1. Introduction
With the number of car ownership increasing, the global environmental problem due to car emissions is becoming increasingly more prominent [
1,
2]. Now, the development of new energy vehicles has been the focus of automotive research direction. New energy vehicles can be divided into pure electric vehicles, fuel cell hybrid electric vehicles (FCHEVs), hybrid vehicles and so on, according to the use of different power sources [
3]. FCHEVs are considered to be new energy vehicles with great potential due to their advantages of “high efficiency, cleanliness and zero pollution” [
4,
5]. Considering the shortcomings of soft output characteristics, poor power performance and low energy utilisation of single-source fuel cell vehicles [
6], a multi-source power approach is usually adopted. In this paper, a hybrid power system, fuel cell + lithium battery (FCHPS), is selected as the object of study, where the proton exchange membrane fuel cell (PEMFC) is the main power source, and the lithium battery is used as the auxiliary power source. The PEMFC is connected to the bus through a unidirectional DC-DC converter, while the lithium battery is directly connected to the bus [
7]. In fuel cell vehicles, the core of the technology is to implement a reasonable power distribution to ensure the safe operation of the fuel cell and auxiliary power sources [
8], to make the fuel cell work more efficiently and to avoid frequent fluctuations of the fuel cell power as much as possible, so as to improve the economy and reliability of the whole vehicle. There are currently two main energy management strategies (EMSs): rule-based and optimisation-based. Rule-based strategies can be further divided into deterministic rules and fuzzy rules, and optimisation-based energy management strategies can be divided into global optimisation and instantaneous optimisation energy management strategies [
8].
Dynamic programming (DP) is a widely used algorithm in global optimal control strategies [
9,
10,
11]. The DP algorithm requires acquiring all the operating condition information in advance and deriving the control law through backward reasoning. Due to its computationally intensive nature, it is not suitable for real-time applications, but it can generally be used as a benchmark algorithm for other energy management strategies [
12]. The instantaneous optimisation strategy solves the optimisation problem using an instantaneous minimisation of the hydrogen consumption cost function, which is updated in real time. The equivalent consumption minimisation strategy (ECMS) [
13] and Pontryagin’s minimum principle (PMP) [
14,
15] can approximate the global optimal solution by appropriately simplifying the whole vehicle model and selecting the appropriate equivalence coefficients. However, this method requires the precise selection of equivalence coefficients and construction of the corresponding prediction model, which are computationally complex and not easy for real-time applications.
The rule-based energy management strategy is not as good as the optimisation-based strategy in terms of optimising the control effect, but because it does not need to anticipate all the information about the driving conditions, and the formulation of the rules is mainly based on the professional knowledge and experience of the engineers and technicians, the real-time performance of the rule-based strategy will be a bit better. Based on the IF-THEN rules and the membership functions [
15], we can design the FLCS. In the design process of fuzzy logic, fuzzification, fuzzy inference and defuzzification are required. Among them, fuzzy reasoning is based on the IF-THEN rule. Literatures [
16,
17] propose an energy management strategy based on FLCS, which aims to reduce hydrogen consumption by considering its dynamic constraints as well as the state of charge of the batteries, while improving the durability of the power source, making the energy flow perfectly distributed among the sources under the UDDS cycle condition, and taking the response time of each power source into account to prolong its lifetime. Zhou [
18] proposed a composite fuzzy logic control strategy (FLCS) by designing the main fuzzy controller and sub-fuzzy controller, respectively. The results showed that the hydrogen consumption of this strategy is reduced by 0.66 g compared to the PFS, and the state of charge (SOC) of the battery is maintained in the desired range, which further improves the economy of the whole vehicle and extends the life of the battery. However, without much engineering experience as theoretical support, the fuzzy controller will deviate from optimality if the fuzzy rules are not well designed. To address the above problems, researchers have proposed to solve the problem of unreasonable fuzzy rule design by optimising the parameters of the fuzzy controller using an intelligent optimisation algorithm. Zhang R [
19] proposed a new fuzzy predictive controller for hybrids, including a low-pass filter and an improved genetic algorithm. The results showed that the strategy can effectively reduce the fluctuation of fuel cell output power and extend the service life of the hybrid system. However, hydrogen consumption increased by 10%. Qiang Li [
20] proposed a global optimisation of fuzzy controller parameters using a multi-objective genetic algorithm NSGA-II to obtain the Pareto optimal solution set through multi-objective optimisation, completing the optimisation of the membership function and the fuzzy control rules in order to improve the economy and durability of the fuel cell. The simulation results showed that after the optimisation process, the performance of the fuel cell was significantly improved, and it was able to operate in the efficient power range for a longer period of time. In addition, the number of detrimental variable loads was significantly reduced from 54 to 8. Overall, the approach significantly improves vehicle economy and fuel cell durability. Common energy management strategies are deterministic rule-based approaches, which include state machine control strategy, thermostat control strategy and power following strategy (PFS). These rule-based design methods are widely recognized as the most practical energy management methods due to their simplicity and practicality. State machine-based energy management strategies require information about the previous state of the system as well as the current inputs, and they execute the outputs based on a defined flow chart or decision tree [
21,
22]. The core of the state machine control strategy is to ensure that the fuel cell has different output powers in different states [
23]. The literature [
24] proposed an improved state machine energy management strategy, which is simulated and verified under two cycle conditions, New European Driving Cycle (NEDC) and Urban Dynamometer Driving Schedule (UDDS), and the results showed that the improved strategy can achieve an optimal effect close to that of DP. In addition, the thermostat energy management control strategy maintains the SOC to fluctuate within a certain range by controlling the start and stop of the fuel cell, while ensuring that the fuel cell outputs power at a high-efficiency operating point. However, this control strategy results in frequent starts/stops of the fuel cell, which significantly reduces its lifetime. The PFS is an improved thermostat strategy that generally controls the output of the fuel cell according to the SOC of the battery and the power demanded by the whole vehicle, maintaining the SOC while reducing the frequent fluctuations of the fuel cell, which is conducive to improving the lifetime of PEMFC [
25]. Comparison of various EMSs is shown as
Table 1.
The PFS is one of the most widely used control strategies in automobiles due to its simple design, easy implementation, and high real-time performance. This strategy also has some defects: when directly applying PFS to fuel cell vehicles, there will be a situation when the fuel cell output operating point is in the low-efficiency region after SOC correction, which will not be conducive to the improvement of vehicle economy.
In this study, we adopt FLCS to take the lithium battery SOC and fuel cell demand output power before SOC regulation as input variables, and the power correction coefficient as the output variable, to realize real-time adjustment of the correction coefficients, to maintain the SOC fluctuating within a certain range, and, at the same time, as far as possible, to move the fuel cell output power to the high-efficiency operating point correction [
25] so as to improve the economy and durability of the whole vehicle [
26].
The remainder of the paper is structured as follows. In
Section 2, the configuration of a FCHPS and the components are modelled. The PFS-FLCS is proposed, and the control rules are introduced in
Section 3. In
Section 4, simulation validation is carried out. The performance of the proposed strategy is compared with the PFS and the FLCS.
Section 5 draws the main conclusions of the paper.
Notes on abbreviations: Fuel Cell Hybrid Electric Vehicle (FCHEV), Fuel Cell Hybrid Power System (FCHPS), Energy Management Strategy (EMS), Fuel Cell + Lithium Battery (FC+B), Proton Exchange Membrane Fuel Cell (PEMFC), State of Charge (SOC), Power Following Strategy (PFS), Fuzzy Logic Control Strategy (FLCS), Hybrid Power-Following-Fuzzy Control Strategy (PFS-FLCS), Dynamic Programming (DP), Equivalent Consumption Minimisation Strategy (ECMS), Pontryagin’s Minimum Principle (PMP), Globally Harmonised Light Vehicle Test Cycle Conditions (WLTC), New European Driving Cycle (NEDC) and Urban Dynamometer Driving Schedule (UDDS).
3. Hybrid Energy Management Strategies
3.1. Power Following Strategy
The core of PFS is to keep the SOC of a battery in the optimal range. If the SOC is lower than the desired value, the fuel cell provides power as the sole energy source and the battery stops working and receives a charge; if the SOC is higher than the desired value, the battery starts discharging until the SOC is close to the desired value again. The PFS can be divided into the drive mode and brake mode control strategies.
3.1.1. Control Strategy in Drive Mode
When the car initially starts, the power demand of the whole vehicle is supplied by the lithium battery alone, as it takes longer for the fuel cell to start. At this time:
where
is the overall vehicle demand power,
is the fuel cell output power, and
is the lithium battery output power.
When the car is driving normally, the power demand of the vehicle and the state of the power battery can help to determine whether the two power sources work together or take turns. In this case, the output power of the fuel cell is the main source, and the power battery plays the role of “peak shaving and valley filling” with the main power source.
- 1.
When the SOC value is lower than the minimum SOC value
The SOC of the power battery is low, and its power output should be minimised, and all the energy required by the vehicle is supplied by the fuel cell, which also recharges the lithium battery. At this point, the power distribution satisfies the following equation:
where
is the maximum output power of the fuel cell.
- 2.
When the SOC value is the ideal SOC value
The power battery is in an ideal state of charge, at which point PEMFC should be operating in the high-efficiency range as much as possible to meet the power requirements of the whole vehicle and improve the efficiency of the fuel cell. When additional power is required, the power battery can provide peak power supplementation, and when residual energy is available, the power battery can also provide energy recovery. At this time, the power distribution satisfies the following equation:
where
is the minimum output power of the fuel cell.
The battery output power value is:
- 3.
When the SOC value is higher than the maximum SOC value
If the SOC of the power battery is too high, the demanded power of the whole vehicle will be provided by the battery, and the fuel cell will operate at a lower power. This promotes the consumption of the power battery charge while keeping the SOC within a certain range.
3.1.2. Control Strategy in Braking Mode
When the braking intensity is low, the engine can fully absorb the braking energy and use it to charge the power battery; when the braking intensity is high, the power battery cannot fully absorb the regenerative braking energy, and the excess energy is dissipated by the mechanical braking system through friction into thermal energy. In this state, the power relationship is:
The PFS consists of four modules: the fuel cell on/off control module, the source-generated power calculation module, the SOC power correction module, and the fuel cell operating-point-determination module.
Fuel cell turn-on and turn-off control module: handling the start–stop process of a fuel cell;
Source-generated power calculation module: based on the vehicle’s demanded pow-er , the demanded output power of the fuel cell before regulation is calculated;
SOC power correction module: regulating the demanded output power of the fuel cell;
Fuel cell operating-point-determination module: it is mainly responsible for protecting the fuel cell, limiting the power output, making it work in the region of high efficiency, improving the life of the fuel cell and ensuring its normal operation.
3.2. Shortcomings of the PFS
Compared to the thermostat control strategy, the PFS can effectively solve the problem of frequent start–stop occurrences of the fuel cell, thus prolonging its life and improving the economy of the whole vehicle. However, this strategy also has some shortcomings. Considering only the power correction of the battery’s SOC can cause the fuel cell to operate in an inefficient region, which may have an impact on the economy of the vehicle as a whole. The shortcomings of the above PFS are analysed in detail below.
The following is the calculation of the demanded output power of the fuel cell after SOC correction, as shown in Equations (16) and (17):
In Equation (16), is the output power required by the fuel cell after SOC correction, ; is the demanded output power of the fuel cell before SOC correction, ; is the corrected power of the fuel cell, .
In Equation (17), is the correction coefficient, which is positive. is the maximum value of the battery’s SOC and is the minimum value of the SOC set in the control strategy. The main purpose of power correction is to keep the SOC in the range of and to avoid overcharging and overdischarging of the power battery. This will optimise the operating point of the battery, and thus enhance the lifetime of the power battery. However, since the correction factor is a constant value, there may be a decrease in the output operating point efficiency of the fuel cell after power correction. For example, if is 22 , the efficiency at this point is 60%; after correction, the actual output power of the fuel cell may be 16 , and the corresponding efficiency drops to 53%. Therefore, the fuel cell output power corrected by considering only the battery’s SOC may cause the operating points of the fuel cell to be distributed in a low-efficiency region, thus affecting the economy of the whole vehicle to a certain extent.
3.3. PFS-FLCS Hybrid Strategy
In order to solve the defects of PFS, we propose a hybrid PFS-FLCS energy management control strategy. This strategy uses FLCS to take the lithium battery SOC and the fuel cell demand output power
before SOC regulation as input variables and the correction coefficient
as the only output variable when performing SOC power correction, and the fuzzy control framework is shown in
Figure 5. The main feature of the PFS-FLCS hybrid control strategy is to adjust the correction coefficients in real time, so that the correction coefficients are changed from constant values and adjusted according to real-time conditions of the output quantity. By formulating fuzzy rules, the SOC is maintained within a certain range, and the fuel cell output power is corrected to a higher-efficiency operating point, thus solving the problem of vehicle economy.
A fuzzy controller consists of fuzzy inputs, a fuzzification interface, an inference rule base, a defuzzification interface and fuzzy outputs. At present, the main methods of defuzzification are the maximum membership method, centre of gravity method and weighted average method. Compared with the maximum membership method, the centre of gravity method has a smoother output inference control, even if the output changes corresponding to a small change in the input signal. Therefore, we select the centre of gravity method (centroid) as the defuzzification method.
Formulation of the membership function for the input variable
: from the three horizontal lines corresponding to the efficiencies of 0.52, 0.55, and 0.59, the efficiency curve of the 40
fuel cell is divided into seven intervals, and the midpoint of each interval segment corresponds to the value of the membership function of 1. The divisions of the operating intervals and the membership functions of the input variables are shown in
Table 4 and
Figure 6,
Figure 7,
Figure 8 and
Figure 9.
From the purpose of satisfying the SOC correction of lithium battery and the operating point of the fuel cell in the high-efficiency region, the fuzzy rules formulated are shown in
Table 5. When the
is small and the SOC of the battery is low, the correction coefficient will take a large value to keep the operating point of the fuel cell in the high-efficiency region and at the same time charge the battery to keep its SOC within a certain range. When the
is large and the SOC of the battery is high, the correction coefficient will take a large negative value, which will reduce the actual output power of the fuel cell to work in the high-efficiency region, and the remaining power will be supplemented by the battery to correct the SOC.