--- title: "Generator choice and SCR versus stability" subject: "Power Plant Design" chapter: 4 key: "semester_8/power_plant_design:generator-choice-scr-stability" source: https://www.bctengineer.com/q/semester_8/power_plant_design/generator-choice-scr-stability site: BCT Engineering --- # Generator choice and SCR versus stability Power Plant Design · Chapter 4: Electric System Design of a Power Plant - Asked in: 2071 Bhadra, 5+5 marks - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_8/power_plant_design/generator-choice-scr-stability - Whole chapter: https://www.bctengineer.com/md/semester_8/power_plant_design/chapter-4 ## Question Discuss the various factors which should be considered for the choice of generator during the design of a power plant. Also clarify analytically that lower the short circuit ratio (SCR), lower be the stability of the system. ## Short answer Factors: MVA/pf, voltage, speed/poles, shaft type, reactances/SCR, inertia, efficiency, insulation, cooling, excitation, NGT grounding, grid spec, transport limits. Lower SCR means higher Xd, so maximum power Pmax = EV·SCR decreases, load angle increases for same power, and synchronizing power coefficient reduces, lowering steady-state and transient stability margins. ## Answer #### Factors for the choice of generator 1. **Rating (MVA) and power factor:** $S = P_{turbine}\,\eta_g / \cos\phi$; power factor usually 0.85–0.9 lagging so the unit can supply reactive power. Some overload margin (e.g. 10%) is often specified. 2. **Rated voltage:** usually 6.6 kV or 11 kV for hydro units (higher, e.g. 13.8–15.75 kV, for very large units); chosen with GSU and bus/cable cost. 3. **Speed and number of poles:** fixed by the turbine: $N = 120f/p$. Hydro units are slow, salient-pole machines with many poles. 4. **Shaft arrangement:** vertical (large Francis/Kaplan) or horizontal (small Pelton/Francis). 5. **Reactances and SCR:** $X''_d$ sets fault level and breaker rating; SCR and $X_d$ set stability and voltage regulation. 6. **Inertia constant (GD²):** larger inertia limits speed rise on load rejection and improves stability, but costs more. 7. **Efficiency and losses:** high efficiency (above 97–98%) saves energy over the plant life. 8. **Insulation and temperature rise:** class F insulation with class B temperature rise is common; altitude derating above 1000 m. 9. **Cooling:** air-cooled (open or closed with air–water coolers) for hydro. 10. **Excitation system:** brushless for small/medium units, static for large units. 11. **Neutral grounding:** high-resistance grounding via NGT. 12. **Grid requirements:** capability curve, reactive power range, fault ride-through, harmonics. 13. **Transport and erection limits:** weight and size on hill roads; split stator if needed. 14. **Standards and cost:** IEC 60034; capital cost versus loss capitalisation. #### Lower SCR gives lower stability (analytical proof) **Short circuit ratio (SCR)** is the ratio of 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 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 $P_s$). Physically, a low SCR means a high synchronous reactance, i.e. weak magnetic coupling between rotor and stator through a small air gap; the generator must swing to a larger angle to transmit the same power, leaving less margin before it slips a pole. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How is the short circuit ratio related to the synchronous reactance? A. SCR is approximately Xd (p.u.) B. SCR is approximately 1/Xd (p.u., saturated) C. SCR is independent of Xd D. SCR is approximately Xd^2 Answer: B. SCR is the field current for rated open-circuit voltage divided by that for rated short-circuit current, which is about 1/Xd in p.u. (Key point: SCR and Xd) 2. Why does a lower SCR reduce the steady-state stability limit? A. Pmax = E V / SCR, so it rises B. Pmax = E V (SCR), so Pmax falls in proportion to SCR C. Pmax is unaffected, only the voltage changes D. Pmax depends only on the turbine Answer: B. Since P = (EV/Xd) sin(delta) = E V (SCR) sin(delta), the maximum power is directly proportional to SCR. (Key point: Maximum power) 3. For the same load P, what happens to the load angle when SCR is reduced? A. Delta becomes negative B. Delta increases, nearer the 90° limit C. Delta stays the same D. Delta decreases Answer: B. sin(delta) = P/(E V SCR), so a lower SCR needs a larger delta for the same power, leaving less margin. (Key point: Load angle) 4. What does the synchronizing power coefficient Ps = E V (SCR) cos(delta) show at lower SCR? A. Higher speed of the rotor B. No change in restoring torque C. Smaller restoring torque after a disturbance D. Larger restoring torque after a disturbance Answer: C. Lower SCR and larger delta both reduce Ps, so the machine is less able to return to synchronism after a disturbance. 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