More thoughts about inverters, power, speed and operating voltage.

Sometimes a writer writes just to get something off his chest.  Nothing could be more true of this blog post.  
I've still been mulling over the matter of understanding what is going on when my Powerspout generates electricity: 

• Why does it settle at a particular speed; 
• Why does the operating voltage settle at a particular point; 
• Why do speed and operating voltage change with different levels of power output; 
• How does the inverter control the output of the alternator; 
• How does the inverter have an effect on the speed of the pelton; 
• How significant is it if the system is not operating at the "sweet spot" speed.

If these are not questions that have ever kept you awake at night, this post is not for you.  Skip it and I'll try to write something more engaging next time.

For those as seriously obsessed as I find myself to be, see if you can follow my line of thought below.  I must give full credit to Hugh Piggott at Scoraig Wind for his corrections of my earlier efforts to articulate understanding in these matters, and by his corrections leading me on to a more clear-headed grasp; and also to "Flux" who writes on the Fieldlines discussion board and who has been giving me personal tuition to improve my comprehension.  These credits mentioned, any errors or plain wrong reasoning below are entirely mine.

1. A Powerspout in operation is a system in steady state; the speed is steady; the operating voltage is steady; the power output is steady.
2. The steadiness of this steady state happens because the energy available for conversion to electricity is un-altering; it is un-altering because for a water turbine having fixed nozzles, the flow does not change and neither does the net head.  
3. Fundamentally the steady state depends on an equilibrium being established between the torque output of the pelton and the torque requirement of the alternator.  
4. Not all the torque output of the turbine is available for generation of electricity.  Some is taken up in overcoming rolling resistance in bearings and some in overcoming ‘windage’: - the loss incurred as the pelton turns through the fog of spray inside the pelton housing, but since these losses are constant, the balance available to the alternator remains constant.
5. For an alternator whose output is fed to a grid tied inverter, this torque equilibrium demands that the alternator’s torque requirement be manipulated until it matches the torque available from the pelton, or more precisely that it matches the torque left over for the generation of electricity after bearing and windage losses are subtracted.
6. Such manipulation is carried out by an algorithm within the inverter. The algorithm can be either one which seeks the maximum power point (mppt mode) or one which ‘commands’ how much current is drawn from the alternator by reference to the voltage the alternator is producing (table mode). 
7. Whichever mode is employed, manipulation of the alternator torque is not without effects on the torque output and rotational speed of the pelton: the manipulation  actually changes that which it is trying to match. This comes about, not because of any change in the basic parameters, flow and head, which are respectively the primary determinants of torque and speed, but because the efficiency of the pelton in converting flow and head into useful torque is optimal at a certain rotational speed.  When the alternator imposes load on the pelton it changes the pelton's rotational speed, and this change, by moving the speed away from (or towards) the optimum speed, in other words improving or degrading the pelton’s efficiency, will have the effect of changing the pelton’s torque output.
8. So the steadiness of the steady state comes about by being the end point of a process of accommodation, between on the one side the alternator functioning under the influence of the inverter, and on the other side the pelton, which itself is ever responding to changes in the alternator. In effect there is a continuously operating feed back loop which comes eventually to settle at a point giving constant speed, constant voltage and constant power output.
9. The time it takes to reach this point varies depending which algorithm the inverter is using: mppt mode can take tens of minutes, much depending on the make of inverter, whilst turbine mode takes less than a minute.
10. Apart from the time  factor, another difference between the modes is that the point at which mppt mode settles should be the point where the rotational speed of the pelton is optimal.  It should truly be the ‘sweet spot’ for the system. Why - because it should be, by definition, the maximum power point, the point at which pelton efficiency is greatest and most power is extracted from the system’s head and flow. 
11. But if the algorithm is table mode, there is no such expectation.  The steady state rpm may, and almost certainly will, settle at a figure which is off from the ideal speed and the effect of this will be to make the system as a whole less efficient: it will generate less into the grid than the prevailing flow and head are capable of.  It will not be operating at the ‘sweet spot’ speed.
12. Two things need to be said to qualify these last mentioned differences between the two modes, leading to a deduction from the second:                                                                                                 (i) MPPT mode was devised to extract maximum power from solar panels.  There is a huge gulf between manipulating voltage and current from a photo-diode and manipulating the same parameters from a rotating generator. The complexities which apply to a pma alternator when it comes under load make it very different from a photo-diode, such that it may not be the case that the true maximum power point gets to be identified. Bench tests done by EcoInnovation do, however, lend support to mppt mode seeming to function with a pma in a satisfactory way.         (ii) The apparent draw back of table mode settling on a rotational speed which is not optimal may not be as dire as it might seem.  The fall-off in efficiency for a pelton turbine operating either above or below its optimum speed is not great: just a 3% fall in efficiency for operating 15% away from its optimum speed. So if the equilibrium point settles where operating speed is not further away than +/-15%, the loss in generating capacity will be slight. There will still only be a loss of 5% of attainable power when operating speed is 25% below optimal speed.
13. The deduction from this last point is that the one power curve programmed into a table mode inverter can probably be used to control turbine speed across a range of flows, without as has been suggested, the need to program in a new curve for each new flow regime.  As long as the output voltage of the pma falls broadly within the range of input voltage that the inverter is programmed to expect, the one power curve will cope with a range of flows albeit by fixing rotational speed differently for different flows.  So long as the different speeds are within + 15% and - 25% of optimal speed, the result will be acceptable.
14. Ensuring that the output voltage of the pma falls broadly within the range expected by the inverter is not an issue: it is the purpose of the EcoInnovation calculator tool to predict what the optimal rotational speed will be for a pelton at a site with a given head, and then to suggest which SmartDrive stators will give an output voltage of a chosen value at that rotational speed.

Well, that's got that off my chest: where I am at the moment in my understanding. But it could all change in the future ! 

For any one reading this far and wanting more, there is a description in the comments section following this earlier post, of what happens in a permanent magnet alternator to make the voltage rise as power output increases be less than would be expected from the increase in operating rpm; the piece includes definitions of the various terms used to describe the effects seen.