Flow duration curve and unit sizing

The flow duration curve (FDC) shows how long each flow is available, so it decides how many units are needed and how big each should be, so that turbines run near their best efficiency for most of the year.

How the FDC affects unit sizing

1. Total design flow: the plant's design discharge is taken at a chosen exceedance (e.g. $Q_{45}$). This fixes total capacity $P = \eta \rho g Q H$.
2. Minimum turbine flow: every turbine has a minimum stable flow (Francis about 40% of rated, Pelton about 10–20%, Kaplan about 20–30%). The dry-season flow from the FDC (e.g. $Q_{85}$–$Q_{95}$) must be at least the minimum flow of one unit, or the plant must shut down in the dry season.
3. Steep FDC → more units: if the flow drops far below the design flow for long periods, divide the capacity into two or more units. In the dry season one unit runs near full load instead of all units at poor part load.
4. Flat FDC → fewer, larger units: steady flow allows one or two large units, which are cheaper per kW.
5. Equal-sized units are preferred for interchangeable spares and simple operation; unequal units are used only when the FDC is very steep.
6. Reliability and maintenance: with at least two units, maintenance can be done in the low-flow season while the other unit uses all the available water.

Example

If $Q_{45} = 10$ m³/s and $Q_{95} = 2.2$ m³/s, a single Francis unit would need at least $0.4 \times 10 = 4$ m³/s and would stop in the driest months. With two units of 5 m³/s each, one unit needs only 2 m³/s, so it keeps running even at $Q_{95}$.