Efficient Integration of PV Sources in Distribution Networks to Reduce Annual Investment and Operating Costs Using the Modified Arithmetic Optimization Algorithm

The optimal integration of photovoltaic generation systems is a challenge for distribution utilities since these devices have a direct impact on company finances due to the large amount of investment required at the beginning of the planning project. In this investigation, the problem regarding the optimal siting and sizing of photovoltaic resources in medium-voltage levels is addressed from an economical point of view, where the optimization model that represents said problem corresponds to a mixed-integer nonlinear programming model. The maximum allowed size for single photovoltaic units in the distribution network is set at 2400 kW. The investment costs, energy purchase costs and maintenance costs for photovoltaic units, are considered in the objective function. Typical constraints such as power balance, generation capacities, voltage regulation, among others, are considered in the mathematical formulation. The solution of the optimization model is addressed by implementing a modified version of the Arithmetic Optimization Algorithm, which includes a new exploration and exploitation characteristic based on the best current solution in iteration t, i.e., $x_{\mathrm{best}}^t$. This improvement is based on a Gaussian distribution operator that generates new candidate solutions with the center at $x_{\mathrm{best}}^t$, which are uniformly distributed. The main contribution of this research is the proposal of a new hybrid optimization algorithm to solve the exact optimization model, which is based on a combination of the Arithmetic Optimization algorithm with the Vortex Search algorithm and showed excellent numerical results in the IEEE 34-bus grid. The analysis of quantitative results allows us to conclude that the strategy proposed in this work has a greater effectiveness with respect to the General Algebraic Modeling System software solvers, as well as with metaheuristic optimizers such as Genetic Algorithms, the Newton–Metaheuristic Algorithm, and the original Arithmetic Optimization Algorithm. MATLAB was used as a simulation tool.