Correction Procedures for Temperature and Irradiance of Photovoltaic Modules: Determination of Series Resistance and Temperature Coefficients by Means of an Indoor Solar Flash Test Device

I-V (current-voltage) curves are an important tool to estimate the performance of photovoltaic (PV) modules and strings. In fact, during their lifetime, the components of PV plants can be subject to degradation, and this leads to loss of power and consequent decrease of expected production [1]. The comparison between I-V curves measured on site and I-V curves declared by the manufacturers offers the possibility to control the degradation of PV systems and detect decreases of performance.

On site, I-V curves can be obtained by means of commercial I-V curve tracers, which work according to the international standard IEC 60891 [2]. Since the operating conditions (OPCs) of PV modules do not generally coincide with the standard conditions (STCs), which consider a global irradiance (G) equal to 1000 W/m² and a temperature (T) of the module of 25°C, I-V curves need to be translated. Only with this correction it is possible to compare the deviation between the power measured in the examined module and the maximum power declared by the manufacturer.

Based on the standard IEC 60891, three correction procedures can be used to translate OPC curves into STC curves. Commercial I-V curve tracers usually follow the second procedure proposed by the standard, which requires two correction parameters: R_s’, the internal series resistance of the test specimen, and k’, that can be interpreted as the temperature coefficient of the internal series resistance R_s’. The second procedure also considers an additional parameter a, defined as the irradiance correction factor for open circuit voltage; the standard IEC 60891 suggests a value of 0.06 for a, if no additional data are available. According to the IEC 60891, the correction parameters can be determined by means of specific experimental procedures, with natural sunlight or with a solar simulator able to carry out flash tests.

As outlined by the authors in a previous publication [3], in the technical literature a systematic evaluation of the correction parameters is difficult to be found. Therefore, it is not an easy task to find reference values for R_s’ and k’. It should be noted that the two correction parameters are not provided both by manufacturers in the datasheets of PV modules and by the software of commercial I-V curve tracers; without the coefficient parameters, it is thus impossible to check the accuracy of the STC I-V translation carried out by a curve tracer and there is no possibility to determine STC translations with other systems. For this reason, we believe that an analysis focused on the experimental determination of the two parameters could be of academic and technical interest. In the following, we will summarize some of the main contributions that can be found in literature about correction procedures for I-V curves of PV modules.

In 2010, Paghasian [4] applied the correction procedures reported in IEC 60891 to PV modules of different technology, and found the following values for R_s’, k’ and a, respectively: (0.5 Ω, -0.045 Ω.°C^-1, -0.075) for Si-based monocrystalline cells, (-17 Ω, -0.09 Ω.°C^-1, -0.0095) for Si-based amorphous cells, (1.5 Ω, -0.7 Ω.°C^-1, -0.1) for CdTe-based cells, and (2.85 Ω, -0.005 Ω.°C^-1, -0.06) for CIGS-based cells. To obtain data at different irradiance levels, various mesh screens with changing light transmittance were used; on the other hand, to obtain data at different temperatures, the tested modules were pre-cooled in an air-conditioned wooden cabinet or an environmental chamber. The I-V curves were performed under sunlight while the modules warmed up in natural way.

 In a successive work, Paghasian and TamizhMani [5] considered four correction procedures (three from IEC 60891 and one from NREL) and evaluated their accuracy. The correction parameters were determined with natural sunlight for the same technologies described above: mono-Si, a-Si, CdTe, and CIGS. The I-V curves of the modules were evaluated at different temperatures, by pre-cooling them and then allowing them to warm up naturally under solar radiation. In addition, mesh screens of varying light transmittance were used to evaluate the performance of the modules at different irradiation values.

In 2011, Abella and Chenlo [6] used a class AAA solar simulator to determine the temperature coefficients and the correction parameters of several Si-based polycrystalline cells PV modules, extrapolating these data from the I-V curves. Tests were carried out at temperatures ranging from 20 to 50°C for a fixed irradiance of 1000 W/m², and at irradiances ranging from 700 to 1200 W/m² for a fixed temperature of 25°C. The former tests allowed to the determine the parameters k and k’, which refer, respectively, to the correction procedures 1 and 2 reported in the IEC 60891. The authors found that the value of k that allowed to obtain the minimum dispersion of the maximum power (0.5%) was 0.0039 Ω.°C^-1, while the value of k’ that allowed to obtain the minimum dispersion of the maximum power (0.4%) was 0.00345 Ω.°C^-1. Instead, the tests carried out at a fixed temperature allowed to evaluate the parameters R_s and R_s’, for procedure 1 and 2, respectively. It was found that the value of R_s that gave the minimum dispersion of maximum power (0.4%) was 0.36 Ω, while the value of R_s’ that gave the minimum dispersion of power was 0.35 Ω.

In 2015, a systematic procedure was described by Dubey et al. [7] to measure temperature coefficients of PV modules in the field. The authors analyzed temperature coefficients for three modules of different PV technology (mono c-Si, multi c-Si and CIGS), and the coefficients were then compared to the values obtained by means of an indoor test rig. The temperature coefficient of voltage found for mono c-Si modules from field measurements was -0.31 %/°C, value that is similar to the one obtained with the indoor test rig, equal to -0.28%/°C. For the other two technologies, similar results were confirmed: for c-Si, -0.27%/°C in the field and -0.30%/°C in laboratory; for CIGS, 0.28%/°C in the field and -0.27%/°C indoor. For the same PV panels, the authors also measured the temperature coefficients of current; in this case, larger deviations were detected. The temperature coefficient of current for mono c-Si modules was found to be 0.021%/°C in the field and 0.03%/°C in laboratory; for multi c-Si modules, the temperature coefficient of current measured in the field was 0.026%/°C and 0.028%/°C in laboratory; for CIGS modules, the coefficient was determined to be 0.0029 %/°C in the field and 0.003%/°C in laboratory.

In 2016, Trentadue et al. [8] determined the internal series resistance of several PV modules of different technology (Si-based crystalline, Si-based amorphous, CdTe and CIGS), following the standard IEC 60891. Three aspects were investigated by the authors to evaluate the overall uncertainty for the determination of the series resistance. The first aspect was the temperature variation of the PV modules, which was found to have a relevant influence on uncertainty (5%). The second aspect was electrical noise, which led to a variation of 5%. The third aspect was the repeatability of the solar simulators used for the tests: while an average repeatability value of 5% was determined for most of PV modules, variations up to 15% were detected for CIGS thin-film systems. According to the results of the experimentation, an overall uncertainty of ±10% was found for the series resistance of the modules.

Piliougine et al. [9] studied the variation of series resistance respect to the module temperature and defined an experimental methodology to estimate the temperature coefficient k. The results obtained in their work are based on outdoor measurements. The work also presents the results of a study concerning the suitability of the single diode model (SDM) or the double diode model (DDM) for estimating R_s and calculating k by means of a linear regression with a high coefficient of determination R². By using the SDM, the estimation of k ranges between 1.19 and 1.74 mΩ/°C, with a mean value of 1.43 mΩ/°C. Using the DDM, a range for k from 0.89 to 1.34 mΩ/°C, with a mean value equal to 1.06 mΩ/°C, was obtained. As for the series resistance R_s, the SDM gave an estimated value ranging from a minimum of 262 mΩ to a maximum of 320 mΩ, with an average of 288 mΩ. Using the DDM, higher values were estimated, i.e. ranging from 345 mΩ to 395 mΩ with a mean equal to 374 mΩ.

Based on the considerations reported above and the analysis of the literature, it is possible to state that the experimental evaluation of correction parameters needs to be deepened and discussed. For this reason, in this work a set of brand-new PV modules was experimentally characterized determining their I-V curves by means of an indoor solar flash test device based on a class A+ AM 1.5 solar simulator. Through the OPC I-V curves, obtained at several conditions of irradiance and temperature, it was possible to determine the correction parameters of the PV modules under study, referring to the second procedure reported in the IEC 60891.

The paper is organized as follows. The technical specifications of the indoor solar flash test device, together with the specification of the PV modules considered, are provided in Section 2. Section 3 describes the experimental procedure followed to determine the two correction parameters, R_s’ and k’. Section 4 reports the results of the study, and their discussion. The conclusions of the work can be found in Section 5.

On-site, I-V curves are being measured in provided operating conditions (OPCs), and they must be therefore translated into standard test conditions (STCs) to obtain measures independent of actual on-site temperature and irradiance. The international standard IEC 60891 defines three different correction procedures. It also defines the procedures used to determine the parameters relevant for these corrections.

The first procedure is equal to the procedure given in the first edition of the IEC 60891, but the equation has been rewritten for easier understanding. The second procedure is an alternative algebraic correction method which yields better results for large irradiance corrections (>20%). The two procedures require the correction parameters of the PV device to be known. If the parameters are not known, they need to be determined before performing the correction. The third procedure is an interpolation method that does not require correction parameters as input: it can be applied when a minimum of three I-V curves have been measured for the test device. These three I-V curves span the temperature and irradiance range for which the correction method is applicable.

The first correction procedure requires that the measured I-V curves shall be corrected to standard test conditions or other selected temperature and irradiance conditions by applying the following equations:

$I_{2}=I_{1}+I_{\mathrm{sc}} \cdot\left(\frac{G_{2}}{G_{1}}-1\right)+\alpha \cdot\left(T_{2-} T_{1}\right)$        (1)

and

$V_{2}=V_{1}-R_{S} \cdot\left(I_{2-} I_{1}\right)-k \cdot I_{2} \cdot\left(T_{2-} T_{1}\right)+ \beta\cdot\left(T_{2-} T_{1}\right)$        (2)

where:

• I₁ and V₁ refer to current and voltage measured at OPC conditions;
• I₂ and V₂ refer to current and voltage measured at STC conditions;
• G₁ is the irradiance measured at OPC conditions;
• G₂ is the standard irradiance (1000 W/m²);
• T₁ is the cell temperature measured at OPC conditions;
• T₂ is the standard cell temperature (25°C);
• I_sc is the measured short-circuit current at OPC conditions;
• α and β are the current and voltage temperature coefficients of the test specimen in the standard or target irradiance for correction and within the temperature range of interest;
• R_s is the internal series resistance of the test specimen;
• k is a curve correction factor.

The second correction procedure is based on the simplified one-diode model of PV devices. It is defined by the following equations for current and voltage, respectively:

$I_{2}=I_{1}\left[1+\alpha_{\mathrm{rel}}\left(T_{2-} T_{1}\right)\right] \frac{G_{2}}{G_{1}}$              (3)

and

$\begin{aligned} V_{2}=V_{1} &+V_{\mathrm{oc} 1}\left[\beta_{\mathrm{rel}}\left(T_{2-} T_{1}\right)+a \ln \left(\frac{G_{2}}{G_{1}}\right)\right] \\ &-R_{\mathrm{s}}^{\prime}\left(I_{2-} I_{1}\right)-k^{\prime} I_{2}\left(T_{2-} T_{1}\right) \end{aligned}$                (4)

where:

• I₁ and V₁ refer to current and voltage measured at OPC conditions;
• I₂ and V₂ refer to current and voltage measured at STC conditions;
• G₁ is the irradiance measured at OPC conditions;
• G₂ is the standard irradiance (1000 W/m²);
• T₁ is the cell temperature measured at OPC conditions;
• T₂ is the standard cell temperature (25°C);
• V_oc1 is the open circuit voltage at OPC conditions;
• α_rel and β_rel are, namely, the current and voltage temperature coefficients of the test specimen measured at 1000 W/m²;
• a is the irradiance correction factor for the open circuit voltage;
• R_s’ is the internal series resistance of the test specimen;
• k’ is the temperature coefficient of the internal series resistance R_s’.

The third correction procedure is based on the linear interpolation or extrapolation of two measured I-V curves. The measured I-V characteristics shall be corrected to STC or other selected temperature and irradiance values by applying the following equations:

$V_{3}=V_{1}+a \cdot\left(V_{2}-V_{1}\right)$                  (5)

and

$I_{3}=I_{1}+a \cdot\left(I_{2}-I_{1}\right)$             (6)

The pair of points (I₁, V₁) and (I₂, V₂) should be selected so that I₂ - I₁ = I_sc2 – I_sc1, where:

• I₁ and V₁ are the coordinates of the points on the measured characteristics at an irradiance G₁ and temperature T₁;
• I₂ and V₂ are the coordinates of the points on the measured characteristics at an irradiance G₂ and temperature T₂;
• I₃ and V₃ are the coordinates of the points on the measured characteristics at an irradiance G₃ and temperature T₃;
• I_sc1, I_sc2 are the measured short-circuit currents of the test specimen;
• a is a constant used for the interpolation, which has a relation with the irradiance and the temperature as follows:

$G_{3}=G_{1}+a \cdot\left(G_{2}-G_{1}\right)$                 (7)

$T_{3}=T_{1}+a \cdot\left(T_{2}-T_{1}\right)$                 (8)

Since most of commercial I-V curve tracers follows the second correction procedure, only this method will be analyzed in the following. From Eqns. (3) and (4), it can be seen that, besides the temperature coefficients for short circuit current α_rel and open circuit voltage β_rel, generally indicated in the module datasheet, other three correction parameters have to be defined to perform the correction procedure from OPC to STC conditions: a, R_s’ and k’. While IEC 60891 indicates for a a typical value of 0.06, no reference values can be found for R_s’ and k’, which should be determined experimentally (in natural or simulated sunlight).

IEC 60891 defines the experimental methods to determine R_s’ and k’ in natural sunlight or simulated sunlight according to two different steps. In the first step, experimental tests are performed to determine a and R_s’. To perform the flash tests at different irradiations and at constant temperature, four different metallic grids were placed on the modules. As described above, the four metallic grids are characterized by a different mesh width in mm, such as to guarantee a different useful surface for the passage of the sunlight with an emitted radiation reduction. To determine all the I-V curves, each of the three modules was placed on a dedicated support inside the tower system and was placed underneath the flasher, connected to the PSS. For the first module, the following measurement phases were performed at constant temperature:

• flash test of the module;
• flash test of the module covered by the metallic grid with a mesh width equal to 0.132 mm;
• flash test of the module covered by the metallic grid with a mesh width equal to 0.297 mm;
• flash test of the module covered by the metallic grid with a mesh width equal to 0.395 mm.

The same procedure was repeated for the other two modules.

In the second step, experimental tests are performed to determine k’. In this phase, flash-tests are carried out at constant irradiance but at different temperatures. To determine all the I-V curves, each of the three modules was placed on a dedicated support inside the tower system and was placed underneath the flasher, connected to the PSS. For the first module, the following measurement phases were performed at constant irradiance:

• flash test of the module at the temperature equal to 10.80°C;
• flash test of the module at the temperature equal to 15.50°C;
• flash test of the module at the temperature equal to 19.50°C.

Even in this case, the procedure was repeated for the other two PV modules.

In this work, an experimental procedure was carried out to determine the correction parameters of a set of PV (photovoltaic) modules according to the standard IEC 60891. The PV modules were characterized by determining their I-V (current-tension) curves through an indoor solar flash test device based on a class A+ AM 1.5 solar simulator. The I-V curves were obtained at different conditions of temperature and irradiance.

Based on the results of the experimental analysis, the procedure suggested by the standard IEC 60891 allowed to determine the correction parameters within the maximum tolerance of 5%. In order to confirm the validity of the experimental procedure, the STC (standard test condition) I-V curves determined with the correction parameters were compared with those provided by a commercial curve tracer. In this case, deviations smaller than 1% were obtained; this result can be considered a good validation of the experimental tests.

The knowledge of the correction parameters is very useful, as it allows to evaluate the electrical performance of PV modules without using curve tracers, that generally do not declare the values of the internal corrections parameters used. With the correction parameters, it is also possible to build and validate mathematical models of PV systems, which allow to evaluate the performance of such energy devices without using experimental testing.