A comparison of battery modelling techniques

Battery modelling is crucial in modern energy storage development, influencing everything from electric vehicle performance to grid-scale storage solutions.

As we push the boundaries of battery technology, our modelling approaches must evolve to meet increasingly complex demands.

This post examines the transition from traditional physics-based models to modern data-driven approaches, highlighting why machine learning techniques are becoming indispensable in battery testing and development. 

Traditional physics-based models: Strengths and limitations

Engineers have historically relied on three primary modelling approaches: Equivalent Circuit Models (ECM), Pseudo Two-Dimensional (P2D) Models, and Single Particle Models (SPM). Each serves distinct purposes but carries inherent limitations. 

Equivalent Circuit Models (ECM)

ECMs represent batteries through electrical circuit elements, offering simplicity and computational efficiency. These models typically incorporate resistors, capacitors, and voltage sources arranged in specific topologies to mimic battery behaviour. The Thévenin model, for instance, uses an open-circuit voltage source in series with a resistor and multiple RC parallel networks.

This configuration captures immediate voltage responses through the series resistor and time-dependent relaxation effects through the RC networks. While these models excel in real-time applications and basic battery management systems, they struggle to capture complex electrochemical phenomena. Temperature dependencies, aging mechanisms, and dynamic responses under varying conditions often elude ECM representations

Pseudo Two-Dimensional (P2D) Models 

P2D models, based on Newman's porous electrode theory, provide detailed insights into electrochemical processes. These sophisticated models solve coupled partial differential equations that describe mass transport, charge transport, and electrochemical kinetics across multiple physical domains.

They account for the movement of lithium ions through the electrolyte (liquid phase) and the solid-state diffusion within active material particles (solid phase). The 'pseudo' dimension refers to the radial dimension within these particles, adding another layer of complexity to the spatial considerations.

These models accurately capture internal states and transport phenomena, making them valuable for research and development. However, their complexity demands significant computational resources and extensive parameterisation, rendering them impractical for real-time applications. 

Single Particle Models (SPM)

SPMs strike a balance between ECMs and P2D models, simplifying the physics while retaining key electrochemical principles. These models represent each electrode as a single spherical particle that undergoes lithiation and delithiation.

The simplification dramatically reduces computational complexity while maintaining essential physics-based characteristics. SPMs solve for concentration profiles within these representative particles and link them to electrode potentials through Butler-Volmer kinetics.

Despite their elegance, SPMs falter at high C-rates and struggle with complex chemistry types, limiting their practical applications. The model's assumptions break down when significant concentration gradients develop in the electrolyte phase, particularly during rapid charging or discharging scenarios. 

The data-driven revolution 

Modern battery development faces challenges that traditional models struggle to address. Manufacturing variations, new chemistry compositions, and the need for rapid development cycles demand more flexible approaches. This is where data-driven modelling demonstrates its superiority. 

Machine learning models excel in capturing complex, non-linear relationships without requiring detailed physical parameters. By learning directly from operational data, these models adapt to manufacturing variations and new chemistry compositions more readily than their physics-based counterparts. 

Consider a typical battery testing scenario. Traditional models require careful parameterisation for each new cell design or chemistry modification. In contrast, machine learning models can rapidly adapt to new data, learning from existing test results and adapting to variations in manufacturing processes. This capability significantly reduces development time and resources. 

Real-world applications 

In battery testing and development, data-driven approaches demonstrate several key advantages: 

1. Accelerated Testing: ML models identify patterns in degradation data, enabling more efficient test protocols. What traditionally required months of cycling can now be predicted with shorter test periods and higher confidence. 

1. Manufacturing Quality Control: ML models detect subtle deviations that might escape physics-based models by learning from production data. This capability enables early identification of potential issues in the manufacturing process. 

1. State Estimation: Neural networks achieve higher accuracy in state-of-charge and state-of-health estimation, particularly under varying operating conditions where traditional models often struggle. 

The future: Hybrid approaches

While data-driven approaches offer compelling advantages, the future likely lies in hybrid solutions. Physics-Informed Neural Networks (PINNs) combine the best of both worlds – the adaptability of machine learning with the fundamental insights of physics-based models. These hybrid approaches ensure predictions remain physically meaningful while benefiting from the pattern recognition capabilities of ML. 

Organisations transitioning to data-driven approaches should consider several factors: 

Data Quality: ML models require substantial, high-quality data for training. Establishing robust data collection protocols becomes crucial. 

Computational Infrastructure: While training may demand significant resources, deployed ML models often run more efficiently than complex physics-based simulations. 

Validation Strategies: Hybrid approaches enable validation against physical principles and empirical data, ensuring reliable predictions. 

Conclusion 

The evolution from traditional physics-based models to data-driven approaches represents more than a mere shift in methodology. It enables faster development cycles, accurate predictions, and adaptation to manufacturing variations.

While physics-based models remain valuable, particularly for understanding fundamental mechanisms, the future of battery modelling lies in combining these insights with the power of machine learning. 

As battery technology evolves, the flexibility and adaptability of data-driven approaches will become increasingly crucial. Organisations that embrace these methods while maintaining physical insights will be best positioned to lead the next generation of battery development.