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Reactance diagram of eight-bus system

Short answer

Base 10 MVA, 11 kV generator side, 66 kV lines. Per-unit reactances: X_G1 = X_G2 = 0.1093, X_G3 = 0.0874, X_T1 = X_T2 = X_T3 = 0.10, X_T4 = 0.0514, each line 0.0459 pu. Motor reactance is unspecified.

Construct a reactance diagram for the system given below and express all the reactances in per unit system. G1, G2: 10 MVA, 11.5 kV, 10%; G3: 15 MVA, 11.5 kV, 12%; T1, T2: 10 MVA, 11/66 kV, 10%; T3: 15 MVA, 11/66, 15%; T4: 35 MVA, 66/11 kV, 18%; L1 = L2 = L3 = L4 = j20 Ω/ph. [Figure: G1 (bus 1) → T1 → bus 2; G2 (bus 3) → T2 → bus 4; line L2 from bus 2 to bus 6, L1 from bus 2 to bus 4, L3 from bus 4 to bus 7, L4 from bus 6 to bus 7; T3 between bus 6 and bus 5 feeding G3; T4 between bus 7 and bus 8 feeding motor M (no motor rating printed).]

Choice of base: 10 MVA, with 11 kV in the generator circuits (the transformer LV rating) and 66 kV on the lines. The motor rating is not printed, so its reactance is left as XMX_M (pu on its own rating). Its value on the common base is XM10SM(VM11)2X_M\frac{10}{S_M}\left(\frac{V_M}{11}\right)^2.

Zb,66=66210=435.6 ΩZ_{b,66} = \frac{66^2}{10} = 435.6\ \Omega

Per-unit reactances (10 MVA base)

XG1=XG2=0.10×1010×(11.511)2=0.1093 puXG3=0.12×1015×(11.511)2=0.0874 puXT1=XT2=0.10 puXT3=0.15×1015=0.10 puXT4=0.18×1035=0.0514 puXL1=XL2=XL3=XL4=20435.6=0.0459 pu\begin{aligned} X_{G1} = X_{G2} &= 0.10\times\frac{10}{10}\times\left(\frac{11.5}{11}\right)^2 = 0.1093\ \text{pu}\\ X_{G3} &= 0.12\times\frac{10}{15}\times\left(\frac{11.5}{11}\right)^2 = 0.0874\ \text{pu}\\ X_{T1} = X_{T2} &= 0.10\ \text{pu}\\ X_{T3} &= 0.15\times\frac{10}{15} = 0.10\ \text{pu}\\ X_{T4} &= 0.18\times\frac{10}{35} = 0.0514\ \text{pu}\\ X_{L1} = X_{L2} = X_{L3} = X_{L4} &= \frac{20}{435.6} = 0.0459\ \text{pu} \end{aligned}
ElementX (pu, 10 MVA)
G1, G20.1093 each
G30.0874
T1, T20.1000 each
T30.1000
T40.0514
L1 to L40.0459 each

Reactance diagram

 (E1)-j0.1093-[1]-j0.10-[2]---j0.0459(L2)---[6]
                         |                   |
                   j0.0459(L1)          j0.0459(L4)
                         |                   |
 (E2)-j0.1093-[3]-j0.10-[4]---j0.0459(L3)---[7]

 [6]-j0.10(T3)-[5]-j0.0874-(E3)
 [7]-j0.0514(T4)-[8]-jXM-(Em)

 All sources (E1, E2, E3, Em) return to the
 common reference (neutral) bus.

Answer: On 10 MVA (11 kV / 66 kV bases): XG1=XG2=0.1093X_{G1} = X_{G2} = 0.1093, XG3=0.0874X_{G3} = 0.0874, XT1=XT2=XT3=0.10X_{T1} = X_{T2} = X_{T3} = 0.10, XT4=0.0514X_{T4} = 0.0514, and each line 0.0459 pu.

✓ Answer checked by Claude Opus 5.5 (high effort)

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