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Droop for capacity sharing: 250 and 500 MW

Short answer

Both generators must have a droop of 6.25 % on their own rating.

Two generators are supplying power to a system. Their rating are 250 MW and 500 MW respectively. Each generator is half loaded and operating at a frequency of 60 Hz. If the system load is increased by 100 MW, the frequency drops to 59.5 Hz. What must be the individual droop of these generators so that they share the load according to their capacity?

To share a load change in proportion to capacity, the change on each unit must be the same fraction of its rating. Then from R=(Δf/f0)/(ΔP/Pr)R = (\Delta f/f_0)/(\Delta P/P_r), both droops come out equal.

Sharing by capacity: total capacity =750= 750 MW, ΔPL=100\Delta P_L = 100 MW.

ΔP1=100×250750=33.33 MWΔP2=100×500750=66.67 MW\begin{aligned} \Delta P_1 &= 100 \times \frac{250}{750} = 33.33\ \text{MW} \\ \Delta P_2 &= 100 \times \frac{500}{750} = 66.67\ \text{MW} \end{aligned}

Frequency change: Δf=59.5−60=−0.5\Delta f = 59.5 - 60 = -0.5 Hz, so Δf/f0=0.5/60=0.008333\Delta f/f_0 = 0.5/60 = 0.008333 pu.

Droop of each unit (pu on own rating):

R1=Δf/f0ΔP1/Pr1=0.00833333.33/250=0.0083330.1333=0.0625R2=Δf/f0ΔP2/Pr2=0.00833366.67/500=0.0083330.1333=0.0625\begin{aligned} R_1 &= \frac{\Delta f/f_0}{\Delta P_1/P_{r1}} = \frac{0.008333}{33.33/250} = \frac{0.008333}{0.1333} = 0.0625 \\ R_2 &= \frac{\Delta f/f_0}{\Delta P_2/P_{r2}} = \frac{0.008333}{66.67/500} = \frac{0.008333}{0.1333} = 0.0625 \end{aligned}

Answer: Each generator needs a droop of 6.25 % on its own rating. G1 then goes from 125 to 158.33 MW and G2 from 250 to 316.67 MW, both at 63.3 % load, at 59.5 Hz.

✓ Answer checked by Claude Opus 5.5 (high effort)

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