Overdischarging Oops

I've had a chance to experiment some more with the small Lithium Iron Phosphate (LiFePO4) cells that I purchased from batteryspace.com.  I originally purchased 4 of these 1300 mAh cells.  I've since learned what happens when you over-discharge a cell.  I was discharging the 4-cell pack using a stepper motor as I described in this earlier post.  I was periodically recording the cell voltages, with the goal of spotting the knee when the cell becomes fully discharged.  This was going okay but at some point I ended up in a hallway conversation (this was at work), and when I got back to check, one of the cells had a negative voltage (about -0.6 volts).  Interestingly the motor was still running and the other cells were still delivering current.  I disconnected the cells and let them sit for a while.  The reversed cell eventually became positive again, about 0.2 volts.  I attempted to charge it, and when I did the cell voltage pretty quickly came back into a normal range.  But when I stopped charging, the voltage eventually dropped back to about 0.6 volts.  Clearly this cell is no longer good.

Why balancing is needed

This particular cell was at a noticeably lower voltage than the others.  Likewise there was a cell that was at a higher voltage than the others.  And when I discharged them the "low" cell ran out first, while the other cells still had charge.  And when I charged, the "high" cell reached 4.0 volts pretty quickly, while the others still needed charging.  These cells are not balanced, and this is a very good demonstration of the reason that cell balancing is needed (although I hope the thundersky batteries will have an initial better balance than these cheap cells).

In the chart below, you can see that the starting voltages were very close but that one cell dropped faster than the others:

Initial battery discharge
Initial battery discharge

The chart below shows charging.  One cell is obviously much worse than the others (the one I damaged), but the other 3 cells are very close to the same voltage at the start of charging.  Yet one of these reaches 4 volts well before any of the others.  This one cell is fully charged while the others are not.  There is no way for me to fully charge all cells in series without some kind of balancing scheme.

Initial Charging
Initial Charging

Simple Capacitor Balancing Scheme

In the remainder of this post I am going to talk about a simple balancing scheme that uses capacitors.  I saw this idea mentioned in an article I was reading about battery pack management.  In this scheme there is a capacitor between every cell.  There is a pair of switches that switch the capacitor such that it is in parallel with one of the cells at a time.  The capacitor is switched between the two cells at some frequency.  If there is a difference in voltage between the two cells, then when connected to the "higher" cell, current will flow into the capacitor from the cell, charging it up to match the cell voltage.  Then when the capacitor is switched to the lower cell, it will have a higher voltage than the "lower" cell, and current will flow out of the capacitor and into the cell until the capacitor voltage is the same as the lower cell.  Switching back and forth like this allows small pulses of current to transfer from the "higher" cell to the "lower" cell, and this charges the lower cell from the higher cell.

Here is a schematic of a circuit I built to test this scheme:

Capacitor Balancing Circuit
Capacitor Balancing Circuit

In the above schematic, the capacitor is connected in parallel to either the upper cell or lower cell depending on the state of the half-bridge driver.  I used a PWM signal at 50% duty cycle to drive this circuit.  I used two cells with a large voltage difference to maximize the effect.  The lower cell was 2.39 volts and the upper was 3.34 volts.  Then I started the PWM running, initially at 20 kHz.  In the scope plot below the top trace is the switching waveform.  When it is high, the capacitor is connected across the "high" cell.  The lower trace is the current flowing in the capacitor, using a current probe.  When the capacitor is connected to the high cell, there is a pulse of current flowing into the cell, about 750 mA peak.  Then when the capacitor is switched to the low cell, the same amount of current flows out.

Capacitor switching at 20 kHz
Capacitor switching at 20 kHz

As you can see in the plot above, once the initial current surge passes, there is not really any current flowing in the capacitor.  So I increased the switching frequency to 60 Hz and eliminated the "flat" part of the waveform.  Here is the same signal but with switching at 60 Hz.  This shows the same current pulses but now occurring more often, allowing more charge to be transferred.

Capacitor switching at 60 kHz
Capacitor switching at 60 kHz

Next I looked at the current flowing in the low cell.  In this scope plot you can see that there is no current flowing, and then there is a pulse of current flowing into the battery, providing a small amount of charge.

Current charging the low cell
Current charging the low cell

At this point I feel that this circuit is in fact working as expected.  But in a real system we need to be able to do this while it is charging at the same time.  So I connected up 4 cells in series, and my circuit remained installed between the same two cells.  I started charging the cells and then took a look at the same waveforms.  Here is the "high" cell, showing current flowing into the cell (from the charger), but with a periodic dip in current.  This is the capacitor charging from this cell, effectively diverting some of the charging current that is flowing into the high cell.

High cell balancing during pack charging
High cell balancing during pack charging

And here is the same thing shown for the low cell.  Steady-state charging plus a periodic pulse of extra current.

Low cell balancing during charging
Low cell balancing during charging

Conclusion

I think it works because I can see that charge is being transferred from the high cell to the low cell.  And when I measured the voltage during the time I was conducting this experiment I saw the low cell voltage rise from 2.39 volts to 3.10 volts.  The high cell went from 3.34 volts to 3.30 volts.  I think that the low voltage cell had such a large change because it was almost completely discharged and so a little bit of charge really made the cell voltage jump up.

I was also pleased to see that this scheme continued to work while the pack was being charged.  Likewise I would expect it to behave the same way during pack discharge, though I didn't try that.

However ... if you look at the plots above, which are in time order during the time I was running this experiment, you will see that the magnitude of the current pulse becomes progressively smaller over time.  This is because the voltage difference between the cells became less as the lower cell started to charge.  I think this is the fundamental flaw with this scheme.  When the cells are almost the same there is little or no charge transfer, and as you can see from my battery plots at the beginning of this post, two cells with different levels of charge can have almost the same voltage.  This means that this scheme would  not really transfer any significant charge until the point at which one of the cells is almost fully charged or discharged.  And at that point it is probably too late to try to make up for the charge difference by balancing in this way.  I don't think it is possible to transfer enough charge, especially considering that for the car battery, it will probably need to achieve balancing currents on the order of 10A.

So, my conclusion is that this was an interesting experiment and may deserve further investigation.  But I don't think this balancing scheme is going to work for the car battery.


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