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| Dynamic Hysteresis Modeling Method for Iron Core Based on Permeance-Capacitance Analogy and Analytic Preisach Model |
| Chen Bin1,2, Wang Chuanyuan2, Liu Yang3, Yang Fuyao3, Huang Li1,2 |
1. Hubei Provincial Engineering Technology Research Center for Power Transmission Line Yichang 443002 China;
2. College of Electrical Engineering and New Energy China Three Gorges University Yichang 443002 China;
3. State Grid Smart Grid Research Institute Co. Ltd Beijing 102209 China |
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Abstract With the introduction of a large number of nonlinear loads into the power system, transformers work more frequently at high frequencies, and ferromagnetic materials show strong frequency dependence under high-frequency conditions. Therefore, this paper establishes an electromagnetic loss model considering the eddy current effect and relaxation effect of ferromagnetic materials, which can simulate the voltage and current characteristics at both ends of the transformer and predict the core loss of the transformer.
Firstly, the Lorentz function replaces the distribution function of the classical Preisach model. The ascending and descending branch expressions are derived with the input of the magnetic field strength Hand the output of the magnetic induction intensity B. The reversible component expression is introduced in the classical Preisach model to simulate the static hysteresis characteristics of ferromagnetic materials accurately. The characteristic parameters of the Preisach model are obtained according to static hysteresis loop data from experimental measurements and particle swarm optimization algorithm. Based on the permeance-capacitance analogy method and the analytical Preisach model, the static hysteresis permeance model of the core is established in the simulation software PLECS, which can adjust the permeance value in real-time according to the change of magnetic field strength H. According to the experimental data, the static hysteresis permeance model can simulate the static hysteresis loop of the core.
Secondly, based on the traditional loss statistical theory and field separation theory, the loss of ferromagnetic materials is divided into hysteresis loss, eddy current loss, and residual loss. Constant magnetoresistive and controlled magnetomotive force sources are introduced to characterize the eddy current loss and residual loss of ferromagnetic materials. The traditional core dynamic hysteresis permeance model is established. Based on the electrical steel measurement system, the hysteresis loop and loss value of silicon steel core at different frequencies and magnetic densities aremeasured. Under high-frequency conditions, the internal magnetic flux of ferromagnetic materials is not uniformly distributed due to the skin effect. As a result, the average error of the traditional dynamic hysteresis permeance model is 14.04% compared with the experimental data.
Finally, to consider the non-local, frequency, historical, and other dependent processes of eddy current loss of ferromagnetic materials, the R-L fractional derivative is used to modify the eddy current loss expression, and its parameters are extracted according to the experimental loss value and quantum genetic algorithm. The controlled magnetomotive force source characterizes the eddy current effect, and an improved core dynamic hysteresis permeability model is established. The average relative error of the improved model is 6.59%, which verifies that the improved model can shorten the error.
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Received: 12 July 2023
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2024, Vol. 39 
