EEE 471/591: Power System Analysis [Face-to-Face]

Homework #4

Problem 1 (25 Points)

Three single-phase, two-winding transformers, each rated 450 MVA, 20 kV/288.7 kV, with leakage reactance  xeq  = 0.20 pu, are connected to form. a three-phase bank. The high-voltage windings are connected in Y with a solidly grounded neutral. Draw the per-unit equivalent circuit if the low-voltage windings are connected: (a) in  Δ  with American standard phase shift, or (b) in Y with an open neutral. Use transformer ratings as base quantities. Winding resistances and exciting current are neglected.

Problem 2 (25 Points)

Consider a bank of three single-phase two-winding transformers whose high-voltage terminals are connected to a three-phase, 13.8-kV feeder. The low-voltage terminals are connected to a three-phase substation load rated 5 MVA and 3 kV. Determine the required voltage ratings, current ratings, and MVA ratings of both windings of each transformer, when the high-voltage/low-voltage windings are connected (a) Y-Δ, (b)  Δ-Y, (c) Y-Y, (d)  Δ-Δ .

Problem 3 (25 Points)

The ratings of a three-phase three-winding transformer are:

Primary (1): Y connected, 66 kV, 15 MVA

Secondary (2): Y connected, 13.2 kV, 10 MVA

Tertiary (3):  Y  connected, 2.3 kV, 5 MVA.

Neglecting winding resistances and exciting current, the per-unit leakage reactances are:

X12  = 0.08  on a 15-MVA, 66-kV base.

X13  = 0.10  on a 15-MVA, 66-kV base.

X23  = 0.09  on a 10-MVA, 13.2-kV base.

(a) Determine the per-unit reactances  X1, X2, X3   of the equivalent circuit on a 15-MVA, 66-kV base at the primary terminals.

(b) Purely resistive loads of 7.5 MW at 13.2 kV and 5 MW at 2.3 kV are connected to the secondary and tertiary sides of the transformer, respectively. Draw the per-unit impedance diagram (in per-phase analysis), showing the per-unit impedances on a 15-MVA, 66-kV base at the primary terminals.

Problem 4 (25 Points)

In a three-phase system, two buses abc and a’b’c’ are connected by two parallel lines L1 and L2 with positive-sequence series reactances  XL1  = 0.25 pu  and  XL2  = 0.20 pu. The two parallel lines supply a balanced load with a load current of  1.0∠ — 30opu. Determine the real and reactive power supplied to the load bus from each parallel line with (a) no regulating transformer, (b) the voltage-magnitude- regulating transformer, placed in series with line L1 at bus a’b’c’, providing a 0.05 per-unit increase in voltage magnitude toward bus a’b’c’, (c) the phase-angle-regulating transformer, placed in series with line L1 at bus a’b’c’, advancing the phase angle by 3o toward bus a’b’c’ . Assume that the voltage at bus abc is adjusted so that the voltage at bus a’b’c’ remains constant at 1.0∠0opu. Also assume positive sequence.