Partial or complete shading can provoke genuinely drastic power loss in a string comprising only a few modules (see Figure 4.22). In a string with nMS modules wired in series that integrate bypass diodes, the power loss induced by partial shading of individual modules increases with higher nMS. In such a case, the unshaded modules shift their operating point towards an open-circuit state, the voltage in these modules rises, and current flows via the bypass diodes to the partly or fully shadowed module. This is the second most important task of bypass diodes, after preventing hot spots.
The conditions associated with module shading for various nMS values for individual strings will now be discussed for scenarios where the insolation of each shaded module is only 100 W/m2 while the remaining (nMS — 1) modules continue to present 1 kW/m2 insolation. The diagrams below also display VMPP voltage (MPP voltage at insolation of all nMS modules at 1 kW/m2), VA1 voltage (12 V per module around the time of initiation of the charging process for a completely discharged battery whose nominal power is nMS ■ 12 V) and VA2 voltage (14 V per module around the time of completion of the charging process). In the interest of keeping the complexity of the conditions that come into play here within reasonable bounds, the discussion that follows also presupposes that (a) the shaded module is bypassed by an ideal bypass diode (0 V passband voltage loss) and (b) the module temperature of all modules is 40 °C (aggregate average of winter and summer temperatures). Although the examples described below are based on the M55 monocrystalline module (36 series-connected cells), they actually apply to all types of crystalline modules.
Figure 4.37 displays the conditions for the following: (a) nMS — 2 modules wired in series (e. g. in a 24 V stand-alone system), where current and power account for only 10% of the value of the unshaded string for VMPP, VA2; and (b) VA1. Hence, partial shading of a module in a string with only nMS — 2 has a very drastic effect on energy yield.
Figure 4.38 displays the conditions for nMS — 4 modules wired in series (e. g. in a 48 V stand-alone system). The VMPP power and current amount to more than 70% of the value of the unshaded string. VA2 and VA1 current have increased to around 62% and around 95% of baseline respectively, i. e. the power loss is relatively low owing to the bypass diodes.
Figure 4.39 displays the conditions for nMS — 9 modules wired in series (e. g. in a 110 V stand-alone system). Owing to the bypass diodes, the VMPP power and current amount to more than 70% of the value of the unshaded string. VA2 and VA1 current have returned to around 97% and nearly 100% of baseline respectively.
Figure 4.37 Solar generator string comprising two M55 modules (e. g. for a 24 V stand-alone system) with shading of a module that is bypassed by an ideal bypass diode and the following conditions obtain: cell temperature TZ — 40 °C; one module at 1 kW/m2 insolation; VMPP — MPP voltage of the fully insolated string; VA2 — 14 V; VA1 — 12V per module
A more general investigation can be realized for string power in nMS modules, nMSB of which are shaded (i. e. irradiation is still 100 W/m2), whereas the remaining modules (nMS — nMSB) present full 1kW/m2 insolation. Figure 4.40 displays an example for M55 modules where TZ — 40 °C cell temperature and relative string power is a function of the relative number of shaded modules aMB — nMSB/nMS. Although the
Figure 4.38 Solar generator string comprising four M55 modules (e. g. for a 48 V stand-alone system) with shading of a module that is bypassed by an ideal bypass diode and the following conditions obtain: cell temperature TZ— 40 °C; one module with 1 kW/m2 insolation; VMPP — MPP voltage of the fully insolated string; VA2 — 14 V; VA1 — 12 V per module
a E < c
0 50 100 VA1 VA2 150 200
Figure 4.39 Solar generator string comprising nine M55 modules (e. g. for a 110 V stand-alone system) with shading of a module that is bypassed by an ideal bypass diode and where the following conditions obtain: cell temperature TZ — 40°C; one module with 1kW/m2 insolation; VMPP — MPP voltage of the fully insolated string; VA2 — 14 V; VA1 — 12 V per module
calculation here was based on the characteristic curves of the M55 module, the resulting curves apply to all crystalline modules. Thus
where nMS — number of modules per string (total number) and nMSB — number of shaded modules per string.
As Figure 4.40 shows, when the fully insolated string is operated at MPP voltage VMpp, a power loss already occurs with low aMB values, whereby this power loss is small at first and then increases. However, if the string uses a lower voltage VA2 (14 V per module) or Va1 (12V per module), the power loss is virtually nil with low aMB values and only begins climbing as these values increase. Indeed, owing to the bypass diodes, the power loss induced by shading of individual modules is gradual in strings with large numbers of modules, whereby power only begins dropping precipitously when a substantial number of modules is shaded.