To determine if microhydro is viable for your homestead or community, you need to run some calculations. Using your measurements of head and flow rate from the last post on microhydro, it’s a simple matter to calculate the available power. Wikipedia has a good summary of the necessary equations.
If we define h as our head height and φ as our flow rate, we see that P = ρφgh (where P = power, ρ is mass density of water, and g is gravitational acceleration).
So for an average flow rate of 0.01 m3/s (~162 gallons per minute (GPM)) and a head of 10 m:
P = (1000 kg/m3)*(9.8 m/s2)*(10 m)*(0.01 m3/s) = 980 W
you get an ultimate power of 980 W. This is not equivalent to electrical power potential, but rather the total amount of available work energy. Be sure to repeat this calculation for you varying (seasonal) flow rate numbers and for all possible installation locations on your property.
[It should be noted that the above equation for available power neglects 2 terms from the speed of the water. This equation is derived from the energy equation as follows:
E = mgh + ½mv2
If we take the first derivative with respect to time:
P = ρφgh + ½ρφv2 + mva
The nature of v and a (the water velocity and acceleration, respectively) allow us to neglect these terms under most circumstances. The acceleration term (mva) goes to 0 for steady (non-accelerating) flow, but the other term (½ρφv2) becomes significant for high speed flows. In the example, for 1 m/s water speed, ½ρφv2 = ½(1000 kg/m3)*(0.01 m3/s)*(1m/s)2 = 5 W, but for 10 m/s the additional available power shoots to 500 W.]
Now that we have knowledge of our stream’s ultimate power potential, we can start looking at various turbine options. Wikipedia (what a great resource, eh?) has an excellent chart to aid in selecting the best type of turbine to use, given your particular combination of head and flow conditions.
Looking at the lines of equivalent power in the chart, you can see that it’s highly unlikely for any of us to need anything other than a Kaplan turbine or a cross-flow turbine. Very few here will be able to make use of anything approaching 1 MW, and given the environmental concerns, I would encourage you to explore multiple smaller turbines at various locations if you do perceive a need for that kind of power. (Note that there are many other smaller turbine types more suitable for microhydro that are not pictured here.)
The amount of ultimate water power you calculated above does not transfer into the amount of usable electricity, as there are efficiency losses to consider. Some turbines have efficiencies upward of 90%, but 50% is more likely for microhydro turbines. Additionally, there are losses in electrical transmission through the lines, which depends heavily on several variables (e.g. corrosion, temperature, distance, wire gauge). Typically these losses do not exceed 10%.
Additionally, I found a good reference(pdf) that gives even more detailed instructions for the flow measurements procedures I outlined in the last post. One point brought up in this guide that I neglected to mention earlier was applying a correction factor to the flow rate. This accounts for the fact that water moving past air (at the surface – i.e. the velocity your float sees) versus water moving past the higher-friction stream bed. So, for a rough rock or gravel bed multiplying your flow rate by 0.8, and for a smoother mud or silt bed use 0.9.
So, our modified power availability equation is now: PA = ηtηeρφgh where ηt is the flow rate efficiency factor and ηe is the electrical transmission efficiency factor. For our (rocky bottom) example this yields PA = (0.8)*(0.9)*(980) = 706 W
It is well within your capacity (I don’t care who you are!) to build your own water turbine, but it takes patience and careful craftsmanship. A day’s effort produced this machine. It yields only 22 W, but that’s due primarily to the very limited head and flow, not the ability of the machine.
Mother Earth News built a very powerful water turbine out of cheap parts and has plans available to build your own. When looking at the costs in the article, keep in mind it was written in 1980; still, it shows how inexpensive microhydro can be.
Building the turbine is not enough, of course. As mentioned in the Mother article, you’ll need to use either an AC alternator or a DC generator plus an inverter. Their design used an alternator with a novel system for carefully regulating turbine speed. You could avoid this mechanical complexity by going DC plus inverter, but you introduce further power losses.
The AC/DC conundrum is common to several types of alternative power. I’ll address this topic at length in the future. Hopefully this discussion leads you to consider the potential for microhydro in your designs along with the many other options.
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