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Energy management strategy (EMS) is a key issue for hybrid energy storage system (HESS) in electric vehicles. By innovatively introducing the current speed information, the vehicle speed optimized fuzzy energy management strategy (VSO-FEMS) for HESS is proposed in this paper. Firstly, the pruned fuzzy rules are formulated by the SOC change of battery and super-capacitor to preallocate the required power of vehicle. Then, the real-time vehicle speed is used to optimize the pre-allocated results based on the principle of vehicle dynamics, so as to realize the optimal allocation of required power. To validate the proposed VSO-FEMS strategy for HESS, simulations were done and compared with other EMSs under the typical urban cycle in China (CYC-CHINA). Results show that the final SOC of battery and super-capacitor are optimized in varying degrees, and the total energy consumption under the VSO-FEMS strategy is 2.43% less than rule-based strategy and 1.28% less than fuzzy control strategy, which verifies the effectiveness of the VSO-FEMS strategy.

The development of vehicle technology has helped to improve people’s lives, but at the same time has created adverse effects such as environmental pollution and energy shortages. Electric vehicles are becoming the focus of vehicle development [

As the key issue of HESS control, energy management strategy (EMS) has a vital impact on battery life, economy, and power performance of electric vehicles. The physical characteristics and working modes of the battery and the super-capacitor are also quite different. Hence, it is crucial to achieve effective energy management for both of them [

However, the fuzzy control rules are predesigned and cannot be adjusted according to real-time changes in driving cycle. Consequently, the vehicle speed optimized fuzzy energy management strategy (VSO-FEMS) for HESS is proposed in this paper. The VSO-FEMS analyzes the driving state of electric vehicles, monitors changes of battery and super-capacitor SOC in the driving process, and formulates corresponding fuzzy control rules. The required power is preallocated by the fuzzy controllers. Then, based on the principle of vehicle dynamics, the reference value of super-capacitor SOC is calculated according to the real-time vehicle speed, and the error between the reference value of super-capacitor SOC with its actual SOC is obtained. The final allocation result is optimized by the error value to achieve a reasonable power allocation. To the best of our knowledge, it is the first time to directly introduce the vehicle speed information into the EMS design among the research literature.

In this paper, the vehicle model is built in ADVISOR (Advanced Vehicle Simulator), and the VSO-FEMS strategy is compared with other EMSs. The simulation results show that under the same driving cycle, the total energy consumption of pure battery is the smallest, but the vehicle required power is provided by the battery, which causes great damage to the battery. Compared with rule-based strategy and fuzzy strategy, VSO-FEMS strategy has better performance in prolonging battery life, covering longer vehicle driving distance, and improving energy economy.

This paper is organized as follows: In Section

Currently, the conventional structures of HESS can be divided into three types: passive, semiactive, and fully active [

Structure of the semiactive HESS.

The focus of this paper is the energy management strategy of hybrid energy storage system, where the battery model is optional and the battery model shown in Figure _{bat} and an equivalent series resistance _{bat}. This model can simulate the charging and discharging process of the battery and is widely used in the hybrid energy storage system. The main advantage of this model is its simple structure and satisfactory accuracy. The model of the super-capacitor is shown in Figure _{sc}.

The models of battery and super-capacitor. (a) Battery. (b) Super-capacitor.

The corresponding state space equations are shown in equations (_{bat} is battery current, _{sc} is super-capacitor current, _{bat} and _{sc} represent the terminal voltage of battery and super-capacitor, respectively. The state of charge (SOC) is defined as the ratio between the remaining charge to the total charge of the battery or super-capacitor, which can be calculated from equations (_{remain} represents the remain charge, _{total} represents the total charge, _{sc,max} is the maximum operation voltage of super-capacitor, _{sc,min} is the minimum operation voltage of super-capacitor, and _{sc} is the real-time voltage of super-capacitor. Figure _{ch} and discharge efficiency _{disch} can be calculated by equations (

(a) Charge efficiency of battery. (b) Discharge efficiency of battery.

From Figure

As a key component of HESS, the DC/DC converter can not only effectively control the charge and discharge currents of the super-capacitor, but also ensure the high efficiency of HESS. In this paper, the efficiency of DC/DC converter is mainly considered, and the transient process of DC/DC is ignored. The efficiency of DC/DC converter is defined as the ratio of output power to input power, which can be calculated by equation (_{dc/dc} represents the efficiency of the DC/DC converter, _{out} represents the output current, _{out} represents the output voltage, _{in} represents the input current, and _{in} represents the input voltage.

Efficiency interpolation table of DC-DC converter.

DC/DC converter efficiency _{dc/dc} | Power of super-capacitor (W) | ||||||||
---|---|---|---|---|---|---|---|---|---|

2000 | 5000 | 10000 | 15000 | 20000 | 30000 | 40000 | 60000 | ||

Voltage ratio | 0.2 | 0.8 | 0.854 | 0.910 | 0.941 | 0.954 | 0.952 | 0.949 | 0.946 |

0.4 | 0.8 | 0.857 | 0.916 | 0.948 | 0.964 | 0.957 | 0.954 | 0.949 | |

0.6 | 0.8 | 0.861 | 0.923 | 0.950 | 0.965 | 0.960 | 0.956 | 0.952 | |

0.8 | 0.8 | 0.865 | 0.926 | 0.958 | 0.971 | 0.969 | 0.964 | 0.962 | |

1 | 0.8 | 0.872 | 0.930 | 0.963 | 0.975 | 0.973 | 0.968 | 0.966 |

The vehicle is regarded as a discrete-time dynamic system, and the required power during the driving of the vehicle can be simplified as [_{i} represents the inertial force, _{a} represents the aerodynamic drag, and _{r} represents the rolling resistance, and their can be calculated as follows:_{a} represents the air drag coefficient,

The goal of the energy management strategy design of HESS is to take full advantage of the characteristics of high-power density and long-cycle life of the super-capacitor, reduce the damage of high current on the battery, prolong battery life, increase vehicle driving distance, and improve energy economy. The overall scheme of the proposed VSO-FEMS strategy is shown in Figure

Structure of VSO-FEMS strategy.

The input synthetically considers three factors including required power, battery SOC, and super-capacitor SOC to get better reasonable allocation results. The preallocation uses fuzzy control to preallocate the required power in the VSO-FEMS strategy. Compared to traditional energy management strategies, fuzzy control uses the concept of fuzzy logic and membership function and has the advantage of good adaptability and robustness. The final allocation considering that super-capacitor needs to frequently provide the required peak power and recover braking energy, the voltage changes rapidly, and there will be errors between the actual SOC and the reference SOC, hence, the speed optimization module is introduced to optimize the pre-allocation results and get the optimal allocation results. Finally, the output allocates the power to the battery and the super-capacitor.

The power preallocation based on fuzzy control is presented in Section

During the operation of HESS, the parameters are not constant and may be varying. Also, HESS is a nonlinear system under complex driving cycle, which is difficult to be described with an accurate mathematical model. Compared with the traditional control strategy, fuzzy control has no need of accurate mathematical model of the system and uses natural language to describe system performance for effective control. It would be seen that the application of fuzzy control into EMS of HESS is very effective.

Considering that electric vehicles have both driving and braking conditions, the corresponding HESS has two working modes of discharge and charge. The different working modes require different control rules. Hence, two fuzzy controllers, fuzzy-discharge and fuzzy-charge, are designed that corresponds to the discharge and charge modes of the HESS.

In the discharging mode, the super-capacitor is mainly used to provide high instantaneous power to ensure that the battery discharges smoothly. The design is realized by detecting the SOC of the battery and super-capacitor. When the required power is small and the battery SOC is large, the power allocated to the battery should be large to utilize the characteristics of high energy density of the battery fully. When the required power is large and the super-capacitor SOC is also large, the power allocated to the battery should be small. Using the characteristics of the high-power density of super-capacitor, high-current discharge of the battery is prevented. In the charging mode, the super-capacitor is used to receive high instantaneous power, fully recover the braking energy, and protect the battery from damage due to high currents.

According to the above mentioned rules, the required power _{req}, the state of charge SOC_{bat} of battery, and the state of charge SOC_{sc} of super-capacitor are selected as the input of the fuzzy controller. The battery power allocation coefficient _{bat} is used as the output of the fuzzy controller. The power _{bat} of the battery is expressed as follows:_{req} is the required power under the driving cycle of the vehicle. The loss in power transfer process is neglected. The power _{sc} of the super-capacitor can be obtained by power conservation law:

When the battery SOC and super-capacitor SOC are too low or too high, the charging and discharging efficiency will be affected, so the SOC of the both should be controlled within an appropriate range. Through the analysis of the working HESS model under the vehicle’s driving cycle, the domain of fuzzy sets of variable of the fuzzy controller is shown in Table _{req} is [0, _{max}], the quantitative factor _{p} = 1/_{max} is needed to change it from actual domain to fuzzy domain, where _{max} is the maximum required power under driving cycle.

The domain of fuzzy sets.

Variables | _{req} | SOC_{bat} | SOC_{sc} | _{bat} |
---|---|---|---|---|

Domain | [0, 1] | [0.2, 0.9] | [0.1, 1] | [0, 1] |

Due to the control precision and operation speed, the fuzzy control strategy will be affected by the number of fuzzy language values. After analyzing the fuzzy variables, the language value of the fuzzy variables is shown in Table

The language value of fuzzy variables.

Mode | Variables | Language value |
---|---|---|

Discharge (_{req} > 0) | _{req} | TS, S, M, B, TB |

SOC_{bat} | S, M, B | |

SOC_{sc} | TS, S, M, B | |

_{bat} | TS, S, M, B, TB | |

Charge (_{req} < 0) | SOC_{bat} | S, M, B |

SOC_{sc} | TS, S, M, B | |

_{bat} | TS, S, M, B, TB |

Membership function of fuzzy variables.

Fuzzy rules in charge mode.

_{bat} | SOC_{sc} | ||||
---|---|---|---|---|---|

TS | S | M | B | ||

SOC_{bat} | S | TS | TS | M | B |

M | TS | TS | S | M | |

B | TS | TS | TS | S |

Fuzzy rules in discharge mode.

_{bat} | _{req} | |||||
---|---|---|---|---|---|---|

TS | S | M | B | TB | ||

SOC_{bat} (SOC_{sc} = TS) | S | TB | TB | TB | B | B |

M | TB | TB | TB | TB | TB | |

B | TB | TB | TB | TB | TB | |

SOC_{bat} (SOC_{sc} = S) | S | TB | M | S | S | S |

M | TB | B | M | M | S | |

B | TB | B | B | M | S | |

SOC_{bat} (SOC_{sc} = M) | S | M | S | S | TS | TS |

M | B | M | M | S | S | |

B | B | B | M | S | S | |

SOC_{bat} (SOC_{sc} = B) | S | TS | TS | TS | TS | TS |

M | TB | B | M | S | S | |

B | TB | B | M | S | S |

(a, b) Relation of inputs and output in discharge. (c) Relation of inputs and output in charge.

Under urban driving cycle, the super-capacitor needs to frequently provide the required peak power and recover braking energy, which leads to the rapid change of super-capacitor SOC. Hence, the speed optimization module is introduced. Based on the model of vehicle dynamics, the reference value of super-capacitor SOC is calculated according to the real-time vehicle speed, and the error between the reference value of super-capacitor SOC with its actual SOC is obtained. And the output variable _{bat} of the fuzzy controller is optimized by the error value. The specific design is described below.

According to the theory of vehicle dynamics, there is a functional relationship between the super-capacitor and maximum speed as follows:

Similarly, for other speeds, there is also the following relationship:

From equations (

Then, the reference value of super-capacitor SOC can be calculated from equation (

According equations (

By comparing the reference value of super-capacitor SOC with its actual SOC, an error value ∆SOC_{sc} is obtained:

By ∆SOC_{sc}, the output variable _{bat} of the fuzzy controller in the pre-allocation module is optimized. In the discharge mode, when ∆SOC_{sc} is positive, it shows that the actual value of super-capacitor SOC is larger than the reference value. Then _{bat} is reduced appropriately to increase the power allocated to super-capacitor to avoid excessive battery discharge. When ∆SOC_{sc} is negative, it shows that the actual value of super-capacitor SOC is less than the reference value. In this case, _{bat} is increased correspondingly to reduce the power given to the super-capacitor so that the power of HESS can be allocated most reasonably. In the charge mode, when ∆SOC_{sc} is positive, it shows that the actual value of super-capacitor SOC is larger than the reference value. Here, _{bat} is increased appropriately to increase the power of battery recovery and avoid excessive charging of super-capacitor. In contrast, negative ∆SOC_{sc} shows that the actual value of super-capacitor SOC is less than the reference value. Then, _{bat} should be reduced appropriately to increase the power recovered by the super-capacitor and maximize the recovery of the braking energy.

Therefore, the final power allocation results in discharge mode are as follows:

If ∆SOC_{sc} > 0,

If ∆SOC_{sc} < 0,

In charge mode, the final power allocation results are:

If ∆SOC_{sc} > 0,

If ∆SOC_{sc} < 0,

_{1},

_{2},

_{3}, and

_{4}are the proportional coefficients, used to optimize the allocation of the preallocation results and make the power allocation more valid.

Consider the optimal operation state of battery and super-capacitor with the following constraint range of parameters:_{1}, _{2}, _{3}, and _{4} in this paper are chosen by trial and error method and finally determined as in Table

Parameters of VSO-FEMS strategy.

Parameters | _{1} | _{2} | _{3} | _{4} |
---|---|---|---|---|

Value | −0.05 | 0.1 | 0.1 | −0.05 |

The overall flow chart of VSO-FEMS is depicted in Figure

Stage 1: By analyzing the operation state of HESS, determine the input and output variables and formulate fuzzy control rules as well as the membership functions. The power allocation coefficient _{bat} is obtained and the preallocation stage is completed.

Stage 2: Based on the model of vehicle dynamics, the reference value of super-capacitor SOC is calculated according to the real-time vehicle speed, and the error ∆SOC_{sc} between the reference value of super-capacitor SOC with its actual SOC is obtained. The allocation results in Stage 1 are optimized by ∆SOC_{sc} to complete the final allocation.

The flow chart of VSO-FEMS strategy.

The vehicle model with VSO-FEMS strategy is built in ADVISOR. The parameters of the vehicle model are shown in Table

Parameters of electric vehicle model.

Parameters | Value |
---|---|

Air drag coefficient _{a} | 0.55 |

Transmission system efficiency | 0.9 |

Rolling resistance coefficient | 0.01 |

Frontal area ^{2}) | 8.7 |

Curb weight | 12500 |

Capacity of battery (Ah) | 60 |

Rated voltage of battery (V) | 495 |

Capacity of super-capacitor (F) | 9500 |

Rated voltage of super-capacitor (V) | 780 |

(a) The speed of CYC-CHINA. (b) The required power of CYC-CHINA.

The power allocation of HESS in driving cycle are shown in Figure

(a) Power allocation of HESS. (b) Comparison currents of battery and super-capacitor.

Under road driving of electric vehicle, the operation states change of the battery and the super-capacitor (operating voltage, SOC, maximal current, etc.) and total energy consumption are the important indices of the performance of energy management strategy. In addition, many stress factors, like high fluctuations in battery SOC, high rates of required power, and operation in low and high temperatures have shown to be effective in battery aging. Therefore, the battery current root mean square (BCRMS) has been used as the indicator of the aging parameters and used to evaluate the battery lifespan, which is defined as follows [_{f} is the driving duration.

To demonstrate the effectiveness of the VSO-FEMS strategy, it is compared with the pure battery, rule-based strategy, and fuzzy strategy under CYC-CHINA. The comparison of performance results is presented in Table

Results comparison.

Pure battery | Rule-based | Fuzzy | VSO-FEMS | |
---|---|---|---|---|

Max battery current (A) | 357.78 | 224.47 | 100.44 | 135.40 |

Final battery voltage (V) | 462.64 | 476.68 | 483.59 | 479.39 |

Final battery SOC | 0.7412 | 0.8648 | 0.9157 | 0.8846 |

Final super-capacitor SOC | N/A | 0.4319 | 0.3938 | 0.5495 |

Energy consumption (kJ) | 24929 | 26158 | 25853 | 25522 |

Time consumed (s) | 3.76 | 3.88 | 4.30 | 4.21 |

(a) Comparison of battery current. (b) Comparison of battery voltage. (c) Comparison of battery SOC. (d) Comparison of super-capacitor SOC.

The BCRMS of different strategies.

From Figures

By comparing the simulation results, the VSO-FEMS strategy proposed in this paper can reasonably allocate the required power and achieve the design objectives of optimizing battery current to prolonging battery life, increasing the electric vehicle driving distance and improving energy economy. The effectiveness of VSO-FEMS strategy is demonstrated.

In this paper, the structure of HESS is analyzed, and a vehicle speed optimized fuzzy energy management strategy (VSO-FEMS) is proposed to allocate the required power between the battery and the super-capacitor. The specific work is as follows:

Two fuzzy controller is designed to control the charging and discharging modes of HESS, and fuzzy control rules are designed to realize preallocation of the required power.

Based on fuzzy control and the vehicle dynamics, for the first time, the speed optimization module is introduced to calculate the reference value of super-capacitor SOC according to the real-time vehicle speed. The preallocation results are optimized by the SOC error value to achieve reasonable power allocation results.

The vehicle model is built in ADVISOR, and the VSO-FEMS strategy is compared with other energy management strategies. The simulation results show that under the same driving cycle, the VSO-FEMS strategy has better performance in prolonging battery life, covering longer vehicle driving distance, and improving energy economy. The effectiveness of VSO-FEMS strategy is demonstrated.

No data were used to support this study.

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by the National Natural Science Foundation of China (61673164), the Natural Science Foundation of Hunan Province (2020JJ6024) and, the Scientific Research Fund of Hunan Provincial Education Department (17A048 and 19K025).

_{4}batteries for electric vehicles