Higher-Order Markov Chain-Based Probabilistic Power Flow Calculation Method Considering Spatio-Temporal Correlations

The uncertainty caused by renewable energy (RES) and diverse load demands may cause power flow fluctuations in modern power systems, where the probabilistic power flow (PPF) is a reliable method for quantifying and analyzing such power flow fluctuations. This paper proposes a higher-order Markov chain-based modeling framework to represent the stochastic behaviors of the photovoltaic (PV) output and load profiles. The proposed method effectively captures nonlinear temporal autocorrelations across multiple time intervals. In addition, by constructing joint probability distributions, the proposed method can not only handle the situation of linear correlations among distinct PV outputs and similar load types but also reveal nonlinear correlations between co-located PV generation and load variations. In addition, an inverse transformation strategy is developed to generate spatially and temporally correlated PV-load scenarios, ensuring more realistic system representations. Finally, the Mehler formula is adopted to calculate equivalent correlation coefficients under high-linearity conditions, which enhances the computational tractability of the overall approach. Numerical case studies demonstrate that our method achieves both accuracy and efficiency in PPF computations while preserving critical spatio-temporal correlation characteristics.