Abstract
In this study, a new methodology is proposed to perform optimal selection of conductors in three-phase distribution networks through a discrete version of the metaheuristic method of vortex search. To represent the problem, a single-objective mathematical model with a mixed-integer nonlinear programming (MINLP) structure is used. As an objective function, minimization of the investment costs in conductors together with the technical losses of the network for a study period of one year is considered. Additionally, the model will be implemented in balanced and unbalanced test systems and with variations in the connection of their loads, i.e., Δ- and Y-connections. To evaluate the costs of the energy losses, a classical backward/forward three-phase power-flow method is implemented. Two test systems used in the specialized literature were employed, which comprise 8 and 27 nodes with radial structures in medium voltage levels. All computational implementations were developed in the MATLAB programming environment, and all results were evaluated in DigSILENT software to verify the effectiveness and the proposed three-phase unbalanced power-flow method. Comparative analyses with classical and Chu & Beasley genetic algorithms, tabu search algorithm, and exact MINLP approaches demonstrate the efficiency of the proposed optimization approach regarding the final value of the objective function.
Highlights
Electrical distribution networks represent the largest portion of power systems entrusted with distributing electrical services to endusers via medium- and low- voltage levels by interfacing transmission/sub-transmission grids with consumers in rural and urban areas [1,2]
Even if the optimal selection of the conductors in electrical distribution networks is a sub-problem in the general planning of the distribution systems, this is a complex problem to solve because it is represented by a mixed-integer nonlinear programming (MINLP) model [9]
The main complications of this model are as follows: (i) existence of binary variables; (ii) strong nonlinearities in the power balance and objective functions; and (iii) the necessity for recalculating the admittance nodal matrix for each combination of the conductors. To deal with these difficulties in the mathematical model of the studied problem, we propose a master-slave optimization approach to solve the MINLP model based on the vortex search algorithm and a three-phase power flow method
Summary
Electrical distribution networks represent the largest portion of power systems (i.e., thousands of kilometers of length) entrusted with distributing electrical services to endusers via medium- and low- voltage levels by interfacing transmission/sub-transmission grids with consumers in rural and urban areas [1,2]. The main characteristics of these grids are as follows: (i) a radial configuration reduces the investment and operation costs as well as simplifies the coordination scheme of the protective devices [3]; (ii) the constructive structure of the network, i.e., horizontal and vertical configurations, ensures that the line impedances are unbalanced [4]; and (iii) the nature of the loads is unbalanced with ∆- and Y-connections [5]. Even if the optimal selection of the conductors in electrical distribution networks is a sub-problem in the general planning of the distribution systems, this is a complex problem to solve because it is represented by a mixed-integer nonlinear programming (MINLP) model [9] Note that this problem is binary ( integer) in relation to the selection of a particular caliber for each route and nonlinear due to the three-phase power balance equations [5]
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