Multi-Objective Mixed-Integer Dynamic Optimization Method Applied to Optimal Allocation of Dynamic Var Sources of Power Systems

For large power systems with huge proportions of industrial loads, dynamic var sources (DVSs) such as STATCOMs and generators provide significant protection against short-term voltage instability. Simultaneously optimizing the locations and capacities of STATCOMs and the settings for adjustment coefficients of generator excitation systems is a goal of this paper; thus, we formulate a multi-objective, mixed-integer dynamic optimization (MOMIDO) model subject to short-term voltage security and rotor-angle stability under multiple contingencies. We also present a reduced convex relaxation (RCR) method to handle STATCOM locations (which are integer variables) and to avoid their combinatorial explosion, and convert the MOMIDO model into a multi-objective nonlinear programming problem via Radau collocation. To obtain complete Pareto optimal solutions for the MOMIDO model, we propose a reduced wide normalized normal constraint (RWNNC) method by enlarging the Utopia plane so that the Pareto optimal solutions are covered completely by its vertical projection, while pruning redundant sections on the Utopia plane to reduce the amount of calculations. Moreover, the simulation results on an IEEE standard 39-bus system and a real provincial power system demonstrate that the proposed method can handle integer variables effectively and obtain complete Pareto optimal solutions.