Harvesting energy

Harvesting is a seasonal affair.  Whether the crop be potatoes, apples or kWh's, there is a season when the bulk of the crop is gathered in.  For my Powerspout the season for harvesting most kWh's is now showing signs of tailing off.

In the past seven days, I have seen the energy generated fall from its maximum of 18.86 to 13.82 kWh's per day, these figures representing the energy yield when instantaneous power is 786 and 576 watts respectively.

To track the diminishing water as tightly as possible requires having a series of nozzles of different sizes: - the available flow is steadily diminishing in a linear fashion but reducing the flow to the turbine necessarily has to follow a step-wise pattern as successively smaller nozzles are employed. 

The way I operate my Powerspout is to have a small nozzle at the top position and a large one at the bottom.  The top one delivers just 0.3 l/s and I never change this one, only turning it on or off.  The bottom nozzle delivers most of the flow and is always on. It has to be changed when in-flow to the header tank falls to be less than the nozzle's delivery rate.  

The difference in size of the orifices is really quite small, - just a difference in diameter amounting to fractions of a millimetre as the picture below shows.  

The nozzle I'm using at the moment is the one missing from the line up above: nozzle X; it's in the bottom position with the top, small nozzle turned off. Here it is in operation this morning, delivering 2.13 l/s and putting 576 watts into the grid:

As I go down through the nozzles, I'm measuring the speed of the turbine at each flow to see how far off the 'sweet spot' speed ( i.e. the optimum speed) the pelton is operating at:

The theoretical optimum speed* for my installation is 1200 rpm near enough, so with the rpm being 924, the operating rpm is 23% below optimum speed.  As discussed in an earlier post, whilst this is not ideal, neither is it as bad as it might seem.  The efficiency of the pelton in converting pressure energy into rotational energy is probably only diminished by 5% by operating at this slower than optimum speed, and this 5% loss of efficiency translates into a loss of about 30 watts, or 0.72 kWh in a day.  I think I can live with that though it would be nice to think of a work around to improve things.

Whilst the harvest of kWh's from hydro generation seems to be ending its season, the good news is that the harvest from solar panels is just starting.  I look forward to seeing how well the two blend their respective outputs and will report the outcome at the end of the year.

* to calculate theoretical optimum speed: 
1. calculate jet velocity (m/s): Vjet = 0.96√(2g x Hnet)
2. calculate optimum runner velocity at pcd (m/s): Vpcd = 0.46 x Vjet
3. optimum speed (rpm) = (Vpcd / 0.69**) x 60

So for my installation: 
Vjet = 0.96 x √(2 x 9.81 x 53) = 30.96 m/s
Vpcd = 0.46 x 30.96 = 14.24 m/s
optimum speed = (14.24 / 0.69) x 60 = 1238 rpm

** the pcd (pitch circle diameter) of a Powerspout pelton is 220mm; 0.69 is the circumference, in metres, of the circle having a diameter of 0.22m.