To calculate the effective capacity of a power plant, two factors are required, flow rate and head. What one must not disregard is that each element of the construction reduces capacity. Between the time when the water is extracted from the stream until the consumer receives the electricity, a substantial part of the power is converted to heat. This happens through friction between two different kinds of solids or prefabricated parts, for example:
- Running water in a steel penstock generates wall friction = heat
- When water hits the turbine, friction is excited = heat
- Rotary motion of the turbine shaft in the ball bearings produces friction = heat
- Power generation through rotary motion in the generator = heat
- The transmission of electricity through the transmission line simply said produces friction = heat
Exception: The power reduction in the canal results from loss of water, which means the flow
rate is fractionally reduced through evaporation, percolation (leak) or drainage
Pic.1 Typical system efficiencies for a scheme
The listed efficiencies, shown in the illustration above, are merely standard values. Some of them must be calculated on their own; others depend on the prefabricated parts (generator, turbine) and must be requested from the producer.
The different partial efficiencies are multiplied and added to equal the overall efficiency η.
According to the illustration the overall efficiency must be
Example: power equation
Example 1: You are on a possible site and have to design a micro hydropower unit which must supply 40kW to a remote village. There is a potential slope which has a difference in height of 20 metres. Roughly how much water is needed?
Example 2: You did flow measurements in a small stream near a feasible site. The head of 90 feet is measured roughly using a water-filled tube. The flow in the stream is more than 160 litres per second. How much power can be delivered to the village?
To ensure that the units are correct, use only SI units. Flow is given in m3/s and head is listed in meters. 90 feet is about 27.5 metres (exact: 100 ft = 30.48 meters) and 160 I/s is 0.16 m3/s.
Pnet = 0.5 ∙ 0.15 ∙ 10 ∙ 27.5 = 22 [kW]
Source: “Civil Works for Micro Hydro Power Units” by Christian Arduser and Leif Kartcheter, University of Applied Sciences Northwestern Switzerland