Abstract
The problem of the optimal siting and sizing of fixed-step capacitor banks is studied in this research from the standpoint of convex optimization. This problem is formulated through a mixed-integer nonlinear programming (MINLP) model, in which its binary/integer variables are related to the nodes where the capacitors will be installed. Simultaneously, the continuous variables are mainly associated with the power flow solution. The main contribution of this research is the reformulation of the exact MINLP model through a mixed-integer second-order cone programming model (MI-SOCP). This mixed-integer conic model maintains the nonlinearities of the original MINLP model; however, it can be solved efficiently with the branch & bound method combined with the interior point method adapted for conic programming models. The main advantage of the proposed MI-SOCP model is the possibility of finding the global optimum based on the convex nature of the power flow problem for each binary/integer variable combination in the branch & bound search tree. The numerical results in the IEEE 33- and IEEE 69-bus systems demonstrate the effectiveness and robustness of the proposed MI-SOCP model compared to different metaheuristic approaches. The MI-SOCP model finds the final power losses of the IEEE 33- and IEEE 69-bus systems of 138.416kW and 145.397kW, which improves the best literature results reached with the flower pollination algorithm, i.e., 139.075 kW, and 145.860kW, respectively. The simulations are carried out in MATLAB software using its convex optimizer tool known as CVX with the Gurobi solver.
Highlights
We can observe that (i) the proposed approach identifies nodes 12, 24, and 30 as the optimal places to locate capacitor banks with 450 kvar, 450 kvar, and 1050 kvar, respectively. One of these nodes differs from the solution reported by the fuzzy-real coded genetic algorithm (FRCGA) in which node 12 is replaced by node 13, and (ii) regarding the objective function, it is possible to observe that the proposed mixed-integer second-order cone programming (MI-second-order cone programming (SOCP)) model reduces grid power losses by about 34.40%, followed by the FRCGA and the two-stage method (TSM) with 34.08% and 33.06%
To demonstrate the effectiveness of the proposed MI-SOCP model in solving the problem of the optimal placement and sizing of capacitor banks in distribution networks, we economically compare the proposed MI-SOCP model and two recent literature reports presented by Riaño et al, in [3], in which the Chu & Beasley genetic algorithm (CBGA) and the exact solution in the GAMS software were applied to the IEEE
This paper focused on the optimal siting and sizing of fixed-step capacitor banks in electrical alternating current (AC) distribution using an MI-SOCP approach
Summary
Electrical distribution grids are responsible for delivering electricity to all end-users at medium- and low-voltage levels in rural and urban areas [1] These grids are typically built with radial configuration, as this topology allows reducing investment costs in conductors and grid infrastructure [2]. In the case of reactive power compensation with capacitor banks and distribution static compensators, the first devices are cheaper compared to the latter [14] Their maintenance is minimum, and their useful life is greater than 25 years [15], and they have high reliability [16], which makes capacitors the most reliable and efficient strategy to reduce power losses with minimum investment costs [13]
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