Update on output & more on temperature effect

Just a couple of light weight matters to post in this diary entry.  I call them light weight to mark them as more easy to follow than the heavy weight stuff discussed in the last entry and in the "Thoughts about Inverters" entry further back.  
Much useful discussion resulted from those posts, only some of it in the comments section after them. I'm still working to understand it all and perhaps will post about it if I can get my newly found understanding into an intelligible form. The comment which encouraged me most (which was not published), came from someone who really understands motors and generators when he said, after giving as lucid an account as anyone could give: "I hope this makes some sense, there are few explanations that make any reasonable attempt to explain what is really happening in an alternator as you load it", - my thoughts entirely.

So the light weight matters are:

1. Generation so far this year.
It has been extraordinarily wet here in Wales, (UK) and the Powerspout has had an uninterrupted spell at full power since 1st Dec.  This, together with it generating 30 watts more for the same flow than in previous years, has seen the record of energy generated outstrip previous years; long may it continue!

2. Confirmation of temperature effect on generation.
Early in January we had a brief period of cold weather.  Night time temperature dropped to below freezing for a few nights making the temperature inside the SmartDrive housing 19.4 deg C. Compared to the normal operating temperature of about 26-29 deg C, it was thus some 7 to 10 degrees cooler than usual.  As the records of power output below show, power increased by 15 watts when it was colder, confirming my earlier observation.

Both these records were with a de-finned rotor.  The aim of de-finning was to reduce energy lost to the extra work of revolving a finned rotor. But de-finning necessarily reduces ventilation and thereby raises temperature.  Since raising the temperature clearly reduces power, it has to be wondered whether de-finning gains anything at all.  When I looked at this a while back, the gain from de-finning was only 1 to 2 watts but no consideration was given in that study to holding temperature constant. 

So there's another research project in the making ! 

The relationship between power, speed and voltage.

Note added after this post was published: the comments section at the end corrects some of what I write below.

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, - Faraday and Lenz.

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:

Take note that the scales on the two vertical axes, rpm and dc volts, are numerically the same. Because the scales are the same, we can make an observation, a valid one, about the slopes of the two plots: the slopes are not the same.  To put it another way, operating voltage does not increase proportionately with rpm. 

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 operating voltage 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.