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Adaptive real-time optimal energy management strategy for extender range electric vehicle
Journal Pre-proof Adaptive real-time optimal energy management strategy for extender range electric vehicle
Ye Yang, Youtong Zhang, Jingyi Tian, Tao Li PII:
S0360-5442(20)30344-3
DOI:
https://doi.org/10.1016/j.energy.2020.117237
Reference:
EGY 117237
To appear in:
Energy
Received Date:
24 August 2019
Accepted Date:
22 February 2020
Please cite this article as: Ye Yang, Youtong Zhang, Jingyi Tian, Tao Li, Adaptive real-time optimal energy management strategy for extender range electric vehicle, Energy (2020), https://doi.org/10. 1016/j.energy.2020.117237
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Journal Pre-proof
Adaptive real-time optimal energy management strategy for extender range electric vehicle Ye Yang1,2, Youtong Zhang1, Jingyi Tian3, Tao Li1 1 2 3
Laboratory of Low Emission Vehicle, Beijing Institute of Technology, Beijing 100081, China Qing Gong College, North China University of Science and Technology, University Road No. 11,Tangshan 063000, China School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China; [email protected]
Highlights: 1. An improved shooting method is designed. 2. The intrinsic operation mechanism of ECMS is revealed. 3. An adaptive real-time optimal energy management strategy is proposed. 4. The fuel economy and adaptability of different control strategies are discussed.
Abstract: The extender range electric vehicle (EREV) is an effective way to solve the "mileage anxiety" of pure electric vehicles, and the fuel economy of EREV is the key point of energy optimization. This paper designed an adaptive real-time optimal energy management strategy for EREV. Firstly, an improved shooting algorithm is proposed, which can determine the range of the equivalent factor (EF) according to the power configuration parameters of the vehicle, and then the secant method is used to quickly calculate the initial value of the EF. Secondly, from the perspective of energy flow, the intrinsic operation mechanism of equivalent consumption minimization strategy (ECMS) control strategy is revealed, and the working relationship between the five working modes of EREV is clarified. Thirdly, based on the car navigation and geographic location information system, the EF is periodically updated to achieve effective maintenance of the battery state of charge (SOC), so as to obtain the optimal power allocation. Finally, The fuel economy and real-time performance of the proposed energy management strategy are simulated and compared. To verify fuel economy, the rule-based control strategy and the power following control strategy were used as comparison. The results show that the proposed control strategy has better fuel economy and adaptability. To verify real-time performance, the proportional integral derivative ECMS (PID-ECMS) and shooting method ECMS (S-ECMS) were used as comparison. The results show that the proposed strategy is better in both fuel economy and real-time performance. Keywords: extended range electric vehicle; real-time optimization；adaptive energy management； improved shooting method；equivalent consumption minimization strategy
1. Introduction In recent years, new energy vehicles have developed rapidly for energy conservation and environmental protection. While taking into account the advantages of electric vehicles and traditional vehicles, Extended-range electric vehicle (EREV) extends the driving range and eliminates the driver's mileage anxiety. Hence, it is considered to be a promising new energy 1
Journal Pre-proof vehicle [1-2]. As there are two power sources in the EREV, the key to ensure vehicle power performance and system efficiency is to coordinate the energy distribution between two power sources through reasonable energy management strategies [3-4]. The energy management problem of hybrid vehicles has been a major concern for researchers in the past decade. A large number of research institutes and scholars have conducted extensive and in-depth research [5-8]. Specifically, control strategies can be divided into two categories: rule-based control and optimization-based control. Rule-based control strategy is based on engineering experience and experiments to formulate control rules [9-10], which has short computing time and reliable application, low requirement for memory and processing speed of control chip, high reliability of control algorithm and easy implementation [11-12]. Although the rule-based control is easy to design, the development of rules requires a lot of experimentation and calibration. Moreover, these rules are only applicable to a single drive cycle. Once the drive cycle changes, they need to be re-set, otherwise the fuel economy will become worse. The optimization-based control strategy is divided into global optimization and real-time optimization. The former is based on the global optimal theory, and uses the relevant optimization method to obtain the energy distribution. Dynamic Programming (DP) [13-14] and Pontryagin's Minimum Principle (PMP) [15-16] are the two most widely used global optimization methods. Although DP and PMP can obtain the optimal solution in the whole time domain, they need to get the driving information in advance, and the calculation time is too long to be applied in real vehicles online. But the research on them is meaningful: on the one hand, the results of these two strategies can be used as a benchmark to evaluate the control effects of other strategies; on the other hand, some control rules can be extracted offline from them to improve the performance. In addition to the above two commonly used methods, there are some other global algorithms including genetic algorithms, particle swarm optimization (PSO) and intelligent neural network algorithms [17,18]. In [17], Chen et al. used genetic algorithms to optimize power threshold for engine to turn on, which made the engine work more efficiently and thus reduced the fuel-consumption. In [18], PSO algorithm was proposed to optimize the power split between power sources and the sizing of the powertrain components. The simulation results showed that the optimal components sizing and the fuel consumption have been improved. For real-time optimal control, the equivalent consumption minimum strategy (ECMS) and model predictive control (MPC) are the two most representative methods. Based on historical driving data, mathematical models or real-time information provided by intelligent transportation systems, MPC predicts the torque demand of the vehicle in the future time domain, and optimizes the energy distribution ratio to achieve low fuel consumption and low emission [19-20]. ECMS simplifies the dynamic optimization problem to an equivalent instantaneous optimization problem, and minimizes the equivalent fuel consumption at each time to improve the fuel economy [21-22]. Compared with global optimization, it has less computation time and better real-time performance. Therefore, many scholars are working on the ECMS method. According to the idea of ECMS, Sivertsson et al.[23] proposed an adaptive energy management strategy, which could improve the mechanical efficiency of the drive train. Youngkwan et al. [24] designed an ECMS energy management strategy for a series of hybrid electric power system. A driving-style-oriented adaptive ECMS was designed in [25]. The authors analyzed the impact of driver's style on the fuel consumption, and divided driving style into six levels, achieving good fuel economy. In [26], three adaptive energy management strategies: adaptive ECMS (A-ECMS), Optimal Control Method 2
Journal Pre-proof (OCL) and Stochastic Dynamic Programming (SDP) were discussed, and the pros and cons of each method were evaluated. In the application of ECMS, equivalent factor (EF) is a key dynamic variable, which determines the performance of real-time optimization [27]. Therefore, some papers focus on how to resolve the EF. In [28-30], the EF is solved by traditional shooting method. Yang et al. [31] divided the driving cycles into several segments according to the actual bus stations, and then used the linear particle swarm optimization algorithm to solve the EF of each segment. Zhou et al. Ref [32] used pseudo-spectral optimization algorithm to solve EF and achieved good fuel economy. In [33], a fuzzy tuned ECMS was proposed to obtain the EF. In [34] the future vehicle velocity was predicted to obtain the EF. The EF is very sensitive to the actual driving conditions. If the constant EF is used, once the driving conditions change greatly, the SOC of the battery may fluctuate greatly. Therefore, in order to obtain better fuel economy, it is necessary to adjust the EF according to the real-time driving condition. In view of this, some researchers have proposed adaptive ECMS (A-ECMS), which can be divided into three categories: predictive A-ECMS, instantaneous A-ECMS and look-up A-ECMS. Predictive A-ECMS adjusts the EF by predicting upcoming road conditions to achieve real-time control [32,35-36]. Ref [32] updated the EF every 400m based on the predicted driving cycle and road grade information. Instantaneous A-ECMS calculates the EF based on the current driving information [28, 30, 37-38]. Ref [28] proposed a tracking-reset method to adjust the EF. When the road is flat, the tracking part ensure that the SOC is tracking the reference SOC; when the road is hilly, the reset part brings the SOC to its initial profile. In [30], the PID control was used to adjust the EF to follow the reference SOC in real time. The look-up A-ECMS is implemented in two steps. In the first step, a map of EF is established offline with respect to the relevant characteristics, such as speed [29], distance, or initial SOC values [31]. In the second step, the EF is obtained by looking up the map based on the real-time characteristic value. Generally, this method is applicable to urban buses with fixed routes. The various methods mentioned above showed good fuel economy and better performance than others. However, most of the methods were only performed in a specific environment or only under single or partial driving cycles. When there is some ramp or severe congestion on the driving conditions, the adaptive control strategy will be greatly discounted. In addition, some literatures used shooting method to solve EF, but no detailed description of the range of initial values of the EF was discussed. If the range is not selected properly, it will greatly increase the calculation time and affect the implementation of the algorithm. At the same time, few literatures have analyzed the operation mechanism of ECMS. Based on the above analysis, this paper proposes a method to quickly calculate the equivalent factor. This method can determine the range of EF according to the vehicle's power configuration parameters (APU efficiency, battery efficiency, generator and its controller efficiency). In addition, based on the periodic update of the equivalent factor, an adaptive real-time energy management strategy is designed, which can achieve better fuel economy and real-time performance. This paper is organized as follows. Section 2 discusses the powertrain and mathematical models of the EREV. Section 3 describes the optimal control problem and introduces the improved shooting method to solve the EF. Section 4 proposes the development of an adaptive real-time optimal energy management of EREV. Section 5 discusses and analyzes the simulation results. Conclusions and perspectives are made in Section 6. 3
Journal Pre-proof 2. EREV powertrain and vehicle modeling 2.1 Powertrain and parameters EREV is a plug-in series hybrid electric vehicle driven by pure electric drive. Its power system consists of power battery, auxiliary power unit （ APU ） , drive motor and control system ， as shown in Fig. 1. The APU which consists of an engine and a generator is directly connected to the DC bus, and no mechanical connection with the wheel. Therefore, the engine can be worked at its best point, with high efficiency and low emissions. EREV has two power sources, namely, APU and power battery, which can be switched freely in five working modes according to different power requirements. The five working modes are battery working only mode, APU working only mode, hybrid drive mode, driving charging mode and brake energy recovery mode, respectively. (1) Battery working only mode. When the battery SOC is high, the battery completely provides the power demand of vehicle. In this mode, the power battery can meet the power demand under all working conditions. (2) APU working only mode. When the battery SOC drops to the minimum limit, in order to protect the battery, the battery no longer provides energy. At this time, the APU works alone to provide the energy for vehicle. (3) Hybrid drive mode. When the battery SOC is low, the APU is turned on, together with the battery, to provide the energy for vehicle. (4) Driving charging mode. In some special cases, the energy provided by the APU not only meets the energy demand of the vehicle, but also charges the battery with extra energy. (5) Brake energy recovery mode. When the vehicle is braked, the drive motor works in the power generation state, and the power generated is used to charge the battery. The specific parameters of EREV are list in Table 1.
APU
Motor
Engine
Generator
Mechanical Electrical
Battery
Fig. 1. Powertrain architecture of the studied EREV
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Journal Pre-proof Table 1 The EREV parameters Component
Parameter Name
Value
Unit
EREV
Curb weight
14500
kg
Frontal area
7.5
m2
Air drag coefficient
0.73
—
Air density
1.2
Kg/m3
Wheel radius
0.484
m
Rolling resistance coefficient
0.008
—
Final drive ratio
6.17
—
Rated power
96
kW
Maximum speed
3000
r/min
Rated power
75
kW
Maximum speed
3500
r/min
Capacity
120
Ah
Voltage range
550
V
Rated power
115
kW
Peak torque
540
Nm
Engine Generator Battery Drive Motor
2.2 Main component model 2.2.1 Vehicle Longitudinal Dynamics According to the dynamic equilibrium relation of the vehicle, the power Pwh acting on the wheel can be expressed as
1 Pwh mv fmg cos a Cd Af v 2 mg sin v 2
(1)
Where m is the vehicle mass, g is the gravity acceleration, f is the rolling resistance coefficient, ρa is the air density, Cd is the air dynamic drag coefficient, Af is the bus frontal areas, α is the road angle, v is the vehicle speed. The relationship between traction motor demand power Pd and wheels power Pwh is as follows：
Pwh , Pd tm ( P P ) , wh m br t m
Pw 0
(2)
Pw 0
Where ηt is the drive-line efficiency, ηm is the efficiency of the driving motor, Pm-br is the power of the mechanical braking force.
2.2.2 APU model The optimal fuel consumption curve of APU is obtained by bench test. The bench test and optimal fuel consumption curve are shown in Fig.2 and Fig.3, respectively. Therefore, the functional relationship between APU fuel consumption quality and APU power is defined:
5
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m f be
Papu
t 1000 3600
(3)
Where be is the APU optimal fuel consumption rate, which can be obtained from Fig.3. Fuel consumption meter
Battery
Engine
Generator Dynamometer
Generator controller
Fig. 2. APU test bench for fuel consumption
Fig. 3.Optimal fitting curve of fuel consumption rate related to APU power
2.2.3 Battery model For simplification, most studies used Rint model to model batteries and obtained reliable accuracy[39-40]. The output current of battery Ib can be calculated by Ohm's law,
Ib
Voc (soc) Voc2 (soc) 4 Pb Rb (soc) 2 Rb (soc)
(4)
Where Voc and Rb are the open circuit voltage and internal resistance of the battery, respectively, and both of them are related to SOC. Pb is the battery power, Qb is the nominal capacity of the battery.
soc soc0 6
Ib dt Qb
(5)
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soc
Voc (soc) Voc2 (soc) 4 Pb Rb (soc) 2Qb Rb (soc)
(6)
A number of tests were conducted to obtain the characteristic parameter of battery cell at ambient temperature 25℃. Fig.4 shows the open circuit voltage (Voc) curves as a function of SOC. Fig.5 shows the discharge resistance (Rb) curve as a function of SOC.
Fig.4. Battery cell open circuit voltage curves as a function of SOC at 25℃
Fig.5. Battery cell resistance curves as a function of SOC at 25℃
3. Optimal control problem description Since EREV has two power sources, the core problem of the energy optimization is how to distribute the energy between APU and power battery reasonably to satisfy the energy requirement of the vehicle.
Pd (t) Papu (t) Pbat (t)
(7)
In this paper, the fuel economy is taken as the optimization objective, and the performance function is as follow: 7
Journal Pre-proof J min m f u t dt tf
t0
(8)
f is the instantaneous fuel consumption quality. The control Where u(t) is the control variable, m variable and state variable are set to:
x(t) SOC (t) u (t) Papu (t)
(9)
Considering the actual operation characteristics of EREV, the components need to work within a reasonable range, so the operation status of the engine, motor and battery should be constrained,
m,min m (t ) m,max T m,min Tm (t ) Tm,max e,min e (t ) e,max Te,min Tm (t ) Te,max SOCmin SOC (t ) SOCmax
(10)
where, ωm,min and ωm,max are the minimum and maximum speed of the generator, ωe,min and ωe,max are the minimum and maximum speed of the engine, Tm,min and Tm,max are the minimum and maximum torque of the generator, Te,min and Te,max are the minimum and maximum torque of the engine, SOCmin and SOCmax are the minimum and maximum limits of the SOC.
3.1 Pontryagin's minimum principle PMP is a classical analytical method for solving optimal control problems. The Hamilton function of the above optimal control problem is:
H SOC (t), u t , t m f (u(t)) (t) SOC(t)
(11)
According to the PMP, the optimal control is obtained by finding the minimum value of the Hamilton function,
u * (t) argminH soc t , u t , t
(12)
Where λ(t) is the co-state. They can expressed as follows:
SOC t
H f SOC t , Pbat t
t
H SOC SOC SOC
(13)
(14)
As shown in Equation (6), the value of SOC is related to Voc(soc) and Rb(soc). Fig.4 and Fig.5 show that the Voc and Rb are almost constant when the SOC is between 0.3-0.9. Therefore,
t
SOC 0 constant SOC
(15)
From the above derivation, when the driving cycle is known, the co-state λ is constant, namely, λ=λ0. Some studies shows that λ is mainly affected by the driving cycles, the driving conditions and the initial value of SOC. Since PMP is a global optimization algorithm, the calculation time is too long to be realized online. So, the ECMS is often used in practice. In fact, ECMS can be derived from the PMP. The equivalent fuel consumption meqv(t) consists of the actual fuel 8
Journal Pre-proof f (t) and the nominal fuel consumption me(t): consumption m
f (t) s(t) m e (t) m f (t) s(t) meqv (t) m
Pb (t) Qlhv
(16)
where s(t) is the equivalent fuel consumption factor (EF), reflecting the conversion relationship between the chemical energy of the fuel and the electrical energy of the battery, the value of which is crucial for achieving optimal power distribution between the engine and the battery. Further, the (16) can be written as:
f (t) s(t) meqv (t) m
SOC (t) Voc (t) Qb Qlhv
(17)
The relationship between the s(t) and the λ can be easily obtained by (11) and (17)
s (t)
Qlhv QbVoc
(18)
3.2 EF optimization 3.2.1. Bounds of the EF In order to achieve better optimal performance of ECMS, the initial value of EF is especially critical. At present, the Shooting Method is widely used to solve the EF. This method first guesses a value of initial co-state, and then calculates the terminal SOC according to formula (11)-(14). If the terminal SOC is equal to the constraint value (or the difference between them is small), then the guess is considered. If it is not equal, the initial guess value is changed, and the above process is repeated until the terminal constraints is satisfied. It can be seen that the key to solve the EF by the shooting method depends on the reasonable guess of the initial value or the initial range. However, it is difficult to estimate the initial range in the actual calculation process. In order to solve the above problems, an improved shooting method is proposed in this paper, which can predetermine the EF bounds and greatly reduce the calculation time. The specific methods are as follows: (1) Lower bound for EF Considering the law of conservation of energy
E fuel Ebat Ed Eloss
(19)
where Efuel and Ebat are the fuel energy and battery energy consumed during the trip, respectively. Ed and Eloss are the required energy and dissipated energy for finishing the trip, respectively. In order to reduce energy loss during the trip, Eloss should be the smallest,
arg min Eloss arg min E fuel Ebat Ed arg min
P tf
0
fuel
Pbat Pd dt
Since Pd is known at each moment, so
9
(20)
Journal Pre-proof arg min arg min
tf
0
tf
0
P
fuel
m
fuel
Pbat dt
Qlhv Pbat dt
(21)
t f 1 arg min m fuel Pbat dt 0 Qlhv In order to obtain the minimal instantaneous power, the cost function of ECMS should be
J m fuel
1 Pbat Qlhv
(22)
Comparison of (16) with (22) shows
s 1
(23)
From the above derivation, the optimal s can be obtained. However, the above derivation process does not consider the SOC limit, so the optimal value may not be suitable. Simulations show that when s=1, the battery SOC quickly reaches its minimum limit SOCmin. When s<1, the discharge rate of the battery is higher compared with s=1 , and its instantaneous fuel economy is no longer optimal. Therefore, the optimal s should be equal or higher than 1, depending on the actual driving cycle.
s* s min 1
(24)
(2) Upper bound for EF From the previous description, The EREV has five working modes, which can be represented by control space Γ .
u fuel , ubattery , uhybird , uch arg e , ubrake
(25)
where ufuel, ubattery, uhybird, ucharge and ubrake are the five working modes: APU working only mode, battery working only mode, hybrid drive mode, driving charging mode and brake energy recovery mode, respectively. When Pd ≤ 0 , the vehicle is in braking energy recovery mode, and the vehicle can absorb the braking energy as much as possible as long as the SOC does not exceed its maximum limit. So the EF is only related to the case of Pd>0. When Pd>0, the vehicle will work in one of three modes: APU working only mode, battery working only mode, or hybrid drive mode. At this time, the ECMS needs to find the optimal control mode to reduce the cost function (16).
u * u fuel or ubattle or uhybird
(26)
Now, if u*є{ufuel}, the optimal ECMS can be described by
ECMS u fuel m fuel
(27)
sPbat Qlhv
(28)
Similarly, if u*є {ubattery }
ECMS ubattery and, if u*є {uhybird }
ECMS uhybird m fuel 10
sPbat Qlhv
(29)
Journal Pre-proof If the s is large, u* tends to{ufuel }; when sis infinite, the vehicle will always work in fuel only mode, and the fuel economy is no longer optimal. Therefore, the upper bound of s need to be restricted. Thus, the battery only mode or the hybrid drive mode may have the lowest system energy consumption,
ECMS ubattle ECMS u fuel ECMS uhybird ECMS u fuel
(30)
The above inequality will yield two upper bounds: smax1 and smax2, then the optimal upper bound will chooses smax= min{smax1, smax2}. However, even if only one of the above inequality is solved, then the value is also met. The first inequality in (30) gives
Papu s*
m fuel Qlhv
Pbat
apu Pem
embat
Pd / trs
smax1
apu em bat Pd / trs apu embat
(31)
where ηtrs ，ηapu ，ηem ，and ηbat are the efficiencies of the transmission, APU, motor and battery, respectively. The second inequality in (30) gives
s*
m fuel (u fuel ) m fuel (u hybird ) Pbat / Qlhv
Pd / trs smax 2
apu
Pd / trs Pem (u hybird )
apu Pem (u hybird )
(32)
embat The Pd and Pem in (32) change with the driving cycle, so they cannot be eliminated. The specific value of smax2 cannot be determined. Fortunately, as mentioned previously, the upper bound of s only needs to satisfy one of the inequalities. Thus, the upper bound of s is
s* smax1
embat apu
(33)
In summary, for the EREV powertrain shown in Fig. 1, the optimal EF bounds are
1 s*
embat apu
where the value of ηapu，ηem，and ηbat are ηapu=27.63%, ηem=92.72% and ηbat=98.45%.
11
(34)
Journal Pre-proof 3.2.2 Improved shooting method The flowchart of the calculation of EF is shown in Fig. 6. First, the range of EF is obtained according to the above calculation. Then, the Secant method [30] is used to search the optimist EF in each shooting process. Last, the terminal SOC is obtained according to formula (11)-(14). If the terminal SOC is equal to the constraint value (or the difference between them is small), the EF is considered. If not, repeat the above process and re-optimize until the terminal constraints are met. Start
1 s*
embat apu
smin smax ，i=1 2 s2 =s1 +，i 2 s1
si si 1
SOCi 1 SOC f SOCi 1 SOCi 2
(i 1 i 2 )
i 3,4
Discrete control variables
Papu 0 : Papu : Papu _max
Papu * (t) argminH SOC t , u t , t SOC t f SOC t , Pbat t SOC t SOC Qlhv s (t) Q V b oc
t tf
N
Y N
SOC (t f ) SOC f Y
End
Fig.6. Algorithmic flowchart of the improved shooting method
4. Adaptive energy management strategy 4.1 Standard-ECMS In standard ECMS, the EF is constant. In fact, EF has a very close relationship with the driving conditions. For a certain driving cycle, the initial value of EF can effectively maintain the SOC, but under other driving cycles, the trajectory of the SOC may be uncontrolled and completely deviate from its normal working range. As shown in Fig. 7, under the same initial value, SOC can be well maintained around 0.3 in Chinese typical urban cycle, while in UDDS and US06 cycles, the SOC continue to decline. This is mainly because the characteristics of UDDS and US06 cycles are different from Chinese typical urban cycle. Therefore, in order to enable the ECMS-based control strategy to be implemented online, it is necessary to solve the adaptability of the SOC maintenance under different driving cycles. In order to find out the causes of these differences and reveal the intrinsic working mechanism 12
Journal Pre-proof of ECMS, three scenarios are set up to simulate the performance of EREV, the simulation is implemented in Matlab/simulink. These scenarios have the same speed trajectory, but different altitude profiles: No Grade, Downhill, and Uphill. The speed trajectory, downhill and uphill are shown in Fig. 8, respectively. Constant EF is adopted in the simulation process, the value of which is 2.8. Table 2 shows the equivalent fuel consumption, terminal SOC, APU start-stop times and the proportion of working time of each mode. It can be seen from Table 2 that under the uphill, the hybrid drive mode, the driving charging mode and the APU driving mode have a relatively high proportion; under the downhill, the brake recovery mode has the highest proportion, and the battery independent driving mode take the highest proportion under the no grade.
Fig.7. The same EF corresponds to the SOC curves in different driving cycles.
As shown in Table 2, the terminal SOC and equivalent fuel consumption are different under different road gradients. In the uphill, the equivalent fuel consumption is much higher than the other two conditions, and the terminal SOC is the lowest. The specific reasons are as follows: on the one hand, APU start-stop more times in the uphill, which result in higher instantaneous fuel consumption; on the other hand, the fixed EF restricts the optimal distribution of energy. When going uphill, the battery should be discharged to assist the APU to drive the vehicle together. However, due to the EF causes the actual SOC to follow the reference SOC, forcing the battery to charge at some uphill points, which results in the APU working at the maximum power and the fuel consumption increasing. In downhill, fuel consumption is slightly higher than that of no grade. The reason is: when going downhill, the vehicle should work in braking energy recovery mode. However, due to the limitation of fixed EF, the battery is forced to discharge at some downhill points, resulting in the waste of energy. From the results in Table 2, two viewpoints are obtained: one is that the terminal SOC is quite different from the ideal value; the other is that the ramp information is not used in the process, and the equivalent fuel consumption is quite different. Therefore, it is necessary to adjust EF in real time according to actual road conditions to obtain the best fuel economy. Through the above analysis, the internal operation mechanism of ECMS can be obtained:1) The initial value of EF is a key parameter affecting ECMS performance. when EF increases, the battery tends to charge; when EF decreases, the battery tends to discharge. 2) ECMS achieves 13
Journal Pre-proof optimal fuel economy by adjusting the reasonable energy distribution of the APU and power battery. The energy distribution of the APU and the power battery is specifically reflected by the proportion of the working time of the five working modes of EREV. The higher the ratio of working time of the brake recovery mode and the battery independent driving mode, the better the fuel economy of EREV.
(a)
(b)
(c) Fig.8.Velocity and topographical profile.(a) Velocity trajectory. (b) Downhill. (c) Uphill
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Journal Pre-proof Table 2 Performance of ECMS for different topographical profile with s(t)=2.8 Parameters Equivalent fuel consumption [L/100KM]
No Grade
Downhill
Uphill
25.25
27.12
33.36
Final SOC
0.56
0.52
0.45
APU ON/OFF times
82
98
176
Regenerative brake
25.32%
28.41%
20.18%
Hybrid driving
15.25%
16.82%
19.52%
Driving charging
20.15%
18.32%
22.26%
Battery driving only
27.12%
24.86%
19.81%
APU driving only
12.16%
11.59%
18.23%
4.2 Adaptive-ECMS Based on the previous analysis, this paper proposes an online optimization energy management strategy based on ECMS. The structure is shown in Fig.10. Firstly, the global position system (GPS) and geographic information system (GIS) are used to obtain the driving information in the future time domain, such as traffic lights, speed limit information and road gradient, etc., which can be utilized in the energy management strategy. Taking the road gradient as example, if it is known that the vehicle is going to be in the uphill condition, the energy management strategy will make the power battery store as much energy as possible to improve the power during the climbing process. When the vehicle is about to be in downhill condition, even if the SOC is lower than the reference value, no additional APU power is needed for charging, because the upcoming downhill condition can improve SOC through energy recovery. Secondly, the improved shooting algorithm is used to solve the initial EF. Then, based on the predicted upcoming speed and road topographical profile, the EF is periodically updated. In order to select the appropriate period, several experiments were conducted to evaluate the impact of the updating period on the terminal SOC. As shown in Fig.9, both 200m and 300m meet the SOC maintenance performance, and the updating period is shorter, the terminal SOC maintenance performance is better. In order to balance computational cost and performance, the updating period is chosen to be 300m. Finally, the optimal control variable, namely Papu, is calculated by ECMS at each time step.
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Fig. 9.The terminal SOC value affected by the EF updating period Runs periodically
GIS
GPS
Driving cycle predicted Improved shooting method s(k) Pd
A-ECMS
SOC
Pb_cmd Papu_cmd
Battery
Pb
Wheel
APU
Engine
Generator
AC/DC
Motor dive system
Papu
Wheel
Fig.10.Structure of the proposed energy management strategy
16
Journal Pre-proof 5. Simulation and verification 5.1 Control Performance In order to verify the control effect of the energy management strategy proposed in this paper, Rule-based control strategy, power following control strategy and DP are used for comparison. The simulation is implemented in Matlab/simulink. Fig. 11 shows the SOC trajectory curves of the three control strategies under Chinese typical urban cycle. It shown that under rule-based control strategy, the SOC trajectory is between 0.25 and 0.35, showing a variation pattern of the zigzag shape. The SOC curve of rule-based and power following control strategy have a large variation range, and the terminal SOC cannot be guaranteed to reach 0.3. The proposed strategy can maintain SOC near the reference SOC, which is due to the real-time update of the EF. As shown in Fig.12, the variation range of EF is 1-3.5, and it is updated every 300m. When the battery SOC decreases, the EF increases, trying to promote SOC and keep it near 0.3; When SOC increases, the EF decreases, trying to make SOC decrease and keep it near 0.3. At the beginning of the journey, the SOC curve rises and gradually deviates from the reference value (0.3). When the vehicle runs to about 300m, the EF decreases from 2.7 to 1.8, which prevents the SOC from rising. Then the SOC curve began to decline. In order to prevent the continuous decline of SOC and keep it near 0.3, the EF increased from 1.8 to 3.4 between 600m and 1500m. It can be seen that the battery SOC can be maintained near 0.3 through the adjustment of the EF. It also can be seen that the SOC working range based on the proposed strategy is much narrower than the former two strategies. This indicates that the battery is in shallow charge and discharge, which is beneficial for improving the working efficiency and prolonging the durability of the battery.
Fig.11.SOC trajectory curves of three control strategies under Chinese Typical Urban Conditions
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Fig.12. Trajectory of the EF
Fig. 13 shows the power-time curves of each component under Chinese typical urban conditions. In order to clearly see the details of the power curve, only part of the trajectory segment is intercepted here. It is easy to find that all three control strategies have realized the designed control logic. The output power of the rule-based control strategy is basically maintained at the maximum efficiency point after APU start-up. Under the power following control strategy, the APU output power follows the required power all the way. Different from the above two control strategies, the proposed is relatively intelligent. It usually chooses to start the APU when the demand power is large, and once the APU starts, it will quickly transfer to its maximum efficiency point. This feature is similar to the DP algorithm. Therefore, the proposed has higher energy distribution efficiency.
(a)
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(b)
(c) Fig.13.Comparison of component powers of three control strategies in Chinese typical urban cycle:(a)rule-based control method, (b) power following control method, (c) the proposed method
5.2 Fuel economy comparison In order to verify the fuel economy of the proposed control strategy, two other cycles are simulated, namely, Beijing urban bus cycle and new European driving cycle (NEDC). Because the terminal SOC of the four control strategies are different, it is impossible to directly evaluate the fuel consumption of the vehicle. In order to evaluate the fuel economy fairly, it is necessary to modify the impact of the terminal SOC. Then, the relative fuel consumption efficiency is calculated.
FC FCopt FCopt
100%
(35)
where, FC is the fuel consumption of the each strategy, FCopt is the optimum which is calculated by DP, from the four strategies. The smaller the η, the better the economic performance of the control strategy. Table 3 and Fig. 14 show the comparison of 100 km fuel consumption between four control strategies under the three driving cycles after the modification of terminal SOC. Obviously, the fuel economy of A-ECMS is better than that of rule-based and power following control strategy. Compared with the rule-based control strategy, the A-ECMS can lower6.9% in Beijing urban bus cycle, 4.7% in Chinese typical urban cycle, and 7.8% in NEDC. Compared with the power 19
Journal Pre-proof following control strategy, the A-ECMS can lower4% in Beijing urban bus cycle, 7.5% in Chinese typical urban cycle, and 3.1% in NEDC. Table 4 shows the average working efficiency of engines and power batteries under different control strategies. It can be seen that under the rule-based control strategy, the engine has high working efficiency, but the battery efficiency is low. The power following control strategy can improve the average charging and discharging efficiency of the battery, but the APU working efficiency is reduced a lot. In contrast, the A-ECMS has higher engine efficiency and average charge-discharge efficiency, which would contribute to its fuel economy. In addition, Table 3 and Fig. 14 also show the off-line optimum value (DP) under each driving cycle. It found that the A-ECMS is almost the same as the DP. The biggest difference occurs in Chinese typical urban cycle, only 2.4%. Table3 Fuel economy comparison of different control strategies Cycle
Control strategies
Fuel consumption(L/100km)
Terminal SOC
Beijing urban bus cycle
Rule-based
32.6
0.326
7.9%
Power following
31.7
0.324
5.0%
A-ECMS
30.5
0.312
1.0%
DP
30.2
0.300
0
Rule-based
27.1
0.296
7.1%
Power following
27.8
0.321
9.9%
A-ECMS
25.8
0.308
2.4%
DP
25.3
0.300
0
Rule-based
30.1
0.326
8.9%
Power following
28.9
0.312
4.2%
A-ECMS
28.1
0.298
1.1%
DP
27.8
0.300
0
Chinese typical urban cycle
NEDC
Table4 Average operating efficiency of engine and battery under different control strategies APU Cycle
Battery
Control
Power
Average
strategies
generation
efficiency
Discharge energy（kWh）
（kWh） Beijing urban bus cycle Chinese typical urban cycle
NEDC
Rule-based
Charging
Charge and
energy
discharge
（kWh）
efficiency
72.35
33.28%
54.34
61.24
90.53%
67.23
30.75%
13.25
14.73
93.21%
A-ECMS
69.15
33.58%
31.25
33.56
94.15%
Rule-based
90.13
33.12%
48.23
59.32
83.32%
84.23
32.15%
39.06
42.32
87.10%
A-ECMS
85.24
33.45%
44.35
51.23
87.88%
Rule-based
79.25
33.78%
29.36
35.51
86.65%
75.36
32.81%
27.36
32.54
88.42%
76.65
33.72%
28.45
33.12
88.96%
Power following
Power following
Power following A-ECMS
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Fig.14.Comparison of fuel consumption per 100 kilometers under different control strategies
5.3 Real-time performance In order to show the advantages of real-time performance of the proposed control strategy, two other adaptive control strategies were introduced for comparison, namely, PID-ECMS and Shooting method-ECMS (S-ECMS). 1）PID-ECMS：Through the PID control, the EF is adjusted in real time to make the actual SOC follow the reference SOC. For simplicity, this paper does not discuss the PID-ECMS, detailed information can be found in [21]. 2）S-ECMS: This method is basically the same as A-ECMS, the only difference is that a traditional shooting method is used instead of the improved shooting method. The downhill scenario in Fig.8(b) is taken as the simulation cycle, and the results are shown in Fig.15. In Fig. 15, the SOC trajectory of A-ECMS decreases significantly before the slope arrives. After entering the ramp, the braking energy is recovered as much as possible so that the SOC reaches its maintenance value. However, the PID-ECMS cannot predict the upcoming slope, and the PID control keeps the SOC closely following the reference SOC. When entering the ramp, the braking energy rarely charges the battery, and most of it is dissipated by the mechanical brake. So, most of the energy is completely wasted. Although S-ECMS can predict future slopes like A-ECMS, the tradition shooting algorithm takes longer time and its SOC trajectory cannot quickly follow the change of driving conditions. As shown in Fig 15, the SOC trajectory of S-ECMS even exceeds the lower limit of the battery, which may cause damage to the health of the battery. The fuel consumption of the three methods is shown in Table 5. It is shown that the proposed A-ECMS performs substantial fuel reduction than PID-ECMS, which signifies that future road information plays an important role in achieving good fuel economy. Hence, it can be concluded that A-ECMS is slightly better than the S-ECMS.
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Fig.15. SOC trajectories in the presence of road grade Table 5 Fuel consumption of the three strategies Initial SOC
Terminal SOC
Fuel Consumption/kg
PID-ECMS
0.7
0.72
1.55
29.1%
S-ECMS
0.7
0.71
1.29
7.5%
A-ECMS
0.7
0.69
1.23
2.5%
Fig. 16 shows the computational time to update the EF every 300m, using the tradition shooting algorithm and the improved shooting algorithm, respectively. It shows that the calculation time of the tradition shooting algorithm is much longer than that of the improved shooting algorithm. This is because the improved shooting algorithm has calculated the EF range in advance, so the initial value of the EF can be quickly obtained. However, the tradition shooting algorithm does not know the range and needs continuous trial and iteration. Since S-ECMS needs more time to update the EF, its adaptability is not as good as A-ECMS. Once the calculation time is longer than the time for the vehicle to travel 300m, the EF can not to be updated in time, thus affecting the energy allocation. Therefore, the S-ECMS strategy may have real-time problems in some cases.
(a)
(b)
Fig.16. Computational time for updating EF using two strategies.(a)S-ECMS.(b)A-ECMS 22
Journal Pre-proof 6.Conclusion In this paper, an improved shooting algorithm is proposed and an adaptive real-time optimization energy management strategy is designed for an EREV. The specific work is as follows: (1) To quickly calculate the initial value of the EF, an improved shooting algorithm is proposed, which can determine the range of the EF according to the power configuration parameters(APU efficiency, battery efficiency, generator and its controller efficiency) of the vehicle. In addition, the internal operation mechanism of the ECMS is revealed from the perspective of energy flow, and the working relationship among the five working modes of EREV is clarified. The higher the ratio of working time of the brake recovery mode and the battery independent driving mode, the better the fuel economy of EREV. (2) An adaptive online optimal energy management strategy is proposed. This strategy uses the improved shooting algorithm to quickly calculate the initial value of the EF and updates the EF periodically based on the GPS and GIS, to achieve the effective maintenance of SOC. Then the optimal power allocation of APU is obtained. (3) The proposed energy management strategy is simulated and analyzed, and the effectiveness of the designed control strategy is verified. In order to verify the adaptability and fuel economy of the proposed control strategy, a detailed comparison with the rule-based control strategy and the power following control strategy is carried out. The results show that the strategy proposed in this paper has better control effect both in fuel economy and in robustness of SOC control. In addition, in order to reflect the advantages of the proposed control strategy in real-time performance, PID-ECMS and S-ECMS are choose to make comparison, respectively. The simulation results show that the fuel economy of A-ECMS is better than PID-ECMS, and the real-time performance is better than S-ECMS. At present, for family cars, their daily driving situation is random, and long-term prediction of driving conditions is difficult to achieve. But in the near future, with the rapid development of intelligent transportation, the real-time road information and environmental changes of the driving cycle will be timely fed back to the vehicle controller. Combined with the above information, the control strategy proposed in this paper can be applied to more complex scenarios.
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Journal Pre-proof Author contributions:
Ye Yang: Conceptualization, Methodology, Software, Investigation, Writing - Original Draft. Youtong Zhang: Validation, Formal analysis, Supervision. Data Curation. Jingyi Tian: Validation, Formal analysis, Writing - Review & Editing. Tao Li: Resources, Writing - Review & Editing, Software.
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Declaration of interests ☑The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
Ye Yang, Youtong Zhang, Jingyi Tian, Tao Li PII:
S0360-5442(20)30344-3
DOI:
https://doi.org/10.1016/j.energy.2020.117237
Reference:
EGY 117237
To appear in:
Energy
Received Date:
24 August 2019
Accepted Date:
22 February 2020
Please cite this article as: Ye Yang, Youtong Zhang, Jingyi Tian, Tao Li, Adaptive real-time optimal energy management strategy for extender range electric vehicle, Energy (2020), https://doi.org/10. 1016/j.energy.2020.117237
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Adaptive real-time optimal energy management strategy for extender range electric vehicle Ye Yang1,2, Youtong Zhang1, Jingyi Tian3, Tao Li1 1 2 3
Laboratory of Low Emission Vehicle, Beijing Institute of Technology, Beijing 100081, China Qing Gong College, North China University of Science and Technology, University Road No. 11,Tangshan 063000, China School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China; [email protected]
Highlights: 1. An improved shooting method is designed. 2. The intrinsic operation mechanism of ECMS is revealed. 3. An adaptive real-time optimal energy management strategy is proposed. 4. The fuel economy and adaptability of different control strategies are discussed.
Abstract: The extender range electric vehicle (EREV) is an effective way to solve the "mileage anxiety" of pure electric vehicles, and the fuel economy of EREV is the key point of energy optimization. This paper designed an adaptive real-time optimal energy management strategy for EREV. Firstly, an improved shooting algorithm is proposed, which can determine the range of the equivalent factor (EF) according to the power configuration parameters of the vehicle, and then the secant method is used to quickly calculate the initial value of the EF. Secondly, from the perspective of energy flow, the intrinsic operation mechanism of equivalent consumption minimization strategy (ECMS) control strategy is revealed, and the working relationship between the five working modes of EREV is clarified. Thirdly, based on the car navigation and geographic location information system, the EF is periodically updated to achieve effective maintenance of the battery state of charge (SOC), so as to obtain the optimal power allocation. Finally, The fuel economy and real-time performance of the proposed energy management strategy are simulated and compared. To verify fuel economy, the rule-based control strategy and the power following control strategy were used as comparison. The results show that the proposed control strategy has better fuel economy and adaptability. To verify real-time performance, the proportional integral derivative ECMS (PID-ECMS) and shooting method ECMS (S-ECMS) were used as comparison. The results show that the proposed strategy is better in both fuel economy and real-time performance. Keywords: extended range electric vehicle; real-time optimization；adaptive energy management； improved shooting method；equivalent consumption minimization strategy
1. Introduction In recent years, new energy vehicles have developed rapidly for energy conservation and environmental protection. While taking into account the advantages of electric vehicles and traditional vehicles, Extended-range electric vehicle (EREV) extends the driving range and eliminates the driver's mileage anxiety. Hence, it is considered to be a promising new energy 1
Journal Pre-proof vehicle [1-2]. As there are two power sources in the EREV, the key to ensure vehicle power performance and system efficiency is to coordinate the energy distribution between two power sources through reasonable energy management strategies [3-4]. The energy management problem of hybrid vehicles has been a major concern for researchers in the past decade. A large number of research institutes and scholars have conducted extensive and in-depth research [5-8]. Specifically, control strategies can be divided into two categories: rule-based control and optimization-based control. Rule-based control strategy is based on engineering experience and experiments to formulate control rules [9-10], which has short computing time and reliable application, low requirement for memory and processing speed of control chip, high reliability of control algorithm and easy implementation [11-12]. Although the rule-based control is easy to design, the development of rules requires a lot of experimentation and calibration. Moreover, these rules are only applicable to a single drive cycle. Once the drive cycle changes, they need to be re-set, otherwise the fuel economy will become worse. The optimization-based control strategy is divided into global optimization and real-time optimization. The former is based on the global optimal theory, and uses the relevant optimization method to obtain the energy distribution. Dynamic Programming (DP) [13-14] and Pontryagin's Minimum Principle (PMP) [15-16] are the two most widely used global optimization methods. Although DP and PMP can obtain the optimal solution in the whole time domain, they need to get the driving information in advance, and the calculation time is too long to be applied in real vehicles online. But the research on them is meaningful: on the one hand, the results of these two strategies can be used as a benchmark to evaluate the control effects of other strategies; on the other hand, some control rules can be extracted offline from them to improve the performance. In addition to the above two commonly used methods, there are some other global algorithms including genetic algorithms, particle swarm optimization (PSO) and intelligent neural network algorithms [17,18]. In [17], Chen et al. used genetic algorithms to optimize power threshold for engine to turn on, which made the engine work more efficiently and thus reduced the fuel-consumption. In [18], PSO algorithm was proposed to optimize the power split between power sources and the sizing of the powertrain components. The simulation results showed that the optimal components sizing and the fuel consumption have been improved. For real-time optimal control, the equivalent consumption minimum strategy (ECMS) and model predictive control (MPC) are the two most representative methods. Based on historical driving data, mathematical models or real-time information provided by intelligent transportation systems, MPC predicts the torque demand of the vehicle in the future time domain, and optimizes the energy distribution ratio to achieve low fuel consumption and low emission [19-20]. ECMS simplifies the dynamic optimization problem to an equivalent instantaneous optimization problem, and minimizes the equivalent fuel consumption at each time to improve the fuel economy [21-22]. Compared with global optimization, it has less computation time and better real-time performance. Therefore, many scholars are working on the ECMS method. According to the idea of ECMS, Sivertsson et al.[23] proposed an adaptive energy management strategy, which could improve the mechanical efficiency of the drive train. Youngkwan et al. [24] designed an ECMS energy management strategy for a series of hybrid electric power system. A driving-style-oriented adaptive ECMS was designed in [25]. The authors analyzed the impact of driver's style on the fuel consumption, and divided driving style into six levels, achieving good fuel economy. In [26], three adaptive energy management strategies: adaptive ECMS (A-ECMS), Optimal Control Method 2
Journal Pre-proof (OCL) and Stochastic Dynamic Programming (SDP) were discussed, and the pros and cons of each method were evaluated. In the application of ECMS, equivalent factor (EF) is a key dynamic variable, which determines the performance of real-time optimization [27]. Therefore, some papers focus on how to resolve the EF. In [28-30], the EF is solved by traditional shooting method. Yang et al. [31] divided the driving cycles into several segments according to the actual bus stations, and then used the linear particle swarm optimization algorithm to solve the EF of each segment. Zhou et al. Ref [32] used pseudo-spectral optimization algorithm to solve EF and achieved good fuel economy. In [33], a fuzzy tuned ECMS was proposed to obtain the EF. In [34] the future vehicle velocity was predicted to obtain the EF. The EF is very sensitive to the actual driving conditions. If the constant EF is used, once the driving conditions change greatly, the SOC of the battery may fluctuate greatly. Therefore, in order to obtain better fuel economy, it is necessary to adjust the EF according to the real-time driving condition. In view of this, some researchers have proposed adaptive ECMS (A-ECMS), which can be divided into three categories: predictive A-ECMS, instantaneous A-ECMS and look-up A-ECMS. Predictive A-ECMS adjusts the EF by predicting upcoming road conditions to achieve real-time control [32,35-36]. Ref [32] updated the EF every 400m based on the predicted driving cycle and road grade information. Instantaneous A-ECMS calculates the EF based on the current driving information [28, 30, 37-38]. Ref [28] proposed a tracking-reset method to adjust the EF. When the road is flat, the tracking part ensure that the SOC is tracking the reference SOC; when the road is hilly, the reset part brings the SOC to its initial profile. In [30], the PID control was used to adjust the EF to follow the reference SOC in real time. The look-up A-ECMS is implemented in two steps. In the first step, a map of EF is established offline with respect to the relevant characteristics, such as speed [29], distance, or initial SOC values [31]. In the second step, the EF is obtained by looking up the map based on the real-time characteristic value. Generally, this method is applicable to urban buses with fixed routes. The various methods mentioned above showed good fuel economy and better performance than others. However, most of the methods were only performed in a specific environment or only under single or partial driving cycles. When there is some ramp or severe congestion on the driving conditions, the adaptive control strategy will be greatly discounted. In addition, some literatures used shooting method to solve EF, but no detailed description of the range of initial values of the EF was discussed. If the range is not selected properly, it will greatly increase the calculation time and affect the implementation of the algorithm. At the same time, few literatures have analyzed the operation mechanism of ECMS. Based on the above analysis, this paper proposes a method to quickly calculate the equivalent factor. This method can determine the range of EF according to the vehicle's power configuration parameters (APU efficiency, battery efficiency, generator and its controller efficiency). In addition, based on the periodic update of the equivalent factor, an adaptive real-time energy management strategy is designed, which can achieve better fuel economy and real-time performance. This paper is organized as follows. Section 2 discusses the powertrain and mathematical models of the EREV. Section 3 describes the optimal control problem and introduces the improved shooting method to solve the EF. Section 4 proposes the development of an adaptive real-time optimal energy management of EREV. Section 5 discusses and analyzes the simulation results. Conclusions and perspectives are made in Section 6. 3
Journal Pre-proof 2. EREV powertrain and vehicle modeling 2.1 Powertrain and parameters EREV is a plug-in series hybrid electric vehicle driven by pure electric drive. Its power system consists of power battery, auxiliary power unit （ APU ） , drive motor and control system ， as shown in Fig. 1. The APU which consists of an engine and a generator is directly connected to the DC bus, and no mechanical connection with the wheel. Therefore, the engine can be worked at its best point, with high efficiency and low emissions. EREV has two power sources, namely, APU and power battery, which can be switched freely in five working modes according to different power requirements. The five working modes are battery working only mode, APU working only mode, hybrid drive mode, driving charging mode and brake energy recovery mode, respectively. (1) Battery working only mode. When the battery SOC is high, the battery completely provides the power demand of vehicle. In this mode, the power battery can meet the power demand under all working conditions. (2) APU working only mode. When the battery SOC drops to the minimum limit, in order to protect the battery, the battery no longer provides energy. At this time, the APU works alone to provide the energy for vehicle. (3) Hybrid drive mode. When the battery SOC is low, the APU is turned on, together with the battery, to provide the energy for vehicle. (4) Driving charging mode. In some special cases, the energy provided by the APU not only meets the energy demand of the vehicle, but also charges the battery with extra energy. (5) Brake energy recovery mode. When the vehicle is braked, the drive motor works in the power generation state, and the power generated is used to charge the battery. The specific parameters of EREV are list in Table 1.
APU
Motor
Engine
Generator
Mechanical Electrical
Battery
Fig. 1. Powertrain architecture of the studied EREV
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Journal Pre-proof Table 1 The EREV parameters Component
Parameter Name
Value
Unit
EREV
Curb weight
14500
kg
Frontal area
7.5
m2
Air drag coefficient
0.73
—
Air density
1.2
Kg/m3
Wheel radius
0.484
m
Rolling resistance coefficient
0.008
—
Final drive ratio
6.17
—
Rated power
96
kW
Maximum speed
3000
r/min
Rated power
75
kW
Maximum speed
3500
r/min
Capacity
120
Ah
Voltage range
550
V
Rated power
115
kW
Peak torque
540
Nm
Engine Generator Battery Drive Motor
2.2 Main component model 2.2.1 Vehicle Longitudinal Dynamics According to the dynamic equilibrium relation of the vehicle, the power Pwh acting on the wheel can be expressed as
1 Pwh mv fmg cos a Cd Af v 2 mg sin v 2
(1)
Where m is the vehicle mass, g is the gravity acceleration, f is the rolling resistance coefficient, ρa is the air density, Cd is the air dynamic drag coefficient, Af is the bus frontal areas, α is the road angle, v is the vehicle speed. The relationship between traction motor demand power Pd and wheels power Pwh is as follows：
Pwh , Pd tm ( P P ) , wh m br t m
Pw 0
(2)
Pw 0
Where ηt is the drive-line efficiency, ηm is the efficiency of the driving motor, Pm-br is the power of the mechanical braking force.
2.2.2 APU model The optimal fuel consumption curve of APU is obtained by bench test. The bench test and optimal fuel consumption curve are shown in Fig.2 and Fig.3, respectively. Therefore, the functional relationship between APU fuel consumption quality and APU power is defined:
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m f be
Papu
t 1000 3600
(3)
Where be is the APU optimal fuel consumption rate, which can be obtained from Fig.3. Fuel consumption meter
Battery
Engine
Generator Dynamometer
Generator controller
Fig. 2. APU test bench for fuel consumption
Fig. 3.Optimal fitting curve of fuel consumption rate related to APU power
2.2.3 Battery model For simplification, most studies used Rint model to model batteries and obtained reliable accuracy[39-40]. The output current of battery Ib can be calculated by Ohm's law,
Ib
Voc (soc) Voc2 (soc) 4 Pb Rb (soc) 2 Rb (soc)
(4)
Where Voc and Rb are the open circuit voltage and internal resistance of the battery, respectively, and both of them are related to SOC. Pb is the battery power, Qb is the nominal capacity of the battery.
soc soc0 6
Ib dt Qb
(5)
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soc
Voc (soc) Voc2 (soc) 4 Pb Rb (soc) 2Qb Rb (soc)
(6)
A number of tests were conducted to obtain the characteristic parameter of battery cell at ambient temperature 25℃. Fig.4 shows the open circuit voltage (Voc) curves as a function of SOC. Fig.5 shows the discharge resistance (Rb) curve as a function of SOC.
Fig.4. Battery cell open circuit voltage curves as a function of SOC at 25℃
Fig.5. Battery cell resistance curves as a function of SOC at 25℃
3. Optimal control problem description Since EREV has two power sources, the core problem of the energy optimization is how to distribute the energy between APU and power battery reasonably to satisfy the energy requirement of the vehicle.
Pd (t) Papu (t) Pbat (t)
(7)
In this paper, the fuel economy is taken as the optimization objective, and the performance function is as follow: 7
Journal Pre-proof J min m f u t dt tf
t0
(8)
f is the instantaneous fuel consumption quality. The control Where u(t) is the control variable, m variable and state variable are set to:
x(t) SOC (t) u (t) Papu (t)
(9)
Considering the actual operation characteristics of EREV, the components need to work within a reasonable range, so the operation status of the engine, motor and battery should be constrained,
m,min m (t ) m,max T m,min Tm (t ) Tm,max e,min e (t ) e,max Te,min Tm (t ) Te,max SOCmin SOC (t ) SOCmax
(10)
where, ωm,min and ωm,max are the minimum and maximum speed of the generator, ωe,min and ωe,max are the minimum and maximum speed of the engine, Tm,min and Tm,max are the minimum and maximum torque of the generator, Te,min and Te,max are the minimum and maximum torque of the engine, SOCmin and SOCmax are the minimum and maximum limits of the SOC.
3.1 Pontryagin's minimum principle PMP is a classical analytical method for solving optimal control problems. The Hamilton function of the above optimal control problem is:
H SOC (t), u t , t m f (u(t)) (t) SOC(t)
(11)
According to the PMP, the optimal control is obtained by finding the minimum value of the Hamilton function,
u * (t) argminH soc t , u t , t
(12)
Where λ(t) is the co-state. They can expressed as follows:
SOC t
H f SOC t , Pbat t
t
H SOC SOC SOC
(13)
(14)
As shown in Equation (6), the value of SOC is related to Voc(soc) and Rb(soc). Fig.4 and Fig.5 show that the Voc and Rb are almost constant when the SOC is between 0.3-0.9. Therefore,
t
SOC 0 constant SOC
(15)
From the above derivation, when the driving cycle is known, the co-state λ is constant, namely, λ=λ0. Some studies shows that λ is mainly affected by the driving cycles, the driving conditions and the initial value of SOC. Since PMP is a global optimization algorithm, the calculation time is too long to be realized online. So, the ECMS is often used in practice. In fact, ECMS can be derived from the PMP. The equivalent fuel consumption meqv(t) consists of the actual fuel 8
Journal Pre-proof f (t) and the nominal fuel consumption me(t): consumption m
f (t) s(t) m e (t) m f (t) s(t) meqv (t) m
Pb (t) Qlhv
(16)
where s(t) is the equivalent fuel consumption factor (EF), reflecting the conversion relationship between the chemical energy of the fuel and the electrical energy of the battery, the value of which is crucial for achieving optimal power distribution between the engine and the battery. Further, the (16) can be written as:
f (t) s(t) meqv (t) m
SOC (t) Voc (t) Qb Qlhv
(17)
The relationship between the s(t) and the λ can be easily obtained by (11) and (17)
s (t)
Qlhv QbVoc
(18)
3.2 EF optimization 3.2.1. Bounds of the EF In order to achieve better optimal performance of ECMS, the initial value of EF is especially critical. At present, the Shooting Method is widely used to solve the EF. This method first guesses a value of initial co-state, and then calculates the terminal SOC according to formula (11)-(14). If the terminal SOC is equal to the constraint value (or the difference between them is small), then the guess is considered. If it is not equal, the initial guess value is changed, and the above process is repeated until the terminal constraints is satisfied. It can be seen that the key to solve the EF by the shooting method depends on the reasonable guess of the initial value or the initial range. However, it is difficult to estimate the initial range in the actual calculation process. In order to solve the above problems, an improved shooting method is proposed in this paper, which can predetermine the EF bounds and greatly reduce the calculation time. The specific methods are as follows: (1) Lower bound for EF Considering the law of conservation of energy
E fuel Ebat Ed Eloss
(19)
where Efuel and Ebat are the fuel energy and battery energy consumed during the trip, respectively. Ed and Eloss are the required energy and dissipated energy for finishing the trip, respectively. In order to reduce energy loss during the trip, Eloss should be the smallest,
arg min Eloss arg min E fuel Ebat Ed arg min
P tf
0
fuel
Pbat Pd dt
Since Pd is known at each moment, so
9
(20)
Journal Pre-proof arg min arg min
tf
0
tf
0
P
fuel
m
fuel
Pbat dt
Qlhv Pbat dt
(21)
t f 1 arg min m fuel Pbat dt 0 Qlhv In order to obtain the minimal instantaneous power, the cost function of ECMS should be
J m fuel
1 Pbat Qlhv
(22)
Comparison of (16) with (22) shows
s 1
(23)
From the above derivation, the optimal s can be obtained. However, the above derivation process does not consider the SOC limit, so the optimal value may not be suitable. Simulations show that when s=1, the battery SOC quickly reaches its minimum limit SOCmin. When s<1, the discharge rate of the battery is higher compared with s=1 , and its instantaneous fuel economy is no longer optimal. Therefore, the optimal s should be equal or higher than 1, depending on the actual driving cycle.
s* s min 1
(24)
(2) Upper bound for EF From the previous description, The EREV has five working modes, which can be represented by control space Γ .
u fuel , ubattery , uhybird , uch arg e , ubrake
(25)
where ufuel, ubattery, uhybird, ucharge and ubrake are the five working modes: APU working only mode, battery working only mode, hybrid drive mode, driving charging mode and brake energy recovery mode, respectively. When Pd ≤ 0 , the vehicle is in braking energy recovery mode, and the vehicle can absorb the braking energy as much as possible as long as the SOC does not exceed its maximum limit. So the EF is only related to the case of Pd>0. When Pd>0, the vehicle will work in one of three modes: APU working only mode, battery working only mode, or hybrid drive mode. At this time, the ECMS needs to find the optimal control mode to reduce the cost function (16).
u * u fuel or ubattle or uhybird
(26)
Now, if u*є{ufuel}, the optimal ECMS can be described by
ECMS u fuel m fuel
(27)
sPbat Qlhv
(28)
Similarly, if u*є {ubattery }
ECMS ubattery and, if u*є {uhybird }
ECMS uhybird m fuel 10
sPbat Qlhv
(29)
Journal Pre-proof If the s is large, u* tends to{ufuel }; when sis infinite, the vehicle will always work in fuel only mode, and the fuel economy is no longer optimal. Therefore, the upper bound of s need to be restricted. Thus, the battery only mode or the hybrid drive mode may have the lowest system energy consumption,
ECMS ubattle ECMS u fuel ECMS uhybird ECMS u fuel
(30)
The above inequality will yield two upper bounds: smax1 and smax2, then the optimal upper bound will chooses smax= min{smax1, smax2}. However, even if only one of the above inequality is solved, then the value is also met. The first inequality in (30) gives
Papu s*
m fuel Qlhv
Pbat
apu Pem
embat
Pd / trs
smax1
apu em bat Pd / trs apu embat
(31)
where ηtrs ，ηapu ，ηem ，and ηbat are the efficiencies of the transmission, APU, motor and battery, respectively. The second inequality in (30) gives
s*
m fuel (u fuel ) m fuel (u hybird ) Pbat / Qlhv
Pd / trs smax 2
apu
Pd / trs Pem (u hybird )
apu Pem (u hybird )
(32)
embat The Pd and Pem in (32) change with the driving cycle, so they cannot be eliminated. The specific value of smax2 cannot be determined. Fortunately, as mentioned previously, the upper bound of s only needs to satisfy one of the inequalities. Thus, the upper bound of s is
s* smax1
embat apu
(33)
In summary, for the EREV powertrain shown in Fig. 1, the optimal EF bounds are
1 s*
embat apu
where the value of ηapu，ηem，and ηbat are ηapu=27.63%, ηem=92.72% and ηbat=98.45%.
11
(34)
Journal Pre-proof 3.2.2 Improved shooting method The flowchart of the calculation of EF is shown in Fig. 6. First, the range of EF is obtained according to the above calculation. Then, the Secant method [30] is used to search the optimist EF in each shooting process. Last, the terminal SOC is obtained according to formula (11)-(14). If the terminal SOC is equal to the constraint value (or the difference between them is small), the EF is considered. If not, repeat the above process and re-optimize until the terminal constraints are met. Start
1 s*
embat apu
smin smax ，i=1 2 s2 =s1 +，i 2 s1
si si 1
SOCi 1 SOC f SOCi 1 SOCi 2
(i 1 i 2 )
i 3,4
Discrete control variables
Papu 0 : Papu : Papu _max
Papu * (t) argminH SOC t , u t , t SOC t f SOC t , Pbat t SOC t SOC Qlhv s (t) Q V b oc
t tf
N
Y N
SOC (t f ) SOC f Y
End
Fig.6. Algorithmic flowchart of the improved shooting method
4. Adaptive energy management strategy 4.1 Standard-ECMS In standard ECMS, the EF is constant. In fact, EF has a very close relationship with the driving conditions. For a certain driving cycle, the initial value of EF can effectively maintain the SOC, but under other driving cycles, the trajectory of the SOC may be uncontrolled and completely deviate from its normal working range. As shown in Fig. 7, under the same initial value, SOC can be well maintained around 0.3 in Chinese typical urban cycle, while in UDDS and US06 cycles, the SOC continue to decline. This is mainly because the characteristics of UDDS and US06 cycles are different from Chinese typical urban cycle. Therefore, in order to enable the ECMS-based control strategy to be implemented online, it is necessary to solve the adaptability of the SOC maintenance under different driving cycles. In order to find out the causes of these differences and reveal the intrinsic working mechanism 12
Journal Pre-proof of ECMS, three scenarios are set up to simulate the performance of EREV, the simulation is implemented in Matlab/simulink. These scenarios have the same speed trajectory, but different altitude profiles: No Grade, Downhill, and Uphill. The speed trajectory, downhill and uphill are shown in Fig. 8, respectively. Constant EF is adopted in the simulation process, the value of which is 2.8. Table 2 shows the equivalent fuel consumption, terminal SOC, APU start-stop times and the proportion of working time of each mode. It can be seen from Table 2 that under the uphill, the hybrid drive mode, the driving charging mode and the APU driving mode have a relatively high proportion; under the downhill, the brake recovery mode has the highest proportion, and the battery independent driving mode take the highest proportion under the no grade.
Fig.7. The same EF corresponds to the SOC curves in different driving cycles.
As shown in Table 2, the terminal SOC and equivalent fuel consumption are different under different road gradients. In the uphill, the equivalent fuel consumption is much higher than the other two conditions, and the terminal SOC is the lowest. The specific reasons are as follows: on the one hand, APU start-stop more times in the uphill, which result in higher instantaneous fuel consumption; on the other hand, the fixed EF restricts the optimal distribution of energy. When going uphill, the battery should be discharged to assist the APU to drive the vehicle together. However, due to the EF causes the actual SOC to follow the reference SOC, forcing the battery to charge at some uphill points, which results in the APU working at the maximum power and the fuel consumption increasing. In downhill, fuel consumption is slightly higher than that of no grade. The reason is: when going downhill, the vehicle should work in braking energy recovery mode. However, due to the limitation of fixed EF, the battery is forced to discharge at some downhill points, resulting in the waste of energy. From the results in Table 2, two viewpoints are obtained: one is that the terminal SOC is quite different from the ideal value; the other is that the ramp information is not used in the process, and the equivalent fuel consumption is quite different. Therefore, it is necessary to adjust EF in real time according to actual road conditions to obtain the best fuel economy. Through the above analysis, the internal operation mechanism of ECMS can be obtained:1) The initial value of EF is a key parameter affecting ECMS performance. when EF increases, the battery tends to charge; when EF decreases, the battery tends to discharge. 2) ECMS achieves 13
Journal Pre-proof optimal fuel economy by adjusting the reasonable energy distribution of the APU and power battery. The energy distribution of the APU and the power battery is specifically reflected by the proportion of the working time of the five working modes of EREV. The higher the ratio of working time of the brake recovery mode and the battery independent driving mode, the better the fuel economy of EREV.
(a)
(b)
(c) Fig.8.Velocity and topographical profile.(a) Velocity trajectory. (b) Downhill. (c) Uphill
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Journal Pre-proof Table 2 Performance of ECMS for different topographical profile with s(t)=2.8 Parameters Equivalent fuel consumption [L/100KM]
No Grade
Downhill
Uphill
25.25
27.12
33.36
Final SOC
0.56
0.52
0.45
APU ON/OFF times
82
98
176
Regenerative brake
25.32%
28.41%
20.18%
Hybrid driving
15.25%
16.82%
19.52%
Driving charging
20.15%
18.32%
22.26%
Battery driving only
27.12%
24.86%
19.81%
APU driving only
12.16%
11.59%
18.23%
4.2 Adaptive-ECMS Based on the previous analysis, this paper proposes an online optimization energy management strategy based on ECMS. The structure is shown in Fig.10. Firstly, the global position system (GPS) and geographic information system (GIS) are used to obtain the driving information in the future time domain, such as traffic lights, speed limit information and road gradient, etc., which can be utilized in the energy management strategy. Taking the road gradient as example, if it is known that the vehicle is going to be in the uphill condition, the energy management strategy will make the power battery store as much energy as possible to improve the power during the climbing process. When the vehicle is about to be in downhill condition, even if the SOC is lower than the reference value, no additional APU power is needed for charging, because the upcoming downhill condition can improve SOC through energy recovery. Secondly, the improved shooting algorithm is used to solve the initial EF. Then, based on the predicted upcoming speed and road topographical profile, the EF is periodically updated. In order to select the appropriate period, several experiments were conducted to evaluate the impact of the updating period on the terminal SOC. As shown in Fig.9, both 200m and 300m meet the SOC maintenance performance, and the updating period is shorter, the terminal SOC maintenance performance is better. In order to balance computational cost and performance, the updating period is chosen to be 300m. Finally, the optimal control variable, namely Papu, is calculated by ECMS at each time step.
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Fig. 9.The terminal SOC value affected by the EF updating period Runs periodically
GIS
GPS
Driving cycle predicted Improved shooting method s(k) Pd
A-ECMS
SOC
Pb_cmd Papu_cmd
Battery
Pb
Wheel
APU
Engine
Generator
AC/DC
Motor dive system
Papu
Wheel
Fig.10.Structure of the proposed energy management strategy
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Journal Pre-proof 5. Simulation and verification 5.1 Control Performance In order to verify the control effect of the energy management strategy proposed in this paper, Rule-based control strategy, power following control strategy and DP are used for comparison. The simulation is implemented in Matlab/simulink. Fig. 11 shows the SOC trajectory curves of the three control strategies under Chinese typical urban cycle. It shown that under rule-based control strategy, the SOC trajectory is between 0.25 and 0.35, showing a variation pattern of the zigzag shape. The SOC curve of rule-based and power following control strategy have a large variation range, and the terminal SOC cannot be guaranteed to reach 0.3. The proposed strategy can maintain SOC near the reference SOC, which is due to the real-time update of the EF. As shown in Fig.12, the variation range of EF is 1-3.5, and it is updated every 300m. When the battery SOC decreases, the EF increases, trying to promote SOC and keep it near 0.3; When SOC increases, the EF decreases, trying to make SOC decrease and keep it near 0.3. At the beginning of the journey, the SOC curve rises and gradually deviates from the reference value (0.3). When the vehicle runs to about 300m, the EF decreases from 2.7 to 1.8, which prevents the SOC from rising. Then the SOC curve began to decline. In order to prevent the continuous decline of SOC and keep it near 0.3, the EF increased from 1.8 to 3.4 between 600m and 1500m. It can be seen that the battery SOC can be maintained near 0.3 through the adjustment of the EF. It also can be seen that the SOC working range based on the proposed strategy is much narrower than the former two strategies. This indicates that the battery is in shallow charge and discharge, which is beneficial for improving the working efficiency and prolonging the durability of the battery.
Fig.11.SOC trajectory curves of three control strategies under Chinese Typical Urban Conditions
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Fig.12. Trajectory of the EF
Fig. 13 shows the power-time curves of each component under Chinese typical urban conditions. In order to clearly see the details of the power curve, only part of the trajectory segment is intercepted here. It is easy to find that all three control strategies have realized the designed control logic. The output power of the rule-based control strategy is basically maintained at the maximum efficiency point after APU start-up. Under the power following control strategy, the APU output power follows the required power all the way. Different from the above two control strategies, the proposed is relatively intelligent. It usually chooses to start the APU when the demand power is large, and once the APU starts, it will quickly transfer to its maximum efficiency point. This feature is similar to the DP algorithm. Therefore, the proposed has higher energy distribution efficiency.
(a)
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(b)
(c) Fig.13.Comparison of component powers of three control strategies in Chinese typical urban cycle:(a)rule-based control method, (b) power following control method, (c) the proposed method
5.2 Fuel economy comparison In order to verify the fuel economy of the proposed control strategy, two other cycles are simulated, namely, Beijing urban bus cycle and new European driving cycle (NEDC). Because the terminal SOC of the four control strategies are different, it is impossible to directly evaluate the fuel consumption of the vehicle. In order to evaluate the fuel economy fairly, it is necessary to modify the impact of the terminal SOC. Then, the relative fuel consumption efficiency is calculated.
FC FCopt FCopt
100%
(35)
where, FC is the fuel consumption of the each strategy, FCopt is the optimum which is calculated by DP, from the four strategies. The smaller the η, the better the economic performance of the control strategy. Table 3 and Fig. 14 show the comparison of 100 km fuel consumption between four control strategies under the three driving cycles after the modification of terminal SOC. Obviously, the fuel economy of A-ECMS is better than that of rule-based and power following control strategy. Compared with the rule-based control strategy, the A-ECMS can lower6.9% in Beijing urban bus cycle, 4.7% in Chinese typical urban cycle, and 7.8% in NEDC. Compared with the power 19
Journal Pre-proof following control strategy, the A-ECMS can lower4% in Beijing urban bus cycle, 7.5% in Chinese typical urban cycle, and 3.1% in NEDC. Table 4 shows the average working efficiency of engines and power batteries under different control strategies. It can be seen that under the rule-based control strategy, the engine has high working efficiency, but the battery efficiency is low. The power following control strategy can improve the average charging and discharging efficiency of the battery, but the APU working efficiency is reduced a lot. In contrast, the A-ECMS has higher engine efficiency and average charge-discharge efficiency, which would contribute to its fuel economy. In addition, Table 3 and Fig. 14 also show the off-line optimum value (DP) under each driving cycle. It found that the A-ECMS is almost the same as the DP. The biggest difference occurs in Chinese typical urban cycle, only 2.4%. Table3 Fuel economy comparison of different control strategies Cycle
Control strategies
Fuel consumption(L/100km)
Terminal SOC
Beijing urban bus cycle
Rule-based
32.6
0.326
7.9%
Power following
31.7
0.324
5.0%
A-ECMS
30.5
0.312
1.0%
DP
30.2
0.300
0
Rule-based
27.1
0.296
7.1%
Power following
27.8
0.321
9.9%
A-ECMS
25.8
0.308
2.4%
DP
25.3
0.300
0
Rule-based
30.1
0.326
8.9%
Power following
28.9
0.312
4.2%
A-ECMS
28.1
0.298
1.1%
DP
27.8
0.300
0
Chinese typical urban cycle
NEDC
Table4 Average operating efficiency of engine and battery under different control strategies APU Cycle
Battery
Control
Power
Average
strategies
generation
efficiency
Discharge energy（kWh）
（kWh） Beijing urban bus cycle Chinese typical urban cycle
NEDC
Rule-based
Charging
Charge and
energy
discharge
（kWh）
efficiency
72.35
33.28%
54.34
61.24
90.53%
67.23
30.75%
13.25
14.73
93.21%
A-ECMS
69.15
33.58%
31.25
33.56
94.15%
Rule-based
90.13
33.12%
48.23
59.32
83.32%
84.23
32.15%
39.06
42.32
87.10%
A-ECMS
85.24
33.45%
44.35
51.23
87.88%
Rule-based
79.25
33.78%
29.36
35.51
86.65%
75.36
32.81%
27.36
32.54
88.42%
76.65
33.72%
28.45
33.12
88.96%
Power following
Power following
Power following A-ECMS
20
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Fig.14.Comparison of fuel consumption per 100 kilometers under different control strategies
5.3 Real-time performance In order to show the advantages of real-time performance of the proposed control strategy, two other adaptive control strategies were introduced for comparison, namely, PID-ECMS and Shooting method-ECMS (S-ECMS). 1）PID-ECMS：Through the PID control, the EF is adjusted in real time to make the actual SOC follow the reference SOC. For simplicity, this paper does not discuss the PID-ECMS, detailed information can be found in [21]. 2）S-ECMS: This method is basically the same as A-ECMS, the only difference is that a traditional shooting method is used instead of the improved shooting method. The downhill scenario in Fig.8(b) is taken as the simulation cycle, and the results are shown in Fig.15. In Fig. 15, the SOC trajectory of A-ECMS decreases significantly before the slope arrives. After entering the ramp, the braking energy is recovered as much as possible so that the SOC reaches its maintenance value. However, the PID-ECMS cannot predict the upcoming slope, and the PID control keeps the SOC closely following the reference SOC. When entering the ramp, the braking energy rarely charges the battery, and most of it is dissipated by the mechanical brake. So, most of the energy is completely wasted. Although S-ECMS can predict future slopes like A-ECMS, the tradition shooting algorithm takes longer time and its SOC trajectory cannot quickly follow the change of driving conditions. As shown in Fig 15, the SOC trajectory of S-ECMS even exceeds the lower limit of the battery, which may cause damage to the health of the battery. The fuel consumption of the three methods is shown in Table 5. It is shown that the proposed A-ECMS performs substantial fuel reduction than PID-ECMS, which signifies that future road information plays an important role in achieving good fuel economy. Hence, it can be concluded that A-ECMS is slightly better than the S-ECMS.
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Fig.15. SOC trajectories in the presence of road grade Table 5 Fuel consumption of the three strategies Initial SOC
Terminal SOC
Fuel Consumption/kg
PID-ECMS
0.7
0.72
1.55
29.1%
S-ECMS
0.7
0.71
1.29
7.5%
A-ECMS
0.7
0.69
1.23
2.5%
Fig. 16 shows the computational time to update the EF every 300m, using the tradition shooting algorithm and the improved shooting algorithm, respectively. It shows that the calculation time of the tradition shooting algorithm is much longer than that of the improved shooting algorithm. This is because the improved shooting algorithm has calculated the EF range in advance, so the initial value of the EF can be quickly obtained. However, the tradition shooting algorithm does not know the range and needs continuous trial and iteration. Since S-ECMS needs more time to update the EF, its adaptability is not as good as A-ECMS. Once the calculation time is longer than the time for the vehicle to travel 300m, the EF can not to be updated in time, thus affecting the energy allocation. Therefore, the S-ECMS strategy may have real-time problems in some cases.
(a)
(b)
Fig.16. Computational time for updating EF using two strategies.(a)S-ECMS.(b)A-ECMS 22
Journal Pre-proof 6.Conclusion In this paper, an improved shooting algorithm is proposed and an adaptive real-time optimization energy management strategy is designed for an EREV. The specific work is as follows: (1) To quickly calculate the initial value of the EF, an improved shooting algorithm is proposed, which can determine the range of the EF according to the power configuration parameters(APU efficiency, battery efficiency, generator and its controller efficiency) of the vehicle. In addition, the internal operation mechanism of the ECMS is revealed from the perspective of energy flow, and the working relationship among the five working modes of EREV is clarified. The higher the ratio of working time of the brake recovery mode and the battery independent driving mode, the better the fuel economy of EREV. (2) An adaptive online optimal energy management strategy is proposed. This strategy uses the improved shooting algorithm to quickly calculate the initial value of the EF and updates the EF periodically based on the GPS and GIS, to achieve the effective maintenance of SOC. Then the optimal power allocation of APU is obtained. (3) The proposed energy management strategy is simulated and analyzed, and the effectiveness of the designed control strategy is verified. In order to verify the adaptability and fuel economy of the proposed control strategy, a detailed comparison with the rule-based control strategy and the power following control strategy is carried out. The results show that the strategy proposed in this paper has better control effect both in fuel economy and in robustness of SOC control. In addition, in order to reflect the advantages of the proposed control strategy in real-time performance, PID-ECMS and S-ECMS are choose to make comparison, respectively. The simulation results show that the fuel economy of A-ECMS is better than PID-ECMS, and the real-time performance is better than S-ECMS. At present, for family cars, their daily driving situation is random, and long-term prediction of driving conditions is difficult to achieve. But in the near future, with the rapid development of intelligent transportation, the real-time road information and environmental changes of the driving cycle will be timely fed back to the vehicle controller. Combined with the above information, the control strategy proposed in this paper can be applied to more complex scenarios.
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Journal Pre-proof Author contributions:
Ye Yang: Conceptualization, Methodology, Software, Investigation, Writing - Original Draft. Youtong Zhang: Validation, Formal analysis, Supervision. Data Curation. Jingyi Tian: Validation, Formal analysis, Writing - Review & Editing. Tao Li: Resources, Writing - Review & Editing, Software.
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Declaration of interests ☑The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: