A modified Primal-Dual Logarithmic-Barrier Method for solving the Optimal Power Flow problem with discrete and continuous control variables

The aim of solving the Optimal Power Flow problem is to determine the optimal state of an electric power transmission system, that is, the voltage magnitude and phase angles and the tap ratios of the transformers that optimize the performance of a given system, while satisfying its physical and operating constraints. The Optimal Power Flow problem is modeled as a large-scale mixed-discrete nonlinear programming problem. This paper proposes a method for handling the discrete variables of the Optimal Power Flow problem. A penalty function is presented. Due to the inclusion of the penalty function into the objective function, a sequence of nonlinear programming problems with only continuous variables is obtained and the solutions of these problems converge to a solution of the mixed problem. The obtained nonlinear programming problems are solved by a Primal–Dual Logarithmic-Barrier Method. Numerical tests using the IEEE 14, 30, 118 and 300-Bus test systems indicate that the method is efficient.

[1]  G. L. Torres,et al.  On a nonlinear multiple-centrality-corrections interior-point method for optimal power flow , 2001 .

[2]  S. Granville.  Optimal reactive dispatch through interior point methods , 1994 .

[3]  Edméa Cássia Baptista,et al.  Loss minimization by the predictor–corrector modified barrier approach , 2009 .

[4]  L. Wehenkel,et al.  Sensitivity-Based Approaches for Handling Discrete Variables in Optimal Power Flow Computations , 2010, IEEE Transactions on Power Systems.

[5]  Lamine Mili,et al.  Optimal transformer tap selection using modified barrier-augmented Lagrangian method , 2003 .

[6]  R. G. Fenton,et al.  A MIXED INTEGER-DISCRETE-CONTINUOUS PROGRAMMING METHOD AND ITS APPLICATION TO ENGINEERING DESIGN OPTIMIZATION , 1991 .

[7]  Ralf Östermark,et al.  A multipurpose parallel genetic hybrid algorithm for non-linear non-convex programming problems , 2004, Eur. J. Oper. Res..

[8]  William F. Tinney,et al.  Optimal Power Flow Solutions , 1968 .

[9]  T. Westerlund,et al.  An extended cutting plane method for solving convex MINLP problems , 1995 .

[10]  Anthony V. Fiacco,et al.  Nonlinear programming;: Sequential unconstrained minimization techniques , 1968 .

[11]  Sven Leyffer,et al.  Solving mixed integer nonlinear programs by outer approximation , 1994, Math. Program..

[12]  H. Happ,et al.  Quadratically Convergent Optimal Power Flow , 1984, IEEE Transactions on Power Apparatus and Systems.

[13]  Lorenz T. Biegler,et al.  On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming , 2006, Math. Program..

[14]  Lamine Mili,et al.  Optimal transformer tap selection using modified barrier-augmented Lagrangian method , 2003, 2003 IEEE Power Engineering Society General Meeting (IEEE Cat. No.03CH37491).

[15]  Xifan Wang,et al.  A Robust Approach to Optimal Power Flow With Discrete Variables , 2009, IEEE Transactions on Power Systems.

[16]  K. Clements,et al.  An efficient interior point method for sequential quadratic programming based optimal power flow , 2000 .

[17]  John E. Beasley,et al.  Improving benders decomposition using a genetic algorithm , 2009, Eur. J. Oper. Res..

[18]  A. Monticelli,et al.  Adaptive movement penalty method for the Newton optimal power , 1991, IEEE Power Engineering Review.

[19]  W. Tinney,et al.  Discrete Shunt Controls in Newton Optimal Power Flow , 1992, IEEE Power Engineering Review.

[20]  G. L. Torres,et al.  An interior-point method for nonlinear optimal power flow using voltage rectangular coordinates , 1998 .

[21]  Laleh Behjat,et al.  Interior point models for power system stability problems , 2006, Eur. J. Oper. Res..

[22]  W. Tinney,et al.  Optimal Power Flow By Newton Approach , 1984, IEEE Transactions on Power Apparatus and Systems.

[23]  Yu-Chi Ho,et al.  An ordinal optimization theory-based algorithm for solving the optimal power flow problem with discrete control variables , 2004, IEEE Transactions on Power Systems.

[24]  S. Tso,et al.  An Extended Nonlinear Primal-Dual Interior-Point Algorithm for Reactive-Power Optimization of Large-Scale Power Systems with Discrete Control Variables , 2002, IEEE Power Engineering Review.

[25]  Sven Leyffer,et al.  Integrating SQP and Branch-and-Bound for Mixed Integer Nonlinear Programming , 2001, Comput. Optim. Appl..

[26]  W. F. Tinney,et al.  Some deficiencies in optimal power flow , 1988 .