IEEE Transactions on Power Systems, Vol. 14, No. 4, November 1999
1292
A HYBRID GENETIC ALGORITHM FOR OPTIMAL REACTIVE POWER PLANNING BASED UPON SUCCESSIVE LINEAR PROGRAMMING Alberto J. Urdaneta
Juan F. Gomez
Senior Member, IEEE
Student Member, IEEE
Elmer Sorrentino
Universidad Simon Bolivar, Caracas, Venezuela Email:
[email protected]
Luis Flores
Ricardo Diaz C V.G EDELCA Caracas,Venezuela
Abstract. A hybrid methodologyis presented for the solution of the problem of the optimal allocation of reactive power sources. The technique is based upon a modified genetic algorithm (G.A.), which is applied at an upper level stage, and a successive linear program at a lower level stage. The objective is the minimization of the total cost associated to the installation of the new sources. The genetic algorithm is devoted to defining the location of the new reactive power sources, and therefore to handle the combinatorial nature of the fixed costs problem. At the lower level, the variable cost problem is solved by, calculating the magnitude of the sources to be installed at the previously determined locations by means of a linear prngram iterated successively with a fast decoupled load flow. Results are presented for the application of the proposed methodology when applied to the Venezuelan electric network.
Several techniques from the optimization field have been applied to different statements of this problem. [1,2,3]. The application of Benders decomposition technique was proposed [4] [5] to separate the integer variables associated with (i) from the real variables. Fuzzy set theory was applied to the Var planning problem with security constraints.[6] Global optimization techniques, such as genetic algorithms and simulated annealing have been applied in different fashions to the problem, [7] [SI [9] [lo] leading to improved solutions but with relatively slow performance. Hybrid algorithms have been proposed to combine the strengths of the approaches that search for global solutions with the speed of algorithms specifically adapted to the particular characteristics of the problem. [ 1I] [7] [121
I. INTRODUCTION
Genetic algorithms apply to a very broad class of optimization problems. However, they are specially competitive and recommended for solving optimization problems of combinatorial nature [13]. The separationofthe problem into two sub-problems, the planning sub-problem and the operation subproblem, solving the first one with a genetic algorithm and the second one by means of the successive linear programming technique, is proposed in [12]. The genetic algorithm at the planning stage decides the sites for the installation of the new reaclive power sources (associated to binary variables of a combinatorial nature), as well as the type and size of the sources to be installed. In this work the optimal reactive power source planning problem is solved, deciding the location of the new sources at a higher layer, while the type and size of the sources is decided at a lower layer. This partition is made to take advantage of the fact that at the upper layer the decision problem consists solely of binary variables, representing a combinatorial optimization problem, and therefore its solution by means of a genetic algorithm is proposed, considering that this type of algorithms are specially competitive for combinatorial optimization problems 1131. The problem at the lower layer, where the locations of the new sources are assumed as known and previously determined, is solved using successive linear programming, where a linear program is iterated successively with a fast decoupled algorithm for the load flow problem solution.
The optimal reactive power planning problem refers to the decision for the future locations, types, sizes and times of the installation of reactive power sources which guarantee a satisfactory system operation and particularly, adequate voltage levels throughout the system, at a minimum cost. The reduction of the transmission losses as well as the consideration of the system security and adequacy are aspects that may also be treated in the statement of the problem. In general, the mathematical formulation leads to a mixed nonlinear-integer problem of constrained optimization. The integer variables appear in the formulation with the mathematical representation of: i.- the installation or fixed cost of new reactive power sources at the different locations, ii.- the discrete availability of sizes or capacities of the reactive sources, and iii.- the discrete characteristics of the transformer tap positions. PE-241-PWRS-0-10-1998 A paper recommended and approved by the IEEE Power System Analysis, Computing and Economics Committee of the IEEE Power Engineering Society for publication in the IEEE Transactions on Power Systems. Manuscript submitted May 12, 1998: made available for printing November 10, 1998.
0885-8950/99/$10.00 0 1998 IEEE
1293
. - VAr. Generation Limits:
SLP has been successfully applied to the solution of the operation problem with continuous variables [14]. It permits the handling of the nonlinear characteristics of the problem, taking advantage of the speed and robustness of the linear programming algorithms and of the presently available methods for the load flow problem solution, such as the fast decoupled load flow method. Although the application of the methodology is performed for a single development scenario, its application may be extrapolated to the case of multiple planning stages, taking into account the set of equations of each of the stages, as well as some extra considerations to couple the scenarios one with each other.
Q"'"-q, 5 Q < Q"" + q ,
(5)
. - VAr. Installation Limits: q y
4,
