Improved Analytical Algorithm for Magnetic Field of End Windings in 300Mvar Synchronous Condenser

Abstract

The magnetic field of end windings affects the leakage reactance of end windings and the eddy current losses of end structures in the large electrical machine. With the rising of single-machine capacity, such effect becomes more obvious. However, due to the complexity of end structures of large electrical machine, it will cause difficulty in meshing and long calculation time to calculate the magnetic field of end windings by using 3-D finite element method (FEM). In order to calculate the magnetic field of end windings quickly and accurately, an improved analytical algorithm (IAA) is proposed based on the mirror image principle, which takes into account the influence of stator back core and air-gap on the magnetic field of end windings by adding the fictitious boundary current and air-gap current, respectively. Taking a 300Mvar synchronous condenser (SC) as an example, the boundary current, air-gap current and magnetic field of end windings are calculated. Then, the influence of stator back core and stator involute segment current on the magnetic field of end windings are analyzed, which provides a theoretical support for the design and optimization of SC. To validate the accuracy of IAA, the calculation result is compared with 3-D FEM.INDEX TERMS Synchronous condenser, magnetic field, analytical algorithm, mirror image, stator back core.

Calculation of magnetic field and eddy current loss in end clamping ring of 300MVA synchronous condenser based on a novel semi‐analytical method

“…The external magnetic field generated by the armature current and excitation current in the end region of the SC can be calculated by the analytical method presented in refs. [23, 24]. The radial and the axial external magnetic flux densities of the clamping ring in the SC can be expressed as: $$$\left\{\begin{array}{l}{b}_{\mathrm{c}r}^{\prime }(r,\theta ,z,t)={B}_{\mathrm{c}r}^{\prime }(r,z)\mathrm{cos}(\omega t-\theta )\\ {b}_{\mathrm{c}z}^{\prime }(r,\theta ,z,t)={B}_{\mathrm{c}z}^{\prime }(r,z)\mathrm{cos}(\omega t-\theta )\end{array}\right.$$$ where $${B}_{\mathrm{c}r}^{\prime }(r,z)$$ and $${B}_{\mathrm{c}z}^{\prime }(r,z)$$ are the amplitudes of $${b}_{\mathrm{c}r}^{\prime }(r,\theta ,z,t)$$ and $${b}_{\mathrm{c}z}^{\prime }(r,\theta ,z,t)$$ respectively, which are functions of r and z .…”

“…The external magnetic field generated by the armature current and excitation current in the end region of the SC can be calculated by the analytical method presented in refs. [23,24]. The radial and the axial external magnetic flux densities of the clamping ring in the SC can be expressed as:…”

“…In this paper, an new semi-analytical method (NSM) for calculating the eddy current loss of the clamping ring in the SC is proposed, which builds on the external magnetic field calculation presented in refs. [23,24]. In Section 3, the corresponding relationship between the external magnetic field and the global magnetic field of the clamping ring in the simple calculation model is obtained by the 3-D FEM.…”