lect 1 basic principles

7/30/2019 Lect 1 Basic Principles

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Magnetically coupled circuits

Magnetically coupled electric circuits are central to the

operation of transformers and electric machines. In the

case of transformers, stationary circuits are magnetically

coupled for the purpose of changing the voltage and

current levels.



Transformer



Transformer

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Basic_principlse

http://en.wikipedia.org/wiki/transformer







Transformer

In general, the flux produced by each coil can beseparated into two components:

a leakage component denoted with ILand

a magnetizing component Im

Each of these components is depicted by a single

Streamline with the positive direction determined

by applying the right-hand rule to the direction of

current flow in the coil. Often, in transformer analysis, i2 is selected positive out of the top of

coil 2, and a dot is placed at that terminal.



Flux in Transformer

The leakage flux l1 is produced by current flowing in coil1, and it links only the turns of coil 1. Likewise, the

leakage flux l2 is produced by current flowing in coil 2,

and it links only the turns of coil 2. The magnetizing flux

m1 is produced by current flowing in coil 1, and it links all

turns of coils 1 and 2. Similarly, the magnetizing flux m2 isproduced by current flowing in coil 2, and it also links all

turns of coils 1 and 2.



Transformer Model



Equivalent Circuit



Mechanical Analogy



Transformer in action



Transformer Core Design



Transformer Model

where r = diag [r 1 r 2], a diagonal matrix, and

The resistances r 1 and r 2 and the flux linkages l1 and l2

are related to coils 1 and 2, respectively. Because it is

assumed that 1 links the equivalent turns of coil 1 and 2

links the equivalent turns of coil 2, the flux linkages may

be written as

Voltage Equation of a transformer in matrix form is:

Where



Linear Magnetic System

Reluctance is impossible to measureaccurately, could be determined using:

1 1 1 1 2 21

1

2 2 2 2 1 12

2

l m m

l m m

l

A

N i N i N i

N i N i N i

mÂ =

= + +

Â Â Â

= + +

Â Â Â



2 2

1 1 1 21 1 1 2

1

2 2

2 2 1 2

2 2 2 12

l m m

l m m

N N N N

i i i

N N N N

i i i

l

l

= + +Â Â Â

= + +Â Â Â



Flux Linkage of a Coil

Fig. 1 shows a coil of N turns. All these N turns link fluxlines of Weber resulting in the N flux linkages.

In such a case:

Where

N is number of turns in a coil;

e is emf induced, and

is flux linking to each coil

N

d e N

dt

y f

f

=

=



Change in Flux

The change in the flux linkage can be

brought about in a variety of ways:

1. coil may be static and unmoving but the flux

linking the same may change with time2. flux lines may be constant and not changing in

time but the coil may move in space linking

different value of flux with time.

3. both 1 and 2 above may take place. The flux

lines may change in time with coil moving in

space.



Magnetically coupled M/C

In the case of electric machines, circuits in relative motionare magnetically coupled for the purpose of transferring

energy between mechanical and electrical systems.

Because magnetically coupled circuits play such an

important role in power transmission and conversion, it isimportant to establish the equations that describe their

behavior and to express these equations in a form

convenient for analysis.



Experiment LHR



RHR & LHR



Change in Flux Linkage

The magnitude of B is assumed to be varyingsinusoidal, and can be expressed as:

sinm

B B t w=

Which of electrical machine that is applicable?

Where

Bm is the peak amplitude of the flux density. is the

angular rate of change with time. Then, the

instantaneous value of the flux linkage is given by:

= N = NLXBm sin t



(MatLab) Flux and Emf



EMF induced

The Peak emf induced:

rms value of induced emf is:

m m e N f w=

2

m N

E volts f w

=

lect 1 basic principles

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