--- title: "Reactance diagram of eight-bus system" subject: "Power System Analysis I" chapter: 3 key: "semester_4/power_system_analysis_i:reactance-diagram-eight-bus" source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/reactance-diagram-eight-bus site: BCT Engineering --- # Reactance diagram of eight-bus system Power System Analysis I · Chapter 3: Computational Technique - Asked in: 2069 Bhadra, 6 marks - Video: [Problem #2 | Impedance & Reactance diagram | PSA](https://www.youtube.com/watch?v=Mq3pAkxuIjc) — FOR STUDENTS - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/reactance-diagram-eight-bus - Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-3 ## Question 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).] ## 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. ## Answer **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 $X_M$ (pu on its own rating). Its value on the common base is $X_M\frac{10}{S_M}\left(\frac{V_M}{11}\right)^2$. $$ Z_{b,66} = \frac{66^2}{10} = 435.6\ \Omega $$ #### Per-unit reactances (10 MVA base) $$ \begin{aligned} X_{G1} = X_{G2} &= 0.10\times\frac{10}{10}\times\left(\frac{11.5}{11}\right)^2 = 0.1093\ \text{pu}\\ X_{G3} &= 0.12\times\frac{10}{15}\times\left(\frac{11.5}{11}\right)^2 = 0.0874\ \text{pu}\\ X_{T1} = X_{T2} &= 0.10\ \text{pu}\\ X_{T3} &= 0.15\times\frac{10}{15} = 0.10\ \text{pu}\\ X_{T4} &= 0.18\times\frac{10}{35} = 0.0514\ \text{pu}\\ X_{L1} = X_{L2} = X_{L3} = X_{L4} &= \frac{20}{435.6} = 0.0459\ \text{pu} \end{aligned} $$ | Element | X (pu, 10 MVA) | |---|---| | G1, G2 | 0.1093 each | | G3 | 0.0874 | | T1, T2 | 0.1000 each | | T3 | 0.1000 | | T4 | 0.0514 | | L1 to L4 | 0.0459 each | #### Reactance diagram ```text (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): $X_{G1} = X_{G2} = 0.1093$, $X_{G3} = 0.0874$, $X_{T1} = X_{T2} = X_{T3} = 0.10$, $X_{T4} = 0.0514$, and each line 0.0459 pu. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which bases are used? A. 10 MVA, 66 kV everywhere B. 10 MVA, 11 kV in generator circuits and 66 kV on lines C. 35 MVA, 11 kV on lines D. 15 MVA, 11.5 kV on lines Answer: B. Transformer ratios 11/66 define the zones. (Key point: Choice of base) 2. Why is X_G1 = 0.1093 pu rather than 0.10? A. The generator rating 11.5 kV differs from the 11 kV base: 0.10 x (11.5/11)^2 B. The MVA is different C. The line impedance modifies it D. T1 reactance is added Answer: A. pu reactance scales with (kV_rated/kV_base)^2. (Key point: Generator correction) 3. How is a 20 Ω line converted to pu? A. 20/66 = 0.303 B. 20/10 = 2 C. 20 x 435.6 D. 20/435.6 = 0.0459 pu, using Zb = 66^2/10 Answer: D. Zb = 435.6 Ω. (Key point: Line reactance) 4. The motor rating is missing. How is its X handled? A. Taken as zero B. Taken equal to G3 C. Left as X_M, converted by X_M x 10/S_M x (V_M/11)^2 D. Taken as the T4 value Answer: C. General change-of-base formula. 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