Cumulant-based stochastic nonlinear programming for variance constrained voltage stability analysis of power systems

This paper proposes a Cumulant Method-based solution to solve a maximum loading problem incorporating a constraint on the maximum variance of the loading parameter. The proposed method takes advantage of some properties regarding saddle node bifurcations to create a linear mapping relationship between random bus loading variables and all other system variables. The proposed methodology is tested using a sample system based on the IEEE 30-bus system using random active and reactive bus loading. Monte Carlo simulations consisting of 10 000 samples are used as a reference solution for evaluation of the accuracy of the proposed method.

[1]  G. Heydt,et al.  Stochastic Optimal Energy Dispatch , 1981, IEEE Transactions on Power Apparatus and Systems.

[2]  Y. B. Lee,et al.  Cumulant Based Probabilistic Power System Simulation Using Laguerre Polynomials , 1989, IEEE Power Engineering Review.

[3]  Roy Billinton,et al.  Bibliography on power system probabilistic analysis (1962-88) , 1990 .

[4]  Claudio A. Canizares,et al.  Point of collapse and continuation methods for large AC/DC systems , 1993 .

[5]  Kumaraswamy Ponnambalam,et al.  Probabilistic optimal power flow , 1998, Conference Proceedings. IEEE Canadian Conference on Electrical and Computer Engineering (Cat. No.98TH8341).

[6]  John M. Wilson,et al.  Introduction to Stochastic Programming , 1998, J. Oper. Res. Soc..

[7]  N. D. Hatziargyriou,et al.  Probabilistic load flow for assessment of voltage instability , 1998 .

[8]  W. Rosehart,et al.  Optimal power flow incorporating voltage collapse constraints , 1999, 1999 IEEE Power Engineering Society Summer Meeting. Conference Proceedings (Cat. No.99CH36364).

[9]  R. H. Lasseter,et al.  Stochastic optimal power flow: formulation and solution , 2000, 2000 Power Engineering Society Summer Meeting (Cat. No.00CH37134).

[10]  Costas D. Vournas,et al.  Relationships between static bifurcations and constrained optima , 2000, 2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353).

[11]  D. Yap,et al.  Microfixtured assembly for lensed optoelectronic receivers , 2001, IEEE Transactions on Advanced Packaging.

[12]  Joaquim R. R. A. Martins,et al.  The complex-step derivative approximation , 2003, TOMS.

[13]  Claudio A. Canizares,et al.  Multiobjective optimal power flows to evaluate voltage security costs in power networks , 2003 .

[14]  S.T. Lee,et al.  Probabilistic load flow computation using the method of combined cumulants and Gram-Charlier expansion , 2004, IEEE Transactions on Power Systems.

[15]  J. Aguado,et al.  Cumulant based probabilistic optimal power flow (P-OPF) , 2005, 2004 International Conference on Probabilistic Methods Applied to Power Systems.

[16]  J. Aguado,et al.  Cumulant-based probabilistic optimal power flow (P-OPF) with Gaussian and gamma distributions , 2005, IEEE Transactions on Power Systems.

[17]  W. Rosehart,et al.  Cumulant based stochastic optimal power flow (S-OPF) for variance optimization , 2005, IEEE Power Engineering Society General Meeting, 2005.