Skip to main content

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).

Zb,line=220250=968 ΩZ_{b,line} = \frac{220^2}{50} = 968\ \Omega

Per-unit reactances (50 MVA base)

XG1=0.20×5020×(2533)2=0.2870 puXG2=0.30×5030×(2533)2=0.2870 puXT1=0.15 puXline=50968=0.0517 puXT2=0.15 pu (assumed)XM1=0.30×5020=0.75 puXM2=0.20×5030=0.3333 pu\begin{aligned} X_{G1} &= 0.20\times\frac{50}{20}\times\left(\frac{25}{33}\right)^2 = 0.2870\ \text{pu}\\ X_{G2} &= 0.30\times\frac{50}{30}\times\left(\frac{25}{33}\right)^2 = 0.2870\ \text{pu}\\ X_{T1} &= 0.15\ \text{pu}\\ X_{line} &= \frac{50}{968} = 0.0517\ \text{pu}\\ X_{T2} &= 0.15\ \text{pu (assumed)}\\ X_{M1} &= 0.30\times\frac{50}{20} = 0.75\ \text{pu}\\ X_{M2} &= 0.20\times\frac{50}{30} = 0.3333\ \text{pu} \end{aligned}
ElementBase kVX (pu)
G1 (20 MVA, 25 kV)330.2870
G2 (30 MVA, 25 kV)330.2870
T133/2200.1500
Line (j50 Ω)2200.0517
T2 (assumed 15 %)220/110.1500
M1 (20 MVA)110.7500
M2 (30 MVA)110.3333

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: XG1=XG2=0.287X_{G1} = X_{G2} = 0.287, XT1=0.15X_{T1} = 0.15, Xline=0.0517X_{line} = 0.0517, XT2=0.15X_{T2} = 0.15 (assumed), XM1=0.75X_{M1} = 0.75, XM2=0.333X_{M2} = 0.333 pu.

✓ Answer checked by Claude Opus 5.5 (high effort)

All Power System Analysis I chapter 3 questions →