Nonlinear control and optimization of hybrid electrical vehicle under sources limitation constraints

https://doi.org/10.1016/j.ijhydene.2018.12.227Get rights and content

Highlights

  • Energy management of the FC/battery/SC hybrid system is studied.

  • The passivity based control is used for the control design.

  • The Hamilton Jacobi Bellman optimization is used to define the optimal energy/power.

  • The global stability proof of the studied system is demonstrated.

  • The experimental results exhibit good functioning.

Abstract

This work presents a new contribution on energy management of hybrid electric systems for vehicle applications. The studied hybrid electrical vehicle is composed of fuel cell as a main source and the auxiliary system containing the battery and supercapacitor. A programmable load is used to emulate a vehicle load profile. Two methods are combined to smartly and optimally control the energy flow between the used sources. These methods are the Interconnection and Damping Assignment Passivity Based Control (IDA-PBC) and the Hamilton-Jacobi Bellman (HJB) optimization. The source limitation is considered here in terms of the battery state of charge. The experimental works validate the efficiency of the proposed control where the obtained results demonstrate that the used strategy allows regulating the power flow under a realistic load drive profile. The global stability proof is demonstrated using Lyapunov theory.

Introduction

Global energy demand is growing rapidly because of demographics and economic growth. Fossil energies, and oil in the forefront, ensure actually the main of the world's energy supply [1]. Our great daily-life dependence on fossil energies raises the question on the sustainability of our life style in terms of industry production, and transportation mainly [2]. Using Renewable energies is one of the challenges for the development of efficient, less polluting and economically viable means of transport in a sustainable way [3]. To do so, ecological and economic constraints must be respected [4], [5]. In addition, the transport sector, mainly using oil, is participating largely in the depletion of fossil resources and is dramatically increasing the pollution in big cities [6], [7]. In recent decades, a lot of research appears on new transport solutions using hybrid electric vehicles based on Fuel cells (FCs), which are becoming an attractive technology [6], [8].

FCs which generate electricity from the chemical reaction between oxygen and hydrogen, represent a promising solution for the development of cleaner means of transport [9]. Indeed, the energy density of hydrogen allows reaching a significant autonomy without emitting local pollution [10]. This technology has gained renewed interest as a promising alternative solution for powertrain propulsion and stationary applications [11]. Proton Exchange Membrane FCs (PEMFCs) operate at relatively low temperatures and have a high power density, a simple and safe operating mode. These advantages make PEMFCs serious candidates for electric vehicle propulsion. Indeed, the hydrogen energy density allows to reach a significant autonomy without emitting local pollution. Unfortunately, this solution has low dynamics, due to auxiliaries, and does not allow recovering energy during braking [12].

For this, coupling the FC with an additional energy subsystem as battery and/or supercapacitor (SC) improves the vehicle performances [13]. In a hybrid electric vehicle, the storage system based on SCs and/or batteries associated with FCs is essentially designed to provide the additional power during high accelerations, when the FC reaches its maximum power, and to recover braking energy [14]. With this hybridization, it is not only possible to compensate for the low specific power, but also to compensate for the high time constants of FC auxiliaries [14]. Consequently, the lifespan of the FC can be increase and can recover the braking energy. Indeed, the SC can assist the FC and allow reaching high powers according to a dedicated energy management strategy [15]. The battery can be used with FC in steady state phases [14]. Consequently, the energy control of the FC hybrid system attracts actually many scientists and researchers around the world trying to define, optimize and control the parameters to optimally share the power and energy [15]. Thus, the wise choice of the control method is recommended to manage the energy between the sources.

The control of the vehicle must consider the constraints linked to the association of its components. First, the subsystems that make it up are strongly coupled. For example, FC and SC alone are not able to satisfy the power and energy demands of the system traction. . To do this, a smart control method is required to manage the energy flow between the used sources and the load. Furthermore, the majority physical systems have nonlinear behaviors such as saturation. The control designer has the choice of considering the nonlinearity or linearity of the studied system over a particular operating range. Interactions and nonlinearities affect the stability of the entire system, which can generate energy losses and potentially damage the vehicle. Another important criterion is that the developed control must be able to be implemented in real time.

The design of a smart control for the hybrid system allows to the used sources to share the tasks when ensuring the energy demand, where the storage devices take in charge the power transients that allows increasing the FC lifespan [16]. In fact, the storage systems can support the FC, achieve high power levels and protect the FC from fast dynamics [17]. In addition, because of the slow FC startup time and thanks to the battery high specific energy, this later can supply the load and the FC auxiliaries that allows the vehicle startup [18]. In addition, SCs have the highest specific power and cycle numbers. Hence, they will be used first in the transient and to recover the breaking energy [19]. Consequently, the most performing solution is the association of the three sources in a same hybrid system FC/SC/battery in order to increase the lifetime of the FC and the availability of the vehicle [20], [21].

In the hybrid system, the optimal power flow dispatch between sources/storages is a key point. Also, the chosen control should ensure the system stability taking into account the nonlinear behavior of physical system, source limitations and the implementation in real time [19]. The energy management of hybrid vehicle (FC/SC, FC/Battery, FC/SC/Battery) by the classical control [22], [23] and the Fuzzy Logic (FL) [24] have been the subject of several studies and the power distribution optimization of electric vehicle have taken a large place for scientific researchers. The following section is focused on the discussion of the previous works on the optimal energy management of hybrid electric vehicle to show the main contribution of our study in this paper.

Section snippets

Discussion of the previous works on optimal energy management of the hybrid electric vehicle

The authors of [19] have focused to the optimal energy management based on FL controller of hybrid system PEMFC/batteries. The objective of this study is to minimize the FC start-stop time in order to increase its lifespan. In fact, in Ref. [12], two technics are used to predict the long and short-term vehicle speed that are K-Nearst Neighbor (K-NN) and the averaging method, respectively. From the results shown in Ref. [12], good results, compared to the rule based strategy, are obtained

Architecture of the proposed hybrid system

The electric system proposed here is constituted of the FC as the main source providing the mean power to the load, and storage systems composed of SC and battery. The used sources are connected in parallel architecture. In the proposed structure, each component is connected to the DC bus by using its own DC/DC converter. This topology has certain advantages, namely, independent control of storage unit currents and limitation of their dimensioning powers. With the converters connected in

Cost function using Hamilton-Jacobi Bellman method

In order to guarantee the operation and the requested autonomy of the hybrid electric vehicle, it is necessary to optimize the operation of the embedded sources. The optimal control is one of the methods, which treats the problem of optimization in the electric cars field. In this work, the constraints optimization of the used sources is solved by the resolution of the HJB equations. For this, the constraints must be formulated in the form of an optimality criterion to be solved. The optimal

Experimental setup

Experiments were carried out at the IRH (Institue de Recherche sur l’Hydrogène) at Trois Rivière University, Canada. In this study, the FC/SC/Battery electric vehicle is emulated by using a dynamic power with reduction of the Nemo vehicle scale (see Fig. 3, as proposed in Ref. [35]). Consequently, the used test bench does not pretend to the vehicle sizing but to the validation of the portability in real time of the proposed control and the energy management by considering source limitations.

The

Experimental result and discussion

The experimental results demonstrate that passivity based control is adapted in real time, given the good and rapid performance of the current and voltage tracking and provides the stability proof of the system.

Fig. 5, Fig. 6 present the electrical responses of FC, IFC, VFC, respectively. These curves show the slow dynamic of the FC source and the FC provide the energy at permanent phases.

The battery electrical behavior is provided on Fig. 7 and Fig. 8 as current and voltage, respectively.

Conclusion

Through this study, the optimal control and the energy management of DC hybrid sources have been presented. The system complexity due to the system nonlinearity and to the source limitations makes it difficult to find the control that optimally dispatches the power flow between sources and load and at the same time providing the global stability proof. Our contribution consists on a new combination of the nonlinear IDA-PBC (Interconnection and Damping Assignment-Passivity Based Control)

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