Abstract
The optimal placement and sizing of distributed generators is a classical problem in power distribution networks that is usually solved using heuristic algorithms due to its high complexity. This paper proposes a different approach based on a mixed-integer second-order cone programming (MI-SOCP) model that ensures the global optimum of the relaxed optimization model. Second-order cone programming (SOCP) has demonstrated to be an efficient alternative to cope with the non-convexity of the power flow equations in power distribution networks. Of relatively new interest to the power systems community is the extension to MI-SOCP models. The proposed model is an approximation. However, numerical validations in the IEEE 33-bus and IEEE 69-bus test systems for unity and variable power factor confirm that the proposed MI-SOCP finds the best solutions reported in the literature. Being an exact technique, the proposed model allows minimum processing times and zero standard deviation, i.e., the same optimum is guaranteed at each time that the MI-SOCP model is solved (a significant advantage in comparison to metaheuristics). Additionally, load and photovoltaic generation curves for the IEEE 69-node test system are included to demonstrate the applicability of the proposed MI-SOCP to solve the problem of the optimal location and sizing of renewable generators using the multi-period optimal power flow formulation. Therefore, the proposed MI-SOCP also guarantees the global optimum finding, in contrast to local solutions achieved with mixed-integer nonlinear programming solvers available in the GAMS optimization software. All the simulations were carried out via MATLAB software with the CVX package and Gurobi solver.
Highlights
The proposed methodology for the IEEE 33-bus system is to multiples strategies presented in the literature, such as hybrid intelligent water drops and GA (GA-IWD) [31], mixed genetic algorithm with particle swarm optimization (GA-PSO) [32], loss sensitivity factor simulated annealing (LSFSA) [12], constructive heuristic vortex search algorithm (CHVSA) [33], teaching-learning based optimization (TLBO) [34], krill herd algorithm (KHA) [12], quasi-oppositional teaching-learning-based optimization (QOTLBO) [34], heuristic approach (AHA) [35], harmony search algorithm with particle swarm optimization (PSO) embedded artificial bee colony (HSA-PABC) [36], MINLP model [37], and mutated salp swarm algorithm (MSSA) [38]
For the IEEE 69-bus system, the proposed methodology is compared to the same literature reported for Case-1 with the exception of the HSA-PABC approach since it did not report any information for this feeder
Results of Case-2 In Case-2, the proposed convex model is compared to improved analytical (IA) [40], particle swarm optimization (PSO) [41], and MINLP
Summary
Distribution Networks. Appl. Sci. Grupo GIIEN, Facultad de Ingeniería, Institución Universitaria Pascual Bravo, Campus Robledo, Medellín 050036, Colombia Laboratorio Inteligente de Energía, Universidad Tecnológica de Bolívar, Cartagena 131001, Colombia Department of Electrical Engineering, University of Jaén, Campus Lagunillas s/n, Edificio A3, 23071 Jaén, Spain
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