---
title: "Stability limits and factors affecting transient stability"
subject: "Power System Analysis II"
chapter: 6
key: "semester_5/power_system_analysis_ii:stability-limits-factors"
source: https://www.bctengineer.com/q/semester_5/power_system_analysis_ii/stability-limits-factors
site: BCT Engineering
---

# Stability limits and factors affecting transient stability

Power System Analysis II · Chapter 6: Power System Stability

- Asked in: 2071 Chaitra, 8 marks
- Video: [PSA (L12) Stability#factors affecting the steady state stability and transient state stability](https://www.youtube.com/watch?v=pygOW0WW5z4) — power engineering
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/power_system_analysis_ii/stability-limits-factors
- Whole chapter: https://www.bctengineer.com/md/semester_5/power_system_analysis_ii/chapter-6

## Question

What do you mean by steady state and transient stability and their limits in a power system? Describe the factors affecting the transient stability of a power system.

## Short answer

Steady state stability is synchronism under small gradual changes, limit Pmax=EV/X at δ=90°. Transient stability is synchronism after a large sudden disturbance, limit determined by equal area criterion. Factors affecting transient stability include pre-fault loading, fault type and location, clearing time, post-fault reactance, generator inertia, transient reactance, excitation speed, and reclosing schemes.

## Answer

**Power system stability** is the ability of a power system to return to a normal (synchronous) operating condition after being subjected to a disturbance.

- **Steady state stability** is the ability of the system to remain in synchronism when subjected to **small and gradual** changes in load (or generation). The maximum power that can be transmitted through a point without loss of synchronism under such slow changes is the **steady state stability limit**. For a machine connected to an infinite bus through reactance $X$:
$$
P_{max} = \frac{EV}{X} \quad (\text{at } \delta = 90^\circ)
$$
- **Transient stability** is the ability of the system to remain in synchronism after a **large and sudden** disturbance such as a fault, loss of a line, sudden loss of large load or generation. It is studied over the first swing (about 1 s). The maximum power that can be transmitted while the system remains stable after a specified large disturbance is the **transient stability limit**. It is always lower than the steady state limit and depends on the type, location and clearing time of the disturbance.

The limits are shown on the power-angle curve $P_e = \frac{EV}{X}\sin\delta$: the steady-state limit is its peak; the transient limit is the largest $P_m$ for which the equal area condition ($A_1 = A_2$) can still be satisfied after the given disturbance.

#### Factors affecting transient stability
| Factor | Effect on transient stability |
|---|---|
| **Pre-fault loading** ($P_m$, $\delta_0$) | Higher loading gives larger $\delta_0$ and a smaller margin |
| **Type of fault** | 3-phase fault is most severe, then LLG, LL, LG |
| **Location of fault** | Fault near the generator bus reduces $P_e$ most (close to zero) |
| **Fault clearing time** | Longer clearing increases the accelerating area; critical factor |
| **Post-fault network reactance** | Higher reactance after clearing lowers $P_{max3}$ and the decelerating area |
| **Inertia constant $H$** | Larger $H$ slows the rotor swing, giving more time |
| **Generator transient reactance $X_d'$** | Lower reactance raises power transfer |
| **Excitation level and speed of the excitation system** | Higher internal emf and fast field forcing raise $P_{max}$ |
| **Reclosing scheme** | Fast and single-pole reclosing restores transfer capability |
| **Speed of governor/fast valving** | Quick reduction of $P_m$ reduces acceleration |

From the swing equation $\frac{2H}{\omega_s}\frac{d^2\delta}{dt^2} = P_m - P_{max}\sin\delta$, any factor that lowers $P_{max}$ during or after the fault, or keeps $P_m - P_e$ large for longer, makes the system less stable.

## Check yourself

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

1. For a machine on an infinite bus, the steady state stability limit occurs at what angle and value?
   A. delta = 45°, EV/(2X)
   B. delta = 180°, zero
   C. delta = 90°, EV/X
   D. delta = 0°, EV/X
   Answer: C. Pe = (EV/X) sin(delta) peaks at 90°, giving the limit EV/X. (Key point: Steady state limit)

2. The transient stability limit is the largest Pm for which:
   A. dPe/ddelta stays positive
   B. The equal area condition A1 = A2 can still be met after the given disturbance
   C. Pe equals EV/X
   D. The fault is a line-to-ground fault
   Answer: B. It is defined by the existence of a decelerating area equal to the accelerating area for the specified fault and clearing. (Key point: Transient limit meaning)

3. What happens when the fault clearing time is increased?
   A. The decelerating area grows
   B. Pmax3 increases
   C. The accelerating area increases, reducing stability
   D. The inertia constant increases
   Answer: C. A longer fault gives more time for acceleration, a larger A1 and less margin. (Key point: Fault clearing time)

4. Which order of fault severity for transient stability is correct?
   A. LG, LL, LLG, 3-phase
   B. 3-phase, LLG, LL, LG
   C. LL, 3-phase, LG, LLG
   D. LG, 3-phase, LL, LLG
   Answer: B. A 3-phase fault reduces Pe the most, then LLG, LL and LG. (Key point: Fault type severity)

## Close variants set in other exams

- [Stability limits and enhancement techniques](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Asteady-transient-stability-limits-enhancement) — Power System Analysis II, chapter 6, asked 2×

## Related in Power System Analysis II

- [Types of stability and factors affecting transient](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Astability-difference-factors) — Power System Analysis II, chapter 6
- [Factors affecting transient stability](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Atransient-stability-factors) — Power System Analysis II, chapter 6
- [Steady state vs transient stability; enhancement](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Asteady-transient-stability-enhancement) — Power System Analysis II, chapter 6, asked 2×
- [Voltage stability; transient study assumptions](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Avoltage-stability-transient-assumptions) — Power System Analysis II, chapter 6
- [Stability definitions, improvement and factors](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Astability-define-methods-factors) — Power System Analysis II, chapter 6
- [Equal area criterion for transient stability](https://www.bctengineer.com/question.md?key=semester_5%2Fpower_system_analysis_ii%3Aequal-area-criterion-concept) — Power System Analysis II, chapter 6, asked 4×

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