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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 IF E1 Qc Im f The no load current If is needed to supply the no load losses and to magnetize the transformer core. E1 If IF 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. I12 R1 I 22 R2 Magnetic losses, these losses are divided into eddy current losses and hysteresis losses. Pmag Peddy Physterises V1I m 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 ' V1 V2 ' I 2 ( Req jX eq ) Performance Measures The percent regulation The transformer efficiency Voltage Regulation VR V1 V2' I 2' Req cosf I 2' X eq sin f 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 P1 P2 PL Where, PL is the power loss in the transformer = Pcopper + Piron V2' I 2' cosf2 V2' I 2' cosf2 I 2'2 Req Piron P2 P1 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 ' VR V1 V2 ' I 2 Req cosf ' I 2 X eq sin f VR 225 0.02 0.8 225 0.06 0.6 VR 11.7V 11.7 %VR 2.84% 411.96 Efficiency