A novel fuzzy logic Levenberg-Marquardt method to solve the ill-conditioned power flow problem

Abstract This paper presents a new three-step Levenberg-Marquardt (TSLM) algorithm by using fuzzy logic theory (FLT) for solving power flow equations in ill-conditioned power systems. Using the proposed fuzzy TSLM (FTSLM) method reduces computation times and the number of iterations. In most cases, the FTSLM method converges in the first iteration due to its biquadratic convergence. The reactive and real power mismatches at each bus of the electrical power system are chosen as the input values for fuzzification. The output values of the FTSLM (after defuzzification) are voltage magnitudes and angles of the buses. The proposed method is tested on standard ill-conditioned 11-bus, 13-bus, 43-bus, 118-bus and 2383-bus test systems and the results are compared with the benchmark methods.

[1]  A. Shahriari,et al.  The Non-divergence Newton-Based Load Flow Method in Ill Conditioned system , 2012 .

[2]  F. Milano.  Continuous Newton's Method for Power Flow Analysis , 2009, IEEE Transactions on Power Systems.

[3]  S. Iwamoto,et al.  A Fast Load Flow Method Retaining Nonlinearity , 1978, IEEE Transactions on Power Apparatus and Systems.

[4]  B. Stott,et al.  Review of load-flow calculation methods , 1974 .

[5]  Sayed Yaser Derakhshandeh,et al.  Application of high-order Newton-like methods to solve power flow equations , 2016 .

[6]  Pʻei-chih Chao,et al.  On the solution of ill-conditioned, simultaneous, linear, algebraic equations by machine computation , 1961 .

[7]  A. Griewank.  On Solving Nonlinear Equations with Simple Singularities or Nearly Singular Solutions , 1985 .

[8]  O. Malik,et al.  Load-Flow Solutions for Ill-Conditioned Power Systems by a Newton-Like Method , 1982, IEEE Transactions on Power Apparatus and Systems.

[9]  Hsiao-Dong Chiang,et al.  Fast Newton-FGMRES Solver for Large-Scale Power Flow Study , 2010, IEEE Transactions on Power Systems.

[10]  Hongbin Wu,et al.  A new approach combing connection number and fuzzy simulation to calculating power flow of distribution network considering uncertainty , 2013 .

[11]  Sayed Yaser Derakhshandeh,et al.  Application of high-order Levenberg–Marquardt method for solving the power flow problem in the ill-conditioned systems , 2016 .

[12]  Madan M. Gupta,et al.  Fuzzy mathematical models in engineering and management science , 1988 .

[13]  Fernando L. Alvarado,et al.  Interval arithmetic in power flow analysis , 1991 .

[14]  Eduardo M. Gouveia,et al.  Symmetric AC fuzzy power flow model , 2009, Eur. J. Oper. Res..

[15]  William F. Tinney,et al.  Power Flow Solution by Newton's Method , 1967 .

[16]  Miguel Heleno,et al.  A linearized approach to the Symmetric Fuzzy Power Flow for the application to real systems , 2014 .

[17]  Y. Tamura,et al.  A Load Flow Calculation Method for Ill-Conditioned Power Systems , 1981, IEEE Transactions on Power Apparatus and Systems.

[18]  O. Alsac,et al.  Fast Decoupled Load Flow , 1974 .

[19]  H. Mori,et al.  Optimal fuzzy inference for short-term load forecasting , 1995 .

[20]  Xiaolei Zheng,et al.  Ill-conditioned Load Flow Study Based on Asynchronous Parallel Computing in Rural Power Distribution Networks , 2012 .

[21]  J. G. Vlachogiannis,et al.  Fuzzy logic application in load flow studies , 2001 .

[22]  Mohammad Shahidehpour,et al.  Handbook of electrical power system dynamics : modeling, stability, and control , 2013 .

[23]  Mo-Yuen Chow,et al.  Application of fuzzy logic technology for spatial load forecasting , 1997 .

[24]  M. Karimi,et al.  Quadratic Discriminant Index for Optimal Multiplier Load Flow Method in ill conditioned system , 2014 .

[25]  A. Bakushinskii,et al.  Ill-Posed Problems: Theory and Applications , 1994 .

[26]  Ali Reza Seifi,et al.  Fuzzy load flow in balanced and unbalanced radial distribution systems incorporating composite load model , 2010 .

[27]  H. Keller.  Lectures on Numerical Methods in Bifurcation Problems , 1988 .

[28]  Xiaoyu Yang,et al.  Application of asymptotic numerical method with homotopy techniques to power flow problems , 2014 .

[29]  James A. Momoh,et al.  Overview and literature survey of fuzzy set theory in power systems , 1995 .

[30]  N. Rao,et al.  Power System Static State Estimation By the Levenberg-Marquardt Algorithm , 1980, IEEE Transactions on Power Apparatus and Systems.

[31]  Venkataramana Ajjarapu,et al.  The continuation power flow: a tool for steady state voltage stability analysis , 1991 .

[32]  R D Zimmerman,et al.  MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education , 2011, IEEE Transactions on Power Systems.

[33]  Sayed Yaser Derakhshandeh,et al.  A powerful method for solving the power flow problem in the ill-conditioned systems , 2018 .

[34]  Liang Chen,et al.  A high-order modified Levenberg-Marquardt method for systems of nonlinear equations with fourth-order convergence , 2016, Appl. Math. Comput..

[35]  Ying Chen,et al.  A Jacobian-free Newton-GMRES(m) method with adaptive preconditioner and its application for power flow calculations , 2006, IEEE Transactions on Power Systems.