A MIQP model for optimal location and sizing of dispatchable DGs in DC networks
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A MIQP model for optimal location and sizing of dispatchable DGs in DC networks Oscar Danilo Montoya1,2 · Walter Gil‑González3 Received: 16 March 2019 / Accepted: 19 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The allocation and dimensioning of distributed generators (DGs) in direct current (DC) power grids were addressed in this study by using a mixed-integer quadratic programming (MIQP) formulation. The MIQP model corresponded to an approximation of the mixed-integer nonlinear programming (MINLP) model that represents this problem correctly. The proposed MIQP had, for its objective function, the minimization of the power losses; as constraints, it had power balance, voltage regulation, distributed generation capacity, and the number of DGs available, among others. The general algebraic modeling system (GAMS) was employed for solving the proposed MIQP as well as the MINLP formulation. Simulation results for one DC network with 21 nodes and another with 69 revealed that the proposed MIQP model obtains high-quality results regarding the locations of the generators, the objective function, and the power dispatch in comparison to the exact MINLP model and metaheuristic techniques recently reported in specialized literature. Keywords Direct current power grids · Distributed generators · Mixed-integer programming model · Mixed-integer nonlinear programming model · Optimal power flow Abbreviations AC Alternating current CONOPT Solver for mixed-integer optimization problems * Oscar Danilo Montoya [email protected]; [email protected] Walter Gil‑González [email protected] 1
Facultad de Ingeniería, Universidad Distrital Francisco José de Caldas, Carrera 7 No. 40B ‑ 53, Bogotá D.C 11021, Colombia
2
Laboratorio Inteligente de Energía, Universidad Tecnológica de Bolívar, km 1 vía Turbaco, Cartagena 131001, Colombia
3
Grupo GIIEN, Facultad de Ingeniería, Institución Universitaria Pascual Bravo, Campus Robledo, Medellín 050036, Colombia
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Vol.:(0123456789)
O. D. Montoya, W. Gil‑González
CPLs Constant power loads CRLs Constant resistive loads DC Direct current DGs Distributed generators GAMS General algebraic modeling system MINLP Mixed-integer nonlinear programming MIQP Mixed-integer quadratic programming SCIP Solver for mixed-integer optimization problems
1 Introduction The optimal design of direct current (DC) networks is a complicated topic, related to optimization [1, 2]. A DC network is an interconnection of ideal power sources (voltage-controlled nodes), distribution lines (pure resistive elements), constant power loads (CPLs), distributed generators (DGs), and constant resistive loads (CRLs), as shown in Fig. 1 [3–5]. Using circuit theory (Kirchhoff’s laws and Tellegen’s theorems), the combination of these elements generates a nonlinear set of algebraic equations that constitute a classical and well-known power flow problem [6, 7]. To solve this problem, numerical methods must be employed, e.g., GaussSeidell [1], Newton–Raphson [
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