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Example 1
Example 1

A 9375 kVA, 13,800 kV, 60 Hz, two pole, Y-connected synchronous generator is delivering rated current at rated voltage and unity PF. Find the armature resistance and synchronous reactance given that the filed excitation voltage is 11935.44 V and leads the terminal voltage by an angle 47.96°.


Example 2
Example 2

A cylindrical rotor machine is delivering active power of 0.8 p.u. and reactive power of 0.6 p.u. at a terminal voltage of 1 p.u. If the power angle is 20°, compute the excitation voltage and the machine’s synchronous reactance.


Announcement
Announcement

  • Quiz I : Next Tuesday (April 5, 2011) at 12:00 in H11

  • Assignment I: will be posted today and due Next Tuesday (April 5, 2011) at 12:00 in H11



Transformation ratio
Transformation ratio

Primary (supply)

Secondary (Load)


Transformers at no load
Transformers at no load

Ic

E1

IF

Qc

E1

If

Im

f

IF

Ic

Im

The no load current If is needed to supply the no load

losses and to magnetize the transformer core.


Transformer losses
Transformer losses

  • The transformer losses are divided into electrical losses (copper losses) and Magnetic losses (Iron losses).

  • Copper losses in both the primary and secondary windings.

  • Magnetic losses, these losses are divided into eddy current losses and hysteresis losses.


Loaded transformer
Loaded Transformer

Z2’ is the load impedance

referred to the primary


Equivalent circuit
Equivalent circuit

V1: Primary voltage (supply)

I1 : Primary current.

V2: Secondary voltage (load)

I2: : Secondary current



Approximate circuit
Approximate Circuit

(a)

(b)

The no load current ranges from 1% to 3% of the full load current.

Therefore, the circuit can be simplified to circuit (b).



Performance measures
Performance Measures

  • The percent regulation

  • The transformer efficiency



Efficiency
Efficiency

  • The efficiency of the transformer is the ratio of output (secondary) power to the input (primary) power. Formally the efficiency is η:

Where,

P1 : The input power (Primary) = V1I1 cosf1

P2 : The output power (Secondary) = V2I2 cosf2

Where,

PL is the power loss in the transformer = Pcopper + Piron


Example
Example

A 100-kVA, 400/2000 V, single-phase transformer has the following parameters

R1 = 0.01 R2 = 0.25 ohms

X1 = 0.03 ohms X2 = 0.75 ohms

The transformer supplies a load of 90 kVA at 2000 V and 0.8 PF lagging.

  • Calculate the primary voltage and current using the simplest equivalent circuit.

  • Find also the V.R. and efficiency for the transformer





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