In comparison with traditional point forecasting method, probability density forecasting can reflect the load fluctuation more effectively and provides more information. This paper proposes a hybrid hourly power load forecasting model, which integrates K-means clustering algorithm, Salp Swarm Algorithm (SSA), Least Square Support Vector Machine (LSSVM), and kernel density estimation (KDE) method. Firstly, the loads at 24 times a day are grouped into three categories according to the K-means clustering algorithm, which correspond to the valley period, flat period, and peak period of the load, respectively. Secondly, the load point forecasting value is obtained by LSSVM method optimized by SSA algorithm. Furthermore, the kernel density estimation method is employed to fit the forecasting error of SSA-LSSVM in different time periods, and the probability density function of the error distribution is obtained. The final load probability density forecasting result is obtained by combining the point forecasting value and the error fitting result, and then the upper and lower limits of the confidence interval under the given confidence level are solved. In this paper, the performance of the model is evaluated by two indicators named interval coverage and interval average width. Meanwhile, in comparison with several other models, it can be concluded that the proposed model can effectively improve the forecasting effect.

The dynamic nonlinear order reduction, preserving the dominant state variables of wind turbine units, is a prerequisite for analyzing the stability of large-scale wind power integration systems under large disturbances. Therefore, this paper proposes a dynamic dimension reduction method for wind turbine models, which is applicable for analyzing large disturbance scenarios while retaining the state variables and could give the quantitative indicators for state variables. The direct drive permanent magnet synchronous generator (PMSG) model is used as the test example, and the singular perturbation reduced-order model (ROM) is obtained by the proposed nonlinear model reduction method. In the modified test system, the performance results have demonstrated high accuracy, computational efficiency, and robustness of the proposed method.

Unlike single-converter grid-connected systems and multi-converter grid-forming (GFM) systems operating in islanded mode, grid-connected multi-converter systems comprising parallel grid-following (GFL) and GFM converters exhibit more complex internal interactions. The negative damping of GFL converters and the low-frequency inertia of GFM converters can reinforce each other, increasing the risk of wideband oscillations. Conventional impedance models do not fully account for frequency-coupling effects among converters, which can lead to impedance-model mismatch and invalidate the Nyquist criterion. Moreover, the high order of the transfer functions of multi-converter systems makes frequency sweeps difficult. Conversely, time-domain state-space models neglect the dynamics of individual control loops, resulting in inaccurate modeling and distorted parameter-sensitivity results. This paper develops a heterogeneous small-signal model that captures the full dynamics of GFM and GFL converters and uses an eigenvalue-sensitivity criterion to reveal their behavior under coupled parameters. On this basis, the effects of GFM inertia and damping on GFL variables, as well as the effect of phase-locked loop (PLL) bandwidth on the eigenvalues of the GFM system, are investigated. The proposed model and associated stability analysis provide a basis for assessing the stability of such systems and optimizing system parameters. Finally, simulations verify the conclusions.