How does temperature dependence affect the accuracy of parameter estimation in equivalent circuit models?

Temperature dependence significantly affects the accuracy of parameter estimation in equivalent circuit models (ECMs) because the electrochemical processes within a battery are highly sensitive to temperature variations. ECMs use electrical components like resistors, capacitors, and voltage sources to mimic the battery's behavior. The values of these components, or 'parameters', change with temperature, which impacts the model's ability to accurately predict battery performance. For example, the internal resistance of a battery, represented by a resistor in the ECM, typically decreases as temperature increases due to enhanced ion mobility in the electrolyte. Similarly, the charge transfer resistance, which represents the kinetic limitations of electrochemical reactions at the electrodes, also decreases with increasing temperature because higher temperatures provide more energy for these reactions to occur. Diffusion processes, modeled by Warburg impedance elements in ECMs, are also temperature-dependent; higher temperatures accelerate ion diffusion within the electrolyte. If parameter estimation is performed at a single temperature and the ECM is used at significantly different temperatures, the model's predictions will be inaccurate. This is because the parameters estimated at the initial temperature no longer accurately represent the battery's behavior at other temperatures. To address this, temperature dependence must be explicitly considered during parameter estimation. This can be achieved by performing experiments at multiple temperatures and developing mathematical relationships that describe how each parameter varies with temperature. For instance, the Arrhenius equation is often used to model the temperature dependence of reaction rates and transport processes in batteries. By incorporating these temperature-dependent relationships into the ECM, the model can accurately predict battery behavior over a wide range of operating temperatures. Furthermore, online parameter estimation techniques, such as recursive least squares (RLS) with adaptive forgetting factors or Kalman filtering, can be used to continuously update the ECM parameters based on real-time measurements of battery voltage, current, and temperature. This allows the ECM to adapt to changing operating conditions and maintain accuracy even when the battery temperature fluctuates. Neglecting temperature dependence in ECM parameter estimation leads to inaccurate state estimation (e.g., SOC, SOH), suboptimal control strategies, and potentially unsafe operating conditions. Accurate temperature compensation is therefore crucial for reliable BMS performance.