Uncertainty Quantification in Low Voltage Distribution Grids : Comparing Monte Carlo and General Polynomial Chaos Approaches

Changes in load and distributed generation in low voltage distribution systems (LVDS) have made the individual consumer offtake highly uncertain for the system operator. In order to accurately determine hosting capacity of such systems, congestion related stochastic indices, e.g. probability of undervoltage and overvoltage, must be calculated. These require either too many deterministic calculations (simulation-based methods) or the use of analytical probabilistic power flow. Numerical simulation-based methods often use a Monte Carlo (MC) based approach due to its simplicity. Recently, analytical methods such as general polynomial chaos (gPC) expansion have gained increasing interest. This paper develops a non-intrusive gPC formulation for congestion determination in LVDS and illustrates its effectiveness compared to the MC methods. Both MC and gPC methods are compared for computational time, and accuracy, for a set of realistic feeders with high photovoltaic (PV) penetration. The PV power injection uncertainty is characterized by a univariate continuous distribution. The paper illustrates the merits of using the general polynomial chaos expansion with degree 2 and Sobol sequences based testing points for the probabilistic assessment of LVDS with many uncertainty sources