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

Linear approximation commonly used in solving ac optimal power flow (OPF) simplifies the system models but incurs accumulated voltage errors in large power networks. Such errors will make the primal–dual type gradient algorithms converge to solutions with voltage violations. In this article, we improve a recent hierarchical OPF algorithm that rested on primal–dual gradients evaluated with a linearized distribution power flow model. Specifically, we propose a more accurate gradient evaluation method based on an unbalanced three-phase nonlinear distribution power flow model to mitigate the errors arising from linearization. The resultant gradients feature a blocked structure that enables our development of an improved hierarchical primal–dual algorithm to solve the OPF problem. Numerical results on the IEEE 123-bus test feeder and a 4518-node test feeder show that the proposed method can enhance voltage safety at comparable computational efficiency with the linearized algorithm.