Reactance diagram: 300 MVA, 20 kV generator, two motors

In a per-unit reactance diagram every element is expressed on one common MVA base, and the base voltage changes from zone to zone in the ratio of the transformer line-to-line voltages. Resistances, magnetising branches and the grounding impedances are neglected (they carry no current under balanced conditions).

Step 1: Base values in each zone

• Base MVA (all zones): $S_b = 300$ MVA
• Generator zone: $V_{b1} = 20$ kV (given)
• Line zone (T1 is 20/230 kV): $V_{b2} = 20 \times \frac{230}{20} = 230$ kV
• T2 is a Y–Δ bank of single-phase units 127/13.2 kV, so its line-to-line ratio is $\sqrt{3}\times127 / 13.2 = 220/13.2$ kV. Motor zone:

$$V_{b3} = 230 \times \frac{13.2}{220} = 13.8\ \text{kV}$$ $$Z_{b,\text{line}} = \frac{V_{b2}^2}{S_b} = \frac{230^2}{300} = 176.33\ \Omega$$

Step 2: Change of base

$$X_{pu,new} = X_{pu,old}\times\frac{S_{b,new}}{S_{b,old}}\times\left(\frac{V_{old}}{V_{b,new}}\right)^2$$

Step 3: Per-unit reactances

$$\begin{aligned} X_G &= 0.20\ \text{pu (already on its own rating)}\\ X_{T1} &= 0.10\times\frac{300}{350} = 0.0857\ \text{pu}\\ X_{line} &= \frac{0.8\times 65}{176.33} = \frac{52}{176.33} = 0.2949\ \text{pu}\\ X_{T2} &= 0.10\times\frac{300}{300}\times\left(\frac{13.2}{13.8}\right)^2 = 0.0915\ \text{pu}\\ X_{M1} &= 0.20\times\frac{300}{200}\times\left(\frac{13.2}{13.8}\right)^2 = 0.2745\ \text{pu}\\ X_{M2} &= 0.20\times\frac{300}{100}\times\left(\frac{13.2}{13.8}\right)^2 = 0.5490\ \text{pu} \end{aligned}$$

(The three-phase rating of T2 is $3\times100 = 300$ MVA.)

Step 4: Reactance diagram

     j0.0857   j0.2949   j0.0915
 +---/\/\/-----/\/\/-----/\/\/---+--------+
 |    T1        line       T2    |        |
j0.2                          j0.2745  j0.5490
 |                               |        |
(Eg)                           (Em1)    (Em2)
 |                               |        |
 +-------------------------------+--------+
            reference (neutral) bus

Answer: On 300 MVA base, $X_G = 0.2$, $X_{T1} = 0.0857$, $X_{line} = 0.2949$, $X_{T2} = 0.0915$, $X_{M1} = 0.2745$ and $X_{M2} = 0.5490$ pu, with base voltages 20 kV, 230 kV and 13.8 kV in the three zones.