---
title: "Significance of H constant"
subject: "Power System Analysis II"
chapter: 6
key: "semester_5/power_system_analysis_ii:h-constant-significance"
source: https://www.bctengineer.com/q/semester_5/power_system_analysis_ii/h-constant-significance
site: BCT Engineering
---

# Significance of H constant

Power System Analysis II · Chapter 6: Power System Stability

- Asked in: 2072 Kartik, 4 marks
- Video: [CONSTANTS M AND H OF ROTATING MACHINES](https://www.youtube.com/watch?v=YLeUpA0hsvk) — P SUMALATHA
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/power_system_analysis_ii/h-constant-significance
- Whole chapter: https://www.bctengineer.com/md/semester_5/power_system_analysis_ii/chapter-6

## Question

What is the significance of H constant in stability of a synchronous machine?

## Short answer

H is the stored kinetic energy at synchronous speed per MVA rating, in MJ/MVA or seconds. It appears in the swing equation, so larger H gives slower rotor acceleration, longer critical clearing time, and lower oscillation frequency. H measures how strongly the rotor resists speed changes.

## Answer

The **inertia constant $H$** is the kinetic energy stored in the rotor at synchronous speed, divided by the machine MVA rating:

$$
H = \frac{\text{stored KE at synchronous speed (MJ)}}{\text{machine rating (MVA)}} = \frac{\tfrac{1}{2}J\omega_{sm}^2}{S}\ \ \text{MJ/MVA (s)}
$$

#### Significance in stability

1. **Appears directly in the swing equation.** $\dfrac{2H}{\omega_s}\dfrac{d^2\delta}{dt^2} = P_a$. For a given accelerating power $P_a$ (for example during a fault), the rotor acceleration is inversely proportional to $H$.
2. **Slower swing and longer clearing time.** With a larger $H$, the rotor angle rises more slowly during a fault. For a fault with $P_e = 0$, the critical clearing time is $t_{cr} = \sqrt{2H(\delta_{cr}-\delta_0)/(\pi f P_m)}$, so $t_{cr} \propto \sqrt{H}$. A machine with a high $H$ gives the breakers and relays more time.
3. **Frequency of oscillation.** For small disturbances, $\omega_n = \sqrt{\pi f P_s / H}$. A larger $H$ gives slower, smaller-frequency rotor oscillations.
4. **Narrow range of values.** In MJ/MVA, $H$ falls in a narrow range for each machine type (about 2–4 for hydro units, 4–9 for turbo-alternators, 1–5 for synchronous motors and condensers). This makes it a convenient, near-standard data value when the actual data are missing.
5. **Equal-area criterion.** The critical clearing **angle** does not depend on $H$; it depends only on the power-angle curves. $H$ converts that angle into the critical clearing **time**.
6. **Frequency response.** A larger total system inertia slows the fall in frequency after a loss of generation (lower rate of change of frequency).

In short, $H$ measures how strongly the rotor resists a change in speed. A higher $H$ improves transient stability margins in time.

## Check yourself

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

1. The inertia constant H is:
   A. Rotor moment of inertia in kg m2
   B. Stored kinetic energy at synchronous speed divided by MVA rating
   C. Electrical power divided by speed
   D. Torque per unit angle
   Answer: B. H = (1/2)J w_sm^2 / S in MJ/MVA. (Key point: Definition of H)

2. For a given accelerating power during a fault, the rotor acceleration is:
   A. Independent of H
   B. Proportional to H
   C. Inversely proportional to H
   D. Proportional to H squared
   Answer: C. From (2H/ws) d2delta/dt2 = Pa, a larger H gives a smaller acceleration. (Key point: Effect on acceleration)

3. The critical clearing time (with Pe = 0 during fault) varies with H as:
   A. Proportional to 1/H
   B. Independent of H
   C. Proportional to H squared
   D. Proportional to sqrt(H)
   Answer: D. t_cr = sqrt(2H(delta_cr - delta0)/(pi f Pm)), so t_cr is proportional to sqrt(H). (Key point: Clearing time dependence)

## Related in Power System Analysis II

- [Swing equation of synchronous machine](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Aswing-equation-derivation) — Power System Analysis II, chapter 6
- [Swing equation and inertia constant](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Aswing-equation-inertia-constant) — Power System Analysis II, chapter 6
- [Stability classification and swing equation](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Astability-classification-swing) — Power System Analysis II, chapter 6
- [Generator reactive power at constant terminal voltage](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Agenerator-reactive-power-infinite-bus) — Power System Analysis II, chapter 1
- [EAC for a two machine system](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Aeac-two-machine-system) — Power System Analysis II, chapter 6
- [Stability definitions and swing equation from dynamics](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Astability-define-swing-from-dynamics) — Power System Analysis II, chapter 6

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