Uncertainty quantification in simulations of power systems: Multi-element polynomial chaos methods

While probabilistic methods have been used extensively in simulating stationary power systems, there has not been a systematic effort in developing suitable algorithms for stochastic simulations of time-dependent and reconfiguring power systems. Here, we present several versions of polynomial chaos that lead to a very efficient approach especially in low dimensions. We consider both Galerkin and Collocation projections, and demonstrate how the multi-element decomposition of random space leads to effective resolution of stochastic discontinuous solutions. A comprehensive comparison is presented for prototype differential equations and for two electromechanical systems used in an electric ship.