Introduction
In recent years, Equivalent Circuit Models (ECMs) have been extensively investigated in the literature as effective tools to accurately predict the current–voltage performance of lithium-ion cells. Batteriy performance is highly influenced by operating conditions: temperature, load current and state of charge (SOC). To characterize the circuit elements of ECMs, Hybrid Pulse Power Characterization (HPPC) tests are commonly employed. This study proposes the characterization of Panasonic NCR18650B lithium-ion batteries as a function of SOC and C-rate at constant temperature, using a modified HPPC-based methodology aimed at reducing testing time while preserving the completeness of the battery characterization: instead of performing separate HPPC tests for each C-rate, the proposed approach integrates multiple C-rates within a single dynamic test profile. A key contribution of this work is the development of a parameter estimation algorithm derived from MATLAB fitting functions originally meant for traditional HPPC tests, generalized to achieve universal applicability to both conventional and modified HPPC test profiles. Based on the identified parameters, a two-parallel ECM battery model is developed in a Simulink/Simscape environment using the Battery Equivalent Circuit block. The model accuracy is finally evaluated by comparing simulated and experimental voltage responses.
Methods
In this work, the model circuit consists of a dc voltage source, a series resistance and two RC parallel networks. The dc voltage source is used to represent the open circuit voltage of battery (Eocv), series resistance (Rs) is used to represent the internal dc resistance and RC parallel branches (R1, C1, R2, C2) are used to characterize the transient response of voltage. The model input is the applied current profile (Iin) and the output is the terminal voltage Vt; the parameters are dependent on SOC and current, while temperature dependance is neglected with tests performed at fixed 25 °C. The model is developed in MATLAB/Simulink using the Simscape Battery Equivalent Circuit block. Parameters are identified from experimental measurements obtained through a modified Hybrid Pulse Power Characterization (HPPC) test. Unlike conventional approaches, where model parameters are identified through separate HPPC tests for each C-rate, the proposed methodology unifies all current levels within a single experimental test in which four different C-rates (0.25C, 0.5C, 0.75C, and 1C) are applied at each SOC level, with SOC ranging from 100% to 0% in 5% intervals. The open-circuit voltage is estimated as the voltage value immediately preceding each current pulses series in each soc value. The ohmic resistance and RC branches parameters are identified using MATLAB’s fitECM function. Since this function is originally intended for standard HPPC datasets, dedicated pre-processing algorithms have been developed to adapt it to the modified test structure. These algorithms automatically detect, classify and extract current pulses directly from the experimental data by associating each pulse with its corresponding C-rate based on the structure of the applied current profile. Pulses belonging to the same current level are grouped and stored in dedicated pulseData objects. Each pulseData object is then used as input to the fitECM routine to estimate the ECM parameters corresponding to the specific operating condition. The identified parameters are finally organized into two-dimensional lookup tables as functions of SOC and current, which are used to parameterize the Simscape ECM block.
Results
The comparison between experimental and simulated voltage profiles shows that the model successfully reproduces dynamic voltage, confirming the effectiveness of the proposed parameter identification strategy. Discrepancies become more evident at low SOC values, where the simulated voltage slightly deviates from the experimental measurements. These errors highlight intrinsic limitations of the chosen second-order ECM in representing complex electrochemical behavior (i. e. nonlinear dynamics caused by phenomena like electrolyte lithium-ion depletion and solid-phase diffusion limitations close to the cell's working limits). This nonlinearity is reflected in the open-circuit voltage (specifically the 'knee' of the OCV curve) and significant parameter variation, which collectively degrade model performance. Nevertheless, the overall accuracy remains suitable for system-level simulations and control-oriented applications.
Conclusions
This study demonstrates that a pulse extraction and MATLAB-based parameter fitting algorithm enable efficient identification of ECM parameters as functions of both SOC and C-rate from a single modified HPPC dataset. The proposed methodology not only reduces experimental effort but also provides a fast and universally applicable tool for ECM parameter estimation.
