**Modelling**

**Chapter 1** 

© 2012 Livadaru et al., licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2012 Livadaru et al., licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Mathematical Model of the Three-Phase** 

**and Transient Duty Under Balanced** 

Alecsandru Simion, Leonard Livadaru and Adrian Munteanu

**and Unbalanced States** 

Additional information is available at the end of the chapter

2005; Krause et al., 2002; Ong, 1998; Sul, 2011).

http://dx.doi.org/10.5772/49983

**1. Introduction** 

**Induction Machine for the Study of Steady-State** 

A proper study of the induction machine operation, especially when it comes to transients and unbalanced duties, requires effective mathematical models above all. The mathematical model of an electric machine represents all the equations that describe the relationships

The theory of electrical machines, and particularly of induction machine, has mathematical models with *distributed* parameters and with *concentrated* parameters respectively. The first mentioned models start with the cognition of the magnetic field of the machine components. Their most important advantages consist in the high generality degree and accuracy. However, two major disadvantages have to be mentioned. On one hand, the computing time is rather high, which somehow discountenance their use for the real-time control. On the other hand, the distributed parameters models do not take into consideration the influence of the temperature variation or mechanical processing upon the material properties, which can vary up to 25% in comparison to the initial state. Moreover, particular constructive details (for example slots or air-gap dimensions), which essentially affects the

between electromagnetic torque and the main electrical and mechanical quantities.

parameters evaluation, cannot be always realized from technological point of view.

The mathematical models with concentrated parameters are the most popular and consequently employed both in scientific literature and practice. The equations stand on resistances and inductances, which can be used further for defining magnetic fluxes, electromagnetic torque, and et.al. These models offer results, which are globally acceptable but cannot detect important information concerning local effects (Ahmad, 2010; Chiasson,
