Sizing turbine to stream

In the planning stages of implementing a small hydro scheme, one of the biggest challenges is to decide what power the flow in the stream will support.  To put in a scheme which under-utilises the available flow is to save money. But it will create a lingering feeling of not making the most of the resource which is available; and having installed too small a scheme, up-sizing is not something easily done at a later time.  Conversely, to put in a scheme which is over-sized such that full power is realised only for a small part of each year, wastes money; what is spent on the cost of a bigger machine, bigger penstock and bigger pretty well everything won't see a commensurately bigger return.

So how does one hit upon the right balance?  

The first thing to know with as much accuracy as possible is the flow in the stream and how this varies through the seasons of a year. Even when you think you have this knowledge however, there is a caveat. By whatever means this knowledge is gained it will not be information that can be wholly relied upon: - year to year changes in wetness happen, and climate change may introduce longer term changes too. "Past performance is not a reliable guide to future returns" is an epithet often applied to financial investments; it applies in hydrology too.

In the previous diary entry, I mentioned that it is possible to purchase information about the flow in any river or stream in the UK, made available in the form of a flow duration curve (FDC); that the accuracy of such a computer generated FDC is questionable for the smallest streams of the kind where a Powerspout is likely to be used; and that purchase is expensive. But purchasing knowledge is one way of getting the knowledge you need about your stream's flow.

An alternative way which is cheap but time consuming is to measure flows oneself; this is what I did: every week for a year I measured the time it took to fill a coal scuttle thrust into the flow at a point where the entire flow fell freely over a rock face and I had arranged for it to discharge from a pipe: 

Not being able to hold a stop watch at the same time as holding the coal scuttle, I simply counted the seconds it took to fill its 10 litre capacity.  The method was probably not very accurate but it gave data which was useable to make the following plot:

Once gathered, this time-sequenced data can be manipulated; such manipulation is how an FDC is constructed. Instead of showing what flow was present in each week, an FDC shows the length of time (i.e.duration of time, expressed as a percent of the recording period) specified flows were equalled or exceeded. There is a lot of number crunching which goes into creating an FDC and it needs to be done using a spreadsheet programme such as Microsoft Excel. The easy to follow description of how to do it which I gave before is given again in this link.  

Once constructed, an FDC is useful because it begins to indicate what size of turbine might be suitable for the flows in the stream.  But it only begins to give an idea; many are the factors which massage the actual flow figure that can be used, foremost of which is the amount of flow the regulatory body in your country will allow you to take.


For the flows I measured in my stream, this is the flow duration curve I constructed; on it I have marked a point which is called Qmean*. As can be seen it is at a flow of 1.86 l/s, a flow which is equalled or exceeded, on aggregate**, for 39% of the year. But, and it is an important but, - 1.86 l/s was the Qmean only in the year in which I took the flow measurements. This one year will not necessarily be predictive for future years and as we will see below, it wasn't.

Qmean is an important term to comprehend; the value of it for your stream is a good first-off guesstimate of the size of turbine that suits your site; a rough rule of thumb is that the Qmean value, or a flow close to it, will be the flow to use in your calculations of the maximum power the installation will be capable of producing. Although flows higher than the Qmean flow will be present during the course of a year, experience shows that sizing the installation to the Qmean flow gives a good compromise between being able to use the higher flows of winter and also the lower flows of the drier months.

The way to calculate Qmean depends on the way you do it.  If you have a series of flow measurements taken at equal intervals over a period of time***, then Qmean is straightforward; it is simply the arithmetic mean (sum of flows divided by number of measurements).  But if you have a flow duration curve without actual flow measurements, say because you have purchased it, then Qmean is the point where the area under the curve to the left of the Qmean point equals the area under the curve to the right of it.  Determining this can be done by overlaying a grid on the curve and finding the point where the number of squares to the left of the point equals the number to the right. 

In terms of reliability, the weight that can be born by the figure for Qmean really depends on the way it is reached.  The figure given above for my stream,1.86 l/s, is not reliable; it was derived from measurements, not very precise measurements, taken only weekly, over only one year. To illustrate how unreliable it was, the plot below shows the FDC for that year, 2008/9, together with the FDC for the year just ended (2015/16); in the latter year, the flow measurements were calculated from power generated each day****; seen together, the two years give very different Qmean values: 2.43 l/s vs 1.86 l/s:

Only when the period upon which a flow duration curve is based is long enough to represent the long-term picture can the curve be considered reliable and begin to be used in a predictive way. Even this reliability will not be guaranteed if climate change is having an effect, for then even a historical long-term record will not hold true for the future.

To conclude and to emphasise the importance of Qmean, let me relate how abstraction is adjudicated here in Wales. Since the time, 3 years ago, when I applied for my abstraction licence, there has been a complete overhaul of the guidelines for the abstraction of water for micro-hydro. The new recommendations attach great importance to the value of the Qmean measurement; by relating it to the type of stream under consideration, a formula is employed which determines what amount of abstraction will be permitted.  The guidelines can be seen in full here (especially page 5) but in summary either Qmean or a small multiple of Qmean (a factor of 1.3) is set as the maximum flow which can be abstracted from a water course.

The change in the guidelines is a welcome simplification of what existed before; but the pivotal place given now to Qmean in fixing the size of the installation, and take note, fixing it so that future change can scarcely be considered, makes it a very important parameter to get right; the difficulty is that it's a parameter which doesn't lend itself easily to precision.

*Q is the symbol for flow; mean is the average; so Qmean is the point signifying average flow.

** by "on aggregate" it is meant that within the year the time where 1.86 l/s was equalled or exceeded in total came to 39% of the year; this 39% of the year will not be a continuous stretch of time during which 1.86 l/s was equalled or exceeded.

*** only complete years of flow measurements should be used and the records for partial years discarded; otherwise the flow data may be skewed by seasonal wet or dry periods.

****by using power data, the flow duration curve is 'capped' by the design flow of the turbine; the effect of this will be to under-estimate Qmean; in this year, Qmean would actually have been higher than 2.43 l/s.

Productivity viewed 3 ways

The ending of September brings to a close the 12 months I have chosen as my hydro 'accounting year', a period I have come to call a 'water year'.  In previous diary entries I've speculated as to whether I would reach the total I was hoping for of 4000 kWh; now the answer can be revealed !

There is an old saying which goes: "If you ask a man with a watch what the time is, he will tell you; but if you ask a man with two watches, he can't".  Something of the truth in this applies to my ability to reveal the answer; having two ways of measuring the energy total inevitably gives two different figures.

Below is a plot of the cumulative energy output of my turbine for the three water years it has been running; the data is captured automatically from the inverter; as can be seen it gives a total of 4,032 kWh:

But an inverter is not designed for the very accurate capture of data; there is an Elster energy meter also in the circuit which is more accurate, - as it must be for determining FIT payments on energy generated; and the total it gave was 4,168 kWh.

So, as the graph shows pictorially, even with its less than accurate total, the year just finished has exceeded both previous years.  A consequence will be that I'll probably exceed the amount of water I'm licensed to abstract in a twelve month period (it is calculated from the figure for energy generated); but since the accounting period for that twelve months is April 1st to March 31st, the matter will not arise until 2017.

Another way of presenting the data in the above graph is shown below.  Here, instead of plotting the cumulative total reached at each date, what is shown is the actual energy generated each day; this relationship gives an idea, not seen in the above graph, of the variation as the year's seasons come and go:

From this plot it will be seen that peak generation in 2015-16 (18.9 kWh/day) was higher than in the previous two years and also that generation continued throughout the water year, the first time this has been possible.  Both of these improvements resulted from gaining a better grasp of the science behind a Powerspout, the first by squeezing from the system a small improvement in efficiency and the second from using, in the drier months, a modified stator in the alternator.

The third and final way of looking at productivity is rather different from the above graphs but it uses exactly the same raw data.  People familiar with hydros are usually familiar with flow duration curves (FDC's), that type of curve called an exceedance curve which depicts what percent of a period of time, usually a year, a given flow in a watercourse is recorded as being present. 

These days, rather than measured flow data being used to construct an FDC, rainfall data and catchment area are used to compute the flow; computer calculated FDC's can be purchased for any watercourse in the UK, at a price, without the tedium of taking any actual measurements of flow; their accuracy is questionable, especially for the small streams a Powerspout might be installed on; yet the authorities responsible for licensing water abstraction in each of the national regions of the UK often insist on applicants providing them.

A curve called a power duration curve can be constructed in the same way as for an FDC but using power data rather than flow data.  Here is such a plot for the output of my turbine over the past three water years:

Such a plot is rather useful. Whilst it has all the same features evident in the two plots above, it shows in addition something not evident in those plots; it shows a characterisation of the annual flow in the watercourse, just as if it was a flow duration curve.  

For a site like mine where no 'hands off flow' is required, a provision which allows me to take as much flow as I can up to the design flow of the turbine, the shape of the power distribution curve will be almost identical to the flow distribution curve, at least in that part of the curve below the maximum power level. It will only be 'almost identical' for two reasons: because the system efficiency is reduced at very high and very low flows, thus making the relationship between output power and flow to be non-linear; and second because I don't always manage to take all the flow. But notwithstanding this limitation, it will be a far more accurate characterisation of stream flow than any FDC could possibly give, based as it is on daily electrical readings which are so much more precisely captured than water flow readings.

The usefulness of plotting a power duration curve each year will come over time.  If, as we are led to believe, Wales is going to get wetter as climate change happens, successive year plots layered over previous years should show clearly whether greater wetness is indeed happening.  It'll be a very, very, local investigation into the effects, if any, of global warming !

For anybody interested in learning how to construct exceedance curves, I found this pdf document on Phil Maher's Hydromatch site to be much the most helpful.