Decentralized optimal power flow based on auxiliary problem principle with an adaptive core

Abstract

Distributed optimization (DO) for solving optimal power flow (OPF) problems is a fundamental task for coordinated planning, scheduling, and operation of interconnected power grids. Among various distributed OPF (D-OPF) studies, the method based on the auxiliary problem principle (APP), has the advantage of fully parallel and decentralized implementation, which only involves neighbor-to-neighbor communication and no need for a central coordinator. However, due to it taking a fixed quadratic core as the estimator of boundary information, the convergent rate is slow when solving the ill-conditioned D-OPF problems, since the search direction simply relies on the first-order gradient information. Besides, for the non-convexity of AC-OPF, only empirical criteria for the APP’s parameter settings have been provided. Thus, convergence is not always guaranteed when the operation state changes without the criterion to select and readjust algorithm parameters. In this paper, to further exploit the potentialities of the APP during online coordinated scheduling and operation of interconnected power grids, the D-OPF method based on an adaptive core APP (AC-APP) is proposed, in which second-order cone programming (SOCP) is adopted to guarantee the finite convergence. The adaptive core is updated according to the Hessians of the boundary variables at each iterative step to correct the search path with second-order information. Compared to the existing fixed core APP (FC-APP) based D-OPF method, the proposed AC-APP based D-OPF method can obtain branch flow results at a higher accuracy with fewer iterations, which facilitates the online application. On the other hand, a boundary equivalence approach for the D-OPF with SOCP convexification is developed, guaranteeing the convergence prerequisite of the AC-APP. Case studies based on the IEEE-118 bus system verified the effectiveness and superiority of the proposed method.