Probabilistic Energy Flow Calculation Based on Data-Driven Arbitrary Polynomial Chaos Expansion With Mixed Uncertainties

Probabilistic energy flow (PEF) analysis is an essential tool for assessing the impact of uncertainties on the steady-state operation of integrated electricity-gas systems (IEGS). Existing PEF studies primarily focus on the aleatory uncertainties in input variables, which are commonly represented by precise probability distributions. However, epistemic uncertainties arising from limited data and the resulting incomplete knowledge are often neglected, potentially leading to bias in risk assessment. Moreover, computationally efficient PEF analysis remains challenging when a large number of uncertain inputs are involved, due to the high computational burden of conventional methods. To address these issues, this paper proposes a data-driven PEF method for IEGS under mixed aleatory and epistemic uncertainties. An interval probability model based on bootstrap sampling is developed to characterize the uncertainties without strong prior assumptions. On this basis, arbitrary polynomial chaos (aPC) is employed to propagate uncertainties using the generated datasets. To alleviate its dimensionality issue, a compressive sensing model based onl1-l2minimization is adopted to construct a sparse aPC representation. Moreover, an adaptive sparse strategy is further developed to determine an appropriate sparsity level considering the different nonlinear properties of subsystems. Case studies demonstrate that the proposed method improves the computational efficiency of PEF analysis, while maintaining accurate risk assessment.