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Linear approximation commonly used in solving alternating-current optimalpower flow (AC-OPF) simplifies the system models but incurs accumulated voltageerrors in large power networks. Such errors will make the primal-dual typegradient algorithms converge to the solutions at which the power networks maybe exposed to the risk of voltage violation. In this paper, we improve a recenthierarchical OPF algorithm that rested on primal-dual gradients evaluated witha linearized distribution power flow model. Specifically, we propose a moreaccurate gradient evaluation method based on a three-phase unbalanced nonlineardistribution power flow model to mitigate the errors arising from modellinearization. The resultant gradients feature a blocked structure that enablesus to further develop an improved hierarchical primal-dual algorithm to solvethe OPF problem. Numerical results on the IEEE $123$-bus test feeder and a$4,518$-node test feeder show that the proposed method can enhance the overallvoltage safety while achieving comparable computational efficiency with thelinearized algorithm.

A Hierarchical OPF Algorithm with Improved Gradient Evaluation in Three-Phase Networks