2. Transformers

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1 Exercise 2. Transformers R. E. Zich & S. Leva – Politecnico di Milano Electrical Machines PoliTong – A.A. 2010-2011 Sonia Leva 2 2. Transformers 2.1 A…
1 Exercise 2. Transformers R. E. Zich & S. Leva – Politecnico di Milano Electrical Machines PoliTong – A.A. 2010-2011 Sonia Leva 2 2. Transformers 2.1 A transformer is made up of a 1200 turn primary coil and an open-circuited 75 turn secondary coil wound around a closed core of cross sectional area 42 cm2. The core material can be considered to saturate when the rms applied flux density reaches. What maximum 60 Hz rms primary voltage is possible without reaching the saturation level? What is the corresponding secondary voltage? How are these values modified if the applied frequency is lowered to 50 Hz? Sonia Leva 3 2. Transformers 2.1 Solution Sonia Leva 4 2. Transformers 2.2 A transformer is to be used to transform the impedance of a 8 Ω resistor to an impedance of 75 Ω. Calculate the required turns ratio, assuming the transformer to be ideal. 2.2 Solution Sonia Leva 5 2. Transformers 2.3 A 100 Ω resistor is connected to the secondary of an ideal transformer with a turns ratio of 1:4 (primary to secondary). A 10 V rms, 1kHz voltage source is connected to the primary. Calculate the primary current and the voltage across the 100 Ω resistor. 2.3 Solution Sonia Leva 6 2. Transformers 2.4 A single phase 60 Hz transformer has a nameplate voltage rating of 7.97kV:266 V, which is based on its winding turns ratio. The manufacturer calculates that the primary (7.97 kVA) leakage inductance is 165 mH and the primary magnetizing inductance is 135 H. For an applied primary voltage of 7970 at 60 Hz, calculate the resultant open-circuit secondary voltage. 2.4 Solution Sonia Leva 7 2. Transformers 2.5 The manufacturer calculates that the transformer of the previous problem has a secondary leakage inductance of 0.225 mH. 1. Calculate the magnetizing inductance as referred to the secondary side 2. A voltage of 266 V, 60 Hz is applied to the secondary. Calculate (i) the resultant open circuit primary voltage and (ii) the secondary current which would result if the primary were short circuited Sonia Leva 8 2. Transformers 2.5 Solution Sonia Leva 9 2. Transformers 2.6 A single phase load is supplied through a 35 kV feeder whose impedance is 95+j360Ω and a 35kV:2400-V transformer whose equivalent impedance is 0.23+j1.27Ω referred to its low-voltage side. The load is 160 kW at 0.89 leading power factor and 2340 V. 1. Compute the voltage at the high voltage terminal of the transformer 2. Compute the voltage at the sending end of the feeder 3. Compute the power and reactive power input at the sending end of the feeder. Sonia Leva 10 2. Transformers 2.6 Solution Sonia Leva 11 2. Transformers 2.7 The nameplate on a 50MVA, 60 Hz single-phase transformer indicates that it has a voltage rating of 8.0-kV:78-kV. An open circuit test is conducted from the low voltage side, and the corresponding instrument readings are 8.0 kV, 62.1 A and 206 kW. Similarly a short circuit test from the low-voltage side gives readings of 674 V, 6.25 kA, and 187 kW. 1. Calculate the equivalent series impedance, resistance and reactance of the transformer as referred to the low voltage terminals. 2. Calculate the equivalent series impedance of the transformer as referred to the high voltage terminals. 3. Making the suitable approximations, draw a T equivalent circuit for the transformer 4. Determine the efficiency and voltage regulation if the transformer is operating at the rated voltage and load (unity power factor) 5. Repeat the previous point assuming the load to be at 0.9 power factor leading. Sonia Leva 12 2. Transformers 2.7 Solution Sonia Leva 13 2. Transformers 2.7 Solution Sonia Leva 14 2. Transformers 2.7 Solution 452 kVAR Sonia Leva 15 2. Transformers 2.7 Solution Sonia Leva 16 2. Transformers 2.7 Solution Sonia Leva 17 2. Transformers 2.7 Solution Sonia Leva 18 2. Transformers 2.8 The following data were obtained for a 20 kVA, 60 Hz, 2400:240 V distribution transformer tested at 60 Hz: with high-voltage winding open-circuited V=240V, I=1.038A, P=122W with low-voltage terminals short-circuited V=61.3V, I=8.33A, P=257W 1. Compute the efficiency at full-load current and the rated terminal voltage at 0.8 power factor. 2. Assume that the load power factor is varied while the load current and secondary terminal voltage are held constant. Use a phasor diagram to determine the load power factor for which the regulation is greatest. What is this regulation? Sonia Leva 19 2. Transformers 2.8 Solution Sonia Leva 20 2. Transformers 2.8 Solution Sonia Leva 21 2. Transformers 2.8 Solution Sonia Leva 22 2. Transformers 2.9 The high voltage terminals of a three-phase bank of three single-phase transformers are supplied from a three wire, three-phase 13.8 kV (line to line) system. The low voltage terminals are to be connected to a three-wire, three- phase substation load drawing up to 4500 kVA at 2300 V line to line. Specify the required voltage, current and kVA ratings of each transformer (both high and low voltage windings) for each of the following connections: 1. Y-Δ 2. Δ−Y 3. Y-Y 4. Δ−Δ Sonia Leva 23 2. Transformers 2.9 Solution Sonia Leva
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