Battery Modeling

Battery modeling is the process of creating mathematical or computational representations of a battery’s behavior under different conditions. Battery modeling is essential for designing, controlling, and optimizing batteries in various applications, such as electric vehicles, renewable energy systems, and consumer electronics.

Battery Modeling with Simulink and Simscape Battery

There are three different types of battery models: equivalent circuit models (ECMs), electrochemical models, and data-driven models. You can create these models and run simulations using Simscape Battery™ and Simulink^® products.

Equivalent Circuit Models

Battery ECMs use electrical circuit elements such as resistors, capacitors, and voltage sources to mimic the dynamic behavior of a battery cell. Due to their simplicity and computational efficiency, ECMs are used for battery management system (BMS) design and system-level simulation. Simscape Battery has a prebuilt ECM block, the Battery Equivalent Circuit block, which models the electro-thermal dynamics of a battery. The circuit elements in the Battery Equivalent Circuit block are lookup tables depending on temperature, state of charge (SOC), and current.

In addition, the Battery Equivalent Circuit block supports battery hysteresis on open-circuit voltage (OCV), battery degradation (cycling aging and calendar aging), and fault simulation. It supports three types of faults: additional resistance fault, internal short fault, and exothermic reactions. You can inject exothermic reaction faults to simulate thermal runaway and characterize thermal runaway with the accelerating rate calorimetry (ARC) test.

Electrochemical Battery Models

Electrochemical battery models are mathematical models that describe the internal physical and chemical processes occurring within a battery during charging and discharging. Compared with ECMs, electrochemical battery models provide detailed insights into internal battery processes, making them valuable for cell design, degradation studies, fast charging current optimization, and more accurate performance prediction under extreme operating conditions.

Simscape Battery provides the Battery Single Particle block to represent a battery by using a single particle model with electrolyte dynamics (SPMe).

Data-Driven Battery Models

Data-driven battery models use empirical data with methods such as system identification, machine learning, and deep learning to simulate and predict battery behavior. They are ideal when internal dynamics are difficult to capture analytically, for example, battery degradation mechanisms in battery aging modeling. Data-driven battery models are suitable for electric vehicle fleet management, predictive maintenance, advanced diagnostics, and other applications where large data sets are available and enhance accuracy in forecasting battery life.

You can use deep learning to create low-order nonlinear state-space model; The training data for this kind of model can be experimental data or simulation data from very high-fidelity models (e.g., FEA battery models).

Cell Characterization

Cell characterization is the process of fitting a battery model to experimental data. It ensures that the model parameters reflect the actual battery’s behavior under various operating conditions. These parameters tend to change based on product generation, cell supplier, and battery age.

It is important to characterize these cells because the BMS algorithm uses the battery model to set control parameters such as those of a Kalman filter for SOC estimation or power limits based on SOC and temperature to avoid undervoltage or overvoltage conditions. Later in the BMS development stage, engineers can use the same battery model for system-level closed-loop desktop and real-time system simulations.

The cell characterization process involves deciding what tests to conduct in the battery test lab and optimizing model parameters such that model predicted voltage matches well with the experimentally measured voltage. For testing, current profiles, such as hybrid pulsed power characterization (HPCC), need to excite the battery system adequately so that there is enough information for identifying the battery model parameters.

As for the optimization process, you can set up the problem in multiple ways, depending on whether the Jacobian used for optimization is obtained numerically or analytically. To test the accuracy of battery models with these identified parameters, performing a validation step is recommended to check the accuracy of voltage prediction under a drive cycle current profile, compared against experimentally measured voltage.

You can characterize ECM models using use MATLAB^® and Simulink products:

• Simscape Battery includes objects and functions for parameter estimation from HPPC data. Simscape Battery contains foundational optimization methods for estimating ECM parameters. You can also select methods from other toolboxes, such as the tfest function from System Identification Toolbox™. These alternative optimization methods often provide more robust parameter estimation methodologies than the default optimization method. To use these optimization methods, you must have a license for the required toolbox. 
• The MBC Optimization app (CAGE) in Model-Based Calibration Toolbox™ provides more efficient parameter estimation and takes a few minutes for a 3RC ECM model.

To characterize SPMe battery model, you can use Simulink Design Optimization to estimate the parameters in groups, in a sequence of decreasing influence.