NREL is a national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

Use Conditions and Efficiency 

Measurements of DC Power 

Optimizers for Photovoltaic 

Systems

Preprint

Chris Deline

National Renewable Energy Laboratory

Sara MacAlpine

University of Colorado

Presented at the IEEE Energy Conversion Congress & Expo 2013

Denver, Colorado

September 15–19, 2013

Conference Paper

NREL/CP-5200-59214

October 2013
NOTICE

The submitted manuscript has been offered by an employee of the Alliance for Sustainable Energy, LLC 

(Alliance), a contractor of the US Government under Contract No. DE-AC36-08GO28308. Accordingly, the US 

Government and Alliance retain a nonexclusive royalty-free license to publish or reproduce the published form of 

this contribution, or allow others to do so, for US Government purposes.

This report was prepared as an account of work sponsored by an agency of the United States government. 

Neither the United States government nor any agency thereof, nor any of their employees, makes any warranty, 

express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of 

any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately 

owned rights. Reference herein to any specific commercial product, process, or service by trade name, 

trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, 

or favoring by the United States government or any agency thereof. The views and opinions of authors 

expressed herein do not necessarily state or reflect those of the United States government or any agency thereof.

This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Available electronically at http://www.osti.gov/bridge

Available for a processing fee to U.S. Department of Energy

and its contractors, in paper, from:

U.S. Department of Energy

Office of Scientific and Technical Information

P.O. Box 62

Oak Ridge, TN 37831-0062

phone: 865.576.8401

fax: 865.576.5728

email: mailto:reports@adonis.osti.gov

Available for sale to the public, in paper, from:

U.S. Department of Commerce

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22161

phone: 800.553.6847

fax: 703.605.6900

email: orders@ntis.fedworld.gov

online ordering: http://www.ntis.gov/help/ordermethods.aspx

Cover Photos: (left to right) photo by Pat Corkery, NREL 16416, photo from SunEdison, NREL 17423, photo by Pat Corkery, NREL 

16560, photo by Dennis Schroeder, NREL 17613, photo by Dean Armstrong, NREL 17436, photo by Pat Corkery, NREL 17721.

Printed on paper containing at least 50% wastepaper, including 10% post consumer waste.
1

This report is available at no cost from the 

National Renewable Energy Laboratory (NREL) 

at www.nrel.gov/publications.

Use Conditions and Efficiency Measurements of DC 

Power Optimizers for Photovoltaic Systems

Chris Deline

National Renewable Energy Laboratory

Golden, Colorado, USA

chris.deline@nrel.gov

Sara MacAlpine

University of Colorado

Boulder, Colorado, USA

sara.macalpine@colorado.edu

Abstract—No consensus standard exists for estimating annual 

conversion efficiency of DC-DC converters or power 

optimizers in photovoltaic (PV) applications. The performance 

benefits of PV power electronics including per-panel DC-DC 

converters depend in large part on the operating conditions of 

the PV system, along with the performance characteristics of 

the power optimizer itself. This work presents a case study of 

three system configurations that take advantage of the 

capabilities of DC power optimizers. Measured conversion 

efficiencies of DC-DC converters are applied to these scenarios

to determine the annual weighted operating efficiency. A 

simplified general method of reporting weighted efficiency is 

given, based on the California Energy Commission’s CEC 

efficiency rating and several input / output voltage ratios. 

Efficiency measurements of commercial power optimizer 

products are presented using the new performance metric, 

along with a description of the limitations of the approach.

I. INTRODUCTION

The fast-growing field of photovoltaic (PV) power 

generation has seen great innovation in its balance-of-system 

(BOS), including the introduction of power electronics 

devices which are applied at the panel level. The devolution 

of power conversion from central inverters to the panel level 

has been shown to improve performance due to reduced PV 

module mismatch [1-3]. Prior estimates of performance 

improvement from the use of distributed power electronics 

indicate that the potential for mismatch power recovery 

depends greatly on the site-specific details of the PV 

installation [4-6]. Additional potential benefits of distributed 

power electronics include increased design flexibility by 

allowing mismatched or longer strings of PV panels, 

improved monitoring, and increased system availability [7-

9]. Despite these potential benefits, a critical factor in 

distributed power converters’ utility is their conversion 

efficiency, which needs to be high in order to compete with 

conventional centralized inverter approaches [10].

For distributed AC products such as microinverters, a 

weighted DC-to-AC conversion efficiency can be measured 

by the CEC [11] or EN50530 (European) [12] inverter

efficiency method. However, no consensus standard exists 

for estimating the annual weighted efficiency of DC-DC 

converter devices, also known as power optimizers. Existing 

inverter measurement methods use a weighted average of the 

inverter performance over a range of input power Pin / Pmax

and input voltage Vin / Vmax where subscript max denotes 

maximum rated power or voltage. However, power 

optimizers have an additional free parameter, the voltage 

ratio M =Vout / Vin. This additional variable is unaddressed by 

any present power rating standard. A proposal is given in 

[13] to apply existing inverter standards to power optimizers 

by averaging conversion efficiency η over the entire range of 

M, and applying the appropriate power rating. However, this 

approach will likely underestimate η for power optimizers, 

which may operate near Vout / Vin = 1 under many use 

conditions, as will be shown here.

This work examines the conversion efficiency of DC 

power optimizers, and usage scenarios that will help to 

define common metrics for defining and comparing weighted 

conversion efficiency. The paper is arranged as follows: in 

Section II, measured efficiency curves of commercial power 

optimizer devices are provided to investigate the dependence 

of η on voltage and power operating conditions. In Section 

III, typical use scenarios are described for power optimizer 

devices. In Section IV, a computer simulation is described, 

which is used to create annual operating histograms to 

determine the amount of power processed by power 

optimizers under different use conditions. Section V 

discusses different methods of providing weighted 

efficiency, with comparison to the scenarios investigated 

here.

II. POWER OPTIMIZER EFFICIENCY MEASUREMENT

To illustrate how η is a function of both input power and 

Vout / Vin, efficiency plots for a commercial DC-DC converter 

(National Semiconductor SM1230-3A1) are shown in Figure 

1. Conversion efficiency for this device is determined by 

measuring input and output voltage and current to 0.1% 

accuracy using a Keithley 2701 DMM, with input voltage 

provided by a solar array simulator (Agilent E4363-J02), and 

output power dissipated in a digital electronic load (NHR 

4760-1kW). Each input power and output voltage condition 

is monitored over a period of 5 minutes to determine the 

average η for each operating point. The effect of higher or 

This work was supported by the U.S. Department of Energy 

under Contract No. DOE-AC36-08GO28308 with the 

National Renewable Energy Laboratory.
2

This report is available at no cost from the 

National Renewable Energy Laboratory (NREL) 

at www.nrel.gov/publications.

lower values of Vin was investigated for constant Vout / Vin, 

but this was not found to have a strong impact on η.

An empirical model is developed for the various power 

and voltage operating conditions of this power converter, 

with modeled results shown as dashed lines in Figure 1. 

This empirical model is employed to assist in device 

performance simulations in Section IV of this work. The 

empirical equation approximating this device’s conversion 

efficiency is:

0.977 (0.932 0.068 ) 2 η = + C2M − M (1)

Where C2 is a constant based on P = Pin / Pmax:

2

2 C = 0.064+ 0.51 P − 0.88 P for P < 0.25 (2)

0.1365 C2 = for P ≥ 0.25

Two additional commercial DC converter devices were 

measured to compare with the results of Figure 1, labeled 

here as Conv2 and Conv3. These additional measurements 

in Figure 2 show a similar decrease in efficiency with low 

input power and output voltage, even though Conv2 is a 

buck-only converter, and Conv1 and Conv3 are buck-boost 

converters. 

III. TYPICAL USE SCENARIOS OF DC POWER OPTIMIZERS

The potential use cases of DC power optimizers are 

limitless, however we will focus on two main applications: 

partial shading mismatch mitigation, and string length 

optimization. While the first application has received the 

most attention to date, the second is increasingly of interest 

for large-scale unshaded PV systems due to potential 

reduction of BOS costs. All scenarios here assume a fixedtilt PV installation.

A. Scenario 1: Partial shading mismatch reduction

The performance benefit of distributed power electronics 

in partially shaded PV systems is well documented [1-10]. 

Partial shading in PV systems leads to losses due to reduced 

irradiance, and due to mismatch in operating point between 

panels. It is this second power loss that is recovered through 

the use of distributed power electronics, and can make up 

Figure 1. Measured conversion efficiency η of a commercial DC power 

optimizer at three input power levels (top) and at two output voltages 

(bottom). Maximum rated power: 230W. Modeled efficiency is shown as 

a dashed line.

Figure 2: Measured conversion efficiency of three commercial DC power 

optimizers at 50% rated input power (top) and at output voltage Vout = Vin

(bottom). Conv1 is the same converter shown in Figure 1 (National 

Semiconductor SM1230-3A1).

92

94

96

98

100

0.25 0.5 0.75 1 1.25

Conversion Efficiency η (%)

M = Vout / Vin

Pin = 115 W

Pin = 45 W

Pin = 20 W

Vin = 28 V

90

92

94

96

98

100

0 0.2 0.4 0.6 0.8 1

Conversion Efficiency η (%)

P = Pin/ Pmax

Vin = 28 V

Vout = 28 V

Vout = 14 V

90

92

94

96

98

0.25 0.5 0.75 1 1.25

Conversion Efficiency η (%)

G = Vout/Vin

Conv1

Conv2

Conv3

90

92

94

96

98

0 100 200 300

Conversion Efficiency η (%)

Input Power Pin (W)

Conv1

Conv2

Conv3
3

This report is available at no cost from the 

National Renewable Energy Laboratory (NREL) 

at www.nrel.gov/publications.

15% - 50% of the total annual shading power loss, depending 

on the extent of shade and system configuration [4].

To determine a representative amount of shade to 

consider here, site survey information was obtained from a 

large residential installer in California, showing the extent of 

shade on 66 residential PV installations [14]. In these 

installations, a panoramic view of surrounding obstructions 

was taken, and the annual irradiance lost due to shade was 

calculated. Here, annual irradiance is defined as “Solar 

Access” measured by a Solmetric Suneye imaging tool [15]. 

This measurement was averaged across each installation 

using multiple images taken at the corners of the PV array. 

The annual shading losses for these various site surveys are 

given in Figure 3.

For the typical use scenario considered here, we are 

focusing on a ‘moderate’ shading case, highlighted in Figure 

3, and described in more detail in [3]. The 19% annual shade 

loss in this case is greater than average, and perhaps typical 

of sites that would benefit from distributed power 

electronics. Shade is cast by several nearby trees, primarily 

in the early morning and late afternoon. In this scenario, we 

assume a residential roof-mount PV system, 2.9 kW in size 

composed of 14 Sharp ND-208 modules in two parallel 

strings. The system is assumed to be equipped with DC 

power optimizers based on the measured performance of 

Conv1, namely a buck-boost converter with conversion 

efficiency following Eq. (1) and Eq. (2). The PV strings are 

assumed to be connected to a conventional string inverter 

with a wide DC voltage input window from 150 – 500 V. 

Note that while a buck-boost power optimizer is assumed in 

this simulation, a buck-only converter could be substituted 

with little change in the analysis, although the shade 

mitigation capabilities would be diminished somewhat [4].

B. Scenario 2 & 3: 30% and 100% String Expansion

The use of DC power optimizers can enable improved 

performance and reduced cost in another way – by increasing 

the number of PV modules in a series string, thus reducing 

the total number of strings for a given PV system size. This 

reduces per-string costs associated with homerun wiring, 

fuses, and DC combiner boxes, and reduces resistive power 

loss because of higher DC bus voltage. DC-DC converters 

provide this capability because the length of a PV string is 

conventionally limited by the maximum system Voc on the 

coldest day [16]. However, by integrating converters with 

buck capability, the system operating voltage can be 

maintained below this threshold, even if there are a larger 

number of PV modules in the series string [17]. 

Two case studies of string lengthening are considered 

here: a 30% elongation case (Scenario 2), and a 100% 

elongation case (Scenario 3). In both cases, the increased 

string length is based on a default conventional PV string 

sized for a 1000V commercial installation, again using Sharp 

ND-208 PV modules as in section 3.1. Because of the 

module’s Voc and Vmp parameters of 36 V and 28.5 V 

respectively, a conventional series string would have a 

maximum of 23 modules, to remain below 1000V at a low 

temperature of −25 o

C. With the use of DC-DC converters 

however, a 30% longer string of 30 PV modules is possible 

for Scenario 2, and a 100% longer string of 46 modules is 

chosen for Scenario 3. To limit complexity, mismatch 

between strings is assumed to be negligible in this case 

study. As with Scenario 1, each PV module in the system is 

equipped with converter Conv1.

A critical aspect of the string lengthening study is the 

capability of the DC-AC inverter connected to the PV 

strings. The inverter’s DC voltage range will dictate 

operating conditions experienced by the module-level 

electronics. For this 1000V commercial system, a central 

inverter with wide maximum power tracking (MPPT) range 

is assumed – 500V – 850V. However, in the 100% 

elongation case, the PV string voltage is so far above the 

inverter DC input spec that the inverter can be considered to 

have a fixed DC input voltage of 850V. The use of high 

fixed-input-voltage inverters can result in additional 

performance and cost improvements [18].

IV. SIMULATION OF POWER OPTIMIZER OPERATING 

CONDITIONS

A. Partial shading simulation method

A detailed analysis is conducted of the moderate shading 

case described in [14] to estimate the operating conditions of 

either buck or buck-boost power optimizers under such 

shading conditions. The irradiance-weighted histogram of 

operating conditions for the different power optimizers in the 

system forms the basis for a weighted efficiency 

measurement.

A ray-tracing analysis is conducted to estimate the celllevel and module-level irradiance on the system, based on 

irradiance data for a nearby site in Denver, CO. Partial 

shading is assumed to block the direct-beam component of 

irradiance, allowing diffuse irradiance to still reach the 

shaded portion of the module. The performance of the buckboost power optimizer Conv1 is modeled based on its ideal 

Figure 3. Site survey details for 66 residential installations. Distribution 

best fit is log-normal with μ = 2.025 and σ = 1.11. The asterisk * indicates 

the amount of shade for the shaded installation discussed here.
4

This report is available at no cost from the 

National Renewable Energy Laboratory (NREL) 

at www.nrel.gov/publications.

behavior as described in [19]. Output power Pout = ηPin

where η is conversion efficiency, determined from Eq. (1) 

and (2) above. Additional assumed operating constraints of 

Conv1 include a fixed maximum output voltage of Vout = 50 

V and Iout = 9 A.

Input conditions to the power optimizer are determined 

by scaling the module’s Vmp and Imp based on the Sandia 

array performance coefficients [20]. The Sandia model takes 

meteorological inputs including temperature, wind speed and

the reduced irradiance Ee, based on the plane-of-array 

irradiance GPOA and the 1000 W/m2 reference irradiance Gref. 

Shading is accounted for by determining the fraction of a 

module covered by shade. For each 1/3 of a module 

containing shade (representing the 3 bypass-diode protected 

submodules), the input power is reduced by 1/3. If more 

than 1/3 of a module contains shade, the module is assumed 

to operate at a low-current, high-voltage local maximum 

point, such that Ee = Gd / Gref where Gd is the diffuse 

irradiance. This accounts for real-world input voltage limits 

of available power optimizer devices. Note that temperature 

is assumed to be constant across the array.

B. String lengthening simulation method

Annual performance conditions of the modules in 

Scenarios 2 and 3 are based on measured PV performance of 

a crystalline silicon module deployed at NREL’s Outdoor 

Test Facility. These data are measured every 15 minutes 

over a year’s deployment, with power-weighted distributions 

of module temperature, Vmp and Pmp shown in Figure 4. Note 

that for consistency the measured PV current and voltage 

parameters are scaled to match the nameplate ratings of the 

208W Sharp panel used in this work.

To generate annual operating histograms of DC power 

optimizers in the two string lengthening scenarios, the 

converters’ Vin is determined directly by scaled experimental 

Vmp of the modules. Each converter’s module level Vout is 

assumed equal to Vin so long as the associated string voltage 

lies within the inverter MPPT range of 500-850 V; otherwise 

string voltage is clamped to the upper or lower limit 

(typically the upper limit in these scenarios), and the module 

level Vout is scaled proportionally. Pin for each converter is 

also determined directly by the module’s scaled experimental 

Pmp. Efficiency η is calculated based on Eq. (1) and (2). In 

generating operating histograms of M = Vout / Vin and 

weighted efficiency, values at each time point are weighted 

by Pin to reflect their contribution to cumulative energy in 

kWh.

V. SIMULATION RESULTS

Results of annual simulations are distilled into 

histograms of the operating conditions seen by the power 

optimizers in each of the three scenarios. Two operating 

conditions in particular are required for calculation of 

weighted efficiency according to Eq. (1) and (2): input power

and M = Vout / Vin. The next two sub-sections will discuss 

these annual operating conditions for the three scenarios, 

along with annual conversion efficiency based on these 

histograms.

A. Simulation results: Power histogram

An annual histogram of the module-level power 

optimizers’ input power Pin is given in Figure 5 for the three 

scenarios. Also plotted in Figure 5 is the CEC efficiency 

scaling for inverter static efficiency, given by:

PCEC = 0.04 P10% + 0.05 P20%+ 0.12 P30% +

0.21P50%+ 0.53 P75% + 0.05 P100% (3)

where PXX% indicates input power in Watts at XX % of the 

maximum power optimizer output, set here to P100% = 245W.

Both CEC plot and scenario histograms are scaled to a total 

annual probability of 1.

Figure 5 shows that there is a slight difference between 

the modeled power histograms and the CEC weighting, 

Figure 4. Module temperature (top) Vmp distribution (center) and Pmp 

distribution (bottom) of one year’s deployment of an open-rack crystalline 

– Si PV module. Parameters are scaled to match nameplate parameters of a 

Sharp ND-208 module, and weighted by power.

Figure 5. Power-weighted Pin histogram of the module-level power 

optimizers for a full year simulation, Scenarios 1 - 3. The power weighting 

for the CEC inverter test method is shown for reference.

-20 -10 0 10 20 30 40 50 60

Module Temp (C)

15 20 25 30 35

Module Vmp (V)

0 50 100 150 200 250

Module Power (W)

0

0.02

0.04

0.06

0.08

0.1

0.12

0 50 100 150 200 250

Annual probability

Power Optimizer Pin (W)

Scenarios 2 & 3

Scenario 1

CEC Weight
5

This report is available at no cost from the 

National Renewable Energy Laboratory (NREL) 

at www.nrel.gov/publications.

however the general shape remains the same. For the shaded 

histogram of Scenario 1, there is a flattening of the 

distribution and a shift towards lower Pin. This reduction in 

Pin can be understood as the effect of partial shading on the 

system, dropping the production of shaded modules for a 

portion of the time while the system experiences partial 

shading. The unshaded histogram of Scenario 2 & 3 

indicates that there may also be climactic differences 

between these simulations (Denver, CO) and the California 

location chosen for the CEC weighting.

B. Simulation results: Vout / Vin and η histogram

The second operating histogram required to calculate 

power optimizer η is M = Vout / Vin which is shown in Figure 

6 for the three scenarios. Again, histogram counts are scaled 

by Pout and normalized such that total annual probability = 1. 

For Scenarios 1 & 2, operation at M = 1 is much more 

prevalent than any other operating mode. M = 1 accounts 

for 60% of the annual kWh produced for the Scenario 1 

simulation, and 83% of annual kWh for the Scenario 2 

simulation. For Scenario 3, the distribution was not centered 

at Vout / Vin = 1, instead having a more broad distribution 

between M = 0.7 – 0.8. This is due to the inherent mismatch 

between the string Vmp of 1300 V and the inverter’s input 

voltage of 850 V, requiring the power optimizers to 

constantly operate in buck mode to match the string voltage 

to the inverter input voltage.

Given the annual operating conditions of Figure 5 and 

Figure 6, DC converter efficiency η can be calculated for 

each scenario with Eqs. (1) and (2). An annual histogram of 

η is compiled for each use scenario, and shown in Figure 7. 

The partially shaded installation of Scenario 1 and the 30% 

elongated string system of Scenario 2 each have similar 

efficiency distributions, centered around η = 0.978. The 

efficiency distribution of Scenario 3 is shifted to lower 

efficiency, due to the large percentage of time operating at M

≠ 1.

The η histograms of Figure 7 can be integrated to obtain 

annual power-weighted efficiency of the DC-DC converter 

in each of the three scenarios considered. These integrated 

values are shown below in Table I.

TABLE I. ANNUAL SIMULATED EFFICIENCY OF DC

POWER OPTIMIZER CONV1 IN THREE SCENARIOS

Scenario # Power-weighted η

1: Partial shading 97.5 %

2: 30% Longer String 97.6 %

3: 100% Longer String 97.0 %

VI. ALTERNATE WEIGHTED EFFICIENCY CALCULATION 

Section V illustrated a method for calculating weighted 

efficiency of a DC power optimizer for specific scenarios. 

However, detailed knowledge of an intended use scenario is 

not necessarily available. Also, to be generally usable, 

calculations of power optimizer efficiency (which could be 

included in datasheets, etc) should represent a wide range of 

operating conditions, yet require only limited data 

measurement points.

For these reasons, a proposed standard weighted 

efficiency method is suggested which does not require sitespecific power or Vout / Vin histograms. Instead, more general 

functions for both Pin and M are used. Several measurement 

options will be considered, with the impact on calculated η

compared with full simulated η’s of Table I.

A. General Pin histogram

Close agreement between Eq. (3) and simulated power

histograms (Figure 5) suggests that we use the existing CEC 

power weighting method for our standardized η

measurement. Eq. (3) provides the values of Pin at which η

measurements are made, and the weight to apply to each 

measurement. This power weighting is most accurate for 

similar fixed-tilt, high irradiance locations.

B. General M=Vout / Vin histogram

An impediment to determining a general histogram for M

is that the use scenario greatly affects the shape of M. We 

Figure 6. Annual histogram of Vout / Vin, three power optimizer scenarios. 

Histogram is scaled by Pin and plotted on a log scale. Scenarios 1 and 2 are 

peaked and centered at M = 1. Scenario 3 has a maximum at M = 0.7.

Figure 7. Annual power-weighted conversion efficiency for the three power 

optimizer scenarios.

0.001

0.01

0.1

1

0.6 0.8 1 1.2

Annual probability (log scale)

M = Vout / Vin

Scenario 2

Scenario 1

Scenario 3

0

0.2

0.4

0.6

0.8

1

0.96 0.965 0.97 0.975 0.98 0.985

Annual probability

Conversion efficiency η

Scenario 2

Scenario 3

Scenario 1
6

This report is available at no cost from the 

National Renewable Energy Laboratory (NREL) 

at www.nrel.gov/publications.

will begin by assigning a general histogram to apply in cases 

such as for Scenario 1 and Scenario 2, then discuss possible 

histogram choices for cases such as Scenario 3.

As shown by the peaked Vout / Vin distributions for

Scenario 1 and Scenario 2 (Figure 6), DC power optimizers 

operate under M = 1 conditions for a majority of the time, 

even in PV systems with moderate partial shading. This will 

generally be true for PV systems where the string Vmp is 

within the inverter’s input voltage window; for instance, 

where PV strings are designed to have equal length, and 

where string length is chosen by conventional methods, or 

with a moderate increase in string length ≤ 30%. For these 

cases, M can be modeled relatively closely by a single-point 

distribution at M = 1, since probability drops off rapidly for 

M ≠ 1. Therefore, the first standard η measurement method 

considered here is one where each power measurement 

condition of Eq. (3) is taken at the single point M = 1.

However, as is shown by the analysis of Scenario 3, 

when a significant mismatch exists between the string 

voltage and the inverter input voltage, DC power optimizers 

play a more active role in mitigating mismatch. This would 

also be the case if PV strings of unequal length are connected 

to the same inverter channel. In these constant mismatch 

cases, power optimizers operate continuously at M ≠ 1.

For systems resembling Scenario 3, where string Vmp is 

outside the inverter’s MPPT range, a different annual 

histogram for M may be more appropriate. Of course, a sitespecific distribution would be ideal, but in this study we 

consider two general distributions: a uniform distribution 

assigning equal weight for all values of M across the 

conversion range of the device from M = 0.25 to M = 1.25 

(suggested in [13]), and a linear triangle distribution, peaked 

at M = 1 and reaching a probability of zero at M = 0.25 

(suggested in [21]). These general distributions are illustrated 

in Figure 8 along with the single-point voltage distribution 

already discussed.

By measuring the efficiency of Conv 1 at each 

combination of CEC power value (Eq. 3) and value of M

called out in Figure 8, one may calculate a non-site-specific 

weighted converter efficiency. The measured weighted 

efficiency values resulting from these three distributions are 

given in Table II.

C. Comparison of weighted efficiency methods

Table II shows a comparison between the site-specific

simulated η values of Table I and the proposed weighted 

efficiency distributions as described above. Weighting 

values are applied at the Pin / Pmax values shown in Eq. (3) 

and the Vout/Vin values of M = [0.25, 0.65, 0.85, 1, 1.25]. 

Three distributions of M are represented along with a singlepoint η value based on the maximum efficiency measured 

during the test.

The most accurate general method for calculating η for 

each scenario is highlighted in green. For Scenarios 1 and 2, 

the M = 1 distribution provides an estimate of η that matches 

particularly well. The fact that these two scenarios (partial 

shading and 30% string lengthening) operate for a great deal 

of time at M = 1 means that neglecting other M operating 

conditions has limited impact on η calculation accuracy. 

However, Scenario 3 has an annual weighted efficiency that 

is much lower than the other two scenarios, and is not 

modeled particularly well by either the Uniform or Triangle 

distribution of Figure 8. Scenario 3 would best be 

represented by a uniform distribution from M = 0.7 – 0.8, or 

a single-point value of M in that range. It would be more 

appropriate to utilize a site-specific distribution for M in the 

case of such a large mismatch between string Vmp and the 

inverter input window.

In all scenarios the maximum measured efficiency of 

98.0% is not representative of the weighted efficiency, since

it does not represent the total operating conditions 

experienced by power optimizers in real PV installations.

VII. CONCLUSIONS

Weighted power optimizer conversion efficiencies have 

been presented based on three scenarios, including a 

moderately shaded scenario and two ‘string lengthening’ 

scenarios. The power optimizer conversion efficiency was 

found to depend greatly on how well matched the inverter 

input voltage was with the PV string Vmp. For PV systems 

with a designed string-level Vmp within the inverter’s input 

voltage window, a site-independent measurement method 

was described for simplified weighted efficiency calculation. 

Namely, the CEC power weighting should be used, along 

with a single-point M = 1 voltage distribution. However, for 

Figure 8. General M distributions considered for a weighted efficiency 

method. Green line is single-point M = 1 distribution for Scenarios 1 & 2. 

Red box is a uniform distribution. Blue lines indicate a triangle 

distribution. 

TABLE II. EXPERIMENTAL η OF CONV1 POWER OPTIMIZER,

EVALUATED WITH FOUR WEIGHTING METHODS. 

CEC, M = 1

CEC, 

Uniform M

CEC, 

Triangle M

Max 

efficiency

Scenario 1: 

97.5 %

97.6% 96.7% 97.3 % 98.0%

Scenario 2: 

97.6 %

97.6% 96.7% 97.3 % 98.0%

Scenario 3: 

97.0 %

97.6% 96.7% 97.3 % 98.0%
7

This report is available at no cost from the 

National Renewable Energy Laboratory (NREL) 

at www.nrel.gov/publications.

systems using fixed input voltage inverters, or those with 

significant voltage mismatch between parallel strings, a sitedependent analysis may be required for accurate conversion 

efficiency estimates, since significant site-to-site variation 

may exist in the annual weighted efficiency.

REFERENCES

[1] C. Podewils and M. Levitin, “Hidden powers,” Photon magazine, 

November 2010

[2] M. Gross, S. Martin and N. Pearsall, “Estimation of Output 

Enhancement of a Partially Shaded BIPV Array by the use of AC 

Modules,” in 26th IEEE Photovoltaic Specialists Conference, 1997

[3] C. Deline, “Partially Shaded Operation of Multi-String Photovoltaic 

Systems,” IEEE Photovoltaic Specialists Conference, Honolulu, HI, 

2010. 

[4] C. Deline, B. Marion, J. Granata and S. Gonzalez, A Performance and 

Economic Analysis of Distributed Power Electronics in Photovoltaic 

Systems. NREL Report No. TP-5200-50003. Golden, CO: National 

Renewable Energy Laboratory, December 2010. 

http://www.nrel.gov/docs/fy11osti/50003.pdf.

[5] S. MacAlpine, R. Erickson and M. Brandemuehl, “Characterization 

of Power Optimizer Potential to Increase Energy Capture in 

Photovoltaic Systems Operating Under Nonuniform Conditions,” 

IEEE Transactions on Power Electronics 28 pp 2936-2945, 2013

[6] S. Poshtkouhi, V. Palaniappan, M. Fard, and O. Trescases, “A general 

approach for quantifying the benefit of distributed power electronics 

for fine grained mppt in photovoltaic applications using 3-d 

modeling,” IEEE Transactions on Power Electronics, vol. 27, no. 11, 

pp. 4656–4666, 2012.

[7] N. Femia, G. Lisi, G. Petrone, G. Spagnuolo and M. Vitelli, 

“Distributed Maximum Power Point Tracking of Photovoltaic Arrays: 

Novel Approach and System Analysis,” in IEEE Transactions on 

Industrial Electronics, Vol. 55, No. 7, July 2008, pp. 2610-2621.

[8] B. Burger, B. Goeldi, S. Rogalla and H. Schmidt, “Module Integrated 

Electronics – An Overview,” in 25th European Photovoltaic Solar 

Energy Conference and Exhibition, 2010.

[9] A. Elasser, M. Agamy, J. Sabate, R. Steigerwald, R. Fisher and M. 

Harfman-Todorovic “A Comparative Study of Central and 

Distributed MPPT Architectures for Megawatt Utility and Large 

Scale Commercial Photovoltaic Plants,” Proceedings of Industrial 

Electronics Conference(IECON) 2010, pp. 2753-2758.

[10] M. Agamy, M. Harfman-Todorovic, A. Elasser, J. Sbate, R. 

Steigerwald, Y. Jiang and S. Essakiappan, “DC-DC Converter 

Topology Assessment for Large Scale Distributed Photovoltaic Plant 

Architectures,” proceedings, IEEE Energy Conversion Congress and 

Exposition, 2011 

[11] W. Bower, C. Whitaker, W. Erdman, M. Behnke, and M. Fitzgerald. 

Performance test protocol for evaluating inverters used in gridconnected photovoltaic systems, 2004, available online at 

http://www.energy.ca.gov/renewables/02-REN1038/documents/2004-12-01_INVERTER_TEST.PDF

[12] EN 50530, Overall efficiency of PV inverters, CENELEC, December 

2008

[13] R. Bründlinger, N. Henze, G. Lauss and J. Liu, “Module integrated 

power converters – a comparison of state-of-the-art concepts and 

performance test results,” 26th European Photovoltaic Solar Energy 

Conference and Exhibition, 2011 

[14] Solar Works. Private communication. August 2011.

[15] Solmetric Inc. “Application Note: Understanding the Solmetric 

SunEye,” March 2011. http://resources.solmetric.com 

/get/UnderstandingTheSolmetricSunEye-March2011.pdf. 

[16] 2008 National Electrical Code, Section 690.7 National Fire Protection 

Association, Inc., Quincy, MA, 2002.

[17] L. Gun, “Module Level Power Management Decreases PV Costs and 

Risks,” Proceedings, ASES World Renewable Energy Forum, 2012 

[18] HDPV alliance website, http://www.hdpv.org/

[19] P. Tsao, “Simulation of PV systems with power optimizers and 

distributed power electronics,” 35th IEEE Photovoltaic Specialists 

Conference (PVSC), 2010.

[20] D.L. King, W.E. Boyson, J.A. Kratochvil, “Photovoltaic array 

performance model,” Sandia Report No. SAND2004-3535, 2004

[21] SolarEdge. Private communication. May 2013.