Probabilistic Load Flow for Power Grids With High PV Penetrations Using Copula-Based Modeling of Spatially Correlated Solar Irradiance

This paper presents and applies an improved model for the instantaneous power generation from distributed photovoltaic (PV) systems intended for probabilistic load flow (PLF) simulations. The model combines a probability distribution model for the instantaneous solar irradiance at individual sites with an improved spatial correlation model and uses a Gaussian copula to allow correlated sampling from the distributions for an arbitrary set of distributed PV systems. We show that the model realistically reproduces the spatially distributed clear-sky index over a set of sites, based on comparisons with irradiance sensor network data. We also demonstrate that the probability distributions for system parameters such as customer voltage, substation loading, and power losses, obtained from PLF simulations with the model, differ substantially from those of a nonspatial approach. The results show that spatial irradiance modeling needs to be incorporated in PLF simulations in order not to overestimate the grid impacts of PV systems.