Mathematical Problems in Engineering

Volume 2019, Article ID 7860214, 12 pages

https://doi.org/10.1155/2019/7860214

## A Game Theory Energy Management Strategy for a Fuel Cell/Battery Hybrid Energy Storage System

The School of Automobile and Traffic Engineering, Liaoning University of Technology, Jinzhou 121001, China

Correspondence should be addressed to Qiao Zhang; moc.361@526_qz

Received 8 November 2018; Accepted 16 December 2018; Published 9 January 2019

Academic Editor: Denizar Cruz Martins

Copyright © 2019 Qiao Zhang and Gang Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper introduces a game theory approach to implement power flow distribution mission for a fuel cell/battery hybrid system considering uncertain power information. To fully describe the vying interaction relationship between the fuel cell and the battery, we design the power distribution problem as a noncooperative game problem, in which the fuel cell and the battery are deemed to be two interactional players, and each one chooses proper amount of power supply to maximize its own optimization function relying on the other chosen. Different from all previous research work in the published papers, the power demand information of the adopted driving cycle is assumed to be absolutely known. In this paper, we discuss the case that when the power demand is uncertain how the players act and the Nash Equilibrium can be effectively achieved. Three original contributions are made. First, we develop the utility function for each player taking into account the uncertain behavior of the power demand due to inaccurate prediction of driving cycle. Second, an iterative algorithm with a fuzzy logical controller for correction is proposed to reduce the influence of uncertain power demand information on the decisions of the players. Finally, the effectiveness is validated by a comparison simulation test.

#### 1. Introduction

In the last two decades, the worsening environment and energy shortage problem have brought significant challenge to the global automotive industry. Again, new energy vehicles, which are powered using alternative energy for replacing traditional gasoline and diesel oil, have been paid more close attention [1–3]. Of all the candidate energy storage devices, the fuel cells are supposed to be good potential for directly superseding automobile internal combustion engines to power electric vehicles with considerable driving range for users. However, the slow dynamic response of the fuel cells will directly influence vehicle speed-up and speed-down performance. In addition, the fuel cells cannot supply negative power demand, which thus give a limit to recover the braking energy of the vehicle. To correct for these flaws and improve vehicle performance, the fuel cell hybrid systems have been suggested in the literature for practical vehicle application. In a fuel cell hybrid system, a battery or a supercapacitor pack is usually considered as auxiliary device for supply the drastic components of the power demand [4–6].

For a fuel cell/battery hybrid system, energy management control strategy is crucial for exploiting the advantages of the hybridization by coordinating the power flow between the fuel cell and the battery. State machine energy strategies were introduced to realize the state switch of the fuel cell and the battery to satisfy the load power demand as well as maintain the energy level within predefined range in [7, 8]. This strategy is simple and effortless for online implementation. However, the strategy lacks flexibility and adaptation to variation of the load power demand due to the limit of these fixed rules. To deal with complex and uncertain variable relation of the control strategy, fuzzy controllers were developed for a fuel cell hybrid system [9, 10]. Compared with the state machine strategy, the control performance can be improved to some extent due to improved flexibility and adaptation. However, the two types of strategies mentioned above are developed based on predefined deterministic or fuzzy logical rules, which largely depend on knowledge and experience of a designer. Therefore, these strategies cannot achieve optimal control performance.

To obtain enhanced control performance, the rules of the strategies are often optimized using an offline optimization algorithm for a given driving cycle. The introduced algorithms include genetic algorithm [11], particle swarm optimization [12], simulated annealing optimization [13], DIRECT global optimization [14], and dynamic programming algorithm [15]. However, these optimization algorithms are centralized and only deal with single objective optimization problem. When a system has multiple optimization objectives, they are usually weighted and transformed into a single objective function to optimize using these algorithms. These weights were usually set to be fixed and rely on the preferences of the designers. In this way, however, the interaction between the competing optimization objectives (such as hydrogen economy and battery life cost) cannot be captured fully and the optimization result therefore lacks of objectivity.

Game theory provides one promising solution to the centered optimization dilemma by implementing independent optimization operation for each control object. Owing to its unique advantage in dealing with interaction and conflicting interests for coupled multiagent system, they have been widely applied to smart grid for demand response management [16–18] and sustainable energy system planning problem [19]. Some literatures have reported its successful application for energy management in different hybrid systems. A game theory (GT) controller was developed to capture tradeoff between driver operation and vehicle performance for a JLRF2 HEV in [20]. This application anticipates that the driving style of the driver is intrinsically coupled with vehicle fuel economy and emission performance. Test conclusions indicated that the GT control strategy by less calibration cost could achieve better performance compared with the baseline control for real world driving cycles. In [21], the GT strategy is applied for a fuel cell/battery/supercapacitor hybrid system to maximize a payoff function consisting of powertrain efficiency and vehicle performance. Simulation conclusions demonstrated the GT approach could benefit the two objectives simultaneously. Another example of the GT to energy management for an engine/battery/supercapacitor hybrid system is described in [22]. The author formulated a current control problem among the three power sources using noncooperative game theory approach. It was analytically proved that the Nash equilibrium can be iteratively calculated and the preference of each player, namely, the fuel consumption and battery life, could be satisfied simultaneously.

For energy management problem of hybrid system, each power source is personalized as a participant and which chooses certain amount of power supply to maximize its own optimization function depending on the actual power demand of driving cycle, which can be predictively obtained by employing some predictive algorithms, such as neural network [23], support vector machine [24], and Markov chain models [25], as well as advanced sensor technologies, such as radar [26] or geographic information system (GPS) [27]. For most of previous research works, the games are developed based on the assumption that the prediction is completely accurate. The decision of each participant is completely believable. From the opposite perspective, this paper focuses on the problem when the predictive driving cycle information is inaccurate and how the players in the game to adjust their individual strategies and achieve their final equilibrium. The main contributions that are fundamentally different from prior research in the literature are summarized as follows. First, we propose the game scenario that the players make their decisions encountering uncertain power demand information. Second, an iterative algorithm with a fuzzy logical controller for correction is proposed to ensure that the Nash Equilibrium can be effectively reached. Finally, the effectiveness is validated by a comparison simulation test.

The remainder of the paper is organized as follows. Section 2 presents the fuel cell and the battery hybrid energy storage system modeling. The game theory energy management strategy considering uncertain power information is described in Section 3. A case study is given to evaluate the effectiveness of the strategy in Section 4, followed by conclusive remarks in Section 5.

#### 2. Hybrid Energy Storage System Modeling

The object plant of this study is a fuel cell/battery hybrid energy storage system with parallel topology structure, as shown in Figure 1.