emf lecture

8/7/2019 emf lecture

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1. Complicated structure of equivalent circuits of

networks.

2. The construction of modern generators

requires new more accurate methods.

3. The unit power of these generators is

approaching large scales.


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The requirements for new programs &

algorithms

1. Increase the capacity of modulated

networks

2. Increase the speed of operations3. Increase the accuracy of mathematical

models.


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Factors that should be considered

1. Motion of synchronous machines

2. Variation by time of emf of machines (in

certain cases under the operation ofautomatic excitation system)

3. Saturation of machines, especially in the

paths of flux linkages in the armature and

field circuits.


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Models of Synchronous Machine

The model is based on Parks equations.

rDqaqaq

rQqdadad

rDsrqaqaqrqrq

rQsrdadadrdrd

qsradadrr

EiX

EEiX

EXXX

EXXX

EXXX

!=

!=

=!=

=!=

=!=


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Equivalent circuit of machine


8/19

Subtransient equivalent emf

The equations are:

adsrdsr

rdad

rd

srdr

ad

r

srq

111

11

''

==

!

rq

aqsrq

rq

aq

rq

srq

d

XX

X

X

XE =!

=

!

11

1

''


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Armature equations

The equations are:

dqqd

qddq

VIXE

VIXE

!

!

''''

''''


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Rearrangement

Multiply 2nd Eq. By j and subtract the

equations, yields:

qqdddqdq IjXIXjjEE'''''''' !


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Adding & subtracting from the right

part of equation

qqqd IjXorIjX""


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The following equations are

obtained:

qdqqdddqqd IXXjIjXVE''''''''

!

dqdqdqqdqd IXXIjXVE

''''''''!


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If we add the two Eqs. And divide

by 2 and rearrangeThe following equation is obtained:

qdqdqdqd IjXIXjE''''

!


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If we consider the armature

resistanceThe final equation will be:

qdqdqdqd IZIXjE ''''

!


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The procedure:

1. From a/m Eqs. we calculate subtransient

emf.

2. Subtransient emf is required to calculatesource current.

3. And that source current is required to

calculate voltage.

4. The a/m procedure is a successive

aproximation.


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Dynamic asymmetry of machine

The equation is:

Eiqdqdqdi YIXjEJ '' !


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Knowing direct and quadrature

components of SMWe use these Eqs. To calculate:

rd

ad

rd

ad

adadadrr

q

X

X

X

XXX

E2

1

1

===

!

q

rd

ad

d

rd

ad

rdr E

X

XI

X

XE =!

2

rqq

rq

aq

r I

X

XE =!

2


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Integration

Now, we can integrate the followings:

qrr

r EEdt

d!

=V

rQrdrd E

dt

dV!

=

rDrq

rqE

dt

dV!

=


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Conclusions

1. Magnetic asymmetry of machine is obtained by adding

additional member in equations.

2. SM is represented by fictitious emf behind complex

impedance.3. Calculation of magnetic asymmetry requires

successive approximations which has good

convergence.

4. Emf variation by time can be obtained by integrating

the field equations.

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emf lecture