--- title: "Short circuit ratio and system stability" subject: "Power Plant Design" chapter: 4 key: "semester_8/power_plant_design:scr-significance-stability" source: https://www.bctengineer.com/q/semester_8/power_plant_design/scr-significance-stability site: BCT Engineering --- # Short circuit ratio and system stability Power Plant Design · Chapter 4: Electric System Design of a Power Plant - Asked in: 2078 Kartik, 4 marks; 2074 Magh, 3+5 marks; 2074 Bhadra, 6 marks (asked 3 times) - Video: [Power System Stability Lecture 19:- Short Circuit Ratio](https://www.youtube.com/watch?v=JmiIZ5kUTjE) — Krunal Panpaliya - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_8/power_plant_design/scr-significance-stability - Whole chapter: https://www.bctengineer.com/md/semester_8/power_plant_design/chapter-4 ## Question What is the significance of short circuit ratio (SCR) in design of synchronous generator? Show analytically its impact on stability of the power system. ## Short answer SCR ≈ 1/Xd influences air gap size, cost, voltage regulation, and stability. Higher SCR raises the steady-state power limit Pmax = EV·SCR and synchronizing power Ps = EV·SCR cosδ, reducing load angle. Lower SCR gives a smaller, cheaper machine but reduces stability margin, making loss of synchronism more likely. ## Answer #### Significance of SCR in generator design - **Air gap and size:** a high SCR needs a low $X_d$, i.e. a larger air gap and more field ampere-turns; the machine becomes larger, heavier and costlier. - **Stability:** a higher SCR gives a higher steady-state power limit and stronger synchronizing torque. - **Voltage regulation:** higher SCR → smaller voltage drop with load, so better regulation. - **Fault level:** higher SCR → higher steady short-circuit current, so heavier switchgear. - **Line charging:** a high-SCR machine can charge long, lightly loaded lines without self-excitation. - **Losses:** a larger field current increases field losses. So SCR is a compromise between cost and performance; hydro generators connected through long lines are usually given an SCR of about 1.0–1.2 or more. #### Definition of SCR **Short circuit ratio (SCR)** is the ratio of the field current needed to produce rated open-circuit voltage to the field current needed to circulate rated armature current on a sustained three-phase short circuit: $$ SCR = \frac{I_f\ (\text{rated OC voltage})}{I_f\ (\text{rated SC current})} \approx \frac{1}{X_d\,(\text{p.u., saturated})} $$ Typical values: salient-pole hydro generators 1.0–1.5; cylindrical-rotor turbo generators 0.5–0.7. #### Analytical relation with stability Power delivered by a generator (neglecting resistance and saliency) to an infinite bus: $$ P = \frac{E V}{X_d}\sin\delta = E\,V\,(SCR)\sin\delta $$ - **Maximum (steady-state limit) power:** $P_{max} = \dfrac{EV}{X_d} = E\,V\,(SCR)$. Lower SCR → lower $P_{max}$. - **Load angle for a given load:** $\sin\delta = \dfrac{P}{E\,V\,(SCR)}$. Lower SCR → larger $\delta$, closer to the 90° limit. - **Synchronizing power coefficient:** $P_s = \dfrac{dP}{d\delta} = E\,V\,(SCR)\cos\delta$. Lower SCR → smaller restoring torque after a disturbance. **Numerical illustration** ($E = 1.8$ p.u. kept the same, $V = 1$ p.u., $P = 0.85$ p.u.): | SCR | $X_d$ (p.u.) | $P_{max}$ (p.u.) | $\delta$ | $P_s$ (p.u./rad) | Margin $(P_{max}-P)/P_{max}$ | |---|---|---|---|---|---| | 1.2 | 0.833 | 2.16 | 23.17° | 1.986 | 60.6% | | 1.0 | 1.000 | 1.80 | 28.18° | 1.587 | 52.8% | | 0.6 | 1.667 | 1.08 | 51.91° | 0.666 | 21.3% | So the **lower the SCR, the lower the stability margin** (higher $\delta$, smaller $P_{max}$ and $P_s$). On a $P$–$\delta$ graph, a lower SCR gives a flatter sine curve with a lower peak, so the operating point sits closer to the peak and a smaller disturbance can push the machine out of step. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. SCR is approximately equal to: A. Xd (p.u.) B. 1/Xd (p.u., saturated) C. Xd squared D. Terminal voltage / current Answer: B. SCR is the ratio of field current for rated OC voltage to that for rated SC current, about 1/Xd. (Key point: Definition of SCR) 2. Maximum steady-state power for a generator connected to an infinite bus is: A. EV x sin(delta) x Xd B. EV/Xd x cos(delta) C. E V (SCR) D. V^2 / E Answer: C. P = (EV/Xd) sin(delta) = EV(SCR) sin(delta), so Pmax = EV(SCR). (Key point: Power-angle relation) 3. Lowering SCR causes: A. Smaller load angle and larger synchronizing power B. No change to delta C. Higher Pmax D. Larger load angle, lower Pmax and smaller synchronizing power Answer: D. sin(delta) = P/(EV SCR) increases; Ps = EV SCR cos(delta) falls, so the stability margin reduces. (Key point: Effect of low SCR) 4. A high SCR needs: A. Larger air gap, more field ampere-turns, bigger and costlier machine B. Smaller air gap and cheaper machine C. Higher Xd D. Lower fault level Answer: A. High SCR means low Xd, requiring a larger air gap and more field MMF. (Key point: Design cost of high SCR) ## Related in Power Plant Design - [Generator choice and SCR versus stability](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Agenerator-choice-scr-stability) — Power Plant Design, chapter 4 - [Generator choice and significance of SCR](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Agenerator-choice-scr-significance) — Power Plant Design, chapter 4 - [Consequences of higher or lower SCR](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Ascr-higher-lower-consequences) — Power Plant Design, chapter 4, asked 3× - [Choice of generator circuit breaker](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Agenerator-circuit-breaker-choice) — Power Plant Design, chapter 4, asked 2× - [Design: 260 m head plant, generator lead](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Adesign-2078-260m-generator-lead) — Power Plant Design, chapter 4, asked 5× - [Design: 245 m head plant, standby generator](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Adesign-2073-245m-standby) — Power Plant Design, chapter 4, asked 14× ## Related in other subjects - [Per unit circuit of three-generator system, 30 MVA base](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Apu-circuit-30mva-g1-g2-g3) — Power System Analysis I, chapter 3 - [Stability after tripping one circuit](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Aone-line-tripped-stability) — Power System Analysis II, chapter 6 - [Synchronous generator working; armature reaction](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Async-gen-working-armature-reaction) — Electrical Machines, chapter 6 - [Armature reaction in synchronous generator](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Aarmature-reaction-sync-generator-loads) — Electrical Machine, chapter 6, asked 2×