Asset Earning Potential

A big business thinking of building a new manufacturing plant or purchasing a new bit of equipment, will want to know what the earning potential for the new venture is. In no less a way, someone putting in a small hydro will want to know what the earning potential is and whether it makes financial sense to install it.

In big business, working out 'asset earning potential' is relatively easy because costs and benefits can be estimated.  But for hydro it's not so straight forward; there is the imponderable of Mother Nature: - years will be wet or dry, some very wet and some very dry.

Is it possible to bring systematic thinking to 'asset earning potential' under such circumstances ?

Some years back I heard a talk about the subject. It was given by Kieron Hanson who is a director of Hydroplan, an engineering and consultancy company installing hydros throughout the UK.  In his talk he put up this slide, headed AAEP, which stands for Annual Asset Earning Potential:

• What it depicts (insofar as I remember his talk) is this:
• for a hydro, there is a central value for AAEP which will be the average income, calculated over several years, that the hydro brings in
• to factor in the normal variation in rainfall this AAEP will have an "upside" error band and a "downside" error band indicating the extent to which income will be affected by wet and dry years
• the upside wetter years can be 12% above AAEP whilst the downside drier years 34% below 
• exceptionally, years may be very wet or very dry leading to a greater variation from the AAEP central estimate than is seen in usual years
• these exceptional years can increase income if the year is wet by 21 to 34 % above central AAEP but decrease it if the year is dry by 26 to 34 %. (where he quotes percentages, I'm not sure how they were arrived at).

So much for the theory.  Does it seem to apply in practice  ?

For my small hydro, rather than taking earning potential in money, I've looked at it simply as kWh's of energy generated; doing so avoids needing to 'monetise' the energy generated and therefore avoids thinking about feed-in tariff, and avoids also the monetary value of the saving being made by not importing grid energy, which is tricky to calculate.

For my scheme, the central AAEP in kWh's over the past 6 years has been 3575; the highest figure for generation has been 4083 and this gives an upside error band of 14%; the lowest generation figure has been 2773, giving a downside error band of 22%.  So my generation figures tie in quite nicely with what Mr Hanson's slide showed, - broadly similar upside and downside error bands compared to his predictions.

So far no year for which I have a full data set has been exceptionally wet or exceptionally dry. But the current year just started (my years run Oct 1st to Sep 30th) is looking very much as if it might be an exceptional year; the start is proving to be very wet. Here is the graph of cumulative kWh's generated, with the current year shown by the black line; I am updating it each month after having written this post:

It can be seen that the trajectory of the line is hugely different from any previous year. If it proves to follow the rule of the slide and be 34% over AAEP, the total for the whole year should come in at 4790 kWh. (note added 1st Oct 2020: as the graph shows, the total came in at 5133 kWh, 44% over AAEP).

Does any of this help with deciding if a hydro is worthwhile ? - not really ! But it should make one cautious about proceeding with a scheme on the basis of a single year such as this present one; such a year would give a false impression of how productive a scheme might be and make a borderline scheme have the appearance of being worthwhile when in truth for most years it may not be.

6 years of output data

With September coming to an end, another 12 months of data is complete to illustrate how my Powerspout has performed.  Happily, it has been a good year with total energy generated as good as the best of the previous years.
Below are three plots showing:

1. output on a day to day basis between October of one year and September of the following year, covering the past 6 years
2. cumulative output through the same 12 month period for the past 6 years
3. the total number of days in each 12 month period that a given output was achieved, also for the past 6 years

In each plot, the 2018-19 year is represented by a black line and previous years by coloured lines.

1

2

3

Cutting an in-between nozzle

In Wales, September and October is when water supply is at its lowest.  It's the time when the water available to my Powerspout is diminishing steadily. 

Such is the series of nozzles I use that as water supply decreases, a step change happens in the amount of water delivered to the turbine every time I put in a nozzle with a smaller orifice.  

But the rate at which the autumn decrease in flow occurs is steady and leisurely, and sometimes the change between two nozzles in my series is too great, - the system gets to miss out on some of the flow of water even though it is there for the taking. It is for this reason I have found myself needing to cut a nozzle which is an 'in-between' size, in-between the size of two existing nozzles. 

The challenge facing me was twofold: first to decide what orifice diameter would deliver the in-between size I was aiming for, and second how to cut that size precisely.

To resolve the first, I needed to understand the relationship between orifice size and flow. Clearly, head pressure determines how much water passes through an orifice, but when considering a single installation, head pressure will remain the same for all sizes of orifice and so doesn't enter into the relationship.**

This leaves orifice size and flow being the only two variables, and knowing these for all the nozzles I use, I plotted one against the other to get the graph below. The mathematical formula defining the relationship of flow (y axis) to orifice diameter (x axis) is conveniently given by the Excel graphing program:

The two red arrows mark the positions of the two nozzles between which there was too big a step, - I needed to cut a nozzle which was as near as possible midway between them, and that would be a nozzle having an orifice of 5.7 mm, giving a flow of 0.73 litres / sec. 

So far so good !

But cutting the nozzle to the required size was not easy.  I do this job on a wood lathe (see here) and if you take off too much the orifice is too big. For this reason my first effort failed and the second almost ended the same way.  In the end, I had to be content with a diameter of 5.8 mm which, according to the graph, will deliver 0.75 l/s. It's the point on the graph marked with a blue arrow.

You might think that such precision in trying to cut a nozzle to an accuracy of 1/10 of a millimetre is over the top, - and you're probably right ! But this 'in between' nozzle will probably be the right one to use for the next 2-3 weeks until the steadily diminishing flow eventually makes it too big to use.  My reckoning is that the extra kWh's of generation it will make possible in that 2-3 weeks, as compared with the smaller nozzle I would have had to use, will make the exercise worthwhile.

Time will tell.

Noted added later: to my surprise, the rains came early; instead of flow diminishing, it started picking up; so the in-between nozzle only found itself in use for 10 days.

**  Head pressure can drop with higher flows if the penstock has too small a bore but having a generously sized penstock and with the meagre flows my turbine takes, head pressure can be taken as constant.
Note that the plot will only be true for sites having the same head as mine, i.e. 53 m, and will not be correct for a site with a different head.

Fine tuning

Summer dryness is making itself felt here and today I've made the change I make every year at about this time, - changing the 42 pole stator to the reduced version which has only 18 poles*.  The effects of doing this were two:

1. the rpm of the turbine increased from 793 to 885; this makes the efficiency at which the pelton converts hydraulic power to shaft power rather better (my optimum pelton speed is about 1000 rpm)
2. the rotor, which had to be packed off maximally to keep the rpm up to 793 with the 42 pole stator, could now not be packed off at all; this makes magnetic flux linkage between stator windings and rotating magnets better and so improves the efficiency of the alternator.

The benefit of these two efficiency improvements are apparent in the record of the turbine's output to the grid.  The output can be seen to have been lifted from 206 to 227 W.

OK, so it's not a huge increase in output, - just half a kWh per day.  But I needed to do the change so that as flows decrease further, I have the Smart drive set up for the coming weeks as I go down through my nozzle sizes.  As you can see from the output record, it only took 30 mins to do.

*see here and here to read about the reduced core stator

Measuring nozzle Cd

EcoInnovation, the company in New Zealand making Powerspout turbines, has developed a new jet nozzle.  It's longer and more tapered than the original and the change in design slightly changes the way the nozzle performs.  There is a theoretical flow an ideal nozzle will deliver which is dependant on the orifice size and the pressure head.  However in the real world the actual flow is less than the ideal by what is called the Discharge Coefficient (CD), and it was the CD  for the new nozzle which needed to be measured.  This is how it was done.

1. The formula* for determining CD requires net head to be known, - net head being the water pressure at the entry to the nozzle when it is operating.  The very large pressure gauge in the picture, calibrated in metres head of water, provided the means for measuring it.  Plumbing it to the manifold required the temporary removal of the upper pelton jet.

2. The formula also requires the flow through the nozzle to be known. This was determined by measuring with a stop watch the time it took for a defined volume of water to pass through the orifice.  This defined volume was 429.5 litres. It was known to be this because a drop in water level in the header tank of 104 mm could be calculated to be equal to this volume.  The height drop of 104 mm was determined by two knitting needles set exactly with their points that distance apart. The stop watch was started when the surface tension 'grab' to the upper needle was broken and was stopped when broken again at the bottom needle. The inflow of water to the header tank was diverted while each measurement was made.  The measurement time varied between 131s for the nozzle with the largest orifice and 20m 11s for the smallest.

3. For 13 nozzles with different sized orifices, paired sets of net head and flow measurements were obtained. The Discharge Coefficient for each nozzle was then calculated and the results, with the flow for each nozzle, plotted in MS Excel:

4. As can be seen, the Discharge Coefficient is not the same for all sizes of nozzle.  For the smallest size, nozzle I, where the flow is least, the CD is close to unity** indicating that actual flow is the same as would be expected from an ideal nozzle.  But as orifice size increases, the CD falls.  

5. The new type of nozzle performs better than the old.  Old nozzles had a mean CD of 0.85 whereas the new 0.90.  

6.The value of Discharge Coefficient for a nozzle depends on the pressure difference between the pressure of water entering the nozzle and the pressure once it has left through the orifice.  So although on my site (which has a pressure head of between 51.5 and 53.6 m depending on flow) the CD has been measured as indicated above, the same nozzle on another site with a different pressure head will have a different CD, though it won't be greatly different .

* Q = CD x Anoz x Sqrt (2g x Hnet) whence CD = Q / (Anoz x Sqrt (2g x Hnet))

** The result obtained was 1.01, i.e. better than unity, which is not possible and represents experimental error.

Stopping water entry

I've been experimenting recently with trying to stop wetness from the pelton side of the turbine creating dampness on the alternator side. There's a seal around the shaft which should prevent water in any quantity getting across but an investigation I've done using bags of silica gel indicates that in spite of the seal about 300mls per month still gets across.

These photos tell the story of the sequence of steps I've taken:

1. Limescale deposits on the shaft indicated that a considerable amount of water enters the top-hat labyrinth chamber

2. A V-ring seal (purchased here) was mounted on the shaft; the seal turns with the shaft and its lip seals against the plastic face of the top-hat, with the idea of preventing water tracking alongside the shaft

3. Inspection after 3 weeks running showed the seal had badly scored the plastic face of the top-hat, presumably from softening of the plastic by the heat of frictional contact, - I must have applied it too tight to the face.

4. A friend who is skilled on his metal lathe kindly turned a stainless steel cap to fit over the plastic top-hat so the seal rubbed on metal; the cap is held on only by being a tight fit.

5. Suspecting that water might also enter the top-hat via its drain hole, a deflector was devised to shield the hole from the upward direction of water leaving the pelton from the lower jet.

6. So the complete arrangement as it is at the moment looks like this:

Only time will tell if it makes any difference.  The early signs are that the silica gel bags do seem to be taking up less water but I'm yet to be convinced this is a genuine observation.

Whilst I was working through these stages of development, EcoInnovation have come up with a slightly different approach:

Theirs is a neater solution but care will be needed not to apply the V ring seal too tightly against the face of the top-hat.  The seal only needs to just touch. After observing the scoring illustrated above, a new top hat with the seal just touching ran for 3 weeks with not even a mark being caused.  A smear of grease is also a good idea.