Research On Residual Flux Prediction Of The Transformer

When the transformer is energized,the core may be driven into deep saturation in half cycle due to the prospective flux and the residual flux,which leads to the inrush current.The magnitude of the inrush current is 6-8 times higher than the rated current of the transformer,which has a bad effect on the relay protection malfunction and the primary equipment.Currently,the phase selection technology is the mostly powerful method to reduce the inrush current.Based on the initial phase angle calculated by the residual flux,the prospective flux produced by the energization of the transformer is built with the same magnitude and the opposite polarity to the residual flux.Therefore,the measurement,calculation,prediction and reduction for the residual flux are necessary,which has great value in both theory and practice.To investigate the residual flux,the main contents are as follows.1.The estimation method of the overvoltage and current by the chopping of the transformer and their influence on the hysteresis loopWhen the small inductance current is interrupted by the circuit breaker,the current flowing through the primary side of transformer is chopped before zero due to the breaking capacity of the circuit breaker.Considering the equivalent capacitors of the transformer and the circuit breaker,the energy is converted between the magnetic field energy stored by the transformer and the electric field energy stored by the capacitors,which leads to the overvoltage and current of the primary side of transformer.Thus,the hysteresis loop and the residual flux are changed due to the overvoltage and current.Aiming at these problems,first,the equivalent single-phase no-load transformer is built,and the estimation method for the overvoltage and current is obtained based on the Laplace transformation and the loop current method.Based on the per unit value range of the transformer,per unit values for the transformer of this paper are determined.The validity of the estimation method is conformed,compared with the simulation results by the MATLAB/Simulink.Second,the overvoltage times,the angular frequency of the damped oscillation and the decay factor influenced by the per unit values of the capacitors,model parameters of the transformer and the circuit breaker opening time are analyzed theoretically.Finally,combined the estimation method with the measured magnetic flux,the magnetic flux density are determined when the transformer is chopped.It is found that the magnetic flux density in the core includes the dc magnetic flux density and ac magnetic flux density which is decaying with time,the frequency of the overvoltage varying with time is greater than the rated frequency,and the minor loops are generated according to the decaying magnetic flux density.Thus,the magnetic field is complicated based on the above property.To obtain the accurate residual flux,the hysteresis model becomes the focus of this research,which has the characteristics as follow,the hysteresis phenomenon,the minor loops,the frequency-dependent dynamic loss(the eddy current loss and the anomalous loss)and the dc magnetic flux density.2.Dynamic hysteresis model based on the Jiles Atherton hysteresis theoryThe Jiles Atherton(JA)static hysteresis model which accords the physical nature of the hysteresis phenomenon well and has fewer parameters is widely used in the field of magnetic hysteresis simulation and modeling.However,the minor loops,dynamic loss and dc magnetic flux density cannot be represented by the origin JA static hysteresis model.To reflect the above characteristics,the dynamic hysteresis model is established based on the JA hysteresis theory.The contents of the model are as follows.The JA static hysteresis model is deduced where the magnetic flux density is set as the input of the model,and the model solving method,the model parameters range,the effect of the model parameters on the hysteresis loop and the model parameters identification method are analyzed.Sequently,considering the difficulty of the model parameters identification,a fuzzy-shuffled frog leaping algorithm(F-SFLA)is proposed in this paper to identify the parameters of JA hysteresis model.In order to speed up the convergence and avoid falling into local optimal solution of shuffled frog leaping algorithm(SFLA),a dynamical feedback factor F,which is the output of the fuzzy logic,is added to the step length of SFLA.The input of the fuzzy logic is the relative error of the measured and the calculated value at the special points(the coercive field amplitude,the dM/dH on the coercive field amplitude).By the fuzzy logic,the analyticity characteristics of the JA hysteresis model are combined with the SFLA.F-SFLA,SFLA,particle swarm optimization(PSO)and genetic algorithm(GA)are applied to determine the parameters of major hysteresis loop and minor hysteresis loop.Compared with the measured hysteresis loops and the calculated hysteresis loops,the results show that F-SFLA has less computational time and is not easy to fall into local optimal solution.Additionally,the relationship between the parameters of minor loop and magnetic flux density is analyzed,and the parameters of minor loop varying with magnetic flux density are fitted.Depending on the JA hysteresis theory and the Bertotti’s field separation approach,the dynamic hysteresis model is established without dc magnetic flux density considering the eddy current and the anomalous loss,and the model parameters are identified.Based on the prospective flux produced by the energization of the transformer,the experimental setup under dc and ac magnetic flux density is built by adopting Epstein frame and programmable power-supply which is relied on the digital feedback.The magnetic performance measuring system is set up to guarantee the accurate and controllable dc magnetic flux density,which provides a base for this paper.Additionally,the hysteresis loop without dc magnetic flux density can also be measured by this system.Based on the measured hysteresis loops under different dc magnetic flux density,the identification results of model parameters are obtained.The model in this paper is verified by the comparison between the calculated and experimental exciting current and core loss.The influence of dc magnetic flux density on the parameters of the dynamic hysteresis model is analyzed,we can find that when the magnetic flux density includes the ac magnetic flux density and the dc magnetic flux density,the first five parameters of JA static hysteresis model vary with different ac magnetic flux density,which are independent of the dc magnetic flux density.Dynamic loss coefficients are influenced by different ac magnetic flux density and dc magnetic flux density.Thus,the dynamic loss coefficient is normalized and fitted,and the forecasting method of core loss based on the dynamic hysteresis model is proposed under dc bias(dc magnetic flux density).The method in this paper is verified by the comparison between the calculated and experimental results.Furthermore,the core loss under dc bias(dc magnetic flux density)is calculated by the proposed Steinmetz equation.Depended on the same experiment examples,the calculation results based on the Steinmetz equation are accurate.Compared with the Steinmetz equation,the forecasting method of core loss based on the dynamic hysteresis model can predict the core loss,exciting current and the hysteresis loop under dc bias,which is suitable for industry application.3.Research on residual flux prediction of the transformerThe residual flux prediction method is proposed,which is combined the external magnetic field(the overvoltage)with the magnetization mechanism(dynamic hysteresis model).Firstly,the overvoltage caught by the chopping current is simulated by the experimental setup.The preset test voltage that is used to simulate the overvoltage is output by the programmable power-supply of magnetic performance measuring system,which is used to excite the Epstein frame,where the measuredvoltage and current are obtained.Compared with the estimation method,the preset test voltage corresponds to the estimation method can be simulate the different conditions when the transformer is de-energization.Secondly,due to the winding loss and leakage inductance,the iterative method is proposed.The integral of overvoltage is set as the initial input of the model,the current are then calculated by the iterative method where the ac magnetic flux density and the dc magnetic flux density are repeatedly adjusted to determine the parameters of dynamic hysteresis model.When the current has converged to a reasonable tolerance,the sequential hysteresis loops are formed and the final point is the residual flux.The current obtained by the final iteration agrees well with the measured one,which validates the dynamic hysteresis model and the iterative method.Finally,the residual flux cannot be measured directly,which leads to the difficulty of verification.Thus,based on the phase selection technology and the relationship curves of the dc magnetic flux density vs the max magnitude of the inrush current,the residual flux is verification and evaluated.