--- title: "Droop calculation: 800 MW and 300 MW units" subject: "Power Plant Equipment" chapter: 2 key: "semester_7/power_plant_equipment:droop-calculation-800-300" source: https://www.bctengineer.com/q/semester_7/power_plant_equipment/droop-calculation-800-300 site: BCT Engineering --- # Droop calculation: 800 MW and 300 MW units Power Plant Equipment · Chapter 2: Power/Frequency Control in Hydro Generator System - Asked in: 2079 Bhadra, 10 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/droop-calculation-800-300 - Whole chapter: https://www.bctengineer.com/md/semester_7/power_plant_equipment/chapter-2 ## Question Shows figure below two generators operating in parallel and supplying a load of 800 MW. G1 is rated as 800 MW and G2 is rated as 300 MW. G1 supplies 600 MW and G2 supplies 200 MW and system frequency is 50 Hz. At no-load, they operate at a common frequency of 51 Hz. Calculate droop regulations R1 and R2 of G1 and G2 with respect their ratings. Assume base power = 1000 MW. When the load is decreased below 800 MW, the frequency increases to 50.2 Hz. Calculate the power supplied by each generator at reduced load. [Figure: G1 (800 MW, R1 = ?) supplying P1 = 600 MW and G2 (300 MW, R2 = ?) supplying P2 = 200 MW to a common bus feeding load PL = 800 MW] ## Short answer From no-load 51 Hz to full-load lines: stiffness from operating points gives droops. On own ratings, R1 = 2.67%, R2 = 3%. At 50.2 Hz (drop 0.8 Hz from no-load), G1 supplies 480 MW, G2 supplies 160 MW, total 640 MW. ## Answer The droop line of each unit passes through its no-load point (51 Hz, 0 MW) and its present operating point (50 Hz, given MW). Extending the line to rated output gives the droop. **Frequency drop from no load to present load:** $\Delta f = 51 - 50 = 1$ Hz. **Stiffness of each unit:** $$ K_1 = \frac{600}{1} = 600\ \text{MW/Hz}, \qquad K_2 = \frac{200}{1} = 200\ \text{MW/Hz} $$ #### Droop on own ratings Frequency drop at rated output: G1: $800/600 = 1.333$ Hz; G2: $300/200 = 1.5$ Hz. $$ \begin{aligned} R_1 &= \frac{1.333/50}{1} = 0.02667 = 2.67\ \% \\ R_2 &= \frac{1.5/50}{1} = 0.03 = 3\ \% \end{aligned} $$ #### Droop on the common base of 1000 MW $$ R_{new} = R_{own} \times \frac{S_{base}}{S_{rated}} $$ $$ \begin{aligned} R_1 &= 0.02667 \times \frac{1000}{800} = 0.0333 = 3.33\ \% \\ R_2 &= 0.03 \times \frac{1000}{300} = 0.10 = 10\ \% \end{aligned} $$ Check: $\Delta P_i = (\Delta f/f_0)\,S_{base}/R_i$: G1 $= 0.02 \times 1000/0.0333 = 600$ MW ✓, G2 $= 0.02 \times 1000/0.1 = 200$ MW ✓. #### Load sharing at 50.2 Hz Frequency drop from no load $= 51 - 50.2 = 0.8$ Hz. $$ \begin{aligned} P_1 &= 600 \times 0.8 = 480\ \text{MW} \\ P_2 &= 200 \times 0.8 = 160\ \text{MW} \end{aligned} $$ Total load $= 640$ MW, i.e. the load has decreased by 160 MW (G1 sheds 120 MW, G2 sheds 40 MW). **Answer:** $R_1 = 2.67\ \%$ and $R_2 = 3\ \%$ on own ratings (**3.33 %** and **10 %** on 1000 MW base). At 50.2 Hz, **G1 = 480 MW, G2 = 160 MW** (total 640 MW). ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Which two points define each unit's droop line? A. (51 Hz, 0 MW) and (50 Hz, present load) B. (50 Hz, 0) and (51 Hz, rated) C. (50 Hz, rated) and (49 Hz, 0) D. (51 Hz, rated) only Answer: A. Each line passes through no-load at 51 Hz and the present operating point at 50 Hz. (Key point: Droop line points) 2. What are K1 and K2? A. 800 and 300 MW/Hz B. 600 and 200 MW/Hz C. 75 and 66.7 MW/Hz D. 600 and 300 MW/Hz Answer: B. K = P / (51 - 50) = 600/1 and 200/1. (Key point: Stiffness) 3. What are R1 and R2 on their own ratings? A. 3.33% and 10% B. 2% and 2% C. 2.67% and 3% D. 1.33% and 1.5% Answer: C. Rated-output drops are 800/600 = 1.333 Hz and 300/200 = 1.5 Hz; divide by 50 Hz. (Key point: Droop on own base) 4. How are droops converted to a 1000 MW base? A. Multiply by Srated/Sbase B. Add the ratio C. No change D. Multiply by Sbase/Srated Answer: D. R_new = R_own x Sbase/Srated: 3.33% and 10%. 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