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 V and leads the terminal voltage by an angle 47.96°.

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.

3. 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

4. Power Transformers

5. Transformation ratio
Primary (supply)
Secondary (Load)

6. Transformers at no loadIc 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.

7. 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.

8. Loaded Transformer
Z2’ is the load impedance
referred to the primary

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

10. Exact Circuit

11. 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).

12. Phasor Diagram

13. Performance Measures
The percent regulation
The transformer efficiency

14. Voltage Regulation

15. 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

16. Example
A 100-kVA, 400/2000 V, single-phase transformer has the following parameters
R1 = 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

17. Solution

18. Voltage Regulation

19. Efficiency