part 4 emachines EEP 3243

8/14/2019 part 4 emachines EEP 3243

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ELECTRICAL MACHINE

EEP 3243

Lt Cdr Ong Khye Liat RMN

20Jan 2010

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RECAP/ADDITION

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Ideal Transformer Ideal transformer should be:

No winding resistance. No leakage flux.

No iron losses. Its coefficient of coupling is unity.

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Voltage induced in a coil

Alternating flux induces a sinusoidal ac voltage in the coil,whose effective value is given by

E = 4.44fNmax V

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Ideal Transformer at No-Load

Voltage Ratio

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Fig5: The ideal transformer at no-load.

Equations for voltage ratio andturn ratio, a of an idealtransformer :


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Ideal Transformer Under Load;Current Ratio

When connect a load, Z across the secondary coil, a

secondary current I 2 willimmediately flow:

I 2 = E 2 /Z

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Fig 1: Ideal transformer under load.The mutual flux remains unchanged.


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Cont.The E 2 does not change when load isconnected because:

In ideal transformer the primary andsecondary coils are linked by amutual flux, m only.

The supply voltage E g is kept fixed,then primary induced voltage E 1remains fixed, mutual flux m alsofixed and follows that E 2 alsoremain fixed.

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Cont.

S o the voltage ratio under load isthe same as at no-load:

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Cont.

By examine the magneto motiveforces at primary and secondary,and the currents are in phase.

N1I 1 = N2I 2

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Cont.B

y examine the magneto motiveforces at primary and secondary,and the currents are in phase.

N1I 1 = N2I 2then

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Cont.

The phasor diagram of an idealtransformer under load. Assuming aresistive -inductive load, current I 2 lagsbehind E 2 by an angle . Flux m lags90o behind E g.

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Fig 2: Phasor relationships under load.


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EXAMPL

E1

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Ideal Transformer Circuit SymbolIdeal transformer can besimplified to a box having 2terminals in symbolic form.Polarity marks indicate thedirection of current flow as wellas the polarities of voltageE1and E2.In an ideal transformer E1 and E2, I1 and I2 are always in phase.The angle depends upon thenature of the load.

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Fig 3: Symbol for an ideal transformer andphasor diagram.


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Cont

For example, an idealtransformer T is connectedbetween a source and loadZ. The ratio of transformer is a:

and

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Fig 4: Impedance transformation using atransformer.


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ContAn impedance Z x between the primary terminal given by:

The secondary sees an impedance Z given by:

Z x can be expressed in another way:

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ContThis means that the impedance seen by the source is a2 times thereal impedance.

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Fig 5: The impedance seen by the source differs from Z .


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ContAn ideal transformer can modify the value of anycomponent (resistor, capacitor or inductor).

For example: 1000 resistor is placed across secondary of transformer having turn ratio of 1:5, it will appear across the primary as aresistance of 1000 (1/5)2 = 40 .

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Cont 1000 reactance of capacitor is placed across secondary of

transformer having turn ratio of 1:5, it will appear across theprimary as a reactance of 40 .

However, because the reactance of the capacitor is inverselyproportional to its capacitance, the apparent capacitance btwthe primary terminal is 25 times greater than its actual value.

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Shifting Impedances from Secondary toP

rimaryWhile shifting from secondary to primary, these rules applied:

S hifted impedance values are multiplied by a2.S hifted voltage E values becomes aE.S hifted current I values becomes I/a.The secondary of the transformer is on open-circuit and both

current are zero, therefore can remove the transformer.

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Shifting Impedances from P rimary to

SecondaryWhile shifting from primary to secondary, these rules applied:

S hifted impedance values are divided by a2.

S hifted voltage E values becomes E/a. S hifted current I values becomes aI. The primary of the transformer is on open-circuit and both current are

zero, therefore can remove the ideal transformer completely.

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END OF PART 4

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part 4 emachines EEP 3243