Most PV installations contain more than two series-connected cells. In such cases a short circuit in a partially/completely shaded cell and the resulting far greater voltage load on the cell in question can provoke a hot spot, as the cell is then subjected to all of the voltage produced by the other cells (see Figure 4.18).
Figure 4.19 displays the characteristic curves for the scenario illustrated in Figure 4.18 for a 36-cell module with a cell area of around 102 cm2 (without bypass diodes); 35 of the cells have 1kW/m2 insolation and the aggregate characteristic curve is designated as K35. For locally shaded characteristic curves (whose mean insolation is indicated in the figure), voltage Vin the direction illustrated is negative.
Figure 4.18 Series connection of n solar cells during a short-circuit event. Here, a shaded or defective solar cell is subjected to the aggregate voltage of all other cells, i. e. around —(n — 1) ■ 0.5 V. The consequent operating point and the V and P of the shaded cell can be precisely determined using the characteristic curves in Figure 4.19. This overload voltage can be substantially reduced through the use of bypass diodes (dashed line)
In order to allow for determination of the operating point, the barrier characteristic curves as in Figure 4.16 are also shown here in the reverse voltage and current direction.
For a short-circuit scenario, the operating point can in principle be deemed simply to comprise the intersection of the barrier characteristic curve of the locally shaded cell (with the corresponding insolation) and the curve for the 35 fully insolated cells. Nonetheless, owing to the thermal instability of barrier characteristic curves, precise determination of the operating point is no easy matter. In many cases, however, the defined power loss can greatly exceed the approximate value indicated by
ITEM AVG TEMP DiffMean
Figure 4.20 Formation of a hot spot in a solar cell that is in normal operating mode and partly shaded by a shrub (the solar generator is operating at the MPP). The thermographic image shows that the reference module temperature (‘Ref’) is 38.7 °C but that the temperature of the insolated portion of the shaded cell has increased to 50.4 °C (‘S01’)
Equation 4.3, resulting in damage not only to partly or fully shaded solar cells, but also to the solar module as a whole.
Use of a bypass diode for each cell is of course very expensive. Hence one diode is normally used for each group of solar cells, e. g. for 12-24 cells (see Figure 4.23). By way of illustration of the conditions that obtain within such a group in this situation, Figure 4.19 displays the relevant characteristic curve for the scenario involving one bypass diode for 12 cells.
Noteworthy here is the fact that the highest power loss in the shaded cell is induced not by full shading, but rather by a partial shading scenario where the characteristic curve of the shaded cell traverses an element such as the MPP or I-V curve of the cell group (in the example, n — 12) that is bypassed by a bypass diode. The voltage in conductive bypass diodes is roughly the same as in an insolated cell.
Although a scenario where a solar module is operated at short-circuit current constitutes an unusual load, such a scenario is well within the realm of possibility. But partly shaded solar cells also heat up during normal operation, albeit to a lesser degree (see Figure 4.20).
Figure 4.21 displays the characteristic curves for the module illustrated in Figure 4.19 (35 fully insolated cells, 1 partly shaded cell), while a 12 V battery bank is being charged. In order to allow for determination of the operating point for the partly shaded cell, in addition to characteristic curve K35 for the 35 fully insolated cells the residual voltage (curve K35/12 V) for the partly shaded portion of the cell is also shown. Here, too, the operating point for the partly shaded cell comprises the intersection of the barrier characteristic curve for this cell (with the relevant insolation) and curve K35/12 V. Although the power loss attributable to the partly shaded cell is appreciably lower than at short-circuit current, it is still in the range of the approximate value from Equation 4.3, i. e. the partly shaded cell can become very hot, but without causing any damage.
Partial shading of a solar module solar cell also greatly alters the module’s characteristic curves and drastically reduces maximum power Pmax at the MPP. Figure 4.22 displays the resulting characteristic curves for the 36-cell solar module in Figure 4.19 (35 cells at 1 kW/m2 and 1 partly shaded cell with the indicated mean irradiance GBZ).