Analytic calculation and analysis of the magnetic field for the single-phase two-limb transformer

The vibration analysis method is widely used in transformer diagnosis. However, to our knowledge, the researches about the magnetic field for the vibration method are mainly based on numerical modelling rather than analytic calculation. But the analytic calculation is quite essential for the application of the vibration method. This paper calculates and simulates the magnetic flux density distribution of the winding and core in a single-phase two-limb transformer, respectively based on the Biot-Savart law and Maxwell's equations. The proposed results and simulations are consistent with the precedent researches. It is believed that this analytic calculation and analysis of the transformer magnetic field may help developing the transformer condition monitoring and fault diagnosis based on the vibration analysis method.