The growing amount of distributed generation has brought great uncertainty to power grids. Traditional probabilistic load flow (PLF) algorithms, such as the Monte-Carlo method (MCM), can no longer meet the needs of efficiency and accuracy in large-scale power grids. Latin Hypercube Sampling (LHS) develops a sampling efficiency and solves the correlation problem of distributed generation (DG) access nodes for accuracy analyses. In this paper, a modified Latin Hypercube-Important Sampling method is proposed for higher efficiency and precision by using the importance sampling method before LHS and the Cholesky decomposition method in correlation calculations. The simulation results are presented using a modified IEEE 30-bus system and are compared with traditional MCM and LHS.

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.

With the increasing integration of large-scale renewable energy sources, the coordinated participation of hydropower and energy storage in frequency regulation has become a critical means of ensuring the safe and economical operation of power grids. This paper proposes an optimization method for the allocation of frequency regulation reserves between hydropower and energy storage based on marginal substitution rate (MRS) analysis. First, a frequency response model that captures the synergistic interaction between hydropower and energy storage is established, with the root mean square error (RMSE) of the area control error (ACE) serving as the performance metric for frequency regulation. To reduce simulation computational burdens, key simulation data are obtained via Gaussian process regression (GPR), and a piecewise polynomial fitting method is employed to generate the marginal substitution curve. Experimental results indicate that under the condition of achieving equivalent frequency regulation performance (ACE_RMSE), 51.60 MW of energy storage reserve can replace 68.38 MW of hydropower reserve, thereby reducing the total regulation capacity reduction of 13.42%. Furthermore, by incorporating the differing cost characteristics of hydropower and energy storage, the optimal configuration is determined, resulting in an overall cost reduction of 17.58%. This method not only ensures system frequency stability but also fully leverages the potential of the available frequency regulation resources.