A new technique for optimal size and location of capacitor banks in the presence of harmonics and distortion

Abstract This paper presents a new technique to optimize the number, location, and size of shunt capacitors on a radial distribution feeder in the presence of harmonics and distortion. The optimization objective is to achieve maximum savings resulting from reduced line losses. The mathematical model devised is a mixed 0–1 polynomial program, with restrictions imposed to limit the harmonic current magnification that resukts from parallel resonance. A global optimization algorithm for polynomial programs is utilized to solve this formulation. The effectiveness of this state-of-the-art algorithm ensures optimality to a complex mathematical model which more accurately represents the physical problem than other formulations. The method presented is suitable for solution on a personal computer, and has yielded promising initial results.

[1]  R. F. Cook,et al.  Optimizing the Application of Shunt Capacitors for Reactive-Volt-Ampere Control and Loss Reduction , 1961, Transactions of the American Institute of Electrical Engineers. Part III: Power Apparatus and Systems.

[2]  J. Grainger,et al.  Optimum Placement of Fixed and Switched Capacitors on Primary Distribution Feeders , 1981, IEEE Transactions on Power Apparatus and Systems.

[3]  Warren P. Adams,et al.  A hierarchy of relaxation between the continuous and convex hull representations , 1990 .

[4]  Warren P. Adams,et al.  A Tight Linearization and an Algorithm for Zero-One Quadratic Programming Problems , 1986 .

[5]  Miles Maxwell.  The Economic Application of Capacitors to Distribution Feeders , 1960, Transactions of the American Institute of Electrical Engineers. Part III: Power Apparatus and Systems.

[6]  M. Kaplan.  Optimization of Number, Location, Size, Control Type, and Control Setting of Shunt Capacitors on Radial Distribution Feeders , 1984, IEEE Transactions on Power Apparatus and Systems.

[7]  J. Grainger,et al.  Optimum Size and Location of Shunt Capacitors for Reduction of Losses on Distribution Feeders , 1981, IEEE Transactions on Power Apparatus and Systems.

[8]  R. F. Cook,et al.  Analysis of Capacitor Application as Affected by Load Cycle , 1959, Transactions of the American Institute of Electrical Engineers. Part III: Power Apparatus and Systems.

[9]  Hanif D. Sherali,et al.  Linearization Strategies for a Class of Zero-One Mixed Integer Programming Problems , 1990, Oper. Res..

[10]  Hanif D. Sherali,et al.  A Hierarchy of Relaxations and Convex Hull Characterizations for Mixed-integer Zero-one Programming Problems , 1994, Discret. Appl. Math..

[11]  Hernando Dura,et al.  Optimum Number, Location, and Size of Shunt Capacitors in Radial Distribution Feeders A Dynamic Programming Approach , 1968 .

[12]  Hanif D. Sherali,et al.  A global optimization algorithm for polynomial programming problems using a Reformulation-Linearization Technique , 1992, J. Glob. Optim..

[13]  J. V. Schmill,et al.  Optimum Size and Location of Shunt Capacitors on Distribution Feeders , 1965 .

[14]  Hanif D. Sherali,et al.  Mixed-integer bilinear programming problems , 1993, Math. Program..