Probabilistic Energy Flow Calculation of Integrated Power-Gas Systems Based on Sparse Polynomial Chaos Expansion

Abstract

Probabilistic energy flow (PEF) is the foundation for the operation and planning of integrated power-gas systems (IPGS) considering multiple uncertainties from sources and loads. However, the PEF calculation based on traditional polynomial chaos expansion (PCE) incurs significantly higher computational cost in high-dimensional scenarios. Hence, an efficient PEF calculation method based on the sparse polynomial chaos expansion (SPCE) is proposed. First, a steady-state energy flow calculation model for IPGS is established considering the source-load uncertainty and the wind-solar correlation. Then, based on the principle of PCE, the bias estimation and cross-validation methods are used to choose the optimal expansion terms. Through a cyclic iteration involving the addition and deletion terms, the contribution of each expansion term is assessed to acquire the sparse polynomial. Finally, the probability distributions of each energy flow state variable of two typical IPGS are studied by the proposed SPCE method. Results indicate that the SPCE method can efficiently calculate the PEF and substantially reduce the computational cost compared with the traditional PCE and existing q-PCE methods while ensuring accuracy, particularly in the multidimensional input variables.