Hunting, Damper Windings and Short-Circuit Ratio

i Learning Objectives

By the end of this chapter you should be able to:

Explain hunting as an oscillation of the load angle about its steady value.
Define the synchronising power coefficient and compute the natural frequency of oscillation.
Describe the construction and the two functions of damper windings.
Define the short-circuit ratio (SCR) and relate it to \(X_d\), stability and machine size.

Section 81-1

What Is Hunting?

A synchronous machine carries its load at a definite load angle \(\delta\). When the load changes suddenly, the rotor must move to a new angle, but its inertia makes it overshoot. A restoring torque pulls it back, it overshoots the other way, and the rotor swings about the new equilibrium. This periodic swinging of \(\delta\) — and with it of speed, current and power — is called hunting.

Causes: sudden changes in load (motor) or in prime-mover torque (generator); pulsating loads such as reciprocating compressors; faults and switching on the network; periodic torque from diesel prime movers.
Effects: large current and power swings, mechanical stress, flicker, and — if the swing passes the stability limit — loss of synchronism (pole slipping).
If the forcing frequency is close to the machine's natural frequency, resonance magnifies the swing dramatically.

Section 81-2

Synchronising Power and Natural Frequency

For a cylindrical-rotor machine \(P = (E_fV/X_s)\sin\delta\). A small displacement \(\Delta\delta\) produces a restoring power

\[\Delta P = P_s\,\Delta\delta, \qquad P_s = \frac{dP}{d\delta} = \frac{E_fV}{X_s}\cos\delta\]

\(P_s\) is the synchronising power coefficient. It is largest at no load (\(\delta = 0\)) and falls to zero at the stability limit \(\delta = 90^\circ\). Combining it with the swing equation \(\frac{2H}{\omega_s}\frac{d^2\Delta\delta}{dt^2} + P_s\Delta\delta = 0\) gives simple harmonic motion:

∿

Undamped natural frequency

Stiffer coupling and lighter rotor → faster swings

\[\omega_n = \sqrt{\frac{\omega_s P_s}{2H}}~\text{rad/s}, \qquad f_n = \frac{\omega_n}{2\pi}\]

\(H\) is the inertia constant (stored kinetic energy at synchronous speed ÷ rated VA, in seconds), \(P_s\) in pu per electrical radian and \(\omega_s = 2\pi f\) electrical rad/s. Typical \(f_n\) is 0.5–2 Hz.

1 Worked Example 81.1 — Natural Frequency of Hunting

Problem. A 50 Hz generator with \(H = 4\) s operates at \(E_f = 1.5\) pu, \(V = 1.0\) pu, \(X_s = 1.0\) pu and \(\delta = 30^\circ\). Find the synchronising power coefficient and the natural frequency of oscillation.

\[P_s = \frac{1.5(1.0)}{1.0}\cos 30^\circ = 1.299~\text{pu/rad}\]

\[\omega_n = \sqrt{\frac{314.16(1.299)}{2(4)}} = 7.14~\text{rad/s}, \qquad f_n = 1.14~\text{Hz}\]

At heavier load (larger \(\delta\)) \(P_s\) falls, so the oscillation becomes slower and the machine is closer to instability.

Section 81-3

Damper Windings

A damper (amortisseur) winding consists of copper or brass bars embedded in slots in the pole faces, short-circuited at both ends by rings or segments — effectively a partial squirrel cage on the rotor.

Function 1 — damping hunting

At synchronous speed the bars carry no current. When the rotor swings, it moves relative to the stator field, EMFs are induced in the bars, and the resulting induction-motor torque opposes the relative motion, damping the oscillation.

Function 2 — starting

A synchronous motor has no starting torque of its own. The damper winding lets it start as an induction motor and run up close to \(N_s\), after which the field is excited and the rotor pulls into step (Chapter 79).

Dampers also reduce the negative-sequence field under unbalanced load and help suppress oscillations caused by harmonic fields.
They lower the subtransient reactance \(X''_d\), which raises the initial short-circuit current — a trade-off for the protection engineer.

Turbo-alternators. Cylindrical rotors usually have no separate damper bars: the solid steel rotor body and the metallic slot wedges carry eddy currents that provide the same damping action.

Section 81-4

Short-Circuit Ratio

The short-circuit ratio is read from the open-circuit characteristic (OCC) and short-circuit characteristic (SCC) of Chapter 75:

\[\text{SCR} = \frac{I_f \text{ for rated voltage on open circuit}}{I_f \text{ for rated armature current on short circuit}} \approx \frac{1}{X_{d,\text{sat}}~(\text{pu})}\]

Table 81.1 — Consequences of a high or low short-circuit ratio.
Property	High SCR (≈ 1.0–1.5)	Low SCR (≈ 0.5–0.7)
Synchronous reactance	Low	High
Voltage regulation	Better	Poorer
Steady-state stability limit	Higher	Lower
Air gap, size and cost	Larger, heavier, dearer	Smaller, cheaper
Short-circuit current	Higher	Lower
Typical machine	Hydro (salient-pole)	Turbo-alternator

2 Worked Example 81.2 — SCR and Saturated Reactance

Problem. An alternator needs 20 A of field current for rated voltage on open circuit and 25 A for rated armature current on short circuit. Find the SCR and the approximate saturated synchronous reactance.

\[\text{SCR} = \frac{20}{25} = 0.80, \qquad X_{d,\text{sat}} \approx \frac{1}{0.80} = 1.25~\text{pu}\]

Section 81-5

Summary and Common Mistakes

Key Points

Hunting is oscillation of \(\delta\) after a disturbance; its natural frequency is \(\sqrt{\omega_sP_s/2H}\).
\(P_s = (E_fV/X_s)\cos\delta\) falls as load rises.
Damper windings damp hunting and allow induction starting.
\(\text{SCR} \approx 1/X_{d,\text{sat}}\); high SCR means a larger, stiffer, more stable machine.

Common Mistakes

Inverting the SCR ratio (short-circuit field current goes in the denominator).
Using mechanical rather than electrical radians in the natural-frequency formula.
Claiming damper bars carry current in steady synchronous operation.

Section 81-6

Chapter Review

Practice Problems

P81.1 Recompute \(f_n\) for Example 81.1 at no load (\(\delta = 0\)).

Show answer
\(P_s = 1.5\) pu/rad; \(\omega_n = \sqrt{314.16 \times 1.5/8} = 7.67\) rad/s; \(f_n = 1.22\) Hz.
P81.2 A machine has \(X_{d,\text{sat}} = 0.8\) pu. Estimate its SCR and say whether it is more likely a hydro or a turbo machine.

Show answer
SCR ≈ 1/0.8 = 1.25 — typical of a salient-pole hydro generator.

Multiple-Choice Questions

MCQ 1. Damper windings are placed:
(a) on the stator yoke (b) in the pole faces (c) in the armature slots (d) on the shaft

Show answer
(b)
MCQ 2. A machine with a high SCR has:
(a) high \(X_d\) (b) poor regulation (c) high stability limit (d) small air gap

Show answer
(c) — low reactance means a high maximum power \(E_fV/X_d\).

Conceptual Questions

Why is hunting more dangerous when a pulsating load has a frequency near \(f_n\)?
Explain how a damper winding produces a damping torque.
Why do turbo-alternators have a lower SCR than hydro generators?

Looking Ahead

Part 6 begins with the motor found in almost every home: the single-phase induction motor. Chapter 82 describes its construction, and Chapters 83–84 explain why a pulsating field can produce torque at all.