Application of Differential Evolution Algorithm for Transient Stability Constrained Optimal Power Flow

Consideration of transient stability constraints in optimal power flow (OPF) problems is increasingly important because modern power systems tend to operate closer to stability boundaries due to the rapid increase of electricity demand and the deregulation of electricity markets. Transient stability constrained OPF (TSCOPF) is however a nonlinear optimization problem with both algebraic and differential equations, which is difficult to be solved even for small power systems. This paper develops a robust and efficient method for solving TSCOPF problems based on differential evolution (DE), which is a new branch of evolutionary algorithms with strong ability in searching global optimal solutions of highly nonlinear and nonconvex problems. Due to the flexible properties of DE mechanism, the hybrid method for transient stability assessment, which combines time-domain simulation and transient energy function method, can be employed in DE so that the detailed dynamic models of the system can be incorporated. To reduce the computational burden, several strategies are proposed for the initialization, assessment and selection of solution individuals in evolution process of DE. Numerical tests on the WSCC three-generator, nine-bus system and New England ten-generator, 39-bus system have demonstrated the robustness and effectiveness of the proposed approach. Finally, in order to deal with the large-scale system and speed up the computation, DE is parallelized and implemented on a Beowulf PC-cluster. The effectiveness of the parallel DE approach is demonstrated by simulations on the 17-generator, 162-bus system.

[1]  Riccardo Poli,et al.  New ideas in optimization , 1999 .

[2]  Deqiang Gan,et al.  Stability-constrained optimal power flow , 2000 .

[3]  Tony B. Nguyen,et al.  Dynamic security-constrained rescheduling of power systems using trajectory sensitivities , 2003 .

[4]  Message P Forum,et al.  MPI: A Message-Passing Interface Standard , 1994 .

[5]  Vassilios Petridis,et al.  Optimal power flow by enhanced genetic algorithm , 2002 .

[6]  K.N. Shubhanga,et al.  Stability-constrained generation rescheduling using energy margin sensitivities , 2004, IEEE Transactions on Power Systems.

[7]  Luonan Chen,et al.  Optimal operation solutions of power systems with transient stability constraints , 2001 .

[8]  Anthony Skjellum,et al.  Using MPI - portable parallel programming with the message-parsing interface , 1994 .

[9]  William Gropp,et al.  Beowulf Cluster Computing with Linux , 2003 .

[10]  B. Jeyasurya,et al.  Integrating security constraints in optimal power flow studies , 2004, IEEE Power Engineering Society General Meeting, 2004..

[11]  R. Adapa,et al.  A review of selected optimal power flow literature to 1993. I. Nonlinear and quadratic programming approaches , 1999 .

[12]  R. Adapa,et al.  A review of selected optimal power flow literature to 1993. II. Newton, linear programming and interior point methods , 1999 .

[13]  Peter W. Sauer,et al.  Power System Dynamics and Stability , 1997 .

[14]  René Thomsen,et al.  A comparative study of differential evolution, particle swarm optimization, and evolutionary algorithms on numerical benchmark problems , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[15]  C. K. Tang,et al.  Hybrid transient stability analysis (power systems) , 1990 .

[16]  Hiroshi Sasaki,et al.  A solution of optimal power flow with multicontingency transient stability constraints , 2003 .

[17]  Vijay Vittal,et al.  Power System Transient Stability Analysis Using the Transient Energy Function Method , 1991 .

[18]  Mania Pavella,et al.  Generalized one-machine equivalents in transient stability studies , 1998 .

[19]  R. Storn,et al.  Differential Evolution - A simple and efficient adaptive scheme for global optimization over continuous spaces , 2004 .

[20]  K. R. Padiyar,et al.  ENERGY FUNCTION ANALYSIS FOR POWER SYSTEM STABILITY , 1990 .