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Residual flux density in the single-phase transformer core can dramatically increase inrush current when the transformer is energized. To reduce inrush current, it is necessary to study residual flux density measurement. This paper proposes a new residual flux density measurement method based on time constant. Firstly, the generation principle of residual flux density is analyzed under different magnetization states, and it is found that the positive relative differential permeability is smaller than the negative at different residual flux density. To obtain the relative differential permeability, when an appropriate DC excitation is applied, the measurement circuit is equivalent to a first-order RL circuit. Then, combining magnetic circuit and transient circuit analysis, the relationship between time constant and relative differential permeability is obtained. It is conclusion that the positive time constant is less than the negative. Residual flux density direction is determined by comparing the positive and negative time constant, and the magnitude of residual flux density is calculated by the relationship between residual flux density and the difference of the positive and negative time constant. Finally, the empirical formula between residual flux density and time constant difference of the square core is obtained in finite element method, and then verified on the experimental platform. Compared with other measurement methods, the relative error of proposed empirical formula is within 4.58 %, and it has higher accuracy in this paper. The proposed method in this paper can provide a reference for selecting the demagnetization voltage, which improves the effectiveness of demagnetization. INDEX TERMS Residual flux density, relative differential permeability, time constant difference, empirical formula.

In this paper, a new extended (3+1)-dimensional shallow water wave equation is discussed via Lie symmetry analysis. Making use of symmetric nodes, we obtain two kinds of symmetrically reduced ODEs. By means of power series, we obtain the two kinds of exact power series solutions. By invoking a new conservation theorem of Ibragimov, the conservation laws are constructed.

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