Load shedding processes are widespread in hydropower stations, which has great influence on the safe and stable operation of the hydro–turbine governing system. In order to study the dynamic characteristics of the hydro–turbine governing system during the load shedding process, a novel nonlinear mathematical model of the hydro–turbine governing system is established considering the hydro–turbine system, the generator system and the governor system. In particular, a novel nonlinear mathematical model of the six hydro–turbine transfer coefficients is presented based on the definitions and hydro–turbine internal characteristics. After that, from the viewpoint of nonlinear dynamics and the practical engineering, the dynamic characteristics of the hydro–turbine governing system are investigated utilizing bifurcation diagrams, time series, Poincare maps, power spectrums and phase planes. Some meaningful results are found. The advantages of the novel nonlinear mathematical model are illustrated and commented in detail in comparison with the previous model. Finally, these models and analysis results will provide some theoretical references for the operation of hydropower stations in the load shedding transient.

In order to accurately diagnose the fault type of power transformer, this paper proposes a transformer fault diagnosis method based on the combination of time-shift multiscale bubble entropy (TSMBE) and stochastic configuration network (SCN). Firstly, bubble entropy is introduced to overcome the shortcomings of traditional entropy models that rely too heavily on hyperparameters. Secondly, on the basis of bubble entropy, a tool for measuring signal complexity, TSMBE, is proposed. Then, the TSMBE of the transformer vibration signal is extracted as a fault feature. Finally, the fault feature is inputted into the stochastic configuration network model to achieve an accurate identification of different transformer state signals. The proposed method was applied to real power transformer fault cases, and the research results showed that TSMBE-SCN achieved 99.01%, 99.1%, 99.11%, 99.11%, 99.14% and 99.02% of the diagnostic rates under different folding numbers, respectively, compared with conventional diagnostic models MBE-SCN, TSMSE-SCN, MSE-SCN, TSMDE-SCN and MDE-SCN. This comparison shows that TSMBE-SCN has a strong competitive advantage, which verifies that the proposed method has a good diagnostic effect. This study provides a new method for power transformer fault diagnosis, which has good reference value.

To address the difficulty of early fault diagnosis of rolling bearings, this paper proposes a rolling bearing diagnosis method by combining the attention entropy and adaptive deep kernel extreme learning machine (ADKELM). Firstly, the wavelet threshold denoising method is employed to eliminate the noise in the vibration signal. Then, the empirical wavelet transform (EWT) is utilized to decompose the denoised signal, and extract the attention entropy of the intrinsic mode function (IMF) as the feature vector. Next, the hyperparameters of the deep kernel extreme learning machine (DKELM) are optimized using the marine predators algorithm (MPA), so as to achieve the adaptive changes in the DKELM parameters. By analyzing the fault diagnosis performances of the ADKELM model with different kernel functions and hidden layers, the optimal ADKELM model is determined. Compared with conventional machine learning models such as extreme learning machine (ELM), back propagation neural network (BPNN) and probabilistic neural network (PNN), the high efficiency of the method proposed in this paper is verified.

Long time field tests of a 200 MW prototype Francis turbine over its full range of operation were conducted. From the experimental data, the time domain and frequency domain characteristics of the pressure fluctuations in the Francis turbine at different operation conditions were analyzed. Furthermore, the reason for the amplitude increase of pressure fluctuations and the correlation between the vibration and the pressure fluctuation was studied by using a multidimensional frequency band energy ratio analysis method. Based on the above analysis, some hydraulic stability characteristics of the large prototype Francis turbine are found, and other results are also obtained.

The pressure fluctuation has multiple influence on the steady operation of Francis turbine, and the impact degree varies with the operation condition. In this paper, for the analysis of pressure fluctuation in the Francis turbine, a novel feature extraction method of multidimensional frequency bands energy ratio is proposed based on Hilbert Huang Transform (HHT). Firstly, the pressure fluctuation signal is decomposed into intrinsic mode functions (IMFs) by EEMD. Secondly, the Hilbert marginal spectrum is utilized to analyze the frequency characteristics of IMFs. Then, according to the inner frequency of IMFs, each of them is divided into high, medium, or low frequency band which are constructed based on the frequency characteristic of the pressure fluctuations in the Francis turbine. Afterward, the energy ratio of each frequency band to the original signal is calculated, which is to realize the feature extraction of multidimensional frequency band energy ratio. Actual applications verify that this method not only can extract the time-frequency characteristics but also can analyze the condition feature of the pressure fluctuation. It is a novel method for extracting the feature of pressure fluctuation in the Francis turbine.