# Online Model Adaption for Energy Management in Fuel Cell Electric Vehicles (FCEVs)
## 1 Introduction
ECUs continuously monitor parameters based on sensor inputs to optimize performance, contributing to the overall functioning of the vehicle powertrain [15]. The predominant approach implemented in EMSs and commercial ECUs to model nonlinear and operating-point-dependent behaviours is the use of look-up tables because, even though they require substantial calibration efforts, this is a well-established process in the automotive industry that produces robust performance [16]. The ageing processes in FCs may lead to important differences between the map included in the calibration and that representing the actual fuel cell behaviour. These deviations increase the fuel consumption because the EMS employs a calibration that does not correspond to the actual system state. As a result, these deviations encourage the implementation of techniques that are able to adapt the previously calibrated look-up tables. In this line, ref. [17] proposed a method based on the Lyapunov adaptation law to estimate the linear and nonlinear parameters such as voltage, power, and internal resistance of a polymer electrolyte membrane fuel cell (PEMFC). Also, ref. [18] developed an extended Kalman filter approach for PEMFC to obtain robust real-time-capable state estimations of a high-order FC model for observer applications mixed with control or fault detection. The use of Kalman-filter-based approaches for state estimation in automotive control strategies has been extensively used, as in [19; 20; 21; 22]. In addition, the Kalman filter can be used for model parameter estimation and, specifically, look-up table adaption. In this context, ref. [16] developed an online adaptive algorithm for NOx map calibration and updating for ICE control based on a simplification of the Kalman filter that allows consideration of updates of the table elements around the measured values instead of the complete table. This proposed solution showed results with similar accuracy to a standard Kalman filter but required lower computational time and memory. In the same field of ICE control, ref. [23] developed a method for bias compensation and online adaption of the air mass flow map of a diesel engine using an extended Kalman filter. As an example of an application in the field of electric vehicles, ref. [24] proposed a method wherein a Kalman filter is used to estimate the ohmic resistance of a lithium-ion battery by updating an entire look-up table based on local estimation at the current operating conditions; the results of the simulations show that the method is able to update the look-up table, even in operating conditions that were barely excited. In line with the previous discussion, this paper introduces an adaptive approach to enhance calibration of the fuel cell model utilized within the EMSs of FCEVs. The primary aim is to enhance the accuracy of the fuel cell model, consequently improving the overall energy management performance. While existing research utilizes observers to estimate the internal states of fuel cells for vehicle control applications [25; 26] or to approximate look-up table parameters in conventional ICE vehicles [16; 23], this work brings the novelty of developing an adaptive strategy for online map calibration and updating fuel cell models implemented in the EMS of an FCEV. In this way, the paper analyses the potential of updating the FC model by an extended Kalman filter (EKF) used in the EMS, highlighting the effect of the improved accuracy with respect to fuel consumption. These parameters are adjusted based on FC power measurements using an EKF approach. The EMS maintains a simple look-up table but with improved performance by correcting calibration errors, drift, or ageing. The article is structured as follows: In Section 2, 'Methodology', we introduce a case study, describe the fuel cell model calibration process, provide details about the vehicle model, and discuss the energy management strategy along with the proposed approach.