Fuel cell hybrid electric vehicles are currently being considered as ideal means to solve the energy crisis and global warming in today’s society. In this context, this paper proposes a method to solve the problem related to the dependence of the so-called optimal equivalent factor (determined in the framework of the equivalent consumption minimum strategy-ECMS) on the working conditions. The simulation results show that under typical conditions (some representative cities being considered), the proposed strategy can maintain the power balance; for different initial battery’s states of charge (SOC), after the SOC stabilizes, the fuel consumption is 5.25 L/100 km.

As one of the most ideal means to solve the energy crisis and global warming in today’s society, electric vehicles have the characteristics of zero fossil fuel consumption and zero exhaust emissions [

As one of the most promising electric vehicles, fuel cell vehicles use fuel cells to generate electricity from hydrogen and air, which is used to drive the vehicle. Meanwhile, surplus power is stored in the energy storage system (ESS), such as batteries or super capacitors [

Thermal characteristics of batteries and fuel cells are one of the focuses of research. The high or low temperature will cause the change of the internal structure of the battery, that is, the internal resistance of the Li-ion battery will have different effects on electrode materials, thereby affecting the capacity, cycle life, safety, and reliability of the battery [

In the ECMS method, the acquisition of equivalent factors is the focus of research [

In order to solve the proposed optimization problem, it is necessary to model the vehicle longitudinally. The fuel cell hybrid vehicle used in this paper is shown in

Energy management strategies based on dynamic programming algorithms require a known mathematical model of the hybrid power system and its components. Since the hybrid vehicle is only a hybrid of power sources, the driving is completely performed by the electric motor, which is different from the traditional engine hybrid power system. The longitudinal dynamics equation of the vehicle in the normal driving state is [

The required power of the motor is provided by the proton exchange membrane fuel cell and the lithium-ion power battery. When the required torque exceeds the limit that the motor can provide or exceeds the maximum current that the battery can provide, the motor will provide braking torque. The formula for motor torque and power demand is as follows:

The power provided by the electric motor outputs the power to the wheels of the vehicle through the transmission system. The relationship between the required power of the vehicle and the power of the electric motor is as follows:

The fuel cell is a power generation device that directly converts the chemical energy present in hydrogen and oxidant into electrical energy. Due to the characteristics of the fuel cell, its internal structure is extremely complex, so it is difficult to establish a complete FCS model. Therefore, the FCS model used in this study is a simplified model. The goal of EMS is to reduce hydrogen consumption, improve system efficiency, and keep the battery’s state of charge (SOC) within a reasonable range. The hydrogen consumption of FCS is determined by the power of FCS and the corresponding efficiency [

Since the battery dynamic model is more complicated, the estimation algorithm of the battery state of charge (SOC) also has a certain complexity. For time cost considerations, the internal resistance-open circuit model shown in

From the circuit shown in the figure, it can be known from Kirchhoff’s voltage law [

The battery charging and discharging efficiency is:

The relationship between battery power and motor demand power is:

The battery SOC is calculated using the ampere-hour method as:

Dynamic programming is an important method to solve the multi-stage decision-making process. Its core idea is to decompose the problem to be solved into several sub-problems, first solve the sub-problems, and then obtain the solution of the original problem from the sub-problems. For hybrid energy management strategy issues, dynamic programming requires that the system control requirements in the entire driving road be known in advance, and energy is allocated to meet the requirements of basic dynamics to achieve the optimal goal. The DP method can analyze the impact of operating conditions on the strategy in detail, and evaluate and screen the strategy. Therefore, it has become the most important reference method in the hybrid energy management strategy. The specific process of using DP for energy optimization can be divided into three stages: division stage, determination of decision-making and state transition equations, and determination of optimization equations [

1. Division stage. According to the time or space characteristics of the problem, the problem is divided into several stages in an orderly manner. State variables are the parameters of objective performance problems at each stage, and the choice of state variables needs to satisfy no aftereffect. For the energy management strategy problem, the battery state of charge SOC is one of the most important parameters that characterize the objective state of the hybrid system at a certain energy distribution ratio, so it can be used as the state variable of the problem.

2. Determination of decision-making and state transition equations. In the problem studied, the decision is the allocation ratio u of the total required power of the system at each stage between the power battery and the proton exchange membrane fuel cell. The state transition equation is the current stage k, the state x (and SOC) is under the action of the decision u, the stage k+1 system state, which can be expressed as:

3. Determination of optimization equations. According to the optimization requirements of the problem, the optimization equation can be directly written. Energy management strategy requires the system to consume the least fuel:

Regardless of external energy input (such as braking energy recovery), the energy consumption of the hybrid power system is ultimately provided by fuel. The minimum equivalent fuel consumption strategy, from the perspective of energy conservation, equates electrical energy to the hydrogen mass of the fuel cell, and provides theoretical support for the instantaneous optimization control of the hybrid power system. The calculation model of ECMS is [

The purpose of the ECMS strategy is to obtain the most core parameter in the minimum equivalent fuel consumption value when the control variable u selects different values is the equivalent factor s. If the penalty factor added due to power maintenance is not considered, it is essentially a numerical embodiment of the conversion efficiency between energies. The reason why the equivalent factor is an uncertain value is that, in order to make the battery power consistent with the initial state in the future, the current consumption of electric energy is regarded as being compensated by the hydrogen consumption or recovered energy of the fuel cell engine in the future. Since the future working conditions are unknown, it is unknown under which working conditions this part of energy will be compensated, that is, the equivalent factor is an uncertain value. Therefore, the key of ECMS is to find the optimal equivalence factor, so that the current energy has the optimal conversion efficiency in the future compensation. Under this premise, the energy distribution at the current moment has the optimal conditions. Research shows that, for a given driving mode, the equivalent factor in

Use DP to obtain the best output power P of the power battery at time t, and the best SOC of the battery is

The above methods are used to extract the optimal equivalent factors under several typical driving conditions. In order to ensure that the proposed A-ECMS has good adaptability to working conditions, the selected typical working conditions should cover most of the vehicle driving conditions and have good representativeness. Select the working conditions that cover the average vehicle speed from low to high and the relative idle time is long to short, and cover the urban and suburban working conditions, The sequence is: Japanese JN1015 cycle combined with urban and suburban working conditions, ECE_EUDC combined with steady-state high-speed driving conditions, NEDC steady-state working conditions with strict emissions, American UDDS working conditions with typical representative car commuting routes, and The U.S. Environmental Protection Agency’s EPA-designed urban road cycle FTP75, which has a high average vehicle speed and includes cold transition conditions, steady-state operating conditions, and hot transition conditions, and US06 that takes into account road changes. The optimal equivalent factor is extracted from the battery output power range of 0–35 kw, and the resulting equivalent factor distribution statistics are shown in

It can be seen from

Because in the calculation process, the equivalent factor in some data points (such as the point where the speed is 0 and the demand torque is 0) is meaningless zero or non-number, so the abscissa no longer represents all the state points, but in the order from left to right, removing the status points remaining after the meaningless data points. In order to make the results clearer, only the optimal equivalent factor change trends when the initial SOC is 0.7 and 0.3 are selected in

The law of change obtained by fitting is:

The charging and discharging efficiency of the battery will have a large gap under different SOC maintenance levels. In order to further improve the system efficiency, it is necessary to explore the optimal SOC interval of the battery. Limited to the main content and length of the research in the article, the optimal power maintenance level interval is only determined by a relatively simple statistical screening method. In the case of keeping the initial SOC consistent with the end SOC, the DP algorithm is used to calculate from the minimum allowable SOC 0.3 at intervals of 0.001 to the maximum allowable SOC 0.9 to obtain each different SOC under each driving condition. Maintain different fuel consumption values per 100 kilometers at the same level. The lower 20%~30% continuous interval is selected as the optimal power maintenance interval for this working condition, and all the driving conditions used are combined, and the result is roughly the power maintenance level between 0.6 and 0.8, so that the used the driving condition reached is the lowest fuel consumption per hundred kilometers; Taking the average SOC = 0.7 as the power maintenance standard, the same initial conditions as the DP method can be guaranteed. At the same time, based on the foregoing analysis, the effective range of the equivalent factor is 2~6, so the following energy management strategy based on power balance is designed:

It can be seen from

The effectiveness of the method in this paper needs to be verified from two aspects: optimization effect (fuel economy, power maintenance) and adaptability to working conditions. Due to the large battery capacity used in the article, the battery capacity does not change significantly when a shorter driving cycle is used for simulation. Therefore, a superimposed typical driving cycle is used for long-distance simulation. The optimization process was performed in MATLAB R2020a environment using an AMD Ryzen 5600x processor.

In order to verify the fuel economy of the method in this article, the superposition of 10 typical NEDC driving cycle is used to verify the power maintenance characteristics of the method used. Use DP and the method in the text to verify, and obtain the results shown in

It can be seen from

It can be seen from

Stage | SOC final difference | Hydrogen consumption per hundred kilometers/L | ||||
---|---|---|---|---|---|---|

AECMS | DP | Relative error/% | AECMS | DP | Relative error/% | |

Transition | 0.078 | 0.071 | 1.1 | 5.08 | 5.00 | 1.6 |

Stability | 0.002 | 0 | 0.4 | 5.25 | 5.20 | 0.9 |

It can be seen from

It can be seen from

It can be seen from the figure and table that the ECMS method based on DP can obtain fuel consumption almost the same as the DP method. This strategy minimizes the total energy consumption of the vehicle per unit time by optimizing the power distribution of the fuel cell and the power battery under each instantaneous working condition, and at the same time achieves the maintenance of the battery state of charge. As a better method for global optimization, the DP method has strong credibility. As an instantaneous optimization strategy, ECMS can achieve the same results as DP through a smaller amount of calculation. It proved the feasibility of the proposed AECMS method

In order to verify whether the method in this paper can be applied to different working conditions, a variety of typical driving conditions such as FTP75, NEDC, UDSS, etc., were selected, and simulations were also performed in the way of working conditions superimposed, and the results shown in

It can be seen from

Stage | Hydrogen consumption per hundredkilometers in a single cycle in the stable phase/L | Relative error/% | |
---|---|---|---|

AECMS | DP | ||

FTP75 | 5.16 | 5.14 | 0.51 |

NEDC | 4.87 | 4.85 | 0.4 |

UDDS | 5.57 | 5.51 | 1.1 |

As analyzed in the previous article, if the appropriate initial SOC value is given, the DP method and the method in the text can obtain relatively consistent control results. Therefore, only the fuel consumption comparison in the stable phase is given in

In this paper, the dynamic programming algorithm is used to obtain the optimal control results of the hybrid power system under typical driving conditions. On this basis, the ECMS model is used to obtain the law between the average optimal equivalent factor and the power maintenance level, and the corresponding A-ECMS algorithm is designed according to the optimal initial SOC interval. The simulation results of working conditions in NEDC show that the method in this paper can finally maintain the level of electricity to stabilize, and the whole process is divided into two stages. In the transition stage, the fuel consumption difference with DP is only 1.6%, while it can be obtained in the stable stage. The control result is more consistent with the dynamic programming, and the error is only 0.4%. It fully shows that the method proposed in the article can reduce fuel consumption while maintaining power balance. At the same time, verified by multiple working conditions such as FTP-75, NEDC, UDDS, etc., the SOC change trend is consistent with the simulation results of NEDC driving cycle, and the error of the comparison result with the DP method in the stable phase is only 0.1%~1.1%, indicating that the paper proposed The method has strong adaptability to working conditions, and can provide a certain reference value for the optimal control of hybrid vehicles with regular driving.

_{dem}:

vehicle demand power

vehicle mass

vehicle speed

gravitational acceleration

rolling resistance coefficient

road slope

_{D}:

air drag coefficient

vehicle front area

ambient air density

_{EM}:

torque of electric motor

_{EM}:

power of electric motor

_{brk}:

fraction brake torque

motor efficiency

transmission efficiency

_{fc}:

power of fuel cells

_{b}:

battery power

_{a}:

auxiliary power

_{(H2,l)}:

the lower heating value of hydrogen

hydrogen consumption

fuel cell efficiency

_{bat}:

battery current

_{ocv}:

open circuit voltage

resistance

battery discharge efficiency

battery charge efficiency

_{0}:

initial value of battery

battery capacity

Instantaneous equivalent fuel consumption

_{bat}:

battery power

_{L}:

the lower heating value of fuel

average optimal equivalence factor

Fuel cell hybrid electric vehicle

Dynamic programming

Equivalent consumption minimization strategy

Adaptive equivalent consumption minimization strategy