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Modeling of Power Transformers A Static Device Transformers The transformer enables us to utilize different voltage levels across the system for the most economical value. Stepping up the generator voltage to high voltage, is done through power transformers to minimize losses and increase the transmission capacity of the lines. This transmission voltage level is then stepped down in many stages for distribution and utilization purposes. General Theory A transformer contains two or more windings linked by a mutual field. The primary winding is connected to an alternating voltage source. The input current results in an alternating flux whose magnitude depends on the voltage and number of turns of the primary winding. The alternating flux links the secondary winding and induces a voltage in it with a value that depends on the number of turns of the secondary winding. Transformers Primary winding Supply NP Secondary winding NS Laminated iron core Basic components of single phase transformer Load Transformers Primary Winding Multi-layer Laminated Iron Core Secondary Winding H1 H2 X1 X2 Winding Terminals 5.2 Single phase transformer arrangement Transformers H2 X2 H2 X1 Vp Vs Vp Vs H1 X1 H1 X2 100 100 Vp ( t ) Vs( t ) Vp ( t ) 0 100 Vs( t ) 0 5 10 15 20 0 100 0 5 10 t t milli s milli s (b) (a) Polarity for transformer 15 20 Transformers Iron core Insulation Secondary winding Terminals Small transformer construction a) Lamination b) Iron core with winding Transformers Dry-type three-phase transformer Transformers Bushing Steel tank Iron core behind the steel bar Winding Insulation Radiator Oil Insulated and cooled transformer 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 Loaded Transformer Z2’ is the load impedance referred to the primary 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 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 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