Influence of Module Temperature on Array Level

Analytical Description

As for the PV system level, also the instantaneous array performance ratio (prA) can be considered a linear function of module temperature. Like for the yield values in Section 2.2.4, it isolates the capture losses from the system losses as they occur in the inverter. If the array power is measured, this approach is preferred because the resulting temperature coefficient  also physically represents the temperature coefficient of the PV array. The array behavior can then be described analytically as

prA = prA,0(1 + T, (4) with

T Tmod – TSTC the module temperature above 25 °C standard test conditions,

 the temperature coefficient of power (usually negative),

prA the instantaneous array performance ratio and

prA,0 the model array performance ratio at 25 °C.

If the module temperature is measured in addition to in-plane irradiance and PV array output power, the coefficients  and prA,0 can be determined by linear regression. In practice this works well for high irradiance levels and we recommend omitting the samples measured at low irradiance from the regression, i.e., with GI < 600 W/m2. When prA values based on measurements are plotted over the module temperature, their relationship can be approximated by a straight line. Its slope can be interpreted as temperature coefficient of the PV array’s output power.

Plotting the scatter plot with a new regression line for each week (Figure 13) allows identifying the slope and intercept per week. Both values are expected to remain approximately constant over time. Consequently, sudden changes in these parameters from week to week would hint at acute disturbances. A significant trend over several weeks would hint towards a gradual change in system performance.

Examples and Interpretation

Figure 13 shows plots of array performance ratio versus module temperature for one PV system in different situations. Figure 13a is based on the same data set as Figure 12. The slopes and intersects of the regression lines are the same for weeks 1, 2 and 4. For week 3, the line is completely different and contrasting with the physical understanding that, for crystalline PV modules, the array efficiency decreases with increasing temperature. The reason for the exceptionally low prA values at low temperatures as they occur in this week could be snow on the PV array while the radiation sensor was free. In Figure 13b no such exceptional behavior is visible. Although the scatter clouds are relatively wide in terms of prA, all regression lines are close to each other. Notably, the review of data from several years and installations has shown many inconsistencies of the kind seen in Figure 13a especially during the winter months.

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(a) March 2011 (b) April 2013

Figure 13: Array performance ratio (prA) versus module temperature (Tmod) for

5 minute averages from SE2 (see Annex A) (inverter 1, samples with GI > 600

W/m2); different subsequent weeks in March 2011 and April 2013

The combined use of array yield versus reference yield and array performance ratio versus module temperature is illustrated in Figure 14 for two different installations in Malaysia.

For each of the four plots, the regression lines for the different weeks are virtually identical; hence, the system operation is stable over the four weeks. Comparing the amorphous silicon installation (a and b) with the crystalline silicon installation (c and d) reveals a significantly larger scatter for crystalline silicon. The array performance ratio (prA) is relatively low for the crystalline silicon plant. The influence of module temperature on the array performance ratio is much stronger for crystalline silicon than for the amorphous silicon plant. This is immediately visible when comparing Figure 14b) and d) and it also explains why in Figure 14c the scatter of yA versus yr bends to the right for high yr values.

Practical Use

As for performance ratio, the relationship of array performance ratio versus module temperature describes the thermal behavior of the PV array. And it complements the relationship of array yield versus reference yield with module temperature as additional parameter. Together both relationships can be used to determine a high-level parametric model of the PV array as they are typically used for power forecasting or the calculation of expected yield. Moreover, since they reflect physical relationships, any changes in their parameters point towards a change in the underlying physical reality, e.g., degradation, a fault, snow or shadow.

Altogether, the previous examples show how already with two linear relationships based on three data sets, the PV array can be described distinctively even for relatively short periods. The analysis may be sophisticated further. For example, if the behavior at low irradiance is of particular interest, non-linear terms of reference yield could be added. However, in line with the objectives of the present report, no such models will be treated here. Instead, in the following subsections, the same linear approach will be applied in order to include further parameters.

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(a) a-Si, yA vs yr (MY1) (b) a-Si, prA vs Tmod (MY1)

(c) c-Si, yA vs yr (MY2) (d) c-Si, prA vs Tmod (MY2)

Figure 14: Array yield and array performance ratio for two installations at the same site MY1 and MY2 with 5-min averages (see Annex A); four subsequent weeks in October 2012