A Mixed-Integer Convex Model for the Optimal Placement and Sizing of Distributed Generators in Power Distribution Networks

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) mod...

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Bibliographic Details
Published inApplied sciences Vol. 11; no. 2; p. 627
Main Authors Gil-González, Walter, Garces, Alejandro, Montoya, Oscar Danilo, Hernández, Jesus C.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.01.2021
Subjects
Approximation
bound
branch &amp
Computer programs
Convex analysis
convex optimization
Distributed generation
distributed generators
Electric power distribution
Flow equations
Generators
Genetic algorithms
Heuristic
Integer programming
Mathematical models
method
Nonlinear programming
Optimization
Optimization techniques
Photovoltaics
Power factor
Power flow
second-order cone programming
Simulation
Sizing
Software
Solvers
Variables
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Summary: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.
ISSN:2076-3417
2076-3417
DOI:10.3390/app11020627