RoR capacity, peaking capacity and benefit

i) Pure run-of-river plant

Minimum flow is 74 m³/s (February).

$$P_1 = 9.81\times0.85\times74\times200 = 123,410\ \text{kW} = 123.41\ \text{MW}$$

ii) Peaking plant with three units, 4 h peaking

One unit (discharge $Q_u$) runs at full load for the 20 off-peak hours; all three units ($3Q_u$) run for the 4 peak hours. Daily water balance on the minimum flow of 74 m³/s:

$$20\,Q_u + 4\,(3Q_u) = 24\times74 \Rightarrow 32\,Q_u = 1776 \Rightarrow Q_u = 55.50\ \text{m}^3/\text{s}$$

Peak discharge $=3Q_u=166.50$ m³/s.

$$P_2 = 9.81\times0.85\times166.50\times200 = 277,672\ \text{kW} = 277.67\ \text{MW}$$

(Each unit is 92.56 MW. Check storage: off-peak stored $=(74-55.5)\times20 = 370$ m³/s·h; peak draw $=(166.5-74)\times4=370$ m³/s·h, equal.)

iii) Increase in benefit during the minimum flow month

Daily energy is the same in both cases ($24\times123.41 = 2,962$ MWh).

• RoR (constant output): 4 peak hours at Rs 12 and 20 off-peak hours at Rs 6 per kWh:

$$B_1 = 123,410\times(4\times12+20\times6) = \text{Rs }20,732,846\text{ per day}$$

• Peaking plant: $B_2 = 92,557\times20\times6 + 277,672\times4\times12 = \text{Rs }24,435,140$ per day

Increase $=3,702,294$ Rs/day $\approx$ Rs 3.70 million per day, or about Rs 111.1 million for a 30-day month.

Answer: (i) 123.4 MW; (ii) 277.7 MW; (iii) extra benefit ≈ Rs 3.70 million per day (≈ Rs 111 million per month).