A binary SFLA for probabilistic three-phase load flow in unbalanced distribution systems with technical constraints

► Probabilistic three phase load flow in radial distribution networks. ► Voltage regulation is one of the principal problems in distributed generation. ► Shuffled Frog-Leaping Algorithm and three phase probabilistic load flow. ► Numerical applications are presented regarding an unbalanced distribution system. This paper shows that in order to solve a probabilistic three phase load flow in radial distribution networks, it is necessary to apply effective techniques that take into account their technical constraints. Among these constraints, voltage regulation is one of the principal problems to be addressed in photovoltaic distributed generation. This paper applies a new method utilizing Shuffled Frog-Leaping Algorithm and three phase probabilistic load flow combined with the Monte Carlo method to solve this problem. The objective function used is the power losses expected value. Acceptable solutions are reached in a small number of iterations. Results prove that the proposed method can be applied for the keeping of voltages within desired limits at all load nodes of a photovoltaic grid-connected system. To evaluate the performance of photovoltaic system this paper has developed a probabilistic model that takes into account the random nature of solar irradiance and load. Numerical applications are presented and considered regarding the unbalanced distribution system IEEE 13-nodes and including photovoltaic generators at several nodes. The results obtained show the decrease of the power losses due to the presence of distributed generation.