2.1 Problems - chapter 2  (Page 5/5)

2.29Consider the potential transformer of Problem 2.27.

a. Use MATLAB to plot the percentage error in voltage magnitude as a function of the magnitude of the burden impedance (i) for a resistive burden of 100 3000 $\Omega$ and (ii) for a reactive burden of 100 3000 $\Omega$ . Plot these curves on the same axis.

b. Next plot the phase error in degrees as a function of the magnitude of the burden impedance (i) for a resistive burden of 100 ≤ 3000 $\Omega$ and (ii) for a reactive burden of 100 3000 $\Omega$ . Again, plot these curves on the same axis.

2.30 A 200-A:5-A, 60-Hz current transformer has the following parameters as seen from the 200-A (primary) winding:

X1 = 745 $\mu \Omega$ $X_2^{\text{'}}$ = 813 $\mu \Omega$ Xm = 307 $m\Omega$

R1 = 136 $\mu \Omega$ $$ $R_2^{\text{'}}$ = 128 $\mu \Omega$

a. Assuming a current of 200 A in the primary and that the secondary is short-circuited, find the magnitude and phase angle of the secondary current.

b. Repeat the calculation of part (a) if the CT is shorted through a 250 $\mu \Omega$ burden.

2.31 Consider the current transformer of Problem 2.30.

a. Use MATLAB to plot the percentage error in current magnitude as a function of the magnitude of the burden impedance (i) for a resistive burden of 100 1000 $\Omega$ and (ii) for a reactive burden of 100 1000 $\Omega$ . Plot these curves on the same axis.

b. Next plot the phase error in degrees as a function of the magnitude of the burden impedance (i) for a resistive burden of and (ii) for a reactive burden of . Again, plot these curves on the same axis.

2.32 A 15-kV: 175-kV, 125-MVA, 60-Hz single-phase transformer has primary and secondary impedances of 0.0095 + j0.063 per unit each. The magnetizing impedance is j148 per unit. All quantities are in per unit on the transformer base. Calculate the primary and secondary resistances and reactances and the magnetizing inductance (referred to the low-voltage side) in ohms and henrys.

2.33 The nameplate on a 7.97-kV:460-V, 75-kVA, single-phase transformer indicates that it has a series reactance of 12 percent (0.12 per unit).

a. Calculate the series reactance in ohms as referred to (i) the low-voltage terminal and (ii) the high-voltage terminal.

b. If three of these transformers are connected in a three-phase Y-Y connection, calculate (i) the three-phase voltage and power rating, (ii) the per unit impedance of the transformer bank, (iii) the series reactance in ohms as referred to the high-voltage terminal, and (iv) the series reactance in ohms as referred to the low-voltage terminal.

c. Repeat part (b) if the three transformers are connected in Y on their HV

side and $\Delta$ on their low-voltage side.

2.34 a. Consider the Y-Y transformer connection of Problem 2.33, part (b). If the rated voltage is applied to the high-voltage terminals and the three low-voltage terminals are short-circuited, calculate the magnitude of the phase current in per unit and in amperes on (i) the high-voltage side and (ii) the low-voltage side.

b. Repeat this calculation for the Y- $\Delta$ connection of Problem 2.33, part (c).

2.35 A three-phase generator step-up transformer is rated 26-kV:345-kV, 850 MVA and has a series impedance of 0.0035 + j0.087 per unit on this base. It is connected to a 26-kV, 800-MVA generator, which can be represented as a voltage source in series with a reactance of j1.57 per unit on the generator base.

a. Convert the per unit generator reactance to the step-up transformer base.

b. The unit is supplying 700 MW at 345 kV and 0.95 power factor lagging to the system at the transformer high-voltage terminals. (i) Calculate the transformer low-side voltage and the generator internal voltage behind its reactance in kV. (ii) Find the generator output power in MW and the power factor.