---
title: "Limits of the alternator capability curve"
subject: "Power Plant Design"
chapter: 4
key: "semester_8/power_plant_design:capability-curve-limits"
source: https://www.bctengineer.com/q/semester_8/power_plant_design/capability-curve-limits
site: BCT Engineering
---

# Limits of the alternator capability curve

Power Plant Design · Chapter 4: Electric System Design of a Power Plant

- Asked in: 2075 Bhadra, 6 marks
- Video: [GENERATOR CAPABILITY CURVE : simplest way to derive](https://www.youtube.com/watch?v=KsG6qERjvC0) — Electrocean
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_8/power_plant_design/capability-curve-limits
- Whole chapter: https://www.bctengineer.com/md/semester_8/power_plant_design/chapter-4

## Question

List out the major elements that limits the alternator's capability curve. Draw a typical capability curve of alternator and explain it.

## Short answer

The alternator's P–Q capability curve is bounded by armature current (MVA circle), field current (lagging circle), prime mover power limit, under-excitation steady-state stability, and stator end-core heating. The enclosed area defines safe operation.

## Answer

The **capability curve** of an alternator is a P–Q chart that shows the safe region of operation, i.e. the combinations of active power P and reactive power Q that the machine can deliver continuously at rated voltage without exceeding any limit.

#### Elements that limit the curve

1. **Armature (stator) current heating limit:** $S = \sqrt{P^2 + Q^2} = 3V_tI_a$. At rated $V_t$ this is a circle centred at the origin with radius equal to rated MVA.
2. **Field (rotor) current heating limit:** the maximum excitation $E_f$ allowed by rotor heating. It is a circle centred at $(0, -3V_t^2/X_s)$ with radius $3V_tE_f/X_s$. It limits operation at lagging (over-excited) power factor.
3. **Prime mover (turbine) limit:** maximum mechanical power, a vertical line $P = P_{max}$.
4. **Steady-state stability limit:** at leading power factor the load angle approaches $90^\circ$. A practical limit with margin is used.
5. **Stator end-core heating limit:** in under-excited operation leakage flux heats the stator ends and limits leading-var absorption.
6. **Minimum excitation / minimum turbine load:** for example cavitation zones in hydro turbines limit low load.

#### Typical capability curve

```text
  Q lagging (MVAr)
   ^
   |~~~~~--..    <- field current limit
   |    A     `.
   |            o  <- rated MVA, rated pf
   |            |  <- stator current limit
   |            |  <- turbine (max P) limit
   +------------+------> P (MW)
   |            |
   |    B      /
   |       ..-`  <- stability / end-core limit
   |..--~~
   v  Q leading (MVAr)
```

#### Explanation

- **Region A (over-excited, lagging pf):** the field current limit is the binding curve from zero P up to the rated power factor point. Above rated pf (more P), the stator current limit governs.
- **Rated point:** where the field and stator limit circles meet, i.e. rated MVA at rated pf (e.g. 0.85 lagging).
- **High P region:** the stator circle and the turbine limit line cut off the curve.
- **Region B (under-excited, leading pf):** the steady-state stability limit (with margin) and stator end heating limit how much reactive power the machine can absorb.
- The operator must keep the operating point inside the enclosed area. The AVR limiters (OEL, UEL) are set from this curve.

## Check yourself

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

1. What shape does the armature current limit take on the P-Q chart?
   A. A circle centred at -3Vt^2/Xs
   B. A circle centred at the origin with radius equal to rated MVA
   C. A horizontal line
   D. A vertical line
   Answer: B. S = sqrt(P^2+Q^2) = 3VtIa is constant, giving a circle about the origin. (Key point: Armature limit)

2. Which operating region does the field current heating limit govern?
   A. Leading (under-excited) power factor
   B. Only high P
   C. Only no-load
   D. Lagging (over-excited) power factor
   Answer: D. It limits maximum excitation, so it binds when the machine supplies lagging vars. (Key point: Field limit)

3. What limits the absorption of reactive power at leading power factor?
   A. Field heating
   B. Turbine limit
   C. Cavitation
   D. Steady-state stability and stator end-core heating
   Answer: D. In under-excited operation the load angle approaches 90° and end leakage flux heats the core. (Key point: Leading side)

4. How does the prime mover limit appear on the curve?
   A. A vertical line at P = Pmax
   B. A circle
   C. A horizontal line at Q = 0
   D. A curve through the origin
   Answer: A. The maximum mechanical power is fixed, so it caps P regardless of Q. (Key point: Turbine limit)

## Related in Power Plant Design

- [Capability curve of a generator](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Agenerator-capability-curve) — Power Plant Design, chapter 4, asked 2×
- [Protection for alternator and step-up transformer](https://www.bctengineer.com/question.md?key=semester_8%2Fpower_plant_design%3Amega-project-protection) — Power Plant Design, chapter 4

## Related in other subjects

- [Power capability curve of alternator](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machines_ii%3Apower-capability-curve) — Electric Machines II, chapter 1
- [Transition elements; non-typical 3d element](https://www.bctengineer.com/question.md?key=semester_2%2Fengineering_chemistry%3Atm-not-typical) — Engineering Chemistry, chapter 5
- [T/F: capability curve inversely proportional to length](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Atf-capability-curve-inverse-length) — Transmission and Distribution System Design, chapter 2
- [d-block elements; 3d configuration; non-typical metals](https://www.bctengineer.com/question.md?key=semester_2%2Fengineering_chemistry%3Adblock-config-not-typical) — Engineering Chemistry, chapter 5