Design of an integrated energy management strategy for a plug-in hybrid electric bus

Journal of Power Sources xxx (xxxx) xxx

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Design of an integrated energy management strategy for a plug-in hybrid electric bus Likang Fan a, Youtong Zhang a, *, Haishi Dou a, Runnan Zou b a b

Low Emission Vehicle Research Laboratory, Beijing Institute of Technology, Beijing, 100081, China National Engineering Laboratory for Electric Vehicles, Beijing Institute of Technology, Beijing, 100081, China

H I G H L I G H T S

� The boundary of mode switching and shift schedule are extracted by dynamic programming. � A proportion-integration algorithm is used to modify equivalent fuel consumption algorithm. � An integrated energy management strategy for online application of PHEV is established. � An experiment platform for PHEV was built to verify the energy management strategy. � The results show that this approach can obvious improve economy and drivability. A R T I C L E I N F O

A B S T R A C T

Keywords: Plug-in hybrid electric vehicle (PHEV) Energy management Drivability Control strategy Equivalent consumption minimization strategy (ECMS) Dynamic programming (DP) PI algorithm

The performance of Plug-in Hybrid Electric Vehicle (PHEV) depends on the energy management strategy (EMS). An optimal EMS guarantees the maximum use of the energy through electric power grid, coordinates power output of main power sources and exerts comprehensive advantages of both engine and motor. However, the current EMS cannot react to the dynamic driving cycles in the future and thus have a bad real-time performance. In order to solve these problems, a novel EMS based on rule-based energy strategy (RE), dynamic programming algorithm (DP) and equivalent fuel consumption algorithm (ECMS) is proposed. First, DP is used to extract the boundary of mode switching and shift schedule under three typical driving cycles in offline, especially, RE is corrected using the boundary of mode switching. Second, an instantaneous optimization strategy-ECMS is used to replace the Charge-Depleting Mode (CD) of RE for finding the real-time optimal solution in a wider range in online, in this part, owe to the fixed distance of urban public transport, a reference State of Charge (SOC) is formulated, and the Proportion-Integration (PI) algorithm is used to make the actual SOC always follow the reference SOC by adjusting the equivalent factor. Finally, combine all the above efforts, a real-time optimization EMS is proposed and validated through simulation and experiment. The results show that this approach can significantly enhance the vehicle drivability, with overall obvious improvement of the comprehensive perfor­ mance qualification based on both fuel economy and drivability.

1. Introduction PHEV is a derivative of hybrid electric vehicles. Its performance is between pure electric vehicle and conventional hybrid electric vehicle, and it is equipped with large motor power and battery capacity, so it can realize diversification of energy drive and reduce vehicle’s dependence on internal combustion engine [1,2]. Especially for urban buses with fixed routes, PHEV can give full play to its advantages of energy diver­ sification. The main characteristics of urban bus driving conditions are

that part of the driving conditions are known (such as traffic lights, stations, etc.), the average speed is low, the distance between stations is short, the number of in-situ start and stop is more, and the idle time of engine is longer than that of general vehicles. According to the working conditions of urban buses, PHEV can combine the advantages of motor and engine and the characteristics of known path information to opti­ mize the EMS and improve the efficiency of engine operation. At the same time, the vehicle has the advantage of high torque reserve of power system at low speed, which can achieve the purpose of frequent start and

* Corresponding author. E-mail addresses: [email protected] (L. Fan), [email protected] (Y. Zhang), [email protected] (H. Dou), [email protected] (R. Zou). https://doi.org/10.1016/j.jpowsour.2019.227391 Received 17 September 2019; Received in revised form 25 October 2019; Accepted 31 October 2019 0378-7753/© 2019 Elsevier B.V. All rights reserved.

Please cite this article as: Likang Fan, Journal of Power Sources, https://doi.org/10.1016/j.jpowsour.2019.227391

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stop, and also has the function of braking energy recovery [3–5]. The principal control strategy of PHEV is termed as “energy man­ agement strategy (EMS)” which has a significant impact on PHEV fuel efficiency while ensuring the optimal control of engine, battery, and engine state and shifting. The EMS for PHEV has been studied by using various control methods, which can be classified as rule-based EMS (RE) and the optimization-based EMS [6,7]. RE has been widely used because of its less computational burden and better robustness. However, because the RE with deterministic rules from practical engineering experience can not adapt to different driving conditions, it brings bad fuel consumption performance. In recent years, more attention has been paid to the optimal control rules regarding engine optimal operating points and offline optimization strategy extraction [8]. For example, some researchers proposed fuzzy logic rules to enhance the adaptability of RE to driving conditions [9,10], others used the global optimization methods including dynamic programming algorithm (DP) [11], genetic algorithm (GA) [12], particle swarm optimization (PSO) [13] to extract the operating points of the engine under different driving conditions offline to further optimize the control rules. For example, Peng [14] proposed a recalibration method to improve the performance of the RE through the results calculated by DP algorithm. Zhen [15] used DP to find the optimized power optimization rules of engine and motor, which were used to design fuzzy logic controller considering SOC balance and driving pattern identification. Zhang [16] used a fuzzy logic algorithm to identify and classify the typical cycle conditions, and then used DP algorithm to get the suboptimal control strategy under different condi­ tions. Chen [17] used the PSO algorithm to optimize the threshold pa­ rameters of the RE under a certain driving cycle. Li [12] presented an enhanced GA to solve the multi-objective optimal energy management problem. In contrast, the parameters tuned by global optimization al­ gorithms are better than those deterministic rules. However, the global optimization algorithm has a large computational burden and this method is only beneficial to the vehicles running on a fixed route. Once the route changes or the working conditions are unknown in advance, it is not applicable. To solve the above problems, driving pattern recog­ nition have recently been put forward in the literature [16,18], Zhou [19] not only gives a comprehensive analysis and review of existing driving pattern recognitions but also indicates suitable application sce­ narios for each prediction algorithm and summarizes potential ap­ proaches for handling the prediction inaccuracies. Besides, considering the time consuming of DP, if the computing time can be controlled within a reasonable range, it is helpful for online operation. Model predictive control (MPC) [20,21] uses some prediction models including typical Markov chain [22,23], neural network [24], exponential model [25] and Kalman filter [26] to predict the velocity curve in a relatively short period of time in the future, and uses some optimization methods mainly including quadratic programming [27], nonlinear programming

[28], Pontryagin’s minimum principle [29], and stochastic DP [30] in this area to distribute the energy distribution of engine and motor reasonably. Zhang [31] built up a MPC scheme for plug-in HEV with a hybrid energy storage system, the results show that the proposed control strategy can promote fuel economy effectively. Li [32] combined MPC and modified PSO algorithm to improve braking energy recovery effi­ ciency. However, it is still an open problem to choose the appropriate prediction model and prediction time domain. For real-time optimization control, the equivalent consumption minimization strategy (ECMS) which based on Pontryagin’s minimum principle is the representative methods. Similar results of DP can be achieved by setting the equivalent factorsðtÞreasonably. In order to obtain accuratesðtÞ, many scholars have presented improved methods. The variation of equivalent factors under different driving conditions is analyzed in literature [33], but this method needs a lot of accurate prediction. Kessels [34] used fuzzy control-based ECMS to deal with the complex relationship between fuel economy and the SOC. Zhao [35] used the fuzzy tuning method that combines the expert human knowl­ edge and experience using comprehensible linguistic rules to control the diesel HEV. However, the accuracy of this method depends on the knowledge and experience of the expert. Aiming at this problem, C. Musardo [36] proposed an adaptive equivalent consumption minimi­ zation strategy (A-ECMS) based on the driving condition. However, only a local optimized result rather than the global one can be obtained. So these strategies are not appropriate to be directly applied to a PHEV due to its own limitations. To make online optimization feasible, many advanced intelligent algorithms, such as game theory (GT) [37], and reinforcement learning (RL) [38], have been proposed to settle the EMS. Zou [39] used the RL to optimize the control strategy for the hybrid tracked vehicle, the simulation results indicated the proposed EMS can significantly improve fuel efficiency and be applied in real-time. Xiong [40] compared the performance of RL and RE, and the simulation results showed the RL strategy can lessen the energy loss effectively. However, the transition probability matrix in the RL algorithm cannot be imme­ diately updated online, thus, the robustness of this strategy cannot be guaranteed for different driving conditions. These optimization methods have been well studied in the related works, among which, however, there is hardly any research to assemble the advantages of both global and instantaneous optimization methods as well as to avoid the disadvantages of them. For computational burden, Global optimization solutions are hard to be implemented in real-time applications. ECMS is the only implementation in real-time but as an instantaneous optimization method, cannot make full use of available information as global optimization processes. And it should also be concerned that fewer variables and constraints are beneficial for the reduction of the computational burden in the control unit. Consid­ ering these and combine the characteristics of urban public transport road operation, an integrated EMS presented in this paper. The RE strategy is used as the framework, in which the mode switching and shift schedule that have obvious influence on the drivability are obtained offline by global optimization algorithm (DP) from three typical driving cycles. Further, these parameters, which make the decision of engine start/stop and shift, are employed as known quantities in the EMS directly, further decreasing the computational burden. Especially, in the blend part of the RE strategy, a modified ECMS with an entire-process SOC reference is employed by the online optimization in embedded control systems owing to its fewer amounts of calculations, preferable instantaneity and simple implementation. Due to the known driving path, the current SOC can be available controlled to follow the ideal SOC range by PI control method. It is worth mentioning that explicit limits of torque change between two adjacent times have been settled in this ECMS to avoid drastic fluctuations of torque as well as to improve the speed and precision of the calculation. The paper is organized as follows: PHEV model including the explanation of the steady-state maps and theories applied in the model building is described in section 2. The modified ECMS problem with

Fig. 1. Configuration of the PHEV powertrain. 2

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known path and the DP procedure for the extraction of boundary con­ dition parameters of engine state switching and shift schedule are expressed in section 3. The simulation and experiment results of the optimization of fuel consumption and drivability are given in section 4 and section 5 respectively. Finally, conclusions are presented in section 6.

Table 1 The transmission ratio of the AMT and final drive.

2. Power flow modeling

Table 2 Vehicle parameters considered.

The hybrid electric bus structure discussed in this paper has a par­ allel, single-axle topology, which utilizes a permanent magnet syn­ chronous motor (PMSM) laid before the transmission and is coupled with the engine via a clutch, as shown in Fig. 1. The battery supply energy to the PMSM or store the electricity generated from it through the drive motor control module (DMCM). Like most passenger cars of the same type, the powertrain uses a rear-drive rearrangement. By disposing the clutch between the engine and the motor, the engine power is cut off or intervened during running. The power flows from the power sources (including engine and motor) to the wheels through the automated mechanical transmission (AMT) and the final drive. The model consists of three parts, namely, the vehicle driving resistance model, the trans­ mission system model and the power system model. According to the acceleration and speed of driving cycle, the required speed and torque/ power of wheel edge can be determined by the driving resistance model. The power system model composed of motor, battery and engine can be used to calculate the change of battery power and fuel consumption.

m � g � cr

1 � ρL � cw � Af � v2f ðtÞ 2

2

3

4

5

R

Final drive

Ratio

6.11

3.82

2.17

1.47

1.00

5.89

6.20

Symbol

Parameter

Value/Unit

Te

Engine torque

Nm

Tm

Motor torque

Nm

Twh

Edge Torque

Nm

Edge angular velocity

Rad/s

Engine angular speed

Rad/s

ωEM

Motor angular speed

Rad/s

Pwh

Edge power

W

Pe

Engine output power

W

Pm

Motor output power

W

vf

Vehicle speed

m/s

m

Vehicle mass

18000 kg

Af

Vehicle lateral surface

7.5m2

cw

Aerodynamic coefficient

0.73

cr

Rolling coefficient

0.8%

ρL

Aerodynamic resistance coefficient

1.2 kg/m3

Ft

Traction resistance

N

i0

Final drive ratio

ig

AMT ratio

r

Tire radius

0.484 m

η

Driving System Efficiency

0.90

Q0 SOC IBT PBT VOC Ri VBT socCD

Maximum battery charge Battery state of charge Electric current Electric power of battery Open circuit voltage Internal resistance of battery Voltage of the load Threshold of CD mode

C

socCS

Threshold of CS mode

Vl

ωICE

Vehicle driving resistance includes air resistance, rolling resistance, ramp resistance and acceleration resistance caused by overcoming its inertia. Because the driving cycle studied in this paper does not consider the influence of gradient, the mathematical description of the resistance model is as follows and Table 2 shows the variables that appear in the following formulas. ⋅

1

ωwh

2.1. The vehicle driving resistance model

m � vf ¼ Ft ðtÞ

Gear

(1)

A W V Ω V

2.2. The transmission system model

soclow

Minimum allowable value Current speed

Km/h

The function of the transmission system model is to transfer the required speed and torque of the wheel edge to the engine and motor for calculating the power and fuel consumption. As mentioned above, the purpose of this model is to predict fuel consumption rather than to analyze the dynamic response of the system. Therefore, the dynamic characteristics of the clutch combination process and shift process sys­ tem are neglected. The model is described in detail as following formula.

Vdown

Minimum speed of starting engine

Km/h

Td

Demand Torque

N

Temin

Minimum torque of engine at current speed

N

Temax

Maximum torque of engine at current speed

N

Teopt

Optimal torque of engine at current speed

N

Tmmax

Maximum torque of motor at current speed

N

ωwh ¼

vf 3:6 � r

ωICE ¼ ωEM ¼ ωwh � i0 � ig

(3)

Twh ¼ Ft � r

(4)

Te þ Tm ¼

Twh i0 � ig � η

Pwh ¼ Twh � ωwh Pe þ Pm ¼

Pwh

η

engine is neglected, so the fuel consumption model is expressed by the nonlinear fuel consumption map measured by the engine steady-state experiment. At the same time, it is considered that the working pro­ cess of the engine is always in the warm-up state, so the influence of temperature on fuel consumption is not considered in the modeling. The engine model and motor model are built by steady-state maps. Here it is assumed that the engine has been fully warm-up, hence the engine temperature effect is not considered. The engine start/stop state variable (se ðkÞ) has been set as the representation of the engine start/ stop control. 8 engine on < 1; se ðkÞ ¼ (8) : 0; engine off

(2)

(5) (6) (7)

The automatic transmission is modeled as a ratio device with a gear number. The gear number can only take the values ofg ¼ f1; 2; 3; 4; 5gand a state model of the AMT has also been developed to represent the gear shifting.

2.3. The power system model Power system models include engine, motor and battery models. According to the quasi-static assumption, the dynamic process of the 3

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8 < gðk þ 1Þ ¼

gðkÞ þ ug ðkÞ > 5 gðkÞ þ ug ðkÞ < 1 otherwise

5; 1; : gðkÞ þ ug ðkÞ

Table 3 Revised rule-based energy management strategy.

(9)

where, gðk þ1Þ is the current gears of the AMT, and ug ðkÞ represent the shifting decision in each account step, whose values can only take the value of u ¼ {-1, 0 1} to downshift, upshift and sustaining the current gears. 8 1; downshift > > > > < ug ðkÞ ¼ 0; sustaining (10) > > > > : 1; upshift

PBT ¼ VBT ⋅IBT ¼ Voc ⋅IBT

Ri ⋅I 2BT

VBT ðSOC; IBT Þ ¼ Voc ðSOCÞ � signðIBT Þ ¼

1 1

Ri ðSOC; signðIBT ÞÞ⋅IBT

IBT > 0; IBT < 0;

CD Mode

soc > socCD j0 < Vl < Vdown j0 < Td < Temin

Tm ¼ Td; Te ¼ 0

socCS < soc < socCD &ðVl > Vdown jTd � Tmmax Þ

Tm ¼ Tmmax ; Te ¼ Td Tm

soclow < soc < socCS &Vl � Vdown

Tm ¼ Td; Te ¼ 0

soc < soclow &Teopt � Td � Temax

Tm ¼ 0; Te ¼ Td

soc < soclow &Td < Teopt

soclow < soc < socCS &Td � Tmmax

Tm ¼ Td; Te ¼ 0

Tm ¼ Td Te; Te ¼ Teopt

Tm ¼ Tmmax ; Te ¼ Td Tm

by the motor alone or mainly by the motor, the electric energy in the energy storage system decreases gradually. In this stage, the PHEV runs in the charge-depleting mode (CD Mode). When the electric energy reaches a lower level, the engine becomes the main power source. The motor regulates the engine to work in the efficient region and maintains the fluctuation of the energy storage system in a reasonable range. In this stage, the PHEV runs in the charge-sustaining mode (CS Mode). Based on the two modes described above, as shown in Table 3, a RE management is proposed and the definition of variables in Table 3 are shown in Table 2. From the above table, no matter what kinds of working conditions, a large proportion of engine operating points are located in inefficient areas. This is because in the CD stage, the main strategy is electricity. As a supplement to the motor torque, the torque of the engine can not be guaranteed to work in a more economical torque region. In the CS stage, the engine works mainly. Because of the too large randomness of the working conditions, the rules including the boundary of mode switching and shift schedule set by the RE are difficult to ensure that the engine always works with high efficiency due to the use of fixed logical thresholds which were developed from the experience of engineers. Therefore, there are two problems to be solved, one is to extract the boundary of mode switching which has a significant impact on driving performance, the other is to improve the torque distribution of the en­ gine and motor in blend drive of RE. It’s worth considering that when the vehicle’s driving distance is far beyond the pure electric driving distance, compared with the CD þ CS strategy or the EV þ CS strategy, the optimized CD mode can make PHEV get better fuel economy [41].

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V 2oc ðSOCÞ 4Ri ðSOC; signðIBT ÞÞ⋅PBT 2Ri ðSOC; IBT Þ

Torque Distribution

CS Mode

Knowing that IBT ðSOC; signðPBT ÞÞ ¼

Constraint Condition

socCS < soc < socCD &Vl � Vdown &Td � Tmmax

The detailed ratio of the transmission and final drive is shown in Table 1. The complex electrochemical reaction is involved in the battery operation. Referring to the internationally accepted modeling method, the battery model is simplified into an equivalent circuit composed of a voltage source and a resistor, regardless of the influence of temperature change on performance. At the same time, the transient process due to the existence of internal capacitance is ignored, and the characteristics of the charge and discharge process are assumed to be the same. The open circuit voltage (Voc ) is the function of battery SOC and temperature while, battery temperature is assumed to be constant. The established time-discrete model is as follows: In the battery model, the SOC is calibrated by the electric current, as shown in equation (11). Z t 1 SOCðtÞ ¼ IBT ðSOCðt 1Þ; signðPBT ÞÞ⋅dt þ SOCðt 1Þ (11) Q0 t 1

Voc ðSOCÞ

Operating Mode

(12) (13) (14) (15)

3. Design of the PHEV optimal power management approach

3.2. Parameter extraction based on dynamic programming

Because PHEV can be connected with an external power supply, the vehicle’s energy storage system can obtain additional energy from the external power grid, rather than just generate electricity by enginedriven generators. Therefore, compared with hybrid electric vehicles (HEV), PHEV usually has larger power batteries to store cheaper electric energy from external power grids. At the same time, a matched drive motor also has higher power performance to meet the demand that the motor can drives vehicle independently under most operating condi­ tions. Therefore, the core of PHEV’s EMS is to use as much electric power as possible and a good control strategy not only considers the online application, but also allocates energy reasonably. Based on this, this paper formulates a rule-based control strategy which is preferred to use electricity, in which the shift schedule and mode switching boundary with obvious influence on drivability are extracted offline by DP, and the modified ECMS strategy is adopted to replace the blend drive part of the rule-based control strategy.

RE strategy cannot make full use of the advantage of the PHEB, DP can efficiently handle the constraints and nonlinearity of a problem and find a global optimal solution. To avoid the unnecessary workload, the offline DP method has been introduced to extract the boundary of mode switching and shift schedule which need a mass of road tests to adjust the parameters conventionally for their dependence of running condi­ tions. The optimal results of DP are sensitive to the driving cycles, leading to the untruthfulness of the reflected driving performance of vehicle if only one driving cycle is adopted. In this paper, 3 typical driving cycles have been introduced to the simulation: Manhattan bus drive cycle (CYC_MANHATTAN), West vir­ ginia suburban driving schedule (WVUSUB) and China typical city drive cycle. Certainly, if the work condition has already been known, it can be applied for the extraction of the parameters directly. As shown in Fig. 2 (A) below, three different driving cycles are shown. Being a mathematic method of multilevel decision making optimi­ zation, the dynamic programming method applied in this strategy, re­ quires a reasonable discretization of driving cycle to transform the optimization of vehicle performance to the decision making of different time phase. The system model has been built to imitate the performance

3.1. Rule-based energy management strategy When the electric energy is sufficient and the whole vehicle is driven 4

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Fig. 2. Results of the DP in three driving conditions: speed profiles are shown in (A); flow diagram of DP is shown in (B); optimal mode switch boundary and gears distribution are shown in (C) and (D) respectively.

5

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of the vehicle ignoring the transient response. The whole travel is divided into N sections, with 1 s each section. The discrete-time state space model is shown as equation (16): Xðk þ 1Þ ¼ fk ðXðkÞ; UðkÞÞ þ XðkÞ k ¼ 0; 1; …; N

1

them is adopted directly here. Combining equation (24) and equation (25), the final cost function be obtained as equation (26).

k¼0

J *N 1 ðXðN

Te;min ðωe ðkÞÞ � Te ðkÞ � Te;max ðωe ðkÞÞ

(21)

Tm;min ðωm ðkÞ; SOCðkÞÞ � Tm ðkÞ � Tm;max ðωm ðkÞ; SOCðkÞÞ

(22)

SOCmin � SOCðkÞ � SOCmax

(23)

N 1 X

N 1 X

LðXðkÞ; UðkÞÞ ¼ k¼0

Δmf ðXðkÞ; UðkÞÞ

π ¼ fU * ð1Þ; U * ð2Þ; …; U * ðN

(28)

(29)

(30)

1Þg

(31)

As for the solution of the continuous nonlinear system, the common method is to discretize both the status variables and control variables to limited gridding. Specific to this parameters optimization problem, components of the state space (shown in equation (17)) can be dis­ cretized as the following showing:

εk 2 f0:3; 0:4; 0:5; 0:6; 0:7; 0:8g

(32)

gðkÞ 2 f0; 1; 2; 3; 4; 5g

(33)

se ðkÞ 2 f0; 1g

(34)

Components of the control space (shown in equation (18)) can also be discretized as the following showing: um ðkÞ 2 f

1; 0:9; 0:8; …; 0:2; 0:1; 0; 0:1; 0:2; …; 0:8; 0:9; 1g

ug ðkÞ 2 f 1; 0; 1g

(35) (36)

The flow diagram of the application of DP is shown in Fig. 2(B). Adopting the above algorithm, the boundary of mode switch and shifting schedule are obtained by inputting the 3 typical drive cycles as shown in Fig. 2 (C) and Fig. 2 (D). Fig. 2(C) shows the boundary curve of mode switch from motor only mode to engine participating mode and the opposite process can be extracted (the black full line and the black dotted line respectively). Fig. 2(D) shows the upshift curve can be extracted (the black full line) and the downshift curve can also be extracted considering the hysteretic behavior (the black dotted line).

(24)

k¼0

3.3. Modified ECMS

To embody the consideration of the vehicle drivability, a penalty function containing the engine start/stop and shifting should be added to the cost function. SðkÞ ¼ αjgðk þ 1Þ

1ÞÞ

The optimal parameters are torque split ratio and gear sequence. *

where, ωe ðkÞ is the engine speed, ωe;min and ωe;max are the idling and the maximum speed of the engine respectively; Temin and Temax are the limits of engine torque at each instant (k); Tmmin and Tmmax are the limits of motor torque at each instant (k), SOCðkÞis the current SOC of the battery; SOCmin ,SOCmax are the allowed SOC range of the battery. To solve the parameter optimization problem of the PHEV energy management, the specific fuel consumption of the engine is generally set as the global optimization goal (cost function). J¼

1Þ; UðN

½U * ðkÞ� ¼ argminJk ðXðkÞÞ

where, N is the duration of the cycle running and L is the transient cost value. To ensure every component working in a suitable range, the oper­ ating status of the engine, motor, battery and transmission have to be constricted as the following shows: (20)

1ÞÞ ¼ minLðXðN

where, J*k ðXðkÞÞ is the indicator function of the optimal performance. The optimal control variables can be solved by reverse method, which means that there is always a U* ðkÞ enabling the indicator function to be optimized in each k.

k¼0

ωe;min � ωe ðkÞ � ωe;max

(26)

(27)

SOCðNÞ ¼ 0:3

Step k (0 � k < N 1): � � J *k ðXðkÞÞ ¼ min LðXðkÞ; UðkÞÞ þ J *kþ1 ðXðk þ 1ÞÞ

(19)

LðXðkÞ; UðkÞÞ

SðkÞ k¼0

Bellman dynamic programming algorithm has been applied in this parameters achievement. Equation (28~29) give the optimization procedures: Step N-1:

Here, the optimal control problem of the PHEV energy management strategy considering drivability can be described as to find the optimal control vector (U* ðkÞ) which minimize the cost function (J). J¼

k¼0

SOCð0Þ ¼ 0:8

For single-axle parallel hybrid power systems, the input torque of the transmission is composed of the engine output torque and the motor output torque which make it possible that the power split ratio (PSR) could be replaced by the torque split ratio (TSR). Therefore, the control vector can be confirmed as: the torque split ratio (um ðkÞ) and the shifting decision (ug ðkÞ). � �T UðkÞ ¼ um ðkÞ; ug ðkÞ (18)

N 1 X

N 1 X

mf ðXðkÞ; UðkÞÞ þ

The electric energy should be made full use to ensure the overall fuel economy of the vehicle, which calls for a proper setting of the SOC in both the starting and stop points.

(17)

XðkÞ ¼ ½SOCðkÞ; gðkÞ; se ðkÞ�

LðXðkÞ; UðkÞÞ ¼

J¼

where, XðkÞis the system state vector, UðkÞis the system control vector, and its dimensionality depends on the desired accuracy. Vehicle speed of every moment can be seen as a known quantity in the offline optimization of the PHEV energy management for the process being done in known typical operation. Since the torque requirement can be calculated through the vehicle longitudinal dynamics theory, the engine torque could be determined with both the motor torque and the current gears being known. Therefore, in the situation of considering the vehicle drivability the state variables can be confirmed as: battery SOC, gears of AMT and the engine start/stop status. T

N 1 X

N 1 X

(16)

gðkÞj þ βjse ðk þ 1Þ

se ðkÞj

It can be seen from the above that the DP algorithm is only used to optimize the working range of pure electric mode. With the increase of vehicle power, the engine starts to intervene. At this time, because the RE is based on electrical control strategy, when the engine starts, the engine often works in the low efficiency range, so it is necessary to use real-time optimization strategy to rationally distribute the power of the engine and motor. To achieve real-time optimum results, HEV usually

(25)

Where, αandβare the penalty factors which have a significant influ­ ence on the result of the optimization. More details about the choice of them could be found in Refs. [42,43], and the acquisition method of 6

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Fig. 3. An Integrated Energy Management Strategy: relation between the objective battery SOC and running distance is shown in (A); an adaptive ECMS is shown in (B); torque limit method of ECMS algorithm is shown in (C).

applies ECMS or Pontryagin’s minimal principle (PMP) [44], where the PMP based on the minimal principle requires highly precise model for parameters setting, while ECMS is convenient to be adopted in PHEV and can be programmed accordingly. The objective of PHEV energy management strategy is to choose an optimal control vector [u*ECMS ðtÞu�ECMS ðtÞ] to minimize the system per­ formance cost function (JECMS ðtÞ), as the following equations shown: min JECMS ðtÞ ¼

u*ECMS ðtÞ

N 1 X � � m_ f ðtÞ þ sðtÞ � m_ m;eq ðtÞ

speed of motor once the clutch closed, which allows the energy distri­ bution rates to be replaced by torque distribution rates. As explained in the introduction, the energy distribution strategy based on partly known path developed in this paper only considers the energy distribution on the choice of control variables, while the shift schedule will be obtained through the offline DP. Therefore, the control vector is only related to engine torque and motor torque. ½uECMS ðtÞ� ¼ ½TeðtÞ TmðtÞ�T

(37)

Knowing that

t¼0

� * � uECMS ðtÞ ¼ argminJECMS ðtÞ

(39)

TeðtÞ þ TmðtÞ ¼ TdðtÞ

(38)

.

where, m_ f ðtÞis the fuel consumption of the engine, which is obtained by

(40)

The equivalent fuel consumption of the motor (m_ m;eq ðtÞ) can be ac­ quired by the following equation: 8 1 > Tmreq ðtÞ > 0 1 < η Tm ðtÞ; ω ðtÞ�⋅Tmreq ðtÞ⋅ωm ðtÞ; req m m m_ m;eq ðtÞ ¼ ⋅ (41) Qlhv > � : ηm Tmreq ðtÞ; ωm ðtÞ ⋅Tmreq ðtÞ⋅ωm ðtÞ; Tmreq ðtÞ < 0

look up the fuel consumption map, u*ECMS ðtÞis the real-time optimally local variable, m_ m;eq ðtÞis the individual equivalent fuel consumption contributions of the motor, sðtÞis the equivalent factor and is used to convert electrical power into equivalent fuel consumption. For single-axle parallel PHEV, the speed of engine is equal to the 7

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Journal of Power Sources xxx (xxxx) xxx

Fig. 4. The simulation results: the Beijing typical city bus cycle is shown in (A); the simulation analysis are shown in (B); the operating points of engine and motor are shown in (C) and (D) respectively.

8

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Journal of Power Sources xxx (xxxx) xxx

Table 4 Detailed information of Beijing typical city bus cycle.

where, Qlhv is the low calorific value of the fuel, ηm ðTm;req ðtÞ; ωm ðtÞÞis the overall efficiency of the motor, Tmreq ðtÞis the demand torque of motor, ωm ðtÞis the speed of the motor. To ensure each component working in reasonable range, the constraint condition of parts’ operating status should be created as the (20)–(23) shown. In the optimization of PHEV energy management strategy, the con­ version coefficient (sðtÞ) between electric energy consumption and fuel consumption is pivotal for the fuel economy of ECMS control strategy. A too large value ofsðtÞ, which means electric energy consumption oc­ cupies more high share in the cost function, will increase the fuel con­ sumption. Contrary to this, a too low value ofsðtÞmeans a high consumption of electric energy thus leads to a high speed of the decline of SOC. Therefore, the value ofsðtÞneeds to be optimized based on the driving condition and SOC. In the situation of unknown driving path, the setting ofsðtÞis always been conducted by looking up maps [45], but for city buses discussed in this paper, thesðtÞcan be set in EMS based on the partly known running path, the almost constant driving distance every day and the accumu­ lative total running distance during the process. The ideal range of battery SOC considered during the whole driving mileage is shown in Fig. 3(A), when the vehicle finishes the whole distance, SOC just reaches the predetermined limit. Based on this, an adaptive ECMS is proposed, as shown in Fig. 3(B). The difference between the ideal battery SOC, ob­ tained from Fig. 3(A), and current SOC is input to the PI controller, to adjust the real-time output:sðtÞ.And then the ECMS control strategy calculates the instantaneous optimal engine torque and motor torque based on thesðtÞoutput from PI controller to ensure the actual SOC following the objective SOC all the process. To conform the hardware requirement of ECMS strategy, the rapid prototyping controller (dSPACE control unit) has been incorporated in this research as hybrid vehicle control unit (HCU). In the real control system, torque require of the power system can be calculated through the percentage of the accelerator pedal (raccpel ), the maximum torque on the output shift of AMT (Tdrivetrain max ) and the current gear ratio of AMT (iAMT ). Td ¼

raccpel %⋅Tdrivetrain 100%⋅iAMT

max

Time

Distance

Average speed

Max speed

Max acceleration

1800s

6.81 km

13.6 km/h

63.8 km/ h

2.33 m/s2

Max deceleration 3.44 m/s2

in the same method, which belongs to the protection strategy of the engine and can be accomplished through the calibration in engine control logic. The maximum rise of engine torque (ΔTe;inc;max ) and the minimum decline of engine torque (ΔTe;dec;max ) can be defined as the following equation shown: � � ΔTe;inc;max ¼ max T dqInc;Lim ; TðdNInc;Lim Þ; TðdPInc;Lim Þ (45) � � ΔTe;dec;max ¼ min T dqDec;Lim ; TðdNDec;Lim Þ

(46)

where, dqInc;Lim is the maximum rise rate of cyclic fuel-injection quantity; NInc;Lim is the maximum rise rate of revolving speed; dPInc;Lim is the maximum rise rate of common rail pressure; dqDec;Lim is the maximum reduce rate of cyclic fuel-injection quantity; NDec;Lim is the maximum reduce rate of revolving speed. 4. Simulation To certificate the performance of the integrated energy management strategy as Fig. 3 shown as well as laying the foundation of its applica­ tion in the rapid prototyping controller, PHEV system model has been built in Matlab/Simulink as the part 2 described. To ensure the instantaneity of this PHEV energy management strat­ egy, a city bus cycle approaching the real operating of the vehicle should be employed in this reverse simulation. In this paper, the Beijing typical city bus cycle (shown in Fig. 4(A)) has been applied, whose distance is 6.81 km. The simulation takes 10 cycles as the inputs. The detailed in­ formation of this cycle is shown in Table 4. Based on the certain cycle and the PHEV real-time energy manage­ ment strategy developed above, simulation analysis has been accom­ plished as shown in Fig. 4, where (a) gives 10 cycles, (b) shows the change of the SOC, it can be clearly seen from the graph that the SOC just reaches the limit value at the end of the trip, indicating that the battery is fully utilized. (c) shows the engine torque and motor torque respec­ tively, at low speed and small torque, the power system is powered by the motor; when the torque demand is large or the speed is high, the engine participates in the work, working in pure engine mode or hybrid mode, at this time, ECMS real-time control strategy is adopted to calculate the optimal torque distribution of the engine and motor. (d) and (e) show the engine state and gear. Fig. 4(C) and Fig. 4(D) are the operating points of engine and motor. It can be seen from the figure that the working points of the engine and motor are basically running in the high efficiency area. To pinpoint the superiority of the strategy designed in this paper, it must be compared with the strategy based on pre-decided rules and the Classical ECMS strategy (without the partly known path for SOC tracing and the optimization of DP) in perspective of overall performance. To evaluate the effect of this control strategy comprehensively, the overall performance index (Jmulti) is introduced as shown in equation (47).

(42)

Fig. 3 presents the flow diagram of this ECMS control algorithm, in which the require torque from the vehicle is continuous, and a widely oscillation of torque value will deteriorate the drivability, which is also not allowed by both the engine control unit and the motor control unit. For the PMSM, there are a maximum rise of torque (ΔTm;inc;max ) and a minimum decline of torque (ΔTm;dec;max ), which exist also in the engine control strategy. Given this, a limit of torque change between two adjacent times have been added in this ECMS algorithm, as Fig. 3(C) shown. The optimal torque value with the addition of ΔTm;inc;max in the pre­ sent moment is the maximum torque value of the next moment, while the optimal torque value with the subtraction of ΔTm;dec;max in the present moment is the minimum torque value of the next moment. These two limits improve both the speed and the precision of the ECMS algorithm. In this method, it is worth noting that the choices of ΔTm;inc;max and ΔTm;dec;max is significant for the whole algorithm and should be set ac­ cording to the characteristics of the PMSM. They can be defined as the following equation shown:

(47)

ΔTm;inc;max ¼ maxðTðdIInc;Lim Þ; ΔTInc;SOC Þ

(43)

Jmulti ¼ Mf þ α⋅shift þ β⋅state

ΔTm;dec;max ¼ minðTðdIDec;Lim Þ; ΔTDec;SOC Þ

(44)

where, Mf is the fuel consumption, shiftis the average shift frequency per kilometer, stateis the average engine state switch frequency per kilo­ meter, αandβare the same weighting factors to those in equation (25). Simulations have been accomplished in the same method, as shown in Table 5, From the comparison it can be observed that the Integrated EMS has the least fuel consumption and processes a lower frequent en­ gine start/stop switching and shifting with regard to the drivability. And

where, dIInc;Lim is the maximum rise rate of the current; dIDec;Lim is the maximum reduce rate of the current; ΔTInc;SOC is the maximum rise rate of motor torque in the present SOC and ΔTDec;SOC is the maximum reduce rate of motor torque in the present SOC. Additionally, the engine torque responsiveness should be considered 9

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Table 5 Comparison of the Simulations with different control strategy.

Table 6 Main parameters of components.

EMS

Mf (m3/ 100 km)

shift

state

Jmulti

Comparison

Strategy with predecided rules Classical ECMS Integrated EMS

12.21

3.44

2.98

18.63

–

CNG Engine

9.74 9.86

3.33 3.14

2.87 2.56

15.94 15.56

14.43% 16.48%

PMSM

Overall evaluation

Components

Li-Ion Battery

its overall performance increases by 16.48% contrasting with the control strategy based on pre-decided rules.

The experiment platform adopted in this paper is a plug-in hybrid electric city bus with single-axle parallel structure and CNG engine, shown in Fig. 5, the main parameters of its components are shown in Table 6. The strategy designed below is implemented by adopting dSPACE controller. The whole energy consumption (WEC) contains not only the actual fuel consumption (AFC) but also the net energy change (NEC). Hence, both the natural gas consumption and the net energy change in the battery should be recorded to get the total energy consumption. The NEC can be transformed into fuel consumption by equation (48)~(49). Ek � 3600 Dfuel � Qfuel low � ηeng � ηgen

Parameters

Value

Power Peak Torque Power Peak Torque Rated voltage Capacity

172 kW 678 Nm 115 kW 540 Nm 336 V 120 Ah

Table 7 The energy consumption experiments data.

5. Experiments

Vfuel ¼

Main parameters

3

AFC (m /100 km) NEC (kWh/100 km) WEC (m3/100 km)

Z

final

Ek ¼ NEC ¼

I � Udt initial

Test 1

Test 2

Test 3

24.8 18.5 31.3

21.4 16.7 27.3

23.2 19.1 29.9

(49)

where, Vfuel is the equivalent fuel consumption, Ek is the electricity power consumption, Dfuel is the fuel density,Qfuel low is the low heating value of the fuel, ηeng is the average working efficiency of the engine in generating process, ηgen is the average working efficiency of electric generator.

(48)

Fig. 5. Configuration of PHEV test platform. 10

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Journal of Power Sources xxx (xxxx) xxx

Fig. 6. The results of experiment: work points distribution of motor is shown in (A); work points distribution of engine is shown in (B).

based on the partly known driving condition in the engine partici­ pating modes. Its benefits is the uttermost use of the quality of power grid and hence the promotion of fuel economy. 2) From the perspective of drivability improvement, an offline param­ eter extraction method is presented adopting the DP algorithm. In this method, three typical driving cycles have been considered and applied to extract the boundary conditions of engine starting/stop­ ping status switch and gear shifting, which significantly affects the drivability. The whole PHEV energy management strategy is accomplished by combining these parameters with the torque split strategy. The most noteworthy is that the three driving cycles adopted in this paper just give an example to present the method, which means this strategy could be applied in any other plug-in hybrid electric city bus energy management strategy design by adopting the local driving cycles. 3) To verify this EMS, simulations have been conducted based on Matlab/Simulink and experiments have also been done in a plug-in hybrid electric city bus by adopting the control model on dSPACE controller. According to the simulation and experiment results, this strategy exerts a better comprehensive performance in the balance of economy and drivability, as compared to the control strategy based on certain rules and traditional ECMS.

Table 8 Comparison of the Experiments with different control strategy. EMS

Mf(m3/ 100 km)

shift

state

Jmulti

Comparison

Strategy with predecided rules Classical ECMS Integrated EMS

38.78

9.24

9.16

76.04

–

32.44 29.50

9.87 6.66

11.25 7.71

70.58 64.20

7.18% 15.57%

Overall evaluation

Three tests have been conducted in almost the same weather and temperature by operating the typical Chinese city bus driving cycle 35 times each test. The experiments result are shown in Table 7. To analyze the running conditions of the power sources, partly point set is extracted in the energy consumption contour maps of both CNG engine and PMSM, as shown in Fig. 6. It can be observed that both the engine and PMSM works almost in the high efficiency area and the braking points distribute in a wide range. The reason is that braking performance is the first consideration with a balance of braking efficiency. To validate the effect of this strategy, 2 contrast experiments have also been conducted in the same platform. The results is shown in Table 8. From the experimental comparison, it can also be observed that the Integrated EMS has the least fuel consumption and processes a lower frequent engine start/stop switching and shifting with regard to the drivability. And its overall performance increases by 15.57% contrasting with the control strategy based on pre-decided rules, which demonstrate the simulation results in Section 4.

Declaration of competing interest 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.

6. Conclusions

Appendix A. Supplementary data

This paper has described a PHEV energy management strategy based on partly known path to promote as well as trade off the energy con­ sumption and drivability. To overcome the insufficiency of the real-time optimization algorithm, the EMS has been divided into two parts: the torque split and extraction parameters affecting drivability, which is developed based on ECMS and DP algorithm respectively. This partic­ ular work can be concluded in the following aspects:

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1) Aiming at the torque split problem of the EMS, a modified energy split strategy has been proposed based on the characteristics of the city bus operating cycle. This strategy obtains the optimum torque split ratio through the setting of the energy conversion factor (S(t)) 11

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