7. Shadow sensitivity of a photovoltaic generator
7.5. The effect of shadowing on the characteristics of maximum power point
are naturally minimized. These simulation results are consistent with data, which shows that parallel connection PV cells suffers less from shading compared to series connection of PV cells, provided by, for example, Ramabadran & Mathur [Ram09a].
7.5. The effect of shadowing on the characteristics of maximum power point
Operating conditions do not only affect the maximum power of the generator, but also the properties of maximum power point itself. In simulations the effect of shadowing on the maximum power point was also investigated. This was done only to the ‘Long string’ generator, because the effect of partial shadowing is most severe to long series connection of PV modules. The results of the simulations are shown in Figures 7.9 to 7.15. Figure 7.9 illustrates the number of maximum power points in varying shadowing conditions.
Figure 7.9. Number of maximum power points in the ‘Long string’ generator under varying shadowing conditions.
There is an area in the middle of the Figure 7.9 where the generator has two maximum power points. Around that area, there is only one maximum power point except in the corner of the figure, where both the system shadowing and shadow opacity are almost 100% where there are no maximum power points at all. This means that no power can be extracted, because the voltage is not sufficient to switch the bypass diodes on. It can also be seen that when only a small portion of the generator is shadowed or when the shadow opacity is low, there is only one maximum power point although there are two different irradiance values influencing the PV generator. The fact that there is only one maximum power point although the PV generator has two different irradiance values is consistent with data provided by, for example, Ramabadran & Mathur [Ram09b] and Patel & Agarwal [Pat08].
Figure 7.10 illustrates the power difference of the maximum power points that the generator have under varying shadowing conditions. The absolute value of the power difference of the two maximum power points is shown in Figure 7.10 relative to the power of global maximum power point.
0.1
Figure 7.10. The power difference between two maximum power points relative to the larger maximum power points.
As can be seen from Figure 7.10, the power difference between two maximum power points is largest at the boundary between the condition with only one maximum power point and two maximum power points. This can be seen when comparing Figures 7.9 and 7.10. In Figure 7.10, the difference in power of two maximum power points is smallest in the diagonal from the origin to the corner in which both the system
shadowing and shadow opacity are 100%. This means that if the maximum power point tracker operates in wrong maximum power point, the amount of energy lost can be significant if the operating conditions are such as in the boundary between conditions with one and two maximum power points. In the diagonal of the Figure 7.10, failing of the maximum power point tracking is not so harmful, because the maximum power points are almost the same in these conditions, as long as the generator operates in some maximum power point.
The power that can be extracted when the generator is operating in a maximum power point is very important when evaluating the performance of the photovoltaic generator. It is also important to know the voltage of the maximum power point in order to track the maximum power point. Figure 7.11 illustrates the effect of shadowing on the voltage of the maximum power point.
50
Figure 7.11. Voltage of the maximum power point in varying operating conditions. The values in the contour graph are in volts.
It can be seen from Figure 7.11 that the voltage of the maximum power point is highest in the middle of the figure, where the voltage is over 450 V. It can also be seen that in over half of the cases, mostly below the diagonal, the voltage of the maximum power point is higher than 400 V. It can also be seen that the voltage of the maximum power point changes rapidly if system shadowing or shadow opacity changes so that the diagonal in the Figure 7.11 is crossed. This is because when a PV generator has two maximum power points, one has higher voltage than the other as was shown in Figure 4.4. In the diagonal of Figure 7.11, the power of the maximum power point with lower
voltage becomes greater than the power of the maximum power point with higher voltage or vice versa depending on the system shadowing or shadow opacity. For example, if the system shadowing is 50% and shadow opacity changes from 40% to 60%, then the power of the maximum power point with lower voltage becomes greater than the power of the maximum power point with higher voltage. As was seen from Figure 7.10, in the diagonal the power of the maximum power points are the same.
Figure 7.12 is a crosscut from figure 7.11 and it illustrates the voltages of the maximum power points when shadow opacity is 20%. There is only one maximum power point when system shadowing is less than 6% or more than 75%.
0 10 20 30 40 50 60 70 80 90 100
0 50 100 150 200 250 300 350 400 450 500
System shadowing (%)
Maximum power point voltage (V)
UMPP1 UMPP2 P > P
MPP1 MPP2 P < P MPP1 MPP2
Figure 7.12. Voltages of two maximum power points of the generator when shadow opacity is 20%.
0 10 20 30 40 50 60 70 80 90 100 0
500 1000 1500 2000 2500
System shadowing (%)
Maximum power (W)
PMPP1
PMPP2
Figure 7.13. Powers of two maximum power points of the generator when shadow opacity is 20%.
The vertical line in Figure 7.12 illustrates the point where two maximum power points have the same power. This point can clearly be seen from Figure 7.13, which shows the maximum powers of the situation in Figure 7.12. As can be seen from Figures 7.12 and 7.13, in case of shadow opacity of 20%, maximum power point with higher voltage becomes the global maximum power point when only 9% of the generator is shadowed.
Figure 7.14 is a crosscut from figure 7.11 and it illustrates the voltages of the maximum power points when shadow opacity is 80%. There is only one maximum power point when system shadowing is less than 18% or more than 93%.
0 10 20 30 40 50 60 70 80 90 100 0
50 100 150 200 250 300 350 400 450 500 550
System shadowing (%)
Maximum power point voltage (V)
UMPP1
UMPP2
P > PMPP1 MPP2 P < P
MPP1 MPP2
Figure 7.14. Voltages of two maximum power points of the generator when shadow opacity is 80%.
0 10 20 30 40 50 60 70 80 90 100
0 500 1000 1500 2000 2500
System shadowing (%)
Maximum power (W)
PMPP1 PMPP2
Figure 7.15. Powers of two maximum power points of the generator when shadow opacity is 80%.
The vertical line in Figure 7.14 illustrates the point where two maximum power points have the same power. This point can clearly be seen from Figure 7.15, which
shows the maximum powers of the situation in Figure 7.14. As can be seen from Figures 7.14 and 7.15, in case of shadow opacity of 80%, maximum power point with higher voltage becomes the global maximum power point when 76% of the generator is shadowed.
When comparing Figures 7.12 to 7.15, it can be seen that it doesn’t matter if the shadow opacity is 20% or 80%, UMPP1 and PMPP1 are the same, excluding the fact that they exist in different system shadowing. UMPP2 and PMPP2, on the other hand, are different from each other in case of different shadow opacity. It can be seen from Figures 7.13 and 7.15 that the level of PMPP2 is much lower when shadow opacity is increased from 20% to 80%. This means also that the point where the maximum powers PMPP1 and PMPP2 are equal to each other shifts to higher system shadowing as shadow opacity increases.