Algorithm of inclusion and interchange of variables for capacitors placement

This work develops the algorithm of inclusion and interchange of variables to obtaining the sizes, the placements and the control schemes of the capacitors banks that minimize the annual total cost while complying with the maximum and minimum voltage constraints. This is a new and very efficient search method that improves the results of the previous contributions. The method considers all the possible locations for capacitors placement as well as the correct interrelation between sizes of all the capacitors of fixed and switched type. Instead of to place the capacitors on candidate nodes that are previously selected by sensitivity factors and then to select their time-controls, the presented method examines the placement of the capacitors in all available positions (node, control) by evaluating directly the effects of the inclusion and the interchange of variables (capacitors) in the value of the objective function. The fact that the optimization of the placements and the time-controls of the capacitors is coordinated with the selection of their sizes, allows the obtaining of a high quality solutions for the optimization problem. The effectiveness of the proposed method is tested by solving various examples and by comparing the obtained results with several previously published solutions for these examples.