Traditional gasoline and diesel engines have led to many problems, such as global warming, environmental pollution, and waste of fossil fuels [1]. As a clean fuel that is widely recognized worldwide, hydrogen energy can effectively reduce greenhouse gases and global warming caused by the burning of fossil fuels [2]. Fuel cells are power generation devices that directly convert the chemical energy in fuel into electrical energy through electrochemical reactions. They were first used in special fields such as aviation, aerospace, diving, and military. Conventional internal combustion engines are limited by the Carnot cycle and have an energy utilization rate of only about 35%. The energy conversion efficiency of fuel cells can reach more than 50%. If waste heat recovery technology is adopted, the total energy utilization rate of fuel cells can reach 80% [3].

Despite the advantages of PEM fuel cells, their low dynamic response cannot meet the rapid power changes of vehicles in real time. Frequent power changes can accelerate the aging of fuel cells and affect their service life. Therefore, ancillary devices such as batteries are used to complement this feature to the vehicle’s transient response [4]. In order to coordinate the power distribution of vehicles with multiple power sources, a rational EMS is required [5]. Current EMSs are classified into two types: rule-based energy management strategies and optimization-based energy management strategies [6]. The rule-based energy management strategy is based on the experience of engineers or experts to design some simple rules to guide the energy distribution of the hybrid system [7,8]. The execution of deterministic rule-based strategies is relatively simple and requires low computing power for on-board processors. With these advantages, this strategy has become the most common energy management strategy for fuel cell hybrid electric vehicles. Power tracking and its improved strategies have been successfully applied to models such as Toyota Mirai [8] and Honda Clarity. Common rule-based strategies include deterministic rules and fuzzy rules [9,10]. Fares et al. designed the PID controller algorithm, which reduces hydrogen fuel consumption by 30% and system cost consumption by more than 10% under the FUDS driving cycle compared to the state control algorithm. Fuzzy logic rules, as a type of deterministic rules, use an imprecise system model where the states are represented by different affiliation functions [11]. Zhang et al. [12] proposed a fuzzy controller and low-pass filter to extend FC lifetime and reduce hydrogen consumption. Simulation results from highway fuel economy certification tests, urban dynamometer driving schedules and the new European driving cycle show that the proposed approach smoothes the fuel cell output and performs in real-time, resulting in a 19% reduction in current variation but an increase in hydrogen consumption of about 10%.

Optimization-based energy management strategies have received a lot of attention in recent years. This strategy usually establishes a cost function with fuel consumption or component durability as the optimization objective. The steps to solve the problem are: construct the optimization problem, establish the optimization objective function, consider the parameter constraints, and finally solve the solution that satisfies the optimization objective function. The DP algorithm is an optimization method that transforms a multi-stage process into a series of single-stage problems, utilizing the relationships between each stage to solve them one by one. The global optimal energy management strategy based on dynamic programming developed by Xu et al. [13] reduces the computation time by optimizing the coefficients of the dynamic programming algorithm and finds the optimal solution for the battery and fuel cell configuration under typical cycles of Chinese urban buses. Sun et al. obtained the optimal energy distribution using the PMP, which reduced hydrogen consumption by an average of 20.3% and 28.9% through simulation and experimentation compared to rule-based energy management strategies. However, these algorithms require the entire driving cycle information to be known in advance as a priori knowledge, making the algorithm impossible to apply in the real process [14].

The ECMS method is a typical example of a local optimization strategy. It incorporates the electricity in the batteries into the fuel consumption to ensure the minimum fuel consumption of the total power source, i.e., to calculate the instantaneous equivalent consumption; in addition, the algorithm is computationally small and has good real-time performance. However, the value of EF is optimized based on the vehicle’s operating conditions and performance requirements [15,16]. It directly affects the fuel consumption and performance of vehicles. Current ECMS-based studies have focused on the construction of equivalence factors. Han et al. [17] proposed a method to extract the global optimal EF trajectory from DP. The method is applied to the design of EF adaptive strategy and investigated for hilly road sections. The results show that the optimal EF significantly improves the fuel economy under hilly road sections. Han et al. [18] proposed a real-time update method for the ECMS equivalence factor based on the operating mode of the motor. The results show that the algorithm can improve fuel economy and fuel cell lifetime at different test cycles.

However, most of the previous studies on the penalty function are based on a fixed SOC reference, which leads to unnecessary fuel economy loss due to excessive penalty at some moment points [19–22]. In this paper, to this end, a fuel cell hybrid semi-trailer is used as a prototype, and a variable SOC-referenced ECMS energy management strategy based on road spectrum segmentation is proposed in the paper. By dynamically adjusting the SOC reference value of the penalty function, the same result as that of the fixed SOC-referenced ECMS can be achieved in maintaining the balance of the power supply, and at the same time the optimum value of the battery charging and discharging torque can be retained to the maximum extent, so that fuel consumption can be avoided from increasing by too much penalization. The fuel consumption increase caused by excessive penalties is avoided. Recording starts from the time when the vehicle speed is zero and is recorded as a segment when the vehicle speed is zero again. By segmenting the operating road conditions, the SOC reference value of the penalty function is dynamically adjusted so that the battery can give full play to the function of assisting fuel cell operation and braking energy recovery. At the same time, the optimal value of battery charging and discharging power is retained to the maximum extent to avoid the increase in fuel consumption caused by excessive penalties.

The main contents of the article are as follows, the second part is the introduction of the system structure and model, and the third part is the proposal of the adaptive ECMS method. The fourth part is the discussion and conclusion, this part presents the simulation results and discussion, and the fifth part is the conclusion.

In this section, the fuel cell hybrid vehicle is modeled. In order to satisfy the realism of the simulation, we also conducted experimental verification. The fuel cell hybrid electric truck studied in this paper mainly consists of a fuel cell, a battery, a unidirectional DC/DC converter, a drive motor, and a vehicle controller, as shown in Fig. 1. The fuel cell is connected in parallel with the battery through the unidirectional DC/DC controller to form a composite energy system. The fuel cell consists of auxiliary devices such as an air compressor, condenser, humidifier, pressure-reducing valve, and fuel cell stack cooling system. The battery pack is a power pack consisting of multiple individual cells [23].

The primary source of vehicle power is the hydrogen-oxygen electrochemical reaction that occurs in the hydrogen fuel cell, which converts chemical energy into electrical energy. The other part of the vehicle’s power supply is the power battery. Compared to other vehicle configurations, this topology eliminates the DC/DC converter between the battery and the DC bus, improving energy conversion efficiency and space utilization [24].

In this section, three ECMS methods are described in detail, namely conventional ECMS, ECMS based on fixed SOC reference and ECMS based on segmented brake energy recovery.

To verify the effectiveness of the proposed method, the hybrid system parameters shown in Table 1 were selected for modeling and simulation.

The model shown in Fig. 7 was built in Matlab/Simulink and simulated with the new European cycle condition (NEDC) (shown in Fig. 8) as the test condition.

The penalty function in ECMS2 is as follows:

(27)f(SOCref)=f0+K(SOCref−SOC(t))where f0=1; SOCref takes a dynamic value according to the selection result in the ECMS3 model; K=2.08, which is taken as the optimal value by the results of multiple simulations.

According to the kinematics interval definition, NEDC can be divided into 13 kinematics intervals, of which 1–12 have only one deceleration section and interval 13 has two deceleration sections. The braking recovery energy and the corresponding SOC reference value for each interval are calculated according to Eqs. (21)–(23), as shown in Table 2.

In order to facilitate comparative analysis, the variation of battery SOC obtained from ECMS1, ECMS2 and ECMS3 is given (as shown in Fig. 9), as well as the battery power output status and fuel cell output status of the 3 different strategies during the whole cycle, and the optimal equivalent energy consumption for the whole driving cycle is shown in the following Table 3.

Since this paper focuses on the effect of the SOC-based penalty function on the arithmetic results, it is necessary to use the results obtained by ECMS1 as a reference to illustrate the problem. Since the SOC range in the control strategy is defined as 0.4–0.9, it can be seen from Fig. 7 that the SOC of the ECMS1 strategy, even with the largest discharge, remains within this range. In this case, the final SOC of ECMS1 is 0.46 with a deviation from the initial SOC value of 0.72 of 36.1%, which is the highest among the three strategies. The final SOC deviation of ECMS2 is 2.1%, which is the lowest among the three strategies. The final SOC of ECMS3 is 0.69, with a deviation of 4.2%, which is very close to the ECMS2 strategy and can meet the power preservation ECMS strategy’s basic requirements. Combined with the equivalent energy consumption shown in Table 3, the ECMS3 strategy consumes 2380 kJ less than ECMS1, with a reduction rate of 1.7%. The ECMS2 consumes 4880 kJ less than ECMS1, with an increase rate of 3.4%. Therefore, the equivalent energy consumption of ECMS3 is 7260 kJ less than that of ECMS2.

Several phenomena in Fig. 9 can be further analyzed in conjunction with Figs. 10 and 11.

(1) The results of the ECMS1 strategy show that the battery can increase the output power when the vehicle needs high power, while the effect of ECMS2 and ECMS3 is not obvious. the reason for the obvious effect of ECMS1 is that, because there is no SOC feedback, when the battery tends to output high power, the control strategy only considers the minimum SOC limit, so that the battery continues to discharge and the power battery can output high power to assist the fuel cell. The reason for the insignificant effect of ECMS2 and ECMS3 is that, firstly, ECMS2 and ECMS3 can have more significant battery power output like ECMS1 strategy before 800 s when the vehicle power demand is high. After 800 s, the battery power output of ECMS2 and ECMS3 cannot follow the battery power output of ECMS1 and the driving effect is not obvious. In the simulation, it is found that the equivalent fuel consumption is highly sensitive to the equivalence factor, and a small change in the equivalence factor leads to different strategy selection results. Since ECMS2 and ECMS3 have SOC feedback, the final expression is in the form of changing the magnitude of the equivalence factor. In the first 800 s, the power output of ECMS1 can be essentially tracked because the SOC has little penalty due to the small difference from the initial value. In kinematic interval 13, the actual SOC of ECMS2 and ECMS3 is very different from the initial SOC (especially the ECMS3 strategy), so the penalty is very large. When the power output of the battery becomes larger, the penalty to the battery discharge increases and the calculated equivalent fuel consumption will be larger. At this point, the maximum output power of the fuel cell itself can meet the dynamic demand, resulting in the output power of the battery being determined by the control strategy.

(2) Compared to ECMS2, ECMS3 can track the battery power output of ECMS1 for most of the entire cycle. Since the penalty function in ECMS2 is based on a fixed SOC reference, the penalty increases linearly as the SOC deviates from the initial SOC, limiting the battery power output and resulting in a smaller range of SOC variation. In ECMS3, the SOC reference value can be reduced in time for each kinematic range, which makes the penalty function less severe for the first 900 s. The actual output power of the battery can track the output power of ECMS1, and the discharge capacity of the battery increases, leading to a rapid decrease in the actual SOC. Meanwhile, in the 900–1100 s cycle, the penalty increases significantly due to the large difference between the actual SOC and the initial SOC, and the equivalent fuel consumption is more sensitive to the equivalence factor, which limits the battery power output to a certain extent and ensures that the SOC does not drop further, thus maintaining the power balance.

In an ECMS strategy with SOC feedback, the penalty function based on a fixed SOC reference tends to increase fuel consumption due to excessive penalty when the power battery tends to be heavily discharged. To address this problem, this paper proposes a method to continuously adjust the SOC reference value using braking energy recovery during the motion interval to control the penalty intensity and improve fuel economy. The standard driving cycle NEDC simulation results show that when the initial SOC of the battery is 0.72, the proposed method can reach 0.69 with a deviation of only 4.2%, which can meet the basic requirements of electric power maintenance. Compared with the ECMS strategy based on a fixed SOC benchmark, it reduces 7260 kJ equivalent energy consumption, which improves the fuel economy to a certain extent.