On the Conic Convex Approximation to Locate and Size Fixed-Step Capacitor Banks in Distribution Networks

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 wh...

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Veröffentlicht in:Computation Jg. 10; H. 2; S. 32
Hauptverfasser: Montoya, Oscar Danilo, Gil-González, Walter, Garcés, Alejandro
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel MDPI AG 01.02.2022
Schlagworte:
Algorithms
Approximation
Branch and bound methods
Capacitor banks
Capacitors
Computational geometry
Continuity (mathematics)
Convex analysis
Convexity
distribution networks
Energy
Genetic algorithms
Heuristic methods
Integer programming
Linear programming
Methods
Mixed integer
Nonlinear programming
Nonlinearity
Optimization
Power
Power flow
power losses minimization
Robustness (mathematics)
second-order cone programming model
Simulation
System effectiveness
ISSN:2079-3197, 2079-3197
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Zusammenfassung: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.
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ISSN:2079-3197
2079-3197
DOI:10.3390/computation10020032