---
title: "Effect of excitation on synchronous motor"
subject: "Electrical Machines"
chapter: 6
key: "semester_4/electrical_machines:sync-motor-excitation-effect-pf"
source: https://www.bctengineer.com/q/semester_4/electrical_machines/sync-motor-excitation-effect-pf
site: BCT Engineering
---

# Effect of excitation on synchronous motor

Electrical Machines · Chapter 6: Three Phase Synchronous Machines

- Asked in: 2077 Chaitra, 8 marks; 2076 Baisakh, 8 marks; 2072 Asoj; 2070 Bhadra, 8 marks; 2068 Bhadra, 8 marks (asked 5 times)
- Video: [Electrical Machines | Lecture - 9G | Synchronous Motor | Effect of Excitation on Current & PF](https://www.youtube.com/watch?v=tHKvK6tjB1A) — Engineering Devotion
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machines/sync-motor-excitation-effect-pf
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-6

## Question

With the help of phasor diagrams, explain the effect of excitation on the power factor of a three phase synchronous motor.

## Answer

#### Principle
A synchronous motor runs at constant speed. For a constant load and constant supply voltage $V$, the power input $P = \sqrt3 V_L I\cos\phi$ stays constant, so the **active component** $I\cos\phi$ of the armature current stays constant. When the field excitation $I_f$ is changed, the back emf $E_f$ changes, and the current adjusts so that only its **reactive component** changes. This changes the power factor. (Armature resistance is neglected.)

The phasor relation for a motor is $\vec V = \vec E_f + j\vec I X_s$.

#### Three conditions
1. **Normal excitation:** $E_f \cos\delta = V$. The current is minimum, in phase with $V$, and the **power factor is unity**.
2. **Under-excitation ($E_f$ smaller):** the current lags the voltage. The motor draws reactive power from the supply like an inductive load: **lagging power factor**. The current is larger than at unity pf.
3. **Over-excitation ($E_f$ larger):** the current leads the voltage. The motor supplies reactive power to the supply: **leading power factor**. The current is again larger.

```text
 Motor: V = Ef + jIXs   (V is the horizontal reference; Ef lags V by delta)

 (a) Under-excited: I lags V, Ef is short
 O------------------------> V
  `-._                    /
      `-._    Ef         / jIXs
          `-._          /
              `-._     /
                  `-._/

 (b) Normal: I in phase with V, Ef cos(delta) = V
 O------------------------> V
  `-._                    |
      `-._    Ef          | jIXs
          `-._            |
              `-._        |
                  `-._    |
                      `-._*

 (c) Over-excited: I leads V, Ef is long
 O------------------------> V
  `-._                     \
      `-._    Ef            \ jIXs
          `-._               \
              `-._            \
                  `-._         \
                      `-._      \
                          `-._   \
                              `-._*
```
In each case $jIX_s$ is drawn from the tip of $E_f$ to the tip of $V$, at $90^\circ$ ahead of $I$. Because the power is constant, $I\cos\phi$ is constant (the tip of $I$ moves along a line perpendicular to $V$), and $E_f\sin\delta$ is constant (the tip of $E_f$ moves along a line parallel to $V$).

| Excitation | $E_f$ vs $V$ | Current | Power factor |
|---|---|---|---|
| Under | $E_f$ low | Lags $V$ | Lagging |
| Normal | $E_f \cos\delta = V$ | Minimum | Unity |
| Over | $E_f$ high | Leads $V$ | Leading |

#### Application
An over-excited synchronous motor running at no load is a **synchronous condenser**, used for power factor correction. The V-curve plots armature current against field current for each load; the minimum current of each curve corresponds to unity power factor.

## Check yourself

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

1. When excitation is varied at constant load and voltage, what stays constant?
   A. The active component I cos(phi) of the current
   B. The total armature current
   C. The back emf
   D. The power factor
   Answer: A. Input power P = sqrt3 V I cos(phi) is fixed by the load, so I cos(phi) is constant while the reactive component changes. (Key point: What stays constant)

2. What happens at normal excitation?
   A. Current is maximum and lags
   B. Current is minimum and in phase with V, giving unity pf
   C. Current leads
   D. Motor stops
   Answer: B. At normal excitation the current is smallest, in phase with V, with unity pf. (Key point: Normal excitation)

3. An under-excited synchronous motor behaves as what?
   A. A capacitive load with leading pf
   B. An inductive load with lagging pf
   C. A resistive load
   D. A generator
   Answer: B. With low Ef the current lags V and the motor draws reactive power. (Key point: Under-excitation)

4. What is an over-excited no-load synchronous motor called and used for?
   A. Induction generator for speed control
   B. Synchronous condenser for power-factor correction
   C. Pony motor for starting
   D. Damper for hunting
   Answer: B. It supplies reactive power (leading current) to improve the power factor of the system. (Key point: Over-excitation use)

## Related in Electrical Machines

- [Synchronous motor: pf when input rises to 1500 kW](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Async-motor-pf-input-1500kw) — Electrical Machines, chapter 6
- [Single phase motor working; effect of air gap](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Aspim-working-air-gap-effect) — Electrical Machines, chapter 7
- [Scott connection for three-phase to two-phase](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Ascott-connection) — Electrical Machines I, chapter 2
- [3.3 kV synchronous motor back emf](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Async-motor-3-3kv-back-emf) — Electrical Machines, chapter 6, asked 2×
- [Transformer on load and no load, phasor diagrams](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Atransformer-load-phasor-resistive-capacitive) — Electrical Machines, chapter 2
- [Hunting; loaded operation of synchronous motor](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Async-motor-hunting-loaded-operation) — Electrical Machines, chapter 6

## Related in other subjects

- [Effect of excitation on synchronous motor](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Async-motor-excitation-effect) — Electrical Machine, chapter 6, asked 6×
- [Synchronous motor features, applications and excitation](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Amotor-features-applications-excitation) — Electric Machines II, chapter 2
- [Salient pole motor excitation and reluctance power](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Asalient-motor-50mva-pu) — Electric Machines II, chapter 2
- [Excitation emf and maximum power of 1.5 MW motor](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Asalient-motor-1-5mw-max-power) — Electric Machines II, chapter 2