Principles of Electromechanical Energy Conversion
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Transcript of Principles of Electromechanical Energy Conversion
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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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