Hydroelectricity Terms

Hydroelectricity, using the potential energy of rivers, now supplies 17.5% of the world’s electricity (99% in Norway, 57% in Canada, 55% in Switzerland, 40% in Sweden, 7% in the US). Apart from a few countries with an abundance of it, hydro capacity is normally applied to peak-load demand, because it is so readily stopped and started. It is not a major option for the future in the developed countries because most major sites in these countries having the potential for harnessing gravity in this way are either being exploited already or are unavailable for other reasons such as environmental considerations. Growth to 2030 is expected mostly in China and Latin America.

Hydroelectricity is available in many forms, potential energy from high heads of water retained in dams, kinetic energy from current flow in rivers and tidal barrages, and kinetic energy also from the movement of waves on relatively static water masses. Many ingenious ways have been developed for harnessing this energy but most involve directing the water flow through a turbine to generate electricity. Those that don’t usually involve using the movement of the water to drive some other form of hydraulic or pneumatic mechanism to perform the same task.

Water Turbines

Like steam turbines, water turbines may depend on the impulse of the working fluid on the turbine blades or the reaction between the working fluid and the blades to turn the turbine shaft which in turn drives the generator. Several different families of turbines have been developed to optimize performance for particular water supply conditions.

Turbine Power

In general, the turbine converts the kinetic energy of the working fluid, in this case water, into rotational motion of the turbine shaft.

Swiss mathematician Leonhard Euler showed in 1754 that the torque on the shaft is equal to the change in angular momentum of the water flow as it is deflected by the turbine blades and the power generated is equal to the torque on the shaft multiplied by the rotational speed of the shaft.

Note that this result does not depend on the turbine configuration or what happens inside the turbine. All that matters is the change in the angular momentum of the fluid between the turbine’s input and output.

Generation Efficiency

Hydroelectricity generation is by far the most efficient method of large scale electric power generation. See Comparison Chart. Energy flows are concentrated and can be controlled. The conversion process captures kinetic energy and converts it directly into electric energy. There are no inefficient intermediate thermodynamic or chemical processes and no heat losses. The overall efficiency can never be 100%, however since extracting 100% of the flowing water’s kinetic energy means the flow have to stop.

The conversion efficiency of a hydroelectric power plant depends mainly on the type of water turbine employed and can be as high as 95% for large installations. Smaller plants with output powers less than 5 MW may have efficiencies between 80 and 85 %. It is difficult to extract power from low flow rates.

Note: The theoretical Betz conversion efficiency limit of 59.3% which represents the maximum efficiency which can be obtained from a wind turbine, does not apply to hydraulic turbines since there are many variations in turbine designs and more possible controls of the water flows. This means that there are equivalent variations in potential turbine efficiency, many of which can exceed the Betz limit.

Conventional Dam (Potential Energy)

  • Supply Characteristics

A hydroelectric dam installation uses the potential energy of the water retained in the dam to drive a water turbine which in turn drives an electric generator. The available energy depends on the head of the water above the turbine and the volume of water flowing through it. Turbines are usually reaction types whose blades are fully submerged in the water flow. The diagram opposite shows a typical turbine and generator configuration as used in a dam.

The civil works involved in providing hydro-power from a dam will usually be many times the cost of the turbines and the associated electricity generating equipment. Dams provide a large water reservoir from which the flow of water, and hence the power output of the generator, can be controlled. The reservoir also serves as a supply buffer storing excess water during rainy periods and releasing it during dry spells. The build-up of silt behind the dam can cause maintenance problems.

  • Available Power

Potential energy per unit volume = ρgh

Where ρ is he density of the water (103 Kg/m3 ), h is the head of water and g is the gravitational constant (10 m/sec2)

The power P from a dam is given by

P = ηρghQ

Where Q is the volume of water flowing per second (the flow rate in m3/second) and η is the efficiency of the turbine.

For water flowing at one cubic metre per second from the head of one metre, the power generated is equivalent to 10 kW assuming an energy conversion efficiency of 100% or just over 9 kW with a turbine efficiency of between 90% and 95%.

Run-of-River (Kinetic Energy)

  • Supply Characteristics

Run-of-river installations do not depend on flooding large tracts of land to form dams. Instead, the necessary constant water supply may be derived from natural upstream lakes and reservoirs. They are typically used for smaller schemes generating less than 10 MW output power.

Water from a fast flowing river or stream is diverted through a turbine, often a Pelton wheel which drives the electrical generator. The local head of water may be essentially not much more than zero and the turbine is designed to convert the kinetic energy of the flowing water into the rotational energy of the turbine and the generator. The available energy depends on the quantity of water flowing through the turbine and the square of its velocity.

Impulse turbines that are only partially submerged are more commonly employed in fast flowing run-of-river installations while In deeper, slower flowing rivers with a greater head of water, fully submerged Kaplan reaction turbines may be used to extract the energy from the water flow.

Run-of-river projects are much less costly than dams because of the simpler civil works requirements. They are however susceptible to variations in the rainfall or water flow which reduces or even cut off potential power output during periods of drought. To avoid the problems of seasonal river flows, or even daily fluctuations, run-of-river installations may incorporate an additional, limited amount of man-made water storage, referred to as “pondage”, to keep the plant operating during dry periods.

On the other hand, during flood conditions the installation may not be able to accommodate the higher flow rates and water must be diverted around the turbine losing the potential generating capacity of the increased water flow.

Because of these limitations, if the construction of a dam is not possible, run of river installations may also need to incorporate some form of supply backup such as battery storage, emergency generators or even a grid connection. See Capturing Renewable Energy for more details on back-up options.

  • Available Power

The maximum power output from a turbine used in a run of river application is equal to the kinetic energy (½mv2) of the water impinging on the blades. Taking the efficiency η of the turbine and its installation into account, the maximum output power Pmax is given by

Pmax =½ηρQv2

where v is the velocity of the water flow and Q is the volume of water flowing through the turbine per second.

Q is given by

Q = A v

where A is the swept area of the turbine blades.


Pmax =½ηρAv3

This relationship also applies to shrouded turbines used to capture the energy of tidal flows (see below) and is directly analogous to the equation for the theoretical power generated by wind turbines. Note that the power output is proportional to the cube of the velocity of the water.

Thus the power generated by one cubic metre of water flowing at one meter per second through a turbine with 100% efficiency will be 0.5 kW or slightly less taking into account the inefficacies in the system. This is only one-twentieth of the power generated by the same volume flow from the dam above. To generate the same power with the same volume of water from a run of river installation the speed of the water flow should be √20 meters per second (4.5 m/sec).

Tidal Flow

  • Supply Characteristics

Harnessing the power of the tides can be achieved by placing bi-directional turbines in the path of the tidal water flow in bays and river estuaries. To be viable, it needs a large tidal range and involves creating a barrier across the bay or estuary to funnel the water through the turbines as the tide comes in and goes out. Although tidal energy captured in tidal ponds have been used since Roman times to power mills, there are few modern installations. The first plant to utilize tidal energy on a large scale for electricity generation was built at Rance in France in1966. Others followed in Canada and Russia.

Tidal power comes closest to all the intermittent renewable sources being able to provide an unlimited, continuous and predictable power output but unfortunately, there are few suitable sites in the world and environmental constraints have so far prevented their general acceptance.

Shrouded water turbines placed in deep water tidal currents show better potential for exploitation, though the associated civil works are more complicated, and several projects are under development.

Power is available for only six to twelve hours per day depending on the ebb and flow of the tides.

  • Available Power

The maximum power output from a shrouded water turbine used in tidal energy applications is equal to the kinetic energy of the water impinging on the blades, similar to the “run of river” calculation above. Taking the efficiency η of the turbine and its installation into account, the maximum output power Pmax is given by

Pmax =½ηρAv3

where v is the velocity of the water flow and A is the swept area of the blades.

A turbine one meter in diameter with a water current of one meter per second flowing through it would generate 0.4 kW of electricity assuming 100% efficiency. Similarly, a 3-meter diameter turbine with a water current of 3 meters per second would produce 32 Kw of power.