% 95% 

Output Filter Efficiency 99.7 to 99.9% 99.8% 

NASA/CR—2011-217268 84
4.9 AC/DC STATIC RECTIFIER UNIT MODEL

The static rectifier unit model is created by adding filtering after the rectifier stage and including ancillary 

hardware such as control and monitoring and an enclosure/baseplate.

Application Notes: Static rectifier units are used to convert an incoming ac waveform to a dc output. This 

rectifier unit model is best for applications following an alternator, but it can also be used for feeding a load 

or distribution network. The main difference in the two applications is loads are more likely to require an 

actively regulated, low ripple content power feed. The characteristics of a particular application will 

determine its filter specifications, but a ripple factor of 1% or better is suggested for rectifier units that 

supply power to sensitive user loads. Conversely, a ripple factor as high as 5% may be suitable for units 

that follow an alternator or feed a heater. This model is mainly suited for low frequency applications, 5 

kHz or less, but it will accept high frequency inputs. Dc receivers are often used for high frequency ac to 

dc conversions because the loads they are supplying frequently require an actively regulated feed. A 

static rectifier isn’t capable of actively regulating its power output. A dc receiver requires a different model.

Model Input Parameter Ranges: The results generated by this spreadsheet are only valid for a certain 

range of input parameters. Inaccurate mass estimates may result if input parameters outside of the 

ranges defined in Table 36 are used and it is not recommended. Table 36 also identifies the values that 

should yield the best results, and lists sources that should be consulted for certain input parameters. The 

user is responsible for selecting input parameters that do not conflict and are reasonable for the application and operating conditions.

Model Validation: Because there haven’t been any ac power systems flown or even developed to a high 

level, its not possible to validate the ac/dc rectifier model against a flight unit. However, its rectifier and dc 

filter stages are contained in the dc/dc converter, and it was validated against the flight ISS DDCU. See 

the dc/dc converter model validation paragraph.

NASA/CR—2011-217268 85
Table 36: AC/DC Static Rectifier Model Input Parameter Ranges

AC/DC Static Rectifier

Input Parameter

Recommended

Input Range

Default 

Value Comments

Output Power Level 0.5 to 250 kWe 

Output Voltage Level(1) 20 to 10,000 

Vdc

See par 4.2, Low Voltage Design Adjustments, 

for voltages below 120 Vdc

Number of Phases 1 or 3 

Input Frequency 60 Hz to 5 kHz See par 4.1, Frequency Considerations

Ripple Factor Percentage 1 to 20% 2% See par 4.6, Filter Frequency and Ripple Factor 

Considerations

Available Modules 1-5 1 Must be equal to or greater than the number of 

Required Modules

Required Modules 1-5 1 

Enclosure/Baseplate Type FH or CP FH See par 4.3, Enclosure/Baseplate Type 

Selection Considerations

Enclosure/Baseplate 

Material

Al or CC Al See par 4.4, Enclosure / Baseplate and 

Coldplate / Radiator Material Options

Control & Monitoring 

Harness Material

Cu or FO Cu See par 4.5, Control and Monitoring Harness 

Material Considerations

Coldplate and Radiator 

Material

Al or CC Al See par 4.4, Enclosure / Baseplate and 

Coldplate / Radiator Material Options

Single or Two Sided 

Radiator

1 or 2 2 

Maximum Radiator

Sink Temperature

200 to 300 K 294 K 

Maximum Baseplate

Temperature

-30 to 65° C 63° C 

Maximum Baseplate to

Radiator Delta 

Temperature

3 to 20° C 11° C

4° C

11° C Delta T for Finned Heat Exchanger 

4° C Delta T for Coldplate Baseplate

Rectifier Efficiency 98.3 to 99.1% 98.7% Reduce efficiency for low voltages, see par 4.2, 

Low Voltage Design Adjustments

Output Filter Efficiency 99.7 to 99.9% 99.8% 

NASA/CR—2011-217268 86
4.10 TRANSFORMER UNIT MODEL

The transformer unit model is the easiest to create. It simply incorporates the standard transformer stage 

with its associated ancillary hardware.

Application Notes: The transformer unit is used to change the input ac voltage to a different level. The 

transformer stage also isolates the input and output, which reduces the level of transmitted interference. 

The transformer unit can be used anywhere in an ac power system where a change in voltage is required. 

In applications near a load the high transmission voltage is normally stepped down to the level desired by 

the load or selected for distribution. It can also be used after an alternator power source, but normally an 

alternator is capable of providing the desired voltage directly. Since the transformer unit does not use 

filtering, there are no filter considerations. This model is designed to accept any frequency input from 60 

Hz to 100 kHz, but the waveform should exhibit a fairly low harmonic content consistent with external 

sinusoidal power transmission.

Model Input Parameter Ranges: The results generated by this spreadsheet are only valid for a certain

range of input parameters. Inaccurate mass estimates may result if input parameters outside of the 

ranges defined in Table 37 are used and it is not recommended. Table 37 also identifies the values that 

should yield the best results, and lists sources that should be consulted for certain input parameters. The 

user is responsible for selecting input parameters that do not conflict and are reasonable for the application and operating conditions.

Model Validation: There haven’t been any ac power systems flown or even developed to a high level, so 

its not possible to validate the ac/ac transformer model against a flight unit. However, its transformer 

stage is common to other components, and it was checked against two designs. TRW estimated the 

mass of a 5 kWe inverter power stage in a dc/ac resonant inverter would be 6.1 kg. The transformer 

within this stage is estimated to weigh 1.5 kg, consistent with what the transformer model predicts after 

the mass it calculates is increased 10% to reflect an inverter transformer design. The model calculates 

the mass of a standard transformer, where as the TRW inverter naturally contains an inverter transformer. 

The transformer stage is also contained in the dc/dc converter, and it was validated against the flight ISS 

DDCU. See the dc/dc converter model validation paragraph.

NASA/CR—2011-217268 87
Table 37: AC/AC Transformer Unit Model Input Parameter Ranges

AC/AC Transformer Unit 

Input Parameter

Recommended

Input Range

Default 

Value Comments

Output Power Level 0.5 to 250 kWe 

Input Voltage Level(1) 20 to 10,000 

Vdc

 

Output Voltage Level(1) 20 to 10,000 

Vdc

 

Number of Phases 1 or 3 1 

Operating Frequency 60 Hz to 100 

kHz

20 kHz See par 4.1, Frequency Considerations

Transformer Efficiency 98.6 to 99.6% 99.2% 

Available Modules 1-5 1 Must be equal to or greater than the number of 

Required Modules

Required Modules 1-5 1 

Enclosure/Baseplate Type FH or CP FH See par 4.3, Enclosure/Baseplate Type 

Selection Considerations

Enclosure/Baseplate 

Material

Al or CC Al See par 4.4, Enclosure / Baseplate and 

Coldplate / Radiator Material Options

Control & Monitoring 

Harness Material

Cu or FO Cu See par 4.5, Control and Monitoring Harness 

Material Considerations

Coldplate and Radiator 

Material

Al or CC Al See par 4.4, Enclosure / Baseplate and 

Coldplate / Radiator Material Options

Single or Two Sided 

Radiator

1 or 2 2 

Maximum Radiator

Sink Temperature

200 to 300 K 294 K 

Maximum Baseplate

Temperature

-30 to 65° C 63° C 

Maximum Baseplate to

Radiator Delta 

Temperature

3 to 20° C 11° C

4° C

11° C Delta T for Finned Heat Exchanger 

4° C Delta T for Coldplate Baseplate

NASA/CR—2011-217268 88
4.11 DC RBI SWITCHGEAR MODEL

The dc RBI switchgear model integrates several dc RBIs into a single unit. The RBIs are interconnected 

by a main bus. To complete the model control and monitoring, enclosure, and radiator equations are 

incorporated.

Application Notes: The dc switchgear unit interconnects the system power sources and load distribution 

networks. The RBIs contained in the switchgear unit allow the sources and load distribution networks to 

be disconnected from the power system during maintenance periods, and provide fault protection for 

these components when they are operating. In a large power system, one dc switchgear unit is typically 

located by the power sources, while another unit is near the loads. The unit close to the power sources 

makes it possible to bring individual sources on line separately, and remove a source from the system if it 

is malfunctioning or requires maintenance. Switchgear units located near the loads typically feed local 

power distribution networks. The dc RBI switchgear model is intended to be very flexible. The designer is 

able to specify one to eight input RBIs, and one to eight output RBI power feeds.

Model Input Parameter Ranges: The results generated by this spreadsheet are only valid for a certain 

range of input parameters. Inaccurate mass estimates may result if input parameters outside of the 

ranges defined in Table 38 are used and it is not recommended. Table 38 also identifies the values that 

should yield the best results, and lists sources that should be consulted for some input parameters. The 

user is responsible for selecting input parameters that do not conflict and are reasonable for the application and operating conditions.

Model Validation: The dc RBI switchgear model was validated against the ISS DCSU. For comparison 

purposes the model was temporarily modified to include RPCMs and a larger power supply to support the 

external photovoltaic control unit (PVCU). A standard dc switchgear unit isn’t expected to house RPCMs 

or supply an external computer, and these items weren’t included in the model. The ISS DCSU weighs 

98.6 kg (217.5 lbs), including the internal RPCMs and enlarged power supply [Ref. 17]. Removing the 

RPCMs eliminates 13.5 kg (29.7 lbs) based on a mass properties estimate [Ref. 14]. Reducing the size of 

the power supply to only what is required to supply the housekeeping power demand of the DCSU lowers 

the power supply’s mass to 8.8 kg (19.4 lbs) and saves 0.4 kg (0.9 lbs). The modeled RBI design doesn’t 

include snubbers or EMI filters, because the assumed RBI design has a semiconductor switch in parallel 

with the relay to mitigate the turn-on, turn-off voltage spikes and eliminate the need for EMI filtering. 

Semiconductor switches capable of interrupting the ISS fault currents weren’t available when the ISS RBIs 

were manufactured, but they are expected to be available within the timeframe of these models. This 

lowers the DCSU’s mass 4.7 kg (10.4 lbs). Adding up the subassembly mass reductions results in a 

DCSU savings of 18.6 kg (41 lbs). These mass savings combined with a higher electronics packaging 

density allows the modeled DCSU box mass to be reduced 8.6 kg (19.0 lbs). The total electronics and 

box mass savings is 27.2 kg (60.0 lbs). The dc RBI switchgear model currently predicts a mass of 70.4 kg 

(155.3 lbs). Adding on the previously mentioned ISS DCSU items yields 97.6 kg (215.3 lbs). The 

difference between the flight DCSU mass and the model predicted mass with the add-on is 1 kg (2.2 lbs). 

This mass reduction is due to improvements in the RBI design and control and monitoring hardware.

NASA/CR—2011-217268 89
Table 38: DC RBI Switchgear Unit Model Input Parameter Ranges

DC RBI Switchgear Unit

Input Parameter

Recommended

Input Range

Default 

Value Comments

Number of Input RBI 

Units

1 to 8

Number of Output RBI 

Units

1 to 8

RBI Unit Output Power 

Level

5 to 250 kWe 

RBI Unit Output Voltage 

Level

100 to 10,000 

Vdc

 

RBI Efficiency 99.8 to 99.9% 99.85% 

Available Modules 1-5 1 Must be equal to or greater than the number of 

Required Modules

Required Modules 1-5 1 

Enclosure/Baseplate Type FH or CP FH See par 4.3, Enclosure/Baseplate Type 

Selection Considerations

Enclosure/Baseplate 

Material

Al or CC Al See par 4.4, Enclosure / Baseplate and 

Coldplate / Radiator Material Options

Control & Monitoring 

Harness Material

Cu or FO Cu See par 4.5, Control and Monitoring Harness 

Material Considerations

Coldplate and Radiator 

Material

Al or CC Al See par 4.4, Enclosure / Baseplate and 

Coldplate / Radiator Material Options

Single or Two Sided 

Radiator

1 or 2 2 

Maximum Radiator

Sink Temperature

200 to 300 K 294 K 

Maximum Baseplate

Temperature

-30 to 65° C 63° C 

Maximum Baseplate to

Radiator Delta 

Temperature

3 to 20° C 11° C

4° C

11° C Delta T for Finned Heat Exchanger 

4° C Delta T for Coldplate Baseplate

NASA/CR—2011-217268 90
4.12 AC RBI SWITCHGEAR MODEL

The ac RBI switchgear model integrates several ac RBIs into a single unit by interconnecting them with a 

main bus. The model is completed by adding control and monitoring, an enclosure, and a radiator.

Application Notes: The ac switchgear unit interconnects the system power sources and load distribution 

networks. The RBIs contained in the switchgear unit allow the sources and load distribution networks to 

be disconnected from the power system during maintenance periods, and provide fault protection for 

these components during operation. In a large power system, one ac switchgear unit will probably be 

close to the power sources, while another unit is near the loads. The unit near the power sources makes 

it possible to bring individual sources on line separately, and remove a source from the system if it fails or 

requires maintenance. Switchgear units located close to the loads typically feed local power distribution 

networks. The ac RBI switchgear model is designed to be quite flexible and it allows the designer to 

specify one to eight input RBIs, and one to eight RBI power feeds.

Model Input Parameter Ranges: The results generated by this spreadsheet are only valid for a certain 

range of input parameters. Inaccurate mass estimates may result if input parameters outside of the 

ranges defined in Table 39 are used and it is not recommended. Table 39 also identifies the values that 

should yield the best results, and lists sources that should be consulted for some input parameters. The 

user is responsible for selecting input parameters that do not conflict and are reasonable for the application and operating conditions.

Model Validation: There haven’t been any ac power systems flown or even developed to a high level, so 

its not possible to validate the ac RBI switchgear model against a flight unit. An ac RBI switchgear unit is 

expected to be very similar in mass to a dc RBI switchgear unit. Modest mass savings are expected in 

the RBIs because ac RBIs can interrupt fault currents at the zero current crossing. These mass savings 

will allow slight reductions in the internal support structure and box mass. The ac RBI switchgear is 0.6 kg 

(1.3 lbs) lighter than the dc RBI switchgear unit. The minor mass savings are attributable to a lighter ac 

RBI, because it can interrupt fault currents at the zero current crossing, and a slightly smaller volume 

resulting in a reduction in the box mass.

NASA/CR—2011-217268 91
Table 39: AC RBI Switchgear Unit Model Input Parameter Ranges

AC RBI Switchgear Unit

Input Parameter

Recommended

Input Range

Default 

Value Comments

Number of Input RBI 

Units

1 to 8

Number of Output RBI 

Units

1 to 8

RBI Unit Output Power 

Level

5 to 250 kWe 

RBI Unit Output Voltage 

Level

100 to 10,000 

Vdc

 

RBI Efficiency 99.8 to 99.9% 99.85% 

Number of Phases 1 or 3 1 

Available Modules 1-5 1 Must be equal to or greater than the number of 

Required Modules

Required Modules 1-5 1 

Enclosure/Baseplate Type FH or CP FH See par 4.3, Enclosure/Baseplate Type 

Selection Considerations

Enclosure/Baseplate 

Material

Al or CC Al See par 4.4, Enclosure / Baseplate and 

Coldplate / Radiator Material Options

Control & Monitoring 

Harness Material

Cu or FO Cu See par 4.5, Control and Monitoring Harness 

Material Considerations

Coldplate and Radiator 

Material

Al or CC Al See par 4.4, Enclosure / Baseplate and 

Coldplate / Radiator Material Options

Single or Two Sided 

Radiator

1 or 2 2 

Maximum Radiator

Sink Temperature

200 to 300 K 294 K 

Maximum Baseplate

Temperature

-30 to 65° C 63° C 

Maximum Baseplate to

Radiator Delta 

Temperature

3 to 20° C 11° C

4° C

11° C Delta T for Finned Heat Exchanger 

4° C Delta T for Coldplate Baseplate

NASA/CR—2011-217268 92
4.13 DC RPCM RACK MODEL

The dc Remote Power Control Module (RPCM) rack model integrates several dc RPCMs into a single 

unit. The RPCMs themselves contain multiple individual RPC channels. Each RPC channel is a separate 

power feed. The RPCMs are connected to a main bus. The dc RPCM rack model is completed with the 

addition of a coldplate and a radiator.

Application Notes: Dc RPCM racks are normally located in the secondary distribution network. The RPC 

units contained in these racks provide power to individual loads. The design of an RPC allows its power 

feed to be turned on and off frequently. When the RPC is supplying power, it is capable of monitoring load 

power demand and providing fault protection. It is assumed the RPCs in future racks will be programmable so that the current interrupt value can be changed to correspond to different load requirements.

This dc RPCM rack model is designed for external environments. The user is able to specify from one to 

four RPCMs, and within a module up to twenty RPC channels. To obtain the best results, it is recommended the user define RPC channel configurations that will result in RPCM power levels between 10 and 

20 kWe. For example, ten 1 kWe RPCs (10 kWe), four 3 kWe RPCs (12 kWe), and one 16 kWe RPC.

Model Input Parameter Ranges: The results generated by this spreadsheet are only valid for a certain 

range of input parameters. Inaccurate mass estimates may result if input parameters outside of the 

ranges defined in Table 40 are used and it is not recommended. Table 40 also identifies the values that 

should yield the best results, and lists sources that should be consulted for some input parameters. The 

user is responsible for selecting input parameters that do not conflict and are reasonable for the application and operating conditions.

Model Validation: The dc RPCM rack model was validated against an ISS remote power distribution 

assembly (RPDA). An ISS RPCM weighs 4.36 kg (9.62 lbs). Depending on the RPCM configuration and 

power level the RPCM model predicts RPCM masses ranging from 2.9 to 5.5 kg (6.4 to 12.1 lbs). The 

variation in mass is due to power scaling factors incorporated into the models. This is justified by the fact 

that a single channel, 65 amp, RPCM doesn’t use all the connector pins and coldplate capacity. It could 

be lighter, but commonality with the other RPCM designs increases its mass. If this design was optimized 

to reduce connector, enclosure, and coldplate mass, its reasonable to expect its mass to be reduced to 

2.9 kg (6.4 lbs). An eight space RPCM rack, including cable harnesses and cable connector mates, 

weighs 15.9 kg (35 lbs). The model calculates a four space aluminum RPCM rack, with cabling, will weigh 

8.0 kg (17.6 lbs). Basically, half the mass of an eight space RPCM.

NASA/CR—2011-217268 93
Table 40: DC Remote Power Control Module Rack Model Input Parameter Ranges

DC RPCM Rack

Input Parameter

Recommended

Input Range

Default 

Value Comments

Number of RPC Modules 1 to 4

RPCM Rack

Input Power Level

10 to 80 kWe 

RPC Channel Output 

Power Level

600 watts to

20 kWe

Number of RPC

Channels in RPCM

1 to 20 

RPC Output

Voltage Level

20 to 500 Vdc 

RPC Efficiency 99.65 to 99.75% 99.7% 

Available RPCM Racks 1-5 1 Must be equal to or greater than the number of 

Required Modules

Required RPCM Racks 1-5 1 

RPCM Enclosure Material Al or CC Al See par 4.4, Enclosure / Baseplate and 

Coldplate / Radiator Material Options

Control & Monitoring 

Harness Material

Cu or FO Cu See par 4.5, Control and Monitoring Harness 

Material Considerations

Coldplate and Radiator 

Material

Al or CC Al See par 4.4, Enclosure / Baseplate and 

Coldplate / Radiator Material Options

Single or Two Sided 

Radiator

1 or 2 2 

Maximum Radiator

Sink Temperature

200 to 300 K 294 K 

Maximum Baseplate

Temperature

-30 to 65° C 63° C 

Maximum Baseplate to

Radiator Delta 

Temperature

3 to 20° C 11° C

4° C

11° C Delta T for Finned Heat Exchanger 

4° C Delta T for Coldplate Baseplate

NASA/CR—2011-217268 94
4.14 AC RPCM RACK MODEL

The ac RPCM rack model integrates several ac RPCMs into a single unit. The RPCMs contain multiple 

individual RPC channels. Each RPC channel is a separate power feed. The RPCMs are connected to a 

main bus. The ac RPCM rack model is completed with the addition of a coldplate and radiator.

Application Notes: Ac RPCM racks will probably be located in a secondary distribution network. The RPC 

units contained in these racks provide power to individual loads. The design of an RPC allows its power 

feed to be turned on and off frequently. When the RPC is supplying power, it is capable of monitoring load 

power demand and providing fault protection. It is assumed the RPCs in future racks will be programmable so that the current interrupt value can be changed to correspond to different load requirements.

This ac RPCM rack model is designed for external environments. The user is able to specify from one to 

four RPCM, and within a module up to twenty RPC channels. The user can also specify the number of 

phases that are incorporated into each RPCM. If all the RPCMs are single-phase, a single-phase, twowire bus is automatically selected. If only 3-phase RPCMs are specified, a 3-phase, 3-wire bus is selected

by the model. If the rack contains a mixture of single- and 3-phase RPCMs, the model selects a 3-phase, 

4-wire bus. To obtain the best results, it is recommended the user define RPC channel configurations that 

will generate RPCM power levels between 10 and 20 kWe. For example, ten 1 kWe RPCs (10 kWe), four 

3 kWe RPCs (12 kWe), and one 16 kWe RPC.

Model Input Parameter Ranges: The results generated by this spreadsheet are only valid for a certain 

range of input parameters. Inaccurate mass estimates may result if input parameters outside of the 

ranges defined in Table 41 are used and it is not recommended. Table 41 also identifies the values that 

should yield the best results, and lists sources that should be consulted for some input parameters. The 

user is responsible for selecting input parameters that do not conflict and are reasonable for the application and operating conditions.

Model Validation: There haven’t been any ac power systems flown or even developed to a high level, so 

its not possible to validate the ac RPCM rack model against a flight unit. An ac RPCM rack is expected to 

be very similar in mass to a dc RPCM rack. A slight increase in the switch mass is expected due to the 

need to have parallel, back to back semiconductor switches to conduct ac. This, along with a slight 

increase in the rack mass, caused an equivalently configured ac RPCM rack to weigh 1 kg (2.2 lbs) more 

than a dc RPCM rack.

NASA/CR—2011-217268 95
Table 41: AC Remote Power Control Module Rack Model Input Parameter Ranges

AC RPCM Rack

Input Parameter

Recommended

Input Range

Default 

Value Comments

Number of RPC Modules 1 to 4

RPCM Rack

Input Power Level

10 to 80 kWe 

RPC Channel Output 

Power Level

600 watts to

20 kWe

Number of RPC

Channels in RPCM

1 to 20 

Number of Phases

in RPCM

1 or 3 1 

RPC Output

Voltage Level

20 to 500 Vdc 

RPC Efficiency 99.65 to 99.75% 99.7% 

Available RPCM Racks 1-5 1 Must be equal to or greater than the number of 

Required Modules

Required RPCM Racks 1-5 1 

RPCM Enclosure Material Al or CC Al See par 4.4, Enclosure / Baseplate and 

Coldplate / Radiator Material Options

Control & Monitoring 

Harness Material

Cu or FO Cu See par 4.5, Control and Monitoring Harness 

Material Considerations

Coldplate and Radiator 

Material

Al or CC Al See par 4.4, Enclosure / Baseplate and 

Coldplate / Radiator Material Options

Single or Two Sided 

Radiator

1 or 2 2 

Maximum Radiator

Sink Temperature

200 to 300 K 294 K 

Maximum Baseplate

Temperature

-30 to 65° C 63° C 

Maximum Baseplate to

Radiator Delta 

Temperature

3 to 20° C 11° C

4° C

11° C Delta T for Finned Heat Exchanger 

4° C Delta T for Coldplate Baseplate

NASA/CR—2011-217268 96
4.15 SOLAR ARRAY SHUNT REGULATOR MODEL

The solar array shunt regulator matches the power delivered by the array with the power demanded by the 

load. It uses numerous discreet shunt elements to short out individual array strings and control the 

amount of power supplied to the load. The shunt switch control signal is generated by a voltage comparitor. The bus voltage is measured and the corresponding voltage signal and a reference voltage signal are 

fed into a comparitor that generates a voltage error signal. This error signal is utilized by the switch gate 

control logic to control the number of shunt elements that are activated. Because the switches are capable of rapid switching speeds, the shunt regulator can respond to load changes in milliseconds. Coarse 

voltage regulation is provided by turning on and off individual shunt elements, thereby shunting power in 

steps. To achieve fine voltage regulation, the final shunt element is pulse width modulated (PWM). This 

allows the shunted power to be precisely controlled and results in accurate voltage regulation. The shunt 

regulator model is completed by incorporating algorithms for the control and monitoring hardware, enclosure, and thermal management subsystem.

Application Notes: An array shunt regulator would be located immediately after the solar array to regulate 

the bus voltage level. It controls the bus voltage level by shunting excess array current. In effect it 

maintains a balance between the array power being supplied and the load power being consumed.

Model Input Parameter Ranges: The dc shunt regulator model is designed to cover a wide range of input 

parameters; however, using parameters outside of these ranges may result in inaccurate mass estimates 

and it is discouraged. Table 42 lists the acceptable input ranges and provides default values that should 

yield good results under most conditions. The user is responsible for selecting input parameters that do 

not conflict and are reasonable for the application and operating conditions.

Model Validation: The solar array shunt regulator model was validated against the ISS SSU. The ISS 

SSU weighs 89.6 kg (197.6 lbs). The shunt regulator model predicts a mass of 85.0 kg (187.4 lbs). Shunt 

switch, diode, control element, data monitor unit and ramp generator improvements are projected to save 

2.5 kg (5.6 lbs). With these incorporated electronics improvements and an assumed higher electronics 

packaging density, the model calculates the integral box-radiator mass will drop 2.1 kg (4.7 lbs). The total 

mass reduction the model calculates is then 4.6 kg (10.2 lbs). This value equals the difference between 

the ISS flight SSU mass of 89.6 kg (197.6 lbs) and the model calculated mass of 85.0 kg (187.4 lbs).

NASA/CR—2011-217268 97
Table 42: Solar Array Shunt Regulator Model Input Parameter Ranges

Solar Array Shunt 

Regulator

Input Parameter

Recommended

Input Range

Default 

Value

Comments

Array Output Power Level 2 to 100 kWe 

Array Output Voltage 28 to 200 Vdc 

Number of Array Strings 10-200 Equal to the number of array strings

Pulse Width Modulation 

Frequency

15 to 70 kHz 20 kHz

Available Shunt Regulator 

Modules

1-5 1 Must be equal to or greater than the 

number of Required Modules

Required Shunt Regulator 

Modules

1-5 1 

Enclosure/Radiator 

Material

Al or CC Al See par 4.4, Enclosure / Baseplate and 

Coldplate / Radiator Material Options

Control & Monitoring 

Harness Material

Cu or FO Cu See par 4.5, Control and Monitoring 

Harness Material Considerations

Array String Filter 

Efficiency

99.9 to 99.98% 99.94% 

Bus Conductor Efficiency 99.57 to 99.77% 99.67% 

Shunt Switch Efficiency 98.6 to 99.6% 99.10% 

Diode Efficiency 99.23 to 99.43% 99.33% 

Load Bus Capacitor 

Efficiency

99.96 to 99.98% 99.97% 

Array String Ripple Factor 1 to 5% 1.65% 

Maximum Radiator

Sink Temperature

200 to 300 K 294 K 

Maximum Baseplate

Temperature

-30 to 65° C 63° C 

Maximum Baseplate to

Radiator Delta 

Temperature

3 to 8° C 4° C 4° C Delta T assumed for integral 

enclosure/radiator design

NASA/CR—2011-217268 98
4.16 BATTERY CHARGE DISCHARGE UNIT MODEL

A battery charge discharge unit (BCDU) controls the charge power supplied to the battery during 

insolation, and draws power from the battery during eclipse to regulate the primary bus voltage level. It 

utilizes a buck regulator to reduce the bus voltage to the level required by the battery during charging. By 

controlling the battery supply voltage it controls its charging rate. During the eclipse period, it draws power 

from the battery and raises it to the primary bus voltage level using a boost regulator. By controlling the 

battery discharge rate, it regulates the bus voltage level. Its possible to merge the buck and boost 

regulators into a common converter, a bilateral converter. With this design approach, some of the circuit 

elements are shared to reduce the mass of the converter assembly. The BCDU is completed by including 

algorithms for the control and monitoring hardware, enclosure, and thermal management subsystem.

Application Notes: A BCDU is located between the primary dc bus and the battery. During the insolation 

period it controls the battery charge rate to bring it up to a full state of charge. During the eclipse period it 

regulates the primary dc bus voltage level by controlling the discharge rate of the battery. It also includes 

circuitry to monitor the performance of the battery and provide this information to higher level controllers.

Model Input Parameter Ranges: The BCDU model is designed to cover a wide range of input parameters. 

However, using parameters outside of these ranges may result in inaccurate mass estimates and it is not 

recommended. Table 43 lists the acceptable input ranges and provides default values that should yield 

good results under most conditions. The user is responsible for selecting input parameters that do not 

conflict and are reasonable for the application and operating conditions.

Model Validation: The BCDU was validated against the ISS BCDU. The ISS BCDU weighs 105.9 kg 

(233.5 lbs). The BCDU model predicts a mass of 90.8 kg (200.2 lbs). The model does not include the dc 

control bus RBI or the low voltage battery charger. These items were considered unique to the ISS BCDU 

design. This reduces the mass of the BCDU electronics an estimated 8.1 kg (17.9 lbs). The buck and 

boost regulator switch and diode masses, and the control and monitoring controller, data processor, and 

battery monitor masses were reduced a combined 1.8 kg based on projected improvements. With the 

elimination of these items, the assumed electronics improvements, and an overall higher electronics 

packaging density, the box mass declined 5.2 kg (11.4 lbs). The sum of these adjustments is 15.1 kg 

(33.3 lbs). When this is added to the model estimate of 90.8 kg (200.2 lbs), the current BCDU flight mass 

of 105.9 kg (233.5 lbs) is obtained.

NASA/CR—2011-217268 99
Table 43: Battery Charge Discharge Unit Model Input Parameter Ranges

Battery Charge 

Discharge Unit 

Input Parameter

Recommended

Input Range

Default 

Value

Comments

Max Discharge Power to 

Primary Bus

500 watts to 20 

kWe

Max Charge Power to 

Battery

500 watts to 20 

kWe

Max Primary Bus Output 

Voltage

28 to 200 Vdc 

Maximum Battery Charge 

Voltage

20 to 190 Vdc 

Battery Capacity Rating 5 to 150 AH 

Buck & Boost Switching 

Frequency

50 to 120 kHz 80 kHz

Available Modules 1-5 1 Must be equal to or greater than the 

number of Required Modules

Required Modules 1-5 1 

Enclosure/Baseplate Type FH or CP FH See par 4.3, Enclosure/Baseplate Type 

Selection Considerations

Enclosure/Baseplate 

Material

Al or CC Al See par 4.4, Enclosure / Baseplate and 

Coldplate / Radiator Material Options

Control & Monitoring 

Harness Material

Cu or FO Cu See par 4.5, Control and Monitoring 

Harness Material Considerations

Coldplate and Radiator 

Material

Al or CC Al See par 4.4, Enclosure / Baseplate and 

Coldplate / Radiator Material Options

Single or Two Sided 

Radiator

1 or 2 2 

Maximum Radiator

Sink Temperature

200 to 300 K 294 K 

Maximum Baseplate

Temperature

-30 to 65° C 63° C 

Maximum Baseplate to

Radiator Delta 

Temperature

3 to 20° C 11° C

4° C

11° C Delta T for Finned Heat Exchanger 

4° C Delta T for Coldplate Baseplate

(Table 43 continued on next page)

NASA/CR—2011-217268 100
Table 43 (cont): Battery Charge Discharge Unit Model Input Parameter Ranges

Battery Charge 

Discharge Unit 

Input Parameter

Recommended

Input Range

Default 

Value Comments

Primary and Battery Bus 

Filter Efficiency

99.7 to 99.9% 99.8% 

Primary Bus Capacitor 

Efficiency

99.96 to 99.98% 99.97% 

Buck Regulator Switch 

Efficiency

97.0 to 98.0% 97.50% 

Boost Regulator Switch 

Efficiency

97.3 to 98.3% 97.8% 

Buck Inductor Efficiency 99.3 to 99.7% 99.5% 

Boost Inductor Efficiency 98.6 to 99.2% 98.9% 

Buck Regulator Diode 

Efficiency

99.4 to 99.8% 99.6% 

Boost Regulator Diode 

Efficiency

98.4 to 99.0% 98.7% 

Battery Fault Isolator 

Efficiency

99.8 to 99.9% 99.85% 

Primary Bus Filter Ripple 

Factor

0.1 to 5% 0.5% 

Battery Bus Filter Ripple 

Factor

0.1 to 5% 0.9% 

NASA/CR—2011-217268 101
4.17 DC INSULATED TRANSMISSION LINE MODEL

Note, this model uses iterative calculations and its necessary to change the default EXCEL calculation 

settings to run it. The following steps are required. After opening this spreadsheet with EXCEL, click on 

"Tools", go down to "Options" and click on it. Select "Calculation" and in this window check the "Iteration" 

box. The iteration defaults should be: Maximum Iterations = 100 and Maximum Change = 0.001. In the 

calculation area select "Automatic" and it will automatically recalculate every time a number is changed or 

select "Manual" and then after making the input changes hit "F9" and it will recalculate.

Application Notes: The dc transmission line model is used to determine the mass of transmission lines 

connecting dc power conditioning components.

Model Input Parameter Ranges: The dc transmission line model is capable of accepting a wide range of 

power, voltage and frequency inputs. The suggested parameter input ranges are shown in Table 44. In 

most cases these parameters have simply been restricted to typical values and the user can go outside of 

this range and still obtain acceptable results. The dc transmission line model is very robust and it will 

accept almost any combination of values and calculate a result. If the user elects to use values outside of 

the ranges shown below they are responsible for selecting suitable, reasonable values.

Table 44: DC Insulated Transmission Line Model Input Parameter Ranges

Single & 3-Phase AC 

Transmission Line

Input Parameter

Recommended

Input Range

Default 

Value

Comments

Output Power Level 100 watts to 10 MWe 

Output Voltage Level 20 to 10,000 Vrms 

Available Transmission 

Line Circuits

1-5 1 Must be equal to or greater than the 

number of Required Circuits

Required Transmission 

Line Circuits

1-5 1 

Conductor Material Copper (Cu) or 

Aluminum (Al)

Cu 

Transmission Line 

Efficiency

80% to 99.999% 

Transmission Line 

Distance

0.1 to 10,000 m 

Transmission Line

Sink Temperature

200 to 350 K 294 K 

NASA/CR—2011-217268 102
4.18 SINGLE AND 3-PHASE AC INSULATED TRANSMISSION LINE

Note, this model uses iterative calculations and its necessary to change the default EXCEL calculation 

settings to run it. The following steps are required. After opening this spreadsheet with EXCEL, click on 

"Tools", go down to "Options" and click on it. Select "Calculation" and in this window check the "Iteration" 

box. The iteration defaults should be: Maximum Iterations = 100 and Maximum Change = 0.001. In the 

calculation area select "Automatic" and it will automatically recalculate every time a number is changed or 

select "Manual" and then after making the input changes hit "F9" and it will recalculate.

Application Notes: The single- and 3-phase ac transmission line model is used to determine the mass of 

transmission lines connecting ac power conditioning components. It is best suited for moderate to low 

frequency applications. For high frequency applications, a transmission line construction specifically 

designed too minimize the skin effect, such as a litz wire construction, is recommended. The dc transmission line model is recommended for dc power system applications.

The skin effect is a phenomenon that occurs in ac transmission due to a rapidly changing current intensity. 

It arises from the fact that the inductance encountered by the current is higher at the center of the wire 

than at the periphery. This causes an uneven current density over the conductor cross section; the 

current density is a minimum at the wire center and a maximum at the periphery. The net result is an 

increase in the effective resistance of the conductor and higher losses. This effect becomes more 

pronounced as the conductor size and frequency increase. The litz wire transmission line construction was 

specifically developed to reduce skin effect losses and line inductance. Litz wire conductors contain 

numerous, individually insulated wire strands. Because each strand is insulated, the conductor behaves 

like many small wires run in parallel. This dramatically reduces skin effect losses because the useful 

conductor cross section of several individual strands is much larger than that of a single large conductor.

Another issue in ac transmission line design is line inductance. The energy stored in a transmission line is 

proportional to its inductance; consequently, a highly inductive line can make power switching and fault 

interruption more difficult. The stored energy must be controlled and dissipated by the switch. A large 

inductive reactance also results in a large reactive power demand. As a result the current levels in the 

system rise, causing higher I2

R losses, and necessitating larger conductors in the transmission lines and 

power conditioning components. This effect is further compounded as conductor size increases, because

it causes the line inductance to increase. In addition to increasing the PMAD system mass, the power 

source must be oversized to feed the reactive power demand. From a system viewpoint, it is important to 

minimize line inductance and maximize the system power factor.

Model Input Parameter Ranges: The single- and 3-phase ac transmission line model is capable of 

accepting a wide range of power, voltage and frequency inputs. The suggested parameter input ranges 

are shown in Table 45. In many cases these parameters have simply been restricted to typical values and 

the user can go outside of this range and still obtain acceptable results. However, there are combinations 

of input parameters that will cause problems. Specifying power, voltage, and efficiency values that lead to 

a relatively large conductor size and combining this with a fairly high frequency will frequently lead to poor 

results. The problem in this case is the model is calculating a large ac resistance due to the skin effect 

and quite likely a poor power factor because of the calculated line inductance. These effects can be 

mitigated by reducing the size of the transmission line conductors. Three methods are suggested.

1. Increase the transmission line voltage to reduce the size of the conductors.

2. Lower the operating frequency. The skin effect and line inductance both increase as 

the frequency rises.

3. If neither of these is acceptable, the transmission line can be separated into multiple 

lines using the Available Transmission Line Circuits and Required Transmission 

Line Circuits values. For example, a single 300 kWe line can be broken into three 

100 kWe lines by setting both of these equal to 3. This will reduce the size of the 

NASA/CR—2011-217268 103
conductors to one-third their original size, but there will be a small mass penalty in 

the form of additional conductor insulation and more cable jackets.

The user is cautioned to monitor the ac resistance ratio, K, and the power factor. Because of the 

importance of maintaining a K value close to 1 to minimize the size of the conductors, the model will 

automatically inform the user if K exceeds 1.1 and suggest the three approaches noted above to reduce it. 

If the power factor is less than 0.8, this circuit is highly inductive. The steps listed above should again be 

tried. Failure of the model to converge will almost always be marked by a very low power factor, 0.7 or 

less. In general, the user should be able to obtain good results if they limit the conductor size to the 

values shown below for frequencies up to 5 kHz.

Suggested Conductor Size Limits for Selected Frequencies

Operating Conductor Corresponding

Frequency Gauge Conductor Radius

1 kHz 4 AWG 0.2946 cm

1.5 kHz 6 AWG 0.2337 cm

2 kHz 8 AWG 0.1626 cm

3 kHz 8 AWG 0.1626 cm

4 kHz 10 AWG 0.1295 cm

5 kHz 10 AWG 0.1295 cm

Table 45: Single- and 3-Phase AC Insulated Transmission Line Model Input Parameter Ranges

Single & 3-Phase AC 

Transmission Line

Input Parameter

Recommended

Input Range

Default 

Value

Comments

Output Power Level 100 watts to 10 MWe 

Output Voltage Level 20 to 10,000 Vrms 

Single or 3-Phase 1 or 3 

Operating Frequency 0 Hz (DC) to 5kHz 1 See Model Input Parameter Ranges and 

Suggested Conductor Size Limits for 

Selected Frequencies Table above

Available Transmission 

Line Circuits

1-5 1 Must be equal to or greater than the 

number of Required Circuits

Required Transmission 

Line Circuits

1-5 1 

Conductor Material Copper (Cu) or 

Aluminum (Al)

Cu 

Transmission Line 

Efficiency

80% to 99.999% 

Transmission Line 

Distance

0.1 to 10,000 m 

Assumed Load Power 

Factor

0.5 to 1.0 0.9 A power factor requirement is normally 

imposed on loads. 0.9 is a nominal value.

Transmission Line

Sink Temperature

200 to 350 K 294 K 

NASA/CR—2011-217268 104
5.0 CONCLUSIONS AND RECOMMENDATIONS

The purpose of this task was to update eight models previously provided to NASA GRC and deliver four 

new ones. This report documents the basis of these models and the equation development, provides 

instructions on their use and defines their limitations. The models were revised to reflect flight component 

mass data from the ISS, and information on the performance and masses of component devices gleaned 

from properties sheets. They were also expanded to include options to select enclosure types, and 

enclosure, radiator, and control and monitoring harness materials. Dc and ac transmission line models 

were added to estimate the mass of the interconnecting cables. The following models were delivered at 

the completion of this task: (1) dc/dc converter, (2) ac/ac frequency converter, (3) ac/dc static rectifier, (4) 

ac/ac transformer, (5) dc RBI switchgear unit, (6) ac RBI switchgear unit, (7) dc RPCM rack, (8) ac RPCM 

rack, (9) solar array shunt regulator, (10) battery charge discharge unit, (11) dc transmission line, and (12) 

single- and 3-phase ac transmission line.

These models will continue to evolve as more data becomes available. The best way to improve them is to

compare their output with data from completed component designs and revise them as necessary. The 

present power conditioning component data base is relatively small and confined to lower power and voltage levels. Because of this shortage, it was necessary to extrapolate a considerable distance to generate 

component models that will be consistent with future power and voltage levels. To obtain the information 

used to create these models many different sources were consulted, but the resulting models were 

generated by one person and must be reviewed to ensure they are reasonably accurate and can be properly applied. Further validation of the models is recommended as data becomes available.

The power conditioning models were created by generating equations for each of the stages and elements 

in a component. This process was particularly difficult for low frequency filters. A low frequency filter will 

be much heavier than a high frequency one, or the power system must be willing to accept poorer power 

quality. However, because there hasn’t been a low frequency ac system designed for space, its difficult to 

estimate the ripple and efficiency requirements the filter will be expected to meet and from this derive its 

mass. Using a suggested ripple factor of 10% and a filter efficiency of 95% results in a fairly heavy filter 

but one that appears reasonable given the challenges of low frequency filtering. But because of these 

requirements uncertainties and the lack of design information, this part of the models is probably the least 

accurate and it should be checked against other sources as they become available.

The models included in this report are oriented toward low earth orbit applications, but they are designed 

to be flexible and can be employed in a wide variety of applications. To properly define the component 

and transmission line model inputs and interconnect them to form a PMAD system model, the user should 

have preliminary design requirements and be able to form a conceptual design. The power system architecture should be defined, and requirements such as component maintainability and system filtering 

should be considered. An estimate of the vehicle sink temperature should also be developed for input into 

the models to determine the component radiator masses and the cable conductor temperatures. This 

process is illustrated for a Nuclear Electric Propulsion vehicle application.

An NEP system will probably use a modular architecture to enhance reliability. This can be modeled using 

the available and required modules inputs. The power conditioning components in an NEP PMAD system 

will likely be mounted directly on coldplates for cooling. Failed components won’t be replaced. These features support the use of a coldplate box. A CP box is also lighter than a finned heat exchanger box. 

Based on the timeframe the user can choose carbon-carbon boxes and radiators. Next the power, voltage, and frequency values that should be input into the models must be considered. Most of the models 

can accept power levels up to 250 kWe. This should be adequate for the near term NEP vehicles proposed for outer planetary explorations. However, the power levels envisioned for Mars NEP vehicles are 

much higher and may be beyond the scope of these particular models. The voltage capabilities incorporated into the models, up to 10,000 volts, seem to be adequate for all NEP applications. Finally, the 

system filtering requirements should by considered. Discussions with electric propulsion thruster 

designers indicate a ripple factor of 5-percent is acceptable. This information should be enough to allow 

the designer to generate a PMAD mass estimate.

NASA/CR—2011-217268 105
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NASA/CR—2011-217268 109
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Power Management and Distribution (PMAD) Model Development 

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 REPORT NUMBER

E-18023 

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration 

Washington, DC 20546-0001 

10. SPONSORING/MONITOR'S

 ACRONYM(S)

NASA 

11. SPONSORING/MONITORING

 REPORT NUMBER

NASA/CR-2011-217268 

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited 

Subject Categories: 20 and 44 

Available electronically at http://www.sti.nasa.gov 

This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

14. ABSTRACT

Power management and distribution (PMAD) models were developed in the early 1990’s to model candidate architectures for various Space 

Exploration Initiative (SEI) missions. They were used to generate "ballpark" component mass estimates to support conceptual PMAD 

system design studies. The initial set of models was provided to NASA Lewis Research Center (since renamed Glenn Research Center) in 

1992. They were developed to estimate the characteristics of power conditioning components predicted to be available in the 2005 

timeframe. Early 90’s component and device designs and material technologies were projected forward to the 2005 timeframe, and 

algorithms reflecting those design and material improvements were incorporated into the models to generate mass, volume, and efficiency 

estimates for circa 2005 components. The models are about ten years old now and NASA GRC requested a review of them to determine if 

they should be updated to bring them into agreement with current performance projections or to incorporate unforeseen design or

technology advances. This report documents the results of this review and the updated power conditioning models and new transmission 

line models generated to estimate post 2005 PMAD system masses and sizes. This effort continues the expansion and enhancement of a 

library of PMAD models developed to allow system designers to assess future power system architectures and distribution techniques 

quickly and consistently. 

15. SUBJECT TERMS

Transformers; Switches; Circuits; Inverters; Estimates; Voltage converters (DC to DC); Power conditioning; High voltages; 

Transmission lines; Harnesses; High frequencies; Requlators; Frequency converters; AC generators; Inverted converters (DC to AC) 

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF

 ABSTRACT

UU 

18. NUMBER

 OF 

 PAGES

118 

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email:help@sti.nasa.gov) 

a. REPORT

U 

b. ABSTRACT

U 

c. THIS 

PAGE

U 

19b. TELEPHONE NUMBER (include area code)

443-757-5802 

Standard Form 298 (Rev. 8-98)

Prescribed by ANSI Std. Z39-18