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

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

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

Power Transformers

Transformation ratio

Primary (supply) Secondary (Load)

Transformers at no load

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

losses and to magnetize the transformer core.

Im

Ic E1

I

c

E1

I

I

Ic Im

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.

2221

21 RIRI

mhysteriseseddymag IVPPP 1

Loaded Transformer

Z2’ is the load impedancereferred to the primary

Equivalent circuit

V1: Primary voltage (supply)I1 : Primary current.V2: Secondary voltage (load)I2: : Secondary current

Exact Circuit

Approximate Circuit

The no load current ranges from 1% to 3% of the full load current.Therefore, the circuit can be simplified to circuit (b).

(a) (b)

Phasor Diagram

)('2'21 eqeq jXRIVV

Performance Measures

The percent regulation

The transformer efficiency

Voltage Regulation

sincos '2

'2

'21 eqeq XIRIVVVR

Efficiency

The efficiency of the transformer is the ratio of output (secondary)

power to the input (primary) power. Formally the efficiency is η:

1

2

P

P

LPPP 21

Where,

P2 : The output power (Secondary) = V2I2 cos2

P1 : The input power (Primary) = V1I1 cos1

Where,

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

ironeq PRIIV

IV

2'22

'2

'2

2'2

'2

cos

cos

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

Solution

Voltage Regulation

sincos '2

'2

'21 eqeq XIRIVVVR

%84.296.411

7.11%

7.11

6.006.02258.002.0225

VR

VVR

VR

Efficiency