Most people grasp that the power output (P) of a hydro scheme depends on three things:
- the head of water - the height difference down which water is flowing (Hgross)
- the flow available (Q)
- the overall efficiency of the scheme
... and so it is. But actually the head component has its effect because it determines the pressure seen by the turbine's nozzles. To convert head into a pressure, mathematical constants need to be employed to account for the acceleration due to gravity and the density of water.
So the equation for power output, incorporating these constants and adjusted so the units are those of kW, litres/s and metres becomes:
P = 9.8 × Hgross × Q × total efficency
From my records of the operation of this turbine in its first year, I know that when the flow was 2.72 lps, the electrical output to the grid was 0.713 kW. I know this with some confidence because there was a period of 75 days between January and March when the turbine ran continuously at this flow and the Elster export meter (which reads to 0.1 kWh) displayed the accumulated energy generated over this time. By dividing the kWh figure by 24, the number of hours in a day, the instantaneous power output is given, and it comes with the assurance that it is a mean figure arrived at over a lengthy period of time.
I have measured the gross head (Hgross) for my scheme as 53.6 m using the Budenberg gauge pictured in the last post (though I have to admit its calibration has not been checked and being an eBay purchase, it could be out).
Entering into the above equation the knowns for power (0.713), flow (2.72) and gross head, and solving for total efficiency, it turns out to be 0.499, or near enough 50 %.
The phrase "water to wire" efficiency is often, and usefully, used to describe this overall efficiency figure for a hydro electric installation. It is a crucial determinant of the cost / benefit ratio for implementing a scheme, but unfortunately it is almost impossible to know with any certainty before the scheme is up and running.
In the next post, I will look at what factors in my installation contribute to this relatively low figure for "water to wire efficiency", and what happens to its value at flows below 2.72 lps.