Today's article comes from the Space Science & Technology journal. The authors are Sun et al., from the National Active Distribution Network Technology Research Center (NANTEC), in China. In this paper they're building a system that can predict a solid-state battery's state-of-charge in real time.
DOI: 10.34133/space.0198
On August 19th 2016, Samsung released the Galaxy Note 7. There was a tremendous amount of hype: it was supposed to be sleek, powerful, beautiful, useful, and category-defining. Five days later, that all changed, when a user in South Korea reported that the phone had exploded. A few days after that, another report. Then another. Then another. From the US, from China, from Australia, from everywhere that the phone had shipped. Samsung sprang into action, set up a recall, and started shipping out replacement phones to affected users. But then...the replacement phones started catching on fire too. Two months after launch, the Note 7 was fully discontinued. But...it's not as if Samsung had much of a choice at that point. The phone had been banned from airlines and trains and ships around the globe, it had been mocked and vilified on every channel imaginable, and it was quickly becoming the source of innumerable lawsuits, and well...nightmares.
Why was this happening? Good question. But a better question is: why doesn't this happen more often? Lithium-ion batteries (the kind in the Note, and also the kind in virtually every other smartphone, tablet, and laptop) are extremely volatile. They're susceptible to puncture and overheating. They warp and bulge under stress and can easily ignite if short-circuited or over-charged. The fact that our devices aren't blowing up in our pockets and bags every day is kind of a miracle. It's a feat of engineering. We've dealt with Lithium-Ions many many drawbacks because it was the only usable game in town. If you wanted compact, thin, lightweight, batteries that could power a device all day, and stand up to thousands of charging cycles, it was the only option. So engineers did the only thing they could do: build their device's casings and connections as defensively and robustly as possible, do a ton of QA, and just cross their fingers that nothing blew up. That was the status quo for quite a while, but today that's starting to change.
Enter "solid-state" batteries. You've heard of old-school lead-acid batteries (the kind under the hood of a classic car), and nickel-metal hydride batteries (the AA / AAA type in your remote control), and of course lithium-ion. Now there's a fourth major type. "Solid state" are the next generation of lithium-based batteries. They still rely on lithium ions to store and release energy, but they replace the liquid electrolyte with a solid material, often a ceramic, glass, or polymer. This makes them much safer (solid interfaces don't leak or combust) and allows for denser energy storage, since the solid electrolyte can handle higher voltages and support metallic lithium anodes without the risk of short circuits.
The challenge with solid-state batteries is operationalizing them. It's not that they're fundamentally flawed, it's just that they haven't been commercialized yet. They're still very much a research/prototype kind of idea. Getting them from the lab to the factory is going to require years of modeling and refinement. Before they can go into mass production we need to figure out how to characterize them, how to monitor them, and how to manage them in real-world conditions. How to charge them safely and how to estimate their health and state of charge accurately.
That's where today's paper comes in. In it, the authors are biting off one small piece of that puzzle. They're trying to build a system that can predict a solid-state battery's state-of-charge in real time. If they can successfully do that, they'll be able to track battery performance without disassembling or damaging the cell. A critical step towards commercialization.
Let's walk through the authors' experimental setup, explore how they extracted features from impedance spectra to build predictive models, and run-down their approach to making these measurements fast and efficient.
But first, some context. When you're trying to figure out how much charge is left in a battery, you have a few options. The simplest is ampere-time integration, which is basically just keeping a running tally of how much current has flowed in and out. Most battery management systems use this approach because it's straightforward and doesn't require complex modeling. The problem is that it's only as accurate as your initial value and your current sensor. If either of those is off, your estimate drifts over time and there's no way to correct it.
The other common approach is to use a model-based method, typically involving some kind of Kalman filter. You build an equivalent circuit model of the battery, use the model to predict voltage based on current, and then use the difference between predicted and measured voltage to update your state of charge estimate. This works reasonably well for lithium-ion batteries because we have decades of research on how to model them. But not so for solid-state batteries. The material systems are different, the internal processes are different, and critically, the impedance characteristics are different as well.
That last point is what these authors decided to exploit.
Electrochemical impedance spectroscopy, or EIS, is a technique where you apply a small alternating current signal to a battery at different frequencies and measure how the battery responds. The result is a complex impedance spectrum that tells you about the various electrochemical processes happening inside. For a typical lithium-ion battery, you see maybe two semicircles in the impedance plot. The high-frequency semicircle represents charge transfer at the electrode-electrolyte interface. The medium-frequency semicircle represents other interfacial processes or film formation.
For the solid-state batteries, the authors saw three semicircles. That third semicircle appears in the low to medium frequency range, and it represents an additional electrochemical process that doesn't occur in conventional lithium-ion batteries. More importantly, as the state of charge changes, this semicircle moves in a very predictable way.
So how did they use this phenomenon to their advantage? Well, they found three solid-state lithium cobalt oxide batteries with different levels of degradation. One was relatively fresh, one was moderately aged, and one had experienced significant capacity loss. They used an electrochemical workstation for impedance measurements and standard charging-discharging equipment for capacity calibration, all inside a temperature-controlled chamber.
The protocol went like this: First, they calibrated each battery's capacity by running three full charge-discharge cycles and averaging the results. Then they charged the battery fully, rested it for an hour, and ran a complete impedance sweep. The sweep covered a range of frequencies, from very high to very low, capturing all the electrochemical processes happening at different timescales. Then they discharged the battery by ten percent of its capacity, rested it for another hour, and repeated the impedance measurement. They continued this process all the way down to empty, giving them impedance spectra at eleven different charge levels for each of the three batteries.
From these spectra, they extracted feature parameters. Specifically, they looked at the impedance magnitude at five different frequencies in that third semicircle. They also looked at the real part of the impedance at the inflection point, where the semicircle curves most sharply. To verify that the features were useful, they calculated correlation coefficients between each impedance parameter and the state of charge. A correlation coefficient tells you how strongly two variables are related, from -1 to 1. Values close to those poles indicate strong linear relationships, while values in the middle (near 0) indicate no relationship. In this case, their features showed very strong negative correlations, meaning as the state of charge goes up, the impedance goes down in a predictable way.
Then they used Gaussian process regression to build a model that maps these impedance parameters to state of charge. This is an ML technique that's particularly good at handling small datasets and providing uncertainty estimates. It's a Bayesian approach, which means it not only gives you a prediction but also tells you how confident that prediction is. The model was trained on data from the first two batteries, then validated on the third battery. The results were impressive. The maximum error was less than 2%, and the average error was less than 1%.
But here's the catch. Running a full impedance sweep takes time. For the frequency range they used, the measurement took about two minutes. That's not terrible for a laboratory setting, but it's also not fast enough for real-time battery management during operation. And critically, you need to sweep through multiple frequencies to identify where that inflection point actually is, since its frequency shifts as the battery discharges.
To make this approach more practical, they simplified the process by measuring impedance at just five low frequencies instead of sweeping through dozens. This cut the measurement time from 2 minutes to about 25 seconds while maintaining decent accuracy, and still working well on aged batteries. They compared this faster impedance-based estimation to a fractional-order extended Kalman filter. The Kalman filter could track state of charge continuously in real time but required accurate initialization and periodic recalibration as the battery degraded. By contrast, the impedance method provided quick, reliable calibration without knowing the battery's history. That being said, it couldn't run during active use. In the end, the authors concluded that combining the two approaches actually offers the best of both worlds: using impedance measurements to periodically reset or calibrate the state of charge, and running the Kalman filter for continuous estimation during operation. An efficient hybrid framework that could actually work in the wild.
If you're interested in the authors' fractional-order model, the parameter values they identified for different states of charge, or the plots showing how impedance spectra evolve, I'd encourage you to download the paper. They also include detailed comparisons of fitting-quality across different model structures and an extensive error analysis across their test cases. All pieces that we didn't have time to cover today.