Optimal Allocation of Dynamic Var Sources Using the Voronoi Diagram Method Integrating Linear Programing

Dynamic reactive power (var) sources can effectively mitigate fault-induced delayed voltage recovery (FIDVR) issues. This paper optimizes the sizes of dynamic var sources at given locations against FIDVR issues under severe contingencies. First, the geometric characteristics about the non-convex solution space of this problem are studied. Accordingly, a Voronoi diagram approach integrating linear programming (LP) is proposed, which disperses a number of sample points of potential solutions in the searching space to construct a Voronoi diagram blending the local cost functions over the entire space by Barycentric interpolation in Voronoi regions. New sample points are then recursively added, including the tentative optimal point using LP, the most depopulated area point ensuring global fidelity, and the connecting point, until the stopping criterion is met. The new approach is demonstrated in detail on the WSCC 9-bus system. A case study on the NPCC 140-bus system also validates that the proposed approach can effectively estimate the boundary and the geometry of the feasible solution region in the searching space and find the optimal solution.