Micro Hydroelectric Power Plant Overview & Power Calculations
Micro Hydroelectric Power Plant Overview & Power Calculations.  Knowing how to calculate the generating capacity of a Micro-Hydroelectric Power Plant is of prime concern.  The following pages are a compilation of data I've collected over the past 20 years or so on hydro-electric power generation & related subjects.

These pages are meant to be used as a guide only and not an all inclusive "how to book."  I do go into some details of various aspects of power generation such as AC power distribution, Governors & Speed Regulation, Waterhammer, and construction of the Banki / Mitchell Crossflow Turbine. I also discuss various other Turbines & Water Wheels.  As time and Web Space permit, I'll be expanding on these & other subjects.

After searching the internet in vain for many hours for articles on building your own power plant and related items I've come to the conclusion, there's not a whole lot of useful technical information out there.  There's plenty of sites that have systems & components to sell but,  few "technical" sites.  Most of the time no matter what search terms I use, I get either totally unrelated stuff or something about fish ladders at some obscure 500 megawatt hydro-electric dam on the dark side of the moon.

I've been interested in the Banki Turbine for some years and have devoted a great deal of time in it's theory of operation & construction.  I have also been granted permission by Oregon State University's Civil Engineering to re-publish on this Web Site their Engineering Bulletin Number 25, titled  "The Banki Water Turbine",  written my C.A. Mockmore & Fred Merryfield in 1949.  In this bulletin these two Professors of Civil Engineering discuss the mathematics and flow characteristics of the Banki turbine.  Some of their civil & hydraulic engineering students build this turbine from Banki's original papers and publish the results of their experiments in this bulletin.

I'll start discussing rather general aspects of producing your own power then get more detailed as I go along.  Most people would like to produce their own power but don't have the means of doing so.  Assuming you're here because you may have those means, (money, time, and some "smarts") this page is meant as a guide.  Within, you'll find descriptions of the various turbines & water wheels along with their advantages & disadvantages. I'll also be discussing other aspects of power plant construction.

A lot of people have a simplistic & romantic view of producing there own electricity.  To actually do this can be as simple as plunking down a thousand dollars or more and spending a weekend doing some manual labor or in the worst case,  mortgaging the house & selling the children and their pets, months, even years of back breaking labor, fighting with the power company, the EPA & the FCC, the Nature Conservancy, not to mention zoning laws and local governments or neighbors that may want to oppose you.  Still interested? Hopefully we can stay somewhere towards the middle.

If you going to build a hydro-electric plant, you might want to have some extra water laying around!  How much water determines how much power you'll be able to produce.  Water pressure for hydro-power is rated in "feet of Head."  The easiest way to explain "Head" is the number of feet the centerline of the "Intake" is above the "Turbine" or "Water Wheel" centerline.  When I say Water Wheel here, I'm referring to the "runner" of a turbo machine as opposed to the Water Wheels you see on postcards showing old "Grist Mills".  Those Water Wheel will be covered else where in these pages.

Another classification for Turbo Machines is the quantity of water (flow rate) they use.  These can be from just a few GPM (Gallons Per Minute) to several hundred CFS (Cubic Feet Per Second).  The combination flow rate & head determine the type of turbine best used for a specific site. While this page is really dedicated to "Micro-Hydro-Electric Power Production"  (Less than 50 Kilowatts of power), I wanted you to be aware of all the turbine classifications.

 Stuff You'll Need To Know 1 Cubic Foot of Water Weighs 62.4 Pounds 1 Cubic Foot of Water Contains 7.48 Gallons 1 Foot of Head = .433 PSI 1 PSI= 2.31 Feet of Head 1 Gallon of Water = .13368 Cubic Foot 1 HP (Horse Power) = 745.7 Watts

Next you need to know the quantity of water available for your site.  Go the the page "Flow Measurement" When finished use the "Back" button on your browser to return here.

Assume you have measured your flow at about 30 GPM at the source.  Now assume your going to have to lay 435 feet of pipe to get the water to the Turbine.  Now is the time to visit some pipe suppliers.  They can supply you with flow / friction loss charts for various sizes of types of pipe.  The friction loss is usually stated as "loss of PSI or Head) per 100 feet." Be careful in your calculations for the differences listed in PSI & Head.  Your choices in pipe are usually galvanized steel, welded steel, PVC & Polyethylene.

For the above example the black Polyethylene  would be the most economical choice.  The idea is to use as large of a diameter as you can afford & then maybe a little more.  Long friction loss through very long pipelines can be a real killer.  Lets look at some 2" pipe.  Its wall thickness is .065 giving an ID (Inside Diameter) of 1.87 inches.  You can look at the charts for that pipe & see the closest match to 26.19 GPM is 25 GPM with a loss of
2. 3 PSI per 100 ft.

 Loss of Pressure Due to Friction 2. 3 X 3.25 = 7.475 PSI Converting PSI Loss to Head Loss 7.45 X 2.31 = 17.2 Effective or Working Head 196 - 17.2 = 178.8 Feet Rounded to 179 Feet

Now we have some figures to work with.  179 feet of head and 26.19 GPM.
 Basic hydraulic power equation (CFS X Head / 8.8) X Eff

 Convert The GPM To CFS GPM X .13368 or 26.19 X .13368 / 60 = .05835 CFM

The "Eff" in the equation if made up of the following factors

The Turbine efficiency is first & foremost  Commercial Hydro-Electric turbines have efficiencies of close to 95% or better.  The Banki Crossflow generally has a range of 55% ~ 88% depending on how well you construct it and how well you can construct the gate for it.  Realistically, for a well built system, I'd use 85% in calculations. Anything greater, consider it "Gravy"

Generator Efficiency is generally about 95%

Belting & Gearing  V-Belts should be rated about 95% while gears & cog type belts are about 98% efficient.  I'll use 98% in my examples.

 Multiplying all these together we get  Turbine eff * Gen eff * Transmission eff or  .85 X .95 X .98  or  .791

Note:  You can obtain exact efficiencies from the various manufactures of the equipment you plan to use.  For drive systems most any "Bearings & Drives", Dixie Bearing" etc. will be glad to quote you figures and or give you the necessary specification / sales catalogs that have that information.
 Plugging in the overall efficiency  (CFS X Head / 8.8) X .791 or  .056 X 186 / 8.8 X .791 = .901 HP

 Converting Hp to Electrical Power Is   Hp X 745  or  .945 X 745 =671 Watts of Electrical Power

Six Hundred Seventy One Watts is not exactly going to give you an excess amount of power.  However if used wisely and efficiently it should be able to meet your basic needs.  A DC system would be best for such an application where, power would be stored in a battery bank and used as required.  Some loads such as lights could be supplied by the battery(s) directly.  However, AC loads would need to be served by converting the DC battery power to AC with an inverter. Ultimately the kilowatt hour capacity would be dictated by your generation capacity and your battery storage capacity.

If you're "way out there" the power company may want to run solid gold wire out to you.  At least that what you'd think from the money they'll want.  How about \$5,000 a mile! Not unusual.   If this is your cabin out in the woods, 671 Watts might be "roughing it" but you'd probably want to go ahead and do it in light of what it'll cost you to get "connected."  You'll wind paying around \$1500 to \$3000 or so, depending on your requirements and spending the weekend or two installing a small pre-packaged Pelton Wheel or Turgo Wheel system.  If you need a little more power from the above example you only have 3 choices.  None of them however will make any "night & day" differences, unless you really cheat on #3.

1) Shop around for a Turbine with a higher efficiency.
2) Go to a larger pipe size
3) Steal a little more water from the stream. (You'll need bigger pipe now for sure)

The above example is typical of a small Micro-Hydro installation.  I hope the small power out put do not discourage you.  You do have to "dance with the one who brung you" and if that's all the water God's letting you have then use it or loose it.

Here's an example of a goodly amount of power.  I've got a 29 foot water fall with a whole bunch of water just going to waste being pretty.   The penstock would have to be 84 feet long and would have to have 4 each, 45 degree elbows.  Lets see what we can do with this. Being as how this involves a lot water, Cubic Feet Of Water Per Second as opposed to Gallons Per Minute in the above example, we need a different methods to calculate the available water flow.  This is commonly done my building a temporary Weir.  A weir is sort of like a dam but it has a slot of specific dimensions cut into it & when used in conjunction with the depth of water at certain points can yield the flow in CFS.

In this one we're gonna get a little more technical because this is my pet project Power Plant.  Looking at 14 Inch Schedule 80 PVC, with a  inside diameter of 12.5 inches.  PVC pipe had a Friction Coefficient of about 150.  Rather then look at the charts which might not be in front of me I'm gonna calculate the friction losses manually.  To do this you'll need a "Scientific" calculator, Qbasic, or some other program that can raise numbers to "powers" other than 2.  You can also use your calculator in MS Windows if you switch it to the "Scientific" mode under "View".  If you want the convenance of looking up these losses in a chart then go to my "Flow Loss In Pipes" page, then use your "Return" or "Back" button to come back here. Be advised that the page is a very large "Table" a may take a little extra time to load.

After careful consideration of the stream conditions I find that I can use 8 CFS of water from my stream. Remember from "Stuff You Need To Know" that there are 7.41 Gallons of water per Cu. ft. & we have to convert CFS to GPM, therefore:

 CFS X 7.41 X 60  or  8 X 7.41 & 60 = 3556.8 GPM

 Feet Of Head Loss Per 100 Feet Pl = (100 / C) ^1.852 X .2083 X GPM^1.852 / Id^4 X .8644 or Pl = (100 / 150) ^1.852 X .2083 X 3556.8^1.852 / 12.5^4 X .8644 or Pl=(.667) ^1.852  X  740.88^1.852  /  20736  X  .8644 or Pl=.4732 X 206430 / 20736 X .8644 = 4.07 Head Loss

 Plugging in the overall efficiency  (CFS X Head / 8.8) X .791 or  8 X 26 / 8.8 X .791 = 18.69 HP

 Converting Hp to Electrical Power Is   Hp X 745  or  18.69 X 745 =13924 Watts of Electrical Power or  13.9 KW

 Amps Output At 208 Volts: 13924 / 280 = 67 Amps At 240 Volts: 13924 / 240 = 58 Amps

Now that kind of power will float you boat.  It won't allow you to run the air conditioner, the hot water heater, all 4 eyes on the stove, the oven, the dish washer, the cloths washer, and the dryer at the same time. But hey, lets not be stingy now!

One more short example without all the math.  A friend owns an old Grist Mill on a small river with a 30 foot head & he can put 35 CFS through his old Francis Turbine.  That's 94 HP capable of producing 70KW ( 338 Amps @ 208 Volts)  That's some serious power now.  That's becoming your own power company, supplying your close friends with cheap electricity or selling power to the power company. More on that last part later.

Now that you have a little better understanding of hydraulics it time to throw some monkey wrenches into the works with a few flies in the ointment to keep you own your toes.  These are Speed Regulation and Waterhammer.