Impact of Solar Uncertainties on Distribution System Performance: A PEM-Based Probabilistic Load Flow Study

The increasing penetration of photovoltaic (PV) generation into distribution networks introduces significant variability and uncertainty, primarily due to fluctuating solar irradiance. These uncertainties directly affect system performance, particularly in terms of voltage stability, power losses, and overall reliability. Conventional deterministic load flow analysis cannot adequately capture such stochastic behaviour, making probabilistic approaches essential. This study presents a probabilistic load flow (PLF) framework based on the Point Estimate Method (PEM) to quantify the impact of solar uncertainties on distribution system performance. The proposed methodology is applied to the IEEE 34-bus radial distribution system, where solar generation is modelled as a stochastic variable with probability distributions derived from irradiance profiles. PEM is employed to efficiently approximate statistical moments of the system response. Performance metrics such as voltage deviation and system power losses, are evaluated under varying PV penetration levels. Simulation results reveal that solar uncertainties significantly influence the distribution of bus voltages and network losses, with higher penetration levels leading to increased probabilities of undervoltage and overvoltage conditions. The findings highlight the necessity of incorporating probabilistic analysis in planning and operation of PV-integrated distribution systems.