3.6 Photovoltaic cell parameters

Many scientific and industrial laboratories around the world are involved in testing the performance of photovoltaic (PV) cells. From this fact, the need for unified standards for performing these measurements arises. Standard Test Conditions (STC) have been developed for PV cells and panels [1]. These conditions define the parameters for conducting the tests:

illumination with light of solar spectrum AM 1.5 SPECTRUM,
illumination intensity per unit area $ P_{light} $ = 1000 $ \frac{W}{m^{2}} $ (so 100 $ \frac{mW}{cm^{2}} $),
temperature measurement 25 $ _{}^{o}\textrm{C} $.

Conducting tests under standard conditions allows direct comparison of results from different laboratories.

The purpose of the study is to determine the parameters of cells and panels [2]. The basic measurement of a photovoltaic cell is to examine its current-voltage characteristics $ I(U) $.
An important parameter of the cell is to determine the efficiency, which is determined from the characteristic $ I(U) $. The efficiency of a photovoltaic cell is the amount of maximum electrical power obtained from the PV cell, that is $ P_{max} $ to the power provided by solar radiation $ P_{light} $.
The efficiency of a photovoltaic cell is expressed by the following formula:

(1)

$ \eta =\frac{P_{max}}{P_{light}} $

The current-voltage characteristic for the photovoltaic cell is shown in Fig. 1.

From the current-voltage characteristic waveform for a PV cell, the maximum power that can be obtained from the cell under a given illumination is determined. The power maximum $ P_{mm} $ is the maximum area of the rectangle $ U*I $. For the maximum power point $ P_{mm} $ the voltage value $ V_{m} $, at which the power is maximum and the current value $ I_{m} $, at which the power maximum are determined.

$Current-voltage characteristics of the illuminated photovoltaic cell, {OPENAGHMATHJAX()}V_{oc}{OPENAGHMATHJAX} - open circuit voltage, {OPENAGHMATHJAX()}I_{sc}{OPENAGHMATHJAX} - short circuit current, {OPENAGHMATHJAX()}P_{mm}{OPENAGHMATHJAX} - maximum power point, {OPENAGHMATHJAX()}I_{m}{OPENAGHMATHJAX} - current at the point of maximum power, {OPENAGHMATHJAX()}V_{m}{OPENAGHMATHJAX} - voltage at the point of maximum power. Own elaboration.$

Figure 1: Current-voltage characteristics of the illuminated photovoltaic cell, $ V_{oc} $ - open circuit voltage, $ I_{sc} $ - short circuit current, $ P_{mm} $ - maximum power point, $ I_{m} $ - current at the point of maximum power, $ V_{m} $ - voltage at the point of maximum power. Own elaboration.

The term fill factor $ FF $ is also used. The fill factor is the ratio of the maximum power received from a photovoltaic cell $ P_{max} $ to the product of the open circuit voltage $ V_{oc} $ and the short circuit current $ I_{sc} $. The value of the fill factor is determined from:

(2)

$ FF=\frac{P_{max}}{I_{sc}*V_{oc}} $

The efficiency of photovoltaic cells made of monocrystalline silicon in 2019 is about $ 26\% $, and for multicrystalline cells the efficiency is about $ 23\% $. As the temperature increases, the efficiency of PV cells decreases on average by $ 0.2\% $ for each degree of temperature increase above STC conditions. If the temperature rises by 20 $ _{}^{o}\textrm{C} $ then the efficiency decreases by about $ 4\% $ of the nominal value - that is, the panel with an efficiency of $ 25\% $ will have an efficiency of $ 24\% $ after a temperature increase of 20 $ _{}^{o}\textrm{C} $.
By entering a fill factor into the equation for the efficiency of the photovoltaic cell, the equation for the efficiency $ \eta $ takes the following form:

(3)

$ \eta =\frac{FF*I_{sc}*V_{oc}}{P_{light}} $

The efficiency of the cell depends on the wavelength and absorption coefficient. Considering these parameters, the above equation takes the form:

(4)

$ \eta(\lambda ) =\frac{FF(\lambda))*I_{sc}(\lambda)*V_{oc}(\lambda)}{P_{light}(\lambda)} $

Because of the above relationship, it is important to measure the absorption spectra of the materials that make up the PV cell.

The magnitudes of changes in these parameters are given in the data sheets of photovoltaic panels. An example of such a data sheet is the JASOLAR JAM60S09 data sheet $ I(U) $ [3] in which data can be found indicating that the voltage $ V_{oc} $ decreases as the temperature increases.

In summary, the characteristic quantities of a PV cell are:

$ \eta $ – the power conversion efficiency factor of a PV cell under STC conditions,
$ V_{oc} $ – open circuit voltage,
$ I_{sc} $ – short circuit current,
$ V_{m} $ – voltage at which maximum power is transferred to the load,
$ I_{m} $ – current at which maximum power is transferred to the receiver,
FF – fill factor,
$ P_{max} $ – the maximum power that can be obtained from the PV cell,
$ \alpha _{I_{sc}} $ – temperature coefficient $ I_{sc} $ in units of $ \% $ / $ _{}^{o}\textrm{C} $,
$ \beta _{V_{oc}} $ – temperature coefficient $ V_{oc} $ in units of $ \% $ / $ _{}^{o}\textrm{C} $,
$ \gamma _{Pmp} $ – temperature coefficient of power $ P_{max} $ in units of $ \% $ / $ _{}^{o}\textrm{C} $.

In addition to these parameters, the coefficients of change of PV cell properties with time are very often given. Furthermore, the operating time of the cell with an efficiency not less than $ 90\% $ is given.

Bibliography

1. B. Szymański: STC, NOCT. Warunki w jakich badane są baterie PV, GLOBEnergia : Odnawialne Źródła i Poszanowanie Energii 2013/3.
2. A. Luque, S. Hegedus: Handbook of photovoltaic science and engineering, Wiley, Hoboken, New Jork 2003.
3. JA Solar: 330W PERC Module JAM60S09 310-330/PR, [karta katalogowa], dostęp:10.09.2020

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3.6 Photovoltaic cell parameters

Bibliography