A new polynomial fitting model based on a neural network is presented to characterize the hysteresis in piezoelectric actuators. As hysteresis is multi-valued mapping, and traditional neural networks can only solve one-to-one mapping, a hysteresis mathematical model is proposed to expand the input of the neural network by converting the multi-valued into one-to-one mapping. Experiments were performed under designed excitation with different driven voltage amplitudes to obtain the parameters of the model using the polynomial fitting method. The simulation results were in good accordance with the measured data and demonstrate the precision with which the model can predict the hysteresis. Based on the proposed model, a single-neuron adaptive proportional–integral–derivative controller combined with a feedforward loop is designed to correct the errors induced by the hysteresis in the piezoelectric actuator. The results demonstrate superior tracking performance, which validates the practicability and effectiveness of the presented approach.
Study of the vibration mechanisms of transformer windings may lead to useful applications of vibration techniques to transformer online diagnosis. In a power transformer, the clamping force provides a boundary mechanical constraint to ensure the integrity of the winding. Thus, the looseness of the clamping force is an important health indicator for a transformer. Although the effect of clamping force on a winding's stiffness and natural frequencies is known, the effect of time-varying load current on these natural frequencies remains unsolved. In this paper, this effect is investigated by studying the mechanical frequency response function of an on-load single-phase winding under different clamping forces and variation of the harmonic amplitude of in-service transformers with load current. Then, a gated recurrent unit (GRU) neural network is used to explore the relationship between current sequence and vibration sequence for operating transformers. This study shows that the electromagnetic force induced by the load current affects the vibration response of the winding structure, especially when the looseness of the clamping force is significant. A potential application of the observed phenomenon for online detection of winding conditions is also illustrated. INDEX TERMS dynamic winding model, gated recurrent unit, natural frequency change, transformer vibration.
In this paper, a condition assessment model using vibration method is presented to diagnose winding structure conditions. The principle of the model is based on the vibration correlation. In the model, the fundamental frequency vibration analysis is used to separate the winding vibration from the tank vibration. Then, a health parameter is proposed through the vibration correlation analysis. During the laboratory tests, the model is validated on a test transformer, and manmade deformations are provoked in a special winding to compare the vibrations under different conditions. The results show that the proposed model has the ability to assess winding conditions.
The power transformer is a key device in the power grid systems. The mechanical degradation of windings represented by the clamping force looseness will cause the decline of the short circuit withstand ability, and cause further damages. This paper proposes a clamping force diagnosis method for operating windings based on the study of the vibration response. In the theory part, the influence of the load current on the natural frequency of windings is discussed, and the influence of the natural frequency change on the steady-state vibration response is studied to obtain the vibration feature related with the clamping force. The subspace method is used to fuse two vibration sequences with the same characteristics to eliminate the measurement error. In the experiment, the free vibration test was performed on a short circuit on-load winding structure. It was proved that the natural frequency change can be extracted from the relationship between the amplitude change of the 100 Hz component and the current change. In the field tests, the vibration sequences of two typical transformers were compared, and the results show that the vibration feature extracted from the relationship between the amplitude variation and the current change contains the structural information of windings.
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