The temperature coefficients of a photovoltaic (PV) device are generally perceived as its percentage change of the electrical parameters (e.g. short circuit current ISC, open circuit voltage VOC, maximum power PMax, spectral responsivity s()) with change of temperature. The calibration values and hence datasheet values of PV devices always refer to standard test conditions, i.e. irradiance of 1000 W/m², AM1.5g spectral irradiance distribution and device temperature of 25°C. Hence the temperature coefficients are needed to calculate the performance of the PV device for real operating conditions dependent on ambient temperature and the heat load from the solar irradiance. Therefore, the knowledge about the temperature coefficients for specific PV-modules can be of major interest for PV project planners and PV yield modeling. The IEC standard 61853-1 and 60904-10 describe the procedures for such linearity measurements.

This article gives an overview of the measurement procedures and setups currently available or under deployment for temperature coefficient measurements.

The determination of the temperature coefficient for the short circuit current at standard test conditions of a solar cell (SC) can be derived from temperature dependent measurements of the spectral irradiance responsivity using the differential spectral responsivity (DSR) method [1, 2] since the short circuit current ISTC is linked to the spectral responsivity and the spectral irradiance via the following equation:

A differential spectral responsivity (DSR) facility generally consists of a quasi-monochromatic light source providing narrowband monochromatic irradiance in the wavelength regime of the device under test, i.e. for c-Si solar cells from 280 nm - 1200 nm. In this monochromatic light field, the device under test (DUT) is compared against a calibrated reference, wavelengths by wavelength. Additionally, the device under test is exposed to broadband white light bias irradiance usually generated by cold mirror halogen lamps. In order to separate the photocurrent of the DUT generated by the monochromatic light and the bias light, the monochromatic light is chopped with a given frequency and the lock-in technique is applied. Since usually the DUT and the reference are measured subsequently a drift of the monochromatic irradiance between these two measurements have to be corrected for. Hence a fraction of the monochromatic light is coupled onto a monitor device, i.e. a photodiode.

Since a complete DSR calibration at several different temperatures can be very time consuming, such a measurement can be divided into a standard calibration of the spectral responsivity in order to determine and a temperature dependent measurement of the relative differential spectral responsivity by means of the measurement of the monitor corrected Lock-In signal of the solar cell at constant bias irradiance level EBias and at different temperature .

According to IEC 60904-8:2014 7.5 [2] the spectral responsivity can be assumed to be equal to the differential spectral responsivity , if IBias is approximately 30% - 40% of ISTC. Hence the temperature dependent measurements of the relative differential spectral responsivity are performed at IBias ≈ 0.35*ISTC. The measurement procedure would be as follow

1. Measurements of the monitor corrected Lock-In signal of the solar cell at constant bias irradiance level EBias at different temperatures using the differential spectral responsivity method. An example for a crystalline silicon solar cell is shown in the figure below. Please note that the monitor principle is essential for this measurement, since lack of reproducibility is a major uncertainty contribution for such a relative measurement.

2. Perform a linear regression of the temperature dependent differential responsivity of the solar cell at every single wavelength (see Figure below left). The slope corresponds to the spectral temperature coefficient. Express this function in units of [1/K]. An example for a crystalline silicon solar cell is shown in the figure below right.

3. Weighting the spectral temperature coefficient with the spectral responsivity and the spectral irradiance of the AM1.5G spectrum gives the temperature coefficient of the short circuit current under STC.

The major uncertainty contributions for such a measurement are:

- Spectral responsivity: The spectral responsivity of the DUT is needed for the calculation of α out of the spectral TC. Please note, that only the relative is needed. Hence all uncertainties related to the absolute value of can be neglected.

- Over illumination of sample and reference: The monochromatic light field should be larger than the active area of the solar cell. This includes encapsulation materials, since light transmission and reflection characteristics of encapsulation material might be temperature dependent.

- Monitor principle: Since the DUT is subsequently measured at different temperature, a drift of the monochromatic irradiance over that period should be corrected for. This can be realized by coupling a fraction of the monochromatic light onto a monitor detector (e.g. by using a beam splitter)

- Reproducibility: The reproducibility is a key uncertainty contribution. The non-uniformity of the monochromatic light field, the center wavelength of the monochromatic light and the bias irradiance level should be reproducible to a high degree for the temperature dependent measurements.

- Temperature: The DUT should be stabilized with respect to the set temperature. Deviation from the set temperature should be considered in the uncertainties. If the temperature sensor is in direct thermal contact to the DUT, additional uncertainties should be included (i.e. if a temperature gradient can be expected across the solar cell: backside cooling - temperature sensor - solar cell - encapsulant - front side heat load due to irradiation).

- Uncertainty related to linear regression: The uncertainties and should be used as weights for the linear regression for the determination of . The uncertainty of should be derived from the linear regression considering and .

[1] Metzdorf et al. "Calibration of solar cells. 1: The differential spectral responsivity method", Applied Optics Vol. 26 No. 9, 1987

[2] IEC 60904-8:2014, Measurement of spectral response of a photovoltaic (PV) device (2014)

The temperature dependence measurement of the three main electrical parameters ISC, VOC, PMAX under steady-state irradiance conditions is performed by varying the temperature of the PV device while keeping the total irradiance level constant [2]. The latter has to be measured by a calibrated reference cell (RC) kept at 25 °C, because the resulting temperature coefficients (TCOs) of the device under test (DUT) refer to the irradiance level at which they have been measured.

When steady-state solar simulators or natural sunlight are used as light source, the heating component of the radiation can be used to naturally warm up the PV device by keeping it constantly exposed to light.

The usual procedure for measuring the temperature coefficients α (for ISC), β (for VOC) and δ (for PMAX) for large devices (from large-area cells to module size) is as follows:

1. The PV device has to be prepared by cooling it down to a temperature below the lower limit of the range of interest.

2. When the device is ready and temperature uniformity reached, it is connected to a setup suitable for I-V curve acquisition according to IEC 60904-1 [3] and exposed to steady-state artificial or natural sunlight.

3. While the PV device is warming up due to incoming irradiance, a series of I-V curves are acquired in the same way as STC I-V curves would be recorded. Consecutive I-V curves are acquired at least every 5 °C for a total temperature range of at least 30K. The temperature of the DUT and of the RC is recorded together with the irradiance value and the I-V curve.

4. Once the whole temperature range of interest is spanned and the I-V curve sequence is terminated, the three parameters ISC, VOC and PMAX are extracted from each I-V curve and the functions ISC(T), VOC(T), PMAX(T) are fit with a least-square linear fit [2]:

Eq. (1)

where mabs represents the absolute TCO, T is the measured DUT temperature and Y0 is the value of the parameter at 0 °C. The relative TCO is then calculated as [2]:

Eq. (2)

where Y(25 °C) is the value of the parameter Y at 25 °C as calculated from Eq. (1) and mrel is given in units of [%/°C] or [%/K].

When the DUT is a reference cell, a procedure similar in principle to the just-described one is applied, but usually with the addition of a temperature-controlled stage to be able to precisely control the temperature of the DUT through the range of interest. This allows variation of the method. Whereas above the DUT temperature is never in a steady-state condition, here such steady-state conditions can be adjusted. It allows further to measure the TCO with increasing temperatures or decreasing temperatures. For RCs only ISC(T) is measured instead of the full I-V curve dependence on T.

As the TCO measurement is ultimately a relative measurement, many components that would enter the UC budget for a standard measurement at STC are cancelled out. Therefore, the following issues can be considered major measurement uncertainty contributions for relative TCO measurements:

- DUT temperature: the major component of the UC budget comes from the reading of the DUT temperature. First of all, the value measured together with (and therefore associated to) the I‑V curve shall always be used, with a UC component (minor compared to what follows) related to the measuring instrument to be included. However, the most significant contributions to the DUT temperature UC are due mainly to the distance between the point at which the temperature is read by the Pt100 sensor and the actual position of the DUT junction, to the delay between the reading of the temperature and the sweep of the I-V curve and to the non-uniformity of the temperature in the DUT;

- RC temperature: even if actively controlled in temperature, the RC temperature contributes to the overall UC budget due to sequential reading with respect to the I-V curve sweep and to the UC related to the measuring instrument.

- Uncertainty related to linear fit: the standard error for the Y estimate from the linear-square fit is used as UC component for the computational part of the TCO determination.

- Uncertainty related to spectral mismatch: the change in the spectral responsivity with temperature and consequently spectral mismatch for certain materials (e.g. c‑Si) can be a significant contribution. For natural sunlight this contribution can be neglected in first order. For solar simulators it depends crucially on the match of their spectral irradiance to the reference spectrum in the wavelength range where the spectral responsivity of the DUT is most sensitive to temperature changes (i.e. for c-Si the wavelength range between 900 nm - 1200 nm). The full uncertainty can only be calculated if the SR as function of temperature is available for the DUT. In absence of this information, such data for typical devices similar to the DUT can be used to estimate the UC contribution.

[2] IEC, IEC 60891 Photovoltaic devices - Procedures for temperature and irradiance corrections to measured IV characteristics., International Electrotechnical Commission, 2009

[3] IEC, IEC 60904-1 Photovoltaic devices - Part 1: Measurement of photovoltaic current-voltage characteristics, International Electrotechnical Commission, 2006

The measurement of the temperature coefficients by using a flash solar simulator is similar to the previous method. However, as the irradiance produced by the light source is not enough to warm up the DUT, an additional heating system is necessary in order to vary the DUT temperature over the range of interest. Suitable means are an insulated temperature-controlled cabinet with a transparent window or a shutter door, capable of containing the module and producing a quasi-steady and uniform temperature on it. According IEC 60891(2009) [2] the temperature uniformity of the DUT has to be within ±2 °C and has to be verified for large devices by the mean of a minimum of 4 temperature measurements positioned as described in the standard. The average temperature is used as reference value.

The procedure to measure DUT TCOs is as follows:

1. The PV device is mounted on a setup suitable for I-V curve acquisition according to IEC 60904-1 [3] and brought to the lowest temperature of the range of interest. If a temperature-controlled box is used, the RC is mounted on the outside, to be kept at 25 °C. Also, a calibration of the transmittance of the transparent door of the box has to be always carried out at the beginning of the TCO measurements.

2. When the device is ready and its temperature deemed stable, at least three I-V curves are acquired.

3. The DUT temperature is then varied by the chosen method. Additional I-V curves are acquired at least every 5 °C for a total temperature range of at least 30 °C. The temperature of the DUT and of the RC is recorded together with the irradiance value and the I-V curve.

4. Once the whole temperature range of interest is spanned and the I-V curve sequence is terminated, the three parameters ISC, VOC and PMAX are extracted from each I-V curve and the functions ISC(T), VOC(T), PMAX(T) are fit with a least-square linear fit [2] according to Eq. (1). The relative TCO is then calculated according to Eq. 2 [2].

The following issues can be considered major measurement uncertainty contributions for measurements at flash solar simulators:

- DUT temperature: the major component of the UC budget comes from the reading of the DUT temperature. First of all, the value measured together with (and therefore associated to) the I‑V curve shall always be used, with a UC component (minor compared to what follows) related to the measuring instrument to be included. However, the most significant contributions to the DUT temperature UC are due mainly to the distance between the point at which the temperature is read by the Pt100 sensor and the actual position of the DUT junction and to the delay between the reading of the temperature and the sweep of the I-V curve. In the case of flash solar simulators, though, the non-uniformity of the DUT temperature is not influenced by the simulated sunlight. If the procedure achieves a good temperature uniformity of the DUT, this will be a minor component of the overall UC.

- RC temperature: even if actively controlled in temperature, the RC temperature contributes to the overall UC budget due to sequential reading with respect to the I-V curve sweep and to the UC related to the measuring instrument.

- Uncertainty related to linear fit: the standard error for the Y estimate from the linear-square fit is used as UC component for the computational part of the TCO determination.

- Uncertainty related to spectral mismatch: as for TCO measurements under steady-state simulated sunlight.