Probabilistic load flow for radial distribution networks with photovoltaic generators

In this study, analytical techniques and the Monte Carlo method were both applied to solve a probabilistic load flow in radial distribution networks with photovoltaic-distributed generation, but considering the technical constraints that apply to the networks (e.g. voltage regulation). The analytical technique used in this study combined the method of cumulants with the Gram-Charlier expansion to resolve probabilistic load flow. This was performed by modelling the loads and the photovoltaic (PV) distributed generation as random variables. For this purpose, the authors developed a new probabilistic model that took into account the random nature of solar irradiance and load. The results obtained demonstrate that this new analytical technique can be applied to keep voltages within standard limits at all load nodes of radial distribution networks with photovoltaic-distributed generation. A computational cost reduction has demonstrated that the analytical technique used in this study performed better than the Monte Carlo method. Acceptable solutions were reached with a smaller number of iterations. Convergence was thus rapidly attained with a lower computational cost than that needed with the Monte Carlo method.