Hierarchical Learning for Precise and Efficient State-of-Charge Estimation in Sodium-Ion Batteries

Sodium-ion batteries (SIBs) are a great alternative to the more common lithium-ion batteries (LIBs), mainly because they are cheaper to produce, use more readily available materials, and perform well in colder conditions. On top of that, they are considered safer, which is a big deal for large-scale energy storage and electric vehicles. However, one major challenge is figuring out exactly how much charge they have left at any given moment. This is known as state-of-charge (SOC) estimation, and it plays a significant role in ensuring batteries work efficiently, last longer, and stay safe. The problem is that traditional SOC estimation methods that work well for lithium-ion batteries do not transfer easily to sodium-ion technology. Because of differences in the way these batteries handle charge and discharge, new approaches are needed. SOC estimation is at the heart of any battery management system because it tells you how much energy is still available. SIBs do not have the same voltage plateau as lithium iron phosphate batteries. Additionally, factors like internal resistance, charging and discharging behavior, and temperature changes all add extra layers of complexity that must be addressed. Scientists currently use three primary methods to estimate SOC for lithium-ion batteries: direct measurement, which involves measuring things like voltage, current, and impedance in real-time, but this can be unreliable because sensor errors can introduce noise and inaccuracies. The second approach, model-based estimation, uses equivalent circuit models and electrochemical models to estimate SOC. While these methods can be effective, they require a lot of computing power and precise battery modeling, which is not always practical. Then there is machine learning, which has gained popularity because it can handle complex battery behaviors without needing detailed electrochemical models. However, the downside is that many machine learning models require enormous data and computing power, making them difficult to use in real-time applications. According to this account, a new study published in the Journal of Energy Storage by researchers from Shandong University, including Shuquan Wang, Prof. Feng Gao, Prof. Hao Tian, Yusen Zhang, and Wenjia Pan, developed a low-complexity, data-driven model for sodium-ion batteries that uses hierarchical learning to improve SOC estimation. The new model incorporates an enhanced pulse test, which allows researchers to train the system using a carefully designed set of controlled charge and discharge cycles. This approach makes SOC estimation more accurate while also reducing computational demands. The hierarchical learning framework further enhances the model’s ability to capture the unique voltage characteristics of sodium-ion batteries, reducing errors and making it highly reliable, even in noisy or unpredictable conditions.

The researchers began with an enhanced pulse test, an important step to understand how SIBs behave under different charge levels, currents, and temperatures. Instead of relying on controlled lab conditions that do not always reflect real-world use, they pushed the batteries through various operating scenarios. Two types of batteries were tested—one with a 3.2 Ah capacity and another with a 10 Ah capacity, each from different manufacturers. To make things even more realistic, they exposed the batteries to temperatures ranging from a freezing -5°C to a scorching 45°C while applying current pulses of varying strengths. This was not just about testing extremes but about gathering a rich dataset that mapped out the intricate connections between voltage, current, temperature, and SOC. Understanding these relationships is essential for improving SOC estimation accuracy, which is at the heart of efficient battery management.

The authors then trained their model using a hierarchical learning approach. Instead of directly estimating SOC from raw data, like most machine learning models, they took an extra step—predicting the open-circuit voltage (OCV) first. Why does this matter? Introducing OCV as an intermediate step significantly improved the model’s stability. This approach made it less dependent on exact voltage readings, which can be tricky to obtain in real-world settings where data is often messy. To put the model to the test, they simulated how batteries perform in electric vehicles, using well-known driving profiles like the Federal Urban Driving Schedule and the Urban Dynamometer Driving Schedule. These profiles replicate real driving conditions with fluctuating currents and varying loads, making them a tough but fair challenge for the model. The results were impressive—SOC estimation remained highly accurate across different temperatures and battery types. The model achieved RMSEs as low as 0.89% for the 3.2 Ah battery and 0.63% for the 10 Ah battery, outperforming many existing SOC estimation methods. But the real question was—could the model hold up under imperfect conditions? The researchers deliberately introduced artificial noise into the voltage, current, and temperature readings to find out. This mimicked the kind of interference that battery management systems deal with in the real world, where sensors are imperfect. Even with this added challenge, the model barely flinched. The RMSE increased only slightly, to 1.08% for the 3.2 Ah battery and 0.85% for the 10 Ah battery, showing that the system remained highly reliable even when data quality was compromised. This level of robustness is critical for real-world applications, where external factors like temperature fluctuations and sensor inaccuracies are unavoidable. Finally, to see how their approach stacked up against other SOC estimation methods, the team compared their model to several advanced machine learning techniques commonly used for lithium-ion batteries. They tested it against support vector machines, random forest, and deep learning methods like autoencoder-long short-term memory and denoising autoencoder-gated recurrent unit. While these models delivered decent accuracy, they had a major drawback—they required enormous computational resources, which made them impractical for real-time applications. In contrast, the hierarchical learning model developed in this study offered the best of both worlds: high accuracy with a fraction of the computational demand.

In conclusion, the team at Shandong University successfully developed a new SOC estimation model explicitly designed for SIBs that is highly accurate and computationally efficient, and by this solved a key technical challenge that has made sodium-ion batteries difficult to manage. With this advancement, these batteries become a more realistic option for large-scale energy storage and electric vehicles, making them a strong competitor to lithium-based alternatives. Beyond just improving how SOC is estimated, this study also shows how data-driven methods can simplify battery management. One of the standout aspects of their approach is the use of hierarchical learning, which organizes the estimation process into structured steps. The ability to estimate SOC quickly and efficiently means sodium-ion batteries could become a more practical choice for cost-conscious applications, like grid storage and affordable electric vehicles. Moreover, the study showed that the model remained impressively accurate even when exposed to substantial noise in voltage, current, and temperature readings. This level of robustness means SIBs can be used in a broader range of environments, including extreme temperatures and high-energy applications, which makes them even more appealing for long-term use. We believe the work could help speed up the adoption of sodium-ion batteries by solving one of the most significant issues that have slowed their progress. By refining battery management strategies, this research contributes to a more reliable and diverse energy storage future, bringing us one step closer to a cleaner, more sustainable world.