- 2071 Bhadra · 6 marks
Reactance diagram: two generators, two motors, j50 Ω line
Short answer
On a 50 MVA base with 33 kV generator, 220 kV line, and 11 kV motor bases, per-unit reactances are: X_G1 = X_G2 = 0.287 pu, X_T1 = 0.15 pu, X_line = 0.0517 pu, X_T2 = 0.15 pu (assumed), X_M1 = 0.75 pu, X_M2 = 0.333 pu.
Draw the per-unit reactance diagram for the power system shown below, choosing suitable base values. G1: 25 kV, 20 MVA, 20%; G2: 25 kV, 30 MVA, 30%; T1: 50 MVA, 33/220 kV, 15%; T2: 50 MVA, 220/11 kV; M1: 20 MVA, 11 kV, 30%; M1: 30 MVA, 11 kV, 20% (second motor, printed as M1). [Figure: G1 and G2 in parallel on a bus → T1 → line j50 Ω/phase → T2 → bus feeding motors M1 and M2.]
Choice of base: 50 MVA (transformer rating) and 220 kV on the line. Then the generator side base is 33 kV (T1 33/220 kV) and the motor side base is 11 kV (T2 220/11 kV). The reactance of T2 is not printed; it is assumed to be 15 % on its own rating (same as T1).
Per-unit reactances (50 MVA base)
| Element | Base kV | X (pu) |
|---|---|---|
| G1 (20 MVA, 25 kV) | 33 | 0.2870 |
| G2 (30 MVA, 25 kV) | 33 | 0.2870 |
| T1 | 33/220 | 0.1500 |
| Line (j50 Ω) | 220 | 0.0517 |
| T2 (assumed 15 %) | 220/11 | 0.1500 |
| M1 (20 MVA) | 11 | 0.7500 |
| M2 (30 MVA) | 11 | 0.3333 |
Reactance diagram
j0.15 j0.0517 j0.15
+--+---/\/\/---/\/\/-----/\/\/---+------+
| | T1 line T2 | |
j0.287 j0.287 j0.75 j0.3333
| | | |
(E1)(E2) (Em1) (Em2)
| | | |
+--+-----------------------------+------+
reference bus
Answer: On 50 MVA with 33 / 220 / 11 kV bases: , , , (assumed), , pu.
✓ Answer checked by Claude Opus 5.5 (high effort)
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