--- title: "Reactance diagram: 100 MVA base, two parallel paths" subject: "Power System Analysis I" chapter: 3 key: "semester_4/power_system_analysis_i:reactance-diagram-90mva-two-paths" source: https://www.bctengineer.com/q/semester_4/power_system_analysis_i/reactance-diagram-90mva-two-paths site: BCT Engineering --- # Reactance diagram: 100 MVA base, two parallel paths Power System Analysis I · Chapter 3: Computational Technique - Asked in: 2080 Chaitra, 8 marks - Video: [How to Draw Impedance and Reactance Diagram | PSA | Power System Analysis | PU Reactance diagram](https://www.youtube.com/watch?v=ApVXgflKhrs) — Simple n Easy Learning - 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-90mva-two-paths - Whole chapter: https://www.bctengineer.com/md/semester_4/power_system_analysis_i/chapter-3 ## Question What is the significance of reactance diagram? The single line diagram of a three phase power system is shown in the figure. Draw a reactance diagram considering a base of 100 MVA and 13.8 kV on generator side. G: 90 MVA, 13.8 kV, Xg = 18%; T1 = 50 MVA, 13.8/220 kV, XT1 = 10%; T2 = 50 MVA, 220/11 kV, XT2 = 10%; T3 = 50 MVA, 13.8/132 kV, XT3 = 10%; T4 = 50 MVA, 132/11 kV, XT4 = 10%; M: 80 MVA, 10.45 kV, Xm = 20%; Load: 57 MVA, 0.8 pf lagging at 10.45 kV; Xline1 = 50 Ω, Xline2 = 70 Ω. [Figure: generator G at bus 1 feeds two parallel paths to bus 4: T1 (bus 1–2) → Line-1 at 220 kV (bus 2–3) → T2 (bus 3–4); and T3 (bus 1–5) → Line-2 at 132 kV (bus 5–6) → T4 (bus 6–4). Motor M and the load are connected at bus 4.] ## Short answer A reactance diagram uses only p.u. reactances, neglecting resistance and shunt branches, for fault/studies. With 100 MVA, 13.8 kV gen base: G j0.2, all transformers j0.2, line1 j0.1033, line2 j0.4017, motor j0.2256, load 1.2667+j0.95. ## Answer #### Significance of the reactance diagram A reactance diagram is the per-phase equivalent circuit of the system, drawn from the single line diagram, in which: - resistances, magnetising branches and line charging are neglected - all values are in p.u. on a common base It is used for short-circuit (fault) calculations and stability studies, where the reactances dominate. It gives a simple network that can be reduced quickly. #### Base values - $S_b = 100$ MVA, and $V_b = 13.8$ kV at the generator (bus 1). | Section | Base kV | $Z_b$ (Ω) | |---|---|---| | Bus 1 (generator) | 13.8 | – | | Line 1 (via T1 13.8/220) | 220 | $220^2/100 = 484$ | | Line 2 (via T3 13.8/132) | 132 | $132^2/100 = 174.24$ | | Bus 4 (via T2 220/11 or T4 132/11) | 11 | – | Both paths give 11 kV at bus 4, so the bases are consistent. #### Per-unit values $$ \begin{aligned} X_G &= 0.18\times\frac{100}{90} = 0.2\\ X_{T1} = X_{T2} = X_{T3} = X_{T4} &= 0.1\times\frac{100}{50} = 0.2\\ X_{L1} &= \frac{50}{484} = 0.1033\\ X_{L2} &= \frac{70}{174.24} = 0.4017\\ X_M &= 0.2\times\frac{100}{80}\times\left(\frac{10.45}{11}\right)^2 = 0.2256 \end{aligned} $$ **Load:** $S = 57/100 = 0.57$ p.u. at a power factor of 0.8 lagging, and $V = 10.45/11 = 0.95$ p.u. As a series impedance: $$ Z_L = \frac{|V|^2}{S^*} = \frac{0.95^2}{0.57}\angle36.87^\circ = 1.5833\angle36.87^\circ = 1.2667 + j0.95\ \text{p.u.} $$ #### Reactance diagram ```text T1 L1 T2 +--j0.2--j0.1033--j0.2--+ j0.2 | | +-/\/\---+ bus1 bus4 +---+------+ | | | | | (Eg) +--j0.2--j0.4017--j0.2--+ j0.2256 1.2667 | T3 L2 T4 | +j0.95 | (Em) | +------------- reference -----------+----+ ``` | Element | p.u. | |---|---| | G | j0.2 | | T1, T2, T3, T4 | j0.2 each | | Line 1 | j0.1033 | | Line 2 | j0.4017 | | Motor | j0.2256 | | Load | 1.2667 + j0.95 | ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. A reactance diagram is mainly used for A. Fault and stability studies where reactances dominate B. Insulation design C. Cable laying D. Tariff Answer: A. Resistances and shunts are neglected, giving a simple network for fault and stability studies. (Key point: Significance) 2. Which are neglected? A. Resistances, magnetising branches and line charging B. Reactances C. Generator EMFs D. Bases Answer: A. These are neglected in reactance diagrams. (Key point: Neglected quantities) 3. X_L2 = 70 ohm on 132 kV, 100 MVA is A. 0.1033 B. 0.4017 C. 0.7 D. 1.2 Answer: B. 70/174.24 = 0.4017. (Key point: Line 2 p.u.) 4. The motor reactance changes from 0.2 to 0.2256 because A. It is rated 80 MVA and 10.45 kV, base 11 kV B. It is at 132 kV C. The load is added D. Base is 13.8 kV Answer: A. 0.2 x 100/80 x (10.45/11)^2 = 0.2256. 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