A New Adaptive Sparse Pseudospectral Approximation Method and its Application for Stochastic Power Flow

With the increasing integration of various renewable energy resources into electric power systems, the stochastic power flow calculation, which falls into the uncertainty propagation (UP) problems, has attracted renewed interest recently. The adaptive sparse pseudospectral approximation method (A-SPAM) is highly efficient to solve UP problems. However, there still exist two major drawbacks: 1) its global error estimate is not accurate enough to evaluate the actual approximation error; and 2) it is intended for single-output systems and there is no efficient method for its application in multi-output systems. In order to overcome these two defects, in this study a new adaptive sparse pseudospectral approximation method (NA-SPAM) is proposed based on two improvements on A-SPAM. First, a new global error estimate is presented which features much higher estimation accuracy. Second, a revised version of error estimates is given based on unification of the index set, which apparently improves the calculation efficiency for multi-output problems. At last, the effectiveness of the two improvements and NA-SPAM is validated by mathematical and practical cases.