## The equations behind hydropower

Rivers have long been recognised as a source of mechanical power. This has been harnessed for over 2000 years at water mills using waterwheels. Hydropower is now widely used to generate electricity. It is seen as a reliable and well-understood form of renewable energy production. Globally, hydropower produces more renewable electricity than any other technology. The main components of a modern scheme include a turbine, generator, water intake structure with debris and fish screen, and control system to enable operation under varying river conditions. Some types of schemes (high head schemes) will also have a long pipe to convey the water from the intake to the turbine and gather pressure. There are many suitable locations for hydropower schemes, the main requirements are flowing water and head (vertical change in water level across the installation).

# Calculating power output

Hydropower can be estimated using the following formula:

Electrical Power (W) = Flow (m3/s) x Net Head (m) x Gravity ( m/s2) x Density ( kg/m3) x efficiency (%)

Hydromatch calculates the power much more accurately using detailed flow data (manually entered or uploaded) and varying efficiency curves (for the turbine and generator) which depend on the flow conditions.

# Calculating energy generation

Energy is the power output multiplied by a time factor usually expressed in kilowatt-hours. The capacity factor is used to adjust the energy capture prediction to allow for periods when the hydropower system is operating at less than its design (maximum) power, e.g. due to reduced flow rates.

Annual Energy Yield (kWh) = capacity factor x power (kW) x hours in a day x days in a year

Hydromatch does not use a capacity factor to estimate energy generation. Instead, power outputs under varying system efficiencies across the whole range of flows divided into 100 equal time intervals, are combined to give a much more realistic calculation.