Calculation of Output Power

The power available from a river is a function of the volume of water available (rate of flow) and the ‘head’ (the drop in height between the intake at the weir and the turbine down below, in metres).
In most cases the volume abstracted is Qmean which is the average rate of flow across the whole year.  This is measured in cubic metres per second (m3/s) and is determined through a combination of flow measurement in the river and calibration against recorded flows in SEPA flow gauging stations.

The formula:

     Output Power (kW) = Qmean(m3/s) x Head(m) x 7

Why 7?  Well mathematically it should be the force of gravity (9.81m/s2) but to allow for losses (frictional, electrical, transmission, etc) this number is rounded down to about 7.

The energy produced by a scheme over a period of time is a function of the power being generated at an instant and the time for which it is generating, measured in Kilowatt Hours (kWh).  This the unit in which we buy electricity, and indeed the unit which gets rewarded through the Feed-in Tariffs. For example, a turbine producing 5 kW for 2 hours will have produced 10 kWh.

If a turbine ran at full capacity all of the time, its capacity factor would be 100%, but hydro schemes will reduce their output as the river flows decrease. The actual energy output as a percentage of the maximum theoretical output is called the capacity factor, and run-of-river hydropower schemes typically have a figure of 40% or more.  This compares favourably with wind which has an average equivalent figure of 30%.