A New Approach Final Subcontract rt
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Juary 1996 • NRE-411-20279 Photovoltaic tion Equations: A New Approach Final Subcontract A. J. Anderson Sunset Technology Highlands Ranch, Colorado �·� .n����=· ¥ -- Naon Renewable Energy Laboratory 1617 Cole Boulevd Golden, Colorado 80401-3393 A national laboratory of the U.S. Deparent of Energy Managed by Midwest Research Institute for the U.S. Depent of Energy under Contract No. DE-AC36-83CH10093
Transcript of A New Approach Final Subcontract rt
January 1996 • NREUTP-411-20279
Photovoltaic tion Equations: A New Approach
Final Subcontract rt
A. J. Anderson Sunset Technology Highlands Ranch, Colorado
�·� .n����=· ¥
--
National Renewable Energy Laboratory 1617 Cole Boulevard Golden, Colorado 80401-3393 A national laboratory of the U.S. Department of Energy Managed by Midwest Research Institute for the U.S. Department of Energy under Contract No. DE-AC36-83CH10093
NREL/TP-411-20279 • UC Category: 1250 • DE96000507
Photovoltaic lation Equations: A New Approach
Final Subcontract
A. J. Anderson Sunset Technology Highlands Ranch, Colorado
NREL technical monitor: L. Mrig
National Renewable Energy Laboratory 1617 Cole Boulevard Golden, Colorado 80401-3393 A national laboratory of the U.S. Department of Energy Managed by Midwest Research Institute for the U.S. Department of Energy under contract No. DE-AC36-83CH10093
Prepared under Subcontract No. TAD-4-14166-01
January 1996
This publication was reproduced from the best available camera-ready copy
submitted by the subcontractor and received no editorial review at NREL
NOTICE
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INTRODUCTION
The author is grateful for the guidance provided by Richard DeBlasio and Laxmi Mrig, managers for the National Renewable Energy Laboratory. In addition, the author wishes to thank Ben Kroposki, Keith Emery, and Carl Osterwald of the NREL technical staff for their assistance in gathering test data and for providing many helpful suggestions.
FOREWORD
The equations and methodology presented in this report are intended to improve the accuracy and to simplify the translating of PV performance values from one set of temperature and irradiance conditions to any other set of conditions. It should be noted that many such methods are available, all varying in the degree of mathematical and physical sophistication and difficulty. The equations presented herein are intended to provide engineers and analysts with a simple yet accurate means of performing the calculations with an ordinary handheld calculator. The introduction of dimensionless temperature and irradiance coefficients further simplifies matters because these coefficients are the same (or nearly so) for a cell, module, panel, or large complex array, and in many cases are very similar for PV products of different manufacturers.
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INTRODUCTION
This work was performed under NREL Subcontract No. TAD-4-14166-01. It resulted from a need to develop a better method for predicting the performance of photovoltaic devices over a wide range of temperature and irradiance conditions. Frequently such performance is only known at one condition, and the need to extrapolate these results to some other set of conditions is essential. The most commonly used method of translating PV performance from one condition to another was difficult to use and was found to produce poor results at low irradiance levels. Because the mos! frequently occurring irradiance conditions are either very high (900 to 1 000 W/m� or very low (200 to 300 W/m�*, the translation equations need to be valid over a wide range of conditions to be useful.
Some initial work on this subject was performed in collaboration with NREL personnel participating on the IEEE-SCC 21 PV standards committee. During this work, a test program was conducted that revealed the inaccuracies of the then-current methods. This, in tum, led to the support of this new method by NREL. It should be mentioned that work is continuing on the development of new, improved equations. These will be even simpler to use, they will account for changes in fill factor, and they will be expanded to include equations for the current and voltage at the maximum power point (lmax and V..,.J.
* Low irradiance occurs very frequently as a result of overcast conditions, intermittent cloudpassage, and every day at sunrise and sunset.
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CONTENTS
Page Clause
1 SUMMARY ................................................................................................................... 3
2 HISTORY ..................................................................................................................... 5
3 BACKGROUND ........................................................................................................... 6
4 DERIVATION ............................................................................................................... ?
5 EQUATION CHECKS ................................................................................................. 13
6 PROCESS .................................................................................................................. 20
Appendixes
1 APPENDIX A ............................................................................................................. 22
2 APPENDIX 8........................................................................................................ ..... 29
3 APPENDIX C .................................................................. . .......................................... 70
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1 Summary
PHOTOVOLTAIC TRANSLATION EQUATIONS
A NEW APPROACH
New equations were developed for the purpose of evaluating the performance of photovoltaic cells, modules, panels, and arrays. These equations enable the performance values determined at one condition of temperature and irradiance to be translated to any other condition of temperature and irradiance. The equations were developed to satisfy the following goals:
• The equations should more accurately translate the short-circuitcurrent, lsc. and the open-circuit voltage, V0c . In particular, theinfluence of irradiance on V0c should be more accurately treated .
• The equations should more accurately and more simply translatethe 1-V curve data point pairs, I; and V; .
• The equations should be based on the use of dimensionlesscoefficients such that a and J3 have units of oc -1 , and not, forexample, amps/ oc or volts/ °C.
• An equation should be developed for translating the maximumpower without involving the translation of lsc. V0c, or any 1-V datapairs.
All of these goals were successfully met. The data which is presented in this report shows good agreement between the analytical predictions made with the new equations versus actual test measurements, and superior performance when compared to the current translation equations. The agreement is usually within 5%, which is very good considering that the data used undoubtedly contain some measurement errors, and that the translations were made over an extremely wide range of temperature and irradiance conditions:
• For device temperatures from 25 °C to 75 °C
• For irradiance levels from 100 to 1000 W/m2
In spite of the success of this program, further evaluation of these equations is necessary. Additional checks need to be made for other PV technologies, for larger modules, and for modules that have less-than-perfect performance characteristics, such as shunts. Also, some improvements to the equations themselves are possible. The equations presented are a compromise between simplicity, accuracy, and convenience.
A comparison between the currently used equations and the new equations is presented on Table 1.
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Table 1
COMPARISON OF THE ORIGINAL (JPL) TRANSLATION EQUATIONS AND THE NEW EQUATIONS
OLD EQUATIONS
1 ). lsc2 = lsc1 + lsc1 · (�� -1) +a· (T2 · T1)
!!. lsc = lsc2 - lsc1
2). No equation available for direct computation of V0c2
3). 1-V Data Pair Translation:
A. V2 = V1 - p · (T2 - T1 ) - !!. lsc · Rs - k · (T2 - T1) · bB. b = l 1 + !!. lsc
4). P2 = l2 · v2
5). No equations available for PMAX
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1).
NEW EQUATIONS
1 _
lsc1 SC2- [ 1 +a · (T1 -T2 )]· [ E1 I E2]
2). V. _ Voc1 OC2- [1 + P · (T1- T2)]· [1 + 8 -ln(E11E2)j
3).
4).
5).
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1-V Data Pair Translation:
A. v2 = v., . ( voc2) VOC1
B. 12 =I, ·(lsczJ I
set
P2 = l2 · v2
(lsc2) (Voc2) PMAX2 = PMAX1 . lsc1 . Voc1 , or
R - PMAX1 . (E2 I E1) MAX2- [1+y · (T1-T2)]·[1+1l·ln (E11E2)]
,.. b.__d t;_;: �
2 History
The history of the translation equations currently used throughout the world dates back to an IEEE paper' by J. D. Sandstrom of the Jet Propulsion Laboratory (JPL) published in 1967. Thiswork was performed in conjunction with Mars and Venus space mission analysis. The paper presents some very good correlative results between experimental measurements and the resultant analytical predictions over a cell temperature range from 20 °C to 130 °C, and overan irradiance range of 500 W/m2 to 3000 W/m2. The equations presented in this 1967 paperare the same as those used today:
where E = ir�adiance, W/m2
I = current, amps lsc = short circuit current, amps v = voltage, volts T = cell temperature, °C o; = current coefficient, amps/ °C 13 = voltage coefficient, volts/ °C Rs = module series resistance ohms p = power, watts k = curve correction factor
1 and 2 = conditions at a specific irradiance level and cell temperature.
These equations have been in widespread use for nearly 30 years and are employed in ASTM Standard E1 036 and in IEC Standard 891. Almost all of the field performance measurements, all system sizings, and all of the PV manufacturer's factory data analysis are based on these equations.
1"A Method for Predicting Solar Cell Current-Voljage Curve Characteristics as a Function of Incident Solar Intensity and Cell Temperature", J.D. Sandstrom, JPL, Conference Record of the Sixth Photovoltaic Specialist Conference, IEEE, Cocoa Beach, Florida March 1967.
3 Background
Interest in translation equations arose at an IEEE SCC21 meeting in San Ramon, California, on January 16, 1991. This IEEE group was working on some new versions of the Sandstrom equations using dimensionless coefficients (actually °C ·' units) for a and 13. Module testing was conducted to check on the correctness of these new equations.
To perform this equation check, a matrix of 1-V curve data was generated for a wide variety of irradiance levels, module temperatures, and PV technologies. It was found that the proposed equations did not check well with the test data. More importantly, it was found that the original Sandstrom equations did not check well with the test data either.
• The form of the equations for illsc and 12 suggests that the temperature effect oncurrent is independent of irradiance; i.e., the term a · (T2 - T,) gives the samenumber of milliamps of change at 100 W/m2 as it would at 1000 W/m2 irradiance.This is incorrect; the effect is actually proportional to irradiance. Sandstrom notedthis by stating that a is not a constant, but varies with irradiance. However, intoday's usage of these equations, a is treated as a constant. So, the originalequation of Sandstrom is correct, but the usage of it is erroneous. The problem iseasily solved by modifying the current equation as follows:
• The irradiance effect on V0c is accounted for by the term illsc · R8, and for his data(single cell with R8 = 0.5 ohm) Sandstrom found a good correlation. However, if onevisualizes an experiment wherein a variable series resistor is built into a PV moduleand then V0c is measured at two different irradiance levels, it will be found that theVac values measured at these two light levels are the same no matter how much theseries resistance is changed. In fact, for the data presented herein, thepolycrystalline module has a series resistance of 6.1 ohms, and the single crystallinemodule has a series resistance of 1.2 ohms, and yet they have nearly identicalvoltage - irradiance characteristics (neither of which matches the illsc · R8 equation).However, the V0cs do match the following equation:
6). V. _
Voc1 oc2- [1 + 8 ·In (E1/E2)]
Note that this equation is also completely independent of the module series resistance.
The accuracy of the Sandstrom equations can, therefore, be improved by making the two corrections discussed above. However, even better equations can be derived.
4 Derivations
The modified Sandstrom equations still rely on a and i3 coefficients that carry dimensions, amps/ °C and volts/ °C. This means that anytime a manufacturer "rearranges" the circuit by changing cell size, changing the number of cells in a module, or by changing the series-parallel cell arrangement in a module, these coefficients change. Also, if a user has more than one module, the coefficients are different depending on whether he connects the modules in series, in parallel, or in a combination series-parallel arrangement. It was found that much of the time the wrong coefficients were being used. So, modified Sandstrom equations were developed based on "neutered" coefficients because these are independent of the configuration. When used this was they are constants.
When the a and 13 coefficients have dimensions of amps/°C and volts/°C, they are defined as:
7).
8).
Transposing these and solving for lsc2 and V0c2 gives the following:
9). lsc2 = lsc1 +a . (T2 - T1 )
But when the coefficients are "neutered", they are defined as follows:
11).
12).
These equations transpose to the following:
13).
14).
lsc2 = [ ]1 +a · (T1 - T2)
And, if we now account for any irradiance changes, these equations become:
15).
16).
These are the new equations for l5c and V0c that are being presented and evaluated. These equations incorporate the following features and characteristics:
• The form of the 15c equation has been changed such that the irradiance level"magnifies" or "shrinks" the temperature correction effect.
• A V0c equation has been derived that accounts for the irradiance using alogarithmic term rather than as a series resistance effect.
• The coefficients a. and i3 have been "neutered," and the equation form has beenaltered to account for this new definition of a. and !3.
The next major goal pursued was developing a better method for translating 1-V curve data points. The Sandstrom equations were lengthy and difficult to use and relied upon the knowledge of the module (or panel, or array) series resistance and on another mysterious constant, k, known as the curve correction factor. Another bothersome point was the unusual translation of points; lsc1 did not translate to l5c2 and Voc1 did not translate to Voc2· A new idea was tried based on translating 1-V data from condition 1 to condition 2 along lines of constant load resistance. This would result in l5c1 translating to l5c2 along the line R = 0 ohms, and, V0c1 would translate to V0c2 along the line R = co. The 1-V point pairs in between would similarly translate along lines of constant resistance with values of R = V; I I; .
R = OO R =50
R= 200
R = 500
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This idea remained dormant until July 4, 1993 when the analysis was resumed. The idea of translating along lines of constant load resistance was studied, but was never perfected. In the midst of a very lengthy derivation of the constant load resistance translation equations, a new concept evolved. A set of equations that satisfied the goal that lsc1 would translate to lsc2 , and Voc1 would translate to V0c2 was simply to multiply each current point by the lsc ratio, and to multiply each voltage point by the Voc ratio :
17).
18).
19).
12 = I, . (lsc2) ISC1
. These equations were given a preliminary check by translating approximately ten 1-V curve data sets, and then checking these against actual test data. The translations were nearly perfect.
With equations 15), 16), 17), and 18) verified, it was now a simple matter to theorize a new translation equation for the maximum power, PMAX . Because each of the 11 x V1 and 12 x V2 products represents a power point, if equations 17) and 18) are multiplied together, a very simple equation for translating any power point (including Pmax) isobtained:
20). R _ R. (lscz) (Vocz) MAX2- MAX1. •
lsc1 Voc1
Frequently, 150 and V00 values are not known (such as would occur with an inverter operating at maximum power). Therefore, a power translation equation based on temperature and irradiance measurements is also desirable. Substituting 15) and 16) into 20) gives:
21).
To keep things simple, assume for the moment that T1 = Tz , so 21) becomes:
22).
One might be tempted to simplify this by assuming that 8 · In (E1 I E2) "' 0. However, this will cause significant errors. This term is very important, and it helps explain several puzzles:
• For small changes in irradiance (at any irradiance level, low or high), themaximum power seems to be directly proportional to irradiance. The reason isthat the term In (E1 I E2) is small when ( E11 E2) "' 1 because ln(1) = 0 and theterm [1 + 8 · In (E1 I E2)! "' 1. Therefore, P2"' P1 · (E1 I E2).
• A plot of maximum power versus irradiance <Pmax vs E) is usually very linear, butdoes not appear to pass through the 0, 0 point on the plot as it should. Thereason for this is because the term [1 + 8 · In (E1 I E2)] is normally small until E2gets very close to 0. Then, as E2 -+ 0, [1 + 8 · In (E1 I E2)] -+ oo and P2 -+ 0.
Finally, between equations 21) and 22) it was assumed that T1 = T2 to simplify the derivation of 24). We now need to re-insert the temperature effect. This is best accomplished by introducing a new power-temperature coefficient, y, which is defined as follows:
23).
When this is transposed and combined with equation 22), the final equation for PMAX is obtained:
24).
Equations for the maximum power point current and voltage, I max and Vmax translation are also being developed, but have not been adequately checked against test data at this point. However, equations for fill factor (FF1 and FF2) can be stated by definition:
25).
26).
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One final point needs to be discussed. The astute reader has probably noticed that when the coefficients a, J3, y, and o were non-dimensionalized, the neutering denominator was selected as the condition 2 value; e.g., see equations 11), 12) and 23). It might be logically asked: "Why was this done, and what would have happened if condition 1 had been selected as the neutering denominator?" To answer this question, consider the following derivation using V00 as the example.
Because the data correction is normally made from some hot field condition (V 001 , T 1 ) to the standard condition CVoc2 , T2 = 25 °C), the "neutering denominator" could logically be the STC value which in this case is V0c2. Hence, the "neutered J3" is defined as:
27).
Rearranging this equation results in the equation for voltage using the "neutered J3":
28).
Now, one might argue that this equation is good for correcting hot field test data back to STC, but what if the translation were made the other way, from STC (lsc1 , Voc1 , Pmax1 , T1 , E1) to the hot field condition Osc2 , V0c2 , Pmax2 , T2 , E2). In this case, wouldn't adifferent equation 28) evolve? Because the "neutering denominator" used to calculate J3 was Voc at 25 °C, this would now be called V001 as a result of the reverse translation:
29).
Rearranging and solving for V0c2 gives what appears to be a different equation:
30). V0c2 = Voc1 · [ 1 + J3 · (T2- T1)] So, one might think that the basic equation 28) is only valid for a one-way translation, and equation 30) is needed for translating the other way but, it will now be shown that equations 28) and 30) are nearly identical. Consider an example wherein J3 = -0.004°C _, , V001 = 20.0 volts, T1 = 25 °C and T2 = 50 °C:
28). Voc2 = [ 1 + J3 (T1- T2)]20 Voc2 = 1-0.004(25-50) = 18.18 volts
V0c2 = 20 [ 1- 0.004 (50- 25)] = 18.00 volts ./
So, the error is very small (1%), and the same equation can be used for correcting either from STC or to STC, or actually, between any two points. The bottom line is that the neutered coefficients and the resultant equations are not exact (they may in fact not be as accurate as their non-neutered counterparts), but they do give a very good approximation, and they offer one outstanding benefit . . . . the neutered coefficients are constant . . . . they do not change (significantly) for a cell, a series module, a seriesparallel module, a panel, or an array.
The remaining question is: "which numerical value of V0c should be used to "neuter'' the voltage versus temperature slope?" Because this equation is for general use between any two conditions (and STC may not be one of them) the best choice is probably amid-range value of V0c for the irradiance and temperature range of interest.
5 Equation Check
A matrix of data was obtained on three modules: a Siemens single-crystal silicon module, a Siemens amorphous thin-film silicon module, and a Solarex polycrystalline silicon module. This matrix was obtained by warming the module to the desired temperature and maintaining it at that temperature by means of a flat, heater blanket located under the module. The entire module and heater assembly was installed in a solar simulator. When the desired temperature was reached, 1-V curves were taken with various porous filters covering the module. For the test series described in this report, very thin paper tissues were employed for filtration. These are actually full of small openings, so the light that penetrates was not spectrally altered. For each of the six temperature conditions (25, 35, 45, 55, 65 and 75°C) , a total of ten different filter layers were used (0, 1, 2 .... 9 layers). So, a 6X10 matrix (temperature x number of filters) was obtained. The filter layers were selected to give irradiance levels from approximately 100 W/m
2 to 1000 W/m
2.
Although it may seem like a complex task to obtain the required 60 1-V curves for each module, it was actually very simple and was easily accomplished in about 3-4 hours for each of the 3 modules. Tables 1, 2, and 3 (see Appendix A) present a summary of this m·atrix data (18c, V0c, and Pmax ).
Using the summary data from Tables 1, 2, and 3, the coefficients a, 13, y, and 8were determined as follows for the three different PV technologies.
Equation Single- Poly- Thin-Film
Coefficient Crvstal C[Ystalline Silicon
a , oc -1 0.00095 0.00090 0.00036
13 ' oc -1 -0.0031 -0.0040 -0.0028
y, oc -1 -0.0033 -0.0047 -0.0020
8 0.085 0.110 0.063
Note that the coefficient, 8, is inherently dimensionless because of the logarithmic nature of the equation in which it is used.
The equations in which these coefficients are used are reiterated as follows:
I _ lsc1
SC2- [1 +a· (T1 - T2)] · [(E1 I Ez)]
V _ Voc1
OC2-_ [1 + � · (T1 - T2 )] · [1 + 8 · Ari(E1 I E2 )]
(ISC2) (Voc2J PMAX2 = PMAX1 .--
. --lsc1 Voc1 , or
PMAX1 · (Ez I E1) PMAX2 = -
-----"-=-'-------'--..!::...._.......!.:__ __ _ [ 1 + y · (T1 - T 2 )]· [ 1 + 8 · In (E1 I E2 )j p
FFz = MAX2
lscz · Vocz
These equations translate lsc, Voc, and PMAX from the measured value at an irradiance level of E, , and a module temperature of T1 , to a new value at an irradiance level of E2, and a module temperature of T2 .The equations are valid for translation between any two conditions.
To check on the validity of the equations, analytical calculations were performed using these coefficients and equations to predict each of the 60 matrix entries using the single STC value as a starting point. Tables 4, 5, and 6 present these analytically derived matrices (see Appendix A). In other words, using a single STC value for lsc, V0c, and PMAX, the other 59 entries in each matrix were analytically predicted . The comparison between these analytical predictions and actual measurements can be made by comparing Tables 1, 2, and 3 (actual) to Tables 4, 5,and 6 (predicted). It will be noted that good agreement exists between the analytical predictions and the actual measurements for all three PV technologies.
These table-to-table comparisons are provided on the following pages (with the actual vs predicted values shown on the same sheet).
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After translating lsc and Voc using the above equations, the complete 1-V curve can next be translated by using the following equations for each 1-V pair.
for each current point on the 1-V curve, and
for each corresponding voltage point .
A total of 114 1-V curves were translated and were then plotted on the actual measured 1-Vcurve plots for this translated condition. These comparative plots are presented in Appendix B. In these examples, a reverse translation is demonstrated: the 1-V curves at STC are translated to various non-standard temperature and irradiance conditions.
The Appendix B results show that these new translation equations demonstrate good agreement for thin film silicon, polycrystalline, and single-crystal modules.
The new equations were next checked against the ASTM E1036 standard equations. A total of 54 1-V curves were translated using the ASTM E1036 standard equations, 18 each for singlecrystal, polycrystalline, and thin-film silicon modules. Within the group of 18 translations for each technology were a matrix of 1-V curve data for three modules temperatures (25, 45 and 65
°C) and six irradiance levels (approximately 1000, 650, 450, 350, 225, and 125 WI m2 ). Foreach technology, 13-14 1-V data pairs were chosen from the STC 1-V curve, and then a reverse translation was performed, wherein each data pair was translated to a non-standard temperature and irradiance data pair. The new equations were also used to make comparative translations. With the new equations, no modification or algebraic manipulation was necessary to accomplish the reverse translation; i.e. , the equations work properly between any two conditions because "dimensionless" coefficients (actually, units of oc-1 ) are used. For the ASTM E1036 reverse translation, modified equations had to be derived because even though the current coefficient, a, is "dimensionless," the voltage coefficient, J3, is not and carries units of volts/ °C.
Appendix C presents the graphical results for the 54 1-V curves that were translated using both the new equations and the standard ASTM E1036 equations. These analytical results are shown plotted against the actual test 1-V curve traces. The following conclusions can be drawn from these plots and the analytical operations:
• At 1000 WI m2 irradiance, the ASTM standard equations and the new equations givenearly identical 1-V curve translations. Agreement with the actual measured 1-V curves is excellent for all of the module temperatures and for all three technologies.
• As irradiance is reduced, the ASTM E1036 equations become increasingly erroneous.For example, the voltage error for the three technologies and the three module temperatures averages about 6% at 450 W / m2, and about 15% at 125 W / m2.
• As irradiance is reduced, the new equations remain very accurate. For example, the voltage error for the three technologies and the three module temperatures averages about 2% at 450 WI m2, and about 5% at 125 WI m2.
• The ASTM E1 036 standard erroneously treats irradiance and temperature effects oncurrent as additive effects, whereas they are actually multiplicative effects. This results in an erroneous translation of lsc , but the error is small.
• The ASTM E1036 standard equations contain at least three typographical equation errors·, and possibly six sign errors. The obvious typographical errors were corrected before the comparative analysis was performed. The remaining sign errors (if they are in fact actually errors) are believed to have only a small effect on the results, and were not corrected.
The ASTM E1036 standard equations are very complex and difficult to use, particularly when hand calculation methods are employed .
• The new equations are very easy to use, and are well-suited to hand calculationmethods.
• The new equations can be used to translate between any two conditions; STC neednot be one of these conditions.
• The new equations are based on neutered coefficients, and hence, the same coefficients and equations can be used for single cells, series-connected modules, parallel-connected modules, series/parallel-connected modules, panels, and even entire arrays with the modules connected in any manner.
6 Process
The complete process for gathering data, evaluating it, computing coefficients, and, finally, actually using the coefficients, is summarized as follows:
STEP 1 : A matrix of data is first derived. This matrix is obtained by warming the moduleto the desired temperature and maintaining it at that temperature by means of a heater blanket located under the module. The entire module and heater assembly are installed in a solar simulator. When the desired temperature is reached, 1-V curves are taken with various porous filters covering the module. Screens or thin paper tissues can be employed as filters. These have many small openings, so the light that penetrates will not be spectrally altered. For each temperature condition (25, 45 and 65°C as aminimum) , at least three different filter layers shou1d used. These p1ters should givefour irradiance levels from approximately 250 W/m to 1000 W/m (0, 1, 2 and 3 layers). So, a minimum 3X4 matrix (temperature x number of filters) will be obtained resulting in 12 data sets for the module.
Although it may seem like a complex task to obtain the required 12 1-V curves for each module, it is actually very simple, and can be easily accomplished in about 3-4 hours for a module.
STEP 2: The 1-V curve summary data is next transferred to data sheets that tabulate lsc, V0c and Pmax as a function of module temperature and irradiance. An examination of these tabulations will sometimes reveal erroneous data that can then be discarded or corrected by re-test.
STEP 3: The irradiance for each filter set is computed using the measured values oflsc. find assuming that the lsc value measured with no-filter equates to an irradiancelevel of 1000 W/m2.
·
STEP 4: A plot of Voc vs module temperature is made, and a best-fit line (least squaresfit or eyeball) is made through the data points. Because V0c is (nearly always) linear with temperature, discrepancies between the data points and the line can be used to deduce the "true" module temperature. Again, an examination of this plot will sometimes reveal erroneous data, which can then be discarded or corrected by re-test.
Repeat this process for lsc and Pmax vs module temperature.
STEP 5: Determine the slope of lsc , V0c, and Pmax versus temperature for eachirradiance level (actually for each filter set).
STEP 6: For each irradiance level, determine the slope of V0c versus the naturallogarithm of irradiance (In E) for each module temperature.
STEP 7: The coefficients a, 13, y, and o are next computed. Use the average value ofthe slopes obtained for a given variable. For example, for each irradiance level a slope of Voc vs temperature was determined. These should be averaged. For the "neutering denominator," use the aver�e or mid-range value of the dependent variable (for example, use the V0c at 45 C and 600 W/m2 for neutering the average of the V0c vstemperature slopes to compute 13).
STEP 8: Now the equations with the coefficients are ready to use for any combinationof module temperature and irradiance.
STEP 9: To translate an 1-V curve from a field test condition to STC, use the equationsand constants wherein:
Subscript 1 = field test condition
Subscript 2 = STC
To translate an 1-V curve from STC to some field condition, use the same equations and constants, but use:
Subscript 1 = STC
Subscript 2 = field condition
STEP 1 0: The complete 1-V curve (actually the 1-V data point pairs) is very easy totranslate, and can be quickly accomplished using a hand-held calculator:
a). Translate lsc1 to l5c2 using the lsc translation equation.
b). Translate Voc1 to V0c2 using the V0c translation equation.
c). Translate each 1-V current data point by multiplying by the l5c2 / lsc1 ratio.
d). Translate each 1-V voltage data point by multiplying by the V0c2 N oc1 ratio.
STEP 11 : Translate Pmax using one of the two equations provided. One is a "standalone" equation that does not require any lsc, V0c or 1-V data pair translations. The other equation is based on the lsc and V0c translation ratios, and is very simple to use.
In summary, all of the goals have been successfully met. The data that is presented in this report shows good agreement between the analytical predictions made with the new equations versus actual test measurement and superior performance when compared to the current translation equations. In spite of the success of this program, further evaluation of these equations is necessary. Additional checks need to be made for other PV technologies, for larger modules, and for modules that have less-than-perfect performance characteristics, such as shunts. Also, some improvements to the equations themselves are possible.
APPENDIX A COMPARATIVE VALUES FOR lsc, Voc, PMAX
ACTUAL MEASUREMENTS VS ANALYTICAL PREDICTIONS
TABLES 1 -6
NUMBER OF FILTERS-
lsc @ 25 · °C · · ·· ·· ------
@35 oc
.... --� �s_: oc-=-�=:�= @55 oc
·· -@65-"c·------
... . . . ___ @15 oc
- ·--
- Voc- !Y �:, "IJ @ 35 "IJ @45 °\J @55 oc
@65 °C - @75 °C -- -·- -
I:= !'max em �b oc
@35 oc ·t-- @45 ocJ��� ::� :g I - ..
- ... -··
•• · -- --·
@75 oc
"'�"ne WI m"
T ABLE 1-
ACT UAL MEASUREMENT S- MAT RIX DAT A SUMMARY- SINGLE CRYST AL SILICON
0 1 -----···· ··--
•.ct \_!:! . - • 5'78 · - · -��L _,_§,>!?._]___ , 'l3 r ,(,0� .'\38' • >'l� • q'-1?. '{.14 •'l!i3 • (,06
�0.31 111.so '"·''� l'lot"l l'l.l'l. Iii.�.� l!l.S"I! 1&',0'-J IS, 1'-l 11. C311.1.\'7 I'' q'J
I�' t:.'-1 7.'13 1::1.:1'3 1,qo \ lo �3 1.!5'8 \1,4?.. 1o2l llo 07 7.)1 10,57 '·73
IOOO (.35'
2 ......... , ____ .
• 418_! __ ':)�1. ·--
.L\33 ·'13'\.4'-jo.'-\'-\0
1'1.'37 ll'o_"}J li.al
\7, '3 1/.:ll 1�•5'5
5' •. Pi !), y� s,Jo s,o? 1-\, H· 1-J: 75
45C!
3 4 5
-- -------- ---��
• 315 ,l,O • ?.ll _! PL __ -·l'!i. ___ .!.J.18 __ '333 .:.\''1 , liB __
·331. • :l'71 ·117·335 ol70· ''-':l� ·3'-1.3 ,?.n .'l��
1'1.0?. 18'. 73 18'.�3 I i"i"l� _lld-:1 J1. t�11. 'iS l7.S3 17. �y17· :n IC.o&'l I�. Sli IC.o8'3 "So I�. :11 IC..?.o IS. B'i 15.5'3
L/,oe '3.�5 ,.,57 1-J, oq 3.1" :l.5"� \1,93 :3' 0'/ '). '14 3./i'l :l,qr; ?..:11 3.t:.'l :�An ;;1.3?.. �.5'8 :lo76 i :/, l!!
3�(. �g-(. ;l'?3 .
6 7 8 --
·17'. ·.1�1 • !3.3 _D_I'IS ol57 · 133 _. 1 85 ·I�� ol3_'1
"lll • 1.5"'! , IH '185 ol !i'l • I '3"1 • lqo ol �I • 1.18
\!!,Ill 17.�� 17· �� 11·. 0"8 !1. ;!'l l?.o.a I'·'!� "· 70 I'·�� le., ?.6' lr.,o'! 15"o18 1£, li� IS,�;!. \5" • .3'15 • .25' .I'!, '17 1'-lo?O
';! oq 1.73 1.48 ;l,Oq lo11 1.4\ I. '19 I. �5 1.3(. I. 87 I. S'7 l .32. 1.8'-1 lo53 lo �C. 1·78 lo'-17 \. :17..
ICfl I�& 14C..
9 -··· ---·· ···
• II 'I ·II� ·-· -
0 ··-··· ... ·-
•. 'Ill
-��-- ···· · ·· "" . -�j3_8_ ____
.II'! --�j__ .117 'q�o I l:l'J ,qo;.;
17.�1 �D.:" "L17_ lq,,s I t.ol � 1'1.07 IS', 5'f I,PJ� 1)5", II 18, Otf
IJ'l. '15 17.3"1
I, :13 1:1, "" 1.18 1�. I 'I 1.17 llo n. 1.13 II, �;:; l.o, '"·% I, O'i 10 '1'1
I�S I ClO I
------· ----·-·--··------ - · ---------
--
-
-
--- ··--········-······ ·· · - -· ·-·- ··- --·· · - ---·· ·--·-
r--------
--
---
--
-� �--
NUMBE_R OF FILTERS-
- -r;;.; � �ll 0v
! -� r-
1--
@35 oc --- -@ 45-··c·---·-----@55 oc
·--- @65 oc· ----
75"c ··-
.....
- -------
-- -
-�
1--1-
v�� � �ll 'v -- @ �ll 0\.i -- @45 °C @55 °C
1-- @65 °V @75 oc
1-
- P�ax @25 oc; ·+' @35 °C j----
@45 ocr- _ _@_§5 oc
. _ _@65 oc
_ ___ @ 75 oc
····-··· --· --------·-·---
. . - - - --·····--·-
- lrradiance;--w-hn2 ··- -· - - ·
�- -- � ��- ---- - �- �---
TABLE2
ACTUAL MEASUREMENTS. MATRIX DATA SUMMARY- POLYCRYSTALLINE SILICON
0 1 2 3 4 5 6 7 . 8 9 0
• at 'I .�OS" • 11.\8 .\l'l ,()�\ ·07:3 ,o�c '0.5"0 .0'-/3 •037 • 318 ---
'�:23 .lo 'l • IS:l. f-' U_L__ ....!&ll ,074 'Q!,'l_ 'O!}:J.. ,()4� -. 0.3'i. -- _,_1;]_?, __
·3.:1'1 ol.I'J.. • jo.Jq .II:; , O'lt .en> OC.:l. (}!;':) ,0'-15' . • 0.3;1._ ...!..12.3� .3:!..3 , ::11o , IS:l. .ttl • 0'12 • 07?.. . o, :1. (JI)'). Cl '-!� . o 3 -;>. '3�'1 • 3?. 7 ,lJO ·15\ • II 4 .ogg • 07<; .o'i'l • O'I3 ' oLJ<r .a� I �24 • 331 :115 ol5"7 •llq .osr.s ,07C. . Q (, :J. ,()5" � ,oy5 .0?-'l ,, 331
1----··-
;l.O,LJ4 l!f,qo I 'I ·•II Hl'.�f IF;,H 18. :1'l . 17. "' /7,,0 17 �-�C> I C.. C'fq I :Jo.4s \'!.75 \'!. l'l \F;,,'l ��. � 5' 11.lJf. 17.50 17·1' \G .. W".3 \,,So I�' \ q I Ill'. 10 1Cf,0_1_ tF;A8_ \1.'1'1 ,.., .5' :3 11, lo.J J(., 1c> 14o,3q '"" 7 l5, Bl I�. <I>; ��. 'l'l I!(, 33 \"1, 77 li.n I G.. 72 I(., 1-17 If., Ot;, 15".70 \5", 33 15,01 l'i • "10 18' •. 10 17.77 1'7' 1'·1 11..513 lr.. 15 \5", 7:1. ,\5".3'1 t"l.Rr. \1.-\,7 _5' 1'1. 31 !lli I ()!.I ''·'-1 1'1,07 Jt:..44 lSi '12 t.&;', 4S 15"; 01 !JI-J,C.'-1 14.?.1 13. '15 13, S5 \3,::ll 17.0::2.
1.\,Sr.j :;z.7a _lo'lO J.3g 1,07 • 8'3 I "'7 o53 oi.l'-l ·�' 4.51 4 .. 1S 1,, G.'l I, !ri 1,'?.5' I, O'l- ,jq '{._1 • 5'1 .4� 34 •L3'l 4.1'1 I ?. r.t 1.75 t. ;n o,q7 ,?'{ . '0 .'lq • 45 .3:1.. •l.tS 4,01 :;) ' Lj (, 1•70 t. \ 8' o. 'i� ,72 I ')7 ,45 .�8 c3CL_ __ 3...1.7__ _ __
3.�1( :2,3(, I,(. o I. J(, . &. 8� .�L_ I ;j() • •1'1 '11. .�o �,1(2 13.1(') I 2, :1'1 I ' ')'1 ),\� O,R-5 .GoG • 51 ,>.J3 .n �-'---- ...3.'-'.:L __
- -- ·-
\ooo &.43 4bi.J 351 �R'S' :>.:� q \ � \ 15'7 135" II t:. . 'f�'1
----·
------··
·-· .. ... . .. --- ---
-----.....--·-·
-------·-
----------- --
------ ---- - -
-------
······--. --
--·-------- --- --- - - -
-------· -----------
----· . --- . . .. . . -- ··-
------------····
--- ·-- �---·-----
-----------· .. --
------------ -·····
· --- -------····-··-- -·
-------- -
--
--
- .. ----
1-------- -----·-----
---- ---- . - . --· - - ---
-- ·------- --
---· ------
TABLE 3
ACTUAL MEASUREMENTS- MATRIX DATA SUMMARY- AMORPHOUS THIN-FILM SILICON
NUMBER OF FILTERS-+ 0 1 2 3 4 5 6 7 8 9 0 -_ - lsc @25 °1.i .t.j�, .?..70 ,,9, .143 . I ll .oqo _,07'/ .o�, .051 .O'tl ·"�e �E-=--==--��
_ @35 oc ot.l:/1.\ ,'ll.4 •111'7 .IY'l. • 112 ,ocu _ _ 1Ul'f_ ,0,:1. •O.S_o , O..!:U_ ,l.J:\C.1. · @45 oc .4'l7 .:m .. ·'"' ·1'\LL '''3 .o_ti ,o73 ,o�o3 ,e;s?. .o� �- -_ ----�-@55 oc ,431 •11.'1 __ •19Q_ • 143_ > 113 __ ,oqo ___ , o7y _ .o,� , os� _ ,oyy . · .<I.'? I @65oC II•Y35 lo:ll'l. 1·1"11 1•14'\ loll3 l.ocn 1.07.5" l.e>r.?. l.a>:�. looYY I.L/l/0
.-
IH @ 75 oc I\·Y3S j:�'l I :-;� 1 I , 145 I· 1ii I• o 9) I· o-1r I· 6� I · os') I , Oil I.) I; 4?? I II 11 --------�---r--�---�--+--�--+-��--+--�---+--�---�--�1
---71::-<>l�----ll-:---:--t-::--:--+--+--+---+::--t-:-----'l-:----t--:-:--:--t-;-:--�-t--:--:----t---·��------· ·--· _ �.l'l. :11.�,_ :n,'l<�
·+ l· 5'5 ;!\. 0'- ;!O,t.5 I ?..ll·'lS ,_b,4S :�o,oqllj:: le'.:ll 17 lio . ---jJ--- 11 \i, C.£ 17, -:l'i --- -ll-------------· - � __ lll•'l::l. \il\t? _ 17.8'Q_ 17.�7_ i•.�o --
---··-
--
---·----·---------jj---f----t-----1f----t----f----t----t-----+---t-----+----t----+ .... Pmax@ 25 oc T--.. I __ @_�"--�----jf-"<L-"-"--+-"''-'-'=--+ , . .. . ,. . __ __@ 45 oc... . . __ __@�5�5_0,-::C�-
--
---IIl"OL=�f--'L!�-l-�"'--t--'-!.ll.-I---'-'-'U--t-:'-'-'-'"'--1-"-'-'l.L-+-'-"''--t-"-"""--t-'-"'::'--1
--"-'-=-1.-
65 oc =�=--=.:7�5�oc=------lr"'c'-'--"'---i---"''-""''-+�'-'-+-'-'--"'"---f--:L'-.:LL-t-��f..!LL:L!--t--'-'--'----t-''-"-"'-Pc=.--+�""-
·-----�-------11:------t-----t--__ _,,_ ____________ _
-· - . I ;nrnt
t�� ii: II..
0
a::
w
m
::;: ::I
z
: I l ��� i I ��\ �:2:e t
i@l@!@)@ ! ! ol
' I
: I
��
I!
: I
I i<> ��
! ! _l
i II r I
! I !
.. I I
i "'
� !
tl .i i .,
, .,
. ._
I
_I_
: ;
�
NUMBER OF FILTERS-+
- lsc�2t� '\; . . . -- --. -: --.. · -·· -- --
� 3b '\; � 41) '\; � bb '\; � 1)1) '1.,; @ 75 "G
1- V00-"'@'2s---"v - . ··
····-
·- ··--·
·
\!!t .)0 .... \!!t 40 -... � 5b '\; � ljl) '\; � lb '\;
Pmax_@25 ��.,; �36 oc
f- ----- -- --- . --- -- -
@ 46 oc @ 56 °G @ 65 oc @ 75 oc
r--1rradian ,., I ..,2 ' ... f----
� - · - -� - -T ABLES
ANALYT ICAL PRED ICT IONS- MAT RIX D AT A SU MMARY- POLYCRYST ALLINE SILICON
0 1 2 3 4 5 6 7 8 g · 0 --
• 319 .:20 5' I L\ !i • 1 1'2 , O 'tl , o73 , 011 1 . oso • OL/ < -'-031 • 3/B d�?. ,?.07 • 1'19 "' � o q ,_ 0'14- . o� � , 050 , OLI3 • () <'l ' 3:21
:1,�� • �oq ' \5 \ ' \1'1 . O'l 3 . 074 ' 0"?.. , os-1 1 04� . 0� 1\ . ?:111 • �:1o . � \ \ I IS'� 1 I I S' o O'lll • 01 'i . 0 � 3 , OS\ , 0 4</ 1 0 38 · ' � �7 I '33 1 • . :11''1 . \5"'1 , \ I {. • 0'14 o 01(. o O C.:J ' 0 I} ;)_ , CJLJ5 ' 038 ·330 , H4 , 1 I 5' • 15".5" • I I "I .aH , o?c. o C}t, o.l , OS":l. . 0'1 5 0 3'"1 , 3J.3 --
------
--·--··-
-- ------.:!.0 .% /'f; .5" I \0. 87 18.35 \1. 9 8 17. r. l 11 , 3 I 1'7. 0 0 /.{; .1'7 I IG I 5'"1 �0 . 4 5 ·
·-
---- ---- - ---
, q , t,7 18. "I C. 1 8 . 1 4 17 l.4 \'7, :18 " · 9 3 \t. , r.il 14. 311 � � . �� IS, 'l o i l 'l . t.' 19 .• '11.\ l't , or. . \/,L.j4 I� • . 'I B 1 1 10 , 44 I Ii . 30 \� . 0 � I l li o 7 LI 11;' , 5'� 15 · 3 1 \� ' "' .., 1e. n 11.1l� l t. , !l o; ��."i& I G. . 05 15. '7:1. 15. 1.{ c. I 15. 18 1'-1. '1'1 1"1'.77 I 11>. lt. \7, t.LI I(,, 2'l.- IG.,'J-'7 l '.i . j!?, IS.so \S', 18 11\, 'll I '"�· '' 1"1 ,i-1(. l"'.?.r. 11. (. 3 f'7 I 05 J(,, :10 \ ,,,a_ .. lSI � q 14 �qs 14' fl'l \4.\.f� \4 . \1 1 13 . "11 131 78 17 0 1.\ --Lf , S4 .;i, 7R I . Q4 I , o.J<� I ILl O , Rq 0 , "7 � · o , sq o � ;;o o. Y 3 '-l. S� 4 . 34 2· £. (,. l 'B !i I , 37 I, 0 '! o .�s 0, 10 o . .;, 0 '-18 0,'-1 1 1 1-l.� �
1 4 , LS ;;!. ,SI.\ l \ 17 1 . 3 1 I o '\ 0 . ?;1 O.ft>i o . 'iL\ . D , 4G. O o3'1 1-j, I '3 '3 ' '18 ':l.. 44 \ o 1 0 l . :l ,. l . o o 0 . 111! (). I'D4 0 . !i;l.. (J ,"J4 o .is I ?, . Cl(. 3' _8_:1. :l. 3'"1 \ I (.3 I · �0 o,qG. 0. 75 01 (, I I'J. 5o O � LJ :l- 01 3(, 3. Re� 3, ' e ;l., ':l.S I . 5? \ . " . () . q� 0·7� C), 5'1 · 1'.>. 41?> 0 . 14 1 {),J!) 3 "" .. ---------·-
l\000 f.43 Lj '-4 351 �8 5 :l :ll1 \ q I ' "" I :? 5' IJC. CiCf'7 ·: f--· -
--
-
1---
--
-·-·-·
2
0
(.)
::i
iii
:;;
....1
u::
2:
:E
1-C/)
:::1
0
:I:
� 0
:;;
<( '
0
co � w
!:i ii:
LL
0 0::
w
m
::;: :::l
z l i
i i I
! I
I I
I I I ! I
!I II
i I
I 1
I "
0
-:r
0
J
IV">
" e I
-3::
APPENDIX B A COMPARISON OF ANALYTICAL 1-V CURVE
TRANSLATIONS VS ACTUAL 1-V CHARACTERISTICS
1-V TRANSLATION EQUATION CHECK FOR
SINGLE CRYSTAL SILICON MODULE
• 0 : "''' .. ,: .. ....... .:: ... 1 � A •'""" '¥1' • •• • '\o G-' •••• •
o.o"' Cml If MA.Ne-R I·Y
'
n �1'�"1'"11;11 TO \ f(IINTS S'\ WlTH EO.IMTJO�.,r
AMPS
0 . 0 0 . 0
1 . 0
AMPS rt' a '
. .......... .
0 . 0 0 . 0
T�PE � s " r;. L G- • IOOo v>(wo" r • � ,s- . o oc:...
UOLTS
T-/PE. '::: SNCTL G = 4S9 W/ vn' T :: ?..S, O " c.,.
C. I pI IE" I I=' I 1 . .... ... '' ....... .. .. · · · ·� ......... J .
UOLTS
I TRII>uliiTI
OJ" I I 'l\ ' ' � Ki,
' L
25 . 0
DIITA P<:>liJTr TIIII»J �ATEII
FR<1l1 $TC. lll'JIH tli:W EGVATr<>»r
/IC:.T'U .. L �-v <;.URVIil TO V�lll "� ,C.Cil�l\�'1 OF TRFINJI.RTHlN .
,· \ 25 . 0
�
'
�
' • c. I 0 I e-' F ' I
� ...... � . ..... . .... .. .... '" ..... .. ................... .t,AMPS
0 . 0 0 . 0
1 . 0
AMPS
nPo � S"r;.'& • �35 w/w.''r =- �5. o " c..
UOLTS
T'ff'E' = SN G- L G- = 3 4 � .,.,,., .... T = 'J.S , O 0 C.
, , • o ' G ' F' '2.. .. ...:. ..... i;. · - · .. .. ... .... ............... �./
0 . 0 0 . 0 UOLTS
P>4Til \'OTHTl" TllllHJ"LI'ITI: II l'"nDM STC. U$111G NtW l<OIHITlooU
1\tT�/IL r • ..j C.Uih'� Til 'lflifi!JJ"j fiG C. Ill?•"'! O F TRml.ll{lT JOI,I
· \ l<'•t I I I I l'�
""
25 . 0
POTNTS TRIINSLIIT£0 .SH. UShH 1-il.W ,EOU/ITlOIIJ"
I'ICTUIII. I•V CI.IRV� TO VL1'11N 1\I:C:\Ifli'I(Y OF' T"RA�SLIJT"ION
25� 0
J. • tlB c .'
. .... .. ,: .. . . .. ... , ... 1' A ' J. '¥'' ' ' ' ., '\. c;.
' .... . . ..
'"'" ,�., I+ MN'TG"R I·V
.J: E�l:"�,.£0 'rO 0\:. \ P,INTS
F EO.UATTO f.IJ
AMPS
9 . 9 9 . 9
1 . 0
AMPS
T'{PE "" S N <r L G- . {000 <-'(VY> '" r .. f\5. o "(....
UOLTS
T'/ PE = St>�LG = ?.33 W/>n'T = ?S. o o c..
A1 a' c' o' e' ,::' --+··· ..... .. ...... .... ...... ........... .
9 . 9 9 . 9
UOLTS
\ Tl?lll{HI'Tt:l> WfT!l
.,. I I
I
., ' � I< . . . .
, ..
25 . 9
25 . 9
I
f "
t
1 . 0
AMPS
TYPE = SN � L G- = 3 4 � "' '"'"'" T ::; �5" , 0 9 c..
' I E ' F' 1 I c_ 0
.. .. � .. ..:. ..... ... ... .... �. .. ' '"'" ........ �/
0 . 0 9 . 0
1 . 0
AMPS
UOLTS
T'/ P€ � S N <i- LG- = i").fi W{Y<n'-1 � ?.5, 0 ° C...
ll' a' c' o' !>' F' -·· ' ........ ... ..... .. ................ ; ...
0. 90 . 0
UOLTS
M'TI'I POJNT.r Tflf'IN.f\.IIT'II'O Ff!Of>\ .STt. I.IJhiC Nt.W EQOII\'TIOII$
IICTI<Ijl. r.v CI.IRVt. TO VUIIN 1\�(.l,n?FI('i OF TRI\NSI..FITlOI'I
25 . 0
25 . 0
AMPS
' c .: . .... .. ,: .. .... ... :. ... 1' A , •,.J\ ,_., , , , '\o ..,.
••••• •
'"' (IT<) II MAJ'TGR l-V C1l
' ,. �..-�rto ro \ PoiNTS
J"E lTit EO.UI\TTON.I
TiPE "; S: N <T LG- = \OOO ""(""" T :; ?.5. 0 ° C.
I TRIII>H"T�O 'W
. ,. I \ l \ � K
� '-9 . 9 1----t---+----t----tO-b--
9 . 9 25 . 9VOLTS
1 . 9
AMPS
. . , . ,. ' ...... "f" .... �.. . ' " . " . .... " .... ,. ...... "11�:
9 . 9 9 . 9
TYPE: � S N 6- L G- : �3S w(Yh'T -= 35, o 0c...
VOLTS
\ •\k'
l I \ •. �..· . .
25 . 0
AMPS
0 · ····� ...... ........... c. ' �· ()' t. --,
• ..,., ... . ...... .-;. ,. . •• " 'II�
"' .
, .
\ I T'/Po = S N G L 'f'.r' G- = 1 0 oo w lrn., -r = "'3 $" 0 C..
\ \I �k'l
. ·•t..' . . 0. 0 L------+---+----t---�-----1
0 . 0 25 . 0 VOLTS
1 . 0
"T'IPE = SN�LG- = L!S"4 w/..,'-T = 3 5, 0 " t_
AMPS l ' I p' 1:' F' ' -.. -�. ..... .... ' .. ....... .. . .... .... \ ........ \ .. �: 1 •••
0 . 0 \
0 . 0 ·�
VOLTS 25 . 9
.. ....
t �' ,-
•• •
, ;
...1 0 .:z: "' II "' "'
?=" � f 0 --
--. 3
Q ...
,,.. =r-
.... ""
II •
0 1--
.....
""""
::E:
oCC
-_,
" ..
• "
--
· . .
. .... .. .. .. = =
.....
..1 rl f .j
� <.!>
....__
•
<::>
z ]
() =-
" .;;
"'
II <'
<"
Ill II
0..
II
� 0
1-
--� ' •• =
�------+-------P-��--+-----��----:�� =
= = = --<
AMPS
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r
o..-: LE�T"I:O TO \ PoiNTS n WrTH EO.I.II\TH�.s \ Tflll>t$<.-.TEO
. ,. I I i G-L ', T'iPE '=- s M "1-
\ G- - 1000 '-'("" � < r • �s. 0 ' <-
0 : 0 0 0 0 0
9 . 9 : ·
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AMPS
VOLTS
0 0 ''i-""""" . ..... . . '1 ... .. ....... , "t,' 6' . t_, p' e: • r-' '\ .....
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T :: 4 S , '-{ " <- \ k'•'
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9 . 9 ,. �
9 . 9 VOLTS
25 . 9
25 . 9
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9 . 9
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AMPS
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e H'
t'
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T'I P E = S N G L G- = \ 000 W/w. "T = 4 'S , '-/ 0 C-
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25 . 9
T'/PE' " SN G LG- - '! S 'I w(m -.. T :: 4 5' . "/ • c;..
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9 . 9 25 . 9VOLTS
AMPS
0 I< � ' c, ....... ... .. ............ , ., IJI
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r
o ... EeT"I:P 'TO \ ���T.f S"e� II EQU/ITJo�.r
T'J'PE � SNGcL & - 1000 '-'{""' ,_ I =- 01.5. 0 °C.
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9 . 9 : "
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T'/ PE" : S N (; I.. G- = ?.33 w/m'T � 4 S . Y 0 c...
25 . 9
9 . 9 I I I I ��· I I 9 . 9 25 . 9
VOLTS
�
AMPS T'/P!: : S N ii L G- � 3% '-'/l'h'T = Y5".4 • c.
' ....... ' , ... ... ... ................... . ll' e' o' e' r-• (,::
9 . 9 'D _____ _l-'-1-----9 . 9
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1 . 9
AMPS T'IPI: o SNG-LG- "' I ?. S wfm""'T = 4 5" . 4 0 c.
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9 . 9 c
. 9 . 9 VOLTS
25 . 9
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. AMPS
8 c .' ..... .. : .. .... ... :. ... 1 � A J. ' ffl' ' ' ' '" '1. . .... .. . ...
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r E�ECTEfl TO 01: \ 1\oiNTS
F EQU/ITJO>U
T�P� < S('I(>L G- = 1000 w(""'"r :; �5'. o " c.-
\ .,. I \ 1 \
TRIIlU\IITI<O WITH
• •• . . .
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TYPe: • H i G L.G- =- � "> 5 w{n-."" T � 5s. o • c.
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3l
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T"'I PEO : SN G- L.c;. � l cnro w I ""' ..... I = 5"5 , 0 ' C-
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1'/PE = S lV I> L.c;. =- YS� w(m 'T =- 55 . o • c.
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�MPS r;. � 34� w{m� T = � ? . 9 ' <-
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T'i P t: " S N G- L G- = 1-:!S W/W>" · -r =- rJ L\� S" Q c.
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25 . 0
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1-V TRANSLATION EQUATION CHECK FOR
POL YCRYSTALLINE SILICON MODULE
AMPS
·-.-�.- ··'-'···"·"-' """"·�TYI' " = Pot.Y G "' 1 0 0 0 w f.,'-T = � s · e-
0 .0 n ' . 0 , Q
0 . 5
AMPS
UOLTS
A' 11' c.' o' li' . F' , ... , • ..,\\,,, .. � .... •-o••••• 'liD',,. ........ -.... <::Ju' PiPE = f'OC'/ c;. � Y �4 W/m 'T :::. 'l.� o c..
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AMPS 11• e' c' o' E:' p' .-.. ·•·· •• .. ... ' ••·v .. ... ,..,, ... ••• ...... \, c.'
TYPE = POL'/ c;. � (, Y3 w/m' T = l 5 ° C.
j 0 . 0
0 0 � I
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1
0 . 5
AMPS
UOLTS
TY PI:: ? POL.'/ C. = 35 1 w f .,.,-.. T , ?.s. o •c.
ft 1 p' c:' o' IF' F' o ...... ""''•' ..... .............................. (;.
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:- J
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G � \ 0 0 0 w /m'-T : � S ' C-
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0 . 5
AMPS T'/PE ; POL 'JG- " ;>,?,'i w ' "" ' T � l5". 0 ' <.-
UOLTS
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0 . 0 UOLTS
:��1 c��"J 1 �-J (�---,�
25 . 0
i'"' l:l ' ;)
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i . . ' .
TY PE "' POL'/ c. : '35 1 w I ,-..T = �5. 0 'c.
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ll ll J �·
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h . 5 r_,-_, -� ,�HPS T 'I P � = POL'/
G- "' 1 \ G. w(m"T : J.s, o ' c.
l 1
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AMPS
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0 1 5
AMPS T'/ PE" = Po L..'{ G = ?.?-q w/ "".,_ T = 35. s- "c.
UOLTS
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251 il 1
9 1 9 ' 1 1? UOLTS
,�"'-] c.:J ['"-'' 0�01
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TY PE = 'f'Ol'{AMPS I G- : 351 w/ m .,_
T " 35. 5' 0<;-
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c ,.
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9 . 5
AMPS
:
UOLTS
'TY I'E' "' fO /...Y G : I I C. W/ m 'T = 3 o, fi ' t.
'tf II.' C1 D' fi1 F' ,-1/i_ ··•-···• .. · · · •·· .. •••· .. .
9 . 9 I I I 1,��'�·· ,. il il I 'f'r !ji •' 1 tJ 1 lJ
I �5 . 9
UOLTS �cCO"J T -1 cl d c co
AMPS '".; •. ,:., ... .: .. .. L . . .. o .. ._\
TYPIO = PoLY G- "' \ 0 0 0 w ;...,-.. T = :Z S" • e.
, . I \ \ I l �� '
\ 0 . 0 Ln---+-=-----25 0 . 1! 25 1 0
UOLTS
0 1 5
AMPS tt' e· · c:..' o' �;' F' ·-"¥"''"-a .... ''¥"·'·· 11' '"\.••e ... _.j� J�.�·
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v 0 . 0 '-:---t------�----::-:::-1
0 .0 25 1 0 UOLTS
·-,.-
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AMPS
�t' B ' c' t>' _, •-•••••••4 • •t ,.. , .,,.,.,• F0 ....... � ... ,�, · . ..
,. T Y PE = POL'/ ,. G = I O O O w (m '-T � "l5. 5 "<:. '
l, •. \ I
I ' I i l p'i
0 . 0 \ M '
0, 0 UOLTS
0 . 5
:
T'/ P E = POl'lAMPS G- : 4�4 W/m .._
T • 45 · 5" • c..
0 . 0 ..
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25 . 0
25 . 0
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CSI
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.., ..... 4111'.. " •- \1''.'T' .,."1' '1ooltlo.,,,.,,,,.,,,,. .. �
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� · I I I
' I ' �� ' ·, 0 . 0 25 . 0 0 . 0 I
0 . 5
AMPS
UOLTS
Ti P< = ?o�'l G. = � Y 3 .., ,,� 'I :; s-c.' ! .""
t ' c.' t�' �· I (-'
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0. 0 • '
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·--·
j;;' .
AMPS
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0 fi' . .......... , . .......... 1 ... , '{ ,.
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T'l PE. = fo l..Y ,.
G- = )000 .,; ... •
T • s � . s • c. '- ·· \ \ ' \ ' i b •'
0 . 0 \
0 . 0 \ M'
0 . 5
AMPS
UOLTS
l'{Pe = Po'-"1 G. � 'H4 W /Y<>,_ r ::- ,;, . s • c.--
1 8 I <;1 D1 J!i' !==' ' II,-·· ....... . ..... ........ \ .. � ......... ! I "'
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0 . 0 -·
25 . 0
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AMPS
UOLTS
T'lf< � ?oc'{ (l- = ?,?-q W/,., .,_ T = 4 5, 0 ° v
... 13' •'"'
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9 , 9 1 I I )�;'M, I I 9. 9 25 ; 9
UOLTS · j "'� [ 1 [ c::�J
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AMPS T'l FE = Pol.'/ G- = 3Sl w/>vo'" 1"" '= (. S" , t> o c,....
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9 .9 c
9 . 5
AMPS
9 . 9 UOLTS
G199-IU
T'IPE "' POLYG- " I I � w / .-.,'T :: 45', 0 oc,...
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25 . 9
I 1 9 , 9 I �···�·,. I I ....
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1-V TRANSLATION EQUATION CHECK FOR
THIN FILM SILICON MODULE
AMPS
0 E" r- . .•. _.,.. ....... , ..
A 6 ; .. "''' 0 ''" "' o• .. ,., ...... ,..,,.��,
\ Tne � TFS G- .:: tooo w{m'l-T =- ?.5"oC..
\K \
, ,' \ \ . ·• � H
0 . 0
\
0. 0\ .
"
0 . 5
AMPS
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REPORT DOCUMENTATION PAGE Form Approved OMB NO. 0704-0188
Public reponing burden for this collection of information Is estimated to average 1 hour per response, including the time for reviewing Instructions, searching existing data sources, gathering and maintalnin� the data needed, and completing and reviewing the collection of information. Send comments regardln� this burden estimate or any other aspect of this collection of information, ncluding suggestions for redudng this burden, to Washington Headquarters Services, Directorate for �� o[Tcation op;�tions �g
11Aeports, 1215 Jefferson
Davis Hiohwav. Suite 1204 ArllnCiton VA 22202-4302 and to the Office of Manaaement and Budaet Paoerwork Reduction Pro ect 0704-0188 Washin ton DC 20503.
1 . AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED
January 1 996 Rnal Subcontract Report
4. TITLE AND SUBTITLE 5. FUNDING NUMBERS
Photovo�aic Translation Equations: A New Approach C: TAD-4-141 66-01
6. AUTHOR($) TA: PV660103
A. J. Anderson
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER
Sunset Technology 3388 W. Oak Leaf Place Highlands Ranch, CO 80126
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORING AGENCY REPORT NUMBER
National Renewable Energy Laboratory 1 61 7 Cole Blvd. TP-41 1 -20279
Golden, CO 80401 -3393 DE96000507
1 1 . SUPPLEMENTARY NOTES
NREL Technical Monitor: L. Mrig
12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE
UC-1260
13. ABSTRACT (Maximum 200 words) New equations were developed for the purpose of evaluating the performance of photovo�aic cells, modules, panels, and arrays. These equations enable the performance values determined at one condition of temperature and irradiance to be translated to any other condition of temperature and irradiance. The equations were developed to satisfy the following goals: (1) The equations should more accurately translate the short-circuit current and the open-circuit voltage (V .J. In particular, the influence of irradiance on V � should be more accurately treated. {2)The equations should more accurately and more simply translate the 1-V curve data point pairs, 11 and V,. (3) The equations should be based on the use of dimensionless coefficients such that a and � have units of •c·' and not, for example, amps/"C or volts/" C. (4) An equations should be developed for translating the maximum power without involving the translation of I"' V"" or any 1-V data pairs. The data presented in this report show good agreement between the analytical predictions made with thenew equations versus actual test measurements and superior performance when compared to the current translation equations.
14. SUBJECT TERMS 15. NUMBER OF PAGES
135 equations ; photovoltaics ; solar cells 16. PRICE CODE
17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT OF REPORT OF THIS PAGE OF ABSTRACT
Unclassified UnclassHied Unclassified UL
NSN 7540-01 -280-5500 Standard Form 298 (Rev. 2-89) Prescribed by ANSI Std. Z39-18
29S..102
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