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Load sharing: 600 and 300 MW at 49 Hz

Short answer

At 50 Hz, G1 output is 0 MW and G2 output is 150 MW. Total system load is 150 MW.

Two generators of 600MW, 2% and 300 MW, 4% are supplying to a common load. When each generator is fully loaded, they operate at common frequency of 49 Hz. Calculate the system load shared by each unit when frequency increased to 50Hz.

Both units are fully loaded at 49 Hz. When frequency rises to 50 Hz, each sheds load equal to its stiffness times the frequency rise (f0=50f_0 = 50 Hz).

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.

K1=6000.02×50=600 MW/HzK2=3000.04×50=150 MW/HzΔf=50−49=+1 HzΔP1=−600×1=−600 MWΔP2=−150×1=−150 MW\begin{aligned} K_1 &= \frac{600}{0.02 \times 50} = 600\ \text{MW/Hz} \\ K_2 &= \frac{300}{0.04 \times 50} = 150\ \text{MW/Hz} \\ \Delta f &= 50 - 49 = +1\ \text{Hz} \\ \Delta P_1 &= -600 \times 1 = -600\ \text{MW} \\ \Delta P_2 &= -150 \times 1 = -150\ \text{MW} \end{aligned}
UnitAt 49 Hz (MW)Change (MW)At 50 Hz (MW)
G1 (600 MW, 2 %)600−6000
G2 (300 MW, 4 %)300−150150
Total900−750150

Answer: At 50 Hz, G1 = 0 MW (its no-load frequency is 49+0.02×50=5049 + 0.02 \times 50 = 50 Hz) and G2 = 150 MW; the system load is 150 MW.

✓ Answer checked by Claude Opus 5.5 (high effort)

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