Arrays with characteristic's mismatch
This tool allows for the phenomenological study of the resultant I/V characteristic of a module or PV array, composed of non identical cells or modules.
The program simulates the connection of any number of elements in series and in parallel - by affecting to the I/V model parameters of each element a random dispersion. The user can choose between a normal (gaussian) distribution, or a square distribution between 2 limits.
The elements can be cells, assembled in a module, or modules, protected with by-pass diodes.
The parameters that can be modulated are:
- the short-circuit current Isc (analogous to a non-homogenous irradiance distribution),
- the open circuit voltage Voc (which can also reflect temperature differences).
The programme calculates each characteristic according to the standard model, and then adds up point-by-point the voltages of the elements in series and the currents from series in parallel. The user can visually follow these operations. He then obtains the overall resultant characteristic of the field, and the program traces the "mean" characteristic (corresponding to elements, all of which are identical) and two envelope-characteristics which can be chosen as 2-RMS values, or as extreme random values encountered in the sample. The program evaluates the Power loss at maximum power point, and at a fixed operating voltage, with respect to the nominal case.
NB: The parameter dispersion being random, two successive executions of the same process will never give the same result !
You can choose the 3 following modes:
Group of Cells
Corresponds to the behaviour of the chosen PV module according to its cell's dispersion. Usually in a module, all cells form only one chain (sometimes two or more), therefore only the current dispersion is relevant. For such a module, one can see that the resulting characteristics is strongly influenced by the cell with the worst current, resulting in the flattening of the current plateau just below the maximum power point.
In such a figure, a bad cell may work in its reverse characteristics region (that is with a negative voltage) on part of the current plateau.
Remark: You will understand here the difficulty in exactly representing the operation of a real module with the help of usual models describing single cells, and that the use of too sophisticated cell-models (i.e., two-diodes models) will not improve the situation if they do not include this statistical distribution.
Group of modules
Simulates a whole array. In this case, the resulting figure looks quite different, with a "bumped" shape all along the plateau. This is due to the by-pass protection diodes, supposed to be always present in the modules. These give usually even better performances than nominal modules below half the nominal current, but degrade until the Maximum Power Point. One can see that the MPP power is much less affected than at fixed voltage operation below the MPP point.
Remark: in the region of low voltages, some modules are operating in the reverse polarisation region. The by-pass diode blocks the reverse current which normally would flow (be consumed) through the cells. This is the reason why the performances are better. Without diodes, the characteristics would show a linear plateau analogous to the cells behaviour in a single module, near to the worst module characteristics.
Group of modules with sorted modules
If we sort the PV elements to put them in increasing order of short-circuit current, in such a way that each series comprises modules with close characteristics, one can see a quite different behaviour. In this case, the diodes are no longer involved and the curve again becomes perfectly smooth. Each string behaves according to the average of its modules; but connecting them in parallel results in a characteristic very close to the average. This confirms that sorting the modules before mounting them in series can significantly improve the performances of an array, especially when working at fixed voltage.