University of Minnesota
University of Minnesota


Finite Element Analysis for Designing Electrical Apparatus: Electric Machines

Course Learning Objectives 

This course will introduce students to the modern and classical methods used by engineers to design electromagnetic devices such as electric machines and transformers. The course will be separated into three main sections:

  • Introduction to the finite element analysis technique
  • Winding analysisand material modelling
  • Solve problems using commercial finite element analysis software

Course Outcome 

  • Introduction to Finite Element Analysis Modelling
    • Classification of partial differential equations, boundary conditions
    • Review of electromagnetic theory: magnetostatics, quasi-statics, magnetic scalar potential
    • Variationalmethod: solving variationalproblems, PDE’s expressed as a variationalproblem
    • Ritz’s method, weighted-residual methods, Galerkinmethod.
    • Finite element method: illustrated example, shape functions, step-by-step solution procedure
  • Winding Analysis and Material Modelling
    • Permanent magnet material
    • Modelling permanent magnets using equivalent magnetic circuit models
    • Turns function, winding functions
    • Distributed winding function analysis
    • Pitch factor, distribution factor, slot opening factor
    • Fractional slot winding analysis
    • Concentrated winding analysis
    • Star of slot Analysis
    • Carter’s Coefficient
  • Problem Solving using commercial finite element analysis software
    • Magnetic coupling problems (transformer example) using finite element analysis
    • Fractional slot permanent magnet motor design problems
    • Magnetic circuit modelling of a Rotary PM motor
    • Salient Pole PM motors
    • Motor’s Voltage and Current Limit Circles

Slides for Video Clips 

Course Video Clips 

The following video files are in M4V format and can be played on most players including VLC, Quicktime or Windows Media Player.


Power Systems

Electric Power Systems Electricity Markets Power Generation Operation and Control
Power System Protection Advanced Power Systems High Voltage technology related to Power Systems

Power Electronics

Power Electronics Advanced Power Electronics I Advanced Power Electronics II

Electric Machines & Drives

Electrics Machines and Drives           Electric Machine Design
Vector Control of Drives           Vector Control of Drives

Renewable Energy

Wind Energy Essentials

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