Optimizing plant capacity of a RoR project

The installed capacity of a RoR plant is optimised by comparing the extra cost and the extra benefit of each increase in capacity. Since flow varies throughout the year, a bigger plant uses the large flow only for a short time, so there is an optimum point.

Procedure

1. Prepare the flow duration curve (FDC) from the long-term flow series (after the environmental release).
2. Select a number of trial design discharges $Q_d$ (e.g. $Q_{30}$, $Q_{40}$, $Q_{50}$ ...). For each, compute the power $P = 9.81\,\eta\,H_n\,Q_d$ and the energy:

$$E = \sum 9.81\,\eta\,H_n\,\min(Q_i,Q_d)\,t_i$$

3. Compute annual benefit = energy × price (firm and secondary energy may have different prices).
4. Compute annual cost = (fixed cost + variable cost × P) × capital recovery factor + O&M. Fixed cost includes the headworks, civil structures, access and so on; variable cost is proportional to the capacity (turbine, generator, penstock).
5. Plot the net benefit (benefit − cost), the benefit/cost ratio and the marginal values against the capacity.

Criterion

• Maximum net benefit (NPV), or
• Marginal benefit = marginal cost: increase capacity until the extra benefit from the last kW (= price × energy produced by it during the time it is used) equals its extra annual cost. Beyond this point the machines run only a few weeks per year and do not pay back.

Other considerations: the cost per kW, the plant factor (usually 50-70% for RoR), the grid demand, the risk and the possibility of staged development.