--- title: "Isochronous generator transient response" subject: "Power Plant Equipment" chapter: 2 key: "semester_7/power_plant_equipment:isochronous-generator-transient" source: https://www.bctengineer.com/q/semester_7/power_plant_equipment/isochronous-generator-transient site: BCT Engineering --- # Isochronous generator transient response Power Plant Equipment · Chapter 2: Power/Frequency Control in Hydro Generator System - Asked in: 2074 Chaitra, 4 marks - Video: [Speed Droop in Power Control Explained](https://www.youtube.com/watch?v=sQ-AT1WdT3M) — RealPars - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/power_plant_equipment/isochronous-generator-transient - Whole chapter: https://www.bctengineer.com/md/semester_7/power_plant_equipment/chapter-2 ## Question What do you mean by Isochronous generator? Describe its transient response for a step increase in load. ## Short answer An isochronous generator uses an integral governor (zero droop) to maintain constant frequency. Following a step load increase, speed drops, integral action increases prime mover power, and speed exactly recovers with zero steady-state frequency error. ## Answer An **isochronous generator** is a generating unit whose governor is isochronous (integral type, zero droop). It keeps the speed and frequency exactly at the set value for any load within its rating. It is used for a single unit supplying an isolated load, or for one unit that controls frequency in a small system. **Governor law:** $\Delta Y(s) = -\dfrac{K}{s}\,\Delta\Omega(s)$, so the gate keeps moving as long as there is any speed error. #### Transient response to a step increase in load ```text power P0+dPL .________________ Pe | __.-- Pm -> Pe | _.' P0 ______|__/ (Pm) t = 0 speed w0 ______. .---- w0 (restored) \ .' '.____.-' t = 0 time ``` 1. At $t = 0$ the electrical output $P_e$ jumps by $\Delta P_L$; $P_m$ is unchanged, so the rotor decelerates and speed falls (slope $-\Delta P_L/2H$). 2. The integral governor opens the gate; $P_m$ rises (a hydro turbine first dips a little). 3. When $P_m > P_e$ the rotor speeds up again. Because the integrator acts until the error is zero, the speed returns **exactly** to $\omega_0$. 4. Final state: $\Delta\omega = 0$ and $\Delta P_m = \Delta P_e = \Delta P_L$. Frequency error is zero, unlike a droop governor which leaves $\Delta\omega_{ss} = -\Delta P_L/(D + 1/R)$. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What best describes an isochronous generator? A. A unit whose governor has integral action and zero droop, holding speed at the set value for any load in rating B. A unit with 5% droop that shares load in proportion to rating C. A unit whose speed is allowed to fall linearly with load D. A unit with no governor, relying on load damping for self-regulation Answer: A. An isochronous governor is integral type with zero droop, so it keeps speed and frequency exactly at the set value within the rating. (Key point: Isochronous governor) 2. Why does the gate keep moving in an isochronous governor after a load step? A. Because the governor law is dY = -(K/s)dOmega, so it integrates until the speed error is zero B. Because the droop feedback keeps adding gate opening C. Because the turbine has water hammer D. Because load damping D keeps changing Answer: A. The integrator output changes as long as any speed error exists, so the gate moves until the error is zero. (Key point: Integral governor law) 3. Just after a step increase in load at t = 0, what happens to the speed? A. It rises because Pm exceeds Pe B. It stays constant until the governor acts C. It falls at a rate -dPL/2H because Pe jumps while Pm is unchanged D. It jumps instantly to a new lower value Answer: C. Pe jumps by dPL but Pm cannot change instantly, so the rotor decelerates at -dPL/(2H). (Key point: Initial speed response) 4. What is the final steady state of an isochronous unit after a step load increase? A. d(omega) = -dPL/(D+1/R) with dPm = dPL B. d(omega) = 0 and dPm = dPe = dPL C. d(omega) = 0 and dPm = 0 D. d(omega) negative and dPm = 0 Answer: B. The integrator forces speed error to zero, and Pm rises until it equals the increased electrical load; the droop expression applies only to droop governors. (Key point: Final state) ## Related in Power Plant Equipment - [Transient response of turbine-generator with governor](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Agovernor-transient-response) — Power Plant Equipment, chapter 2, asked 3× - [Speed response without governor and isochronous governor](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Aspeed-response-isochronous-block) — Power Plant Equipment, chapter 2, asked 2× - [Water turbine response to step gate change](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Awater-turbine-step-gate) — Power Plant Equipment, chapter 2, asked 2× - [Isochronous governor and speed droop model](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Aisochronous-droop-model) — Power Plant Equipment, chapter 2 - [Steady state and transient behaviour with governor](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_plant_equipment%3Agovernor-steady-transient) — Power Plant Equipment, chapter 2, asked 2× ## Related in other subjects - [Ideal LPF impulse and step response](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Aideal-lpf-impulse-step) — Signals and Systems, chapter 5, asked 5× - [Step response of RC filter](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Arc-filter-step-response) — Signals and Systems, chapter 5, asked 3× - [Closed vs open loop step response analytically](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Acl-vs-ol-step-response) — Control Systems, chapter 1, asked 2× - [Unit step response for h(t) = exp(-at)](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aunit-step-response-exp) — Data Communication, chapter 2