Short circuit ratio and system stability

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.):

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.