Reactive Power Optimization for Distribution Network with Distributed Generators Based on Semi-Definite Programming

Abstract

Reactive power optimization for distribution network with distributed generators is a complicated nonconvex nonlinear mixed integer programming problem. This paper built a mathematical model of reactive power optimization for distribution network and a new method to solve this problem was proposed based on semi-definite programming. The original mathematical model was transformed and relaxed into a convex SDP model, to guarantee the global optimal solution within the polynomial times. Then the model was extended to a mixed integer semi-definite programming model with discrete variables when considering discrete compensation equipment such as capacitor banks. Global optimal solution of this model can be obtained by cutting plane method and branch and bound method. Numerical tests on the modified IEEE 33-bus system show this method is exact and can be solved efficiently.

Reactive Power Potential of Converter-Connected Renewables Using Convex Power Flow Optimization

“…The reactive power potential of a converter depends on two factors; the rated current 𝐼 𝑚𝑎𝑥 and, the minimum and maximum rated voltage for the converter. Most research works focus on the maximum current constraint on the converters and fail to account for the converter voltage constraints, thus leaving the converter reactive power capability model incomplete [13,16,[24][25][26][27][28][29][30][31][32][33][34][35].…”

“…Research works using a semidefinite programming (SDP) relaxation for solving optimal power flow have proven to be quite influential due to the guarantee of a global optimum [48][49][50][51][52]. This approach has been further extended to reactive power optimization, state estimation, securityconstrained optimal power flow, and multi-objective formulations in distribution networks, to name a few [20,24,[53][54][55][56]. The SDP model solves this research's power flow optimization problem as it guarantees a global minimum for the relaxed convex problem, provided the rank conditions are satisfied.…”