EVS28 International Electric Vehicle Symposium and Exhibition 1

EVS28

KINTEX, Korea, May 3-6, 2015

Real-time optimal energy management strategy for range-

extended electric bus in Harbin urban bus driving cycle

Jingfu Chen1, 2, Junfeng Wu2, Jiuyu Du1*

1State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing, 100084, China,

dujiuyu@tsinghua.edu.cn 2 Department of Automation, Harbin University of Science and Technology, Harbin, China

Abstract

Developing electric driving powertrain technology is the core of national strategies for Chinese electric

vehicles. Range-extended electric vehicles, an important configuration, are focused by more and more

automobile manufacturers and consumers. The energy management strategy is a key technology to develop

range-extended electric vehicles. DP strategy can achieve the optimal energy management. However, it

cannot be used in the real-time as the heavy computational burden. This paper establishes the simulation

model of the range-extended electric bus which is developed independently by Tsinghua University. The

model is simulated using the DP control strategy in the Harbin urban bus driving cycle. Minimum energy

consumption is regarded as the optimization target. According to the simulation result, δSOC control

strategy is put forward on the basis of the relationship between the SOC change per second and the motor

power. This strategy can guarantee the fuel saving rate and be applied in the real time simultaneously. The

simulation results show that when the range-extended electric bus runs 189km in the Harbin urban driving

cycles, the fuel saving rate can exceed 30% with DP and δSOC strategies. The energy consumption

difference between these control strategies is no more than 2%, but the δSOC strategy improves the

computational efficiency significantly.

Keywords: DP strategy, Energy management strategy, Range-Extended Electric Bus; Real-time control

1 Introduction The transport sector, a major oil consumer and

greenhouse gas emitter, accounted for 26% of the

world’s energy use and 23% of the energy-related

greenhouse gas emissions (GHG) in 2004. Road

transportation is responsible for over 90% of these

emissions [1] [2]. To overcome the resulting air

pollution and energy crisis, governments are

encouraging automobile manufacturers to develop

electric vehicles (EVs) and hybrid electric vehicles (HEVs). However, the battery cycle life

and the travel range of such vehicles continue to

hinder their development. Therefore, for now,

range-extended electric vehicles seem to be the

most promising among renewable energy vehicles

[3].

Given that the energy required by range-extended

electric vehicles is supplied mainly by range

extenders and the electric power grid, optimal

strategies should be applied to such vehicles’

energy management systems to minimize their

energy consumption [4]. At present, these optimal

strategies can be classified into three categories

EVS28 International Electric Vehicle Symposium and Exhibition 2

[5]: ruled-based strategies, modern control

theory–based intelligent strategies, and optimal

strategies. He et al. [6] presented several rule-

based control strategies such as constant-voltage

control, out-line control, and on-line control. Wei

et al. [7] devised a model-based fuel optimal

control for HEVs. The rule-based control strategy

is easy to understand and realize. However, it

lacks any rigorous mathematical basis, and it

cannot extract the full performance potential of a

hybrid system [8]. Schouten et al. [9] and Gong et

al. [10] designed control rules for energy

management systems by using fuzzy logic and

neural network. The methods achieved better

results than the traditional rule-based control

strategy, but its results still have difference to

those achieved with the optimal strategies. The

dynamic programming (DP) algorithm is widely

used in the optimal strategies. DP is one of the

best methods for dealing with constrained non-

linear optimal problems [11]. It is suitable for

optimizing the control strategy of an energy

management system when the driving cycle is

known in advance. Geng et al. [12] and Barsali et

al. [13] presented an equivalent consumption

minimization strategy based on the DP algorithm.

However, this strategy cannot be applied to real-

time control because of its heavy computational

burden. Given that the rule-based control strategy

can be applied easily to real-time control, the DP

algorithm can be combined with the rule-based

control strategy. The resulting hybrid control

strategy would not only have the global optimal

feature of DP strategy but would also be easily

applicable to real-time control. He et al. [14] used

an optimal control strategy for a specified driving

cycle to control long-distance driving cycle for a

plug-in series–parallel hybrid electric bus. The

strategy reduces the computational time

significantly, while maintaining the desired

precision. Chen et al. [15] designed a DP

algorithm–based energy management strategy for

range-extended electric vehicles. Then, a rule-

based control strategy was designed considering

the global optimal solution and driving cycle

recognition. Peng et al. [16] considered energy

consumption and GHG emissions to design an

energy management strategy by using the DP

algorithm and presented an adaptive rule-based

control strategy based on the DP solution. Bianchi

et al. [17] established a rule-based control strategy

for HEVs by using the DP strategy. The

corresponding simulation result was close to the

optimal result.

We present a DP and rule-based hybrid control

strategy for a range-extended electric bus (REEB)

running the Chinese typical urban bus driving

cycle. This strategy retains the advantages of the

DP and the rule-based strategies, while reducing

the computational burden.

Engine Generator Rectifier

Mechanical

Joint

Range-Extender

Power

battery

Traction Motor

ControllerTraction Motor

Mechanical

Joint

Transmission and

Final Drive

Electrical

Joint

Electrical

Joint

Electrical

Joint

Figure 1: REEB powertrain system structure

2 REEB powertrain model A schematic of the typical REEB powertrain is

shown in Figure 1. The powertrain consists of a

range extender, battery, traction motor,

transmission, and the main reducer. The battery

and the range extender provide power to the

traction motor through electrical connections. The

traction motor drives the wheels directly through

the transmission and the main reducer. The entire

power system is connected in series. One feature

of the REEB is their large battery capacity, which

provides greater power to the REEB, thus

reducing fossil fuel consumption and emissions

[18]. The range extender module of REEB mainly

includes an engine, generator, and rectifier. The

generator is mechanically coupled to the output

shaft of the engine. The range extender can

convert diesel power into electric power for direct

use by the traction motor or for charging the on-

board battery, thus extending the vehicle’s driving

range. Moreover, when the power demand of the

bus is higher than what the battery can supply, the

range extender provides the insufficient power,

thus ensuring dynamic performance.

2.1 Powertrain system modelling

We establish a backward simulation model

considering the features of the DP strategy as well

as the objective of analysing fuel consumption.

The relative speed ur at each discrete time point (k)

can be calculated using Eq.1 by the driving cycle

data.

r3.6

v ku k (1)

where v is the driving speed (km/h).

EVS28 International Electric Vehicle Symposium and Exhibition 3

To fulfil the requirements of the DP strategy, the

vehicle’s longitudinal dynamics model is

expressed as the following state equation:

req T

r

v

1000 ( )1( ) (

( ) ( )p r

P ku k

m m u k

rf w r i

r

( )( )

( )

u kF F u k F

u k (2)

where δ is the conversion coefficient of the

vehicle rotation quality, mv is the bus mass, mp is

the passenger mass, Preq is the demand power of

the transmission, ηT is the efficiency of the

transmission and the main reducer, Ff is the

rolling resistance, Fw is the air resistance and the

function of ur, and Fi is the slope resistance. The

parameters of the REEB are shown in Table 1.

The drive power of the vehicle Pmotor is provided

by the battery Pbat and/or the range extender Pre,

as expressed by Eq. 3.

req

motor re bat

motor

PP P P

(3)

where ηmotor is the efficiency of the traction motor.

Given the computational burden of the DP

strategy, the dynamic characteristics of traction

motor are ignored. The 2D look-up table is used

for the traction motor model, as shown in Figure 2.

0.714

0.714

0.728

0.728

0.742

0.742

0.756

0.756

0.771

0.771

0.785

0.785

0.785

0.799

0.799

0.799

0.813

0.813 0.813

0.827

0.841

0.855

0.869

0.869

0.884

0.898

0.912

speed(r/min)

torq

ue

(Nm

)

500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000

100

200

300

400

500

600

700

800

900

1000

1100

Figure 2: Efficiency map of traction motor

Table 1: Powertrain parameters of range-extended electric bus

Bus Size (Length×Width×Height)/mm 11980×2550×3200

Bus Mass/kg 13400

Passenger Mass/kg 2760

Windward Area/m2 7.83

Air Resistance Coefficient CD 0.75

Rolling Resistance Coefficient f 0.0076+0.00056ua

Rolling Radius r/m 0.512

Speed Ratio of Main Reducer i0 6.2

Speed Ratio of Transmission ig 2.18

Motor Continuous Power/kW 100

Peak Power/kW 180

Maximum Torque/N·m 860

Maximum Speed/r/min 4500

Operating Voltage/V 300~450

Engine Displacement/L 1.9

Power/kW 82/4000r/min

Generator and Generator

Controller

Rated Power/kW 50

Rated Torque/N·m 220

Power Battery Capacity 180Ah

Operating Voltage/V 350~460

EVS28 International Electric Vehicle Symposium and Exhibition 4

Generally, the equivalent battery models include

Rint, PNGV, and GNL. The Rint model focuses

on the charge/discharge resistance and the open

circuit voltage of the battery, and it has a simple

structure. What is more, it meets the demand of

the DP strategy. Considering the features of the

DP strategy, the following form of the state

equation is used in the battery model [19].

bat

( )I kSOC

Q

(4)

SOC OCV( ( )U SOCSOC

2

int( ( ) 4( ( ) )OCV tU SOC R SOC R

1/2

motor re( ( ) ( ))) )P k P k 1

int t bat(2( ( ) ) )R SOC R Q (5)

where I is the battery current, Qbat is the battery

capacity, ηSOC is the Coulomb efficiency, UOCV is

the open circuit voltage of the battery, Rint and Rt

are the internal resistance and thermal resistance,

respectively. Rint and UOCV are functions of the

SOC. The equivalent circuit of the simplified

battery model is shown in Figure 3.

Rint Rt

Uvoc

ib

Figure 3: Equivalent circuit of simplified battery

model

As in [20], the charging ηchg and discharging ηdis

efficiencies are calculated using Eq. 6.

ocv dis dis batdis 2

ocv ocv

411 1 ,

2

U IR R P

U U

motor re 0P k P k

chg batocvchg 2

ocv chg ocv

42 / 1 1 ,

R PU

U IR U

motor re 0P k P k (6)

where Rdis and Rchg are the discharging resistance

and the charging resistance, respectively.

The dynamic characteristics of the engine and

generator models in the range extender are also

ignored to reduce the computational burden of

the DP strategy. Their models are the MAPs,

which are generated by using the data from the

bench tests. Because the generator is

mechanically coupled to the output shaft of the engine, the generator and engine are in the same

working points. The optimal fuel economy curve

of the range extender is developed by the method

described in [15], as shown in Figures 4 and 5.

7.66

7.66

15.3

15.3

23

23

30.6

30.6

38.3

38.3

45.9

45.9

53.6

53.6

61.3

61.3

68.9

68.9

76.6

76.6

84.2

84.2

91.9

91.9

99.5

99.5

107

107

115

115

123

123

130

130

138

138

145

145

153

153

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161

168

168

176

176

184

184

191

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199

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230

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237

245

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245

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352

360

368

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383

390

398

406

413

421429 429

436

444

452

459

467

475

482

490

498

505

513521

528536

544551

559567574582590597605613

5kw

10kw

15kw

20kw

25kw

30kw

35kw40kw

45kw50kw

55kw

Engine Speed(rpm)

En

gin

e T

orq

ue

(Nm

)

1000 1500 2000 2500 3000 3500 400020

40

60

80

100

120

140

160

180

200

220

240

Figure 4: BSFC map of engine

0.4130.425 0.4380.451 0.4630.476 0.4890.502

0.5140.527

0.54

0.552

0.565

0.578

0.59

0.603

0.616

0.628

0.641

0.654

0.666

0.679

0.692

0.705

0.717

0.73

0.743

0.755

0.768

0.781

0.793

0.806

0.819

0.831

0.844

0.857

0.869

0.869

0.869

0.882

0.882

0.882

0.882

0.895

0.895

0.895

0.895

0.908

0.908

0.908

0.908

0.908

5kw

10kw

15kw

20kw

25kw

30kw35kw

40kw45kw

50kw55kw

Generator Speed(rpm)

Ge

ne

tato

r T

orq

ue

(Nm

)

1400 1600 1800 2000 2200 2400 2600 2800 3000 3200

20

40

60

80

100

120

140

160

180

200

220

Figure 5: Efficiency map of generator

3 Driving cycle As driving cycles are an important factor to affect

the energy consumption of electric vehicles, this

paper conducts the simulation on the basis of the

Harbin urban bus driving cycle, as shown in Figure

5. Considering investigation results on typical

cities of electric buses main running lines, the

driving distance is about 200km per day. Therefore,

given the large battery capacity of the REEB and

the one-charge-per-day operation mode, the

driving cycle for the simulation is 20 Harbin urban

bus driving cycles, which spans 189.8km.

0 200 400 600 800 1000 1200 1400 1600 18000

10

20

30

40

50

60

Time(s)

Sp

eed

(km

/h)

Figure 5: Harbin urban bus driving cycle

EVS28 International Electric Vehicle Symposium and Exhibition 5

4 Energy management strategy

4.1 DP strategy

In the horizon [t0，tf], the state variables of the

REEB powertrain system include the SOC of the

battery and the bus speed. As the bus speed can

be determined from the driving cycle, the state

variable is x(t) = [SOC(t)]’. According to the

optimal objective of minimum equivalent fuel

consumption, the range extender is regarded as

the control variable, u(t)=[Pre(t)]. The powertrain

system of the REEB in the discrete form is

shown as follows:

,x f x k u k

(7)

where f represents Eqs. 1–6.

The constraint conditions of the state space are

expressed by Eq. 8.

bat bus,max ocv bus,max chg[ / ,P U U U R

bus,min ocv bus,min dis/ ]U U U R

re re,max0 P P

L HSOC <SOC<SOC

m,min m m,maxT T t T (8)

where Ubus,max, Ubus,min, Uocv, Rchg, and Rdis are

battery parameters that represent the maximum

voltage, minimum voltage, open circuit voltage,

and charging resistance and discharging

resistance, respectively. Pre,max denotes the

maximum power of the range extender. SOCH

and SOCL represent the maximum and minimum

values of the SOC, respectively. Tm denotes the

traction motor torque; Tm,min and Tm,max represent

the maximum torque and the minimum torque of

the traction motor, respectively.

The key to the DP strategy is the reasonable cost

function. In this paper, the electric power is

equivalent to the fuel consumption, and

achieving the minimum fuel consumption is

regarded as the objective for reducing the fuel

consumption and emissions. The cost function J

is shown as follows:

re,k k bat,k

k 0

N

J C k C

(9)

where Cre,k is the fuel consumption of the range

extender in the k-th state, Cbat,k is the equivalent

fuel consumption of the battery in the k-th state,

and kk is the coefficient for constraining the SOC.

The fuel consumption of the range extender,

equivalent fuel consumption of the battery, and

kk can be calculated as follows:

re engC P be t (10)

batsgn re,avg

bat bat dis chg

re,avg

P CC P t

P

(11)

k 1 2 (SOCk

H L H L0.5(SOC SOC )) / (SOC SOC ) (12)

where Peng is the output power of the engine in the

k-th state, be is the specific fuel consumption,

Cre,avg is the average fuel consumption of the range

extender, Pre,avg is the average output power of the

range extender, μ is the balance coefficient

required to maintain the SOC within the

reasonable range [21].

4.2 δSOC strategy

With the DP strategy to achieve minimizing the

energy consumption, this paper analyses the

optimal result features on the basis of the Harbin

urban bus driving cycle. An obvious rule appears

that the SOC changes per second are gathering at

different motor output power. The δSOC strategy

is formulated according to the relationship between

the SOC change per second and the motor power,

which are fitted in a curve, as shown in Figure 6.

This curve is regarded as the control rule for the

battery SOC dropping.

0 20 40 60 80 100 120 140 160 180 200-6

-4

-2

0

2x 10

-4

Pmotor

(kW)

δS

OC

per

sec

on

d

Figure 6: Fitting curve according to the relationship

between the SOC change per second and the motor

power

5 Results and analysis In order to verify the effect of δSOC strategy as

mentioned above, the REEB is simulated to

analyse the energy efficiency on the basis of the

CTUDC. Drop curves of the battery SOC with 2

kinds of control strategies are shown in Figure 7.

0 0.5 1 1.5 2 2.5 3 3.5 4

x 104

0.2

0.4

0.6

0.8

1

time(s)

SO

C

SOC curve of DP strategy

SOC curve of rule strategy

Figure 7: SOC dropping curves using DP and δSOC

strategies

EVS28 International Electric Vehicle Symposium and Exhibition 6

In Figure 7, δSOC-RB strategy which are revised

from the DP strategy have similar SOC dropping

curves with the DP strategy. Figure 8 shows the

relationship among the demand power of the

motor, the output power of the range extender

and the battery in different control strategies.

When the battery output power is negative, the

range extender is charging the battery. Because

the driving cycle duration is long, a segment of

5000 s is extracted from the entire cycle.

2 2.05 2.1 2.15 2.2 2.25 2.3 2.35 2.4 2.45 2.5

x 104

0

50

100

150

200

Time(s)

Po

wer

(kW

)

Demand power of the motor

Output power of the range extender

Output power of the battery

(a) Relationship among power of components based on

the DP strategy

2 2.05 2.1 2.15 2.2 2.25 2.3 2.35 2.4 2.45 2.5

x 104

0

50

100

150

200

Time(s)

Po

wer

(kW

)

Demand power of the motor

Output power of the range extender

Output power of the battery

(b) Relationship among power of components based on

the δSOC strategy

Figure 8: Relationship among power of components

based on the different strategies

As shown in Figure 8, comparing δSOC strategy

with the DP strategy, the output power features

of the range extender are similar. The demand

power of the motor and the battery output power

have the same features in 2 kinds of control

strategies. It means that the performance of the

DP strategy can be approximated by the δSOC

strategy effectively.

5.1 Comparative analysis on fuel and

energy saving

Comparing to conventional bus in the same level,

the energy saving effect and fuel economies of

the REEB are analysed with the δSOC strategy.

As the comparison results shown in Figure 9,

fuel saving rates can reach 32.04% and 30.87%

in the DP and δSOC strategies, respectively.

(a) Fuel consumption comparison in normalization

(b) Energy consumption comparison in

normalization

Figure 9: Comparison between REEB and the traditional

bus with 2 kinds of control strategies

5.2 Comparison of computational

efficiencies

Comparing to the DP strategy, the δSOC control

strategy improve the computational efficiency

significantly. It is more responsive with almost 0

time delay, which can be used in real-time to

control the REEB.

6 Conclusion In order to present an energy management strategy

which can improve the energy efficiency and apply

in real-time for the REEB, this paper design a rule-

based control strategy from the SOC dropping rule

of the DP strategy. The simulation is conducted to

analyse the control effect of different strategies on

the basis of the Harbin urban bus driving cycle.

Conclusions are as follows.

1. On the aspect of energy efficiency

optimization to the REEB, the δSOC control

strategy derived from the DP strategy can

achieve similar optimization effects as the DP

strategy. The fuel saving rate can exceed 30%

with DP and δSOC strategies. The energy

consumption differences among these control strategies are no more than 2%.

EVS28 International Electric Vehicle Symposium and Exhibition 7

2. The δSOC strategy not only keep the energy

efficiency of the powertrain, but also

improve the computational efficiency

significantly. It can achieve real-time energy

management for the REEB with 0 time delay

control.

From the analysis shows above, the optimal

performance of the δSOC strategy is in a high

level. Considering the real-time performance, the

δSOC strategy is ideal energy management

strategy for the REEB in this paper.

Acknowledgments This research is funded by MOST (Ministry of

Science and Technology) ‘International S&T

Cooperation Program of China’ under contract of

No. 2014DFG71590 and 2012DFA81190, and

National Science and Technology Infrastructure

Program under contract of No. 2013BAG06B04.

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Beijing: Tsinghua University doctoral paper,

2009.

Authors

Jingfu Chen is a graduate student

of Department of Automation,

Harbin University of Science and

Technology. He is a member of

U.S.-China CERC-clean Vehicles

Consortium. His current focuses

are plug-in electric vehicles and

electric vehicle R&D technology

roadmap.

Dr. Jiuyu Du is an assistant

professor of Tsinghua University.

She focuses on advanced vehicle

powertrain design, simulation,

energy-saving and new energy

vehicle system analysis, and

performance analysis and

evaluation of vehicle powertrain,

and electric vehicle R&D

technology roadmap.