---
title: "Synchronous generator working; armature reaction"
subject: "Electrical Machines"
chapter: 6
key: "semester_4/electrical_machines:sync-gen-working-armature-reaction"
source: https://www.bctengineer.com/q/semester_4/electrical_machines/sync-gen-working-armature-reaction
site: BCT Engineering
---

# Synchronous generator working; armature reaction

Electrical Machines · Chapter 6: Three Phase Synchronous Machines

- Asked in: 2078 Chaitra, 6 marks
- Video: [Armature Reaction of Alternators [Year - 3]](https://www.youtube.com/watch?v=8HFa_YjZIFc) — Mtutor & Mschool
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machines/sync-gen-working-armature-reaction
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-6

## Question

How does three phase synchronous generator work? What do you mean by armature reaction? Comment on the results of different load power factor on armature flux.

## Short answer

Armature reaction is the effect of stator mmf on the main field flux. For resistive load it is cross-magnetising, for inductive load demagnetising, and for capacitive load magnetising, respectively causing slight drop, large drop, or rise in terminal voltage.

## Answer

#### Working of a three-phase synchronous generator (alternator)
1. The rotor carries a DC-excited field winding (the poles). The prime mover turns the rotor at the constant speed $N_s$.
2. The rotating flux cuts the three-phase armature (stator) windings, which are placed $120^\circ$ (electrical) apart. By Faraday's law, an emf is induced in each phase:
$$
E = 4.44\,f\,\phi\,T_{ph}K_pK_d \quad\text{with}\quad f = \frac{PN_s}{120}
$$
3. The three emfs are equal in magnitude and displaced by $120^\circ$ in time, giving a balanced three-phase supply.
4. When a load is connected, a three-phase armature current flows, and the terminal voltage is $\vec V = \vec E - \vec I(R_a + jX_s)$.

#### Armature reaction
Armature reaction is the effect of the armature (stator) mmf, produced by the load current, on the main field flux (its magnitude and distribution). The armature current produces a field rotating at synchronous speed, which is stationary relative to the rotor, and it either opposes, aids or distorts the main flux.

#### Effect of load power factor
| Load pf | Angle of $I$ with $E$ | Armature reaction | Effect on flux and $V$ |
|---|---|---|---|
| Unity | $I$ in phase with $E$ | Cross-magnetising | Flux distorted (weakens one pole tip, strengthens the other); slight fall in $V$ |
| Zero lagging | $I$ lags $E$ by $90^\circ$ | Fully demagnetising | Main flux reduced, $V$ falls a lot |
| Zero leading | $I$ leads $E$ by $90^\circ$ | Fully magnetising | Main flux increased, $V$ rises |
| General lagging | between 0 and $90^\circ$ | Partly cross, partly demagnetising | $V$ falls |
| General leading | between 0 and $90^\circ$ | Partly cross, partly magnetising | $V$ may rise |

```text
 Zero pf lagging: Fa opposes Ff      Zero pf leading: Fa aids Ff
     Ff --->   <--- Fa                   Ff --->   ---> Fa
     Fr = Ff - Fa                        Fr = Ff + Fa
```
The armature reaction is represented by a reactance $X_a$, which together with the leakage reactance gives the synchronous reactance $X_s = X_a + X_l$.

## Check yourself

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

1. How does a synchronous generator produce emf?
   A. DC-excited rotor turned by a prime mover so its flux cuts the stator windings
   B. Stator is rotated
   C. AC fed to rotor
   D. Capacitors
   Answer: A. The rotating field flux cuts the stator conductors and induces emf by Faraday's law. (Key point: Generation of emf)

2. What is armature reaction?
   A. Effect of armature mmf on the main field flux
   B. Effect of friction
   C. Resistance heating
   D. Harmonics only
   Answer: A. The load current's mmf modifies the magnitude and position of the main flux. (Key point: Armature reaction)

3. What is the armature reaction at zero pf lagging?
   A. Fully magnetising
   B. Cross-magnetising
   C. Fully demagnetising
   D. None
   Answer: C. The armature mmf opposes the field mmf. (Key point: Zero pf lagging)

4. What does unity pf load cause?
   A. Cross-magnetising reaction distorting the flux
   B. Full demagnetising
   C. Full magnetising
   D. No armature flux
   Answer: A. With I in phase with E, Fa acts at 90 deg to the field, distorting the flux. (Key point: Unity pf)

## Related in Electrical Machines

- [Armature reaction in synchronous generator](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Aarmature-reaction-sync-gen-loads) — Electrical Machines, chapter 6
- [Synchronous generator load characteristics, capacitive load](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Async-gen-load-characteristics-capacitive) — Electrical Machines, chapter 6
- [Power to 10 Ω load from shunt generator](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ashunt-gen-378-conductors-10ohm-load) — Electrical Machines I, chapter 3
- [Wave-wound shunt generator, power absorbed by load](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Agen-shunt-378-conductors-load-power) — Electrical Machines, chapter 3
- [Armature reaction in DC machines and its remedies](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aarmature-reaction-effects-remedies) — Electrical Machines I, chapter 3
- [Short note: Armature reaction in dc machine](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Anote-armature-reaction-dc) — Electrical Machines, chapter 3

## Related in other subjects

- [Armature reaction in synchronous generator](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Aarmature-reaction-sync-generator-loads) — Electrical Machine, chapter 6, asked 2×
- [Armature reaction at different load power factors](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Aarmature-reaction-power-factor-effect) — Electric Machines II, chapter 1, asked 7×
- [3-phase synchronous generator construction](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Async-generator-construction-working) — Electrical Machine, chapter 6
- [Synchronous generator working principle](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_and_electronics_engineering%3Asynchronous-generator-principle) — Basic Electrical and Electronics Engineering, chapter 2