{"title":"Analytical Estimation of End-Winding Leakage Inductance of Stator Winding of Electric Machines","authors":"A. A. Afanasyev","doi":"10.3103/s1068371224700548","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Equations of mathematical physics, which are solutions of the Laplace’s partial differential equation using the method of separation of variables for hollow cylinders of finite length, are considered as the basis of an analytical model for electric machines. The yoke and tooth layer of the stator core are represented in the model by two nested cylinders, and the end zone of the core is represented by several cylinders connected to each other and to the inner nested cylinder. The unknown constants of the separation of variables method are determined from the boundary conditions of the electromagnetic field: scalar magnetic potentials and coordinate components of the magnetic induction do not experience a jump (discontinuity). The magnetic field caused by the magnetomotive force (MMF) of the stator winding is analyzed in the core itself and outside of it: in the end-winding zone. It is shown that the well-known formula for the MMF of the winding in the active part of the air gap can be used to determine the MMF of the end conductors. The flux linkage of the end parts of the coil is calculated, and the inductance of the end-winding leakage of the entire winding is determined based on this. The validity of the initial analytical approaches for solving the mentioned problem is dictated by the use of three-dimensional equations of mathematical physics in a cylindrical coordinate system for electric machines, the majority of which have a cylindrical construction in the active zone. The obtained numerical value of this parameter for a 150-kW valve motor is sufficiently close to the calculated value found using a known semi-empirical formula applied in the practice of electric machine design.</p>","PeriodicalId":39312,"journal":{"name":"Russian Electrical Engineering","volume":"46 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Electrical Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s1068371224700548","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
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Abstract
Equations of mathematical physics, which are solutions of the Laplace’s partial differential equation using the method of separation of variables for hollow cylinders of finite length, are considered as the basis of an analytical model for electric machines. The yoke and tooth layer of the stator core are represented in the model by two nested cylinders, and the end zone of the core is represented by several cylinders connected to each other and to the inner nested cylinder. The unknown constants of the separation of variables method are determined from the boundary conditions of the electromagnetic field: scalar magnetic potentials and coordinate components of the magnetic induction do not experience a jump (discontinuity). The magnetic field caused by the magnetomotive force (MMF) of the stator winding is analyzed in the core itself and outside of it: in the end-winding zone. It is shown that the well-known formula for the MMF of the winding in the active part of the air gap can be used to determine the MMF of the end conductors. The flux linkage of the end parts of the coil is calculated, and the inductance of the end-winding leakage of the entire winding is determined based on this. The validity of the initial analytical approaches for solving the mentioned problem is dictated by the use of three-dimensional equations of mathematical physics in a cylindrical coordinate system for electric machines, the majority of which have a cylindrical construction in the active zone. The obtained numerical value of this parameter for a 150-kW valve motor is sufficiently close to the calculated value found using a known semi-empirical formula applied in the practice of electric machine design.
期刊介绍：
Russian Electrical Engineering is a journal designed for the electrical engineering industry and publishes the latest research results on the design and utilization of new types of equipment for that industry and on the ways of improving the efficiency of existing equipment.
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