The Capacity
The BMS does provide a lookup table for the Open Circuit Voltages (OCV) of the cells. When we plot those voltages in 5% steps for the rSOC and add about -2500mV as the lower limit (-2.5% point) and 4200mV for the upper limit of 100%, we get this graph for the Qmax (total chemical energy) of the steady pack with 96 cells:
We have seen that the rSOC is doing well of describing the Ah capacity of the pack during charging. If we think of the rSOC as representation of the amp hours (Ah) we can integrate the area under the OCV curve and will get the Qmax energy of the system:
| [1], Unusable | [2], Reserve | [3], FCC | [4], Headroom | Q max | Energy Window | ||
|---|---|---|---|---|---|---|---|
| % | 1.891 | 3.146 | 89.507 | 5.456 | 100 | FCC+[2]+[4] | Measured |
| Ah | 0.988 | 1.644 | 46.760 | 2.850 | 52.242 | 51.254 | 51.07 |
| kWh | 0.356 | 0.592 | 16.841 | 1.027 | 18.816 | 18.460 | 18.45 |
The BMS will use an intended Full Charge Capacity, of which ~94% will be used for the User SOC (uSOC) window.
This time they have added a reserve buffer at the bottom and a headroom on top of the range. The FCC window will move with the balancing / load conditions and the usable capacity window should also move during aging - but we will seen in the future years ;-)
TI has a nice writeup and videos about battery management, capacity and SOC estimation here. I recommend especially the BMS basics video and it's PPT slides.
The capacity readouts of the BMS are way to high for the measured and extrapolated values. We get those data - by two different measurement algorithms - from within the BMS:
Measured : 57.389, 57.411 (dSOC)
and if we look at the cell values, we get those readouts:
CAP mean: 20694 As/10, 57.5 Ah
CAP min : 20600 As/10, 57.2 Ah, # 84
CAP max : 20810 As/10, 57.8 Ah, # 59
The initial and current estimate is also found within the BMS data:
Capacity : 55.861 (INIT), 55.861 (EST)
The total, chemical voltage range is defined by two variables as: 2504mV to 4194mV implying a mid voltage of 3349mV per Cell and 321.5V for the pack. With the window for the usable capacity moving during aging, the actual mid voltage is not fixed and it seems that the middle of the chemical range was chosen for a normalization:
The Qmax of 18816Wh divided by 321.5V will imply 58,526Ah, so let's calculate the capacity with this value:
| [1], Unusable | [2], Reserve | [3], FCC | [4], Headroom | Q max | Usable Window | ||
|---|---|---|---|---|---|---|---|
| % | 1.891 | 3.146 | 89.507 | 5.456 | 100 | FCC + [4] | Estimate by BMS |
| Ah | 1,107 | 1.841 | 52,385 | 3,193 | 58.526 | 55,578 | 55,861 |
When we subtract the unusable 1,107Ah we get 57,413Ah. So the BMS seems to show the capacity related / normalized to Qmax as the total chemical capacity. If we take the bottom buffer into account, we can further subtract 1.841Ah that result in 55,578Ah for the FCC + Headroom [4] as the possible usable energy window.
In my opinion those numbers make sense and seem to fit for my measurement quality and analysis, but:
If you have a better interpretation, please post it in the issues section - Thanks!
OCV 13th grade polynomial fit (rSOC range of -2.5 to 100):
3064.230357185182 + 119.2920202002487*x + (-24.77636172145991)*x^2 + 3.176074715280294*x^3 + (-0.2529295279543084)*x^4 + 0.01325077507697961*x^5 + (-0.0004741371420283568)*x^6 + 1.183558274576096e-5*x^7 + (-2.078061941524195e-7)*x^8 + 2.55380223818207e-9*x^9 + (-2.149520782642352e-11)*x^10 + 1.180188517923892e-13*x^11 + (-3.806922405136515e-16)*x^12 + 5.470917353007223e-19*x^13