2016 and the start of a new year, - but the science theory I write about in this entry dates from 1831. How true it is that we stand on the shoulders of the giants of former times.
In April 2015 I installed a tachometer, (which you can read about here) and ever since I've been measuring the Powerspout's rpm and dc voltage at different levels of power output.
Gathering this data has produced some interesting results which have helped me understand better how shaft speed and operating voltage* vary according to the power generated. In this post I want to write about what I've found, and to explain my understanding of the physics behind why the results are as they are.
I am not someone who is a little qualified to write about the matter, - I am not qualified to write about it at all ! - and so some may find my explanation incomplete and insufficiently technical. But others like me, trying to work it through for themselves might be helped by an attempt at a simple explanation. For the subject is complicated, and it gets more complicated the deeper you venture into it. Reasoning it all through carries a serious headache warning. You have been warned !
When operating voltage and rpm are plotted on the same graph against power output to grid, this is what the two plots look like:
This seems a strange finding. The first axiom of a pma (permanent magnet alternator) is that its voltage rises as the speed of rotation rises. What can be happening to make voltage rise more slowly?
When 'volts per rpm' (v/rpm**) is plotted at different levels of power output, this is what we find:
Note that the scale along the horizontal axis is the same as in the first graph. This allows us to say that over the same range of power as is depicted in the first graph, the v/rpm decreases.
Putting the findings of these two graphs together, as power increases we can conclude that: rpm increases, v/rpm decreases and the overall effect of the two together is an increase, albeit a modest one, in operating voltage.
The second axiom of a pma says that voltage is inversely proportional to load, ie voltage goes down as load goes up; having established that voltage (expressed as v/rpm) goes down as power increases, it should follow that load increases as power increases, which is to say: more power is more circuit load. Is this the case or have we violated the second axiom?
The way through to answering this is best reached by thinking about the current flowing in the pma stator coils as power increases.
When more water is made to strike the pelton (from having changed the nozzles for larger ones), the torque on the pelton is increased. This increase in torque translates through to the electrical side mostly as increased current flowing through the stator coils. We have to say 'mostly' because it is evident from the first graph that rpm increases too and that must mean some increase in voltage, but the main effect nevertheless is to increase current: more hydro power is more current.
Going back to the second axiom in its re-arranged form, it said "more power is more circuit load". Is this the same as saying "more power is more current ? - and the answer is "yes, it is", because load and current equate to each other. (load is resistance; more load is less resistance; less resistance (at constant voltage) is more current (Ohms Law): therefore more load equates to more current). The second axiom is thus seen to remain intact.
Why should v/rpm decrease as power output increases? It's because of an effect of the higher current flowing when hydro power is more, and that effect is of a magnetic field being created by the current as it passes through the coils of the stator. The field so created opposes the magnetic field which caused the current in the first place, - so it opposes the field created by the spinning magnets of the rotor. The opposing field induces a correspondingly opposing voltage in the coil, called a 'back voltage'***. And because the back voltage opposes the voltage induced by the rotor field, the 'net' voltage actually leaving the pma gets to be reduced.
Well, net voltage (= operating voltage) would be reduced if rpm remained constant. But as we saw above, rpm did not remain constant: it rose with increased power generation to make operating voltage go up, albeit modestly. So the unit we have to use to see that the 'net' voltage does indeed go down is the unit of v/rpm.
The laws of physics that describe these phenomena are Lenz's and Faraday's Laws. For those interested, they can be looked up under the links given, - although some descriptions I found quite difficult to follow because they usually talk about these effects in motors rather than generators. For me, working it out from observed data and relating it all specifically to a Powerspout, has been the way to greater understanding. But as I said at the start, there is much more to it than this basic run through.
They do say it's therapeutic to keep the older brain thinking !
*in an earlier version of this post I used the terms 'operating voltage' and 'MPPv' (maximum power point voltage) to be the same thing. But as Hugh has pointed out in a comment, if I am using a WindyBoy in turbine mode, the term MPPV is not correct: the mode does not seek a maximum power point. So I have dropped the term MPPV as of today: 27Jan 2016.
** v/rpm is simply obtained by dividing the value for MPPv at a given level of power output by the turbine rpm at that power level. The value for v/rpm in open circuit (Voc) is used to designate stators with different coil configurations. When measured in open circuit no current flows, so the v/rpm at Voc will be the highest v/rpm ever possible for that stator.
*** back voltage is more properly termed back electromotive force, or back emf.