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This is an experiment I intend to start working on soon and thought I would first see if anyone has already done this and also see if anyone wants to make any suggestions concerning the methodology.
Background:
Some time back there was a discussion concerning the "two capactior paradox" which I resolved to my satisfaction by learning that the discharge of energy from one capacitor into another follows conservation of charge, which by definition means it may not also follow conservation of energy. A second infrequently noted behavior of discharging one capactior into another is the absence of change in the intial and final states of energy as a function of resistance between the capacitiors. A 10 V 1mF cap discharged into a second empty 1 mF cap yields two caps at 5 volts. If one places a 10 ohm resistor between the caps and repeats the above one again ends with two caps at 5 volts. If one places a 1k resistor between the caps in a few seconds one finds two caps at 5 volts, 100k resistor and repeat, shut off the volt meters and come back in a few minutes and one finds two caps at 5 volts. The initial and ending states of energy are unperturbed by multiple orders of magnitude difference in resistance. This demonstrates that for the discharge of electrostatic energy from one cap to another there is no such thing as a "resistive loss" as a dissipative loss of energy would by definition require a change in the ending state of energy in the caps, there is also no loss of charge. There is only a decrement of power caused by increasing resistance.
Two capacitors placed in series leads to a doubling of the dielectric space between the series capacitor plates. Therefore the capacitance of capacitors in series follows the forumla C(total) = 1/(C1/1+C2/1 ... Cn/1), in the simple case of two capacitors of equal capacitance placed in series this equals a halving of capacitance. Electricity stored electrochemically as opposed to electrostatically does not follow this dielectric spacing driven change seen with capacitors. Therefore, the capacity of batteries in series is unchanged, two 1 Volt, 1000 mA/hr batteries in series yields one 2 Volt 1000 mA/hr battery, not one 2 Volt 500 mA/hr battery as might be expected if the energy were stored electrostatically. Given the above one might envision two batteries placed in series the negative of the series batteries connected to a single battery yielding a voltage difference across the split positive which might power a resistive or other load. This approach is far from new and has been referred to as a common ground, split positive or Tesla switch approach, for the purpose of this write-up it will usually be referred to as charge recycling as I feel the term is more descriptive and catchier. Given the above it might be conjectured that as is the obvious case with two capacitors, discharging two batteries in series to a single battery across the split positive with varying resistive loads also leads to no resistive losses affecting the intital and final states of the batteries. Further as batteries in series do not lose capacity, such a set-up might effectively allow for a recycling of the charge. However, just because electricity is not dissipated by resistance does not at all mean that the electricity is performing the work we might like it to. I.e. if the battery being discharged to is full to start with the electrical energy, though not lost, is also not driving a reaction that alters the chemistry of the battery to store electrical energy it is instead driving a reaction that leads to off gassing and or other phenomena that might damage the battery. It is still reasonable to guess that a portion of the charge after drving the resistive load would lead to recharging of the battery and this charge would be effectively recycled.
This was looked at roughly with three niMH batteries switched by hand. A three volt incandescent flashlight light bulb which remains lit down to about 1,2 volts was used as the resistive load. The measured resistance across this bulb indicated that for a single battery the discharge rate would be approximatley C rate 0.5. For the "control" arm the three batteries were charged fully, bled off down to about 1.4 volts and placed in parallel. The bulb was connected across the batteries for ten mintutes and voltage measured. Load was disconected for ten minutes, voltage measured, this was repeated for two hours. As the three bateries in parallel would have a C discharge rate of 0.17 as opposed to 0.5 for a single battery, secondary to Peukart's law, the null hypothesis is that discharging three batteries in a charge recycling set-up would do worse than simply putting the three in parallel. For the first experimental arm two batteries were again set to 1.4 volts while the third battery was at 1.3 volts (the same batteries are used each experiment). Again the load was placed on for ten minutes, this time across the split positive and voltage measurements taken, followed by a rest period of ten minutes, this repeated (with battery rotation) for two hours. For the batteries in parallel at the end of two hours they had lost 0.082 volts, for the charge recycling set up the three batteries had lost 0.055 volts a 1/3rd improvement in energy utilization. For the second experiment the charge recycling setup was again used however this time all batteries started at 1.4 volts. In this set-up after two hours the batteries had lost 0.08 volts as opposed to the 0.082 volt loss seen with all three in parallel.
At this point I am 90% convinced there is something to this splitting the positive charge recycling. One might argue that in the case that showed a large improvement the average starting voltages were different and so one was on a different part of the battery discharge curve, still it is a pretty large change. It might have been a cleaner experiment if I had used a plain resistor as opposed to a light bulb as the temperature variation would likely be less and resistance of a resistor varies as a function of temperature, still it seems worthwhile to see if one is actually doing something useful such as lighting a bulb. The big one to me is perhaps the battery in the charge position is acting as further resistance as compared to just simply going to battery negative. In this case one has less voltage loss simply because less power flowed, this should be reflected in the brightness of the light. Eyeballing it, they appeared roughly equal, though the charge recycling set-up varied from very bright to less bright as the charge battery filled. Maybe there is 1/3 less voltage lost and 1/3 less light? It also seems to me if the charge battery is a source of resitance, in the case where all three batteries all started at 1.4 volts there would be the least power flow and this set-up would have shown the smallest decrease in voltage over two hours, which was not the case, so I am optimistic about this. To try and look at this more rigourously I am considering the following.
Methodology
Obtain a data logging lux meter, place the bulb in a box the ceiling of which houses the lux meter sensor. Obtain two datalogging volt meters, am looking at this Redfish meter https://redfishinstruments.com/. Use four batteries in the Tesla switch set-up and use an arduino with four relays to swith between parallel and series, a fifth relay for if you want to disconnect the load and let batteries rest. Repeat the above experiment and log all the data. Once you know the lumens produced one can say more definitively whether there is an improved utilization of battery energy or if it is all smoke and mirrors. If there is something interesting, maybe try switching the batteries with no rest period, try one minue on one minute off, 6 seconds on, six seconds off, six seconds switch with no rest period, you get the idea. Once it is all automated and being logged you just set it up come back in a few hours and see what you've got. If there is something to it, there are likely sweet spots in terms of timing and discharge rate. Depending on results, eventually one might look at inductive loads or harvesting magnetic flux with diodes as per the Tesla switch, however this is a more simple question, is there charge recycling going on with such a set-up? If not the Tesla switch would be just a very complicated way of doing what you could do more simply with a cap dump. If there is charge recycling, then for the cost of a few relays maybe you could increase the size of a solar/battery set-up by 1/3rd.
Will likely order parts this week-end or sooner, so if someone (_RS?) has already done this or someone wants to say that's a stupid set-up because ... please let me know in the next few days.
Paul
Background:
Some time back there was a discussion concerning the "two capactior paradox" which I resolved to my satisfaction by learning that the discharge of energy from one capacitor into another follows conservation of charge, which by definition means it may not also follow conservation of energy. A second infrequently noted behavior of discharging one capactior into another is the absence of change in the intial and final states of energy as a function of resistance between the capacitiors. A 10 V 1mF cap discharged into a second empty 1 mF cap yields two caps at 5 volts. If one places a 10 ohm resistor between the caps and repeats the above one again ends with two caps at 5 volts. If one places a 1k resistor between the caps in a few seconds one finds two caps at 5 volts, 100k resistor and repeat, shut off the volt meters and come back in a few minutes and one finds two caps at 5 volts. The initial and ending states of energy are unperturbed by multiple orders of magnitude difference in resistance. This demonstrates that for the discharge of electrostatic energy from one cap to another there is no such thing as a "resistive loss" as a dissipative loss of energy would by definition require a change in the ending state of energy in the caps, there is also no loss of charge. There is only a decrement of power caused by increasing resistance.
Two capacitors placed in series leads to a doubling of the dielectric space between the series capacitor plates. Therefore the capacitance of capacitors in series follows the forumla C(total) = 1/(C1/1+C2/1 ... Cn/1), in the simple case of two capacitors of equal capacitance placed in series this equals a halving of capacitance. Electricity stored electrochemically as opposed to electrostatically does not follow this dielectric spacing driven change seen with capacitors. Therefore, the capacity of batteries in series is unchanged, two 1 Volt, 1000 mA/hr batteries in series yields one 2 Volt 1000 mA/hr battery, not one 2 Volt 500 mA/hr battery as might be expected if the energy were stored electrostatically. Given the above one might envision two batteries placed in series the negative of the series batteries connected to a single battery yielding a voltage difference across the split positive which might power a resistive or other load. This approach is far from new and has been referred to as a common ground, split positive or Tesla switch approach, for the purpose of this write-up it will usually be referred to as charge recycling as I feel the term is more descriptive and catchier. Given the above it might be conjectured that as is the obvious case with two capacitors, discharging two batteries in series to a single battery across the split positive with varying resistive loads also leads to no resistive losses affecting the intital and final states of the batteries. Further as batteries in series do not lose capacity, such a set-up might effectively allow for a recycling of the charge. However, just because electricity is not dissipated by resistance does not at all mean that the electricity is performing the work we might like it to. I.e. if the battery being discharged to is full to start with the electrical energy, though not lost, is also not driving a reaction that alters the chemistry of the battery to store electrical energy it is instead driving a reaction that leads to off gassing and or other phenomena that might damage the battery. It is still reasonable to guess that a portion of the charge after drving the resistive load would lead to recharging of the battery and this charge would be effectively recycled.
This was looked at roughly with three niMH batteries switched by hand. A three volt incandescent flashlight light bulb which remains lit down to about 1,2 volts was used as the resistive load. The measured resistance across this bulb indicated that for a single battery the discharge rate would be approximatley C rate 0.5. For the "control" arm the three batteries were charged fully, bled off down to about 1.4 volts and placed in parallel. The bulb was connected across the batteries for ten mintutes and voltage measured. Load was disconected for ten minutes, voltage measured, this was repeated for two hours. As the three bateries in parallel would have a C discharge rate of 0.17 as opposed to 0.5 for a single battery, secondary to Peukart's law, the null hypothesis is that discharging three batteries in a charge recycling set-up would do worse than simply putting the three in parallel. For the first experimental arm two batteries were again set to 1.4 volts while the third battery was at 1.3 volts (the same batteries are used each experiment). Again the load was placed on for ten minutes, this time across the split positive and voltage measurements taken, followed by a rest period of ten minutes, this repeated (with battery rotation) for two hours. For the batteries in parallel at the end of two hours they had lost 0.082 volts, for the charge recycling set up the three batteries had lost 0.055 volts a 1/3rd improvement in energy utilization. For the second experiment the charge recycling setup was again used however this time all batteries started at 1.4 volts. In this set-up after two hours the batteries had lost 0.08 volts as opposed to the 0.082 volt loss seen with all three in parallel.
At this point I am 90% convinced there is something to this splitting the positive charge recycling. One might argue that in the case that showed a large improvement the average starting voltages were different and so one was on a different part of the battery discharge curve, still it is a pretty large change. It might have been a cleaner experiment if I had used a plain resistor as opposed to a light bulb as the temperature variation would likely be less and resistance of a resistor varies as a function of temperature, still it seems worthwhile to see if one is actually doing something useful such as lighting a bulb. The big one to me is perhaps the battery in the charge position is acting as further resistance as compared to just simply going to battery negative. In this case one has less voltage loss simply because less power flowed, this should be reflected in the brightness of the light. Eyeballing it, they appeared roughly equal, though the charge recycling set-up varied from very bright to less bright as the charge battery filled. Maybe there is 1/3 less voltage lost and 1/3 less light? It also seems to me if the charge battery is a source of resitance, in the case where all three batteries all started at 1.4 volts there would be the least power flow and this set-up would have shown the smallest decrease in voltage over two hours, which was not the case, so I am optimistic about this. To try and look at this more rigourously I am considering the following.
Methodology
Obtain a data logging lux meter, place the bulb in a box the ceiling of which houses the lux meter sensor. Obtain two datalogging volt meters, am looking at this Redfish meter https://redfishinstruments.com/. Use four batteries in the Tesla switch set-up and use an arduino with four relays to swith between parallel and series, a fifth relay for if you want to disconnect the load and let batteries rest. Repeat the above experiment and log all the data. Once you know the lumens produced one can say more definitively whether there is an improved utilization of battery energy or if it is all smoke and mirrors. If there is something interesting, maybe try switching the batteries with no rest period, try one minue on one minute off, 6 seconds on, six seconds off, six seconds switch with no rest period, you get the idea. Once it is all automated and being logged you just set it up come back in a few hours and see what you've got. If there is something to it, there are likely sweet spots in terms of timing and discharge rate. Depending on results, eventually one might look at inductive loads or harvesting magnetic flux with diodes as per the Tesla switch, however this is a more simple question, is there charge recycling going on with such a set-up? If not the Tesla switch would be just a very complicated way of doing what you could do more simply with a cap dump. If there is charge recycling, then for the cost of a few relays maybe you could increase the size of a solar/battery set-up by 1/3rd.
Will likely order parts this week-end or sooner, so if someone (_RS?) has already done this or someone wants to say that's a stupid set-up because ... please let me know in the next few days.
Paul
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