Incremental-Oriented ADMM for Distributed Optimal Power Flow With Discrete Variables in Distribution Networks

In this paper, we present an incremental-oriented alternating direction method of multipliers (ADMM) for distributed optimal power flow with discrete variables in distribution networks. This algorithm consists of outer-loop iterations based on the extended interior-point method (EIPM), and inner-loop iterations based on ADMM. The outer-loop EIPM iteration was used to form a regional linear correction equation with coupling relationships between neighboring areas. This enables us to use ADMM to compute the primal-dual directions in a distributed manner. This novel application of ADMM inside EIPM can be considered as an independent linear equation solver; thus, its convergence can be guaranteed. In particular, the updating of the variable increments can be expressed in a closed form, speeding up ADMM. The resulting algorithm has more attractive convergence properties compared to ADMM directly applied to mixed-integer nonlinear programming problems. The convergence analysis is also given. The test results demonstrated that the proposed algorithm converged reliably and obtained a sufficiently feasible solution.