Abstract
The problem of reactive power compensation in electric distribution networks is addressed in this research paper from the point of view of the combinatorial optimization using a new discrete-continuous version of the vortex search algorithm (DCVSA). To explore and exploit the solution space, a discrete-continuous codification of the solution vector is proposed, where the discrete part determines the nodes where the distribution static compensator (D-STATCOM) will be installed, and the continuous part of the codification determines the optimal sizes of the D-STATCOMs. The main advantage of such codification is that the mixed-integer nonlinear programming model (MINLP) that represents the problem of optimal placement and sizing of the D-STATCOMs in distribution networks only requires a classical power flow method to evaluate the objective function, which implies that it can be implemented in any programming language. The objective function is the total costs of the grid power losses and the annualized investment costs in D-STATCOMs. In addition, to include the impact of the daily load variations, the active and reactive power demand curves are included in the optimization model. Numerical results in two radial test feeders with 33 and 69 buses demonstrate that the proposed DCVSA can solve the MINLP model with best results when compared with the MINLP solvers available in the GAMS software. All the simulations are implemented in MATLAB software using its programming environment.
Highlights
Around the world, electric distribution networks are the channels through which electricity is supplied to millions of end-users at medium- and low-voltage levels [1]
The solution of the mixed-integer nonlinear programming problem (MINLP) model (1)–(6) for the optimal siting and sizing of DSTATCOMs in electric distribution networks using the discretecontinuous version of the vortex search algorithm (DCVSA) was implemented in the MATLAB version 2020b on a PC with an AMD Ryzen 7 3700 2.3-GHz processor and 16.0 GB RAM, running on a 64-bit version of Microsoft Windows 10 Single language
The DCVSA is used for determining the optimal locations for and sizes of the D-STATCOMs and the successive approximations of power flow (SAPF) method entrusted determines the voltage variables to calculate the annual energy losses of the grid and their cost
Summary
Electric distribution networks are the channels through which electricity is supplied to millions of end-users at medium- and low-voltage levels [1]. The conductors add to the investment costs associated with the installation of the DSTATCOMS, which is subjected to the classical power balance equations that generate a mixed-integer nonlinear programming problem (MINLP) This optimization model is solved in this research with the help of a master–slave optimization approach in which the master–slave relationship is based on DCVSA, which is entrusted with the optimal location and sizing of the D-STATCOMs. The slave stage (successive approximation power flow (SAPF) method) deals with the determination of the electrical variables to calculate the costs of the energy losses during the daily operation.
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