For the characteristics of fluctuation, periodicity and nonlinearity of power load data, this paper proposes a short-term power load forecasting model based on VMD-Pyraformer-Adan. Firstly, the variational modal decomposition (VMD) algorithm is used to modally decompose the electric load data, the over-zero rate and Pearson correlation coefficient are introduced to divide the modal components to obtain the low-frequency, mid-frequency and high-frequency parts, and the reconstructed data are formed with the original load data respectively. Secondly, the reconstructed data are input to the Pyraformer prediction network containing pyramidal attention module (PAM) and coarse-scale construction module (CSCM). Then a new momentum optimizer Adan is used to optimize the parameters of the prediction network. The final output prediction results. The experimental results show that the proposed model in the paper exhibits higher prediction accuracy compared with other models.

There are several complex and unpredictable aspects that affect the power grid. To make short-term power load forecasting more accurate, a short-term power load forecasting model that utilizes the VMD-Crossformer is suggested in this paper. First, the ideal number of decomposition layers was ascertained using a variational mode decomposition (VMD) parameter optimum approach based on the Pearson correlation coefficient (PCC). Second, the original data was decomposed into multiple modal components using VMD, and then the original data were reconstructed with the modal components. Finally, the reconstructed data were input into the Crossformer network, which utilizes the cross-dimensional dependence of multivariate time series (MTS) prediction; that is, the dimension-segment-wise (DSW) embedding and the two-stage attention (TSA) layer were designed to establish a hierarchical encoder–decoder (HED), and the final prediction was performed using information from different scales. The experimental results show that the method could accurately predict the electricity load with high accuracy and reliability. The MAE, MAPE, and RMSE were 61.532 MW, 1.841%, and 84.486 MW, respectively, for dataset I. The MAE, MAPE, and RMSE were 68.906 MW, 0.847%, and 89.209 MW, respectively, for dataset II. Compared with other models, the model in this paper predicted better.

Power load prediction plays an important role in the safety and stability of national power system. However, due to the nonlinear and multi-frequency characteristics of the power system itself, power load prediction is difficult. To address this problem, we propose a short-term power load prediction model based on variational mode decomposition (VMD). First, original data are decomposed into intrinsic mode function (IMF) of different frequencies using the VMD algorithm, and the decomposed sub-functions are reconstructed. After smoothing the reconstructed data by Savitzky-Golay (S-G) filtering algorithm, the change trend of raw data (CTRD) is obtained. Then, IMF, CTRD and raw data are used as inputs to predict short-term power load by long short-term memory network (LSTM). Finally, the proposed prediction model is compared with the other two groups of prediction models. The results show that the proposed VMD-SG-LSTM prediction model has high fitting ability and high prediction accuracy, and is an effective method for short-term power load prediction.

In the ultrasonic welding system, the ultrasonic power supply drives the piezoelectric transducer to work in the resonant state to realize the conversion of electrical energy into mechanical energy. In order to obtain stable ultrasonic energy and ensure welding quality, this paper designs a driving power supply based on an improved LC matching network with two functions, frequency tracking and power regulation. First, in order to analyze the dynamic branch of the piezoelectric transducer, we propose an improved LC matching network, in which three voltage RMS values are used to analyze the dynamic branch and discriminate the series resonant frequency. Further, the driving power system is designed using the three RMS voltage values as feedback. A fuzzy control method is used for frequency tracking. The double closed-loop control method of the power outer loop and the current inner loop is used for power regulation. Through MATLAB software simulation and experimental testing, it is verified that the power supply can effectively track the series resonant frequency and control the power while being continuously adjustable. This study has promising applications in ultrasonic welding technology with complex loads.

We investigate the generation of high repetition frequency electron beam from vacuum arc plasma source, which consists of Cu cathode and hollow anode. The frequency and pulse width of the extraction pulse power supply based on MOSFET can be adjusted continuously. A self-trigger circuit is designed to immediately reignite DC arc after its extinguishment and guarantee the discharge duration time and stability. The experimental results show that the repletion frequency and pulse width of the electron beam are controlled by the extraction pulse voltage parameters. With a certain discharge current, the beam current increases with the increasing extraction voltage and shows a saturation limit up to 1A. However, the extraction voltage with too high pulse frequency or pulse width is not conducive to the stability of the beam current.

This paper proposes a hybrid forecasting method (VMD–KPCA–xLSTM–Informer) based on variational-mode decomposition (VMD), kernel principal component analysis (KPCA), extended long short-term memory network (xLSTM), and the Informer model. First, the method decomposes the original power load data and environmental parameter data using VMD to capture their multi-scale characteristics. Next, KPCA extracts nonlinear features and reduces the dimensionality of the decomposed modals to eliminate redundant information while retaining key features. The xLSTM network then models temporal dependencies to enhance the model’s memory capability and prediction accuracy. Finally, the Informer model processes long-sequence data to improve prediction efficiency. Experimental results demonstrate that the VMD–KPCA–xLSTM–Informer model achieves an average absolute percentage error (MAPE) as low as 2.432% and a coefficient of determination ($R^2$) of 0.9532 on dataset I, while, on dataset II, it attains a MAPE of 4.940% and an $R^2$ of 0.8897. These results confirm that the method significantly improves the accuracy and stability of short-term power load forecasting, providing robust support for power system optimization.