# American Institute of Mathematical Sciences

January  2008, 4(1): 143-153. doi: 10.3934/jimo.2008.4.143

## Semismooth reformulation and Newton's method for the security region problem of power systems

 1 Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong 2 Department of Electrical Engineering, Shanghai Jiaotong University, Shanghai 200030, China 3 CAS Research Center on Data Technology and Knowledge Economy, School of Mathematics, Graduate University of Chinese Academy of Sciences, Beijing, 100049, P.R., China

Received  September 2006 Revised  November 2007 Published  January 2008

In this paper, we investigate the reformulation of the steady state security region problem for electrical power systems. Firstly, a simple security region problem with one changeable parameter is reformulated into a system of semismooth equations, which is composed by the normal power flow equations and an additional piecewise smooth equation. Then the semismooth Newton method and the smoothing Newton method can be applied to solve the problem. Preliminary numerical results show that the method is promising. Finally, by using the smoothing technique, a more complicated security region problem, the Euclidean security region problem, is reformulated as an equality constrained optimization problem. These works provide a possibility to implement on-line calculation of the security region of electrical power systems.
Citation: Liqun Qi, Zheng yan, Hongxia Yin. Semismooth reformulation and Newton's method for the security region problem of power systems. Journal of Industrial & Management Optimization, 2008, 4 (1) : 143-153. doi: 10.3934/jimo.2008.4.143
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