A pseudo-polynomial algorithm for optimal capacitor placement on electric power distribution networks

• Published in: European journal of operational research 2012-10, Vol.222 (1), p.149-156
• Main Authors: Vizcaino González, José Federico, Lyra, Christiano, Usberti, Fábio Luiz
• Format: Article
• Language: English
• Subjects: Applied sciences; Dynamic programming; Electric power; Electricity distribution; Exact sciences and technology; Heuristic; Mathematical programming; Operational research and scientific management; Operational research. Management science; Optimal capacitor placement; Optimization algorithms; OR in energy; Polynomials; Power distribution networks; Reduction of energy losses; Studies
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2012.03.042

► The paper rescues dynamic programming for solving the capacitor allocation problem. ► Optimal solutions are obtained with linear time complexity for real life networks. ► Both fixed and switched capacitors are considered. ► Case studies certify the methodology with real world applications. Allocation of shunt capacitor banks on radial electric power distribution networks allow reduction of energy losses and aggregated benefits. Four decades ago Durán proposed the use of dynamic programming to find optimal capacitor placement on these networks; however, with the restricting assumption of single-ended networks, which precluded its application to real capacitor allocation problems. Subsequently heuristic methods prevailed in the capacitor allocation literature. Here the Extended Dynamic Programming Approach (EDP) lifts Durán’s restricting assumption; a richer definition of state and the projection of multidimensional informations into equivalent one-dimensional representations are the supporting concepts. In addition to allow consideration of multi-ended networks, EDP deals with other requirements of capacitor allocation studies, including the use of both fixed and switched capacitors and representation of voltage drops along the networks. When switched capacitors are considered the optimization procedure also solves the capacitor control problem, obtaining the best tap adjustments for them. Case studies with real scale distribution networks put into perspective the benefits of the methodology; EDP has the appeal of providing global optimal solutions with pseudo-polynomial computational complexity in the worst-case, and with linear complexity for practical applications.