Distribution Network Capacitor Planning as a Lattice Approximation Problem

This paper outlines a scalable solution for the capacitor planning problem suitable for large-scale distribution networks. The capacitor planning problem is non-deterministic polynomial (NP) hard, implying that the global solution via mixed-integer optimization is typically limited to smaller networks. The proposed method involves solving a second-order cone programming relaxation and formulating the solution rounding phase as a lattice approximation problem. The lattice approximation problem is constructed using sensitivity coefficients around the continuous solution and solved using the method of conditional probabilities. The outcome is a deterministic polynomial-time rounding algorithm whose solution quality is comparable to that obtained from state-of-the-art mixed-integer optimization. The method is demonstrated on distribution networks having up to 3147 nodes and involving fixed and switched capacitors whose settings can change over the subperiods of the study horizon.