Computing Water Power
Once you’ve determined Net Head and Design Flow, you can begin to estimate the power output from your hydro system. These computations are only rough estimates; consult with your turbine supplier for more accurate projections.
We begin by computing the theoretical power output from your water, before taking into consideration any efficiency losses in the turbine, drive system, and generator.
You can compute the Theoretical Power of your water supply as either Horsepower or Kilowatts using one of these formulas:
Theoretical Horsepower* (HP) = HEAD (feet) x FLOW (cfs)
Theoretical Kilowatts* (kW) = HEAD (feet) x FLOW (cfs)
* Note that these are Theoretical Power equations, which do not account for the inevitable efficiency losses that will occur at various points within your hydro system. The actual power output of your generator will be less, as we’ll discuss later.
A stream in New Zealand has 100 feet of HEAD, with 2 cubic feet per second (cfs) of FLOW. Applying our formula, we find that we should have about 17 theoretical kW available:
kW = 100 (feet) x 2 (cfs) = 16.93 Theoretical Kilowatts*
As you can see, both HEAD and FLOW have a linear effect on power. Double the head, and power doubles. Double the flow, and power doubles.
Also keep in mind that HEAD will remain constant once your system is installed; you can count on it year-round. It is also the least expensive way to increase power generation because it has minimal affect on turbine size. In contrast, FLOW will likely change over the course of a year, and it may not be cost-effective to size your hydro system for maximum, flood-level Flow. Always maximize Head, and work with your turbine supplier to determine the most practical Design Flow.
Accuracy is important! The design of your turbine revolves around your measurements of Head and Flow, and errors will directly impact the efficiency of your system. Take the time to measure Head and Flow accurately before you begin to evaluate hydro system components.
As noted earlier, the Theoretical Power calculations shown above represent a theoretical maximum, and the actual power output from your hydro system will be substantially less. In addition to the pipeline losses discussed earlier, small amounts of power will be lost through friction within the turbine, drive system, generator, and transmission lines.
Although some efficiency losses are inevitable, don’t underestimate the importance of good design. Efficient systems produce greater power output, often at a lower cost-per-watt. For example, a turbine system that is carefully matched to your Head and Flow may not cost any more than a less suitable design, but produce much greater efficiency. Other improvements, such as larger pipeline diameter or a better drive system, may yield enough added power to justify their higher cost.
Because of the many variables in system design, it is impossible to estimate efficiency without first knowing your Head and Flow. As a general guideline, however, you can expect a home-sized system generating direct AC power to operate at about 60% - 70% “water-to-wire” efficiency (measured between turbine input and generator output). Larger utility systems offer much better efficiencies. Smaller DC systems generally have lower efficiencies.
If you have accurate measurements for your Head and Flow, your turbine supplier should be able to provide some preliminary estimates of efficiency, as well as ideas for optimization.
The last important measurement is the length of your transmission line between your generator and the point of electrical usage. As with your pipeline, you can simply measure the distance along the route you plan to run your wiring.
Transmission lines are a lot like pipelines. Instead of moving water, they move electrical current, but the same fundamentals of friction losses apply. Longer transmission lines, smaller wires, and higher current all contribute to power loss through friction. You can minimize these losses, but the power you can actually use will always be somewhat less than what your generator is producing.
Power loss over transmission lines is most evident by a drop in voltage. As you use more power, you'll see the voltage drop and lights glow dimmer.
There are three ways to reduce, or compensate for, transmission line losses:
1. Shorten the transmission line
2. Use a larger wire
3. Increase the voltage on the transmission line
Shorter lines and larger wires will reduce line losses for any system. For very long runs, it may be appropriate to boost the voltage (via a transformer) for transmission, and then reduce it back to normal (via another transformer) at the point of usage. Boosting the voltage reduces the current necessary to produce the same amount of power, allowing the use of smaller wires.
Your turbine supplier can help you determine the best approach.
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