The vibration response of transformer windings under harmonic excitations and its applications

Abstract

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.

Axial and radial electromagnetic‐vibration characteristics of converter transformer windings under current harmonics

“…The current is $$i(t)={I}_{1}\hspace*{.5em}\mathrm{cos}\hspace*{.5em}\omega t$$ and the coil radius is r , so the winding length is denoted as $$L=2{\uppi }r$$. Therefore, according to the Ampere force formula $$F={\boldsymbol{B}}_{\boldsymbol{\sigma }}IL$$ [25], the radial and axial electromagnetic forces $${F}_{x}$$, $${F}_{z}$$ can be calculated. $$$\left\{\begin{array}{l}{F}_{x}=2{\uppi }r{\boldsymbol{B}}_{\boldsymbol{\sigma }\boldsymbol{z}}i(t)={\uppi }r{k}_{z}{I}_{1}{I}_{\sigma 1}\hspace*{.5em}\mathrm{cos}(2\omega t)\\ {F}_{z}=2{\uppi }r{\boldsymbol{B}}_{\boldsymbol{\sigma }\boldsymbol{x}}i(t)={\uppi }r{k}_{x}{I}_{1}{I}_{\sigma 1}\hspace*{.5em}\mathrm{cos}(2\omega t)\end{array}\right.$$$ …”

“…The current is iðtÞ ¼ I 1 cos ωt and the coil radius is r, so the winding length is denoted as L ¼ 2πr. Therefore, according to the Ampere force formula F ¼ B σ IL [25], the radial and axial electromagnetic forces F x , F z can be calculated.…”