Abstract
The problem of the optimal siting and sizing of photovoltaic (PV) sources in grid connected distribution networks is addressed in this study with a master–slave optimization approach. In the master optimization stage, a discrete–continuous version of the Chu and Beasley genetic algorithm (DCCBGA) is employed, which defines the optimal locations and sizes for the PV sources. In the slave stage, the successive approximation method is used to evaluate the fitness function value for each individual provided by the master stage. The objective function simultaneously minimizes the energy purchasing costs in the substation bus, and the investment and operating costs for PV sources for a planning period of 20 years. The numerical results of the IEEE 33-bus and 69-bus systems demonstrate that with the proposed optimization methodology, it is possible to eliminate about 27% of the annual operation costs in both systems with optimal locations for the three PV sources. After 100 consecutive evaluations of the DCCBGA, it was observed that 44% of the solutions found by the IEEE 33-bus system were better than those found by the BONMIN solver in the General Algebraic Modeling System (GAMS optimization package). In the case of the IEEE 69-bus system, the DCCBGA ensured, with 55% probability, that solutions with better objective function values than the mean solution value of the GAMS were found. Power generation curves for the slack source confirmed that the optimal siting and sizing of PV sources create the duck curve for the power required to the main grid; in addition, the voltage profile curves for both systems show that voltage regulation was always maintained between ±10% in all the time periods under analysis. All the numerical validations were carried out in the MATLAB programming environment with the GAMS optimization package.
Highlights
Electricity is a fundamental right worldwide, and all national governments and multiple independent organizations strive together to make this public service universally accessible [1,2]
This graphic shows that 44 solutions with better numerical performance than the BONMIN solver were produced, which means that the proposed DCCBGA ensures, with 44% probability, the finding of a better solution when compared with the BONMIN solution in the IEEE 33-bus system
It is worth mentioning that after 100 consecutive evaluations of the proposed DCCBGA, the following values were obtained: a minimum value of US$/year 2,825,783.32, a maximum value of US$/year 2,844,469.50, a mean value of US$/year 2,829,498.36, and a standard deviation of US$/year 2827.18. These values imply the following: (i) All the solutions are near to the mean value, concentrated inside of a ball with a radius less than dollars. (ii) The minimum annual reduction in the operation costs is 26.65% for the maximum solution provided by the DCCBGA. (iii) The difference between the extreme solutions obtained by the DCCBGA is US$/year 18,686.18, i.e., less than 0.48% of the total annual operative costs in the benchmark case
Summary
Electricity is a fundamental right worldwide, and all national governments and multiple independent organizations strive together to make this public service universally accessible [1,2]. Studied the problem of the optimal siting and sizing of wind energy sources in distribution and transmission systems They solved the exact MINLP model with the help of the GAMS optimization package. The formulation of an MINLP model that represents the problem of the optimal siting and sizing of PV sources in grid-connected distribution networks with the aim of minimizing the total energy purchasing costs in the substation bus and the investment and operating costs of the PV sources for a planning horizon of 20 years. The remainder of this research is organized as follows: Section 2 presents the general optimization model for the optimal location and sizing of PV sources in grid-connected distribution networks considering investment and operating costs for a planning period with Nt years.
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