Decentralized Voltage Optimization Based on the Auxiliary Problem Principle in Distribution Networks with DERs

This paper addresses the problem of optimizing the voltage profile of radially-operated distribution systems by acting on the active and reactive powers provided by distributed energy resources (DERs). A novel voltage optimization procedure is proposed by adopting a decentralized control strategy. To this aim, a centralized voltage optimization problem (VOP), minimizing the distance of all the nodal voltages from their reference values, is firstly formulated as a strictly-convex quadratic program. Then, the centralized VOP is rewritten by partitioning the network into voltage control zones (VCZs) with pilot nodes. To overcome the lack of strictly convexity determined by the reduction to the pilot nodes, the dual centralized VOP working on the augmented Lagrangian function is reformulated and iteratively solved by the method of multipliers. Finally, a fully-distributed VOP solution is obtained by applying a distributed algorithm based on the auxiliary problem principle, which allows for solving in each VCZ a quadratic programming problem of small dimension and to drive the VCZ solutions toward the overall optimum by an iterative coordination process that requires to exchange among the VCZs only scalar values. The effectiveness and feasibility of the proposed method have been demonstrated via numerical tests on the IEEE 123-bus system.