Confidence Level Optimization of DG Piecewise Affine Controllers in Distribution Grids

Distributed generators (DGs) reactive powers are controlled to mitigate voltage overshoots in distribution grids with stochastic power production and consumption. Classical DGs controllers may embed piecewise affine laws with dead-band terms. Their settings are usually tuned using a decentralized method which uses local data and optimizes only the DG node behavior. It is shown that when short-term forecasts of stochastic powers are Gaussian and the grid model is assumed to be linear, nodes voltages can either be approximated by Gaussian or sums of truncated Gaussian variables. In the latter case, the voltages probability density functions (pdf) that are needed to compute the overvoltage risks or DG control effort are less straightforward than for normal distributions. These pdf are used into a centralized optimization problem which tunes all DGs control parameters. The objectives consist in maximizing the confidence levels for which voltages and powers remain in prescribed domains and minimizing voltage variances and DG efforts. Simulations on a real distribution grid model show that the truncated Gaussian representation is relevant and that control parameters can easily be updated even when extra DGs are added to the grid. The DG reactive power can be reduced down to 50% or node voltages variances can be reduced down to 30%.