Inertia is the measure of a power system’s ability to resist power interference. The accurate estimation and prediction of inertia are crucial for the safe operation of the power system. To obtain the accurate power system inertia provided by generators, this paper proposes an estimation method considering the influence of frequency and voltage characteristics on the power deficit during transients. Specifically, the traditional swing equations-based inertia estimation model is improved by embedding linearized frequency and voltage factors. On this basis, the snake optimization algorithm is utilized to identify the power system inertia constant due to its strong global search ability and fast convergence speed. Finally, the proposed inertia estimation method is validated in four test systems, and the results show the effectiveness of the proposed method.

The traditional optimization scheduling of distribution networks has often only considered the volatility and randomness of wind and solar output. When estimating the prediction errors of wind and solar output, wind turbines and photovoltaics are typically considered separately, overlooking the correlation between them. Accurate modeling of wind and solar output prediction errors is crucial for enhancing the reliability and economy of distribution network scheduling. To address this, this paper proposes a new modeling method. First, based on the volatility and randomness of wind and solar output, it considers the characteristic that wind and solar outputs in the same region at the same time are correlated. A multivariate nonparametric kernel density estimation is introduced to fit the joint prediction error distribution of wind and solar output using historical data. Next, the impact of joint prediction errors on system scheduling costs is considered by introducing a penalty cost in the economic objective function for the errors caused by wind and solar predictions. Additionally, energy storage devices are integrated into the system to smooth power fluctuations, thereby constructing an economically optimized scheduling model for wind–solar–storage distribution networks based on stochastic correlations. Finally, testing is conducted using an improved IEEE-33 node system. The results indicate that the model considering the correlation between wind and solar output significantly improves the fitting accuracy of prediction errors compared to traditional models that only consider randomness. It also enhances the utilization rate of wind and solar energy and improves the economic performance of the distribution network.