Combining IV Curves

There are two situations in which we combine IV curves: modules in series in a string, and strings in parallel in an array. As bypass diodes are included at the submodule level, we model behaviour at the submodule rather than module level.

Modules in Series in Strings

For modules in series in a string, we need to combine the IV curves of the individual submodules to create an IV curve for the entire string. The string current will be the identical through each submodule; the string voltage will equal the sum of the individual module voltages. To create the combined IV curve, an array of current values (\(I\)) between 0 and \(I_\text{sc}\) is considered. At each distinct value of \(I\), the corresponding voltages of all submodules are individually calculated and summed. The maximum power point (MPP) of a submodule normally lies at a "knee" in the curve, and it is important that a sufficiently large number of points on the curve are modelled so that the shape of the curve in this region is sufficiently accurate for interpolation.

Strings in Parallel in Arrays

In a PV array, strings are typically connected to inverters in parallel with other strings to form an Array, which is connected to a single set of inverter inputs. The inverter "sees" an IV curve at its inputs that is the net of all the parallel-connected string IV curves. The inverter regulates the operation of the array by controlling and varying the voltage across its inputs.

In such a parallel array, the voltages across the strings are equal (ignoring any small voltage drops that may occur in the DC wiring connecting the strings to the inverter). The currents from the individual strings combine and can be summed.

We first derive IV curves for each string as described above. The string IV curves so derived share a common array of current values (used to sum voltages), but the voltage values generally will not match between curves so the individual sting IV curves are interpolated to a common set of voltage values before summing the individual string current values at each voltage to build an IV curve representing the entire array for the given timestamp.