---
title: "Generator reactive power at constant terminal voltage"
subject: "Power System Analysis II"
chapter: 1
key: "semester_5/power_system_analysis_ii:generator-reactive-power-infinite-bus"
source: https://www.bctengineer.com/q/semester_5/power_system_analysis_ii/generator-reactive-power-infinite-bus
site: BCT Engineering
---

# Generator reactive power at constant terminal voltage

Power System Analysis II · Chapter 1: Interconnected Power System

- Asked in: 2073 Shrawan, 6 marks
- Video: [How Generators Keep Voltage Stable - Excitation Control Explained](https://www.youtube.com/watch?v=wn6-jI-hP4Q) — Gaurav J - TheElectricalGuy
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/power_system_analysis_ii/generator-reactive-power-infinite-bus
- Whole chapter: https://www.bctengineer.com/md/semester_5/power_system_analysis_ii/chapter-1

## Question

For a synchronous generator connected to infinite bus, discuss how the generator can supply or consume variable reactive power keeping its terminal voltage constant.

## Short answer

With constant prime mover power, adjusting field excitation changes internal emf Ef, shifting the reactive power output while terminal voltage Vt stays fixed by the infinite bus. Over-excitation supplies lagging reactive power; under-excitation absorbs leading reactive power, subject to field heating and stability limits.

## Answer

A synchronous generator on an infinite bus has its terminal voltage $V_t$ and frequency fixed by the bus. With constant mechanical input (constant P), it can still be made to **supply or absorb any reactive power within limits by changing its field excitation**.

#### Equations
With synchronous reactance $X_s$ (R neglected), internal emf $E_f$ and load angle $\delta$:

$$
E_f = V_t + jX_sI_a,\qquad
P = \frac{E_fV_t}{X_s}\sin\delta,\qquad
Q = \frac{E_fV_t\cos\delta - V_t^2}{X_s}
$$

- P depends on the turbine input; since $V_t$ and $X_s$ are fixed, $E_f\sin\delta$ = constant. So as $E_f$ changes, the tip of $E_f$ moves along a line parallel to $V_t$.
- $I_a\cos\phi$ (active current) also remains constant.
- Q depends on $E_f\cos\delta - V_t$, which changes with excitation.

#### Three cases
| Excitation | Condition | Q | Power factor |
|---|---|---|---|
| Normal | $E_f\cos\delta = V_t$ | 0 | Unity |
| Over-excited | $E_f\cos\delta > V_t$ | Supplied (+) | Lagging |
| Under-excited | $E_f\cos\delta < V_t$ | Absorbed (−) | Leading |

```text
     locus of Ef tip (P constant)
   --------x-------x--------x-------
          /       /        /
     Ef1 /   Ef2 /    Ef3 /     Ef1 < Ef2 < Ef3
        /       /        /
       O--------------------> Vt
   Ef1: under-excited (absorbs Q)
   Ef3: over-excited (supplies Q)
```

#### Explanation
- Increasing field current raises $E_f$; $\delta$ decreases and $I_a$ swings to lagging. The generator sends Q into the bus.
- Decreasing field current lowers $E_f$; $\delta$ increases and $I_a$ becomes leading. The generator draws Q from the bus.
- Terminal voltage remains constant because the infinite bus holds it.

#### Limits
Maximum Q is set by field heating (maximum $E_f$) and armature current; minimum Q (maximum absorption) by the steady-state stability limit ($\delta$ near 90°) and stator end heating. This is how generators are used for voltage/Q support in a real grid.

## Check yourself

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

1. With constant P on an infinite bus, as excitation changes:
   A. Ef cos(delta) stays constant
   B. Ef sin(delta) remains constant
   C. delta stays constant
   D. Vt changes
   Answer: B. P = EfVt sin(delta)/Xs is fixed. (Key point: Constant P)

2. Increasing field current makes the generator:
   A. absorb Q
   B. stop supplying P
   C. supply Q (lagging pf)
   D. change Vt
   Answer: C. Higher Ef gives Ef cos(delta) > Vt. (Key point: Over-excited)

3. Maximum absorption of Q is limited by:
   A. field heating
   B. governor droop
   C. tie-line
   D. steady-state stability (delta near 90 deg) and stator end heating
   Answer: D. Under-excitation increases delta. (Key point: Min Q limit)

## Related in Power System Analysis II

- [Critical clearing angle/time, fault at infinite bus](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Acritical-clearing-infinite-bus-h5) — Power System Analysis II, chapter 6
- [Reactive power injection and generation limits](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Areactive-power-injection-limits) — Power System Analysis II, chapter 1
- [Rotor angle and swing equation, infinite bus](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Arotor-angle-swing-equation) — Power System Analysis II, chapter 6
- [Fault at generator terminal feeding motor](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Afault-generator-terminal-motor-new) — Power System Analysis II, chapter 3
- [Critical clearing, fault at infinite bus, H = 6](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Acritical-clearing-fault-infinite-bus-h6) — Power System Analysis II, chapter 6
- [Reactive power and voltage balance](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Areactive-power-voltage-balance) — Power System Analysis II, chapter 1

## Related in other subjects

- [Generator on infinite bus with 15% excitation rise](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Agenerator-infinite-bus-excitation-15) — Electric Machines II, chapter 1
- [Why infinite bus frequency and voltage stay constant](https://www.bctengineer.com/question.md?key=semester_4%2Fpower_system_analysis_i%3Ainfinite-bus-constant-frequency) — Power System Analysis I, chapter 1
- [Power transfer and pf of motor on infinite bus](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Amotor-infinite-bus-power-transfer) — Electric Machines II, chapter 2
- [Sync generator terminal voltage, leading pf](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Async-generator-1200kva-leading-voltage) — Electrical Machine, chapter 6, asked 2×