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.

Rotor packing - the sequel

Early September and I'm well into the driest time of year.  In actual fact, there has been quite a bit of rain but at this time of year it does little to augment the flow from a spring, - which is the source for my Powerspout; I'm presently running on my second to smallest nozzle and generating 136 w into the grid; I've needed to install the reduced core (i.e. 18 pole) stator to achieve this output, something which I was hoping keeping with the 42 pole stator but using rotor packing would avoid.

Dropping down through my nozzle sizes in the past months has given plenty of scope to experiment with rotor packing at each flow level and collect data about its effects. I have written before of how it increases rpm and thereby keeps the pelton operating at nearer its 'sweet spot' speed; I thought this would make for better power output but reviewing all the data has cast doubt on such an assumption.

Below is the plot of watts output to grid vs dc operating voltage.  Remember I am using a WindyBoy inverter which does not use MPP tracking; it simply draws a current from the turbine which is determined by the dc operating voltage; the magnitude of that dc current is reflected in the ac watts output to grid (LH vertical axis); the dc operating voltage varies with the flow delivered to the pelton (horizontal axis).  The plot shows a polynomial curve on which all the data points sit with remarkably little spread. This was something of a surprise.

It was a surprise because the data points were the result of very different operating states for the turbine; some were with rotor packing and some were not.

For each of the data points on the graph above, I also measured rpm; and for the data points arising from the lower flows, I used rotor packing to keep rpm up to above 900.
With rpm data superimposed on the above graph, using the RH vertical axis for rpm, this is the picture:

As can be seen, for those data points where rpm was kept above 900 by rotor packing, there seems to have been no obvious improvement in ac watts over the trend established by there being no packing. 

But perhaps I'm being unduly negative; perhaps without rotor packing the polynomial curve would have been a straight line relationship between dc volts and ac watts, making for less output than I actually got at the low end of the plot.

What counts for me is that to the eye and the ear the turbine undoubtedly appears happier with rotor packing.  I will continue with it.

Sun and water

The end of August sees the completion of the first full year of having both hydro and solar generation being harvested here where I live. In this brief post, I want to present the data.

The synergy of solar with hydro is well recognised: of benefiting from hydro in winter and solar in summer; so the pattern of yield for the two as seen in the graphs below comes as no surprise.

In the UK, the total amount of generation that can be contributed to the grid at one meter point is restricted, and although my Powerspout could never generate at its maximum at a time of the year when the solar panels were also generating at their maximum, the sizing of the solar array had to be limited to keep the sum of their peak outputs within the permitted total.

For this reason the array is less than the maximum normally allowed; it is a 3.42 kWp installation and its yield is reduced by being in a location which is not ideal, facing east-south-east (S60degE), on a roof pitch which is rather flat (30deg).

Nevertheless it does the job nicely of keeping the energy generated each month in summer up to the peaks the Powerspout reaches in winter.  Totalled over a full year the hydro generates more which, considering its design rating is just 0.75 kW vs the 3.42 kW of the PV, says much for how productive small hydros working 24/7 can be.

A finishing thought: the sun does it all ! - energy from the sun is the source of both solar and hydro generation; were it not for the sun taking water as vapour from sea level up to the sky so it can drop on the hilltops as rain, not a hydro installation in the world could work.

A post script to my last blog post: I have had much interaction with NRW since writing about my 'grievances', all of it good and positive.  Having been decidedly critical in that post, I just want to put on record my thanks and appreciation to all those, from the member of the board downwards, who tolerated with good grace what I wrote and are looking into some of the points I raised. Diolch yn fawr.