Mismatch Loss Attributable to Manufacturing Tolerances

In cases of discrepancies between the characteristic curves of the modules in a specific string (i. e. one or more string modules exhibit power loss), string power loss is greater than would be expected based on the reduced aggregate output of all string modules. This additional power loss is attributable to a phenomenon known as mismatch loss, which will now be discussed in connection with various nMS string values.

All modules Exhibit 1 kW/m2 insolation and a cell temperature of TZ — 25 °C. Moreover, it is assumed that, owing to manufacturing tolerances, one module will exhibit the same characteristic curve as a module with only 900 W/m2 insolation. However, the remaining (nMS — 1) modules will exhibit normal characteristic curves at 1 kW/m2 insolation. The diagrams below also display VMPP voltage (MPP voltage under insolation of all nMS modules at 1kW/m2), VA1 voltage (12 V per module around the time of initiation of the charging process for a completely discharged battery bank whose nominal power is nMS ■ 12 V) and VA2 voltage (14 V per module around the time of completion of the charging process). For reasons of simplification, it is assumed that all modules are bypassed via an ideal bypass diode (passband voltage loss 0 V) and that the module temperature of all modules is 25 °C. These examples are likewise based on the M55 module.

Figure 4.41 displaysaseriesstring comprising nMS — 4M55modules, where outputandvoltageare5.2% and 10% lower for VMPP and VA2 respectively than for an intact string comprising the exact same type of module. These power losses are appreciably higher than the purely arithmetic 2.5% power loss in the string (three modules with 100% nominal module output PMo and one for which the figure is 90%). Even if the string is operated in the resulting new MPP of the string, its output will still be around 4.7% lower than for an intact string. Under Va1 conditions, however (intact string operating at far below MPP), the power loss is only around 2.5% owing to the available voltage buffer and is thus close to the arithmetic string power loss.

Figure 4.42 displays a series string comprising nMS — 9 M55 modules. where output and voltage are 4.2% and 1.5% lower for VMPP and VA2 respectively than for an intact string comprising the exact same type of module. These power losses are appreciably higher than the purely arithmetic 1.1% power loss in the string (eight modules with 100% nominal module output PMo and one for which the figure is 90%). Even if the string is operated at the resulting new MPP of the string, the output is still around 3.1% lower than for an intact string. Only with VA1 operation (intact string operating at far below MPP) is the power loss virtually nil, owing to the large available voltage buffer, and is thus lower than the arithmetic string power loss.

A more general investigation can be realized for mismatch loss in a string with nMS modules, nMSB of which exhibit power loss whereas the remaining modules (nMS — nMSB) exhibit normal characteristic curves. Figure 4.43 displays the resulting mismatch loss (at 1 kW/m2 insolation) compared with nominal string output (nMS ■ PMo) as a function of the relative number of modules with power loss aMM — nMSM/nMS. The resulting power loss under VMPP operation of the intact string (VMPP curve), under the resulting MPP operation of the string (MPP curve), and, for purposes of comparison, the purely arithmetic loss (SPM curve), are indicated for 5% and 10% module power loss relative to PMo. The VMPP curve is of interest here for a solar generator with numerous parallel-connected strings, for determining the effect of mismatch loss on an individual string. On the other hand, the MPP curve is the determining factor for a solar generator

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Mismatch in a PV Array String with 4 Modules

 

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Figure 4.41 Characteristic curves of a solar generator string comprising four M55 modules (cell temperature Tz — 25 0C) where G — 1 kW/m2 (e. g. for a48V stand-alone system). One of these modules exhibits a10% power loss (same characteristic curves as for a normal module at 900W/m2). All modules are bypassed by ideal bypass diodes. Vmpp — MPP voltage of the fully insolated string; VA2 — 14 V and VA1 — 12 V per module

 

Mismatch in PV Array String with 9 Modules

 

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Mismatch Power Losses Compared to Rated String Power

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Figure 4.43 Mismatch loss in a solar generator string comprising Siemens M55 modules, as a function of the relative number of modules with power loss aMM according to Equation 4.13. Suppositions: cell temperature TZ — 25 °C; 1 kW/m2 insolation in all modules; module loss 5% and 10%. All modules are bypassed by ideal bypass diodes. VMPP curve: operation of an intact string under MPP voltage VMPP; MPP curve: operation under the new MPP of the resulting V-I characteristic curve; SPM curve: purely arithmetic power loss induced by module power loss

 

aMM = Relative number of modules with reduced power

Подпись: Relative number of modules with power loss: aMM Подпись: nMSM nMS Подпись: (4.13)

comprising a single string, or in cases where all nSP parallel-connected strings of a larger solar generator have the exact same number of modules with power loss. The following is defined for Figure 4.43:

where nMS — number of modules per string (total number) and nMSM — number of modules per string with power loss (5% and 10%).

The curves in Figure 4.43 presuppose that at equal insolation the current in the weaker modules will be 10% and 5% lower than for a normal module. In other words, it was assumed that, in the solar cell equivalent circuit shown in Figure 3.12, the power source current will be proportionally weaker and that the other circuit elements will remain unchanged.

As Figure 4.43 shows, even with a relatively small number of modules with power loss (i. e. low aMM values), as well as with MPP voltage VMPP operation of an intact string (VMPP curve) and under operation with the newly resulting string MPP (MPP curve), appreciable mismatch loss occurs that far exceeds the expected purely arithmetic loss ( PM curve).

A comparison of these curves with the 5% and 10% module power loss shows that mismatch loss rises disproportionately as power loss increases. Under MPP voltage VMPP operation of an intact string, the power loss is greater than under operation of the newly resulting string MPP. This effect is particularly pronounced for low aMM values and 10% module power loss, where deviations translate into purely arithmetic output of more than 2% (operation under the new MPP) and 3% (VMPP operation of the intact string using modules with no power loss). With 5% module power loss, the curves for operation under the new and old MPP are virtually the same and the maximum deviation from pure arithmetic power loss is 0.6%. It is noteworthy here that even a relatively low proportion of modules with power loss (relatively low aMM) translates into noticeable string power loss. Hence, the energy yield in larger solar generators
can be maximized by using modules with the lowest possible manufacturing tolerances (Pmax and IMPPtolerance < 5%).

Updated: August 5, 2015 — 9:39 pm