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2792 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 64,NO. 7, JULY2015
Correctional DP-Based Energy Management Strategy
of Plug-In Hybrid Electric Bus for City-Bus Route
Liang Li, Chao Yang, Yahui Zhang, Lipeng Zhang, and Jian Song
Abstract—Typical plug-in hybrid electric buses (PHEBs) with
a fast-charged lithium titanate battery, which might fulfill about
70% of the distance of a representative city-bus route, have
been adopted in many Chinese cities. Considering that the de-
tailed information of the driving cycle could be deduced with
the historical driving data and online estimation methods, there
might be an opportunity for applying the dynamic program-
ming (DP)-based global optimal energy management strategy for
these PHEBs. However, road slopes or variable loads might in-
duce transient fluctuations of the driving resistance in a given
driving cycle. Meanwhile, the single-shaft parallel configuration,
with automatic mechanical transmission (AMT), might constrain
the implementability of the optimal energy distribution from a
DP-based strategy. Therefore, in this paper, a novel correctional
DP algorithm is brought forward to balance the optimization of
fuel economy and drivability. Simulation results demonstrate that,
integrated with the correctional logic of AMT gear shifting, the
proposed energy management strategy can guarantee that the
engine and the electric machine work in the high-efficiency area
with optimal energy distribution, while keeping drivability in the
variation of road slope and loads. The proposed method might
give a technical solution to these typical PHEBs with a lower cost
system configuration of the powertrain in China.
Index Terms—Drivability, dynamic programming (DP), en-
ergy management strategy, plug-in hybrid electric bus (PHEB),
single-shaft parallel hybrid powertrain.
I. INTRODUCTION
BECAUSE of the large changing range of the battery
state of charge (SOC) and easy charging from the grid
[1], the plug-in hybrid electric vehicle (PHEV) cannot only
work as an electric vehicle but also has many features of a
traditional hybrid electric vehicle (HEV) [2], [3]. There are
three operating modes for a PHEV, including electric vehicle
(EV) mode, charge-sustaining (CS) mode, and charge-depleting
(CD) mode, according to the battery features [4]. The change
in the battery SOC of these three modes is shown in Fig. 1.
Manuscript received May 16, 2013; revised May 22, 2014; accepted
August 18, 2014. Date of publication September 23, 2014; date of current
version July 14, 2015. This work was supported in part by the National Natural
Science Foundation of the People’s Republic of China under Grant 51275557,
by the National Key Technology R&D Program of the Ministry of Science and
Technology under Grant 2013BAG14B01, and by the State Key Laboratory
of Automotive Safety and Energy in China. The review of this paper was
coordinated by Prof. J. Wang.
L. Li, L. Zhang, and J. Song are with the State Key Laboratory of Automo-
tive Safety and Energy, Tsinghua University, Beijing 100084, China (e-mail:
liangl@tsinghua.edu.cn; evzlp@163.com; daesj@tsinghua.edu.cn).
C. Yang and Y. Zhang are with the Institute of Electric Engineering,
Yanshan University, Qinhuangdao 066004, China (e-mail: yc19861029@
126.com; zhangyahui1990@live.com).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TVT.2014.2352357
Fig. 1. Three operation modes of battery SOC of PHEV.
The curves of SOCHand SOCLrepresent the upper and lower
limits of the battery SOC, respectively. Because the real oper-
ating conditions are hardly obtained in real time, PHEVs might
be bound to work in the CD mode for an approximate optimal
SOC profile [5].
Realizing an optimal SOC profile is a global minimiza-
tion problem of the total energy consumption, which is a
challenge technology for PHEV control. By comparing var-
ious energy management strategies employed in the PHEV,
the optimization-based strategies might be a best solution to
promote fuel economy [4], [6]. Many studies attempted to
find an implementable approximate optimal solution, which is
expected to close to the global optimal utilizing algorithms of
the energy management strategy [7]–[9]. Based on Pontryagin’s
minimum principle, the equivalent consumption minimization
strategy has simplified the dynamic optimization problem to
an equivalent instantaneous optimization question, and then,
the computational complexity of the optimal algorithm is re-
duced and fit for a real-time controller [8]. Moreover, a model
predictive control (MPC) method was employed to design a
novel energy management strategy, which might be adopted
to realize the optimal power split between the engine and the
electric machine (EM) [9]. However, these approximate optimal
algorithms could not obtain a global optimal solution.
Since utilizing a dynamic programming (DP) algorithm
might be an effective way to design a theoretically global opti-
mal energy management strategy [10], [11], [14], [15], a lot of
studies about the DP-based strategy for HEV/PHEV were car-
ried out. An approximate DP algorithm was presented to solve
the power split of a parallel hybrid powertrain, which greatly
improved the computation speed with a simplified model and
the piecewise linear function on a sparse grid [10]. Then, a total
energy cost function for PHEVs within the different charging-
depletion ranges was given in the DP algorithm [11].
0018-9545 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
LI et al.: ENERGY MANAGEMENT STRATEGY OF PLUG-IN HYBRID ELECTRIC BUS FOR CITY-BUS ROUTE 2793
Fig. 2. Configuration of the PHEB powertrain.
Considering that it is difficult for a DP-based algorithm to
be realized in practice from an engineering perspective, many
optimal energy management strategies with extra correctional
terms have been proposed [12]–[14]. Considering the engine
transient characteristics during the frequent engine startup, an
extra cost function was integrated in the MPC-based torque split
strategy; thus, the fuel consumption during the engine startups
was predicted, and then, the accurate energy distribution for
HEVs might be realized [12]. A DP algorithm with a cost
function, including fuel consumption, pollutant emissions, and
drivability, was proposed to deduce a near-optimal solution
that balances the fuel economy, the engine emission, and a
reasonable gear trajectory [13]. To fit for practical conditions,
the effects of frequent gear shifting and engine stop-starting
were considered in a DP optimizing process, and the relevant
cost functions were added to make the optimal gear-shifting
points close to the actual points [14], [15].
Moreover, the DP-based algorithm needs future driving in-
formation in advance [16], [17], which might be predicted with
some related elemental signals [18]. The navigation and the
commuting route data from the driving information database
were used to predict the driving cycles [18]. Moreover, a
recurrent neural network was also employed to estimate the
future vehicle load to create a velocity profile of the future
driving conditions [19]. In recent years, the Global Positioning
System (GPS)/geographic information system have been lead-
in to obtain the data of the traffic flow [20]. These aformen-
tioned methods might increase the possibility of using the DP
algorithm for PHEV energy management.
The future driving conditions might be predicted with histor-
ical traffic information under a fixed driving cycle in a given
city routing [17], [20]. The key vehicle parameters, such as
the vehicle mass and road grade, might be estimated with
some different estimation methods [21]–[23], and all these ap-
proaches give the potential possibility for the application of the
DP algorithm. Moreover, an automatic mechanical transmission
(AMT) used in the plug-in hybrid electric bus (PHEB) could
easily adjust the operating points of the engine and the motor to
fulfill the power demand of complicated real road conditions.
Therefore, in this paper, a correctional DP (CDP)-based algo-
rithm might be brought forward to solve the tradeoff problem
between minimizing the energy consumption and the power
TAB LE I
BASIC PARAMETERS OF THE PHEB
performance by correcting the AMT gear-shifting strategy. This
paper is organized as follows. In Section II, the mathematical
model of the PHEB is described. In Section III, considering
the effect of the equivalent road grade, a new DP-based energy
management strategy is proposed to solve the optimal control
problem for minimizing the energy consumption and, at the
same time, ensure the drivability of PHEBs by AMT gear-
shifting correction. In Section IV, the simulation results verify
the effectiveness of the proposed strategy with different driving
cycles. Finally, conclusions are presented in Section V.
II. CONFIGURATIONS AND MODELS OF THE
PLUG-INHYBRID ELECTRIC BUS
A. System Configuration
The powertrain architecture of the PHEB with a single-shaft
parallel hybrid configuration is shown in Fig. 2, which is widely
used in many cities in China. AMT is a key component to
adjust the operating points of the two power sources, such as the
engine and the EM, to work in their own high-efficiency areas.
The clutch might be used to change the operating modes of the
powertrain, such as EV mode, engine-drive mode, and hybrid-
drive mode or regenerative-brake mode. The EM could work as
a motor or a generator at different modes. Moreover, the battery
SOC can be quickly charged, due to the characteristics of the
lithium titanate battery. The basic parameters of the PHEB are
shown in Table I.
B. System Mathematical Models
1) Vehicle Model: According to the vehicle longitudinal dy-
namics equation, the relationship between the torque of wheel
2794 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 64,NO. 7, JULY2015
and the output torque of two power sources is written as
follows:
Tw=ηT·iAMT ·if(Te+Tm)+Tb(1)
where ηTis the transmission efficiency. iAMT and ifrepresent
the gear ratio of the AMT and the differential gear ratio,
respectively. Teand Tmare the engine torque and the EM
torque, respectively. Tbis the braking torque acted on the wheel.
Twis the torque of the wheel, which can be expressed as
follows:
Tw=mgCrcos θ+1
2CDρdAV 2
a+mg sin θ+δmdVa
dt ·r
(2)
where mis the empty vehicle mass in kilograms, gis the gravity
acceleration in m/s2, and Cris the rolling resistance coefficient
that can be represented as follows:
Cr=C1+C2Va(3)
where C1and C2are different rolling resistance coefficients. θ
is the road-grade angle in degrees, and CD,ρd, and Arepresent
the air drag coefficient, the air density in kg/m3, and the frontal
area of the bus in m2.Vais the vehicle speed in meters per
second, and δis the correction coefficient of rotating mass.
ris the wheel radius in meters. The relationship between the
rotational speed of the wheel and that of the two power sources
are described as follows:
ωw=ωe
iAMT ·if
=ωm
iAMT ·if
(4)
where ωw,ωe, and ωmare the rotational speed of the
wheel, the output shaft of the engine, and the EM in r/min,
respectively.
2) Engine: Here, the consumption model of an engine that
mostly used compressed natural gas (CNG) is considered; the
equation about CNG consumption rate per unit time (Qg)can
be described as follows:
Qg=Peb
367.1ρgg(5)
where bis the CNG consumption rate, corresponding to the
current engine torque and rotational speed, which can be
obtained through a calibration test. Peis the engine power
calculated through Pe=Teωe.ρgrepresents the density of
CNG. The fuel consumption map of the given engine is shown
in Fig. 3.
3) EM Model: The EM in the PHEB is used to drive the
bus or regenerative brake to recover the kinetic energy to the
battery. The EM power can be written as follows:
PEM =Tmωm
ηEM ,motor
TmωmηEM,generator (6)
where ηEM is the EM efficiency, which is a function of the
torque and the rotational speed of the EM, ηEM =E(Tm,ω
m),
the characteristics of which are shown in Fig. 4.
Fig. 3. Fuel consumption contour map of engine (unit of specific gas con-
sumption: g/kWh).
Fig. 4. Efficiency map of a typical EM in PHEB.
Fig. 5. Static equivalent circuit of the battery.
According to the expression of the EM power, the equation of
the electricity power consumption per second in kilowatt-hours,
i.e., Qe, can be described as follows:
Qe=PEM
3.6 ×106.(7)
According to (6) and (7), Qe>0, when the EM is operated in
driving mode, and Qe<0, when the EM provides the braking
torque.
4) Battery Model: Since the SOC is a key variable impor-
tant for PHEB control, the thermal temperature effects and
transients are neglected. A basic physical model of the battery
might be derived from a static equivalent circuit, which is
shown in Fig. 5 [20].
According to Kirchhoff’s voltage law, the equivalent circuit
equation can be written as follows:
U(t)=Uoc(t)−Rint(t)I(t)(8)
where Uoc(t),Rint(t),U(t), and I(t)are the open-circuit volt-
age, internal resistance, terminal voltage, and internal current
LI et al.: ENERGY MANAGEMENT STRATEGY OF PLUG-IN HYBRID ELECTRIC BUS FOR CITY-BUS ROUTE 2795
Fig. 6. Characteristic curves of lithium titanate battery. (a) Open-circuit
voltage. (b) Internal resistance.
of the battery, respectively. The battery SOC can be calculated
as follows [13], [20]:
SOC(t)=Q(t)
Q0
(9)
˙
Q(t)=I(t)(10)
I(t)=Uoc(t)−U2
oc(t)−4Rx(t)PEM(t)
2Rx(t)(11)
where Q(t)and Q0represent the quantity and the capacity of
the battery, respectively. Rx(t)is the resistance of the battery,
which is described as follows:
Rx(t)=Rdis(t),discharging
Rchg (t),charging (12)
where Rdis(t)and Rchg (t)are internal resistances when the
battery is discharged or charged, respectively. Here, Uoc(t),
Rdis(t), and Rchg (t)of a lithium titanate battery at 6C(nC
is the current that could make the battery a full charge in 1/n h)
charge rates of 45 ◦CareshowninFig.6.
5) AMT Gear-Shifting Strategy Description: The detailed
description of the gear-shifting strategy might deduce a real-
izable gear-shifting logic for better adaptability to the changes
in the driving cycle and the road conditions. The dynamical
gear-shifting strategy and the economical gear-shifting strategy
are two basic gear-shifting modes. The basic characteristics
of these two AMT gear-shifting schedules might be shown
in Fig. 7. As shown in Fig. 7, taking gear 2 →3asan
example, the left curve represents the economical gear-shifting
schedule, which indicates upshifting as early as possible to
ensure fuel economy. The right curve represents the dynamical
gear-shifting schedule, which indicates upshifting as late as
possible to make full use of the lager driving torque on the
lower gear [24], [25]. With a given accelerator pedal position,
a balanced gear-shifting point Vpmight be obtained based on
the dynamical gear-shifting point Vdand the economical gear-
shifting point Ve. Moreover, this balanced gear-shifting strat-
egy might be changed with the calculated desired longitudinal
acceleration, which might be corrected with the variation of
estimated equivalent road grade as described in Section III-B2.
The vehicle speed on the gear-shifting point Vpmight be
described as follows:
Vp=Vd
n→n,dynamical gear-shifting strategy
Ve
n→n,economical gear-shifting strategy (13)
Fig. 7. AMT gear-shifting curves in two different strategies.
where nand nrepresent two different gears, respectively. The
calculation of the vehicle speed on the dynamical gear-shifting
point Vdcan be deduced as follows. Taking an engine-drive
mode, for example
Tn
w=ηT·Te(ωn
e)·in
AMT ·if
Tn
w=ηT·Teωn
e·in
AMT ·if.(14)
During the gear-shifting process with the dynamical gear-
shifting strategy, Tn
wand Tn
ware the maximum wheel torque,
obtained by looking for the outer characteristic torque of the
engine with the relevant rotational speed, whereas Tn
w=Tn
w
before and after gear shifting. Hence, the value of Vdcan
be calculated through combining (4) and (14). Similarly, in
the economical gear-shifting strategy, the gear-shifting torque
could be obtained by looking for the least fuel consumption
torque of engine with the relevant rotational speed. Then, the
speed at the economical gear-shifting point Vemight also
be calculated similar to Vd. The calculations of Vdand Ve
for an EM-driven process are similar with that of the engine
driving mode.
The gear-shifting logic for the adopted six-speed AMT
should be modeled as a discrete-time system, i.e.,
gb(k+1)=⎧
⎨
⎩
1,gb(k)+s(k)<1
6,gb(k)+s(k)>6
gb(k)+s(k),otherwise
(15)
where gb is the gear number. The value of the gear-shifting
signal scould be −1, 0, and 1, which represent downshifting,
sustain, and upshifting, respectively [13]. The gear-shifting
logic should be adjusted in a braking mode of the vehicle.
While the vehicle is braked, if the gear-shifting signal s(k)=
−1, the AMT could hold on to the current gear first until the
braking process is over and then downshift to the suitable gear
corresponding to the instantaneous vehicle speed.
III. CORRECTIONAL DYNAMIC PROGRAMMING-BASED
ENERGY MANAGEMENT STRATEGY
For a typical PHEB with a fast-charged lithium titanate
battery used in many cities in China, the electric energy might
fulfill about 70% distance of a representative city-bus route, and
2796 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 64,NO. 7, JULY 2015
Fig. 8. Schematic of the proposed CDP algorithm.
Fig. 9. Diagram of vehicle speed error by the economic gear-shifting strategy
during the slope road.
the driving torque in the rest of the bus trip should be provided
by the engine. Under a very crowded condition, the bus might
frequently stop and start and then slowly move forward. Thus,
it is necessary to utilize electric energy instead of fuel energy,
to improve powertrain efficiency. In this course, a special con-
straint would be used to avoid frequent gear shifting for keeping
acceptable drivability. Further considering the transient varia-
tions of the driving resistance of the PHEB induced by the road
grades or the loads, the AMT gear-shifting strategy might be
corrected accordingly to fit the driver’s acceleration intention.
Integrating these dynamic corrections, a novel CDP algo-
rithm is brought forward to improve the fuel economy and
ensure the drivability in any given city-bus driving cycle. The
diagram of the algorithm is shown in Fig. 8. A general descrip-
tion of the optimization problem at phase t=kis shown in
the upper part in Fig. 8. With the state transition of the related
state variables, the optimization process is executed through the
optimal control variables u(k)to minimize the cost function at
each step. Moreover, as shown in the lower part of Fig. 9, with a
comprehensive gear-shifting strategy of AMT, the equilibrium
between the dynamic and economic performance might be
ensured with the demand from estimated real-world driving
cycle and road conditions. Therefore, the constraints relevant
to AMT, EM, and engine might be fed into the optimization
process. Consequently, a set of near-optimal solutions might be
obtained through iterative computations, until the optimization
criterion and the constraint conditions are simultaneously met.
Moreover, a precondition is that the regular driving cycle and
the instantaneous road conditions might be estimated from the
historical driving data and the vehicle longitudinal dynamics
model, as shown in the upper-left part of Fig. 8. The detailed
derivation of the proposed CDP algorithm might be expressed
in the following.
A. Problem Statement for the Standard DP
The discrete-time form of the system state-space model can
be expressed as follows:
x(k+1)=f[x(k),u(k)] ,k=0,1,...,N −1 (16)
where fis the transition function. The state vector x(k)and the
control vector u(k)of the system are described as follows:
x(k)={SOC(k),R[ig(k)]}(17)
u(k)=[Tm(k),s(k)] (18)
where ig(k),R[ig(k)], and s(k)are the gear number, the gear
ratio, and the gear-shifting command at phase t=k, respec-
tively. Moreover, Tm(k)is the EM torque at phase t=k.
LI et al.: ENERGY MANAGEMENT STRATEGY OF PLUG-IN HYBRID ELECTRIC BUS FOR CITY-BUS ROUTE 2797
The state variables and the control variables should be lim-
ited by the inequality constraints, i.e.,
⎧
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎩
Te_min(ωe)≤Te(k)≤Te_max (ωe)
ωe_min ≤ωe(k)≤ωe_max
Tm_min(ωm)≤Tm(k)≤Tm_max (ωm)
ωm_min ≤ωm(k)≤ωm_max
SOCL≤SOC(k)≤SOCH
(19)
and the equality constraints are described as follows:
ig(k)∈Ig={1,2,...,6}
Te(k)=Tr(k)−Tm(k)(20)
where Te(k)and Tr(k)are the engine torque and the demand
torque of the powertrain at phase t=k, respectively. ωe(k),
ωm(k), and SOC(k)are the rotational speeds of the engine, the
EM, and the battery state of charge at phase t=k, respectively.
Index min and max represent the minimum and maximum val-
ues of the relevant variables, respectively. SOCLand SOCH
are the lower and upper thresholds of the SOC, respectively.
The optimal control problem is to find the control input u(k)
to minimize the following cost function [11]:
J=
N−1
k=0
L[x(k),u(k),k]
=
N−1
k=0
[Y1·Qg(k)·Δt+Y2·Qe(k)·Δt
+Y3·|ig(k)−ig(k−1)|](21)
where Nis the time of the drive cycle. Lis the instantaneous
cost at phase t=k.Yi,i=1,2,3 are the weighting factors. As
(21) shows, the cost function consists of three parts, namely, the
CNG consumption of engine, the electric energy consumption,
and the penalty of the gear-shifting operation in one step size.
Y1and Y2represent the current market prices of CNG and
electricity, respectively. Y3might be selected through repeated
testing [13]. It is noteworthy that the second term of (21) would
be negative when the PHEB runs in the regenerative braking
process.
According to Bellman’s principle of optimality, the overall
dynamic optimization problem can be decomposed into a series
of single-phase decision problems as follows [5], [13].
Step N−1:
J∗[x(N−1)] = min
u(N−1) {L[x(N−1),u(N−1),N −1]
+G[x(N)]}.
Step k,for0≤k≤N−1:
J∗[x(k)] = min
u(k){L[x(k),u(k),k]+J∗[x(k+1),k +1]}
(22)
where J∗[x(k),k]is the optimal cost function with state x(k)
at phase t=k, and G[x(N)] is the cost at t=N.
The standard DP algorithm consists of two procedures. First,
the given recursive (22) is solved backward to search for
the optimal cost, i.e., J∗[x(k),k], and the relevant optimal
control policy u(k)for every state x(k). Then, the second
procedure is computed forward through the state equation to
restore the optimal state trajectory and the optimal control
sequence. It is a standard numerical method to use quantization
and interpolation to solve the procedures [15]. Since the state
variables are in the discrete-time space, cost function J[x(k),k]
is evaluated only at the grid points of the state variables at each
phase. Moreover, the next state variable x(k+1)is not exactly
guaranteed to be a quantized value. Hence, the value of optimal
cost function J∗[x(k+1),k+1]is determined through linear
interpolation.
B. CDP With AMT Gear-Shifting Correction
For a PHEB, with frequent starting and accelerating, the
AMT gear-shifting strategy should not only focus on the fuel
economy but should also take drivability into account under
the specific conditions. As described in Section III-A, the gear
number ig(k), which is obtained through solving the global
optimal problem considering minimizing the energy consump-
tion and the constraint of gear shifting, might be only aware
of the economy [22]. However, due to the power limitation of
engine and EM, the PHEB with a pure economic gear-shifting
strategy might not satisfy the driver’s intention in most bus
driving conditions. In particular, when the PHEB is running in
upslope road conditions, the gear number and the gear-shifting
point Vpobtained by the standard DP algorithm might cause
an obvious deviation between the real speed and the driver’s
intention, as shown in Fig. 9.
To solve this problem, the correction logic shown in Fig. 10
is used, and the basic idea of the flowchart could be described as
follows. First, the online estimation of the equivalent road grade
could be carried out under the road grade or the variation load
conditions. Second, integrated with the estimated equivalent
road grade, the gear-shifting coefficient is determined to obtain
the vehicle speed on the balanced gear-shifting points, which
fulfill the correction from the economical gear-shifting opera-
tion to the dynamical gear-shifting operation. Finally, according
to the preset correctional logic, the drivability of the PHEB
might be ensured through the tradeoff between the dynamical
and the economical gear shifting.
1) Equivalent Road-Grade Estimation: Considering the
cost of sensors and effects of signal noise, a simplified esti-
mation method for equivalent road grade might be employed
instead of the onboard sensor in most vehicle dynamics con-
trollers. Combined with (2), vehicle acceleration aveh might be
obtained as follows:
aveh =Tw
mr −gCrcos θ−1
2mCDρdAV 2−gsin θ. (23)
Generally, the road slope is assumed to be zero; hence,
cos θ=1, and sin θ=0. Then, (23) might be rewritten as
follows:
aveh +gCr+1
2mCDρdAV 2=Tw
mr .(24)
Defining that axesti =aveh +gCr+(1/2m)CDρdAV 2,the
estimated equivalent acceleration axesti might be deduced from
2798 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 64,NO. 7, JULY 2015
Fig. 10. Flowchart of AMT gear-shifting correction.
(2), supposing that θ=0, i.e.,
axesti =Tw|θ=0
mr .(25)
On the other hand, the real acceleration axreal might be
calculated by the following equation:
axreal =Va(k)−Va(k−1)
Δt(26)
where Δtis the time interval. If the rolling resistance is ignored,
the estimated angle of road slope ˆ
θcan be obtained by the
equation as follows:
ˆ
θ=arcsinaxesti −axreal
g.(27)
As described in [22] and [23], the road grade and the
vehicle mass could be simultaneously obtained with the de-
signed observer. However, in this paper, the equivalent road
grade is estimated with (25)–(27). In the real application, the
number of passengers might be variable with the different bus
stations, and then, the driving torque Twmight be changed,
whereas min (25) is still the empty vehicle mass. As a result,
the variable vehicle mass might be reflected in the values of
axesti. Therefore, the estimated road grade ˆ
θcould be regarded
as the equivalent road grade, which contains the effects of
the road grade, the varying vehicle mass, and the driving
resistances.
According to the current required vehicle velocity and the
angle of road grade, the required longitudinal acceleration axr
Fig. 11. Schematic of the relationship between εand axr.
can be obtained by the following equation:
axr =dVr
dt +gsin ˆ
θ. (28)
2) Dynamic Correction: To represent the balanced gear-
shifting strategy, the gear-shifting coefficient εis defined as
follows:
ε=axr
aM
xr ∈[0,1](29)
where aM
xr is the maximum longitudinal acceleration with the
given PHEB.
The axr −εcurve, which is calibrated through the actual
vehicle test with the real-world driving cycles, is shown in
Fig. 11. To be noted, the concave shape of the curve indicates
the strategy inclines to the economical gear-shifting operation.
εMand ε0represent the maximum and minimum values of ε,
respectively. Generally, the gear-shifting operation of the city
bus would not be completely dynamic or completely economic;
hence, εM=0.8, and ε0=0.2 [24].
LI et al.: ENERGY MANAGEMENT STRATEGY OF PLUG-IN HYBRID ELECTRIC BUS FOR CITY-BUS ROUTE 2799
Then, the vehicle speed at the balanced gear-shifting points,
i.e., Vp, can be rewritten as the following simple linear rela-
tionship expression:
Vp=εV d+(1−ε)Ve(30)
where Vdand Veare the vehicle speed at the dynamical and
economical gear-shifting points, which are given by the real bus
test data. As shown in (30), with the increase of ε, the speed at
the gear-shifting points Vptends to the dynamical gear-shifting
points.
3) Correctional Logic for Gear Shifting: The vehicle speed
at the balanced gear-shifting points might be obtained by the
given process and then combined with the current gear number
ig(k)and the gear number at the last phase ig(k−1);theAMT
gear-shifting correction might be carried out as the following
logic.
i) ig(k)−ig(k−1)=−1: The optimal control input ig(k)
generated by the standard DP at phase t=kcan be
accepted in this case.
ii) ig(k)−ig(k−1)=0: If Va(k)≥Vp(k), the optimal
control input ig(k)generated by the standard DP at phase
t=kcan be accepted; otherwise, the AMT executes the
downshifting operation.
iii) ig(k)−ig(k−1)=1: If Va(k)≥Vp(k), the optimal
control input ig(k)generated by the standard DP at phase
t=kcan be accepted; otherwise, the AMT might keep
the gear number ig(k−1)on the last phase.
With the given logic, AMT gear-shifting correction is im-
plemented, and then, the vehicle speed at the economical gear-
shifting points obtained by the standard DP algorithm might be
readjusted to ensure the drivability of the PHEB.
C. Limitation of the Control Set
Because the SOC range of the PHEB might vary in a larger
scope, it is more difficult to determine the quantization accuracy
of the state variable SOC. The searching range of the control
variable Tm(k)is narrowed, keeping the quantization accuracy
of the state variable SOC. The control variable Tm(k)at phase
t=kis selected as follows:
Tm(k)=(−Tm_peak :ΔTm:Tm_peak)(31)
where Tm_peak is the peak torque of the EM, and ΔTmis the
searching increment of the control variable. Because the peak
torque of the EM considered is large, enlarging the increment
ΔTmappropriately might improve the computing speed signif-
icantly at very little cost of computation accuracy.
In addition, the rotational speed of the output shaft of the
engine is the same as that of the EM in the single-shaft parallel
configuration, when the clutch is engaged. Thus, the trans-
mission ratio R[ig(k)] should satisfy the following inequality
constraint:
R[ig(k)] ≤min(ωe_max,ω
EM_max)
ωw(k)(32)
where ωe_max and ωEM_max are the maximum rotational speed
of the output shaft of the engine and the EM, respectively.
ωw(k)is the rotational speed of the wheel at phase t=k,
TAB LE I I
SIMULATION PARAMETERS
which can be inversely calculated via the vehicle model from
the driving cycle. The admissible control variable ig(k)can be
also narrowed through the given inequality constraint.
IV. SIMULATION VALIDATION
Here, the proposed DP algorithm with AMT gear-shifting
correction was tested under a given driving cycle. The quan-
tization increment of the battery SOC is set to 0.006, and
the quantization increment of the EM torque ΔTmis set to
10 N·m. The initial SOC is set to 0.9, and the final SOC is
0.3. The related simulation parameters are listed in Table II.
Because the optimal gear position trajectory might cause
frequent gear shifting, the suitable value of the penalty factor
Y3should be selected through calibrating tests of PHEB [13]. It
is worth noting that a rule-based braking strategy is employed
in the proposed DP algorithm. The peak generating torque of
EM is used as the threshold, below which the braking torque
is completely provided by the EM; when the demand braking
torque exceeds the peak generating torque, the EM provides the
peak torque, and the pneumatic braking system compensates
the rest of the demand braking torque.
A. Simulation Case: Chongqing Bus Driving Cycle
The real-world driving conditions were employed to verify
the effectiveness of the proposed strategy. The velocity–time
curve of the driving cycle was collected from bus route 178 in
Chongqing, China, in which the PHEB is demonstrated running
as a city bus. The route map might be obtained from Google
Maps, as shown in Fig. 12(a). The driving cycle for simulation
starts from Changsheng town government station [Point A in
Fig. 12(a)] to Nanping station [Point B in Fig. 12(a)] and then
returns to Station A, including 24 bus stops. The velocity–time
curve and the filtered values were shown in Fig. 12(b) and (c).
A real grade–distance curve, which reflects the real road-grade
information, is shown in Fig. 12(d). Moreover, the number of
passengers in one 178 bus trip is shown in Fig. 12(e). Note that
there are many slope roads in bus route 178, and the road grade
2800 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 64,NO. 7, JULY 2015
Fig. 12. Characteristic curves of city-bus route 178. (a) Typical bus route 178
map. (b) Original velocity–time curve. (c) Velocity–time curve after filtering.
(d) Grade–distance curve. (e) Regular curve of the number of passengers in bus
route 178.
is obtained through calculating the elevation collected by the
GPS, assuming that the average mass of passengers is 60 kg.
B. Energy Consumption
Using the proposed strategy, simulation results under bus
route 178 are shown in Fig. 13. Fig. 13 shows the basic curves
of the PHEB in the given driving cycle. To be noted, the engine
starts only when the EM max torque cannot satisfy the required
torque from the driving cycle. Owing to the high power of the
EM and the existence of AMT, the bus in most parts of the
trip can be operated in EV mode. In the braking process,
the existence of AMT in the powertrain ensures that the EM
could fully recover the braking energy. On the other hand, the
Fig. 13. Results of the Chongqing bus route 178 driving cycle.
working efficiency of the two power sources is high through
the reasonable distribution of the proposed strategy, as shown
in Fig. 14. Most of the working points of the engine are close
to the engine optimal operating line (as shown in the dotted line
in the left plot in Fig. 14), and the EM mainly operates in the
high-efficiency area.
To verify the energy efficiency, the proposed CDP-based
energy management strategy would be compared with the stan-
dard DP-based strategy without AMT gear-shifting correction.
In addition, a rule-based energy management strategy, which is
called the EV+CS strategy, is employed. The single-parameter
gear-shifting strategy, which only considers the powertrain
speed in choosing the suitable gear, is used in the EV+CS
strategy [12]. The SOC comparison curves are shown in Fig. 15.
Fig. 15 shows that the proposed CDP strategy might be very
close to the global optimal electric energy distribution in the
given driving cycle. From a quantitative perspective, the simu-
lation results with three strategies are shown in Table III. The
results demonstrate that the energy consumption generated by
the proposed strategy is slightly higher than that generated by
the standard DP algorithm but significantly lower than that
of the EV+CS strategy. As the results show, the proposed
CDP-based strategy could reduce the energy consumption by
LI et al.: ENERGY MANAGEMENT STRATEGY OF PLUG-IN HYBRID ELECTRIC BUS FOR CITY-BUS ROUTE 2801
Fig. 14. Operating points of the engine and the EM on bus route 178 (the
dotted line in the left plot is the engine optimal operating line).
Fig. 15. SOC comparison between three strategies.
TABLE III
ENERGY CONSUMPTION COMPARISON
moving the operating points of two power sources into their
own high-efficiency areas.
C. Drivability
To highlight the advantages of the proposed strategy com-
pared with the standard DP, some comparisons are carried out
during the driving process of the PHEB in this part. According
to the AMT gear-shifting correction described in Section III-B,
the comparison curve between the real slope and the estimated
slope in the given driving cycle is shown in Fig. 16. As shown
in Fig. 16, the proposed estimation method for the road grade
is not only saving the cost for the relevant sensors but also
effective for the calculation of the value of axr. Although there
Fig. 16. Slope estimation result in bus route 178.
Fig. 17. Result curve of the gear-shifting coefficient ε.
Fig. 18. Vehicle speed tracking comparison between standard DP and CDP
algorithms in bus route 178.
are some estimation errors, they can also be accepted because
the estimated slope angle might be only used for judging the
demand driver acceleration. Then, the gear-shifting coefficient
ε(k)at each step size is shown in Fig. 17.
Fig. 17 shows the estimated values of ε(k), which might
basically reflect the driving intention during the driving process
of the PHEB. As shown in Fig. 17, the vehicle speed at the
upshifting points by the proposed AMT gear-shifting strategy
ensures the fuel economy of PHEB as well as the power
performance during the upslope condition. Moreover, when the
speed error appears during the upslope condition, the AMT
gear-shifting operation might be executed by the proposed CDP
strategy, which is not found in the standard DP. The gear
number downshifting from 2 to 1 might keep the PHEB running
in the upslope condition with sufficient power, whereas the gear
number obtained by the standard DP can only minimize the
current energy consumption.
Fig. 18 shows the vehicle speed tracking performances by
the standard DP-based strategy and the proposed CDP-based
strategy. As the results indicate, the standard DP-based strategy
might not satisfy the required vehicle speed where the power
demand is high (shown in Fig. 18) due to the inappropriate gear-
shifting operation, whereas the proposed CDP-based strategy
can fulfill the vehicle speed tracking performance requirement
2802 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 64,NO. 7, JULY 2015
Fig. 19. Result of AMT gear-shifting correction in a transient condition.
Fig. 20. Gear-shifting diagram comparison between DP algorithm and CDP
algorithm.
well. As indicated in Fig. 19, when the speed error occurs in
the slope road condition (see Fig. 16), the driver intention is
urgently accelerating (see Fig. 17), the gear number distributed
by the standard DP still increases, whereas the proposed CDP-
based strategy could keep the power performance using the
current gear.
A real gear-shifting curve, which represents the upshifting of
AMT from 3 to 4, is shown in Fig. 20. In Fig. 20, the points
above or below the real upshifting curve represent the case
that the gear-shifting operation inclines to the dynamical or the
economical gear-shifting operation, respectively. In addition,
the red circles represent the upshifting points distributed by the
CDP algorithm, when the acceleration of the PHEB is oversized
in the upslope condition. As Fig. 20 shows, the upshifting points
determined by the CDP are closer to the actual points than those
determined by the standard DP algorithm without the AMT
gear-shifting correction in the slope road condition.
V. C ONCLUSION
This paper has proposed a CDP-based energy management
strategy with AMT gear-shifting correction for the single-
shaft parallel PHEB with fast-charging battery. The standard
DP algorithm with the cost function, including the energy
consumption and the penalty term about frequent gear shifting,
is used to solve the optimization problem of the torque split
between the engine and the EM, when it obtains a set of
gear-shifting points. Considering the effect of the equivalent
road grade, the AMT gear-shifting correction is added into
the strategy to balance the dynamical and the economical
gear-shifting operation to ensure the drivability of the PHEB.
Simulation results demonstrate that the proposed CDP-based
energy management strategy is effective in improving the fuel
economy of the PHEB by moving the working points of the
two power sources into the high-efficiency area. In addition,
the results also verify that the proposed strategy ensures the
drivability by the AMT gear-shifting correction.
Although the vehicle modeling error and the uncertainties of
real-time traffic might bring some difficulties for the application
of the DP algorithm, using the DP algorithm is still a potential
method for the energy management strategy of the PHEB from
an academic point of view. With the development of the relevant
applied techniques, such as the application of the GPS, an
inertial measurement unit, 3-D maps, and so on, the proposed
CDP algorithm would be put into practice sooner or later.
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Liang Li received the Ph.D. degree from the Depart-
ment of Automotive Engineering, Tsinghua Univer-
sity, Beijing, China, in 2008.
Since 2011, he has been an Associate Professor
with Tsinghua University. From November 2011 to
December 2012, he was a Researcher with the In-
stitute for Automotive Engineering, RWTH Aachen
University, Aachen, Germany. His research interests
mainly include vehicle dynamics and control, adap-
tive and nonlinear system control, and hybrid vehicle
develop and control.
Dr. Li received the China Automotive Industry Science and Technology
Progress Award for his achievements in the hybrid electrical bus in 2012.
Chao Yang received the B.E. degree from Yanshan
University, Qinhuangdao, China, in 2010. He is cur-
rently working toward the Ph.D. degrees with the In-
stitute of Electric Engineering, Yanshan University,
and with the State Key Laboratory of Automotive
Safety and Energy, Tsinghua University, Beijing,
China.
His research interests inculde the design of energy
management strategies for hybrid electric vehicles
and the hybrid electric vehicle powertrain control.
Yahui Zhang received the B.S. degree from Yanshan
University, Qinhuangdao, China, in 2011, where he
is currently working toward the M.S. degree with the
Institute of Electric Engineering.
His research interests include control strategy op-
timization of the plug-in hybrid electric bus based on
self-learning driving cycles and Global Positioning
System information.
Lipeng Zhang received the Ph.D. degree from the
National Engineering Laboratory for Electric Vehi-
cles, Beijing Institute of Technology, Beijing, China,
in 2011.
Since 2012, he has been a Postdoctoral Researcher
with Tsinghua University, Beijing. His research in-
terests mainly include vehicle dynamics and control
and electrical vehicle design.
Jian Song received the Ph.D. degree from the De-
partment of Automotive Engineering, Tsinghua Uni-
versity, Beijing, China, in 1992.
Since 2000, he has been a Professor with Tsinghua
University. His research interests mainly include ve-
hicle dynamics and control and automotive power-
train and control.
