Enhanced Equivalent Circuit Model for High Current Discharge of Lithium-Ion Batteries with Application to Electric Vertical Takeoff and Landing Aircraft

TL;DR

This work addresses the challenge of predicting lithium-ion battery performance under high discharge rates relevant to eVTOL fault scenarios. It introduces the LD-ECM, an enhanced equivalent circuit model that adds one dynamic state, a lithium-depletion–driven resistance $R_{LD}$, to a conventional 2RC ECM and captures diffusion-limited voltage drops through a discrepancy-modeling framework. Parameters are learned via LPV LUTs across $SOC$, temperature, and current, using a large, aviation-focused characterization dataset and regularized optimization to ensure smooth, generalizable behavior. Validation on a diverse set of flight profiles shows that the LD-ECM can predict end-of-mlight hover reserve times with a mean error of about $2.9$ seconds and a standard deviation of $6.2$ seconds, demonstrating meaningful gains for flight planning and safety, while also highlighting aging and model sensitivity as important considerations for fleet deployment.

Abstract

Conventional battery equivalent circuit models (ECMs) have limited capability to predict performance at high discharge rates, where lithium depleted regions may develop and cause a sudden exponential drop in the cell's terminal voltage. Having accurate predictions of performance under such conditions is necessary for electric vertical takeoff and landing (eVTOL) aircraft applications, where high discharge currents can be required during fault scenarios and the inability to provide these currents can be safety-critical. To address this challenge, we utilize data-driven modeling methods to derive a parsimonious addition to a conventional ECM that can capture the observed rapid voltage drop with only one additional state. We also provide a detailed method for identifying the resulting model parameters, including an extensive characterization data set along with a well-regularized objective function formulation. The model is validated against a novel data set of over 150 flights encompassing a wide array of conditions for an eVTOL aircraft using an application-specific and safety-relevant reserve duration metric for quantifying accuracy. The model is shown to predict the landing hover capability with an error mean and standard deviation of 2.9 and 6.2 seconds, respectively, defining the model's ability to capture the cell voltage behavior under high discharge currents.

Figures (9)

• Figure 1: Schematic of (a) conventional 2RC ECM, (b) proposed LD enhanced ECM, and model prediction in presence of LD behavior for (c) conventional 2RC ECM, and (d) LD-ECM, and (e) discrepancy modeling framework from brunton2016SINDy used to learn the LD dynamics.
• Figure 2: Characterization test data: (a) test setup, (b) RPT data for all cells used in test campaign, (c) high C-rate CCP pulse showing minimal impact of current interrupts, (d) example high C-rate discharge pulses and their corresponding DC resistance estimated with the interrupt method, (e) example full discharge data at different temperatures, (f) histograms of data coverage for all constant current (CCP and FD) tests, and (g) MPP example and data coverage histograms.
• Figure 3: Creating the cost function for parameter identification: (a) the variable weight for RC-only error, and (b) example LUT results obtained with zero regularization, where the black boundary indicates the convex hull of the test data coverage in this example fitting case.
• Figure 4: Fitted normalized lookup tables to 6C CCP data, where the black boundaries denote the convex hull of the CCP data coverage.
• Figure 5: Impact of characterization data on model quality: (a) voltage prediction error histograms with different training data, where the $y$-axis is in logarithmic scale to better reveal the distribution tails, and (b) example MPP profiles and the corresponding model predictions when fitted to different characterization data.