Energy management strategy of integrated adaptive fuzzy power system in fuel cell vehicles

Abstract

Fuel cell vehicles are a reliable solution to address energy shortages. However, when the road conditions are complex, the system distributes power unevenly between fuel cells and lithium batteries, and cannot effectively absorb the energy generated by braking. In response to this issue, an adaptive control strategy is adopted to allocate the required power of the car to two types of batteries in real time. Fuzzy logic is used to continuously optimize the relevant parameters of the controller based on the vehicle state, and a multi-island genetic algorithm is used to optimize the control strategy, enhancing the global search ability of the control strategy and increasing the vehicle’s ability to absorb and reuse the energy generated by braking. The experiment findings denote that the optimized control strategy increases the remaining capacity of lithium batteries by an average of 1.67%, increases energy recovery by an average of 135 W, increases the overall energy recovery rate by an average of 2.8%, and reduces vehicle fuel consumption by an average of 0.24 L/100 Km. It can be concluded that the optimized adaptive fuzzy control strategy can reduce the probability of over-charging and discharging of lithium batteries and improve the battery life. Meanwhile, the optimized strategy can improve the energy reuse rate, reduce vehicle fuel consumption, lower usage costs. The optimized strategy provides a reference for subsequent research on energy management of fuel cell vehicles.

Introduction

In recent years, with the increasing development of society, the global energy crisis has become more and more severe, and non-renewable fossil fuels will only become increasingly scarce. According to the current consumption rate, the discovered oil reserves worldwide are only enough to last for 53 years, and the continuously increasing number of motor vehicles is a major fuel consumer among them ((Li et al. 2021). The number of motor vehicles in China reached 417 million in 2022, which is about three times the 156 million in 2015 ((Yan et al. 2021). China’s crude oil consumption has increased tenfold from 70 million tons in 2000 to 703 million tons in 2021, of which only 199 million tons are self-produced. The annual energy import volume has reached 504 million tons, accounting for 72% of the annual consumption ((Jia et al. 2021). At the same time, the rapidly increasing consumption of crude oil and the number of cars have also brought enormous pressure to the environment ((Swethamarai and Lakshmi 2022). To solve this problem, the country vigorously develops fuel cell vehicles, but the existing control system has low energy allocation efficiency, system parameters cannot be changed in real time, and the regenerative braking energy of the vehicle cannot be effectively utilized. Trinh et al. proposed a management strategy that combines high-order and low order control to address the energy allocation and controller parameter issues in hybrid electric vehicles. This strategy used an adaptive control system and simulation logic to determine the required power for different operating conditions, and adopted low-level control of the output current of each component. Experiments denote that this strategy can ensure effective power allocation during sudden changes in operating conditions, improve battery utilization efficiency, and reduce energy consumption ((Trinh et al. 2022). Zhou et al. proposed a new adaptive learning network to develop the application of neural networks in energy management of hybrid vehicles. The network was constructed using a global fuzzy method, using real-world signal conditioning network input data to calculate the state function of the vehicle battery. Experiments indicate that the energy utilization rate of this network is 8% higher than traditional methods, while exhibiting good performance and robustness ((Zhou et al. 2021). Suhail et al. proposed an intelligent technology control method to improve the autonomy of hybrid vehicles and reduce usage costs. This method used fuzzy controllers and neural fuzzy to determine battery state parameters, determine the value of forward gain, and used advanced controllers to determine the required engine torque for power. The experiment outcomes indicate that this method has good performance and can effectively reduce fuel consumption ((Suhail et al. 2021).

Zhang et al. raised a dual motor coupling structure based on multi-island genetic algorithm (MIGA) to raise the endurance of new energy vehicles, in response to the problem of low energy utilization of regenerative braking energy caused by empirical setting of controller parameters. The structure adopted a dual motor coupling system as the power source, switched back and forth in eight modes, and optimized the model parameters using anMIGA. The experiment outcomes indicate that the optimized parameters of the structure can follow the real-time changes of the vehicle, and the energy utilization efficiency of the vehicle is significantly improved (Zhang et al. 2021a, b). Zhao et al. proposed a new method to optimize the energy management system to improve the fuel utilization efficiency of fuel cell vehicles. This method used elliptic basis functions to establish a highly similar model, optimized the model using MIGA, and conducted simulation experiments using a fuzzy control system. The experiment shows that the output power of this method is more stable, the average fuel consumption is raised by 5.5%, and the battery life is improved (Zhao et al. 2021). Liu et al. raised a new Six Sigma method to raise the robustness of energy management strategies for hybrid vehicles. This method used MIGA to optimize energy management strategies, evaluated the Sigma level of strategies using Monte Carlo simulation, and responded with terminal charging status and fuel consumption. Experiments denote that this method significantly improves energy efficiency and anti-interference ability (Liu et al. 2022). Wang et al. proposed a multi-objective optimization algorithm to improve the efficiency of hybrid vehicles. This algorithm analyzed the transmission parameters of automobiles from three aspects: objective function, constraint conditions, and decision variables. It introduced the elite strategy algorithm to select the optimal parameters and formulate the best strategy. Experiments illustrate that this algorithm improves engine efficiency by 10%, reduces average fuel consumption by 3%, and enhances the overall fuel efficiency of the vehicle (Wang et al. 2023).

In summary, the existing research has explored the issues of control system energy allocation, parameter setting and brake energy reuse from various aspects, and has achieved certain research results, but the existing control methods can no longer meet the growing demand. Therefore, the research adopts adaptive fuzzy control to improve the system and optimise the output power distribution of two kinds of batteries, and innovatively introduces multi-island genetic algorithm to optimise the system parameters, so that the parameters can be changed in real time according to the state of the vehicle, and improve the efficiency of the power distribution of the batteries. The improvement method aims to improve the reasonableness of the power division of the vehicle, solve the problem of insufficient power of the fuel cell vehicle in some cases, improve the service life of the battery, and increase the energy utilisation.

Methods and materials

Design of adaptive fuzzy control system for fuel cell vehicles

The energy of fuel cell vehicles mainly comes from the fuel cell system, which, although has stable output, lacks the ability for sudden changes in output power. The system lacks power during vehicle start-up and uphill driving, and can no longer meet daily needs. Therefore, the study adopts ternary lithium batteries that can provide transient high output power to solve the problem of sudden power changes, while recovering the braking energy of the car to save energy. The adaptive control system of fuel cell vehicles is designed to allocate energy between two battery systems in a reasonable manner, save energy and reduce emissions, and lower usage costs. The adaptive control system is constructed using mathematical models to continuously obtain the vehicle’s operating status during operation, accumulate and identify vehicle state parameters, and continuously compare them with the set optimal vehicle driving parameters to adjust the corresponding power system output strategy. The existing fuel cell vehicle models have drawbacks such as large data volume, slow calculation speed, and long computation time. The parameter expression of the newly established automotive fuel cell model for these issues is shown in Eq. (1).

$$U={U_1} - {n_a}\ln \left( {\frac{{{i_{oc}}}}{{{i_o}}}} \right)\frac{1}{{\frac{{{T_d}}}{3}+1}}$$

(1)

In formula (1), ${U_1}$represents the terminal voltage of the fuel cell in the open state, ${n_a}$ represents how many cells the fuel cell model is composed of, ${i_{oc}}$represents the output current of the fuel cell model, ${i_o}$represents the exchange current between the cells, and ${T_d}$represents the time required for the battery reaction. The total voltage of the battery model is shown in Eq. (2) ((Hebbi and Mamatha 2023).

$${U_{oc}}=U - {R_{oc}} \cdot {i_{oc}}$$

(2)

In Eq. (2), ${U_{oc}}$indicates the total voltage of the fuel cell, ${R_{oc}}$means the total resistance of the battery model. The battery model adopts a parallel connection between a power converter and a ternary lithium battery, and the expression of the converter is shown in Eq. (3).

$${L_c}\frac{d}{{dt}}{i_{oc}}\left( t \right)= - \left( {1 - d\left( t \right)} \right){U_2}+{U_{oc}}\left( t \right)$$

(3)

In Eq. (3), ${L_c}$represents the inductance generated inside the converter, t is the operating time of the battery model, $d\left( t \right)$represents the proportion of circuit on-time in the converter, and ${U_2}$represents the voltage of the ternary lithium battery. The system control operation process of fuel cell vehicles is shown in Fig. 1.

Fig. 1

Adaptive control system of fuel cell vehicle

In Fig. 1, the fuel cell outputs current to the power converter and adaptive control system, and calculates the vehicle load and real-time power demand through a fuzzy controller. The system adjusts the output current of the fuel cell to meet the different power requirements of the vehicle during operation. The calculation method for adjusting the output current of the battery by the adaptive control system is shown in Eq. (4) ((Jermsittiparsert et al. 2021).

$$i\left( t \right)={i_{oc}}\left( t \right)=\frac{v}{{{v_{oc}}}}\left[ {h\left( t \right) - \mu \left( {v - {v_{oc}}\left( t \right)} \right)} \right]$$

(4)

In Eq. (4), ${i_{oc}}\left( t \right)$represents the real-time output current required by the vehicle, v represents the output voltage of the ternary lithium battery, ${v_{oc}}\left( t \right)$represents the real-time open circuit voltage (OCV) required by the ternary lithium battery, $\mu$represents the control gain, The value of $\mu$ must be a positive number with an upper limit, and the size of $\mu$ should be adjusted according to the specific working conditions to ensure that the output current is appropriate while protecting the lithium battery to prevent excessive charge and discharge. and $h\left( t \right)$is calculated as shown in Eq. (5).

$$\left\{ \begin{gathered} h+t\dot {h}={i_l}\left( t \right) \hfill \\ \hat {L}{{\dot {i}}_l}\left( t \right)={v_{oc}}\left( t \right) - \left( {{i_l} - {{\hat {i}}_j}} \right){{\hat {R}}_j} - 2\mu \hat {R}\left( {v - {v_{oc}}\left( t \right)} \right) \hfill \\ \end{gathered} \right.$$

(5)

In Eq. (5), ${i_l}\left( t \right)$represents the output current of the converter, $\hat {L}$means the inductance throughput of the load, $\hat {R}$means the resistance of the ternary lithium battery, ${\hat {R}_j}$represents the resistance of the load, and ${\hat {i}_j}$represents the current passing through the load. The power demand of fuel cell vehicles can be achieved through adaptive controllers, but due to the time-varying parameters ${v_{oc}}\left( t \right)$ and $\mu$. Therefore, it is necessary to adopt a fuzzy control strategy to optimize the adaptive controller, so that $\mu$and ${v_{oc}}\left( t \right)$can continuously change according to the vehicle’s driving state and maintain the optimal state ((Zhang et al. 2021a, b). The fuzzy controller adopts fuzzy logic to divide the working state and required power of the fuel cell vehicle, and corresponds the calculation input of the adaptive controller to the standardized numerical interval to complete the reasonable division of the output power of each power system. The operation process of the fuzzy controller is denoted in Fig. 2.

Fig. 2

Operation flow of fuzzy controller

In Fig. 2, the fuzzy controller performs fuzzification on the obtained data, converts it into fuzzy data, and makes inferences and decisions based on the established fuzzy database and fuzzy rules. The decision made data is then deblurred. The anti-fuzzy data is transmitted to the vehicle control system, and the specific execution is replicated. Then, the real-time vehicle status data collected by the sensors is transmitted to the adaptive controller for the next adjustment. Data ambiguity refers to the process of converting precise data into fuzzy vectors and determining the types and quantities of corresponding membership functions. The input parameters of the fuzzy controller include the load passing current ${i_l}\left( t \right)$and the difference $\Delta {v_1}$between the set and actual values of the ternary lithium battery voltage. The output parameters include the control gain $\mu$and the difference $\Delta {v_2}$between the set and OCVs of the ternary lithium battery ((Jiang et al. 2022). The establishment of fuzzy rules is the core issue of fuzzy controllers. Firstly, the membership functions of all input and output variables of the fuzzy controller are determined, and the number and types of membership functions are designed. For the convenience of digitizing fuzzy rules, the fuzzy rules followed by the controller are denoted in Table 1.

Table 1 Fuzzy rules of adaptive fuzzy controller

In Table 1, NM (Negative Medium) denotes a medium degree of negativity, NS (Negative Small) denotes a smaller degree of negativity, NB (Negative Big) denotes a larger degree of negativity, NO (Negative) denotes a complete negativity, and Z (Zero) denotes no degree of affiliation or complete uncertainty.PO ( Positive) denotes certainty and is usually used to denote positive attributes but to an unspecified degree.PS (Positive Small) denotes a smaller degree of certainty, PM (Positive Medium) denotes a medium degree of certainty and PB (Positive Big) denotes a larger degree of certainty. In formulating the fuzzy rules, the affiliation of each input data on the fuzzy set is calculated through the affiliation function and each fuzzy rule is determined based on the calculated affiliation. In case of conflict in some of the rules, the confidence level of the conflicting rules is calculated and the rules with low hanging confidence are removed.

Optimization of fuzzy control strategy using MIGA

Due to the different energy losses generated by vehicles during driving and braking, and the fact that energy can be recovered and reused during the braking process, research is being conducted on optimizing fuzzy control strategies for the braking process. Due to the high nonlinear characteristics and variable problems of the braking and energy recovery system of fuel cell vehicles, the study adopts the MIGA with stronger global search capability and higher automation level. The MIGA algorithm generates the initial population individuals in each island, calculates the fitness values of all individuals, and according to the size of the fitness values, performs multiple rounds of selection, crossover, and mutation operations to retain the excellent individuals. In a certain time interval, some individuals are migrated from one island to another to realize information exchange and promote global search.MIGA avoids local optimal solutions and improves the performance of the algorithm by controlling two parameters, namely, population migration interval and migration probability. MIGA divides the initial data into multiple smaller parts, and there is regular data migration between each part, which can ensure the diversity of data in each part. The MIGA algorithm can effectively enhance the ability of the model to solve problems and raise the global search efficiency of the optimal solution. To reduce the subjective influence of MIGA algorithm parameters, the membership function and fuzzy rules of the algorithm are optimized. The specific optimization process is shown in Fig. 3.

Fig. 3

MIGA fuzzy controller optimization process

In Fig. 3, the braking degree, vehicle speed, and battery residual capacity of the fuel cell vehicle are constructed as the corresponding affiliation functions, and the respective affiliation functions are optimized using the multi-island genetic algorithm, and the optimized affiliation functions are used to encode the fuzzy rule table. At the same time, the vehicle motor braking ratio and the objective function are introduced into the multi-island genetic algorithm, and then the fuzzy rule table is constructed with the affiliation function, and the output data are optimized using the multi-island genetic algorithm for the affiliation function and input to the object being controlled. The number of initial data of the multi-island genetic algorithm has a large impact on the operating effect of the algorithm, and if the number is too large, the calculation speed will be reduced significantly. Too little initial data, the calculation accuracy of the algorithm will also be reduced. After selecting the initial data, the variables are optimized using coding operations, and the coding strings are used to calculate the data according to the evolutionary process of biological DNA structure. The optimization ability of the multi-island genetic algorithm is more related to the selection of the initial population, if the initial population is too low, the algorithm’s ability to find the optimal is insufficient and will reduce the accuracy of the search for optimization, and if the initial population is too high, it is easy to have a locally optimal solution and will reduce the computational efficiency. Therefore, the initial subgeneration population of the multi-island genetic algorithm is determined as 10, the number of islands is selected as 2, the number of genetic generations is 10, and the overall number of iterations is 220.The optimized vehicle braking degree, vehicle speed, and battery SOC membership function are shown in Fig. 4.

Fig. 4

The optimized vehicle braking degree, vehicle speed, and battery SOC membership function

In Fig. 4, S indicates higher membership, membership values between [0.7,0.9], M moderate membership, membership values between [0.4,0.7], B lower membership and membership values between [0.1,0.3]. The affiliation function is used to encode the relevant parameters of the automobile braking process, and at the same time, the linguistic variables in the fuzzy dataset are transformed into numerical values with certain rules to reduce the computational complexity and improve the computational speed. The force analysis of fuel cell vehicles on different roads during braking is shown in Fig. 5.

Fig. 5

Analysis of vehicle braking force under different roads

In Fig. 5, v represents the driving speed before braking, Fk represents the wind resistance experienced by the vehicle, k is the wind resistance coefficient, and Fz1 and Fz2 respectively represent the braking force applied to the front and rear wheels. F represents the normal force of gravity, L represents the wheelbase between the front and rear wheels of the car, L1 represents the distance between the front wheels and the vehicle’s center of mass, and L2 represents the distance between the rear wheels and the vehicle’s center of mass. The objective function $f\left( x \right)$ in the multi-island genetic algorithm is a combination of a weighted value of fuel consumption per kilometer and a weighted value of battery margin for the vehicle, and the calculation formula is shown in Eq. (6) ((Moro et al. 2023).

$$f\left( x \right)=\hbox{min} \left( {{r_1}f\left( {{x_1}} \right)+{r_2}f\left( {{x_2}} \right)} \right)$$

(6)

In Eq. (6), ${r_1}$represents the weighting coefficient of fuel consumption, and ${r_2}$represents the weighting coefficient of battery remaining capacity. Through the real-time recognition of the vehicle driving conditions has been the battery SOC, constantly adjust the weighting coefficient, through the reasonable weighting coefficient, reduce the vehicle’s energy consumption, improve the service life of lithium batteries. The calculation of $f\left( {{x_1}} \right)$is shown in (7).

$$f\left( {{x_1}} \right)=\frac{{100\smallint _{0}^{t}b\left( x \right)P\left( X \right)dt}}{{\rho s}}$$

(7)

In Eq. (7), $\rho$represents fuel density, S represents Laplace conversion factor, t represents travel time, b represents fuel consumption rate, and P represents output power. The calculation of $f\left( {{x_2}} \right)$is shown in (8) ((Montazeri-Gh and Mahmoodi 2016).

$$f\left( {{x_2}} \right)=\left| {SO{C_1} - SO{C_2}} \right|$$

(8)

In Eq. (8), $SO{C_1}$and $SO{C_2}$represent the remaining battery capacity at two time points, respectively. The fitness function of MIGA can also affect the computational performance and convergence speed of the algorithm. When solving the maximum value of the objective function, the calculation is shown in Eq. (9).

$$Fit\left( {f\left( x \right)} \right)=f\left( x \right)$$

(9)

When solving for the minimum value of the objective function, it is calculated as shown in Eq. (10).

$$Fit\left( {f\left( x \right)} \right)= - f\left( x \right)$$

(10)

Equations (9) and (10) can only solve problems with positive probabilities. When solving problems with negative probabilities, the boundary construction method is used to calculate the maximum value as denoted in Eq. (11) ((Ding and Jiao 2023).

$$Fit\left( {f\left( x \right)} \right)={s_{\hbox{max} }} - f\left( x \right),f\left( x \right)<{s_{\hbox{max} }}$$

(11)

In Eq. (11), ${s_{\hbox{max} }}$represents the maximum predicted value of the objective function. The minimum value of the objective function is calculated as indicated in Eq. (12).

$$Fit\left( {f\left( x \right)} \right)=f\left( x \right) - {s_{\hbox{min} }},f\left( x \right)>{s_{\hbox{min} }}$$

(12)

In Eq. (12), ${s_{\hbox{min} }}$represents the minimum predicted value of the objective function. When the objective function needs to estimate the function boundary value, the calculation for solving the maximum value problem of the objective function is shown in Eq. (13).

$$Fit\left( {f\left( x \right)} \right)=\frac{1}{{1+p - f\left( x \right)}},p \geqslant 0,p - f\left( x \right) \geqslant 0$$

(13)

In Eq. (13), p represents the estimated boundary value within the limited range of $f\left( x \right)$. When solving the minimum value problem with the objective function, the calculation is shown in Eq. (14).

$$Fit\left( {f\left( x \right)} \right)=\frac{1}{{1+p+f\left( x \right)}},p \geqslant 0,p+f\left( x \right) \geqslant 0$$

(14)

Before optimizing the fuzzy control strategy using MIGA, it is necessary to establish constraints on some parameters of fuel cell vehicles. The algorithm not only needs to consider the reasonable allocation of power during the driving process, but also needs to extend the service life of the ternary lithium battery as much as possible. The constraints of each parameter are shown in Eq. (15) ((Hasheminejad et al. 2022).

$$\left\{ \matrix{ SO{C_{\min }} \ge 30\% \hfill \cr i \ge 20\% \hfill \cr {v_{\max }} \ge 120km/h \hfill \cr {t_{0 - 100km/h}} \le 10s \hfill \cr} \right.$$

(15)

In Eq. (15), ${t_{0 - 100km/h}}$represents the zero to one hundred driving hours of the car, ${v_{\hbox{max} }}$is the maximum speed of the car, i is the slope of the car when going downhill, and $SO{C_{\hbox{min} }}$is the theoretical minimum value of the battery remaining capacity. Traditional genetic algorithms use step-by-step selection, crossover, and mutation operations, but they are prone to local optima, which can prevent the algorithm from completing calculations. Therefore, selection, crossover, and mutation operations are performed simultaneously. The MIGA first calculates the fitness, mutation rate, and crossover rate of all individuals in a certain dataset, and replicates the dataset twice ((Mahmoodabadi and Nejadkourki 2022). One dataset uses genetic operations, while the other dataset uses crossover operations to determine the fitness of all individuals. It extracts the individuals with the highest fitness generated from the three datasets separately and forms a new set with the same number as the first dataset, which will serve as the next generation dataset. It repeats the operation continuously until the algorithm requirements are met. Finally, the ISIGHT parameter analysis software is optimized, and the optimization process is indicated in Fig. 5.

Fig. 6

ISIGHT software parameter optimization process

In Fig. 6, the software Fiuent software is used for the fluid dynamics simulation of the car model, comprehensive design scheme is used to automate the simulation process of the model, Tabulation is used to organize and present the data of the design parameters, the simulation results or the optimization process in the form of a table, and matrix Tabulation is used to organize and present the data in the form of tables for design parameters, simulation results or optimization process, matrixlab is used to create and manage matrix operations. The numerical analysis process is integrated, the problem and the parameters that you want to derive are entered into the software for parameter optimization, as well as the parameters of the affiliation function and fuzzy rule parameters are entered into the software. A batch script, advisor_isight.bat, then needs to be created, which will serve as the basis for the simulation integration. Define the required optimization parameters in the Calculator module of ISIGHT and enter the objective function model in the Calculator-1 module. In the Optimization module, set the necessary constraints and configure the multi-island genetic algorithm. Finally, the whole vehicle model simulation in ADVISOR is initiated by calling the previously created advisor_isight.bat script through the Simcode component. Through an automated cyclic optimization process, the optimal solution is gradually approximated, and the optimal parameter values are finally applied to the ADVISOR model for optimal parameter updating. Assign values to the optimization variables and select similar models to design the optimization method according to the quality requirements.The ISIGHT software and the problem to be solved are connected by means of an interface file, which maximizes the real-time sharing of information.

Results

Analysis of simulation experiment results and real vehicle test results of adaptive fuzzy controller

The simulation experiment used MATLAB visualization simulation tool to construct an energy management model for the power system of fuel cell vehicles. To ensure the reliability of the data obtained from the simulation experiment, all vehicle parameters input into the simulation tool were derived from the measured values of the experimental vehicle. The fuel cell voltage of the vehicle was 42 V, the rated current was 55 A, the capacity of the ternary lithium battery was 45Ah, and the rated voltage was 45 V. The output power of the fuel cell and ternary lithium battery of the adaptive control system in different experimental scenarios is shown in Fig. 7.

Fig. 7

Comparison of parameters under different experimental conditions

In Fig. 7 (a), during the simulation experiment, the output power of the fuel cell managed by the adaptive controller was higher than that of the ternary lithium battery for most of the time. Only when the vehicle required transient high-power output, the output power of the ternary lithium battery was higher. The operation of vehicles was mainly powered by fuel cells, and the power variation of fuel cells was relatively gentle. In Figure (b), during the actual vehicle experiment, the output power of the ternary lithium battery fluctuated back and forth at 0 o’clock, responsible for providing the energy difference during sudden power changes. In Figure (c), the OCV of the ternary lithium battery fluctuated back and forth around 45 V, without a difference of more than 1.5 V, indicating that the remaining charge of the ternary lithium battery was within a controllable range and there is no overcharging or discharging situation. In Figure (d), the OCV of the ternary lithium battery gradually increased with the remaining battery capacity, with a relatively gentle increase, and the control system distributed energy evenly. The comparison of fuel cell outputs between adaptive controller and adaptive fuzzy controller in different experimental environments is shown in Fig. 8.

Fig. 8

Battery output power and current in different scenarios

In Fig. 8 (a), the output current adjusted by the adaptive fuzzy control strategy could identify the vehicle’s current demand faster and more accurately. When there was a significant change in road conditions, the speed at which the adaptive fuzzy control strategy adjusts the current was also significantly faster and more accurate than the adaptive control strategy. Because the adaptive fuzzy control strategy can adjust the parameters in the controller in a timely manner according to changes in road conditions, continuously optimize the output strategy of the controller, and adjust the response methods for different working conditions in a timely manner. In Fig. 8 (b), Because the adaptive fuzzy control has more excellent self-adjustment ability, the response speed is faster in response to changes in working conditions. during actual vehicle testing, the output current adjusted by the adaptive fuzzy control strategy could more effectively identify changes in vehicle load power. When the running time was around 300s, the load power changed more strongly, and the adaptive fuzzy control strategy responded 1–2 s faster than the adaptive control strategy. The comparison of OCV of ternary lithium batteries with different control strategies is shown in Fig. 9.

Fig. 9

Open circuit voltage of the battery under different environments

In Fig. 9 (a), the OCV of the lithium battery in both control states was around 45 V, but the OCV of the adaptive fuzzy controller was closer to the rated voltage than that of the adaptive controller, with an average increase of 0.05 V. From this, under the adaptive fuzzy control strategy, ternary lithium batteries were more likely to meet the power output requirements of vehicles, and there was no overcharging or over discharging phenomenon when the vehicle load changed dramatically. As a result, the service life of ternary lithium batteries could be extended. In Figure (b), during actual vehicle testing, the OCV variation trend of the lithium battery under the two control strategies was basically consistent with the simulation experiment, while the OCV variation trend of the fuel cell was opposite to that of the lithium battery. The ability management capability of the adaptive fuzzy controller was better than that of the adaptive controller.

Simulation experiment analysis of adaptive fuzzy controller for fuel cell vehicle optimized by MIGA

The experimental road conditions were selected as WLTP, FTP75, ECE, and EDUC, and the ISIGHT simulation tool was used to solve the fuel cell vehicle model. The WLTP condition took a total of 1800 s, the total mileage was 23.26 km, and the maximum speed was 131.3 km per hour. The driving time of FTP75 working condition was 1874 s, the mileage was 17.77 km, and the maximum speed was 91.25 km/h. The driving time for ECE condition was 780 s, with a mileage of 4.05 km, while the testing time for EUDC condition was 400 s, with a total mileage of 6.95 km and a maximum speed of 120 km/h. The changes in the remaining capacity of ternary lithium batteries under different road conditions are shown in Fig. 10.

Fig. 10

Comparison of auxiliary battery allowance before and after optimization

In Fig. 10 (a), the decreasing trend of the remaining capacity of the ternary lithium battery after optimizing the control strategy using MIGA was basically the same as that before optimization, but the decreasing curve of the remaining capacity of the optimized battery was smoother, and the decrease from the starting point to the end point was also smaller. Under WLTP conditions, the battery remaining capacity increased from 38.4 to 39.7%, an increase of 1.3%. Under FTP75 conditions, the battery remaining capacity increased from 37.1 to 38.6%, an increase of 1.5%. In Figure (b), the battery remaining capacity increased from 37.9 to 40.1% under ECE conditions, an increase of 2.2%, and from 34.2 to 35.9% under EUDC conditions, an increase of 1.7%. The adaptive fuzzy control strategy optimized by MIGA was more effective in energy allocation and could achieve high results in energy recovery during braking. The comparison of capability recovery effect and fuel consumption under different control strategies is shown in Fig. 11.

Fig. 11

Braking energy recovery and fuel consumption per kilometer for different road conditions

In Fig. 11 (a) and (b), under different operating conditions, the energy recovery of the control strategy optimized by the MIGA was the highest, with an average increase of 147w and 76w compared to the adaptive control strategy and the adaptive fuzzy control strategy. The WLTP condition had the highest energy recovery, as the driving environment in this condition was more complex and required more braking time compared to other conditions. In Figure (c), the fuzzy control strategy optimized by MIGA consumed the least amount of fuel, and the average fuel consumption was reduced by 0.25 L/100km and 0.1 L/100km respectively compared to adaptive control and adaptive fuzzy control. The MIGA optimized adaptive fuzzy control strategy could effectively reduce the fuel consumption of fuel cell vehicles. The braking energy recovery rate and vehicle capacity recovery rate under different operating conditions are shown in Fig. 12.

Fig. 12

Capability recovery rates in different scenarios

In Fig. 12 (a), the MIGA optimized the adaptive fuzzy control strategy with the highest braking energy recovery rate, with an average recovery rate 8.5% and 4.9% higher than the adaptive control strategy and the adaptive fuzzy control strategy, respectively. In Figure (b), the average energy recovery rate of the optimized strategy was 2.7% and 1.3% higher than that of the adaptive strategy and adaptive fuzzy strategy, respectively. The use of MIGA optimization control strategy maximized the improvement of vehicle braking energy recovery, while also improving the energy recovery ability of the entire driving process to a certain extent. It could effectively reduce fuel consumption, lower vehicle driving costs, reduce pollutant emissions, and had certain positive significance for environmental protection. The robustness effects of different driving and road conditions on the control strategies are shown in Table 2.

Table 2 Robustness effects of different driving and road conditions on control strategies

In Table 2, the braking energy recovery of the optimized control strategy of the multi-island genetic algorithm is higher than the other methods in three different conditions, 4.5%, 6.1% and 5.7% higher than the three Adaptive fuzzy control strategy, and 1 7.1%, 21.2% and 22.2% higher than DP, respectively. The fuel consumption of the optimized control strategy of the multi-island genetic algorithm was 0.011 kg / km, 0.009 kg / km and 0.011 kg / km lower than the adaptive fuzzy strategy in the three conditions, which was 0.026 kg / km, 0.022 kg / km, 0.019 kg / km lower than DP. The response time of the control strategy after the multi-island genetic algorithm to the change of vehicle driving condition was 0.9s,1.2s and 1.1s faster than the adaptive fuzzy strategy, and 2.3s,2.6s and 1.9s faster than DP under the three working conditions.

Discussion and conclusion

Addressing the issue of uneven energy distribution and insufficient energy reuse in traditional methods for fuel cell vehicles, the study proposed an adaptive fuzzy control strategy and an energy management method using MIGA to optimize the control strategy. The research results indicated that the fluctuation amplitude of the OCV of lithium batteries managed by the adaptive fuzzy control strategy would not exceed the rated voltage of 1.5v, and the OCV gradually increased with the increase of battery remaining capacity and the increase was gentle. The output power of fuel cells was mostly higher than that of lithium batteries, and the output power of lithium batteries fluctuated around zero, meeting the sudden high power demand of vehicles and supplementing the difference in insufficient power of fuel cells. The fuzzy control strategy recognizes changed in road conditions faster and could adjust the output currents of two types of batteries in a timely manner. The response time of the adaptive fuzzy control strategy was 1–2 s faster than that of the adaptive strategy. The lithium battery remaining capacity reduction curve of the MIGA optimization strategy was smoother, and the minimum remaining capacity of the battery was on average 1.67% higher than the algorithm before optimization. The optimized adaptive fuzzy control strategy increased the braking energy recovery rate by 8.2%, the vehicle energy recovery rate by 2.8%, and reduced fuel consumption by 0.24 L/100km. The adaptive fuzzy control strategy optimized by MIGA could adaptively change the controller parameters in real time, optimize the allocation of battery output power, and improve the power allocation speed when road conditions change. At the same time, optimization strategies could also increase the service life of lithium batteries, improve energy recovery and utilization efficiency, and reduce fuel consumption. Adaptive fuzzy control strategy there are still some problems, such as the working condition classification is not perfect, the working condition classification is only based on the size of the load current passing through the fuel cell, the amount of current change, and the speed of change, the subsequent can be based on the specific conditions of the vehicle to formulate a more detailed working condition classification rules, so as to make the applicability of the strategy is more extensive.