What is the critical role of reversible heating in battery models? We dive into overcoming its challenges for improved accuracy, cost-efficiency, and thermal management in developing energy and power cells.
Introduction
Lithium-ion batteries have emerged as the leading technology for energy storage, powering everything from smartphones to electric vehicles. Yet beneath their seemingly simple exterior lies a complex world of electrochemical processes, temperature dynamics, and thermal management challenges.
At the heart of this complexity lies heat – an often overlooked but incredibly influential factor in the realm of battery models. Heat not only affects battery performance but also plays a crucial role in ensuring safety (see our recent blog on pack thermal modelling) and determining lifespan.
In this blog, we investigate the importance and challenges of including one particular, often overlooked, type of battery heating - reversible heating - in battery models. We'll also explore how About:Energy addresses these challenges, leading to more accurate predictions, quicker turn-around times to characterise reversible heating, lower costs and enhanced thermal management. Reversible heating is important for developing packs or BMS using electrical (also known as equivalent circuit-based models, i.e. ECMs) or electrochemical models. This product development may involve both energy cells, such as the LG M50LT, and power cells, such as the Molicel P50B. (see our previous blog on the Molicel P50B).
Lithium-ion Cell Heat Generation
When it comes to heat generation in lithium-ion cells, it's important to consider both irreversible and reversible heat.
Irreversible, or ohmic, heating arises from the electrical resistance within the cell components, leading to the conversion of electrical energy into heat according to Ohm's law. This heat generation is due to the resistance across the cell, which results in energy loss as it is charged or discharged. Ohm’s law states that:
where I is cell current and R is cell resistance. Irreversible heating is correlated to voltage drop across the cell. We use this same measurement to define even the simplest of electrical models, meaning it is impossible to parameterise an electrical model without also parameterising the irreversible heat generation. As a result, every battery model will approximate the magnitude of irreversible heating.
However, the same principle doesn't apply to reversible heating, which arises from entropy changes within the cell's electrodes. Reversible heating can vary in direction, either cooling or warming the cell, depending on the specific stage of charge or discharge. For instance, if reversible heating is positive during charging at a certain state-of-charge (SOC), it will be negative during discharging at the same SOC. Over a full charge-discharge cycle, the total reversible heat theoretically balances out to zero (when ignoring minor degradation contributions).
where T is the absolute temperature of the cell and partial V OCV T is the entropy coefficient. Temperature and current can be included into a model without complexity; the entropy coefficient is a different matter.
Measuring the Entropy Coefficient
The entropy coefficient quantifies the impact of temperature variations on the open-circuit voltage (OCV) of a cell. Typically, this coefficient is determined through the potentiometric method. In this approach, researchers subject the cell to controlled temperature changes and measure the corresponding alterations in OCV. However there are many issues with the potentiometric method:
Inaccurate temperature control: Many potentiometric methods used in literature fail to control temperature effectively, leading to error in both the temperature measurement during the test, and noise caused by temperature fluctuation in the OCV that must be measured to compute the parameter.
Time: The most problematic aspect of measuring the entropy coefficient is the time it takes to run experiments. This process necessitates experimentation across the entire SOC spectrum and can often take over six weeks to complete! This demands significant resource, driving up the cost of battery modelling.
There is a further problem too - the relaxation of the cell’s voltage back towards its OCV and, in certain cases, self-discharge of the cell under test, mean that long measurement times come riddled with error.
Consequently, many electrical models choose to ignore the contribution of reversible heating.
Is reversible heating important? Spoilers! Yes.
Irreversible heating dominates in most battery applications. Whilst it is hugely dependent on the application, a rough rule of thumb suggests that at least 75% of total cell heat generation stems from irreversible heating. Further, irreversible heating is, as the name suggests, always positive so short discharges followed by short charges would result in irreversible heating in each step, whilst total reversible heat would finish at zero. However, there a many reasons why reversible heat should not be ignored:
Sustained charges or discharges: In circumstances where a cell is in charge or discharge for a sustained period (for example fast-charging or motorway driving), the contribution of total reversible heat becomes significant.
Temperature dependence: Reversible heating increases with temperature, whereas irreversible heating decreases with temperature. This means future cell chemistries (e.g. solid-state, LFP and sodium-ion) where thermal runaway is not a risk until a higher temperature (compared to NMC) will be allowed to ‘run hotter’ where reversible heat is more prominent, whilst irreversible heat contribution reduces.
Low-rate applications: In low-rate applications such as stationary energy storage, reversible heating becomes increasingly dominant. This is because irreversible heating exhibits a quadratic relationship with current flow while reversible heating is linear in current flow, meaning that at lower rates, reversible heating becomes more prominent.
Even with today’s cell chemistries, the effect of reversible heating remains significant. By utilising About:Energy’s electrical model for the LG M50LT, we can observe the contribution of reversible heating to the overall predicted rate of heat generation in the cell during a 1C discharge:
The graph illustrates that, throughout most of the discharge process, the reversible heating component actually exerts a cooling effect on the cell, thereby reducing the total rate of heat generated. Excellent news for thermal management system design engineers, right? No… because the effect of reversible heating will be reversed during a charge, where the vehicle is stationary and the thermal management challenge is greatest:
Over the course of the 1C charge, we find that our model predicts an additional 7.3% of total heat generated, if the reversible heating term is included. This may not appear too detrimental; however, this does not consider the points where the reversible heating contribution is most significant. The graphic below shows that at certain points during the charge, up to 30% of the total heat generation comes from reversible heating.
Failure to consider the reversible heat contribution in models used for Battery Management Systems (BMSs) can result in significant errors in predicting temperature fluctuations during charging. Temperature fluctuations lead to inhomogeneous distribution of current flow through different regions of a single cell and through different cells within a battery pack. These factors all contribute to a less efficient charging process and accelerate the rate of heat generation within the cell. Therefore, accurately modelling reversible heating is crucial for optimising battery performance, enhancing charging efficiency, and thermal management.
About:Energy and reversible heat
For About:Energy, the accurate parameterisation of reversible heat is a critical part of offering market-leading battery modelling. We can include reversible heating in all our models: electrical, thermal and electrochemical models, providing industry access to a parameter that is:
difficult to measure accurately
takes time to measure
important to make robust model-based decisions
So, how does About:Energy achieve this? We leverage our patented thermal control apparatus to reduce the experimental time from 6 weeks to just 7 days. This significant reduction eliminates uncertainties stemming from the cell’s voltage relaxation towards OCV and enables our team to parameterize a greater number of lithium-ion cells in a shorter timeframe, thereby rapidly expanding our Voltt database.
Through extensive validation experiments, we have demonstrated that our approach to predicting reversible heating is notably more reliable than traditional potentiometric methods. This performance advantage translates into tangible benefits for every customer - more accurate thermal predictions, delivered faster, at a lower cost.
Notes from author:
If you are interested in some of my past work which is relevant to About:Energy’s offering, I have included some links below:
If you want to understand more about reversible heating, and the most effective ways to characterise its significance, check out this recent publication
The Cell Cooling Coefficient (don’t worry about the papers, check out the animation!)
TOPBAT: using electrical models to optimise the design of lithium-ion pouch cells for better thermal management
Developing a new generation of electrical model parameterisation methods, only achievable with advanced thermal control apparatus to maintain exact surface temperature of the lithium-ion cell under test [LINK 1] [LINK 2].
