Primary/secondary energy and pondage volume

Primary energy is produced by the minimum flow that is available all year; secondary energy is produced by the flow above this minimum. No design discharge is given, so the plant is assumed to use all the river flow (secondary energy is then the maximum possible). Each month is taken as 730 h ($2.628 \times 10^6$ s).

Power per unit discharge

$$P = 9.81 \times Q \times 200 \times 0.80 = 1569.6\,Q\ \text{kW}$$

Primary energy

Minimum flow = 100 m³/s (January).

$$\begin{aligned} P_f &= 1569.6 \times 100 = 156{,}960\ \text{kW} = 156.96\ \text{MW} \\ E_p &= 156{,}960 \times 8760 = 1374.97\ \text{GWh} \end{aligned}$$

Total and secondary energy

$$E_s = 12{,}592.43 - 1374.97 = 11{,}217.46\ \text{GWh}$$

Pondage for firm capacity increased by 150%

"Increased by 150%" is read as new firm capacity = $1 + 1.5 = 2.5$ times the original.

$$\begin{aligned} P_{f,new} &= 2.5 \times 156.96 = 392.4\ \text{MW} \\ Q_{f,new} &= 2.5 \times 100 = 250\ \text{m}^3/\text{s} \end{aligned}$$

Months with flow below 250 m³/s must be supplied from storage:

$$\begin{aligned} V &= 390 \times 2.628\times10^6 \\ &= 1.025 \times 10^9\ \text{m}^3 \end{aligned}$$

This storage is easily refilled in the monsoon months, when flows are far above 250 m³/s.

Answer: Primary energy ≈ 1375.0 GWh/yr; secondary energy ≈ 11,217.5 GWh/yr; storage (pondage) required ≈ 1.025 × 10⁹ m³ (1025 million m³).

(If "increased by 150%" is taken as 1.5 times, i.e. firm flow 150 m³/s, the deficits are 50 + 30 + 10 = 90 m³/s-month and the storage is $90 \times 2.628\times10^6 = 2.37\times10^8$ m³.)