2.1 Problems - chapter 2  (Page 2/5)

2.10 A 460-V:2400-V transformer has a series leakage reactance of 37.2 $\Omega$ as referred to the high-voltage side. A load connected to the low-voltage side is observed to be absorbing 25 kW, unity power factor, and the voltage is measured to be 450 V. Calculate the corresponding voltage and power factor as measured at the high-voltage terminals.

2.11 The resistances and leakage reactances of a 30-kVA, 60-Hz, 2400-V:240-V distribution transformer are

R1 = 0.68 $\Omega$ R2 = 0.0068 $\Omega$

$X_{1_1}$ = 7.8 $\Omega$ $$ $X_{1_2}$ = 0.0780 $\Omega$

where subscript 1 denotes the 2400-V winding and subscript 2 denotes the 240-V winding. Each quantity is referred to its own side of the transformer.

a. Draw the equivalent circuit referred to (i) the high- and (ii) the low-voltage sides. Label the impedances numerically.

b. Consider the transformer to deliver its rated kVA to a load on the low-voltage side with 230 V across the load. (i) Find the high-side terminal voltage for a load power factor of 0.85 power factor lagging. (ii) Find the high-side terminal voltage for a load power factor of 0.85 power factor leading.

c. Consider a rated-kVA load connected at the low-voltage terminals operating at 240V. Use MATLAB to plot the high-side terminal voltage as a function of the power-factor angle as the load power factor varies from 0.6 leading through unity power factor to 0.6 pf lagging.

2.12 Repeat Problem 2.11 for a 75-kVA, 60-Hz, 4600-V:240-V distribution transformer whose resistances and leakage reactances are

R1 = 0.846 $\Omega$ R2 = 0.00261 $\Omega$

$X_{1_1}$ = 26.8 $\Omega$ $X_{1_2}$ = 0.0745 $\Omega$

where subscript 1 denotes the 4600-V winding and subscript 2 denotes the 240-V winding. Each quantity is referred to its own side of the transformer.

2.13 A single-phase load is supplied through a 35-kV feeder whose impedance is 95+j360 $\Omega$ and a 35-kV:2400-V transformer whose equivalent impedance is 0.23 + j1.27 $\Omega$ referred to its low-voltage side. The load is 160 kW at 0.89 leading power factor and 2340 V.

a. Compute the voltage at the high-voltage terminals of the transformer.

b. Compute the voltage at the sending end of the feeder.

c. Compute the power and reactive power input at the sending end of the feeder.

2.14 The nameplate on a 50-MVA, 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.

a. Calculate the equivalent series impedance, resistance, and reactance of the transformer as referred to the low-voltage terminals.

b. Calculate the equivalent series impedance of the transformer as referred to the high-voltage terminals.

c. Making appropriate approximations, draw a T equivalent circuit for the transformer.

d. Determine the efficiency and voltage regulation if the transformer is operating at the rated voltage and load (unity power factor).

e. Repeat part (d), assuming the load to be at 0.9 power factor leading.