Generator choice and SCR versus stability

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.):

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.