7.8.1 Electrical and Thermal Characteristics

The voltage of the module is, in principle, the number of series-connected cells times the voltage of the single cell, and the module current the number of paralleled cells times the single-cell current. Whichever the combination is, the module power theoretically equals the power of a single cell times their number; however due to ohmic losses (mainly in the tabs), optical losses and the mismatch effects a reduction in power of around 3-4% is observed. Mass-produced modules offered in the catalogs of manufacturers show power ratings that typically range from 150 to 300 Wp, delivered at current levels 5-10 A and at voltages 20-40 V. Lower and higher values in all the parameters are possible for special applications.

The manufacturer usually provides values of representative points (short-circuit, open-circuit and maximum power) of the module I – V curve measured at standard cell conditions (STC), i. e. 1 kW m-2 irradiance (= 0.1W-cm-2), AM 1.5 spectral distribution and 25 °C cell temperature. The maximum power of the module under STC is called the peak power and given in watts peak (Wp). While efficiency has the greatest importance for a solar cell, for a module it is less relevant since part of the area is not occupied by the expensive solar cells.

The conditions in real operation are not the standard ones; instead, they vary strongly and influence the electrical performance of the cell, causing an efficiency loss with respect to the STC nominal value. This loss can be divided into four main categories [188]: [61] 2 [62]

dependence of open-circuit voltage on photocurrent; at very low illumination the efficiency loss is faster and less predictable. Low shunt resistance in the device implies larger decreases in the efficiency at low irradiance levels.

4. Cell temperature. The ambient temperature changes and, because of the thermal insulation provided by the encapsulation, light causes cells in the module to heat above the ambient value; higher temperature means reduced performance. This is usually the most important per­formance loss.

On the other hand, prediction of the module response under different conditions is required to correctly assess the yearly production of a PV system in the field. The physical mechanisms of influence of temperature and irradiance on cell performance are well known, so that in principle prediction of module output could be rooted on physical models. This is however unpractical and a different approach is followed by PV system engineers.

Instead, very simple methods are used for translating the I – V performance to different operating conditions and standardized procedures have been developed for PV modules of indus­trial technologies [189]. These methods are applicable within a limited range of temperature and irradiance conditions that are not very far from those met when testing the module, and require a small number of easily measurable parameters. The module datasheets from the manufacturers use to include some of these allowing simplest estimates to be made:

NOCT -20 C
0.8kW • m-[63]

1. The steady-state power balance determines cell temperature: input is the absorbed luminous power, which is partially converted into useful electrical output and the rest dissipated to the surroundings. Convection is the main mechanism for heat dissipation in terrestrial, flat-plate applications, and radiation is the second non-negligible mechanism of heat dissipation. A com­mon simplifying assumption is made that the cell-ambient temperature drop increases linearly with irradiance. The coefficient depends on module installation, wind speed, ambient humidity, etc., although a single value is used to characterize a module type. This information is contained in the nominal operating cell temperature (NOCT), which is defined as the cell temperature when the ambient temperature is 20 °C, irradiance is 0.8 kW m-2 and wind speed is 1 m s-1. NOCT values around 45 °C are typical. For different irradiance values G this will be obtained:

2. The module short-circuit current is assumed strictly proportional to irradiance. It increases slightly with cell temperature (this stems from a decrease in bandgap and an improvement of minority carrier lifetimes). The coefficient a gives the relative current increment per °C. By combining both assumptions, the short-circuit current for arbitrary irradiance and cell temperature is calculated as:


Isc(TCe„, G) = /5C(STC) X —————– Tx(l +a(Tce„ – 25′:’C))

1kW • m-2

For crystalline Si a is around or 0.025% per °C (derived from an increase of 9 |iA/cm2-°C for a single cell).

3. The open-circuit voltage strongly depends on temperature (the main influence is that of the intrinsic concentration), decreasing linearly with it. Knowledge of the coefficient, called в, allows the open-circuit voltage to be predicted:

Voc (Tcell, G) = Voc (STC) – e(Tceii – 25°C)

The irradiance dependence is implicit in Tcell. For crystalline Si, в is a little above 2mV/°C per series-connected cell, that is, around 0.4% per °C.

4. A lot of factors affect the variation of the maximum power (or, equivalently, the efficiency) with irradiance and temperature. The parameter у is defined as the relative decrease in module efficiency per °C of cell temperature increase:

n(TceU, G) = n(STC) x (1 – y(TceU — 25°C))

Usual у values are near 0.5% per °C.

Updated: August 23, 2015 — 4:25 pm