In this Lecture we will show why it is that the heat generated in a transformer core can be regenerated as electricity, now relying on that experimental evidence presented in Lecture No. 18. In this Lecture 19 some further evidence will also be drawn from the author's experimental research as reported in his Ph.D. thesis and in the author's papers published in the Proceedings of the Institution of Electrical Engineers. The prospect of exploiting such a regeneration phenomena is discussed and deemed viable.
Once it is suspected that the heat generated by magnetization loss in a transformer has a way of regenerating electricity it is logical to look at the physics governing thermoelectricity. In the transformer we do not have current circuits involving junctions between two metals. This rules out the Peltier and Seebeck Effects. The Thomson Effect is one discovered and reported by Lord Kelvin (then Professor William Thomson) in 1855. He showed that an EMF can be set up within a metal simply by there being a temperature gradient in that metal. In the transformer lamination we have such a temperature gradient owing to need for the heat to find an exit path. However there is no circuital EMF such as is needed to enhance eddy current flow and so the Thomson Effect does not account for regeneration. At best, owing to the Thomson Effect, there is an electric potential difference as between the middle section of a lamination and its edges. What we seek is some connection in a metal between EMF or electric current and a temperature gradient. Such an effect was discovered by H.W. Nernst and A. von Ettinghausen, Wied. Ann., v. 29, p. 343; 1886. We shall refer to this as the Nernst Effect, taking note that there is a complementary phenomenon known as the Ettinghausen Effect, the latter being the setting up of a temperature difference in a metal in a direction mutually orthogonal to a magnetic field and a flow of current. The Nernst Effect is the reciprocal phenomenon, namely the production of an EMF in a direction mutually orthogonal with respect to a magnetic field and a flow of heat through that field consequential upon there being a temperature gradient. We have such a situation in the core of a transformer.
Here I should have said that we have such a situation in the magnetic domains existing within that transformer core, meaning within those domains which happen to have their magnetic polarizations suitably orientated. The action of the magnetic field is to cause the heat flow in the plane of a transformer core lamination to develop a Nernst EMF across the thickness of the lamination, thereby encouraging the eddy currents in that lamination to flow selectively through those domains which generate a supporting EMF.
Note my use of the word 'generate' because what we have here is nothing less than the generation of electricity from heat and the action is not related to temperature as an absolute measure, but rather the difference of temperature effective in promoting heat flow by thermal conduction in metal.
Our 20th century eddy current anomaly can be explained simply by taking account of the Nernst Effect, which dates from 1886. It is difficult to believe our ignorance of this as being the true cause accounting for the mysterious loss of billions of dollars worth of electricity every year in power transformers.
Simply stated, the Nernst Effect converts heat into electricity and is very efficient in that action. Indeed, the conversion efficiency can but be 100%. The only problem is that of tapping the electric power generated before it dissipates itself as eddy currents in the metal. It is no wonder that what we see in our power transformers is simply that, the anomalous generation of heat owing to the enhancement of the eddy current action.
In order to understand a little better what I have just described, consider
the following Fig. 1.
To add further confirmation of this interpretation of the anomalous loss phenomenon, ask yourself what happens when a transformer core is d.c. biased, meaning that the magnetic polarization has displaced the hysteresis cycle towards core saturation. As mentioned in TEC III, if the bias is substantial, this will reduce hysteresis loss for a magnetization cycle having the same flux density range. However, if the flux change occurs at the same frequency and the voltage waveform is sinusoidal in form, there should, by standard teaching, be no change in the theoretical eddy current loss. Yet, what we have done is to set up a higher proportion of magnetic domains with their magnetic polarization in one direction than applies in the opposite direction. This reduces the scope for the Nernst Effect to be active in enhancing the bidirectional oscillation of those eddy currents and it will reduce the anomaly. In short, we should expect tests such as are confined to regions near magnetic saturation of the core to show very little anomaly.
This also means that even during the normal magnetization cycle, with no polarizing bias applied to the core, there will be strong enhancement of eddy current flow when the flux density is of low value but much reduced enhancement at high flux densities. Tests expressly conducted to see how the anomaly factor varies instantaneously as we progress around the whole of the B-H loop of the core should confirm this, if the Nernst Effect interpretation is correct.
I am able to report such confirmation because I made those tests long before I came to realize that it was the Nernst Effect that was causing the problem. The following Fig. 3 was in my paper entitled 'An Investigation of the Eddy-current Anomaly in a Low Silicon Sheet Steel', Proc. I.E.E., vol. 104C, pp. 2-7 (1957).
I had devised a technique for measuring the instantaneous loss anomaly factor
arising at different parts of the normal B-H magnetization loop. Fig. 3 shows
the mean loss anomaly factor, such as one would find by normal measurements.
Thus the sample tested had a mean loss anomaly factor of the order of 1.5, but
this reduced for magnetization over a cycle that ranged between the higher flux
densities. That is shown by the broken curve.
The full line curve, however, shows how the loss anomaly factor varied as the flux density climbed during the magnetization cycle. It dropped virtually to the zero anomaly level over the upper flux range where all the magnetic domains are polarized in a common direction.
The technique of measurement used for this purpose depended upon knowledge of the effective incremental permeability over the selected range, the sector selected for test having substantially linear permeability. However, the measurement of that permeability value had to be based on the analysis of the static hysteresis loop, meaning the B-H loop measured by fluxmeter tests at zero frequency rather than one involving a.c. activation. Assuming discrepancy between the measured permeability and that effective owing to a.c. excitation, it was appropriate to estimate a worst case scenario, one, however, which just cannot possibly prevail, just to see if it was at all possible to escape the evidence of that loss anomaly. That worst case adjustment is indicated by the arrows and the findings were clear that there was just no way of avoiding the acceptance of a significant anomalous energy loss. The eddy current anomaly is not something that is fortuitous in the sense that it can be attributed as a consequence of misinterpretation of the measurement data.
When an entirely different method of measurement was tried, one reported in my paper entitled 'The Eddy-Current Anomaly in Electrical Sheet Steel, Proc. I.E.E., vol. 103C, pp. 279-285 (1956), in this case restricting the measurement to instantaneous rate of loss as the magnetic flux traversed to zero flux density state in the B-H loop cycle, some quite substantial anomaly factors were measured.
A typical result, taken from Table I of that paper, applies to Superstalloy laminations having 4.3 Si composition, a lamination thickness of 0.309 mm and a specific resistivity of 59 microhm-cm. It was found that the instantaneous anomaly factor effective at zero B flux density was 4.81 when the B-H loop ranged up to a maximum flux density of 6,775 gauss, 5.22 for a loop having a maximum flux density of 10,250 gauss and 5.03 for one having a maximum flux density of 13,550 gauss.
An entirely different set of tests were performed on solid steel cores where higher frequencies were used to confine the cyclic magnetization to surface layers of the test specimen. These were based on the eddy current effects affecting the phase angle of the magnetizing current in relation to voltage. The action is tantamount to a time-lag effect which affects that phase angle. The hypothesis I was exploring was that hysteresis loss involves transient adjustment of magnetic flux as domain boundary walls move in abrupt steps when there is instability. I reasoned that, if the magnetizing current were to increase so fast that those transient adjustments did not occur at the trigger level of that current, as applied to the zero-frequency B-H magnetization cycle, then there would be added loss. It would, in effect, be a dynamic hysteresis loss, and I wondered if this could be the true cause of the eddy current anomaly.
So I did experiments with that in mind and the results are to be found in my paper Magnetic Time-Lag Effects in Solid Steel Cores, Proc. I.E.E., vol. 103C, pp. 272-278 (1956). Note that the measurements of such a time-lag effect do not tell us whether there is, in fact, a retardation in the magnetization process or whether there is an increase of eddy-currents owing to a reduction of electrical resistivity. Certainly, the thermoelectric effect discussed above should still be of consequence in tests using solid cylindrical steel cores, because the heat escapes radially and the currents flow circumferentially, with magnetic flux polarization being longitudinal. There was no doubt that the time-lags recorded were commensurate with those applicable to laminar core tests, but one vital fact did emerge. The time-lag reduced virtually to the minimal no-anomaly level when the core was polarized close to saturation, though still subject to sufficient oscillatory flux change for eddy-currents to be measurable and of significance.
In summary, my experimental research on the eddy-current anomaly gave results all of which were consistent with the thermoelectric regeneration interpretation, the interpretation which goes against the Second Law of Thermodynamics as having an governing influence upon the heat to electricity conversion.
At this stage it helps to do some quantitative evaluation. The suggestion is that the EMF set up across a flow path equal to the thickness of a sheet steel lamination (0.3mm) is sufficient to overwhelm the EMF set up around the whole eddy current circuital flow path in that transformer. The latter can easily be of the order of 0.05 volt in a moderately large power transformer. One then sees that the Nernst EMF per cm induced in that lamination has to be of the order of volts per cm and, taking the Nernst coefficient of iron at 10,000 gauss as 10.5 volts per cm, per degree C per cm, this really tells us that a temperature gradient of 0.1oC/cm will suffice to account for the eddy current anomaly factors observed. The magnetization loss need only be a few milliwatts per cc to sustain such a temperature gradient, which is consistent with the specification of loss properties of electrical sheet steel. Accordingly the theory does have quantitative support.
Before proceeding I will here comment on my objective in drawing attention to this topic. I believe one could build a solid-state device which will tap the thermal energy of the background environment and provide cooling in combination with electrical power generation. If we can do this we have breached the Second Law of Thermodynamics.
We are in these Web pages exclusively concerned with the physics which has eluded the scientific community at large. If what is presented here were merely a repetition of accepted knowledge as taught in academic institutions, the author would be enjoying his retirement in other ways, rather than striving to attract attention to what is here disclosed. It is a very daring pursuit to try to convince scientists in general that the Second Law of Thermodynamics can be breached to our advantage, but it is even more daring to declare that we can derive our power needs from the energy of the environment or that of the aether.
I am all too aware of the words of Sir Arthur Eddington which I have seen
quoted on page 639 of the book 'The Anthropic Cosmological Principle' by
John D. Barrow and Frank J. Tipler, as first published by Oxford University
Press in 1986 and reissued in 1996:
"The law that entropy always increases - the Second Law of Thermodynamics - holds, I think, the supreme position among the laws of physics. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations - then so much the worse for Maxwell's equations. If it is found to be contradicted by observation - well, these experimentalists do bungle things from time to time. But if your theory is found to be against the Second Law of Thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation."
I am now going to show why these words of Eddington should be ignored, but first I will quote one other item from that book just mentioned. It appears in the Introduction on page 5:
"The Holy Grail of modern physics is to explain why these numerical constants - quantities like the ratio of the proton and electron masses for example - have the particular numerical values they do. Although there has been significant progress towards this goal during the last few years we still have far to go in this quest."
Let me now ask you, the reader, a question. Suppose you set off in search of that Holy Grail. How do you proceed? There are only two routes to follow. Either you say that all the protons in the universe were created in the early phases of the hypothetical Big Bang which marked the beginning of time or you can imagine that protons are being created even now throughout the universe, but only where energy has been shed by proton decay. This presumes that there is a regenerative process, involving, as ever, conservation of energy, but nevertheless a process that can be regulated by physical principles based on what can be measured in the laboratory. You see, you need to understand how a proton is created before you can deduce its mass. All protons are the same. It is as if they come from a common mould and understanding that mould is the secret of that Holy Grail.
If you read that book by Barrow and Tipler, you will learn nothing about Creation, because, as they declare in that quotation from page 5, they do not know how protons are created and yet protons account for 99.9% of the mass of the universe. On the other hand if you read my 1980 book Physics Unified, published six years before that book by Barrow and Tipler, you will see how protons are created and be able to calculate the proton/electron mass ratio. You will see that the theoretical value is slightly greater than 1836.152, which is also its measured value. Further you will see that this explanation of the creation of matter in the form of the proton, was published in the scientific literature five years before that, in 1975. So if you go in search of that Holy Grail all you need to do is to obtain a copy of my book or just look elsewhere in these Web pages, starting with the Tutorial section.
My point in saying this is to stress that it is illogical for physicists to try to understand how matter is created unless they are prepared to accept the regenerative energy process. Energy shed into space in that ever-increasing entropy process has a way of joining in a quantum dance and packaging itself into a form that can materialize to produce protons.
From this position it seems a trivial exercise to argue against the Eddington proposition that the Second Law of Thermodynamics is sacrosanct. Let us therefore now come back to that lesser task, the prospect of building a solid-state device that can cool and generate electricity by tapping the energy of heat in our environment.
Consider what happens when an electric current flows around a circuit formed by connecting two wires, each of a different metal, say nickel and aluminium, with the two junctions maintained at different temperatures. We do not need an electrical power supply to set up this current flow. That temperature difference is sufficient.
It is found that the current will flow from the nickel wire to the aluminium wire at the hot junction and from the aluminium wire to the nickel wire at the cold junction. This phenomenon is known as the Seebeck Effect, discovered in 1826, though at that early date the nickel-aluminium combination was not in Seebeck's list. The heat drives the current. In other words heat is converted into electricity. Now, how efficient is this process?
Well, here we have a problem, because what is happening at the hot junction is a cooling process and that means that the temperature over the restricted interface where the current crosses the junction is substantially reduced. Indeed, it must be well below the temperature of the heat source applied to that junction, because with reduction of temperature these two metals develop an increased conductivity and this can become confined to spot regions owing to the current flow escalating its concentration into those regions. However, whatever the actual spot temperature at the point of junction crossing, it is heat at that temperature that is converted into electricity.
Now, quite obviously, this has to be conversion at 100% efficiency. Heat becomes electricity and if this process were inefficient all that would mean is that there would be some heat produced to augment the heat supplied. Conservation of energy means 100% conservation as between heat and electricity.
There is, of course, something happening at the cold junction, but my concern
here is the part of the circuit on the left hand side of Fig. 4.
I well realize that an overall assessment of the energy conversion efficiency of the circuit needs to allow for some heat loss owing to thermal conduction through the metal, but that need not be too great. What is important is the fact that that voltage generated cannot supply its energy to a normal load such as a resistor. It must, owing to the configuration using two metals, pass that current through the junction from aluminium to nickel, where it converts electricity back into heat and does so with 100% efficiency.
In that process the cold junction will not demand as much electricity as is generated at the hot junction, because it has a lower temperature. Its V value is lower, lower in proportion to absolute temperature. Now, if the EMF acting between the different metals is proportional to the absolute temperature of the junction temperature then the Seebeck Effect cannot convert heat to electricity with an efficiency exceeding the Carnot factor, namely the difference of the two temperatures as divided by the one of higher value, the latter being expressed in absolute units.
With the Nernst Effect that we discussed with our transformer eddy-current anomaly in mind there is no opposing EMF in the circuit other than that attributable to the load. In other words, apart from a little loss owing to circuit resistance, the heat deployed is all active in generating useful electrical power. It is just that in the context of eddy currents in the power transformer there is no 'load' as such other than that circuit resistance, which is why the regenerative feature presents itself as the enhanced loss which is known as 'the eddy current anomaly'.
Now at this point I shall conclude this Lecture. I have contended that there
is in every electrical power transformer a manifestation of an anomalous energy
phenomenon which, if properly interpreted, tells us that low grade heat, meaning
heat at ambient temperatures driven by a temperature differential of 10 or so
degrees C, is being converted back into electricity with remarkable efficiency.
That efficiency is such that one can contemplate harnessing the phenomenon to
advantage, By building a conventional reverse heat engine, a heat pump, and
running it back-to-back with an energy converter harnessing such principles it
seems economically feasible, indeed highly feasible, to expect to be able to
harness heat extracted from our environment at its ambient temperature and
generate useful electrical power.
My hope is that those having the resources needed to fabricate laminar metal assemblies based on bonded core structures for use in a modified type of transformer will show interest in this prospect and take up this proposition. I shall enlarge on this theme as I add to these Web pages.