# American Institute of Mathematical Sciences

July  2007, 3(3): 553-567. doi: 10.3934/jimo.2007.3.553

## A semismooth Newton method for solving optimal power flow

 1 College of Electrical and Information Engineering, Changsha University of Science and Technology, China, China 2 Department of Electrical and Electronic Engineering, The University of Hong Kong, Hong Kong, China 3 Tsinghua University, China 4 Shangsha Jiao Tong University, China

Received  September 2006 Revised  April 2007 Published  July 2007

In this paper, we present some new optimization approaches to solve optimal power flow (OPF) problems. By using a so-called Nonlinear Complementarity Problem (NCP) function, the optimality condition (KKT system) of the original optimization problem is reformulated into a set of nonsmooth equations. The advantage of the new reformulation lies in that the inequality constraints are transformed into equations. The semismooth Newton-type method is applied to solve the reformulated equations. Moreover, we present a decoupled semismooth Newton method according to the inherent weak-coupling characteristics of power systems. The convergence of the new methods, especially for the decoupled method, are established. Numerical examples of both OPF and available transfer capability (ATC) problems demonstrate that the new algorithms are effective.
Citation: Xiaojiao Tong, Felix F. Wu, Yongping Zhang, Zheng Yan, Yixin Ni. A semismooth Newton method for solving optimal power flow. Journal of Industrial & Management Optimization, 2007, 3 (3) : 553-567. doi: 10.3934/jimo.2007.3.553
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