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PRINCIPLES OF ELECTROMECHANICAL ENERGY CONVERSION

1. Introduction2. Principle of induction3. Principle of interaction

4. Principle of alignment5. Energy stored in magnetic field6. Forces and torques in magnetic field systems7. Examples (1) & (2)8. Singly excited and multiply excited magnetic field

systems9. Inductance10. Multiply excited magnetic field systems11. Example (3)

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ReferencesMulukutla S. Sarma, Electric Machines: Steady-State

Theory & Dynamic Performance, West Publishing

Company, St. Paul New York Los Angles San Francisco

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Introduction

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Principle of induction

PRINCIPLE OF INDUCTION

The induced emfis given by Faradays law of induction:

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Principle of interaction PRINCIPLE OF INTERACTION

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The figure indicates a one-turn coil in a magnetic field, andillustrates how torque is produced by forces caused by interactionof current-carrying conductors and magnetic fields.

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Principle of alignmentPRINCIPLE OF ALIGNMENT

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Energy stored in magnetic fieldENERGY STORED IN MAGNETIC FIELD

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Since v = R i + e

v i = R i2 + e i

Where (v i) is the electric input, (R i2

)is the losses inR, and consequently (e i) is the power going tomagnetic circuit.

The energy is given by:

Energy = If the current increases from 0 to i from t=0 to t,

then

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For air r= 1

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The coenergy is defined as:

For a linear magnetic system, the -i characteristic is a straight line, in which

case the magnetic energy and coenergy are always equal in magnitude.

Coenergy Wm

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Forces and torques in magnetic field

systems

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The -i characteristic of the nonlinear magnetic system with no core lossis given by a single-valued nonlinear relationship, typically shown inFigure.

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Thus, if the independent variables are the current iand the coordinate x, then the flux linkage is a

function of both i and x:

= (i,x)

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Substituting, we get:

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Note that Wm in this equation is a function of independent variables and x.This equation may also be written as:

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For a linear magnetic system, the -i characteristic is a straight line, in which case the

magnetic energy and coenergy are always equal in magnitude.

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Example (1)Example (1)

The -i relationship for an electromechanical system show is given by

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Solution

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Example (2)Example (2)

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Solution

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Singly excited magnetic field systemsBefore we proceed to analyze magnetic field systems excited by more than one electrical

circuit, let us consider an elementary reluctance machine that is singly excited, carrying only

one winding on its stationary member, called the stator.

Figure (a), shows an elementary rotating reluctance machine. We shall assume that the

reluctances of the stator and rotor iron are negligible; also, we shall neglect the leakage

and fringing.

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Since the torque in this particular electromechanical energy converter is due to the

variation of reluctance with rotor position, the device is known as a synchronous

reluctance machine. As seen from equation, the torque is zero if L d = Lq , i.e. if there is noinductance or reluctance variation with rotor position. The Figure shows the variation of

the average electromechanical torque developed by the machine as a function of the

angle , which is known as the torque angle.

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Inductance

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Multiply excited magnetic field systemsMULTIPLY EXCITED MAGNETIC FIELD SYSTEMS

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Example (3)Example (3)

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An elementary two-pole rotating machine with uniform air-gap

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Solution

a. With constant Lss and Lrr

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