# Closed-form computation of electromagnetic fields in induction motors

Francisco De Leon, Sujit Purushothaman

Research output: Contribution to journalArticle

### Abstract

A closed-form solution of the electromagnetic field equations for a three-phase squirrel-cage induction motor is presented. The analysis starts from the application of the Galilean transformation to Maxwell equations for moving media at constant speed. The induction motor is modelled as five concentric cylindrical layers representing the different construction components of the motor. By solving the Helmholtz and Laplace equations for conducting and non-conducting layers, we obtain a coupled set of Bessel and Euler equations that are solved analytically. The obtained formulas allow for the efficient calculation of important information for the designer regarding the electromagnetic fields, losses, force and torque. Parametric analyses are shown for illustration of the benefits of the closed form solution. The analytical expressions are validated against finite element simulations. Analytical expressions to compute the parameters of the equivalent circuit from the dimensions of the motor are also provided.

Original language English (US) 62-70 9 International Journal of Power and Energy Systems 33 2 https://doi.org/10.2316/Journal.203.2013.2.203-5079 Published - 2013

### Fingerprint

Induction Motor
Maxwell equations
Closed-form Solution
Induction motors
Electromagnetic fields
Electromagnetic Fields
Closed-form
Bessel's equation
Squirrel cage motors
Helmholtz equation
Equivalent Circuit
Laplace equation
Cage
Euler equations
Concentric
Finite Element Simulation
Helmholtz Equation
Laplace's equation
Maxwell's equations
Euler Equations

### Keywords

• Electromagnetic fields analysis
• Galilean transformation
• Induction motors
• Motor design

### ASJC Scopus subject areas

• Electrical and Electronic Engineering
• Energy Engineering and Power Technology
• Applied Mathematics

### Cite this

Closed-form computation of electromagnetic fields in induction motors. / De Leon, Francisco; Purushothaman, Sujit.

In: International Journal of Power and Energy Systems, Vol. 33, No. 2, 2013, p. 62-70.

Research output: Contribution to journalArticle

@article{f6f885520cd8448dbf459de283587a2f,
title = "Closed-form computation of electromagnetic fields in induction motors",
abstract = "A closed-form solution of the electromagnetic field equations for a three-phase squirrel-cage induction motor is presented. The analysis starts from the application of the Galilean transformation to Maxwell equations for moving media at constant speed. The induction motor is modelled as five concentric cylindrical layers representing the different construction components of the motor. By solving the Helmholtz and Laplace equations for conducting and non-conducting layers, we obtain a coupled set of Bessel and Euler equations that are solved analytically. The obtained formulas allow for the efficient calculation of important information for the designer regarding the electromagnetic fields, losses, force and torque. Parametric analyses are shown for illustration of the benefits of the closed form solution. The analytical expressions are validated against finite element simulations. Analytical expressions to compute the parameters of the equivalent circuit from the dimensions of the motor are also provided.",
keywords = "Electromagnetic fields analysis, Galilean transformation, Induction motors, Motor design",
author = "{De Leon}, Francisco and Sujit Purushothaman",
year = "2013",
doi = "10.2316/Journal.203.2013.2.203-5079",
language = "English (US)",
volume = "33",
pages = "62--70",
journal = "International Journal of Power and Energy Systems",
issn = "1078-3466",
publisher = "ACTA Press",
number = "2",

}

TY - JOUR

T1 - Closed-form computation of electromagnetic fields in induction motors

AU - De Leon, Francisco

AU - Purushothaman, Sujit

PY - 2013

Y1 - 2013

N2 - A closed-form solution of the electromagnetic field equations for a three-phase squirrel-cage induction motor is presented. The analysis starts from the application of the Galilean transformation to Maxwell equations for moving media at constant speed. The induction motor is modelled as five concentric cylindrical layers representing the different construction components of the motor. By solving the Helmholtz and Laplace equations for conducting and non-conducting layers, we obtain a coupled set of Bessel and Euler equations that are solved analytically. The obtained formulas allow for the efficient calculation of important information for the designer regarding the electromagnetic fields, losses, force and torque. Parametric analyses are shown for illustration of the benefits of the closed form solution. The analytical expressions are validated against finite element simulations. Analytical expressions to compute the parameters of the equivalent circuit from the dimensions of the motor are also provided.

AB - A closed-form solution of the electromagnetic field equations for a three-phase squirrel-cage induction motor is presented. The analysis starts from the application of the Galilean transformation to Maxwell equations for moving media at constant speed. The induction motor is modelled as five concentric cylindrical layers representing the different construction components of the motor. By solving the Helmholtz and Laplace equations for conducting and non-conducting layers, we obtain a coupled set of Bessel and Euler equations that are solved analytically. The obtained formulas allow for the efficient calculation of important information for the designer regarding the electromagnetic fields, losses, force and torque. Parametric analyses are shown for illustration of the benefits of the closed form solution. The analytical expressions are validated against finite element simulations. Analytical expressions to compute the parameters of the equivalent circuit from the dimensions of the motor are also provided.

KW - Electromagnetic fields analysis

KW - Galilean transformation

KW - Induction motors

KW - Motor design

UR - http://www.scopus.com/inward/record.url?scp=84880767750&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880767750&partnerID=8YFLogxK

U2 - 10.2316/Journal.203.2013.2.203-5079

DO - 10.2316/Journal.203.2013.2.203-5079

M3 - Article

AN - SCOPUS:84880767750

VL - 33

SP - 62

EP - 70

JO - International Journal of Power and Energy Systems

JF - International Journal of Power and Energy Systems

SN - 1078-3466

IS - 2

ER -