The Allocation of Optimal Capacity of Solar Sources to Achieve the Maximum Penetration Rate and Improve the Voltage Profile in Distribution Systems

The problem of determining the optimal capacity and location of distributed generation resources is one of the important topics in the design and operation of power systems. To address this issue, this paper proposes a multi-objective developed model for optimal allocation of solar resources in radial distribution systems based on objective functions such as improving voltage profile, reducing losses, and maximizing penetration level. The optimal values, in other words, the capacity of solar resources to meet the optimal voltage profile and minimize losses under high penetration levels of these resources, have been obtained. Since these objectives are conflicting, a multi-objective developed algorithm called Gray Wolf Optimizer has been proposed to solve them simultaneously. Compared to other multi-objective problem-solving methods, the proposed Gray Wolf Optimizer demonstrates a high capability in solving multi-objective problems and finding Pareto fronts, while avoiding local optima. Additionally, in order to enhance the capabilities of the Gray Wolf Optimizer, a social hierarchy-based modified method has been employed to reduce solution time and improve the allocation matrix. Finally, the proposed method and the intended model have been evaluated on a standard system under various operating conditions. The obtained results show that the proposed method has been able to maintain an acceptable voltage profile and significantly reduce losses compared to other multi-objective algorithms. For low to medium penetration levels, losses tend to decrease until reaching a minimum value, and for penetration levels above 100%, losses increase. Furthermore, at a penetration level of 300%, the efficiency of the system has improved by about 12% in terms of voltage profile using the optimal allocation, indicating the excellent efficiency of the proposed method even at high penetration levels. Additionally, it has been demonstrated that in comparison to other multi-objective optimization methods, the proposed method has performed well in terms of the inverted generational distance parameter.