Design of Rotating Electrical Machines

Juha Pyrhonen, Tapani Jokinen, Valeria Hrabovcova

• Publisher: Wiley
• Year: 2013
• ISBN:
  9781118701652
• Edition: 2
• Topic: Tecnología e ingeniería
• Subtopic: Recursos energéticos

In one complete volume, this essential reference presents an in-depth overview of the theoretical principles and techniques of electrical machine design. This timely new edition offers up-to-date theory and guidelines for the design of electrical machines, taking into account recent advances in permanent magnet machines as well as synchronous reluctance machines.

New coverage includes:

• Brand new material on the ecological impact of the motors, covering the eco-design principles of rotating electrical machines
• An expanded section on the design of permanent magnet synchronous machines, now reporting on the design of tooth-coil, high-torque permanent magnet machines and their properties
• Large updates and new material on synchronous reluctance machines, air-gap inductance, losses in and resistivity of permanent magnets (PM), operating point of loaded PM circuit, PM machine design, and minimizing the losses in electrical machines>
• End-of-chapter exercises and new direct design examples with methods and solutions to real design problems>
• A supplementary website hosts two machine design examples created with MATHCAD: rotor surface magnet permanent magnet machine and squirrel cage induction machine calculations. Also a MATLAB code for optimizing the design of an induction motor is provided

Outlining a step-by-step sequence of machine design, this book enables electrical machine designers to design rotating electrical machines. With a thorough treatment of all existing and emerging technologies in the field, it is a useful manual for professionals working in the diagnosis of electrical machines and drives. A rigorous introduction to the theoretical principles and techniques makes the book invaluable to senior electrical engineering students, postgraduates, researchers and university lecturers involved in electrical drives technology and electromechanical energy conversion.

1

Principal Laws and Methods in Electrical Machine Design

1.1 Electromagnetic Principles

A comprehensive command of electromagnetic phenomena relies fundamentally on Maxwell’s equations. The description of electromagnetic phenomena is relatively easy when compared with various other fields of physical sciences and technology, since all the field equations can be written as a single group of equations. The basic quantities involved in the phenomena are the following five vector quantities and one scalar quantity:

Electric field strength	E	[V/m]
Magnetic field strength	H	[A/m]
Electric flux density	D	[C/m2]
Magnetic flux density	B	[Vs/m2], [T]
Current density	J	[A/m2]
Electric charge density, dQ/dV	ρ	[C/m3]

The presence of an electric and magnetic field can be analyzed from the force exerted by the field on a charged object or a current-carrying conductor. This force can be calculated by the Lorentz force (Figure 1.1), a force experienced by an infinitesimal charge dQ moving at a speed v. The force is given by the vector equation

(1.1)

Figure 1.1 Lorentz force dF acting on a differential length dl of a conductor carrying an electric current i in the magnetic field B. The angle β is measured between the conductor and the flux density vector B. The vector product i dl × B may now be written in the form i dl × B = idlB sin β.

In principle, this vector equation is the basic equation in the computation of the torque for various electrical machines. The latter part of the expression in particular, formulated with a current-carrying element of a conductor of the length dl, is fundamental in the torque production of electrical machines.

---

Example 1.1: Calculate the force exerted on a conductor 0.1 m long carrying a current of 10 A at an angle of 80° with respect to a field density of 1 T.

Solution: Using (1.1) we get directly for the magnitude of the force

---

In electrical engineering theory, the other laws, which were initially discovered empirically and then later introduced in writing, can be derived from the following fundamental laws presented in complete form by Maxwell. To be independent of the shape or position of the area under observation, these laws are presented as differential equations.

A current flowing from an observation point reduces the charge of the point. This law of conservation of charge can be given as a divergence equation

(1.2)

which is known as the continuity equation of the electric current.

Maxwell’s actual equations are written in differential form as

(1.3)

(1.4)

(1.5)

(1.6)

The curl relation (1.3) of an electric field is Faraday’s induction law, which describes how a changing magnetic flux creates an electric field around it. The curl relation (1.4) for magnetic field strength describes the situation where a changing electric flux and current produce magnetic field strength around them. This is Ampère’s law. Ampère’s law also yields a law for conservation of charge (1.2) by a divergence Equation (1.4), since the divergence of the curl is identically zero. In some textbooks, the curl operation may also be expressed as

× E = curl E = rot E.

An electric flux always flows from a positive charge and...