1. Introduction
In recent years, social problems such as energy shortage and environmental pollution caused by fuel combustion have become increasingly severe, which has strongly promoted the development of new energy vehicles. Fuel cell vehicles have attracted extensive attention from all sectors of society due to the characteristics of high energy conversion efficiency and zero emission [
1].
However, since fuel cells cannot recover energy and respond slowly when they are used as a single power source, additional energy sources such as batteries or supercapacitors are generally added as an auxiliary power to form fuel cell hybrid electric vehicles (FCHEVs). Moreover, the complex power system structure leads to the total cost of FCHEV being too high to meet the needs of the market, especially the operating cost of the onboard fuel cell and battery system [
2]. On the other hand, due to the operational characteristics of the powertrain energy, the complicated and changeable vehicle driving conditions in the actual driving environment will bring a huge burden to the system, thereby reducing the service life and increasing the additional cost [
3]. An appropriate energy management strategy (EMS) is currently a viable approach to manage the distribution of power between different energy sources so that the different energy sources can compensate for each other’s power deficits, use hybrid systems efficiently and healthily, and reduce FCB operating costs [
4]. EMSs for hybrid drive systems have been developed into two main categories: rule-based EMSs and optimisation-based EMSs. Rule-based EMSs include those based on deterministic and fuzzy rules, formulated based on engineering experience by defining a series of rules for the operation of vehicle power systems to determine the working state of the power drive system. This method is technically inexpensive, the amount of online calculation is small, and the industrial application is widely used [
5]. The EMSs based on optimisation use the optimisation algorithm to search for the optimal or suboptimal control strategy of the system control objective function, which is generally manifested as the problem of finding the minimum value of the objective function in the feasible domain, which can be divided into global optimal control strategy and real-time optimal control strategy [
6].
In contrast, rule-based EMSs are the most common way to achieve energy management in FCHEV industrial applications [
7]. Currently, the most common rule-based EMS for FCEVs mainly includes state machine control methods, power follower control methods, and fuzzy logic control strategies [
8,
9]. Banvait, H. et al. developed and established state machine models to achieve power distribution control by executing predefined control rules or logical thresholds [
10]. Chen, Z. et al. used the rules extracted from the optimisation results of 12 typical driving cycles, from which a rule-based EMS was proposed, and the results showed that it can effectively reduce hydrogen consumption [
11]. Trovao, JP. et al. proposed an EMS for assembling rules by combining long-term rules to dynamically limit the search state space with short-term rules for implementing decisions [
12]. Thounthong et al. proposed an EMS based on fuel cell/supercapacitor flatness characteristics to improve system stability [
13]. T. Wang et al. proposed an EMS for air-cooled fuel cell system based on a state machine, which was verified on the established hybrid test platform [
14]. The above studies have conducted extensive and in-depth research on the rulemaking of energy management; however, they did not consider the operating characteristics of fuel cell systems and may be ineffective in practical applications.
Some existing EMSs seek to minimise hydrogen consumption and battery equivalent consumption in fuel cells [
15,
16]. However, these performance indicators are only partially representative of the operating costs of the vehicle, as energy degradation can also increase the operating expenses of the vehicle. Therefore, to comprehensively assess the economics of FCB, several studies have incorporated energy degradation factors into the decision-making framework, resulting in a multi-objective EMS [
17]. Y. Zhou et al. mitigated the degradation of fuel cells by limiting their power transients, further reducing operating costs based on H
2 minimisation strategies [
18]. Y. Zhou et al. proposed an MPC-based EMS comprehensively considering fuel cell efficiency and degradation [
19]. J. P. Ribau et al. applied single-objective and multi-objective genetic algorithms to optimise the powertrain design of fuel cell vehicles to improve system efficiency and extend service life [
20]. Aiming at the fuel economy and system durability of fuel cell hybrid energy systems, Xu et al. established a dual-cycle energy management framework based on a dynamic programming algorithm to solve this multi-objective optimisation problem [
21]. Although the above studies have conducted detailed and extensive research on EMSs, most researchers currently use data sets of typical standard driving cycles, which may influence the performance of EMSs in practical applications.
In order to comprehensively evaluate the economy of a fuel cell hybrid system, this paper combines the control strategy based on Charge-Depleting–Charge-Sustaining (CD-CS) rules with a multi-objective function framework to improve the practicability of the control strategy and uses real-world driving data for simulation validation. The structure of the full text is shown in
Figure 1.
The contributions of this article are as follows:
- (1)
This paper proposes a multi-objective cost function framework that can specifically quantify energy degradation as operating costs to represent the impact of energy degradation visually;
- (2)
The effects of fuel cell power output fluctuation on the life and hydrogen consumption of a fuel cell/battery hybrid system were studied, and it was found that, the more stable the fuel cell power output, the smaller the life degradation of the fuel cell/battery hybrid system and the lower the operating cost;
- (3)
Comparing real-world speed information with typical standard driving cycles, it is found that, in the real world, the working conditions change more drastically, the energy consumption is greater, and the smoother the fuel cell power output, the better the adaptability of the fuel cell system to complex working conditions.
The rest of the paper proceeds as follows. The FCB powertrain model and multi-objective cost function framework are detailed in
Section 2.
Section 3 introduces the CD-CS rules. The control results under the driving cycle are given in
Section 4. The conclusion is summarised in
Section 5.
4. Simulation and Results
In this section, the multi-objective cost function framework proposed in
Section 2 and the EMS based on the CD-CS rule and real-world driving data proposed in
Section 3 are used to study the impact of fuel cell energy output fluctuations on fuel cell/battery hybrid systems. Specifically, this is achieved by setting different fuel cell output power control step limits (
), and six cases of
,
,
,
,
, and
are considered.
Considering the impact of load changes on fuel cell life, the influence of the fuel cell power control step limit on the total cost of the hybrid power system was investigated. The optimised cost outcome is shown in
Figure 7.
From
Figure 7a, the simulation results show that the hydrogen cost under different control step limits increases steadily with the vehicle running; however, it is affected very little by the different power control limits. When
,
reaches the minimum value, 0.6476 USD. In the whole driving cycle,
is always the lowest under
, compared to other control step limits.
From
Figure 7b, the simulation results show that, with the gradual increase in
,
presents an upward trend and is significantly affected by different power control limits. When
,
reaches the minimum value, 0.0535 USD; moreover, when
,
reaches the maximum value, 0.7241 USD, jumping from 8% to 49% of the total cost, greatly affecting the total cost. This may be due to the slow working characteristics of the fuel cell dynamic response. The smaller the control step limit size, the better the energy management effect, and the fuel cell works stably.
From
Figure 7c, the simulation results show that with
increasing gradually,
increases steadily, and it is also affected very little by the different power control limits. The overall value is around 0.0620 USD. This shows that fuel cell power fluctuations have little impact on the battery system.
Specific numerical results are shown in
Table 5. From
Table 5, the hydrogen cost contributes the most, accounting for about 45–83% of the total costs; the fuel cell degradation cost constitutes the second largest expense, accounting for about 8–49% of the total costs; the battery degradation cost is the smallest, accounting for about 4–8% of the total costs. The reason for the large fluctuation is that the cost of fuel cell degradation is significantly affected by the change of different power control step limits. Moreover, fuel cell degradation has a significant impact on the total cost, far greater than the single-factor hydrogen consumption considered by the traditional EMS. Therefore, the study of fuel cell/battery lifetime is necessary, and it provides a feasible idea for future research.
From the above results, it can be seen that the fuel cell power control limit significantly impacts fuel cell degradation, and a smaller fuel cell power control limit will help improve the service life of the fuel cell and reduce the cost of use.
This paper also conducts a comparative study based on the standard China city cycle to find the difference between real-world data and typical driving cycles. The standard China city cycle is shown in
Figure 8.
The
,
, and
under different power control limits are shown in
Figure 9, and the specific values are shown in
Table 6.
From
Figure 9a, the hydrogen cost under the different control step limits’ trends is roughly the same as shown in
Figure 7a; however, the value is reduced by about 7%, and, when
,
reaches the minimum value, 0.5879 USD.
From
Figure 7b and
Figure 9b, the simulation results show that, with a gradual increase in
,
presents a similar trend; however, the final values vary wildly. The difference between the minimum and maximum values of
in
Table 6 is about 1.6 times, while, in
Table 5, the gap widens to 11.33 times. The reason may be that real-world vehicle speeds change more frequently, and fuel cell hybrid systems are more burdensome, leading to greater energy degradation. More granular energy output can effectively alleviate this situation, as can be seen from the fact that the minimum value of
in
Table 5 is nearly 76% smaller than the minimum value of
in
Table 6. It also shows that, with an increase in
, the adaptability of fuel cell hybrid systems to more complex traffic environments decreases significantly. This shows that more detailed control of fuel cell output power can not only reduce the degradation of fuel cells but can also improve the adaptability of fuel cells to complex working conditions.
From
Figure 7c and
Figure 9c, the overall trend of
is similar; however,
in
Table 5 has increased by about three times compared to
in
Table 6, indicating that frequent load changes also have a significant impact on the life of the battery system.
From
Table 6, the hydrogen cost contributes the most, accounting for about 57.6–67.4% of the total costs. The PEMFCS degradation cost constitutes the second most considerable expense, accounting for about 29.8–39.8% of the total costs, and the battery degradation cost is the smallest, accounting for about 2.57–2.8% of the total costs. Compared with
Table 5, the cost of each part in
Table 6 is more negligible, and the change in the proportion of the total cost is relatively more stable, especially in the cost of fuel cell degradation, showing a vast difference.