---
title: "Conditions for induction generator, T-S curve"
subject: "Electrical Machines"
chapter: 5
key: "semester_4/electrical_machines:induction-generator-conditions-ts-curve"
source: https://www.bctengineer.com/q/semester_4/electrical_machines/induction-generator-conditions-ts-curve
site: BCT Engineering
---

# Conditions for induction generator, T-S curve

Electrical Machines · Chapter 5: Three Phase Induction Machines

- Asked in: 2079 Jestha, 8 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machines/induction-generator-conditions-ts-curve
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-5

## Question

What are the conditions to be fulfilled for the operation of induction machine as induction generator? Explain with the help of T-S curve.

## Short answer

The machine must be driven above synchronous speed so slip is negative, and it must receive reactive power from the grid or capacitors. In the T-s curve, s<0 gives negative torque and power flow to the supply. Prime mover torque must stay below the generating pull-out torque.

## Answer

An induction machine works as an **induction generator** when its rotor is driven by a prime mover **above synchronous speed**, so the slip becomes negative and the torque reverses. It then delivers active power to the supply.

#### Conditions for generator operation
1. **Speed above synchronous speed:** $N_r > N_s = \frac{120f}{P}$, so slip $s = \frac{N_s - N_r}{N_s} < 0$.
2. **Source of reactive power:** the machine has no separate field winding. It must take its magnetising current from the grid (grid-connected), or from a capacitor bank across the stator terminals (self-excited, stand-alone).
3. **Frequency and voltage fixed by the grid:** when grid-connected, the grid keeps the frequency and terminal voltage. For stand-alone use, residual magnetism and sufficient capacitance are needed for voltage build-up.
4. **Prime mover with enough power:** a turbine or engine must drive the rotor so that the mechanical input exceeds losses. The speed is only 2 to 5 % above $N_s$ at rated load.
5. Capacitor value must exceed a critical value so that the magnetising line is crossed (self-excited case).

#### Explanation with T-S curve
The torque-slip curve extends on both sides of $s = 0$.

- $0 < s < 1$: **motoring** region (torque positive, power flows from the supply to the shaft).
- $s < 0$: **generating** region. The curve is an inverted image of the motoring part, with torque negative. The maximum (pull-out) generating torque occurs at $s \approx -s_m$.
- $s > 1$: **braking** (plugging) region, rotor runs opposite to the field.

```text
 T
 |        motoring
 |         _.-*-._
 |      _-'       `-._
 +-----+-------+-----------> s
 s=1       s=0   (N=Ns)
 ...  _.-'  generating  (s<0)
 |  *-'
 |
```

Beyond $N_s$ the slip is negative, the rotor emf and current reverse, and the electromagnetic torque opposes the prime mover. The air-gap power $P_g = \frac{P_{conv}}{1-s}$ becomes negative, meaning power is fed to the stator and then to the grid. If the driving torque exceeds the maximum generating torque, the machine runs away (loses stability), so the prime mover torque must stay below the pull-out value.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. For an induction machine to act as a generator, the rotor must be driven:
   A. Below synchronous speed, so slip is positive
   B. Exactly at synchronous speed
   C. Above synchronous speed, so slip is negative
   D. At any speed provided the supply voltage is high
   Answer: C. Generating needs N_r > N_s, giving negative slip and reversed torque. (Key point: Speed condition)

2. Why must an induction generator be connected to a grid or a capacitor bank?
   A. It has no field winding, so it needs a source of magnetising (reactive) current
   B. It needs the grid to supply the mechanical power
   C. The capacitors raise the speed above N_s
   D. The grid is needed to reverse the slip sign
   Answer: A. There is no separate excitation, so lagging magnetising current must come from the grid or capacitors. (Key point: Reactive power)

3. On the T-S curve, what does the region s < 0 represent?
   A. Motoring with positive torque
   B. Plugging (braking) with the rotor against the field
   C. Generating, with negative torque and a pull-out value near s = -s_m
   D. Standstill starting torque
   Answer: C. For s < 0 the curve is an inverted image of the motoring part with negative torque. (Key point: T-S curve generating region)

4. What happens if the prime mover torque exceeds the maximum generating torque?
   A. The generator delivers more power at constant speed
   B. The machine runs away and loses stability
   C. The slip becomes positive and it motors
   D. The voltage settles at a higher value
   Answer: B. Beyond the pull-out generating torque the machine is unstable and runs away. (Key point: Stability limit)

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