---
title: "Special characteristics of hydraulic turbine"
subject: "Power Plant Equipment"
chapter: 2
key: "semester_7/power_plant_equipment:hydraulic-turbine-characteristics"
source: https://www.bctengineer.com/q/semester_7/power_plant_equipment/hydraulic-turbine-characteristics
site: BCT Engineering
---

# Special characteristics of hydraulic turbine

Power Plant Equipment · Chapter 2: Power/Frequency Control in Hydro Generator System

- Asked in: 2076 Chaitra, 5 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/power_plant_equipment/hydraulic-turbine-characteristics
- Whole chapter: https://www.bctengineer.com/md/semester_7/power_plant_equipment/chapter-2

## Question

What are the special characteristics of hydraulic turbine? Explain in brief.

## Short answer

Key characteristics: non-minimum phase response with initial power reversal (opposite to gate movement) due to water inertia; need for large transient droop and slow gate movement to limit water hammer; response governed by water starting time Tw = L U0/(g H0).

## Answer

A hydraulic turbine behaves differently from a steam turbine because of the inertia of water in the penstock; its power output does not follow the gate opening directly.

1. **Non-minimum phase behaviour:** the turbine transfer function
$$
\frac{\Delta P_m(s)}{\Delta G(s)} = \frac{1 - T_w s}{1 + 0.5T_w s}
$$
has a zero in the right half of the s-plane ($s = +1/T_w$). So the power first changes in the **opposite** direction to the gate movement.
2. **Initial reverse power:** when the gate is suddenly opened, the flow cannot rise at once because of water inertia, so the head (pressure) at the turbine falls and power first drops to **−2 times** the gate change. It then rises to +1 times the gate change with time constant $T_w/2$: $\Delta P_m(t) = [1 - 3e^{-2t/T_w}]\Delta G$. Closing the gate first gives a power (and pressure) rise.
3. **Water inertia governs the response:** the response speed is set by the water starting time $T_w$, which is not constant; it rises with load because $U_0$ increases.
4. **Need for transient droop:** a governor with only permanent droop would be unstable. Hydro governors use a **large temporary (transient) droop with a reset time**, so they respond slowly at first and are slower than steam unit governors.
5. **Water hammer and gate rate limits:** gate movements must be slow enough to keep pressure rise in the penstock safe.

```text
 dPm
  1 |                ____________
    |            _.-'
  0 |---.     _-'
    |   |   .'
 -2 |   |_/        (unit step in gate)
    +---+----------------------> t
```

Here $T_w = L U_0/(g H_0)$ is the **water starting time**, the time needed by the head to accelerate the water to its rated velocity (0.5–4 s).

## Check yourself

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

1. What does the zero at s = +1/Tw cause?
   A. Power first moves opposite to the gate movement
   B. Faster response than steam
   C. Constant power
   D. Instability at no load
   Answer: A. RHP zero gives initial reverse response. (Key point: Non-minimum phase)

2. For a unit gate step, how does power behave?
   A. Rises directly to +1
   B. Drops to -2 then rises to +1 with time constant Tw/2
   C. Drops to -1 and stays
   D. Rises to +2 then falls
   Answer: B. dPm(t) = 1 - 3e^(-2t/Tw). (Key point: Step response)

3. Why do hydro governors use large temporary droop with reset time?
   A. To increase speed
   B. To reduce water hammer only
   C. A fast governor with only permanent droop would be unstable
   D. To raise frequency
   Answer: C. Water inertia makes high-gain fast governing unstable, so hydro governors respond slowly. (Key point: Transient droop)

4. Why must gate movement be limited?
   A. Generator voltage
   B. Turbine efficiency
   C. Droop setting
   D. Water hammer pressure rise in the penstock
   Answer: D. Fast gate closing causes pressure surges. (Key point: Gate rate limit)

## Related in Power Plant Equipment

- [Hydraulic turbine characteristics and water starting time](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Ahydraulic-turbine-water-starting) — Power Plant Equipment, chapter 2
- [Water turbine transfer function and characteristics](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Awater-turbine-tf-characteristics) — Power Plant Equipment, chapter 2, asked 2×

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