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Reactance diagram: G, T1, j18 Ω line, T2, M

Short answer

Using 25 MVA and 13.8/66/11 kV bases: generator reactance 0.0858 pu, both transformers 0.12 pu, line j18 ohm gives 0.1033 pu, and motor 0.13 pu. Draw a single loop from generator through T1, line, T2 to motor with these reactances to neutral.

Draw a reactance diagram of the electric power system given below and express all reactances in per unit system by choosing appropriate base values. G1: 14 kV, 30 MVA, 10%; M: 11 kV, 25 MVA, 13%; T1: 66/11 kV, 25 MVA, 12%; T1: 13.8/66 kV, 25 MVA, 12% (as printed; one of these is T2). [Figure: G → T1 → line j18 Ohms/phase → T2 → motor M.]

The two transformers are read as T1: 13.8/66 kV (at the generator) and T2: 66/11 kV (at the motor), both 25 MVA, 12 %.

Choice of base: 25 MVA (transformer rating), 66 kV on the line. Then the base is 13.8 kV in the generator zone and 11 kV in the motor zone.

Zb,line=66225=174.24 ΩZ_{b,line} = \frac{66^2}{25} = 174.24\ \Omega

Per-unit reactances

XG=0.10×2530×(1413.8)2=0.0858 puXT1=0.12 pu (rating = base)Xline=18174.24=0.1033 puXT2=0.12 puXM=0.13×2525×(1111)2=0.13 pu\begin{aligned} X_G &= 0.10\times\frac{25}{30}\times\left(\frac{14}{13.8}\right)^2 = 0.0858\ \text{pu}\\ X_{T1} &= 0.12\ \text{pu (rating = base)}\\ X_{line} &= \frac{18}{174.24} = 0.1033\ \text{pu}\\ X_{T2} &= 0.12\ \text{pu}\\ X_M &= 0.13\times\frac{25}{25}\times\left(\frac{11}{11}\right)^2 = 0.13\ \text{pu} \end{aligned}
ElementBase kVX (pu, 25 MVA)
G (30 MVA, 14 kV)13.80.0858
T113.8/660.1200
Line j18 Ω660.1033
T266/110.1200
Motor M110.1300

Reactance diagram

      j0.12    j0.1033    j0.12
 +----/\/\/----/\/\/------/\/\/----+
 |     T1       line       T2      |
j0.0858                          j0.13
 |                                 |
(Eg)                              (Em)
 |                                 |
 +---------------------------------+
            reference bus

Answer: On 25 MVA (13.8 / 66 / 11 kV): XG=0.0858X_G = 0.0858, XT1=0.12X_{T1} = 0.12, Xline=0.1033X_{line} = 0.1033, XT2=0.12X_{T2} = 0.12, XM=0.13X_M = 0.13 pu.

✓ Answer checked by Claude Opus 5.5 (high effort)

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