Sensitivity analysis for assessing robustness of position-based predictive energy management strategy for fuel cell hybrid electric vehicle

Jihun Han,Dongsuk Kum,Youngjin Park

doi:10.3390/wevj7020330

Abstract

Under hilly road conditions, it is difficult to achieve near-optimal performance of energy management strategy (EMS) of fuel cell hybrid electric vehicle (FCHEV). In order to achieve near-optimality, optimal state reference trajectory is predicted based on future information, and thus reference tracking controller is often considered as real-time predictive EMS. There are two approaches depending on in what way the predicted reference will be used as follows: 1) position-based predictive EMS for tracking position- dependent reference, 2) time-based predictive EMS for tracking time-dependent reference. In this paper, analytical sensitivity analysis based on Pontryagin’s minimum principle (PMP) is performed to prove robustness of position-based predictive EMS with respect to velocity uncertainty. First, optimal control problem is formulated in time and position domain, and PMP approach is used to derive boundary value problem (BVP) that achieves global optimality. Then, sensitivity differential equations are developed which describe sensitivity of original BVP with respect to velocity uncertainty. Finally, these equations will be solved simultaneously with the original BVP to compute first-order sensitivity of time- and position- dependent optimal state. Results show that sensitivity of time-dependent optimal state is much bigger than that of position-dependent optimal state because velocity uncertainty can change predicted travel time, and this effect on sensitivity is significant. Therefore, predictive EMS should use current position to track position-dependent optimal state reference in terms of the robustness with respect to velocity uncertainty.

Highlights

Fuel cell-powered vehicles are equipped with additional energy storage system, which are often called as fuel cell hybrid electric vehicle (FCHEV)
Case study is performed to illustrate an important trend on state sensitivity and prove robustness of position-based predictive Energy management strategy (EMS) for hilly road driving conditions
When state of charge (SoC) reaches the maximum SoC bound during braking, the supervisory controller switches from regenerative braking into conventional mechanical braking to prevent overcharging

Summary

Introduction

Fuel cell-powered vehicles are equipped with additional energy storage system, which are often called as fuel cell hybrid electric vehicle (FCHEV). EVS28 International Electric Vehicle Symposium and Exhibition approach such as dynamic programming (DP) [57] and Pontryagin’s minimum principle (PMP) [8,9], and instantaneous (real-time) optimization approach such as equivalent consumption minimization strategy (ECMS) [10,11,12]. It is difficult to achieve near-optimal performance of real-time EMS using current driving information because upcoming potential energy cannot be predicted [13,14]. As an alternative to achieve nearoptimality, globally optimal state reference trajectory is predicted by using future information, and EMS will track this reference. In ECMS framework, adaptation law of equivalent factor is designed as state feedback controller for tracking the predicted state reference trajectory [17,18,19].

Results

Discussion

Conclusion