Firm and secondary energy from average monthly flows

Firm energy is produced by the minimum flow (available 100% of the time); secondary energy is the extra energy from flow above the minimum.

Assumptions

The head, efficiency and plant capacity are not given, so assume:

• Net head $H = 100$ m, overall efficiency $\eta = 0.85$
• The plant can use all the river flow (no spilling)
• Each month = 730 h

Note: the June flow (100 m³/s) is taken as printed, so June is the minimum-flow month.

Power per unit discharge

$$P = 9.81 \times Q \times 100 \times 0.85 = 833.85\,Q\ \text{kW}$$

Firm energy

Minimum flow = 100 m³/s.

$$\begin{aligned} P_f &= 833.85 \times 100 = 83{,}385\ \text{kW} \\ E_f &= 83{,}385 \times 8760 = 730.45\ \text{GWh} \end{aligned}$$

Total energy

$$\begin{aligned} E_{total} &= 833.85 \times 8475 \times 730 = 5158.82\ \text{GWh} \\ E_s &= 5158.82 - 730.45 = 4428.37\ \text{GWh} \end{aligned}$$

In general form: $E_f = 9.81\,\eta H \times 100 \times 8760$ and $E_s = 9.81\,\eta H \times (8475 - 12\times100) \times 730$ kWh, so the answer scales directly with the assumed $\eta H$.

Answer (H = 100 m, η = 85%): firm energy ≈ 730.5 GWh/yr; secondary energy ≈ 4428.4 GWh/yr.