We have developed our own SOC algorithm which is pretty basic at this stage.

Vocabulary

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SOC (State Of Charge): Present charge level remaining in the battery / full charge in the battery Decreases during every cycle, increases during charge, is 100% at 4.20V Pack’s reported SOC is limited by the lowest cell’s SOC e.g. 4Ah remaining, 10Ah when full ⇒ SOC = 40%

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SOH (State Of Health): Full charge in the battery / full charge when the battery was assembled Decreases slowly along the battery cycles. Can indicate when to retire the battery Pack’s reported SOH is limited by the weakest cell’s SOH e.g. 9.6Ah when full, 10Ah when full when the pack was new ⇒ SOH = 96%

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IR (Internal Resistance): Indication of the battery’s ability to output current. Less is better. Tends to grow DC IR and AC IR readings are different, see BatResearch article on the topic Can be measured at pack level or (better) at cell level (group of // cells) Depending on cell model, can range from 10mOhm to >70mOhm on ours

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OCV (Open Circuit Voltage): Voltage on the cell terminals when the battery has relaxed (current ~0.0A) for more than 90 minutes The curve SOC=f(OCV) is specific to each cell model but ~independent of cell aging so we can easily derive SOC from a relaxed cell’s voltage if we have measured and know the curve

Example of an SOC=f(OCV) curve:

Roadmap

Coulom counting + reset at 4.18V DONE

Add OCV curve + cal at low SOC after 90min DONE

SOH calculation DONE

Two SOC scales

Internal Resistance estimation

IR and SOH at cell-level, SOP, EOL

Preliminary specification (10/03/22)

Basic algorithm:

Coulomb counting for SOC(%)

Reset to 100% when voltage > 4.18 (exact value TBD)

Calibrate SOC based on OCV curve when battery inactive for more than 90min

Update Present Capacity when recharged to 100% after a calibration

Recalculate SOH = Present Capacity / Design Capacity

Initial BMS configuration

When the battery is assembled, some parameters must be entered in the BMS, which depend on the cells inside the battery:

Parameter	Unit	Description
Design Capacity	Ah	For new cells only = nominal capacity found in the datasheet (e.g. 4P * 3350mAh = 13.4Ah)
Factory Capacity	Ah	Real capacity measured after battery assembly, for new and for 2nd Life cells: = measured sum capacity of the weakest group of parallel cells (e.g. 4P * 2.75Ah = 11Ah) Can be measured with a “calibration cycle” right after battery assembly
Present Capacity	Ah	= Design Capacity when assembling the pack, then Factory Capacity when measured
Design Internal Resistance	mOhm	Measured before assembly
Factory Internal Resistance	mOhm	Measured right after assembly.
Present Internal Resistance	mOhm	Design Internal Resistance when assembling the pack, then Factory IR when measured

SOC estimation during use

Normal operation Coulomb Counting

Coulomb counting

Integrate output current (add or subtract depending on current’s direction) in a counter when DSG and/or CHG is activated, to get remaining Ah
Divide this value by Present Capacity ⇒ gives SOC (between 0.00 and 1.00)

Reset SOC to 100% when voltage ~4.2V per cell (exact value TBD) which is a good reference point

Global SOC should be based off of the lowest cell
Only do this calibration if the lowest cell voltage is > a threshold above which we have good confidence in the SOC=f(OCV) curve. Probably around 3.45V, but we will need to have the curve of many cells to make sure we can use a fixed threshold for all, or if it is cell model dependent

SOC calibration phase

Due to the possible drift in Coulomb counting (integration), we have to calibrate the gauge regularly:

At least every few cycles (if 4.2V cal has not been reached)

After the battery has been sitting unused for a long time (SOC does not move while a small current is drawn by the sleeping BMS, which slowly discharges the pack)

We can do the calibration by:

Looking at the lowest cell’s voltage when relaxed for more than 90 minutes (OCV)

Reading the corresponding SOC in a look-up table (interpolate)

To get this SOC=f(OCV) curve we have to measure it on a test bench for each cell model we encounter, it is specific to the cell model used in the pack

📉SOC vs voltage (OCV)

SOH estimation

After an SOC calibration, if a charge to 4.2V is done, we can update Present Capacity:

Present Capacity = Ah_recharged / (1 - SOC_calib)

And then update the SOH:

SOH = Present Capacity / Design Capacity

Example for a 9800mAh nominal pack:

Battery has been sleeping for more than 90 minutes

Voltage of the lowest cell is 3.72V ⇒ from the curve, SOC is 17%

A charger is plugged, the battery charges

Lowest cell reaches full threshold (e.g. 4.18V)

⇒ SOC is set to 100%
8670mAh have been recharged

We update Present Capacity = 7490 / (1 - 0.17) = 9024mAh

We update SOH = 9024 / 9800 = 92%

First cycle calibration

We could have a calibration mode in the BMS.

Assembled pack is connected to dummy load + charger with a mean to control its activation

Charge. Once the cells are in balance at 4.2V, initialize SOC to 100%

Discharge to 2.5V /cell, integrate current and set Design Capacity (Ah)

Charge to storage (e.g. 30%)

During this calibration phase, monitor the balance between the cells, temperature rise and other significative values to check for any faults

Note: we could also have a SOC=f(OCV) curve measurement implemented directly in the BMS with the same hardware setup

IR estimation

During use, we can calculate the Internal Resistance, which gives a good indication, when going too high, that a cell is defective.

Method: measure voltage sag during big current draws, divide it by current to get battery IR:

R = dU / dI

It should be taken at the right times (high current delta), around a certain SOC range (~middle) and the value should be filtered. See Ardupilot method with Kalman filter.

Note: IR should be calculated for global pack and for individual cells. Any imbalance or too high value should be supervised.

To go further (Not implemented yet)

Two SOC scales

We need two SOC scales

One, real, precise for this cell model

= Internal SOC

One for the client / user with configurable reserves at each end

= User SOC
e.g.:

User_SOC_100% = Internal_SOC_95% (to improve cycle life)
User_SOC_0% = Internal_SOC_10% (to prevent deep discharge)

Battery health thresholds and End Of Life criteria

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EOL (End Of Life): Criteria based on SOH and/or IR degradation e.g. 4Ah remaining, 10Ah when full ⇒ SOC = 40%

With multiple-level thresholds, we could :

Warning ⇒ draw attention on an relatively high value

Highlight this battery in our system to study its logs, find the cause and prevent premature failure
Not fault indicated to the user

Alert ⇒ draw user’s attention on a fault

Maintenance required, our system is aware of this and we can inform the user
Carry on battery operation but the user is informed

Fault ⇒ stop operation when the level makes the battery unusable

Our system is aware of the fault
The user has not choice but bring the battery to maintenance

Note: same logic should be applied to other quantities such as battery temperature, cell balancing times, which are indicators of the battery’s use and health

How many km are requested by the fleet operator? EOL if < xkm ? Or capacity?

It seems they ask for cycle life values based on cell datasheet, so their demands are vague (e.g. >80% after 500 cycles...)

SOH thresholds

When any cell’s SOH < SOH_threshold

Threshold	SOH_thr value
Warning	0.92
Alert	0.85
Protection	0.50

Note: we should also monitor max-min differences between cells and have a threshold here too

IR thresholds

When any cell’s (Present IR / Design IR) > IR_threshold

Threshold	IR_thr value
Warning	1.3
Alert	1.6
Protection	2

Note: we should also monitor max-min differences between cells and have a threshold here too

State Of Power

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SOP (State Of Power): A sense of how much power (in watts) the battery can deliver at a given time Depends on present temperature, IR, SOC, and needs pack thermal modeling Can be used to reduce motor power (requires com with the controller) when the battey approaches its limits to prevent damage or protection trigger / operation stopping e.g. battery at 50°C, max continuous current is calculated to be 10A ⇒ 400W at 40V ⇒ controller is asked to not draw more than 400W continous

Calculate SOP?

Not useful at the moment we have no control over max power on most of the controllers used by clients. We could use this indicatively, or to trigger a warning but without stopping operation

Note: we could know the ambient temperature if we have location and time

SOH filtering

LP filtering on the value to reduce variability and improve accuracy

Weight with amplitude of the recharge?

SOC/SOH at cell-level

If we later mix different cell models in a same battery pack, we need to track the SOC/SOH for each different cell group, which may have different SOC=f(OCV)

Individual SOC measurement allows for more efficient balancing

Cycle counting

Two things to implement:

Charge/discharge cycle count

Count the number of charges and discharges (2 consecutive charges or discharges are considered as 1)
Allows e.g. to have a view of how many times the battery has been used. Divide by the time in circulation and we have the use frequency, along other useful stats

Full cycles count

Count the total Wh discharged and Wh charged to estimate the number of “full cycles”
Useful for studying the total energy the pack has been able to give back versus its aging versus the cycle depht etc

Interesting values to log (to discuss):

Mean DOD and DOC?

Each charge > 10%, log temp and start/end SOC, for later analysis

Protections

The voltage-based protections in the BQ should be last-resort. We should primarily use the SOC to limit usage

Algorithm tests

SOH calibration test

Unplug 1 cell (insert insulation paper between cell and contact plate?) and run a calibration

Check if SOH updates correctly

Check if warnings have triggered correctly

Literature

Read this explanation on ImpedanceTrack on TI

See this “how to calibrate a smart battery” article

BMS SOC/SOH algorithm