Flow and power duration curves

Flow duration curve (FDC)

A flow duration curve is a plot of discharge (on the y-axis) against the percentage of time that discharge is equalled or exceeded (on the x-axis). It is a cumulative frequency curve of the river flow.

How it is drawn

1. Collect a long record of daily or monthly flows.
2. Arrange the flows in descending order and give each a rank $m$ (1 for the largest).
3. Compute the exceedance probability $P = \frac{m}{N+1}\times100\%$ (N = number of values).
4. Plot Q against P.

Power duration curve (PDC)

A power duration curve is obtained by converting each flow of the FDC to power:

$$P = 9.81\,Q\,H\,\eta\ \text{kW}$$

It shows the percentage of time a given power is equalled or exceeded. Where the head is nearly constant, the PDC has the same shape as the FDC with a different scale.

Q or P
  |*
  | *
  |  **
  |    ***  installed capacity
  |=======*****======   (e.g. Q40)
  |   secondary  ****
  |                 *****
  |--- firm (Q100) -------****
  +---------------------------->
  0        50             100
       % time equalled/exceeded

Significance in estimating power potential

• Firm power: the power at 100% (or 90–95% in practice) of time gives the firm (dependable) power of a run-of-river plant.
• Installed capacity selection: the design discharge is chosen at a certain exceedance, e.g. Q40 to Q65 for Nepalese run-of-river projects; the PDC shows the power at that level.
• Energy estimation: the area under the PDC (capped at the installed capacity) gives the annual energy; the area below firm power is primary energy and the rest is secondary energy.
• Plant factor: mean power from the capped curve divided by installed capacity.
• Flow character: a steep curve shows a flashy river (needs storage); a flat curve shows a well-regulated, groundwater-fed river.
• Storage and pondage: shows how much storage is needed to raise the firm flow.
• Environmental flow and spill: shows how often water is spilled and how much is left for downstream use.