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Reactance diagram: three generators, 30 MVA 6.6 kV base

Short answer

On 30 MVA base, Vb=6.6 kV at G1, 115 kV in line, 11.5 kV at G3. Reactances: G1 j0.24, T1 j0.10, line (j120 Ω) j0.272, T2 j0.20, G2 j0.30, line (j90 Ω) j0.204, T3 j0.108, G3 j0.1976.

Draw the reactance diagram with all values in p.u. on a base of 30 MVA, 6.6 kV in the circuit of generator G1. Required data are as follows: G1: 25 MVA, 6.6 kV, j0.2 p.u.; G2: 15 MVA, 6.6 kV, j0.15 p.u.; G3: 30 MVA, 13.2 kV, j0.15 p.u.; T1: 30 MVA, 6.6 (delta) kV/115 (star) kV, j0.1 p.u.; T2: 15 MVA, 6.6 (delta) kV/115 (star) kV, j0.1 p.u.; T3: single phase units each rated 10 MVA, 69/6.9 kV, j0.1 p.u. [Figure: G1 (Y, grounded) → T1 (Δ–Y grounded) → line j120 Ω → junction bus; from the junction, T2 (Y grounded on HV side, Δ on LV side) up to G2 (Y, grounded); and a line j90 Ω → T3 (Y–Y, grounded) → G3 (Y, grounded).]

Base values

  • Sb=30S_b = 30 MVA, and Vb=6.6V_b = 6.6 kV in the G1 circuit.
  • Line section (through T1, 6.6/115 kV): Vb=115V_b = 115 kV, so Zb=1152/30=440.83 ΩZ_b = 115^2/30 = 440.83\ \Omega.
  • G2 circuit (through T2, 115/6.6 kV): Vb=6.6V_b = 6.6 kV.
  • T3 is a Y–Y bank of single-phase 69/6.9 kV units. Its line ratio is 3×69=119.5\sqrt3\times69 = 119.5 kV / 3×6.9=11.95\sqrt3\times6.9 = 11.95 kV, and its rating is 3×10=303\times10 = 30 MVA.
  • G3 circuit: Vb=115×11.95119.5=11.5V_b = 115\times\dfrac{11.95}{119.5} = 11.5 kV.

Per-unit reactances

G1:0.2×3025=0.24G2:0.15×3015=0.30G3:0.15×3030(13.211.5)2=0.1976T1:0.1×3030=0.10T2:0.1×3015=0.20T3:0.1×3030(119.5115)2=0.1080Line j120:120440.83=0.2722Line j90:90440.83=0.2042\begin{aligned} G_1&: 0.2\times\frac{30}{25} = 0.24\\ G_2&: 0.15\times\frac{30}{15} = 0.30\\ G_3&: 0.15\times\frac{30}{30}\left(\frac{13.2}{11.5}\right)^2 = 0.1976\\ T_1&: 0.1\times\frac{30}{30} = 0.10\\ T_2&: 0.1\times\frac{30}{15} = 0.20\\ T_3&: 0.1\times\frac{30}{30}\left(\frac{119.5}{115}\right)^2 = 0.1080\\ \text{Line } j120&: \frac{120}{440.83} = 0.2722\\ \text{Line } j90&: \frac{90}{440.83} = 0.2042 \end{aligned}
Elementp.u. (30 MVA base)
G1j0.24
T1j0.10
Line (j120 Ω)j0.2722
T2j0.20
G2j0.30
Line (j90 Ω)j0.2042
T3j0.108
G3j0.1976

Reactance diagram

 j0.24  j0.10   j0.2722        j0.2042  j0.108  j0.1976
+-/\/\--/\/\----/\/\----+(J)+---/\/\----/\/\----/\/\--+
|                        |                            |
(E1)                   j0.20 (T2)                   (E3)
|                        |                            |
|                      j0.30 (G2)                     |
|                        |                            |
|                      (E2)                           |
+------------------- reference -----------------------+

Here J is the junction bus. Winding connections and earthing do not affect these positive-sequence reactances.

✓ Answer checked by Claude Opus 5.5 (high effort)

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