2.1 Problems - chapter 2  (Page 4/5)

2.23 Three 100-MVA single-phase transformers, rated at 13.8 kV:66.4 kV, are to be connected in a three-phase bank. Each transformer has a series impedance of 0.0045 + j0.19 $\Omega$ referred to its 13.8-kV winding.

a. If the transformers are connected Y-Y, calculate (i) the voltage and power rating of the three-phase connection, (ii) the equivalent impedance as referred to its low-voltage terminals, and (iii) the equivalent impedance as referred to its high-voltage terminals.

b. Repeat part (a) if the transformer is connected Y on its low-voltage side and $\Delta$ on its high-voltage side.

2.24 A three-phase ${\rm Y}-\Omega$ transformer is rated 225-kV:24-kV, 400 MVA and has a series reactance of 11.7 $\Omega$ as referred to its high-voltage terminals. The transformer is supplying a load of 325 MVA, with 0.93 power factor lagging at a voltage of 24 kV (line-to-line) on its low-voltage side. It is supplied from a feeder whose impedance is 0.11 + j 2.2 $\Omega$ connected to its high-voltage terminals. For these conditions, calculate (a) the line-to-line voltage at the high-voltage terminals of the transformer and (b) the line-to-line voltage at the sending end of the feeder.

2.25 Assume the total load in the system of Problem 2.24 to remain constant at 325 MVA. Write a MATLAB script to plot the line-to-line voltage which must be applied to the sending end of the feeder to maintain the load voltage at 24 kV line-to-line for load power factors in range from 0.75 lagging to unity to 0.75 leading. Plot the sending-end voltage as a function of power factor angle.

2.26 A Δ-Y-connected bank of three identical 100-kVA, 2400-V:120-V, 60-Hz transformers is supplied with power through a feeder whose impedance is 0.065 + j0.87 $\Omega$ per phase. The voltage at the sending end of the feeder is held constant at 2400 V line-to-line. The results of a single-phase short-circuit test on one of the transformers with its low-voltage terminals short-circuited are

VH=53.4V f=60Hz IH=41.7A P=832W

a. Determine the line-to-line voltage on the low-voltage side of the transformer when the bank delivers rated current to a balanced three-phase unity power factor load.

b. Compute the currents in the transformer's high- and low-voltage windings and in the feeder wires if a solid three-phase short circuit occurs at the secondary line terminals.

2.27 A 7970-V: 120-V, 60-Hz potential transformer has the following parameters as seen from the high-voltage (primary) winding:

X1 = 1721 $\Omega$ $X_2^{\text{'}}$ = 1897 $\Omega$ Xm = 782 $k\Omega$

R1 = 1378 $\Omega$ $R_2^{\text{'}}$ = 1602 $\Omega$

a. Assuming that the secondary is open-circuited and that the primary is connected to a 7.97-kV source, calculate the magnitude and phase angle (with respect to the high-voltage source) of the voltage at the secondary terminals.

b. Calculate the magnitude and phase angle of the secondary voltage if a 1 $k\Omega$ resistive load is connected to the secondary terminals.

c. Repeat part (b) if the burden is changed to a 1 ***SORRY, THIS MEDIA TYPE IS NOT SUPPORTED.***reactance.

2.28For the potential transformer of Problem 2.27, find the maximum reactive burden (mimimum reactance) which can be applied at the secondary terminals such that the voltage magnitude error does not exceed 0.5 percent.