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Load sharing: 600 and 500 MVA, 900 MVA load

Short answer

New frequency is approximately 59.74 Hz. Unit 1 generates 564.29 MVA and Unit 2 generates 435.71 MVA.

Two generating units of capacity 600MVA and 500MVA having droop of 4% and 6% are supplying 500MVA and 400MVA respectively to a common load of 900MVA at 60Hz. Calculate the new frequency and the new generation on each unit if load is increased to 100MVA.

Taking "increased to 100 MVA" as increased by 100 MVA (total 1000 MVA), and treating MVA as MW (unity power factor), both units share the increase in proportion to Pr/RP_r/R.

Method: a unit with droop RR (pu on its own rating PrP_r) and rated frequency f0f_0 changes its output by

ΔP=−PrR f0 Δf=−K Δf\Delta P = -\frac{P_r}{R\,f_0}\,\Delta f = -K\,\Delta f

where K=Pr/(Rf0)K = P_r/(R f_0) is its stiffness in MW/Hz. All units run at the same frequency, so ΔPL=−Δf∑K\Delta P_L = -\Delta f \sum K.

Data: Unit 1: 600 MVA, 4 %, supplying 500; Unit 2: 500 MVA, 6 %, supplying 400; f0=60f_0 = 60 Hz; ΔPL=100\Delta P_L = 100.

K1=6000.04×60=250 MVA/HzK2=5000.06×60=138.89 MVA/HzΔf=−100388.89=−0.2571 Hzfnew=60−0.2571=59.74 HzΔP1=250×0.2571=64.29ΔP2=138.89×0.2571=35.71\begin{aligned} K_1 &= \frac{600}{0.04 \times 60} = 250\ \text{MVA/Hz} \\ K_2 &= \frac{500}{0.06 \times 60} = 138.89\ \text{MVA/Hz} \\ \Delta f &= -\frac{100}{388.89} = -0.2571\ \text{Hz} \\ f_{new} &= 60 - 0.2571 = 59.74\ \text{Hz} \\ \Delta P_1 &= 250 \times 0.2571 = 64.29 \\ \Delta P_2 &= 138.89 \times 0.2571 = 35.71 \end{aligned}
UnitInitialIncreaseNew
1 (600 MVA, 4 %)50064.29564.29
2 (500 MVA, 6 %)40035.71435.71
Total9001001000

Answer: New frequency ≈ 59.74 Hz; Unit 1 generates 564.29 MVA (MW) and Unit 2 435.71 MVA (MW).

✓ Answer checked by Claude Opus 5.5 (high effort)

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