Pseudo-random simulation of node voltages in medium and low voltage grids with photovoltaic micro-installations

Abstract

Power generation by photovoltaic cells depends on random weather conditions, so at the planning stage the active powers output to the grid from photovoltaic micro-installations can be treated as multidimensional random variables with equal probability distribution. Such microinstallations’ passive power outputs depend on the pre-set power factor and therefore should be treated as multidimensional functions of the random active power outputs. Likewise, the received input powers can be treated the same way. Random changes in the output and input powers can be simulated using a pseudo-random number generator. Node voltages corresponding to the random outputs and inputs are derived from the iterative solution of nodal equations for each pseudo-random power balance. The resulting voltages are subjected to statistical analysis. This allows estimating the probability distribution, expected values and standard deviations, and to calculate the probabilities of exceeding the permitted voltage deviations. These considerations will be illustrated by an example calculation.