Battery Modeling

Model batteries when designing battery-powered systems

Battery models have become an indispensable tool for the design of battery-powered systems. Their uses include battery characterization, state-of-charge (SOC) and state-of-health (SOH) estimation, algorithm development, system-level optimization, and real-time simulation for battery management system design.

Battery models based on equivalent circuits are preferred for system-level development and controls applications due to their relative simplicity. Engineers use equivalent circuits to model the thermo-electric behavior of batteries, parameterizing their nonlinear elements with correlation techniques that combine models and experimental measurements via optimization.

Equivalent circuit of a battery with three distinct time constants, internal resistance, and open circuit potential.

Battery Characterization

The first step in the development of an accurate battery model is to build and parameterize an equivalent circuit that reflects the battery’s nonlinear behavior and dependencies on temperature, SOC, SOH, and current. These dependencies are unique to each battery’s chemistry and need to be determined using measurements performed on battery cells of exactly the same type as those for which the controller is being designed. Example battery models are available for download from MATLAB Central.

Voltage response (top) to a pulsed current (middle) discharge, and resulting SOC (bottom) for an NMC Li-ion battery.

SOC Estimation

One common application of battery models is to develop algorithms for SOC estimation. Open-circuit voltage (OCV) measurement and current integration (coulomb counting) may give reasonable estimates for SOC. However, to estimate the SOC in modern battery chemistries that have flat OCV-SOC discharge signatures, you need to use a different approach, such as Kalman filtering.


Batteries degrade over time due to their calendar life and charge-discharge cycles, showing a gradual loss in reserve capacity and an increase in internal resistance. The battery management system (BMS) needs to adapt to these changes for effective control of the battery. Battery models can help you develop a BMS that accounts for degradation.

Progressive degradation of a lithium ion battery reflected on increase in internal resistance (R0) and time constants (τ1 , τ2 , τ3), with minimal variation in open circuit potential (Em).

Real-Time Simulation

Hardware-in-the-loop testing of BMS is another common application of battery models. A battery model built for system-level design can be reused for real-time simulation.

For more information on battery modeling, see the examples, webinars, and conference papers below, which feature MATLAB® and Simulink® products.

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