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 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 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 Z2’ is the load impedance referred to the primary

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

Exact 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).

Phasor Diagram

Performance Measures The percent regulation The transformer efficiency

Voltage Regulation

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 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

Efficiency