# Methods for Magnetic Field Calculation of Electrical Machines, Transformers and Apparatuses

**COURSE:** Methods for Magnetic Field Calculation of Electrical Machines, Transformers and Apparatuses

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**Code****:** ФЕИТ00014

**ECTS points****:** 6 ECTS

**Number of classes per week****:**** **3+0+0+3

**Lecturer****:** prof. Vlatko Cingoski

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**Subject of the course content****: **** **

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General approach to the magnetic field theory. Magnetic field equations. Magnetic fields modelling: scalar magnetic potential, vector magnetic potential, Boundary conditions. Electromagnetic parameters of quasi-stationary fields: electromagnetic force, electromagnetic torque, magnetic flux, electromagnetic energy and coenergy, inductances. Magnetic fields calculation methods: analytical methods-direct analytical and transformation analytical methods; numerical methods-Monte Carlo method, finite diferences method and finite element method.

Two dimensional magnetic field calculation using finite element method. Magnetic field calculation with minimum energy condition. Basics of variation calculation. Mathematical model for two dimensional magnetic field calculation. Methods for solving the system of equations. Algorithm for numerical calculation of two dimensional magnetic filed.

Three dimensional calculation of the magnetic field using finite element method. Magnetic field calculation by using the method of weighted residuals. Automatic finite element mesh generation in the three dimensional domain. Mathematical model of the three dimensional magnetic field. Electromagnetic parameters in the electrical machines, transformers and apparatuses gained from the three dimensional magnetic field calculation.

**Literature****:**** **

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- J. P. Bastos, N. Sadowski, “Electromagnetic Modeling by Finite Element Methods“, CRC Press, 2003.
- J. Jianming, “The Finite Element Method in Electromagnetics“, Wiley IEEE Press, 2002.
- S. J. Salon, “Finite Element Analysis of Electrical Machines“, Springer, 1995.