Probabilistic load flow for photovoltaic distributed generation using the Cornish–Fisher expansion

This paper shows that in order to solve a probabilistic 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. Probabilistic load flows can be solved by analytical techniques as well as the Monte Carlo method. Our research study applied an analytical method that combined the cumulant method with the Cornish–Fisher expansion to solve this problem. The Monte Carlo method is used to compare the results of analytical method proposed.To evaluate the performance of photovoltaic distributed generation, this paper describes a probabilistic model that takes into account the random nature of solar irradiance. Therefore, load and photovoltaic distributed generation are modelled as independent/dependent random variables.The results obtained show that the technique proposed gave a better performance than the Monte Carlo method. This technique provided satisfactory solutions with a smaller number of iterations. Therefore, convergence was rapidly attained and computational cost was lower than that required for the Monte Carlo method. Besides, the results revealed how the Cornish–Fisher expansion had a better performance than the Gram–Charlier expansion, when input random variables were non-Gaussian.

► This paper presents a new probabilistic load flow using Cornish–Fisher expansion.
► Distributed generation are modelled as random variables in photovoltaic systems.
► Proposed method can be applied for keeping of voltages within desired limits.
► Computational cost is low enough than that required for Monte Carlo simulation.