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Conference Paper

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September 2020

Comparison of Load Models for 

Estimating Electrical Efficiency in DC 

Microgrids

Preprint

A. Santos,1 J. Cale,1 A. Othee,1 D. Gerber,2 S. Frank,3

G. Duggan,1 D. Zimmerle,1 and R. Brown2

1 Colorado State University

2 Lawrence Berkeley National Laboratory

3 National Renewable Energy Laboratory

Presented at the IEEE International Conference on DC Microgrids 

(ICDCM 2019)

Matsue, Japan 

May 20-23, 2019
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Conference Paper

NREL/CP-3500-77228

September 2020

Comparison of Load Models for 

Estimating Electrical Efficiency in DC 

Microgrids

Preprint

A. Santos,1 J. Cale,1 A. Othee,1 D. Gerber,2 S. Frank,3

G. Duggan,1 D. Zimmerle,1 and R. Brown2

1 Colorado State University

2 Lawrence Berkeley National Laboratory

3 National Renewable Energy Laboratory

Suggested Citation

Santos, A., J. Cale, A. Othee, D. Gerber, S. Frank, G. Duggan, D. Zimmerle, and R. 

Brown. 2020. Comparison of Load Models for Estimating Electrical Efficiency in DC 

Microgrids: Preprint. Golden, CO: National Renewable Energy Laboratory. 

NREL/CP-3500-77228. https://www.nrel.gov/docs/fy20osti/77228.pdf.

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Comparison of Load Models for Estimating

Electrical Efficiency in DC Microgrids

A. Santos1, J. Cale1, A. Othee1, D. Gerber2, S. Frank3, G. Duggan1, D. Zimmerle1, and R. Brown2

1Colorado State University

2Lawrence Berkeley National Laboratory

3National Renewable Energy Laboratory

Abstract—This paper compares several electrical load models

for estimating the efficiency of DC vs. AC distribution in microgrids. Candidate models include energy balance, harmonic power

flow, and time-domain modeling. Model results are compared

with numerical studies and validated with experimental measurements. Based on quantitative and qualitative considerations,

the most appropriate load modeling approach for larger-scale

DC distribution efficiency studies is proposed.

Index Terms—DC distribution, microgrids, electrical efficiency,

load modeling

I. INTRODUCTION

In recent years, there has been considerable interest in

comparing the efficiency of DC distribution systems versus

traditional AC distribution. This interest is inspired by an

increasing proportion of residential electrical loads, miscellaneous electrical loads (MELs), and building equipment which

can operate from DC distribution systems. In addition, many

renewable power generation systems such as solar photovoltaic

(PV) and energy storage systems natively produce DC power,

making conversions between AC and DC potentially unnecessary and a possible source of energy savings [1]–[10].

Microgrid applications may particularly benefit from the

advantages derived from DC distribution. Microgrids selfgenerate and consume their own power, making energy efficiency a high priority. These systems typically use renewable

and storage systems which provide DC power. Moreover,

in many microgrid applications—particularly remote or rural

microgrids—electrical loads are often dominated by DC plug

loads and LED lighting, making DC distribution a seemingly

beneficial choice [11], [12].

However, quantifying the efficiency and life-cycle cost of

competing distribution systems including AC-only, DC-only,

and hybrid AC/DC can be challenging because of the number

of possible electrical configurations, how system boundaries

are defined, whether the application includes on-site storage

and/or solar PV, and combinations of potential loads and

equipment types [3], [13]. To address this need, the authors are

developing next-generation modeling tools to provide a flexible and modular modeling environment to enable microgrid

practitioners to assess and compare the energy efficiency and

life-cycle cost of competing electrical network designs.

A key component of this research is the development

and validation of electrical load models to evaluate electrical

losses, underlying the comparison between competing network

designs. Energy efficiency comparisons in the future integrated

modeling tool are expected to be made over a wide range of

potential configurations, requiring a trade-off between computational efficiency and sufficient model accuracy. To this

end, this paper describes evaluations which were conducted

between three modeling approaches: energy balance from

device efficiency curves, a harmonic power flow method, and

time-domain simulation. Modeling results were compared to

measurements taken on an experimental testbed and used

to down-select the most appropriate method given the dual

objectives of computational speed and sufficient accuracy, in

addition to scalability and ease of modeling implementation.

Research in [1], [2] described numerical comparisons between AC and DC distribution networks in residential and

commercial buildings, respectively, using parameterized efficiency curves for each device, from which net power losses

were calculated. Harmonic power flow is a well-established

analysis technique used to estimate power flows in systems

which include nonlinear loads [14], [15]. The iterative harmonic power flow technique has been shown to account for

nonlinear loads, voltage distortions and can accurately model

losses based on harmonics in the system, and can be used for

unbalanced systems [16], [17]. Time-domain methods have

been used extensively to simulate power flows and electromagnetic transients in power systems and power electronic

devices, see for example [18], [19].

This paper focuses on the evaluation and comparison of

the three load modeling approaches mentioned above, with

primary consideration placed on down-selecting a method

which yields sufficient accuracy while maintaining computational efficiency, ease of use and modeling implementation.

Key contributions of this work are:

• Evaluation of several load modeling options for the

assessment of DC and AC network efficiencies;

• Description of an experimental testbed and data collection

method for obtaining measurements on various distribution types and configurations;

• Assessment of the load modeling approaches described

above in terms of their appropriateness for use in an

integrated modeling package.

The remainder of this paper is structured as follows. SecThis report is available at no cost from the National Renewable Energy Laboratory at www.nrel.gov/publications. 1
480 VAC ∆–Y

AC Distribution Bus

(a) AC-only distribution.

480 VAC ∆–Y

DC Distribution Bus

(b) DC-only distribution.

Fig. 1. Testbed configurations with AC-only (a) and DC-only (b).

tion II outlines the technical approach used in this work.

Background on the selection of candidate load models is

given in section III. Section IV provides a description of the

experimental testbed. Model validation results are presented

in section V, followed by conclusions in section VI.

II. TECHNICAL APPROACH

The objective of this research was to perform both quantitative and qualitative comparisons of electrical load models

to determine their suitability for integration into a modeling

package when considering: computational efficiency, accuracy,

and ease-of-implementation. The steps used to perform these

comparisons were as follows:

1) Testbed design. A testbed for emulating actual operating

conditions in building distribution systems under both AC

and DC configurations was designed.

2) Selection of candidate load models. Candidate load models were chosen from a set of well-known techniques,

representing a spectrum of expected accuracy, computational efficiency, and implementation effort.

3) Modeling and simulation. Models were created for each

device and network configuration in the testbed to perform estimations of electrical efficiencies.

4) Experimental measurement. The testbed was constructed

and measurements were collected under a variety of

operating scenarios and test configurations.

5) Model validation. The experimental measurements were

compared to simulation results to validate the device- and

system-level efficiency estimations.

6) Model assessment. The candidate models were assessed

in terms of relative accuracy, computational efficiency,

and implementation burden.

For the first step, a testbed was designed to emulate the loads

in a small office, supplied by either AC or DC distribution. A

conceptual representation of the testbed is shown in Fig. 1.

A one-line diagram of the testbed with AC distribution is

shown in Fig. 1a. The configuration comprises a 3-φ AC

building transformer with three parallel load branches; each

branch may be connected to a single phase or multiple phases

as described below. The primary side of the transformer, which

is connected in ∆-Y, is tied to utility mains. Each load branch

consists of a computer laptop with AC/DC power supply, in

parallel with light emitting diode (LED) light fixture, supplied

by an AC/DC driver. The DC configuration of the testbed,

shown in Fig. 1b, consists of an AC building transformer

(the same transformer as in Fig. 1a) with three parallel DConly load branches. The output voltage of the transformer is

converted to DC voltage with an AC/DC converter, which

powers the DC distribution bus. Each load branch consists

of a computer laptop and LED (the same devices in Fig. 1a);

however, in this configuration the computer power supplies

and LEDs are supplied by DC/DC converter types.

To consider both balanced and unbalanced loading conditions on the distribution systems, the testbed was designed to

supply the loads under the configurations shown in Table I.

A detailed description of the testbed hardware and equipment

specifications are given in section IV.

TABLE I. Load configurations for AC and DC distribution tests.

Configuration 1: balanced across three phases

Phase A Phase B Phase C

Laptop 1 X

Laptop 2 X

Laptop 3 X

LED 1 X

LED 2 X

LED 3 X

Configuration 2: unbalanced on one phase

Phase A Phase B Phase C

Laptop 1 X

Laptop 2 X

Laptop 3 X

LED 1 X

LED 2 X

LED 3 X

Configuration 3: unbalanced on two phases

Phase A Phase B Phase C

Laptop 1 X

Laptop 2 X

Laptop 3 X

LED 1 X

LED 2 X

LED 3 X

This report is available at no cost from the National Renewable Energy Laboratory at www.nrel.gov/publications. 2
III. SELECTION OF LOAD MODELING APPROACHES

When choosing candidates for modeling electrical loads,

many potential techniques and their modifications could

have been selected. In this research three techniques were

selected for comparison, with the objective of representing a

broad spectrum of expected model accuracy, computational

efficiency, and implementation effort. A brief description of

the selected modeling approaches is given below.

Notation: In this paper, X ̃ = X∠θ denotes the phasor for

sinusoidal variable x(t) = √

2 X cos(ωt + θ) (note that X is

the root-mean-square of x(t)); | · | symbolizes the absolute

value of a complex number or cardinality of a set; Re{·}

symbolizes the real part of a complex number; {·}∗ denotes

complex conjugation.

A. Energy Balance

The energy balance model determines output power and

power loss at each power conversion stage (device) in the

network using efficiency curves. The efficiency curves are

generated using experimental measurement data, taken in

increments of 10% of rated power, with linear interpolation

between points as described in [2]. Example efficiency curves

for a set of low voltage LED drivers is shown in Fig. 2.

20 40 60 80 100

0.5

0.6

0.7

0.8

0.9

Pout/Prated [%]

η [%]

Fig. 2. Efficiency curves for low voltage LED rectifiers [2].

B. Harmonic Power Flow

The second modeling technique selected for comparison

was based on harmonic power flow [14]. In this method, the

electrical network is modeled in the frequency domain using a

linear network at each frequency of interest; in this work, DC

(0 Hz), AC fundamental (60 Hz), and odd harmonic multiples

h= 1, 3, . . . , 19 of the fundamental were used. In this model,

power electronic converters are assumed to transfer power

between linear networks; these power transfers are modeled

with auxiliary equations for energy balance, converter losses,

and injected harmonic currents [3].

Branch elements such as transformers and cables are represented by their standard frequency-domain models. (In the

experimental testbed there was only a single branch element:

a three-phase transformer.) Higher-order effects, such as nonlinear magnetizing current due to transformer saturation, are

neglected. To accommodate unbalanced loads, the AC linear

network at each frequency is modeled as a set of sequence

networks using the theory of symmetrical components [20].

Power electronics converter losses are modeled as a

quadratic function of the converter output power:

Pin = Pout +



α + βPout + γP2

out

| {z }

Ploss

+Ph, (1)

where Pin is the input power (DC for an inverter and AC

fundamental for a rectifier); Pout is the output power (AC

fundamental for an inverter and DC for a rectifier); Ploss is

converter internal loss; α ∈ R+, β ∈ R, γ ∈ R are fitted

coefficients of the loss model; Ph is a balancing term that

represents power injected at harmonic frequencies. Note that

neglecting Ph in (1) is equivalent to the loss model described

in research published by Sandia National Laboratories, where

the voltage correction terms are omitted [21], [22].

For simplicity, harmonic currents injected by power electronics converters are modeled assuming the current waveform

has a fixed shape, i.e., the waveform may scale but its basic

shape is invariant to power level or line voltage distortion. This

fixed wave shape implies a fixed harmonic reference spectrum,

which is then shifted in amplitude and phase to maintain the

correct converter power input and output with respect to the

voltage at the converter’s AC terminal. Herein, two methods

were investigated for defining the reference spectra:

1) Single reference waveform: For a single device, a representative waveform was captured from a single cycle during

steady-state operation; its reference harmonic spectrum was

obtained using the Fast Fourier Transform (FFT).

2) Generalized impedance model: Several waveform captures

were obtained for a set of similar devices and processed

using FFT. From these measurements, 5th-order polynomials were used to fit the odd harmonic magnitude and

unwrapped phase angle relative to the fundamental, as a

function of harmonic number. The choices of including only

odd harmonic content, the maximum harmonic number, and

degree of polynomial fit were based on observation of fits

to measured waveforms.

The reference waveform method requires less data to implement and is potentially more accurate for the specific

converter used to obtain the reference waveform. However,

the frequency-domain model is more readily generalized to

represent typical injection spectra expected from a broad range

of similar converter types and load levels, i.e., parameterized

over a catalog of device types. An example plot using the

latter approach is shown in Fig. 3, which shows the harmonic

current injection spectrum of an 24 V LED driver.

Herein, only radial networks were considered, from which

a forward/backward sweep algorithm was used to obtain

convergence in computed power flows [23]. The forward

sweep used Kirchoff’s voltage law (KVL) to calculate node

voltages; the backward sweep used Kirchoff’s current law

(KCL) to calculate branch currents. In between forward and

backward sweeps, the algorithm calculates injected currents

from the power converters. These steps are summarized as:

This report is available at no cost from the National Renewable Energy Laboratory at www.nrel.gov/publications. 3
0 5 10 15 20 25 30

0

0.05

0.10

0.15

0.20

h

|Zh| [Ω]

0 5 10 15 20 25 30

−4

−2

0

2

4

h

∠

Zh [rad]

Fig. 3. Modeled harmonic current injection spectrum for 24 V LED driver.

Measurements are shown in black; fitted values are shown in red.

Harmonic Power Flow Algorithm Steps:

1. Initialize voltage at input node (e.g., grid connection).

2. Calculate sequence voltages at each node via KVL, using

most recent estimates of branch current.

3. Transform sequence voltages to phase voltages.

4. Using the phase voltages and known values for Pout,

calculate rectifier currents and compute Pin by shifting

and scaling the reference spectra ensure the:

a) rectifier fundamental frequency AC current phase angle is correct with respect to voltage phase angle;

b) AC real power at fundamental frequency equals Pin;

c) power balance in (1) is satisfied;

d) harmonic power equals the sum of powers injected at

each harmonic frequency, i.e.,

Ph =

X

h

Re{V ̃

h

 ̃I

∗

h} (2)

5. Transform load phase currents to sequence currents.

6. Calculate sequence currents in each branch via KCL

using load sequence currents and most recent estimates

of node voltage.

7. If not converged, return to step 2.

Steps 2-7 of the above algorithm are iterated until both the

real and reactive power consumption at the source node (the

electric grid) converge within a specified tolerance. In this

work, a tolerance of 0.01 VA was used.

C. Time-Domain Modeling

Time-domain modeling of power electronics and systems is

well-described in the literature. While time-domain modeling

can often be used to obtain a high level of accuracy, it poses

several drawbacks including: more effort to derive higherfidelity models, the need to identify a larger number of

model parameters, and comparatively long simulation times.

However, time-domain modeling was compared to the methods described above to (i) compare simulation times versus

accuracy, (ii) indicate the modeling effort required to perform

full time-domain simulation, (iii) provide a further check on

the simulation accuracy of the previous approaches.

The devices which were modeled in this research included:

a three-phase AC transformer, AC/DC converter, computer

power supplies (AC/DC and DC/DC types), and LED drivers

(AC/DC and DC/DC types). The AC transformer was modeled

using the standard equivalent circuit representation of a symmetrical (i.e., identical parameter values on each phase) 3-φ

transformer [19]. Parameters for the transformer model used

in this work are tabulated in the Appendix.

The AC/DC power electronic converters in the studies were

all modeled with the same topology, employing a single-phase

line-commutated diode rectifier preceding a voltage controlled

DC/DC (“buck”) converter, which is a simplified version of

circuits commonly used in these converters. This converter is

depicted in Fig. 4.

−

+

vin

r1 L1

C1

L2

C2 RL

Voltage

Controller

S

vout

v

∗

dc

Fig. 4. Diagram of AC/DC power converter.

In Fig. 4, r1 and L1 are the line resistance and inductance

of the input wire respectively; C1 and C2 are filter capacitors;

L2 is a filter inductor, and RL is the variable equivalent load

resistance. Feedback control of the converter was modeled

using proportional integral (PI) control with proportional and

integral gains kp and ki, respectively; switching state S varies

the switch duty cycle using pulse-width-modulation with sawtooth period Ts to minimize the error between the measured

output voltage vout and commanded voltage reference v

∗

dc as

described in [18]. Circuit and control parameters associated

with Fig. 4 for each AC/DC device used in this research are

tabulated in the Appendix.

The DC/DC power converters were all modeled with

the same assumed topology, employing a voltage controlled

“boost” converter. This circuit is shown in Fig. 5.

−

+

vin

L1

C1 RL

Voltage

Controller

S

vout

v

∗

dc

Fig. 5. Diagram of DC/DC power converter.

This report is available at no cost from the National Renewable Energy Laboratory at www.nrel.gov/publications. 4
In Fig. 5, L1 is a line filter inductance, C1 is a filter

capacitor, and RL is the variable equivalent load resistance.

Feedback control of the converter was implemented with a

PI loop in the same manner described for the buck converter.

Circuit and control parameters associated with Fig. 5 for each

DC/DC device used in this research are given in the Appendix.

To avoid modeling specific DC isolation methods and/or

conflicts in the feedback control between the central distribution and load converters, the DC distribution network configuration employed virtual isolation between the distribution bus

output and load inputs.

IV. EXPERIMENTAL TESTBED

To evaluate the candidate modeling approaches described

in section II under DC-only and AC-only power distribution

scenarios, a testbed was constructed at the Powerhouse Energy Campus at Colorado State University. The testbed was

designed to emulate realistic loads found in a small office

building, comprising three laptop computers and three LED

lighting systems on each load branch (refer to Fig. 1).

A. Testbed Hardware

The testbed was constructed using industrial-grade electrical

equipment, mounted on a panel-board for convenience during

configuration changes and access to measurement points, see

Fig. 6. To implement the configuration scenarios listed in Table

I and provide circuit protection, the electrical enclosure (“load

center”) in Fig. 6 contained DIN-rail mounted switches and

fuse boxes, supplying a total of six possible load branches.

Fig. 6. Testbed hardware with power analyzer, laptop, and LEDs. (Photo

used with permission by Arthur Santos of Colorado State University.)

The load center was connected to utility mains through

a 3 kVA, ∆-Y transformer (Dayton model 44YV25), with

480 V primary and 208 V/120 V secondary. Electrical outlets

on each load branch provided a total of 16 outlets for singlephase 120 V, and two for three-phase 208 V. Each branch was

protected from over-current with a 10 A circuit breaker.

The laptop computers used in the experiments and their

power supplies consisted of:

Laptop 1: HP notebook, model Envy dv6-7210us, with

AC/DC converter model 677774-001 (65 W), and DC/DC

converter model HP F1455A Airline/Auto Adapter (75 W)

Laptop 2: HP notebook, model Elitebook 850 G3, with

AC/DC converter model 740015-002 (45 W), and DC/DC

converter model PA-3900-Z3 (90 W)

Laptop 3: HP notebook, model Pavilion Entertainment dv6,

with AC/DC converter, model 391174-001, (120 W), and

DC/DC converter model PA-4900-OT (90 W)

The LEDs (named LED 1-3) each consisted of a converter

driver and one bar (light), with the following characteristics:

color temperature 4000 K, 2500 lumens, 24 V input, rated at

22 W. The AC/DC LED driver used in the AC configuration

experiments used model APV-25-24. The DC configuration

experiments used DC/DC driver model LDD-1000LW. The

AC/DC central converter for the DC distribution configuration

was an Agilent N7973A DC power supply with 0–60 VDC/0–

33.3 A output, rated at 2 kW.

B. Data Collection

Each load branch in the testbed, in addition to the input and output voltage connections, were instrumented with

terminal boxes to provide access to selected measurement

points. Measurement data was collected using a Keysight

multifunction switch measuring unit (MU) model 34980A with

Keysight 34921T multiplexer and a Keysight PA2203A power

analyzer. Because the MU current channels are rated up to

1 A, higher currents (up to 6 A) were measured with hall

effect sensors, LEM model LTS-6-NP. The PA2203A has four

dual-channel inputs, with each channel measuring current and

voltage. The device can measure AC or DC signals, power

consumption, power efficiency and harmonic analysis, with

maximum sample rate of 5 MS/s. Its basic accuracy is 0.05%

and the best power accuracy is 0.1%, both at 50/60 Hz.

Because of the number of channels needed for obtaining

both voltage and current measurements on the testbed under

all test configurations, and the limitation of four measurement

channels on the PA2203A, data were captured at several

measurement points at different instances in time after the experiments reached steady-state. The next subsection describes

this process on an example configuration.

C. Configuration Example

To illustrate how the testbed was used to provide power

to the loads and perform measurements during one of the

configurations listed in Table I, Fig. 7 depicts the testbed under

the AC-only, configuration 1 scenario.

In the configuration depicted in Fig. 7, all load branches

were connected to the AC distribution bus to obtain approximate load balancing across all three phases. Input voltage and

current on each phase was measured using channels 1-3 on

the power analyzer (see upper left in Fig. 7). Channel 4 was

used to measure voltage and current on one load branch. After

capturing the load voltage and current waveforms, channel 4

was then used to obtain measurements on the remaining load

branches sequentially, with channels 1-3 remaining in place.

Time synchronization of all waveforms was performed during

post-processing.

This report is available at no cost from the National Renewable Energy Laboratory at www.nrel.gov/publications. 5
Fig. 7. Test configuration AC-only, configuration 1 (measuring phase A).

V. MODEL COMPARISONS

To evaluate the candidate models, simulations of the testbed

circuit were performed for each configuration in Table I.

When applying the energy balance model, measured efficiency curves for each device in the testbed were used; all

studies were performed in the Modelica
R

language, using the

computational procedure described in [2]. The HPF model was

executed in MATLAB
R, using the reference impedance waveform and generalized impedance waveform representations,

denoted HPF1 and HPF2, respectively. Time-domain modeling

was performed in MATLAB SimscapeTM. Parameter values

used for the time-domain studies are given in the Appendix.

The comparison of simulated system losses versus the

measured reference (“Ref”) values for all load configurations

is shown in Fig. 8. The magnitude of error in these models

versus the reference is shown in Fig. 9.

AC Config 1 AC Config 2 AC Config 3 DC

0

50

100

150

200

250

300

System Loss [W]

Ref Energy Balance HPF1 HPF2 Time-Domain

Fig. 8. Comparison of simulated losses.

As shown in Figs. 8-9, all four of the simulation models

yielded similar values for system losses; however, error magnitudes varied by configuration. A breakdown of losses vs.

AC Config 1 AC Config 2 AC Config 3 DC

0

2

4

6

8

|Error| [%]

Energy Balance HPF1 HPF2 Time-Domain

Fig. 9. Comparison of error magnitude in simulated losses.

device type under AC configuration 1 and DC configurations

is shown in Figs. 10-11.

Transformer Central

Converter

Load

Converters

Total

0

20

40

60

80

100

120

Predicted Loss [W]

Energy Balance HP1 HP2 Time-Domain

Fig. 10. Breakdown predicted losses by device type (AC Config 1).

In Fig. 10, all four of the simulation models yielded similar

values and relative magnitudes for the device types, with the

majority of losses occurring in the transformer (note that this

configuration does not contain the central AC/DC converter).

Simulations for the other AC configurations showed similar

This report is available at no cost from the National Renewable Energy Laboratory at www.nrel.gov/publications. 6
Transformer Central

Converter

Load

Converters

Total

0

50

100

150

200

250

300

Predicted Loss [W]

Energy Balance HP1 HP2 Time-Domain

Fig. 11. Breakdown predicted losses by device type (DC Config).

results. In Fig. 11, all four of the simulation models again

yielded similar values and relative magnitudes for the device

types, where in this case most of the losses occurred in the

central AC/DC converter, followed by the transformer, and

then the load converters.

Computation times for the system simulations for each

model, averaged over the AC and DC distribution configuration studies, are shown in Table II.

TABLE II. Summary of average simulation times per model.

Energy Balance HPF1 HPF2 Time-domain

0.1 [s] 0.4 [s] 0.4 [s] 5.6 [s]

Discussion: As described in the simulation results above, all

the candidate models yielded similar results for estimated

system losses and breakdown of loss categorized by device

type. The models also showed reasonably good agreement

with measured reference values. In the time-domain modeling

approach, further agreement could likely have been achieved

through increased model fidelity, although this would have also

increased computation time and modeling effort.

When comparing the candidate approaches, since all models

yielded similar results, selection of the appropriate approach

for implementation in a larger modeling package can therefore

be made based on modeling effort, scalability, computation

time, and extraction of additional features of interest (e.g.,

harmonic content). While the energy balance model is simple

to implement, is scalable, and has low computational time,

a limitation of the approach is that it cannot be used to

predict harmonic content. On the other hand, the time-domain

model can be used to predict harmonic content, but is the

most difficult to implement, is not easily scalable, and has

the highest computational cost. The HPF method provides

a balance between accuracy and model development time,

can be scaled to simulate large networks [14], and can also

estimate harmonic content. For these reasons, the HPF model

was selected for further development in future work.

VI. CONCLUSIONS

In this paper, several electrical load modeling approaches

were evaluated for estimating electrical efficiencies in AC

and DC distribution systems: energy balance, harmonic power

flow, and time-domain modeling. These models were selected

to represent a broad spectrum of expected model accuracy,

computational efficiency, and implementation effort. To validate the load models under DC-only and AC-only power

distribution scenarios, a testbed was constructed to provide

realistic loads found in a small office building, comprising

three laptop computers and three LED lighting systems on

each load branch.

Based on these studies, we made the following observations

on model performance: (i) all of the modeling approaches were

found to match the experimental measurements reasonably

well under AC and DC distribution, and all load configurations, (ii) the model results were consistent with each other in

terms of how losses were distributed in each system, and (iii)

there was an order of magnitude difference in computational

time of time-domain modeling over the other methods. In

terms of ease-of-implementation, the energy balance method

was the easiest, time-domain modeling the most difficult, and

harmonic power flow fell between these two extremes.

Overall, the harmonic power flow method was found to

provide a balance between accuracy and model development

time, and has the advantage of predicting harmonic content,

simulation of highly unbalanced conditions, and can be scaled

to simulate large networks. For these reasons, harmonic power

flow was selected for further research under this effort.

Limitations of this work included the relative simplicity

of the testbed circuits, simplification of the time-domain

converter models, lack of non-linear loss terms and temperature effects. In addition, the central DC/DC converter was a

research-grade power supply, not necessarily representative of

commercial converter device efficiencies.

Suggested future research includes further validation of the

harmonic power flow method on more complex network configurations and load types, and co-simulation of the electrical

model with thermal models of the surrounding environment.

ACKNOWLEDGMENTS

This work was authored in part by the National Renewable

Energy Laboratory, operated by the Alliance for Sustainable

Energy, LLC, for the U.S. Department of Energy (DOE)

under Contract No. DE-AC36-08-GO28308, and by Lawrence

Berkeley National Laboratory, operated for the DOE under

Contract No. DE-AC02-05CH11231. Funding was provided

by the DOE Assistant Secretary for Energy Efficiency and

Renewable Energy Building Technologies Office Emerging

Technologies Program. The views expressed in this article

do not necessarily represent the views of the DOE or U.S.

Government.

APPENDIX

TABLE A1. Parameters for central AC/DC converter.

Symbol Value Symbol Value Symbol Value

r1 [Ω] 0.5 C1 [μF] 100 kp [mV] 5.5

L1 [μH] 10 C2 [μF] 5 ki [V/s] 0.89

L2 [mH] 370 Ts [μs] 100 v

∗

dc [V] 12

This report is available at no cost from the National Renewable Energy Laboratory at www.nrel.gov/publications. 7
TABLE A2. Parameters for computer (CL) and LED AC/DC converters.

Symbol CL1 CL2 CL3 LED1 LED2 LED3

r1 [Ω] 0.50 0.50 0.90 1.0 1.0 1.0

L1 [μH] 10 10 10 1.0 1.0 1.0

L2 [mH] 37 37 37 37 37 37

C1 [μF] 100 80 100 70 70 70

C2 [μF] 10 10 10 10 10 10

kp [mV] 55 5.5 550 5.5 5.5 5.5

ki [V/s] 8.86 0.89 88.6 0.89 0.89 0.89

Ts [μs] 100 10 10 10 10 10

v

∗

dc [V] 19.5 19.5 18.6 24.2 24.2 24.2

RL [Ω] 36 51 19.5 21 21 20

TABLE A3. Parameters for computer (CL) and LED DC/DC converters.

Symbol CL1 CL2 CL3 LED1 LED2 LED3

L1 [μH] 40 40 40 40 40 40

C1 [μF] 600 600 600 600 600 600

kp [mV] 55 55 55 55 55 55

ki [V/s] 8.86 8.86 8.86 8.86 8.86 8.86

Ts [μs] 100 100 100 100 100 100

v

∗

dc [V] 19.5 19.5 19.5 19.5 19.5 19.5

RL [Ω] 35 56 17 8 8 8

TABLE A4. Parameters for AC transformer.

Description Value

Rated apparent power 3 [kVA]

Primary voltage (line-line, rms) 480 [V]

Secondary voltage (line-line, rms) 208 [V]

Primary winding resistance 0.01 [pu]

Secondary winding resistance 0.01 [pu]

Primary leakage inductance 0.01 [pu]

Secondary leakage inductance 0.01 [pu]

Shunt magnetizing inductance 6 [pu]

Shunt magnetizing resistance 32 [pu]

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