Predicting battery end of life in solar off-grid systems
This article gives a bit of the background to our recent Joule paper. Here is the actual paper if you want to go straight to it (and here is a preprint in case you cannot access the paywalled version).
Over 10 years ago, when I was a doctoral student at Imperial College London, I remember a senior professor asking me to have a chat with some excited young electrical engineering undergraduates who had started a charity, Equinox, focused on providing electricity to people in Rwanda without grid access. (I’ve always been enthusiastic about engineering for development and at the time was a trustee for Engineers Without Borders UK.) Our conversation was fun and positive, but I remember thinking, “is this really going to go anywhere? They’re being very naive!”.
How wrong I was. Those undergraduates — Mansoor Hamayun, Chris Baker-Brian, and Laurent van Houcke — subsequently founded BBOXX Ltd., a spectacular energy company that now operates across 11 countries and has impacted the lives of more than 2 million people.
My research group in Oxford University’s Department of Engineering Science, the Battery Intelligence Lab, has worked alongside BBOXX for several years, modelling batteries and analysing data. Early on, we realised that data from real products in the field provides a rich opportunity to understand how energy is being used and how batteries perform outside a lab test. A key topic was diagnosis of battery health from measured field data. Battery health can be defined in various ways but is usually quantified by the fade in capacity or increase in resistance over time, as a battery ages. Many of the batteries BBOXX has deployed are lead-acid systems (although they are increasingly also deploying lithium-ion), and an important end-of-life mechanism in these is resistance increase, which at some point begins to rapidly accelerate leading to an “elbow” and then failure. So the exam question for us was this: given measurements of voltage, current, and temperature, estimate the battery internal resistance.
This seems at first sight to be a straightforward task — internal resistance relates to the change in voltage divided by change in current, so our initial approach was to simply extract “jumps” in voltage and current from the data and then do a least-squares fit to estimate resistance. However, when we tried this, it crashed and burned spectacularly as we ended up with series after series of noisy, unusable health estimates.
What was going wrong? Turns out there were two key snags that stopped our unsophisticated initial attempts from working, the first numerical and the second physical.
On the numerical front, a basic challenge with any least-squares data fitting exercise is ill-conditioning, in other words, the parameter we are trying to estimate (in this case resistance) becomes extremely sensitive to small changes in the measurements. This can happen due to noise or lack of richness in the data, for example. After some basic filtering out of unusable data (e.g. dividing zero by zero), the usual solution to this is regularization, which is a fancy way saying add in some more assumptions. The Bayesian statistical framework, which we used subsequently, provides a principled way to bring this all together in a unified approach.
However, even after applying start-of-the-art smoothing and fitting techniques, we realised that we still had a physical issue. The resistance of a battery is highly variable depending on the operating conditions, for example, changes in the temperature and state of charge. Therefore we had to calibrate for these effects; this massively complicated the inference challenge. In fact we ended up having to estimate resistance from data as a four-dimensional function of SOC, temperature, current and time. The juicy details of how this works are buried inside the Supplementary Materials of our recent paper, if you’re interested. We were heavily inspired by the amazing work of Arno Solin, a machine learning professor in Finland who has developed cool new ways of implementing probabilistic ML techniques.
After smoothing and calibrating the resistance estimates we were able to demonstrate battery health trajectories that made sense and were actually useful indicators of impending end of life. However, there was a final snag: how did we know this was in any way “the truth”? After all, it’s just fitting a model/function to data. After much head-scratching, we realised that when a battery fails, it gets taken in for repair and independently checked/tested; this provided the final puzzle piece. We were able to train a classifier to predict probability of failure using the repair data as labels and the smoothed health metrics extracted from the raw measured data as part of the input data. The final results below show resistance/health trajectories of more than 1000 batteries. The failing batteries (at end of life) clearly show up as those with a resistance “elbow” present.
We are very excited about this work; it opens up a whole new area of analysing battery performance from field data. Both the data (all 620 million rows of it) and the code associated with the work, detailed in our recent Joule paper, are available. This kind of analysis shows how field data can complement lab tests to improve our understanding of batteries, with a direct practical benefit being improved logistics for off-grid solar/battery companies. Watch this space for further developments!
