A novel second-order sliding mode control of hybrid fuel cell/super capacitors power system considering the degradation of the fuel cell

Highlights

• The degradation estimation of PEMFC is researched by Cubature Kalman Filter.

• A robust cascaded control loop is developed based on twisting and PI controller.

• For protection purpose, constraints of fuel cell and SCs are considered.

• Effectiveness of proposed control strategy is validated by HIL test experiment.

• Proposed control method has better performance than traditional PI controllers.

Abstract

This paper aims to design a novel control strategy of a single converter hybrid power system including a Proton Exchange Membrane Fuel Cell (PEMFC) and super capacitors for electric vehicle applications. The control objective to be addressed in such systems is to smooth the current of PEMFC considering the transient power and sinusoidal disturbance from the load. Moreover, in real-time applications, it is required to ensure the operation by taking into account the component constraints and the degradation of PEMFC. To achieve these goals, a robust nonlinear cascaded voltage control loop is developed in this paper. For the inner voltage loop, a second order twisting controller with dynamic saturation scheme is adopted to ensure the convergence of the DC bus voltage to its reference value as well as to attenuate the oscillations on PEMFC current. For the outer voltage loop, a Proportional Integral controller (PI) with anti-windup scheme is utilized to control the super capacitors voltage at its desired value. Furthermore, in order to consider the degradation of PEMFC in the controlled system, an estimation of the degradation model parameters has been provided by Cubature Kalman Filter. Comparative Hardware-in-the-loop (HIL) tests between the proposed control strategy and the traditional two PI controllers strategy for the hybrid power system is performed. The results of HIL tests verified the effectiveness of the proposed nonlinear control strategy.

Introduction

In the last few years, with the increasing pressure of energy crisis and environmental protection, fuel cell technologies have received wide attention and application from all over the world [1], [2], [3]. Among the current fuel cell technologies, the Proton Exchange Membrane Fuel Cell (PEMFC) is regarded as the most hopeful choice for vehicle and portable applications due to the numerous advantages of high energy efficiency, low operating temperature, no corrosive fluid hazards, and small size [4], [5]. In spite of these good points, there are still some deficiencies caused by the inherent characteristics of PEMFC [6], [7]. One of the main deficiencies of PEMFC is slow dynamic due to the hydrogen delivery system. Thus, when facing a step demand of load or the load with sudden perturbations, PEMFC will occur fuel starvation phenomena, which will decrease the lifespan of membranes and influence the performance of PEMFC [8]. For these transient loads mentioned above, a fast dynamic auxiliary power source is necessary to be utilized. Compared with battery, super capacitors (SCs) are considered as a better choice as auxiliary source in terms of high power density, good energy effectiveness and high lifespan (superior than one million cycles). Furthermore, SCs are able to work at even low temperature, such as −20 $°\mathrm{C}$ [9]. Therefore, SCs are chosen as auxiliary power source while PEMFC is considered as the main power source in this paper.

The architectures for hybrid fuel cell/SCs power system can be divided into three categories: parallel, series and cascaded. Due to the benefits of high reliability and low component stresses, parallel architecture is regarded as the most suitable architecture [10], [11]. For parallel architectures of hybrid fuel cell/SCs power system, there are three types of topologies [9], [12]. The first type is fully-active topology, which consists of two DC/DC converters and each converter is linked to a power source. The second type is passive topology, in which no DC/DC converter is adopted. The main advantage of the first type topology is flexible control performance while the disadvantage is higher costs for expenses. For the second type topology, it costs less but it has the lower controllability. Hence, taking into account a promising balance between the economy and control performance, the third type topology, namely semi-active topology on the basis of a single converter is utilized in this study.

Currently, there are various control strategies for hybrid multi-source power system studied by other researchers, such as proportional integral (PI) controller and passivity-based controller [13], [14]. However, among these previous researches on control strategies, the solution of suppressing disturbance for a hybrid fuel cell/SCs power system with only one converter is not considered. Moreover, these mentioned control methods have not taken into account the degradation phenomenon of the hybrid power system. When the hybrid system operates, both the PEMFC and the super capacitors will experience degradation in performance. In the long-term operation of the PEMFC, the electrical resistance, exchange current, and limiting current of the PEMFC will change [15]. Compared with PEMFC, the service life for the super capacitors is longer to a large extent. Due to this fact, degradation phenomenon of SCs is ignored in this study [16]. Therefore, the degradation phenomenon of the PEMFC as well as the external disturbance should be taken into account in the design of the control strategy to effectively improve the dynamic response of the hybrid power system.

Sliding mode control approach is one of the most efficient methods for controlling systems with parametric uncertainties and external disturbances [17], [18], [19], [20], [21]. Among the sliding mode controllers, the twisting controller is the conventional second order sliding mode control that is applied for perturbed systems with relative degree two affected by bounded disturbance [22], [23]. However, this controller provides a discontinuous control signal. In order to obtain a continuous control signal and still have finite time convergence, the idea of relative degree extension can be used [24]. This idea consists in considering the extra equation $\dot{u}=v$, where u is a real control input and v is a virtual higher order sliding mode discontinuous control input.

The aim of this paper is to develop a robust control strategy for the hybrid power system with a single converter considering the degradation phenomenon of PEMFC and the external disturbance. This control strategy should reject the sudden disturbance and decrease the oscillations on fuel cell current, i.e. provide a smooth behavior of the fuel cell current. To that purpose, and inspired by the idea of relative degree extension, our strategy proposes the usage of twisting controller as virtual control input to regulate the DC bus voltage to its reference value. Hence, this strategy ensures the finite time convergence of the DC bus voltage to its reference value while compensating the parametric uncertainty and the external disturbance. Moreover, it provides a continuous control signal which leads to smooth the fuel cell current and increase the lifespan of PEMFC. The main contributions of this work are the following:

• The degradation estimation of PEMFC is researched by the method of Cubature Kalman Filter (CKF). The CKF accurately estimates the degradation state and degradation rate for PEMFC. The estimated degradation of PEMFC is applied to the control of the hybrid power system.

• A robust cascaded voltage control loop is developed on the basis of twisting controller and PI controller for the single converter hybrid power system integrating the degradation of PEMFC. For protection purpose, the constraints of fuel cell and super capacitors are taken into account in the proposed control scheme.

• The effectiveness of the proposed control strategy is validated by HIL test experiment. Indeed, the HIL test results show that the proposed control method has better performance than the traditional two PI controllers in view of disturbance suppression in the hybrid fuel cell/SCs power system.

The organization of this paper is as follows: In Section 2, the description of the hybrid fuel cell/SCs power system based on a single converter is detailed. In Section 3, the degradation model of PEMFC based on the PEMFC degradation experiment is firstly given. Then, the PEMFC degradation estimation is made by CKF method. In Section 4, the proposed control strategy with limitation constraints for this hybrid power system is described. In Section 5, the HIL test results are illustrated to validate the effectiveness of the proposed control strategy. Finally, in Section 6, the main conclusions are presented.