Risk-Based Capacitor Placement in Distribution Networks

In this paper, the problem of sizing and placement of constant and switching capacitors in electrical distribution systems is modelled considering the load uncertainty. This model is formulated as a multicriteria mathematical problem. The risk of voltage violation is calculated, and the stability index is modelled using fuzzy logic and fuzzy equations. The instability risk is introduced as the deviation of our fuzzy-based stability index with respect to the stability margin. The capacitor placement objectives in our paper include: (i) minimizing investment and installation costs as well as loss cost; (ii) reducing the risk of voltage violation; and (iii) reducing the instability risk. The proposed mathematical model is solved using a multi-objective version of a genetic algorithm. The model is implemented on a distribution network, and the results of the experiment are discussed. The impacts of constant and switching capacitors are assessed separately and concurrently. Moreover, the impact of uncertainty on the multi-objectives is determined based on a sensitivity analysis. It is demonstrated that the more the uncertainty is, the higher the system cost, the voltage risk and the instability risk are.