A Real-Time Rule-Based Energy Management Strategy With Multi-Objective Optimization for a Fuel Cell Hybrid Electric Vehicle

Energy management strategy (EMS) has a great impact on securing fuel cell durability, battery charge sustenance, and fuel saving in fuel cell hybrid electric vehicles (FCHEVs). This study aims to develop EMS that can be applied in real-time to satisfy above conditions. Real time power separation was performed using rule-based EMS. A genetic algorithm (GA) was implemented to calculate the optimal battery charge/discharge criterion that simultaneously satisfies the minimum hydrogen consumption rate, battery charge rate preservation, and high fuel cell efficiency. The battery charge/discharge parameter values vary according to driving patterns, and in this paper, typical suburban, urban, and highway driving conditions are considered. For the real-time application of this research method, the effectiveness was demonstrated by applying the driving conditions of unknown patterns. The effect on the initial battery SOC on EMS was analyzed, and in order to verify the superiority of this method, it was compared and analyzed with EMS results using dynamic programming and fuzzy logic under the same driving cycles. The effectiveness of this research method was verified through simulation, and it was confirmed through experiments for real-time application. Since there is a limit to the experiment using an actual fuel cell vehicle, the experiment was performed using a fuel cell and battery. This method can be applied to real fuel cell vehicles in the same way.


I. INTRODUCTION
In recent years, the energy concerns resulting from the deple- 19 tion of fossil fuels and air pollution have received increas- 20 ing attention, especially in the automobile industry. Given  With the development of hydrogen storage devices and refu- 26 eling stations, these vehicles have a long mileage and short 27 refueling time. 28 The associate editor coordinating the review of this manuscript and approving it for publication was Gayadhar Panda .
To compensate for the slow chemical response of fuel 29 cell systems, energy storage systems (ESSs), such as battery 30 and/or supercapacitor, are often used. ESSs not only improve 31 the acceleration ability of vehicles and conserve their braking 32 energy but also improve the flexibility of power distribution 33 in a fuel cell hybrid electric vehicle (FCHEV) system. Rapid 34 charging/discharging rate and over-discharging of the battery 35 lead to deterioration of the battery capacity, which in turn 36 leads to replacement of the battery. The main concerns with 37 FCHEV systems are tied to their economic cost, sustainable 38 operation, and system durability, which are closely related 39 to their energy management strategy design. The authors 40 in [1] reviewed various EMSs and advanced optimization 41 algorithms for addressing the above issues and proposed 42 some recommendations for the future development of effi-43 cient EMSs. 44 EMS can be categorized into rule-and optimization-based 45 EMSs. Rule-based EMSs have high practicability and low 46 computation load. In [2], the state of charge (SOC) and power capabilities of ESSs were main parameters in design- 48 ing power distribution rules. A finite state machine-based 49 EMS was designed for fuel cell hybrid source vehicles to 50 benefit system health and fuel economy. To mitigate the 51 power fluctuation of fuel cell system under rule-based EMS, 52 Lopez et al. [3] utilized a low-pass filter to split the power 53 between the fuel cell and supercapacitor system. The wavelet 54 transform algorithm was incorporated into fuzzy logic EMS 55 to smoothen the fuel cell current change and allocate power 56 efficiently [4]. This approach can minimize the damage 57 brought by current fluctuation and improve fuel cell health. 58 Wang et al. [5] proposed a suboptimal online power allocation 59 strategy based on rules and classical cybernetics and found 60 that this strategy can realize near-optimal performance much 61 easier than dynamic programming (DP) EMS. Optimization-62 based EMSs can achieve a globally optimized or a subopti-63 mal power management by applying optimization algorithms 64 with system control objective functions and constraints.

65
As a global optimization algorithm that achieves optimal 66 power distribution under vehicle system constraints, DP 67 serves as a good benchmark for other EMSs [6]. For real- and MPC are necessary to obtain optimal solutions. More-87 over, advanced multi-objective optimization methods [10], 88 [11], [12], [13] have been studied to mitigate the degradation 89 of fuel cell and battery system, save fuel consumption, and 90 keep battery charge sustaining. Recently, machine learning 91 algorithms, such as online learning [14], reinforcement learn-92 ing [15], [16], and rule learning algorithm [17], have been 93 investigated for power management in an FCHEV system.

94
However, the EMS using the optimal solution shows the result 95 using simulation, and there are few real-time optimal EMS 96 development results. Instead of online optimization that requires big data pro-98 cessing, EMS with offline global optimization and real-99 time implementable abilities has been studied extensively for 100 FCHEVs. The controlling parameters are optimized offline 101 and subsequently applied online to obtain the highest prac-102 ticable and optimal deterministic rules for power allocation, 103 thereby guaranteeing online control optimality. To improve 104 the online performance of a fuel cell hybrid power system, 105 a rule-based EMS was developed based on the results of 106 the dynamic programming (DP) algorithm [18]. The fuel 107 cell system works steadily even under drastic load changes, 108 and fuel economy optimization can be optimized like using 109 the DP algorithm. Moreover, fuzzy logic EMS is widely 110 combined with GA for offline optimization, and the system 111 performance can be improved online with the optimized 112 membership functions [19], [20], [21]. The main problem is 113 that since global optimization is obtained based on a given 114 driving pattern, optimal performance deteriorates when these 115 fixed parameter values are applied to other driving cycles. 116 To improve the adaptivity of EMS under changeable driving 117 conditions, the authors in [22] and [23] initially optimized 118 the parameters in different driving conditions offline and then 119 used a driving pattern recognition method to transform the 120 optimized membership function for real-time driving cycles. 121 However, the abovementioned EMSs require many con-122 trol parameters to be optimized, hence this complicates the 123 method to obtain the optimal solution and increases com-124 putation time. In addition, these EMSs are developed in a 125 simulation or in a hardware-in-the-loop simulation and most 126 of them lack physical experiment verification. To satisfy 127 unknown driving pattern with the developed method, this 128 paper presents a real-time optimized rule-based EMS that can 129 be innovatively applied even under similar driving conditions 130 by optimizing small number of parameters for three typical 131 driving conditions. Simulation and experiment results reveal 132 that the proposed EMS has a significant improvement over 133 online rule-based EMS in terms of hydrogen consumption, 134 fuel cell durability, and battery sustainability across each 135 driving condition. The main contributions of this paper can 136 be summarized as follows.   3) The sensitivity of the initial battery SOC value to power 150 distribution and system performance is investigated.  Table 1.
A DC-AC inverter, motor, and mechanical transmission 175 system are assumed to be effective for optimization of power 176 allocation between the fuel cell and the battery. The power 177 balance between the power sources and demand power can 178 be described as follows: where P d is the demand power, P fc is the fuel cell power, 181 P bat is the battery power, η uni_DC is the efficiency of uni-182 directional DC-DC converter, η bi_DC_cha and η bi_DC_disc are 183 the efficiency of bidirectional DC-DC converter in charge and 184 discharge mode, respectively. The working efficiency of PEMFC (η fc ) is essential in 196 ensuring fuel economy and cell health as defined in (3)  where P aux is the auxiliary power consumption in the fuel cell is calculated by (4).

185
Real-time SOC (SOC t ) can be calculated through the 218 Coulomb counting algorithm expressed by (7), where SOC t 0 219 is the initial battery SOC, and C b means the battery rated 220 capacity. The battery efficiency is assumed to be 1 when 221 charging and discharging for the simplicity.
The bus voltage (V bus ) is expected to be controlled to 48V , for charging or discharging the battery. The topology using 230 these two types of converters is shown in Fig. 2. A constant 231 fuel cell current is preferred during the operation because 232 it exhibits a stable two-phase gas flow phenomenon and 233 uninterrupted water transport through the fuel cell mem-234 brane [26]. Therefore, current mode control (CMC) of the 235 unidirectional DC-DC boost converter is used to improve 236 fuel cell system stability, and a proportional-integral (PI) con-237 troller 1 is applied to achieve better transient current response. 238 The current value targeted for control is determined by the 239 desired fuel cell power provided by the EMS. The relationship 240 between the fuel cell current and the fuel cell power is esti-241 mated by a fitted polynomial as (8). To ensure a constant bus 242 voltage, the bidirectional DC-DC converter takes the voltage 243 as a control variable in the battery charging/discharging state 244 and uses voltage mode control (VMC) with a PI controller 2. 245 The architecture of the whole system is presented in Fig. 2, 246 where the EMSs block is the main controller of the FCHEV 247 system that allocates the power between the fuel cell and the 248 battery. 249 In addition, the standard form of PI controller 1 and 2 is 252 presented as (9), where u is the control variable, e is the 253 difference between the tracked reference signal and measured 254 process variable, K p is the proportional gain, and T i is the 255 integral time.
The integral time-weighted absolute error (ITAE) method 258 is utilized to tune the parameters of PI controllers for two 259 designed converters, and the optimized parameters are listed 260 in Table 2. What's more, the stability of the designed PI 261 controllers was studied in our previous works [27], [28], and 262 both converters can stably regulate the power output under an 263 energy management strategy.

266
The proposed EMS combines the advantages of optimization-267 and rule-based EMS, aiming to optimally allocate power 268 between two power sources of FCHEV in real time. Fuel 269 cell durability and efficiency, minimization of hydrogen con-270 sumption, and sustainability of battery charging are consid-271 ered in EMS design to ensure overall system stability and 272 reduce operating cost. Conventional EMSs, such as DP, fuzzy 273 logic, and rule-based EMSs are also studied to compare the 274 advantages of the proposed EMS.   upper threshold (SOC l1 or SOC h2 ), the corresponding value 298 is reassigned to the redefined value (SOC l2 or SOC h1 ). The 299 initial SOC thresholds of SOC l1 , SOC l2 , SOC h1 , SOC h2 in 300 rule-based EMS are 60%, 65%, 70%, and 80%, respectively. 301 The power distribution in rule-based EMS is decided by the 304 battery SOC and demand power. In general, a simple rule-305 based EMS gives a poor performance in terms of fuel cell 306 durability and hydrogen consumption. Therefore, the above-307 mentioned concerns can be solved by multi-objective opti-308 mization using multi-GA method in this section. 309 310 Water flooding and membrane dehydration inside the 311 fuel cell result in an irreversible degradation of the 312 components including membrane, catalyst, and diffu-313 sion layer. These phenomena are mainly caused by the 314 PEMFC's drastic power changes and frequent start or 315 stop operation conditions [3]. In addition, the start-up 316 and shutdown processes of a fuel cell system lead to a 317 rapid decay of fuel cell catalyst and diffusion layer due 318 to imbalance pressure between cathode and anode [29]. 319 Therefore, a low-pass filter is applied to prevent the 320 overshoot or undershoot of the fuel cell power and to 321 protect aging process of the fuel cell system. The effect 322 of the cutoff frequency on the dynamics of fuel cell 323 system is analyzed in [4], and a first-order low-pass 324 filter with a cutoff frequency of 0.05 Hz can mitigate 325 the power fluctuation. Moreover, PEMFC is designed 326 to operate in non-stop driving mode that meets the 327 minimal power threshold P fc_low to avoid major per-328 formance degradation due to frequent fuel cell on-off 329 cycling.    improve fuel cell efficiency and subsequently benefit 356 fuel utilization rate. Given that it is not practical for 357 all objectives to be optimal at the same time, a multi-358 objective GA is pursued to achieve a trade-off among 359 the three objectives over a known driving cycle.

1) Fuel cell durability considerations
For three-objective optimization, the non-dominated sort-362 ing genetic algorithm II (NSGA-II) is used to find a local 363 Pareto front for the cost functions. For each point on the 364 Pareto front, one of the goals can only be further optimized by 365 sacrificing the optimization of the other one or two objectives, 366 and these points are called non-inferior solutions. A non-367 inferior solution is the one that provides a suitable compro-368 mise between all objectives without degrading any of them, 369 which reveals the most appropriate trade-off among these 370  are SOC l1 , SOC l2 , SOC h1 , SOC h2 , and P fc_low , with the 377 constraints listed in (12). Noting that the low limit fuel cell 378 power P fc_low considers the minimum charging power of the 379 battery to prevent fast charging rate of the battery.   highway driving are utilized for multi-objective GA optimiza-394 tion to deal with diverse road scenarios.

395
The optimization process is completed when the given 396 tolerance is met. The Pareto fronts of three objectives under 397 three driving conditions are illustrated by Fig. 6, which 398 reveals the most appropriate trade-off among these cost func-399 tions. As can be seen from the Pareto fronts, the effects of 400 the optimized parameters on three objective functions have 401 coupled each other. Under three driving conditions, the trend 402 of the relationship between any two objectives is similar 403 except for the numerical difference. Given that an absolute 404 variation of SOC can be derived from battery charging or dis-405 charging, the coupling among three objectives can be divided 406 into two cases. In the case of battery charging, an increase of 407 J 2 will lead to greater hydrogen consumption J 1 . Meanwhile, 408 an increase of J 2 caused by battery discharging leads to less 409 hydrogen consumption in energy management.

410
The proposed EMS is designed primarily to save as much 411 hydrogen as possible while maintaining battery charge sus-412 taining. However, due to the uncertain future driving pat-413 tern, the final SOC value is not necessarily the same as the 414 initial value but fall within the acceptable interval. Accord-415 ing to the Pareto front and assumed battery SOC constraint 416 (| SOC| ≤ 1.5%), the final optimization parameters under 417 three driving conditions are determined as shown in Table 3. 418 Under three typical driving conditions, the power distri-419 butions of a downscaled FCHEV system with EMSs are 420 illustrated in Fig. 7. With proposed EMS, the fuel cell system 421 operates smoothly in non-stop mode due to low power limit 422 and low-pass filter, and the battery supports the transient 423 power demand, which is good for fuel cell durability. With the 424 SOC constraint, the final SOC is equal to its initial value with 425 the DP control under three driving cycles, which are indicated 426 by Fig. 8 (a), (c), and (e). As can be seen from Fig. 8, the pro-427 posed EMS realizes a minimum hydrogen consumption at the 428 expense of SOC variation. In highway condition, the fuzzy 429 EMS achieves the nearly same hydrogen consumption as the 430 proposed EMS. However, without optimization, rule-based 431 EMS and fuzzy-based EMS consume too much hydrogen 432 under NEDC and UDDS, because fuel cell operates in ineffi-433 cient area. In addition, the lack of optimization results in more 434 energy being stored in the battery. During the entire driving 435 cycle, the hydrogen consumption depends on the required 436 fuel cell power and efficiency, which is elucidated by (4), and 437 the proposed EMS realizes a low hydrogen consumption with 438 admissible SOC variation.

439
To evaluate the adaptability of proposed EMS with unified 440 optimization parameters under the similar driving conditions, 441     Table 4.
where E bat is the nominal energy capacity of the battery pack,  As can be seen from values. As shown in Fig. 10, with the initial SOC value of 481 75%, the battery SOC is maintained in an admissible range.

482
When the initial SOC changes, the battery SOC is automati-483 cally regulated and follows the SOC path with initial value 484 of 75% in suburban and urban driving conditions, during 485 which the FCHEV system is working in an optimal state. 486 Under highway driving pattern, the battery SOC with initial 487 value lower than 65% will finally reach to the value near 488 65% not 75%. When the initial SOC value is between 65% 489 and 75%, the battery SOC will sustain near its initial value. 490 The fuel cell does not have much power to charge the battery 491 due to high power demand. This phenomenon is related to 492 the optimized parameters. If they are chosen with minimum 493 SOC deviation, the battery SOC with initial value lower than 494 75% will be around 75% during the driving cycle. However, 495 the SOC recovery rate is slow due to the low charge power. 496 In rule-based and fuzzy logic EMSs, the battery SOC greatly 497 fluctuates due to the lack of optimization, which shortens 498 the battery lifetime [32]. Therefore, the battery health is 499 improved with the proposed EMS irrespective of the initial 500 battery SOC.

502
A downscaled test platform is constructed to verify the effec-503 tiveness of the proposed EMS as shown in Fig. 11, and a 504 LabVIEW-based supervisory environment is assembled for 505 real-time monitoring. The experimental conditions are the 506 same as those in simulation environment.

507
To verify the performance of the proposed EMSs in subur-508 ban, urban and highway road conditions, NEDC, UDDS and 509 HWFET driving cycles are tested in experiment. Fig. 12 and 510 Fig. 13 display the performance of FCHEV system with rule-511 based, fuzzy-based, DP and proposed EMSs. Compared with 512 the conventional rule-based EMS under three driving pat-513 terns, the proposed EMS smoothens the fuel cell output power 514 which makes fuel cell system work under non-stop mode, 515 thereby benefiting for the fuel cell durability. The proposed 516 EMS sacrifices SOC variation within an acceptable range and 517 has a lower hydrogen consumption compared with DP EMS. 518 The trajectories of battery SOC and hydrogen consumption in 519 the experiment are almost identical to those observed in the 520 simulation.

521
In addition, the standard deviations (std) of fuel cell power 522 change rate under NEDC, UDDS, and HWFET in the exper-523 iment are calculated and compared to analyze the fuel cell 524 durability, which are listed in Table 5. With proposed EMS, 525 the fuel cell works in non-stop mode, and the output power is 526 smoothed by the low-pass filter. Compared with rule-based 527 EMS, the fuel cell power change rate is greatly improved 528 with proposed EMS, even better than DP EMS under NEDC 529 and HWFET. Under UDDS, the fuel cell provides too much 530 low-power dynamics under the proposed EMS. Even if the 531 hydrogen consumption is minimal, the power variation is 532 slightly larger than that under fuzzy and DP EMSs.

533
To display the fuel cell power distribution in three driving 534 conditions, the histogram of fuel cell power in HWFET is 535 shown in Fig. 14. As shown in the figure, rule-based and 536 fuzzy-based EMSs arrange the fuel cell to work in the less 537  ing sustaining mode, which contributes to energy saving and 565 battery health. The rule-based EMS with multi-objective GA 566 optimization can realize a real-time optimization for similar 567 driving pattern. The shortcoming of this study is that it lacks 568 online pattern recognition for unknown driving patterns to 569 provide an optimal solution, so further study is necessary. 570