How the state of health of a battery is measured

Who this is written for. For someone who doesn't know the industry's terminology and has no obligation to think in it. Every phenomenon is first described in plain words, and only then given its accepted term.

How it's built. First the foundation: six quantities and the relations between them. Then what physically happens during measurement. Then the methods — one per group, each on its own frame: what it gives, what it requires, where it breaks down. At the end — data access and summaries.

Of the six quantities, directly measured is just one: voltage. Current is calculated from the voltage across a known resistance, temperature from the voltage across a thermistor, charge from current and time, and resistance from voltage and current.

Neither capacity nor health appears in this list at all. A state assessment is not a measurement with some margin of error — it is the reconstruction of an unobservable quantity from observable ones.

The frame's label sits in its upper right corner.

The electron is a particle with an electric charge. Every electron's charge is the same and indivisible: nature has no smaller portion.

A piece of matter of any size holds an enormous number of electrons, and counting them one by one is as impractical as counting water by the molecule. So a large unit was adopted — the coulomb, roughly 6.24 × 10¹⁸ electrons. The number itself means nothing — it's just a convenient portion size, inherited from the history of measurement.

The coulomb is a unit of quantity. It says nothing about rate or about energy.

A check against scale. A cell with a capacity of 150 ampere-hours is 540,000 coulombs — that is, 3.4 × 10²⁴ electrons. We will need this number again.

Electrons in a substance don't occupy just any positions — they occupy specific sites, and those sites lie at different energy depths. They fill up in order: the deepest go first, the next electrons take the ones higher up, because the lower ones are already occupied.

The depth at which the topmost of the accepted electrons sit is a property of the substance in its current state. It determines how the substance behaves: if the top ones sit deep, the substance readily accepts another electron; if they sit high, it readily gives up its own.

Everything else follows from this. Two different substances have different depths. Connect them with a conductor, and it becomes favorable for electrons of one to move to the other.

The term. This depth is called the Fermi level, and the quantity that expresses it in electrical units is called the potential. Using the terms isn't required; "depth" describes the same thing.

The difference in depth has to be expressed as a number somehow. Depth cannot be measured directly: it is a level, and a level exists only relative to another level — just as height is meaningless without saying what it's measured from.

So the difference is expressed through the work the transition performs. One volt means that moving one coulomb between two points involves one joule of work.

Three consequences follow from this.

Voltage always exists between two points , never at one. That's why a voltmeter has two probes, while a current meter has one break in the circuit.

Voltage does not depend on quantity. It is work per coulomb, not a total. Like a price per kilogram, which doesn't depend on how much was bought.

Whether work is given up or spent is determined by direction. Going down the slope, a coulomb gives up a joule; going up, it demands one. The magnitude is the same, the sign is different.

When people speak of the potential of a single substance , the second point still exists — it has just been assigned zero by convention. In chemistry, the zero is the hydrogen electrode under agreed conditions: a solution of a specified strength, normal atmospheric pressure, room temperature. In lithium-ion technology, metallic lithium is taken as zero, because the hydrogen electrode doesn't work in an organic electrolyte — there's no water there.

The joule is the unit of work. One joule is roughly what it takes to lift a hundred-gram apple one meter.

Work is done when something is moved against resistance. Three things are needed at once: force, displacement, and their directions coinciding. Holding a suitcase at arm's length does no work on the suitcase: there is force, but no displacement.

The joule is not an electrical unit. It measures a lifted weight, an accelerated car, and heated water alike. This is the result of Joule's experiment: mechanical work and heat turned out to be one quantity in different guises, and so they were given one measure.

That's exactly why the joule can connect a battery's chemical reserve to kilometers of range: the currency is shared. Without a common unit, the question "how many ampere-hours does it take to drive a hundred kilometers" would be meaningless — one thing would be measured in electrical units, the other in mechanical ones.

Work is obtained by multiplication: coulombs × volts = joules. Quantity × rate = total.

If the path is closed, electrons move — that is current.

The magnitude of current is expressed by how much charge passes through a cross-section of the conductor per second. An ampere is one coulomb per second.

The cross-section here is an imaginary plane across the wire, chosen arbitrarily. Physically nothing stands at that spot; it's just where the counting is done.

The same amount passes through any cross-section of the circuit. The reason is simple: charge neither accumulates nor disappears. If more passed through one cross-section than through the next, charge would build up between them — and the resulting repulsion would instantly even out the flow.

Charge and current are linked through time in both directions: charge = current × time, current = charge ÷ time. The first answers "how much has passed," the second "what is the intensity."

The ampere-hour is the same quantity of charge, just in a larger unit: 3600 coulombs. The unit of time enters it twice and cancels out, so time plays no part in capacity.

Electrons in a wire don't fly freely. The lattice of atoms vibrates from heat, and the metal has impurities and defects — an electron is constantly knocked off course, giving its acceleration back to the lattice. The acceleration it gives up becomes heat: the wire heats up not as a side effect, but as the very essence of the phenomenon.

The measure of this obstruction is resistance. One ohm is the resistance at which a voltage of one volt produces a current of one ampere.

From this: current = voltage ÷ resistance. Given the drop, given the difficulty of the path — the current follows.

Resistance depends on the substance and on conditions. Copper conducts well, glass doesn't conduct at all. A heated lattice vibrates more and obstructs more, so metals conduct worse as they heat up.

Work is a quantity. Power is the rate at which it is done: how much work per second.

A watt = a joule per second. And in terms of what we already know: a watt = an ampere × a volt. How many coulombs per second, multiplied by the work per coulomb, gives the work per second.

From this comes the kilowatt-hour: power multiplied by time gives a quantity again. One kilowatt-hour = 3,600,000 joules.

The distinction people trip over most often. Voltage and work are both tied to joules, but they are different quantities: work is the total, voltage is work per coulomb. Like a sum and a price: both in the same currency, but not the same thing.

A battery is two substances with deliberately different depths, separated by an electrolyte.

During discharge, an electron leaves the graphite for the wire, passes through the motor, and arrives at the NMC. The electron's departure leaves an uncompensated positive charge in the graphite lattice, and that charge pushes a lithium ion into the electrolyte, following the electron that left.

The ratio is exact: one electron through the external circuit — one lithium ion through the internal one. Otherwise the crystal would be torn apart by electrostatic forces, which at these scales are incomparably stronger than chemical bonds.

From this follows the key point for everything that comes next: counting the coulombs that passed is counting the lithium that moved. Not approximately — exactly. The entire method of charge accounting rests on this.

A check against scale. 540,000 coulombs in a cell is about 39 grams of lithium moving from the anode to the cathode over a full discharge.

As the lithium moves, the graphite empties: it has fewer electrons, and its filling depth drops. The NMC fills up: its depth rises.

The two depths converge toward each other, and the difference between them shrinks. That is exactly the voltage drop from 4.2 V at the start of discharge to 3.0 V at the end.

What matters is that this happens inside the electrodes. The wires take no part in the change — they only carry what results. So the terminal voltage reflects the state of the electrodes, not the state of the circuit.

This is what makes it possible to judge the filling level from the voltage. Each voltage value corresponds to its own filling level — provided the cell is at rest.

A common assumption: the battery has a stock of electrons, and discharge spends it.

The check disproves it. The cell has discharged — how many electrons are left in it? Exactly as many as before: whatever left the anode arrived at the cathode. Not one was lost.

What is stored is not a quantity of electrons, but their position. As in a pumped-storage hydro plant: the amount of water in the system never changes — what is stored is height.

From this: capacity is set by the number of sites for lithium, not by the number of electrons. There are immeasurably more electrons in the metal than the cell will ever need over its whole life; what limits it is how much lithium fits between the graphene layers and how much can leave the cathode.

Charge — how much lithium has moved. Ampere-hours. Independent of voltage.

Energy — how much work was done in the process. Kilowatt-hours. Equal to charge multiplied by voltage.

From this comes a practical consequence important for assessing state of health: a worn cell can deliver nearly the same charge at lower energy — because under load its voltage sags more. Ampere-hours nearly the same, kilowatt-hours lower, range lower.

An instrument that counts only ampere-hours will not see this loss.

The probe reads nothing. It connects: the metal of the probe touches the metal of the object, and from that moment the point inside the instrument is electrically one with the point on the object.

No signal travels from the object to the instrument. The object gives up no information — through the probe it imposes its own energy height on the instrument.

An analogy. Measuring water level with a tube: lower the tube into a reservoir, and water enters and settles at the same level. The tube does not read the water — it is connected to the reservoir, and the level equalizes on its own. The measurement is then taken in the tube.

The probe is a connector, not a sensor. The only sensor is the comparison circuit inside the instrument.

The instrument carries two known quantities within it. Both are manufactured, not measured at the moment of operation.

Resistance reference — a resistor made to a precisely known value: the right material, the right length and cross-section, then trimming. Like a weight on a scale: its mass is not determined anew at every weighing.

Voltage reference — a component that outputs a constant, known voltage between its terminals. Usually this is a silicon circuit: two of its internal voltages add up so that their temperature dependences cancel each other, and the sum — about 1.2 volts — is set by the band gap of silicon.

Silicon is not essential here. Formerly the reference was a special galvanic cell with a very stable voltage of about 1.018 volts, and for decades it served as the national standard. Silicon won out not through physics, but because it can be made in the same chip as the rest of the instrument. There is one requirement for a reference: stability. What it is made of is irrelevant.

A caveat, without which confusion arises. Silicon here is neither a scale nor a reference point. It belongs to a different category than hydrogen and lithium.

The first answers "measured from what," the second — "measured with what."

And one more thing that often raises a question. A voltmeter does not compare the measured quantity with zero. It compares a difference with a difference: the drop between the probes against the drop across the reference. Zero plays no part in this at all.

Check: a voltmeter shows the voltage of a cell without knowing anything about what it is made of. Apply it to any other source of the same voltage — it will show the same reading. If it compared the object's potential with zero, it would need to know the substance; it does not.

The comparison is done not by calculation but by the way of connecting: two drops are connected opposing each other.

What "opposing" means. A source has two terminals: one at a higher height, one lower, and it drives charge from high to low. The direction is set by which terminal it is connected through. Connect two sources by matching terminals, and they will pull charge in opposite directions, and between the two free terminals there will be the difference of their drops, not the sum.

The first is larger — the difference points its way. The second is larger — it points its way. Equal — zero between the free terminals.

Visually. Two people pull a rope in opposite directions. The mark at the middle shifts toward whoever is stronger; if the forces are equal, the mark stays put. Without measuring either force, the mark shows who is stronger and when they become equal.

Why it is done this way. Instruments measure absolute values poorly, but catch zero very precisely: as long as any difference remains, current flows. So the unknown is not measured directly — instead, a known value is adjusted against it until the difference reaches zero.

How zero is detected. In older instruments — with a needle: the difference drives current through a coil, and the coil rotates in a magnetic field. If it deflects one way, the probes read higher; the other way, the reference is higher; when it settles at zero, the two are equal. The instrument was called a null indicator for exactly this reason: its job is not to measure but to catch zero.

In modern ones — with an amplifier that blows up a tiny difference tens of thousands of times over, so that no intermediate values remain: slightly positive, and the output is full voltage; slightly negative, and it is zero. Inside it, two identical transistors compete for a shared current: equal inputs split the current in half; the slightest imbalance sends almost all the current through the winner. A physical tug-of-war, not a calculation.

The number is obtained through a sequence of attempts, each of which halves the interval.

We are looking for a voltage. The instrument knows only that it lies between 0 and 8 volts — that is its range. Say the actual value is 5.

First attempt: take the midpoint, 4 volts. The opposing connection gives 5 − 4 = +1. Plus sign — the target is greater than 4. The number 1 itself is discarded, only the new boundary is kept: between 4 and 8.

Second attempt: midpoint, 6. Difference 5 − 6 = −1. Minus — the target is less than 6. The minus one is discarded. Between 4 and 6.

Third attempt: 5. Difference zero — hit.

Three things without which the mechanism cannot be understood.

The remainder is not used as a number: only its sign is taken, and the magnitude is discarded. It does not carry over into the next attempt.

What narrows is not the remainder but the boundaries: the instrument does not remember "how much is left," but between which two numbers the target lies.

Each attempt is independent: the same unchanged voltage from the probes goes into the comparison every time, not the result of the previous step.

The number of attempts is fixed and equals the number of bits of the instrument: sixteen bits — sixteen attempts, always, whatever the measured voltage happens to be. This takes microseconds, which is why the instrument seems to show the reading instantly.

This is where resolution comes from. The attempts run out, and what remains is the last interval — that very step. The instrument takes its midpoint and displays it. So what it outputs is not the true value, but the number of the step, the one the measured value fell into. If the step equals one millivolt, then 3.7004 and 3.7009 volts will give the same answer: they are not "measured with an error" — they are indistinguishable, like two points inside the same grid cell.

A voltmeter is connected so that a negligible current flows through it — microamperes or less. Otherwise it would discharge the cell itself and change the very thing it measures.

This is why it can show the voltage of an open circuit: there is no current in it, yet a difference exists, and the instrument sees it while drawing almost nothing.

Three facts together yield the conclusion that defines this whole document.

Electronics knows how to compare two voltages — that is one simple circuit.

Current turns into voltage via a known resistance: pass the current through a precisely known resistor, measure the drop, divide — and you know the current.

Temperature turns into voltage through an element whose resistance depends on temperature: pass a known current, measure the voltage, find the resistance, and from it the temperature.

Hence: a battery controller contains nothing but a voltage meter and a clock. Current is the voltage across a shunt. Temperature is the voltage across a thermistor. Insulation resistance is the voltage in a leakage circuit. One method, different wiring around it.

This is also why per-cell voltage measurement is always present: it requires nothing beyond two wires and a shared measuring section.

Three ways to be sure, in increasing order of rigor.

Accuracy class in the datasheet is a manufacturer's commitment, not a measurement.

Calibration verification — comparison against a more precise instrument, that one against an even more precise one, and so on up to the national standard. The chain of comparisons is physical: every link is a real comparison.

On-site comparison — apply two instruments to the same object.

What matters here for assessing battery state of health. Absolute accuracy usually matters less than repeatability. If an instrument consistently reads two millivolts low, that error cancels out when comparing cells against each other and when tracking change over time — and that is exactly what is needed: the spread between cells and its growth.

Absolute accuracy is needed where a number is compared against an external threshold: a cutoff voltage, a datasheet value.

That is the whole list. Nothing else in the battery is measured.

Not capacity, not internal resistance, not state of charge, not state of health.

The reason is not a poor design, but the nature of the quantities themselves. Capacity — is how much charge a cell will deliver from full to empty; the only way to find out is to go through the whole path. Resistance — is the ratio between current and voltage sag; the only way to find it is to apply a current and see the response.

Both show up in behavior rather than existing as a state at a given moment. There is no sensor for behavior.

Hence a conclusion that shapes everything that follows: estimating state is not a measurement with an error margin — it is reconstructing unobservable quantities from observable ones. Different algorithms on the same data give different answers, and the discrepancy between them is not instrument error but a difference of method.

Voltage resolution. A few millivolts is enough to estimate charge from the NMC curve. For a method that distinguishes degradation modes by the shape of the curve, ten times finer is desirable, and here is why.

That method looks not at the curve itself but at its slope: how much the voltage changes for each added increment of charge. Suppose the instrument rounds to whole millivolts, while the true change per step is a third of a millivolt. The instrument will show either zero or a whole millivolt — three times less than the truth or three times more. The curve itself will barely suffer from the rounding, but the picture of its slope turns into a picket fence.

The finer the step over which the change is computed, the more rounding corrupts the result — not because the instrument is bad, but because it is being asked about the difference between two close values it cannot tell apart.

Sampling rate. For charge counting, sampling once a second is enough. For separating resistance by timescale, you need tens to hundreds of points per second around a current step: the instantaneous component sags within microseconds and, with sparse sampling, is indistinguishable from the rest.

Availability of rest. The equilibrium voltage exists only at equilibrium, and recovering to it after a load takes anywhere from tens of minutes to hours. Some methods are physically impossible on data recorded only while driving.

These three parameters are not properties of the instrument but the boundaries of what methods can apply. They are established before choosing an algorithm, not after.

The controller estimates charge from a combination of two sources: it sums current over time and corrects using the rest voltage. It estimates health from accumulated indicators. It extrapolates remaining life.

Three reasons not to treat its estimate as a reference.

The model drifts away from the object. The model built in at the factory describes a cell of a certain age and chemistry; as the object wears, it drifts away from the model, and accuracy drops exactly when the estimate is needed most.

Reference points may never appear. Correction requires the cell to reach the edges of the range, where the curve is steeper and less ambiguous. A car driven gently — kept between thirty and seventy percent — never produces such points, and the accumulated counting error never gets reset. Gentle use worsens the quality of the estimate while improving the state itself.

Calibration drifts away. The accuracy of the measurement path drifts over time; an error of a few millivolts is noticeable wherever the curve is flat.

Hence, for this work: the health reading from the factory controller is not a reference to check against — it is just another estimate, produced by an unknown algorithm. Calibrating your own algorithm against it means inheriting someone else's errors.

Collect raw data, not derived data. Voltage, current, and temperature with timestamps — not ready-made estimates of charge and health. An estimate can be derived from raw data, but raw data cannot be recovered from an estimate.

Collect rest periods. Records taken after charging ends and during standstills carry what driving records do not: the equilibrium voltage, the shape of the return to it, the rate of self-discharge.

Collect slow charges in full. A full charge from a low level at a small current is a rare and valuable event: curve-shape analysis is only feasible on it. Such sessions are worth flagging and storing separately from ordinary ones.

The method is one, and very simple: watch the current and sum it over time. A second passes at a current of 150 amperes — add 150 coulombs. Another second at 120 amperes — add 120. Summation with sign: subtract on discharge, add on charge.

The industry name is Coulomb counting, from the fact that coulombs are being summed.

What we learn from this. How much charge has passed through the cell. And since every coulomb that passes corresponds to the same amount of lithium having moved (section 9) — we learn how much lithium has moved from one electrode to the other.

The method gives nothing else: not capacity, not health, not even state of charge.

The measurement itself comes down to voltage — if current is measured with a shunt: the voltage across it is divided by its known resistance. If measured with a Hall sensor, the magnetic field around the conductor is measured, though the sensor's output is also a voltage. Traction batteries usually carry both: a shunt for accuracy at low currents, a Hall sensor for high ones.

The only method among all of them that makes no demands on the object. No rest is needed, no particular current, no need to know the chemistry, age, or temperature. Current flows — we count; it doesn't — we add zero.

Hence its place in the system: it is the foundation everything else stands on. The other methods work episodically, when the conditions align. This one runs continuously and ties the episodes together.

It tells you by how much the state has changed, but does not tell you what it has become.

You drive, you count that 50 amp-hours have gone. How much is left? There is no answer: if it was full, a hundred is left; if it was seventy, twenty is left.

Charge counting gives a difference, not a value. There is nowhere within the method itself to get a starting point.

Analogy: an odometer counts distance traveled but does not know where you are. To know your position you need a mark on the map, and from there you can count onward.

From the rest voltage: the cell has sat, the voltage has settled to equilibrium, and from it the fill level is determined. That is the mark on the map. From there, counting carries on until the next chance to mark position.

Hence the coupling of the two methods: counting gives continuity, rest voltage gives anchoring. Neither works without the other.

Current error is systematic, not random. A sensor may consistently read high or low by a small fraction of a percent. Random deviations would cancel each other out; systematic ones add up.

A rough estimate: the sensor reads 0.5 percent low. Over an hour at a current of 150 amperes, that accumulates 0.75 amp-hours. Over a month without a reset — a substantial quantity.

Zero offset is the worst of all. If the sensor shows 0.1 amperes when there is no current at all, a parked car will “consume” 2.4 amp-hours a day — while nothing is happening. That is why zero offset is calibrated separately: when the controller knows for certain that there is no current, it remembers the reading and subtracts it from then on.

The error does not self-correct. There is no reason for it to shrink: it only grows until reset by a new anchor point.

The cell rested — fill level determined, say, 90 percent. You drove. It rested again — determined at 40. Between the two marks, counting showed 60 amp-hours.

So 50 percent of fill corresponds to 60 amp-hours. Full capacity: 60 ÷ 0.5 = 120 amp-hours. It was 150 at manufacture — 80 percent remains.

And that is the whole of the capacity estimate: two marks and the count between them.

But the accuracy is deceptive. The error of each mark enters the result magnified. If the fill level is determined with a 3 percent error at each mark, and the difference between them is 50 percent, the error in capacity comes out to about 12 percent — because we divide by the difference, and the errors of both marks fall into it.

The rule: the wider the difference between the marks, the more accurate the estimate. Fifty percent gives an acceptable result, ten percent — an almost useless one.

Current at a sufficient rate. If the current changes quickly but is sampled rarely, it is unknown between samples. Averaging over sparse points systematically understates peak values.

Timestamps. Gaps in the record are a direct loss of charge in the count: if there is no data for two minutes, those two minutes simply drop out of the count.

Records of rest. Without them there is nothing to anchor the count to.

The current is zero, and enough time has passed for everything inside the cell to settle. The second condition matters more than the first and usually isn't met: you can switch off the current instantly, but you cannot make it settle instantly.

Under current, three kinds of lag arise inside the cell (section 6). The first two clear quickly; the third, slowly.

While current was flowing, lithium had no time to spread deep into the particles: more of it built up at the surface than in the middle. Voltage is set by what's at the surface, not by the average over the particle. After the current is switched off, lithium evens out inside the particle, and while that evening-out goes on, the voltage keeps changing on its own.

This is relaxation. It takes anywhere from tens of minutes to several hours, and the heavier the load was, the longer it takes.

The voltage will be offset, and in a consistent direction.

After discharge it reads lower than the true equilibrium: the surface has less lithium than the average, and the instrument sees the surface. After charge — higher.

The error is not random: a mark taken ten minutes after driving systematically understates the fill level.

There is no strict threshold: the voltage approaches equilibrium gradually, more and more slowly.

In practice the question is framed differently — not “when did it become equilibrium” but how much it is still changing. A working criterion: if the change over the last few minutes is smaller than the instrument's step, further waiting gains nothing.

A consequence for data collection. A single voltage point after a standstill is not enough. You need a record — a sequence of points — because only that shows whether things have settled or not. A single value cannot be told apart: it could be at equilibrium, or it could have been taken halfway there.

In places where the curve is flat: a large change in fill level corresponds to a small change in voltage, and so, conversely, a small error in voltage corresponds to a large error in fill level.

For NMC the curve slopes almost everywhere, flattening a bit in the middle. For LFP it is flat over almost the whole working range: between twenty and eighty percent, the voltage changes by only a few millivolts — within one or two steps of the instrument. Fill level cannot be extracted from it at all.

That is why, for LFP, the charge estimate is built almost entirely on counting, with rare anchor points at the very edges of the range.

The cell's curve is the difference between the two electrodes' curves. Degradation shifts the electrodes relative to each other and shortens them, so the difference changes too.

Anchoring a worn cell against the new-cell curve will give a systematic shift, not a random error. Hence: the curve must be updated as the cell ages, or a correction that grows over time must be applied.

This is also the root of one reason the factory controller cannot be trusted as a reference: the curve built into it matches the cell as shipped.

Bring a cell to 50 percent by discharging from above — you get one equilibrium voltage. Bring it to the same 50 percent by charging from below — you get another, slightly higher. Same fill level, different voltage; the difference depends on which side you approached from.

The cause lies in the electrodes themselves: lithium intercalation and de-intercalation don't follow the same path.

Magnitude. For NMC it's small. For LFP it's noticeable — and it compounds the flatness, making anchoring even less reliable for LFP.

In practice: for an accurate anchor point you need to know not just the voltage, but what happened before the rest period — charging or discharging.

Rest-period recordings, not single values , lasting tens of minutes, with timestamps.

Knowledge of history: whether it was charge or discharge before the rest, how deep, how long ago.

Temperature: the curve depends on it; in cold weather anchoring gives an offset.

A note on which end of the range the anchor was taken from — at the edges the curve is steeper and less ambiguous.

Coulomb counting with anchoring gives one number — capacity. Yet there are three causes behind its decline (Part I of the degradation document), and they call for different responses. One number can't tell them apart.

This method can tell them apart — and it's the only one that does so from voltage alone.

Look not at the curve itself, but at its slope.

During slow charging the voltage curve rises unevenly: steep in places, almost flat in others. The flat stretches aren't random — that's where the electrode is restructuring: it takes in lithium without its potential changing.

These stretches are identifying marks. Graphite has its own, the cathode has its own, each in its own place. The method consists of finding them and tracking how they shift over time.

Lithium in graphite doesn't sit at random: at different fill levels it forms different ordered structures — first it occupies every fourth interlayer gap, then every second, then all of them.

The switch from one structure to another is a restructuring. While it's underway, both coexist in the graphite: part of the volume has restructured, part hasn't. Incoming lithium doesn't raise the potential, it just increases the share of the new structure. The potential holds steady until the restructuring finishes across the whole volume.

Hence the flat stretch. It doesn't mean ‘nothing is happening’ — it corresponds to a specific event in the electrode, and is therefore tied to a specific fill level.

You compute how much the voltage changed for each added increment of charge, and plot that change against voltage.

The flat stretches turn into peaks: on them, the added charge doesn't change the voltage, meaning a lot of charge is being accepted at that voltage. A peak is easier to find and measure than a barely noticeable bend — that's the whole point of the transform.

Industry names: incremental capacity analysis (ICA) and its inverse, differential voltage analysis (DVA).

⚠ Correction to the first edition. This used to say that the first is better suited to cathode features, the second to anode features. No such division exists in the literature. The real distinction between them runs along a different line — what each one detects during metallic lithium plating: the voltage-relaxation profile and differential voltage analysis detect the dissolution reaction of lithium already plated, whereas incremental capacity analysis detects its formation. The relaxation profile shows dissolution as a plateau, differential voltage analysis shows it as a peak at a specific charge value, and incremental capacity analysis shows it as a peak at a specific voltage.

An improvement that removes the influence of resistance. Curves built from terminal voltage are sensitive to the change in resistance and polarization with aging — that is, to exactly what we want to exclude. Building the same curves from state of charge instead of voltage removes that sensitivity. This trick is worth keeping in mind when designing the processing.

What's computed is the difference between two close voltage values. If the instrument rounds to the millivolt, and the true difference is a fraction of a millivolt, the result will be either zero or a whole millivolt — wrong by a factor of several.

The curve itself will barely suffer from the rounding. The picture of its slope will turn into a picket fence.

Requirement: resolution ten times finer than is sufficient for estimating charge. Plus smoothing during processing — but smoothing too aggressively will erase the very features being sought.

The method requires that voltage reflect the state of the electrode, not lag under load. At high current the sag is large and changes over the course of charging, distorting the shape more than the features themselves.

In practice: charging from a home outlet is better than a fast-charging station, and by a wide margin. Slow full charges are a rare and valuable event; they're worth recognizing in the data stream and storing separately.

The features are spread across the whole fill-level range. A charge from 60 to 80 percent will show only those that fall within that stretch.

The information lies in the relative positions of the features, so at least two must be captured. The wider the window, the fuller the picture.

Loss of lithium. The electrodes are intact, their curves haven't changed; there's less lithium, and it no longer fills the anode to the same degree as before. The two electrodes' curves shift relative to each other. What you see: all the features keep their shape and their mutual spacing, but the whole group shifts.

Loss of sites in the anode. The anode curve compresses: the same potential range now fits into a smaller charge, while the cathode curve doesn't change. What you see: the anode features draw closer together, the cathode ones keep their spacing.

Loss of sites in the cathode. Mirror image.

Hence the distinction. A shift of the whole picture without deformation — loss of lithium. Compression of part of the picture — loss of sites, and which part tells you which electrode. The working indicator isn't a peak's absolute position, but the distance between a pair of peaks: preserved means lithium, shortened means sites.

The cause within a regime. The curve says: there are fewer sites in the anode. It doesn't say why — cracking, delamination, drying out, or foil corrosion. All four produce the same compression.

Resistance. The method deliberately operates where the influence of current is minimal.

A fast answer. It requires a slow, wide charge, which happens rarely. The method is episodic by nature.

⚠ LFP — correction to the first edition. This used to say: “the curve is almost flat, the features are weakly expressed, an estimate for LFP can't be built on this.” That is a mistake, and an inverted one at that: I transferred to this method a difficulty that actually belongs to voltage-based anchoring.

The method's strength is exactly that flat stretches turn into clearly distinguishable peaks: the flatter the plateau, the taller and narrower the peak. LFP serves as the textbook example — its curves show four main peaks, two on charge and two on discharge, each corresponding to a plateau and indicating two-phase coexistence. Pictures of how all four kinds of wear affect the peaks of a typical LFP cell have also been published.

What's genuinely bad for LFP is voltage-based anchoring, and that's a different method. The slope of the LFP curve is under one millivolt per percent of charge between 35 and 95 percent; for NMC it's 3–9 millivolts between 25 and 65 percent, and over 9 from 65 to 100. For the same voltage measurement error, the uncertainty in the charge estimate is about 8 percent for NMC and 49 percent for LFP.

Bottom line: for LFP one method works worse (section 37), the other doesn't work worse — it works better. Merging them into one verdict about the chemistry was a mistake.

Parallel groups. The resistance of the inter-cell connections creates an uneven current distribution among cells wired in parallel, which significantly reduces the method's accuracy even at a very low current — on the order of one twenty-fifth of the capacity per hour. So a parallel connection doesn't just hide cells behind one another — it also blurs the features themselves.

Fast charging shifts things in one direction. Under fast charging, the usual intercalation peaks shift and broaden toward higher voltages as polarization grows. The direction is known, so a correction could in principle be applied — but it's simpler to just pick a slow session.

A worn cell. The features don't just shift, they also blur: if some particles are trapped behind a crust or have lost contact, the restructuring happens at different fill levels in different places, and instead of a sharp peak you get a shallow hill. An unfortunate symmetry: the method works worst exactly where it's needed most.

The main consequence for this work. This method is the only source that separates the three regimes, and separating the regimes is what distinguishes a substantive assessment from a single number. So the conditions for it must be created deliberately: recognize suitable sessions in the data stream and, where possible, set them up on purpose.

The three methods covered so far worked either with no current, or with a weak, steady one. This one requires current — and requires it to change abruptly. Resistance only shows up when current flows: no current, no sag, and there's nowhere to get a measure of how hard the path is.

The current jumped by a known amount — the voltage sagged. The ratio of the sag to the jump is the resistance. A jump of 100 amperes, a sag of 0.15 volts — a resistance of one and a half milliohms.

Why a jump is used rather than a steady state. Voltage depends on both fill level and load. With a slow change in current, these influences can't be separated: while the current was ramping up, the lithium had time to move. A jump solves the problem — the fill level has no time to change in a fraction of a second, so the entire voltage change is attributable to the load.

Requirement: what's needed is precisely an abrupt transition; a gradual change is useless.

Instantaneous. Electron collisions with the lattice in the foil, wires, welds, plus the resistance of the electrolyte as a liquid. Appears within microseconds.

Medium, within seconds. The ion crossing the electrode-electrolyte interface: shedding solvent molecules, entering the lattice.

Slow, within minutes. Lithium spreading into the depth of the particle.

This is where the method's whole diagnostic value lies.

Instantaneous speaks to the conduction path: foil, welds, busbars, connectors, the volume of electrolyte — that is, to the mechanics and to how much liquid is left.

Medium — to the interfaces: the protective film on the anode, the layer on the cathode, how thick they've grown.

Slow — to what's inside the particles: restructured surfaces, wetting, how accessible the volume is.

A single total-resistance number mixes three sources together. Separated, it points to exactly where things got worse.

Sampling rate is the main requirement. The instantaneous component sags within microseconds. At a once-per-second sampling rate, both the first and second steps have already happened by the first measurement: they merge into one.

A known step magnitude , measured at the same instants as the voltage.

No other changes at the same time as the step.

Knowledge of temperature — resistance depends strongly on it.

Steps occur on their own: starting to move, hard braking with regeneration (a double step with a sign change), plugging into a charging station, end of charge. The last two are better: the car is stationary, temperature is stable, there are no extraneous changes.

A way to get the separation at once, without sorting out the time constants: instead of a step, apply current oscillations at different frequencies and watch the response.

The logic is simple. Fast oscillations — the slow processes cannot keep up, so the response is set only by the instantaneous component. Slow oscillations — everything keeps up, so the response contains all of it. Sweeping through frequencies yields the contribution of each component separately.

The name for this is impedance spectroscopy.

The limitation that determines everything. A separate instrument is needed, one capable of applying oscillations at a set frequency. The car's standard controller usually does not have one. The method stays a bench technique, or requires special equipment during service.

Resistance is not just a standalone indicator — it distorts the capacity measurement. A cell with increased resistance hits the lower threshold before it is actually empty, and the instrument records a reduced capacity even though the lithium and the sites are intact.

How to tell them apart. Measure at different currents. For a cell that has lost lithium, the result barely depends on current; for a cell with increased resistance, it depends strongly.

This is the only way to separate two states that produce the same drop in measured capacity.

Chemistry sets only the order of magnitude. The actual value depends on electrode thickness and porosity, particle size, amount of electrolyte, wetting quality, the number of current tabs, and the build: two cells of the same chemistry — a power cell and an energy cell — can differ several-fold.

On top of that comes the state: temperature (multiple times higher in the cold), state of charge, age. And on top of that comes the individual cell's history: film thickness, degree of drying-out, condition of the seams.

That is why resistance is not taken from a datasheet — it is measured repeatedly over time, and what matters here is not the absolute value but how much it has grown relative to its own baseline. Comparing a cell against itself a year ago tells you more than comparing it to the datasheet figure.

Chemistry gives only one useful fact: LFP resistance is usually higher than NMC of the same capacity, and it rises more steeply in the cold.

These are two different things, and confusing them is a source of wrong expectations.

It measures: voltage per cell or per parallel group — always, otherwise balancing would be impossible; overall current; temperature at several points per module.

The frequency inside the controller is high enough — it needs this for its own protection: in a short circuit it must react within milliseconds.

What comes out to the outside is incomparably less. Through the diagnostic connector, data is usually output once a second or less often, and per-cell voltages may not be output at all, even though they are measured internally.

Hence the split. The requirements from the previous parts are not wishes addressed to the manufacturer but conditions for the methods to apply. The manufacturer will not meet them, because it is solving its own problem.

Available: coulomb counting, anchoring by open-circuit voltage, curve shape under slow charging, total resistance from a step, the whole pack-level layer.

One thing unavailable: splitting resistance into three components — that needs hundreds of points in the first seconds.

Conclusion: time-domain separation does not work as a basis for field diagnostics. It is available on a test bench and during service with dedicated equipment, but not in the stream of operational data.

Only by testing on the specific car.

Looking at the parameter list. A diagnostic tool polls the controller and gets a list of available parameters. A hundred voltage rows — present; three or four — not.

Checking that these are actually cells. Numbers in the 3-4.2 volt range, the count matches the pack's capacity, the values change consistently under load.

Checking for a substitute. Sometimes parameters are labeled as per-cell, but the same number is output into every row, or the values never change at all. A minute of observation reveals it.

Checking for meaningfulness. Apply a load and see whether the values spread apart. If the spread is always zero to the third decimal, it is probably a calculated value being output, not a measured one.

Record the stream and look at the timestamps between updates of one parameter.

First subtlety. The tool may poll faster than the controller updates: the same value arrives several times in a row. The real rate is the rate of change of the value, not of polling.

Second subtlety. Polling many parameters at once drops the overall rate: the controller answers them in turn. A hundred voltages update slower than one.

You generally cannot force it to output everything. If a parameter was not designed in, it does not exist for the outside world — that is not a setting, it is the makeup of the controller's firmware.

Three workarounds, all worse than the direct route: the manufacturer's service commands (access is restricted); reading the pack's internal bus, where sometimes more travels than is output externally (requires tapping in and decoding an unpublished format); a measurement layer of your own — that is, opening up the pack.

What the minimum and maximum give you. The difference between them is a direct measure of spread, and spread rises earlier than average capacity does. Cell numbers are usually output too: if one number is consistently at the minimum, the weak cell has been found.

What it does not give you. A distribution. One outlier cell and three outlier cells give the same minimum.

Classifying the case. Uniform wear, one outlier cell, several outlier cells — indistinguishable from the extreme values, but distinguished at once from the full set, by the shape of the distribution. This is exactly the "is the wear localized or uniform" distinction that decides whether the pack can be restored by replacing a module.

A map of positions. It shows which locations age faster; they are systematic and set by the cooling geometry. The knowledge carries over from one car to another of the same model.

Module sorting. Eighty sound modules for second life, two defective ones for recycling — without the full set there is no way to say which is which.

Separating chemistry from mechanics. The difference between the sum of the per-cell voltages and the pack voltage points to the busbars and connections. You cannot compute that sum knowing only the extreme values.

What you still will not get, even with the full set. Per-cell current — it does not exist. The temperature of every single cell — there are fewer sensors than cells. Safety risk — it has no measurable precursor.

Yes, if the aim is telling cases apart and deciding what to do with a pack. Without the full set this is impossible, and the analysis yields the same single number as everyone else.

No, if the aim is estimating the capacity of the whole pack. For that, the overall voltage and current are enough.

In other words, this is not a technical requirement but a consequence of what the work is for. And access should be checked from that angle: not "what can be read out" but "is what gets read enough to tell cases apart."

All the previous methods were applied to an object — a cell or a pack — and asked what state it was in. These work differently: they compare cells against each other. The object is the same, the question is different — not "how worn is it" but "is the wear the same."

Hence their special feature: they need neither rest, nor slow charging, nor a high sampling rate. They need just one thing — for the cells to be visible individually.

Where the need comes from. Cells in a string differ in capacity and in self-discharge. The current through them is the same, but they accept it differently, and over time some end up fuller than others.

Why this is bad. Charging stops when the first cell reaches its upper limit, discharging stops when the first one reaches its lower limit. Cells that have drifted apart cut into the pack's usable capacity — not because they are worn, but because they no longer match.

How they are equalized. By bleeding: a resistor is connected to each cell, and the surplus from the cell that got ahead is burned off as heat. Simple, cheap, used almost everywhere; the cost is wasted energy and low power, so equalizing takes a long time. Or by shuttling: the surplus is moved from the full cell to the empty one; more complex, more expensive, less common.

When it operates. Usually at the end of charging, when the divergence is visible, and while parked. Rarely on the move: under load the voltages are distorted by sag, and you cannot tell from them who is actually ahead.

What it can and cannot do. It can equalize how full the cells are. It cannot equalize capacity or resistance: a cell at 60 percent capacity stays exactly that after perfect balancing.

An important consequence for data access. Without per-cell voltage measurement there is nothing to equalize — the controller would not know which cell to trim. So, per-cell measurement exists in every traction pack, and the question is always only about access to it, never about whether it exists.

One caveat about resolution: what is measured is a cell or a parallel group. If a position holds two or three cells in parallel, they share one voltage by construction, and within the group per-cell data does not exist for anyone.

What is counted. The difference between the highest and lowest voltage in the pack; with the full set, the spread of all the values around the mean.

Why it is more informative than the average. Spread feeds on itself: a cell with higher resistance heats up more, heating speeds up its degradation, degradation raises its resistance further. Inhomogeneity grows faster than average wear, which is why spread is an early sign, while a drop in capacity is a late one.

Where to look. At the edges of the range, not in the middle: in the middle, cells of different capacity have nearly the same voltage, and they diverge at the end of charge and the end of discharge. Spread at the end of a charging session carries more information than spread while driving.

What it cannot tell apart. The cause: a cell can lag behind either because it has lost capacity, or because it has elevated self-discharge.

A sign that is right on the surface and usually goes unused.

What it is. Information about which cell the controller trims and how often.

What it tells you. A cell that is constantly trimmed, always in the same direction, loses charge faster than its neighbors — that is, it has elevated self-discharge. Its capacity is otherwise normal; this is a manufacturing defect, not wear.

Why the distinction matters. A cell that has lost capacity and a cell with self-discharge limit the pack in the same way, but they mean different things: the first is the outcome of use, the second is a defect that surfaced over time. Different prognosis, different grounds for a warranty claim.

And the reverse implication. As long as the balancing power is sufficient, the voltage spread looks small: balancing masks the early divergence. By the time the spread becomes visible in the voltages, the cells have already drifted apart substantially. That is why information about the balancing activity itself is more informative than its result.

A caveat. This data is output externally less often than the voltages themselves; availability needs to be checked on the specific car.

A sign that needs only data already being collected, and that separates chemistry from mechanics.

The idea. Per-cell voltages are taken at the cell terminals, pack voltage at the pack's terminals. Between them lie busbars, welded joints, connectors, contactors, and under load a voltage drop appears across all of it.

Sum of the per-cell voltages minus the pack voltage = drop across the connections.

What it gives you. For a sound pack this value is small and stable. Its growth over time points to loosening connections and corrosion, not to electrochemical degradation. This matters because both phenomena look the same — the pack sags more under load — and a single overall voltage cannot tell them apart.

Requirements. The full set of per-cell voltages, and simultaneity of measurement: if the cell voltages and the pack voltage are taken with a delay and the current changed in between, the difference will be garbage.

What it gives you. The difference between sensor readings points to uneven cooling.

Why it is valuable. The temperature gradient is systematic: it is set by geometry, and the map of hot spots for a given design stays constant. It lets you predict which cells will age first — a rare case of a forecast based on the design rather than on a measurement.

Limitation. There are fewer sensors than cells, and the hottest point is usually not covered: the spread across sensors is a lower bound on the true spread.

Separately. A growing temperature spread under unchanged conditions points to worsening cooling — clogged channels, a worn pump. This is a system-level failure that otherwise shows up nowhere else: it simply raises the temperature and speeds up the aging of the whole pack, looking like natural aging.

The only parameter that is measured directly and relates to the construction, not the chemistry.

What it shows. The appearance of a conductive path between the power section and the housing: moisture, a coolant leak, damaged cable insulation.

How it differs. Not gradual but threshold-like: while the insulation is intact, the value is high and stable, and it drops once a leak appears. The only direct measure of the pack's health as a physical structure.

What the whole group does not give. Capacity, resistance, the separation of the three regimes. These are indicators not of state, but of uniformity.

And that is their role. The earlier methods answer "how worn is it". These answer "is it uniform" — and it is precisely the second question that decides whether the pack can be restored and where it should go.

This document is organized by method, because the list of methods is closed. But the question people usually ask is not "what does this method give" but "how do I find this out". Here is the same material, turned around into questions.

How much is left right now. Coulomb counting from the last anchor point; the anchor comes from the open-circuit voltage at rest. Neither works without the other.

How much capacity is left of the original. Two anchor points and the count between them. Accuracy grows with the width of the interval. The result is skewed by resistance if it has grown.

What the capacity loss is due to. Only curve-shape analysis during a slow, wide-range charge. The only method that distinguishes the three regimes. No method gives the cause within a regime.

How much the resistance has grown. The response to a current step. The total value — at an ordinary logging rate; splitting it into components — only at high sampling frequency or on a test bench.

Where exactly it has degraded. Splitting resistance by time constant: the instantaneous component points to the current path and the electrolyte volume, the medium one to protective layers, the slow one to the interior of the particles. Not available in the field.

Is the wear localized or uniform. Voltage spread, better near the edges of the range. The minimum and maximum show the size of the spread, but not the shape of the distribution.

Has the cell lost capacity, or does it have self-discharge. Balancing activity by position.

Has the chemistry degraded, or have the connections weakened. The difference between the sum of the per-cell voltages and the pack voltage under load.

Has the cooling degraded. A growing temperature spread under unchanged conditions.

Has metallic lithium been plating out. The shape of the voltage's return to equilibrium after charging — rest-period recordings tens of minutes long. The indicator exists; its reliability on a real vehicle has not been verified.

What is the risk of sudden failure. No method answers this. What works here is not a measurement but the service history.

First: only the pack's overall voltage and current. State of charge, an estimate of the pack's capacity, and total resistance are available. Everything related to distinguishing between cells is unavailable: uniform wear and a single failing cell look the same. At this level the answer is a single number, as it is everywhere else.

Second: the minimum and maximum across cells are added. This adds the size of the spread and identifies the weakest position by number. It does not add the shape of the distribution: one failing cell and three failing cells give the same minimum.

Third: the full set of per-cell voltages. This adds case classification, a map of aging positions, the sum-versus-whole difference, and a basis for module sorting. The level at which an answer other than a single number becomes possible.

Fourth: high polling frequency. This adds splitting resistance into its components, that is, localizing the degradation. Achievable on a test bench and during servicing, not in the stream of operational data.

Fifth: the laboratory. Direct capacity measurement by a full discharge, separate electrode potentials via a half-cell with a lithium electrode, impedance spectroscopy, teardown. A destructive level.

The current of an individual cell. It does not exist: in a series string the current is single; in a parallel group it splits, but is not measurable.

The temperature of every cell. There are always fewer sensors, and the hottest point is usually not covered.

A warning sign of failure. A cell with a lithium dendrite growing inside it shows normal capacity, resistance, and curve — right up to the moment it pierces through.

The first two are limits of the construction, the third is a property of the phenomenon itself. None of them is removed by better equipment.

First. Only one thing is measured — voltage; everything else is reconstructed. So the quality of the estimate is set not by the algorithm, but by which segments of the record exist: without a rest period there is no anchor point, without a slow charge there is no separation of regimes, without a step there is no resistance. Working with the data starts with recognizing the suitable segments, not with processing them.

Second. The access level determines not accuracy, but the composition of the answer. The first level gives the same thing as everyone else; the third gives a distinction that no one else has. The difference is qualitative, not quantitative.

Third. The measured state and safety are different things, and the second does not follow from the first. An assessment based on capacity and resistance answers the question of residual value; only the service history answers the question of risk, and it must be collected as a source in its own right.

That method waited for the voltage to reach equilibrium and took the final value; the path to it was noise. Here it is the opposite: the final value does not matter, the path does. What is examined is exactly how the voltage returned — fast or slow, smooth or with a step.

The same data, different questions. The first method needs the last point, the second needs the whole curve.

After the load is removed, lithium spreads from the surface of the particles into their depth, concentrations even out, and the voltage settles toward equilibrium. The speed of equalization is set by how easily lithium moves inside the particles.

So the shape of the return speaks to something the other methods stay silent about: the accessibility of the particle's volume. In a new cell the return is fast and smooth; in a worn one it is slower — a crust on the surface gets in the way, and part of the volume is locked away.

The main reason this method exists.

When charging in the cold or charging too fast, lithium does not have time to intercalate into the graphite and plates out as metal on the surface. After charging ends, at rest, this metal starts dissolving back.

While dissolution is underway, it holds the anode potential at the level corresponding to metallic lithium. Ordinary relaxation gives a smooth rise in voltage; the metal dissolving gives a delay or a plateau in that rise, followed by a continuation. A segment appears on the return curve that a healthy cell does not have.

The mechanism is confirmed directly: plating occurs when polarization during charging drives the anode potential below zero relative to metallic lithium, making metal deposition more favorable than intercalation. So the plateau on relaxation is the trace of the reverse reaction.

Three ways to see the same event. The relaxation profile shows the dissolution of the plated lithium as a plateau; differential voltage analysis shows it as a peak at a specific charge value; incremental capacity analysis reveals not the dissolution but the formation of the plating itself — as a peak at a specific voltage. They complement each other, and the indicators agreeing is more reliable than any one alone.

Why this is valuable. The only existing indicator that relates to the safety side. All the other methods measure wear; this one points to an event that creates risk.

From the same rest period, but on a different time scale. The cell sits for a day or a week, the voltage slowly drifts down — the rate of drift is the self-discharge rate.

What it reveals. A cell with an internal defect causing a leak: capacity is normal, but the charge is lost faster than in the others.

Difference from balancing activity. Balancing shows the same thing indirectly — through one position being constantly trimmed. A direct measurement of the drift is more reliable, but requires a long stand-still with no intervention.

The whole rest-period record, not just the last value — the method works with the shape, and a single point does not contain it.

Sufficient frequency at the start: the return is fastest in the first minutes, and that is where the main information lies; sparse sampling will smooth out exactly what is being sought.

Sufficient duration: tens of minutes for relaxation, a day or more for self-discharge.

Knowledge of history: what preceded the rest period — charging or discharging, to what depth, at what temperature.

Temperature during the rest period — affects both the relaxation rate and self-discharge.

The plating indicator is ambiguous. A plateau on the return curve can have other causes too, such as phase transitions in the electrodes. Telling them apart requires knowing exactly where on the curve to expect what.

Reliability on a real vehicle has not been verified. The indicator has been described under laboratory conditions; how distinguishable it is in data from a vehicle, where temperature fluctuates and stops are interrupted, I cannot confirm.

Self-discharge requires a long rest period , which a vehicle used daily does not provide.

All the methods discussed so far work the same way: take a segment of the record where the right conditions occurred, and extract a value.

Model-based methods work differently: they build a description of the cell and fit its parameters so that the description reproduces the observed behavior. The fitted parameters are themselves the answer.

Instead of "find a suitable segment and calculate" — "assume a structure and fit the numbers".

The most widespread approach, and the same one underlying what the controller does.

The idea. The cell is represented as a set of simple elements: a voltage source that depends on the state of fill, plus resistors and capacitors reproducing the three stages of voltage sag. A circuit with two or three links is enough.

How it works. From the current and voltage record, element values are fitted so that the circuit gives the same voltage that is observed. These values are then used as estimates.

Advantage. Works continuously, on any data, with no special conditions. That is why the controller is built on it.

Limitation. The circuit does not describe the cell, it imitates its behavior. Its elements do not correspond to physical parts: a resistance in the circuit is not the resistance of any specific layer. No conclusions about what exactly changed inside can be drawn from the fitted numbers.

The opposite approach: describe not the behavior but the structure — lithium diffusion inside the particles, ion transport through the electrolyte, reactions at the interfaces, the distribution across the electrode thickness.

Advantage. The parameters have physical meaning: a growing interfacial resistance is a statement about the protective film, not about an abstract circuit element.

Limitations. There are many parameters, and not all of them can be recovered from measurements: different sets give the same observable behavior. The computation is heavy. And most importantly — the model requires knowledge of the specific cell's construction, which an outside observer does not have.

Conclusion. For work on someone else's cells with no documentation, this path is closed.

Third approach: find the relationship between what is observed and what is sought from accumulated examples.

How it is built. A set of cases is assembled where both what the instruments saw and the true state — measured destructively or on a test bench — are known. From these pairs a rule is fitted, which is then applied to new records.

Advantage. Requires neither physics nor a circuit; it can catch relationships a person would miss.

Three limitations. Labeled examples are needed — cells whose true state has actually been measured; getting them is expensive and destructive. The rule works only on what it was trained on: one trained on a given chemistry and design does not carry over to another, one trained in a temperate climate does not work in freezing cold. And the rule does not explain: it gives a number but does not say what it follows from.

Where it fits. As an add-on over the methods already covered, not in place of them: physical methods give quantities, a trainable rule links them to a final estimate. Replacing physics with training on a small dataset gives a number that cannot be trusted.

Common to all three. A model adds no information beyond what is in the data — it only extracts it differently. If the record has no rest period, no model will give a reliable anchor point: it will give an estimate indistinguishable from a guess.

This is worth remembering whenever a model-based approach is offered as a substitute for data-collection conditions. It is not one.

Because some processes leave no electrical trace. Gas evolution swells the cell, electrolyte consumption leads to drying out — neither is measured directly by voltage, yet both are conditions that determine remaining life and safety alike.

What is measured. The change in the cell's size — directly, or via the force with which it presses on the restraining structure.

What it tells you. Gas buildup, that is, electrolyte consumption. Swelling is not a failure in its own right but an indication of how much liquid has turned into gas. Plus a reversible part: the cell "breathes" with every cycle from graphite expansion, and a change in the breathing amplitude over time tells you about the anode's condition.

Where it applies. In stationary installations, continuously, with a force sensor. In a vehicle — on inspection, and even then only for pouch-type cells: in a steel case swelling is not visible from outside, but internal pressure rises instead.

Separately. Swelling is the only cell damage discernible without instruments. For accepting used batteries, it is the first sign worth checking.

The idea. A sound wave is passed through the cell, and how it came through is observed: faster or slower, more or less attenuated.

What it gives you. The speed of sound depends on the density and elasticity of the medium, and these change together with how filled the electrodes are with lithium and how much liquid is in the pores. The response carries information that voltage cannot measure: how full the pores are with electrolyte, and whether there are gas bubbles.

Why it is valuable. A direct route to drying-out — a process that produces the kink in the aging curve, after which extrapolation stops working.

Limitations. Requires sensor contact with the cell. Not applicable on an assembled pack. The method is still developing; there is no established practice.

What they detect. Electrolyte decomposition products released on damage or at the onset of thermal runaway.

What sets them apart. The only methods that react to a failure before it develops: gas evolution precedes runaway.

Limitation. They do not measure aging and say nothing about capacity. These are protective tools, not diagnostic ones.

What it gives you. A picture of the pack's heating under load; a spot with elevated temperature points to a locally increased resistance — a poor contact, a loosened weld, a degraded cell.

Why it is valuable. Gives a spatial picture that sensors lack: there are only a few of them, while a thermal camera sees the whole surface.

Limitation. Sees the outer surface; inner layers are hidden, and a hot spot may not show up on the outside.

In common. None is applicable within the stream of operational data: all require either physical access or a stationary setup.

But one closes a gap that could not otherwise be closed. Electrolyte drying-out is poorly distinguished by electrical methods — it shows up as a rise in resistance, indistinguishable from other causes. Ultrasound and thickness measurement give a direct route to it.

Capacity obtained by counting charge between two anchor points, and capacity obtained from the shape of the curve, will always diverge. The reason is not errors, but that the methods measure different things while calling it by the same word.

Coulomb counting gives the usable capacity — how much charge could be obtained under the conditions of measurement: at that current, at that temperature, between those thresholds.

The curve's shape gives the thermodynamic capacity — how many sites are available for lithium, regardless of whether they can actually be reached.

In a cell with increased resistance the first is noticeably smaller than the second: the sites exist, but at the working current the voltage hits the threshold sooner.

Hence the rule. The discrepancy between the two estimates is not a reason to pick the more reliable one, but an indicator in its own right: it is a measure of how much resistance eats into the available capacity.

Explainable. The methods measure different things, as above. The difference is informative; both estimates are kept, with their conditions noted.

Due to conditions. One of the methods was working outside its domain: an anchor point taken without sufficient rest, the curve shape recorded at high current, resistance computed during a gradual change. An estimate obtained outside its conditions of applicability is discarded, not averaged with the correct one.

This requires every estimate to be accompanied by information about the conditions under which it was obtained. An estimate without them cannot be verified and is therefore useless in case of a discrepancy.

Unexplainable. Both methods are within their conditions, yet the answers differ. A signal that some third factor has not been accounted for: the curve has changed with age, the cell is non-uniform, the data are corrupted. Averaging here is the worst option — it hides the contradiction instead of revealing it.

Average estimates of different reliability. An estimate over a wide interval between anchor points and one over a narrow interval differ several-fold; the average is worse than the better of the two.

Issue a number without stating how it was obtained. Whoever consumes the estimate cannot verify it and does not know which case it belongs to.

Hide a discrepancy. It is itself information, often more valuable than either estimate on its own.

Every estimate is stored together with the conditions under which it was obtained: by which method, over which segment of the record, at what temperature and current, how wide the interval was. Without this, discrepancies cannot be resolved.

Discrepancies between methods are stored as a value in their own right , not eliminated on recording.

A final number, if one is needed, is the result of an explicit rule , not of averaging. The rule must be written down and checkable: which estimate is preferred in which case, and why.

The controller polls the cells often — tens of times a second. These readings live in working memory for an instant: it uses them for protection and estimation and immediately overwrites them with the next ones. Nobody stores raw time series at that frequency — it has neither the memory nor the need to.

⚠ Correction to the first edition. This used to say that the controller "stores almost nothing." That is too categorical. Modern controllers log voltage, current, temperature and other parameters throughout the service life, including while the battery is switched off, in order to later extract typical usage profiles. A separate history is kept of charge and discharge cycles, temperature extremes, and fault events, used for diagnostics, warranty assessment, and updates.

What remains true is the distinction: no raw data, but aggregates and trends exist. But the volume and composition of what is stored depend heavily on the generation and manufacturer, and this should be checked on the specific vehicle rather than taken for granted.

Three things, and all of them are totals, not raw data.

Accumulated counters: total charge passed, cycle count, hours of operation, total time in various temperature ranges. One number per lifetime, updated continuously.

Extreme values reached: maximum and minimum temperature, maximum current, the most extreme cell voltages over the whole lifetime.

Event records: fault codes, sometimes with a snapshot of the readings at the moment of triggering. Tens of records, no more.

Detailed voltage-over-time records. Full charge curves. Rest-period records at sufficient frequency. That is, exactly the raw data the methods covered here rely on.

Consequence. There is, as a rule, nowhere to get a retrospective of the needed detail from the vehicle: connecting to a three-year-old car gives you its current state, accumulated totals, and event records — but not how it arrived at that state, in detail sufficient for curve-shape analysis or resistance decomposition.

But it must be checked. Since what is stored varies, some vehicles turn out to have more saved than expected — up to full usage profiles. This belongs to the same checklist as the availability of per-cell voltages (sections 62–64).

Not out of economy, but by purpose. The controller solves three tasks: keep the cells from exceeding their limits, balance them, and tell the vehicle the remaining range. All three need the current state, not history.

Plus constraints: non-volatile memory of limited size, with a limited number of rewrites, operating under the same temperature conditions as the pack.

The history has to be collected yourself, from the moment of connection. Everything before that is gone for good — except the accumulated totals.

The accumulated totals are more valuable than they seem. Total charge passed, cycle count, time at high temperature, extreme values reached — this is precisely the usage history that alone speaks to risk. It should be read out first and at every connection: it cannot be reconstructed from observation.

The volume of your own data collection must be calculated in advance. ≈ Estimate: four quantities with timestamps, recorded once a second, give about 2.6 million points a month. With a compact binary representation — roughly four bytes per point — that is about 40 megabytes; with an ordinary text representation, about twenty bytes per point, it is already about 200 megabytes. The fivefold difference comes down purely to format, and it is worth deciding before, not after, collection begins.

This is also why recognizing segments matters more than processing them. Writing everything indiscriminately at high frequency is impossible. The collection device must recognize the moment when conditions line up — a slow charge has begun, the vehicle has settled into a long rest, a sharp current spike has occurred — and raise the recording rate right there.

The methods were covered by physics. Here the same material is turned around by conditions: which event in the vehicle's life opens which opportunity, and how often it occurs.

State of charge is updated continuously, the anchor — daily. The freshest of the estimates.

Capacity updates once a pair of anchors with a wide gap has accumulated. For a vehicle that cycles between thirty and seventy percent, such a pair may not appear for weeks.

Mode separation — the rarest of all, because it requires a slow, wide charge. For an owner who charges only at fast stations and only up to eighty percent, it is unavailable altogether.

Resistance — frequent, there are plenty of spikes.

Spread — at every charge.

The sign of metal plating — at every overnight charge, if the rest period is logged.

Three things, each inexpensive and each noticeably widening the picture.

Asking the owner to occasionally charge slowly and fully. One such session a month unlocks the only method that distinguishes the modes.

Not interrupting long parking periods with polling. If the data-collection device wakes the controller, the rest is disturbed. Polling during a parked period must be rare and short.

Flagging deep cycles. A rare full discharge gives the best anchor at the lower edge — and along with it, the widest pair for estimating capacity.

State-of-health estimation is not a one-time procedure, but a accumulation of opportunities. The completeness of the picture depends not on the quality of the algorithm, but on whether the right events occurred during the reporting period.

Hence a practical distinction: two vehicles of the same age can be assessed with different levels of completeness simply because one was charged at home and the other at charging stations. This should be reflected in the estimate itself — as completeness, not as accuracy.

A list of boundaries. Not gaps in the document, but properties of the subject.

How much longer the cell will last. Requires an assumption about the future duty cycle. Measurement gives the state; a forecast gives the state plus a scenario. These are different things, and the second does not follow from the first. A forecast issued without stating its scenario carries the hidden assumption "things will go on as before," and that assumption is usually wrong.

What is the risk of sudden failure. Separator puncture, particle indentation, and weld fatigue have no measurable precursor. Here it is service history that matters, not measurement.

What exactly was damaged inside a mode. The curve says: there are fewer sites in the anode. From what — cracking, delamination, drying-out, foil corrosion — no method says.

What the state of a cell is inside a parallel group. A group shares a common voltage by construction. This data does not exist for anyone, including the manufacturer.

What the temperature of each cell is. There are always fewer sensors, and the hottest point is usually not covered.

What happened to the vehicle before the device was connected. The controller does not store history; only accumulated totals are available.

How much material is in the cell for recycling. The question makes sense, but it has nothing to do with measuring state of health: the mass of lithium, nickel, and cobalt barely changes with wear. This is a nameplate value, not a measured one.

Do not answer approximately. An approximate answer to an unmeasurable question is worse than a refusal: it looks like the result of a measurement and inherits its credibility.

The correct form is to state which part of the question is measurable and which is not, and what the unmeasurable part rests on. For a remaining-life forecast, that is the duty-cycle scenario; for risk, it is history; for composition, it is the nameplate.

The question that gets asked first, and one the document has not yet answered.

A breakdown by contribution, for an estimate made by the two-anchor method with counting in between.

Error in determining the fill level at each anchor. Made up of instrument accuracy, incomplete relaxation, hysteresis, and curve shift with age. On the order of a few percent, and it enters the result twice.

Error in charge counting between anchors. Systematic current-sensor error plus zero offset, accumulated over the time between anchors. On the order of fractions of a percent over hours, a few percent over weeks.

Width of the gap. Divides the sum of the first two: the wider it is, the smaller the result.

The effect of resistance. Not an uncertainty but a systematic shift: the measured capacity is understated by exactly as much as the resistance eats into the available range.

With a wide gap — on the order of fifty percent of fill level — a reliable anchor after a long rest, and a fresh current calibration, the resulting uncertainty comes to a few percent.

With a narrow gap, a short rest, and a stale calibration — tens of percent, meaning the estimate stops distinguishing a worn battery from a healthy one.

This is an order-of-magnitude estimate, not a measured value: for a specific dataset it should be computed from the actual contributions.

Accuracy is not a property of the algorithm, but a property of the dataset. The same algorithm on good and bad data gives results whose reliability differs by an order of magnitude.

An estimate without a stated uncertainty is unfit for a financial decision. The difference between "state of health 82 percent plus or minus two" and "82 plus or minus fifteen" is the difference between having grounds for a deal and having none.

Uncertainty must be calculated and stored together with the estimate , not quoted as a general characteristic of the method. It differs from case to case, because it depends on what data happened to accumulate.

The check was carried out on 04.08.2026 against the document's load-bearing claims and all of its calculations. Result: one confirmed verbatim, one confirmed with a qualification, three not confirmed; of twelve calculations, eleven are correct. Plus four findings beyond the check itself. No source turned out to be closed to machine reading.

Applicability of curve-shape analysis to LFP. The claim was: "the curve is nearly flat, its features are weakly expressed, an estimate cannot be built on this." The opposite was found: flat plateaus turn into clearly distinguishable peaks, and LFP serves as a textbook example of the method — four main peaks, two each on charge and discharge. Published figures show the effect of all four types of wear on the peaks of a typical LFP cell. The error consisted in carrying over a difficulty that belongs to voltage-based anchoring onto a different method. Corrected in section 49; numbers on curve steepness and on the uncertainty of the charge estimate were added there too — 8 percent for NMC versus 49 for LFP.

The division of roles between ICA and DVA. The claim was: "the first is better suited to cathode features, the second to anode features." No such division exists in the literature. The real difference is in what each one reveals during metal plating. Corrected in section 44, the consequence is developed in section 81.

The volume of what the controller retains. The claim was: "it stores almost nothing." Too categorical: modern controllers log parameters over the service life, including time spent powered off, as well as a history of cycles, temperature extremes, and events. What remained true was the distinction "no raw data, but aggregates exist." Corrected in sections 100 and 102.

The mechanism of metallic lithium plating: it occurs when polarization during charging drives the anode potential below zero relative to Li/Li⁺, making metal deposition more favorable than intercalation.

Estimate of the volume of the system's own data collection. The claim was "tens of megabytes a month." The calculation gives about 40 megabytes with a compact binary representation and about 200 with a text representation. Corrected in section 104 with the calculation shown.

All twelve of the document's calculations were recomputed: converting ampere-hours to coulombs, the number of ions and the mass of lithium, kilowatt-hours in joules, the accumulation of current-sensor error and zero offset, the capacity estimate from two anchors, error propagation, resistance from the voltage sag, the quantization step, and the data volume. Eleven are correct; the only discrepancy is in the volume estimate.

Parallel groups blur the features. The resistance of inter-cell connections creates an uneven current distribution and significantly reduces the accuracy of the method even at very low current. Section 49.

Plotting curves against charge instead of voltage removes sensitivity to the growth of resistance and polarization with aging. Section 44.

Fast charging shifts the peaks directionally — toward higher voltages as polarization grows. Section 49.

Three independent signs of metal plating instead of one: a plateau during relaxation, a peak in differential voltage analysis, a peak in incremental capacity analysis. Agreement among the signs is more reliable than any one of them alone. Section 81.

The value of a reference galvanic cell at about 1.018 volts and the band gap of silicon at about 1.2 volts are well-known figures; they were not checked against primary sources.

The standard potentials of lithium and oxygen relative to the hydrogen electrode — the same.

The uncertainty estimate in Appendix C is an order-of-magnitude estimate by contribution, not a measured value.

The claim that the sign of metal plating is distinguishable in data from a real vehicle, and not only under laboratory conditions, remains unconfirmed.

The document was closed on 04.08.2026. Outside its scope remain the tools — what exactly to use to collect the data — and the design of their storage and processing.