A Multi-Stage Stochastic Non-Linear Model for Reactive Power Planning Under Contingencies

This paper presents a model for long-term reactive power planning where a deterministic nonlinear model is expanded into a multi-stage stochastic model under load uncertainty and an N-k contingency analysis. Reactive load shedding is introduced in the objective function to measure the reactive power deficit after the planning process. The objective is to minimize the sum of investment costs (IC), expected operation costs (EOC) and reactive load shedding costs optimizing the sizes and locations of new reactive compensation equipment to ensure power system security in each stage along the planning horizon. An efficient scenario generation and reduction methodology is used for modeling uncertainty. Expected benefits are calculated to establish the performance of the expected value with perfect information (EVPI) and the value of the stochastic solution (VSS) methodologies. The efficacy of the proposed model is tested and justified by the simulation results using the Ward-Hale 6-bus and the IEEE 14-bus systems.