It's a J shaped curve.

The aim of this post is to say a bit more about the efficiency of my installation: in particular how the efficiency changes depending upon the flow delivered to the pelton.

In two earlier posts, mention has already been made that overall efficiency turned out to be 50% when water delivered to the pelton was 2.7 lps, and the efficiency dropped from this figure when flow was less than 2.7 lps, mostly due to inefficiencies attributable to the inverter.

Here, I want to show the relationship between efficiency and flow over the full range of flows I have used on my turbine, from under 1lps to the design flow of 3 lps.

Instead of using a numerical value for efficiency, eg 0.5 or 50%, as is usual, I have used instead a unit which is a direct indicator of overall efficiency: the volume of water required to generate one kWh.  This has the unit m³/kWh and is a measurement which I record anyway for the paper return I have to make yearly to Natural Resources Wales (NRW) to tell them how much water I've abstracted.  It's what they call the 'hydro abstraction factor' (HAF) and permits calculation of the volume abstracted simply by multiplying it by the number of kWh's generated.

It is a factor which is easily measured with a fair degree of accuracy: 

• flow rate from the sizes of the nozzles and the net head
• kWh's from the Elster generation meter (reads to 0.1 kWh)
• time from a digital, radio controlled clock with readings taken over a minimum of 24 hrs.

So here is the graph showing the relationship between flow and m³/kWh:

As can be seen, it turns out to be a J shaped curve with optimum efficiency occurring when flow delivered is just under 2.5 lps.

Why should the curve be shaped like this ?  The explanation for the fall in efficiency at flows below 2.5 lps, to the left side of the curve, has already been alluded to in earlier posts: factors intrinsic to the inverter and, at the lowest flows where system voltage rises towards 380 v dc, the onset of power dumping to the heater element within the turbine, which is triggered at that voltage.

As for the fall in efficiency on the right side of the curve with flows higher than the optimal 2.5 lps, the most likely explanation is the 'drag' imposed on the pelton runner from the spray created in the turbine casing by the extra water, - something the text books call 'windage'.

Does any of this have any practical application ? - well yes, it does:  NRW instruct that in working out one's abstraction return, the 'hydro abstraction factor' at Pmax must be used, ie at maximum power output.  For my installation, as can be seen from the plot, this would be 14.5 m³/kWh.  But the optimum point, which is the point on the graph where the installation will be operating for most of each 'water year', the HAF is nearer to 13.5 m³/kWh.

... and that is the figure I'll be using, rounded down to 13 m³/kWh, so as to be sure of keeping my abstraction return for the year as low as possible and within the limit imposed by my licence (49,982 m³).

49,982 m³  ! - it does make you wonder if the people who issue these licences stating such ridiculously specific volumes understand the limitations of the means which will be used to measure said volume.