CHINESE JOURNAL OF MECHANICAL ENGINEERING
·862·
Vol. 22,aNo. 6,a2009
DOI: 10.3901/CJME.2009.06.862, available online at www.cjmenet.com; www.cjmenet.com.cn
Series-parallel Hybrid Vehicle Control Strategy Design and Optimization
Using Real-valued Genetic Algorithm
XIONG Weiwei, YIN Chengliang, ZHANG Yong, and ZHANG Jianlong*
Institute of Automotive Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
Received June 12, 2008; revised August 24, 2009; accepted September 7, 2009; published electronically December 20, 2009
Abstract: Despite the series-parallel hybrid electric vehicle inherits the performance advantages from both series and parallel hybrid
electric vehicle, few researches about the series-parallel hybrid electric vehicle have been revealed because of its complex construction
and control strategy. In this paper, a series-parallel hybrid electric bus as well as its control strategy is revealed, and a control parameter
optimization approach using the real-valued genetic algorithm is proposed. The optimization objective is to minimize the fuel
consumption while sustain the battery state of charge, a tangent penalty function of state of charge(SOC) is embodied in the objective
function to recast this multi-objective nonlinear optimization problem as a single linear optimization problem. For this strategy, the
vehicle operating mode is switched based on the vehicle speed, and an “optimal line” typed strategy is designed for the parallel control.
The optimization parameters include the speed threshold for mode switching, the highest state of charge allowed, the lowest state of
charge allowed and the scale factor of the engine optimal torque to the engine maximum torque at a rotational speed. They are optimized
through numerical experiments based on real-value genes, arithmetic crossover and mutation operators. The hybrid bus has been
evaluated at the Chinese Transit Bus City Driving Cycle via road test, in which a control area network-based monitor system was used
to trace the driving schedule. The test result shows that this approach is feasible for the control parameter optimization. This approach
can be applied to not only the novel construction presented in this paper, but also other types of hybrid electric vehicles.
Key words: series-parallel hybrid electric vehicle, control strategy, design, optimization, real-valued genetic algorithm
1
Introduction∗
Because of the energy and environment issues, the
hybrid electric vehicles(HEV) are considered as one of the
most viable alternatives to the conventional vehicles. HEV
is a complex system combining internal combustion
engine(ICE), electric motor(EM) and energy storage
system(ESS). Energy management is a critical issue for the
implementation of HEVs. Based on a proper strategy, the
control system governs the power flow among the ICE, the
EMs and the ESS to minimize the fuel consumption and
emissions of pollution while meet the driver’s intention.
There are many works focused on this issue. Dynamic
programming(DP), fuzzy logic control(FLC) and artificial
neural networks (ANN), etc are investigated in Refs. [1–8]
for the hybrid control strategies. DP is a global solution
which has the disadvantage of high computational cost, and
it can not be applied in a real vehicle. The instantaneous
optimization algorithm, which is suitable for engineering
application, is often a rule-based type like the FLC. For
such a rule-based control strategy, the parameters derived
from the engineering intuition can not be directly used
since they often result in the failure of achieving
* Corresponding author. E-mail: [email protected]
This project is supported by National Hi-tech Research and
Development Program of China (863 Program, Grant No.
2006AA11A127)
satisfactory overall system efficiency for a high non-linear
system. Therefore, both the control parameters and the
physical parameters for a hybrid vehicle require to be
optimized to satisfy the different driving cycle conditions.
Genetic algorithms(GA) are adaptive heuristic search
technique used in computing to find exact or approximate
solutions to optimization and search problems. Most of the
previous studies depend on the binary coded genetic
algorithm(BGA). POURSAMAD, et al[9] and MONTAZERI, et al[10], described an optimization approach based on
BGA for the parallel hybrid electric vehicles(PHEV); ZHU,
et al[11], also used BGA to optimize EQ7200’s physical
parameters.
Hybrid electric vehicle falls into three categories: series,
parallel and series-parallel. Seen in Fig. 1, a typical series
hybrid electric vehicle(SHEV) incorporates an engine, a
generator, an electric motor and the batteries. The engine is
disconnected with the wheels and it can not directly drive
the wheels for a SHEV. A PHEV often uses a torque
coupler (transmission) to couple the torques from the
engine and the electric motor to drive the wheels together.
Since the development of series and parallel hybrid system
has accelerated over the past decade, the focus of R&D
efforts has recently shifted to series-parallel hybrid electric
vehicle(SPHEV)[12–17]. As is shown in Fig. 2, a SPHEV
combines a series hybrid system with a parallel hybrid
system to extract the benefits of both systems. It involves
CHINESE JOURNAL OF MECHANICAL ENGINEERING
an additional mechanical link compared with the series
hybrid, an additional generator compared with the parallel
hybrid[18]. This system often switches between series and
parallel mode (configuration), which means that the control
strategy is complex and the parameter is hard to be
optimized for such a system.
Conclusions are given in section 8.
2
Series-parallel Bus Configuration
The optimization method has been applied to the case of
an experimental series-parallel hybrid electric city transit
bus. This vehicle is schematically shown in Fig. 2. The ICE
and the generator are located upstream of the clutch, the
crankshaft of the engine is directly linked with the rotor of
the generator. The traction motor is placed downstream of
the transmission; it is linked to the output shaft of the
transmission via a torque converter, then to the propeller
shaft, differential, half shafts and wheels. The
specifications of the vehicle and the major components are
listed in Table 1. The generator also acts as a starter which
is used to start the engine as well as to combine with the
ICE as an on-board generator set when the battery needs to
be charged.
Table 1
Specifications of the vehicle and the components
Vehicle and component
Vehicle
ICE
Fig. 1. Typical scheme of the series and parallel
hybrid electric vehicles
Traction motor
Generator
Battery
3
Fig. 2.
Scheme of the series-parallel hybrid electric vehicle
In this paper, the real-valued genetic algorithm(RGA) is
applied for the control parameter optimization of a
series-parallel hybrid vehicle which adopts a rule-based
energy management strategy. The aim of the application of
this algorithm is to find proper parameters to minimize an
objective function after certain driving cycle. This paper is
built up as follows. The vehicle configuration and the
specifications will be described in section 2. The energy
management strategy is then briefly introduced in section 3.
The problem to be solved is formulated in section 4. The
application of RGA for the parameter optimization is
presented in section 5. The numerical experiment is given
in section 6. The road test results are described in section 7.
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Parameter
Curb weight M/kg
Frontal area AF /m2
Aerodynamic coefficient CD
Wheel radius r /m
Peak power P/kW
Peak torque T/(N•m)
Speed range n/(r•min–1)
Peak power P/kW
Continuous power Pc/kW
Peak torque T/(N•m)
Peak power P/kW
Continuous power Pc/kW
Peak torque T/(N•m)
Type
Power capability C/Ah
Rated voltage U/V
Value
12 000
7.5
0.62
0.502
135
550
0–2 500
80
40
450
30
20
290
NiMH
60
336
Hybrid Control Strategy
For this system, the series typed configuration is
enforced when the vehicle is moving below certain a speed
vCLU. This feature will help to reduce the fuel consumption
as well as the emission of pollutions. When the vehicle
operates as a SHEV, the vehicle is propelled by the traction
motor alone, the engine is shut down unless the battery
requests charging to prevent the depletion.
When the speed is higher than vCLU, the vehicle runs as a
PHEV, and then the requested torque should be distributed
to two energy sources: the ICE and the traction motor. Of
course, the generator can also act as a motor to drive the
vehicle. But in this operation, it is not employed in order to
simplify the strategy.
CHAU, et al[18], presented several types of control
strategy for the parallel hybrid electric vehicles. In this
paper, a “optimal line” typed strategy to operate the engine
according to an optimal speed-torque line is employed.
This strategy can be illustrated in Fig. 3. The optimal
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YXIONG Weiwei, et al: Series-parallel Hybrid Vehicle Control Strategy Design and Optimization
YUsingYReal-valued
in an Isothermal
Genetic
Tank
Algorithm
Y
Y
engine torque at this line is scaled to the engine maximum
torque at a rotational speed:
TOPT = ϕ i TMAX ,
(1)
where TOPT —Optimal torque,
TMAX —Engine maximum torque,
φ —Scale factor.
END
END
where TENG is the engine torque, TCH is the charge torque,
TMOTOR is the traction motor torque, TREQ is the required
torque.
Regenerative braking is another feature exploited by
HEVs to reduce the fuel consumption. If the brake pedal is
depressed (the driver requests a torque below zero), the
traction motor will act as a generator to capture the kinetic
power. A linear braking control algorithm is used for this
vehicle as follows:
TGEN = max(λ iTREQ , TGenMax ),
(2)
where TGenMax —Maximum generative torque of the traction motor at a rotational speed,
TGEN —Regenerative torque commanded to the
motor,
λ —Regenerative factor.
4
Fig. 3.
Brake specific engine fuel consumption
contours (g/(kW•h))
A SOC sustaining policy is also included in the control
strategy. When the SOC drops down below the lowest state
of charge allowed (Sl), the engine should be enforced to
operate at the maximum torque to provide additional
charging power. When the SOC rises up higher than the
highest state of charge allowed (Sh), the original request
power, but not TOPT, should be directly commanded to the
engine to avoid deep charge of the battery when the request
torque is below TOPT.
The control strategy, except the regenerative braking, can
thereby be structurally described as follows:
IF vehicle speed<vCLU (SHEV)
IF Battery Request Charging
Idling Charge (TENG=TCH);
Motor Drives Alone (TMOTOR= TREQ);
Charge State=1;
ELSE
Engine Shuts Down (TENG=0);
Motor Drives Alone (TMOTOR= TREQ);
END
ELSE (PHEV)
IF S>Sh
TENG=min(TOPT, TREQ);
TMOTOR=TREQ–TENG;
ELSE IF S<Sl
Engine Propels Fully (TMOTOR= TMAX);
TMOTOR= TREQ – TMAX;
ELSE
Optimal Line Control (TENG=TOPT);
TMOTOR=TREQ – TOPT;
Problem Formulation
The optimization objectives are as follows: (1) to
minimize fuel consumption; (2) to sustain the battery state
of charge.
The property of an optimization problem can be
exploited by Eq. (3):
⎧⎪min J ( x),
⎨ x∈ X
⎪⎩s.t. g ( x) ≤ 0,
(3)
where x —Solution to the problem including a vector of
the control parameters within the solution
space X which defines the lower and upper
bounds of the parameters,
J(•) —Objective function,
g(•) —Non-linear constraints.
For a fuel targeted instantaneous control strategy, the
objective is to minimize the fuel mass flow rate at each
period for a charge-sustained hybrid electric vehicle:
min m f (t ), ∀t,
x
(4)
where m f —Fuel mass flow rate,
t —Time.
From a global point of view, the objectives are
transferred to minimize the fuel consumption at the
terminal time of a driving cycle, but not at local periods.
The objective is then formulated as follows:
tn
min J ( x) = min ⎛⎜ ∫ m f (t )dt ⎞⎟ ,
x
x ⎝ 0
⎠
(5)
where tn— Terminal time of a driving cycle.
Note that the charge sustaining policy is not included in
CHINESE JOURNAL OF MECHANICAL ENGINEERING
this objective function. So as to recast this multi-objective
nonlinear optimization problem as a single linear
optimization problem, a tangent penalty function (Eq. (4))
is added to the objective function to constrain the final
battery state of charge as well as to minimize the battery
energy consumption as follows:
P (tn ) = α i tan( S0 − S (tn ) ),
is the same as that between Sd and Sh, and then if ∆S and Sd
are determined, Sl and Sh are consequently determined. In
order to operate the battery in a multitude of times, Sd are
all set to 0.55 on the contrary the battery resistance is the
lowest. The relationships between these variables are as
follows:
⎧ Sl = Sd − ΔS ,
⎨
⎩ Sh = Sd + ΔS .
(6)
where P(•) —Penalty function,
α —Penalty factor.
Then the objective function is redefined as follows:
CJ ( x) =
tn
∫0
FC (t )d t + P(tn ).
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(8)
(7)
5 Application of RGA
5.1 Overview of genetic algorithm
GA is premised on the evolutionary ideas of natural
selection and genetic, which relies on the use of selection,
crossover and mutation operations to generate the offspring
of the existing population. GAs do not require derivative
information or other auxiliary knowledge. Only the
objective function and corresponding fitness values
influence the directions of search. The more fit individuals
have, the better chance to be selected as the parents.
The genetic algorithm normally works in this way: first,
a population is created with a group of individuals
randomly; and then two individuals selected based on their
fitness reproduce one or more offspring; after that offspring
are mutated randomly. This continues until a suitable
solution has been found or a certain number of generations
have passed.
Compared with binary coded genes, the real-valued
genes often offer a number of advantages over them[19]. For
example, the binary-coded chromosome should be
converted to a phenotype so as to evaluate the fitness.
However, the real-valued type does not need the additive
process, which increases the efficiency of the GA. RGA is
used to represent the chromosome in this study while most
of the previous studies depend on a binary-coded type.
Fig. 4 shows optimization flowchart of RGA for the
SPHEV. The series-parallel simulation program(SPSP) is
the simulation tool including the vehicle models coded in
the Simulink environment.
5.2
Individuals
The individuals represent the control parameters to be
optimized, since the control strategy switches the mode
mainly based on four parameters which are Sh, Sl, vCLU and
φ. These parameters should be optimized to meet the
objectives. To reduce the computational cost, an approach
described below is used to cut down the individual numbers.
As shown in Fig. 5, Sd represents the desired state of charge.
It is assumed that the interval value (∆S) between Sd and Sl
Fig. 4.
Optimization flowchart of RGA for SPHEV
Fig. 5.
Resistance characteristics of the battery pack
Then, ∆S, φ and vCLU are considered as the optimizing
parameters. The aim of the optimization is thereby to find a
variable vector xOPT to minimize the objective function
above:
OPT
x OPT = (ΔS OPT ϕ OPT vCLU
).
(9)
Based on the desired performance and characteristics of
the components, the bounds of the variables are listed in
Table 2.
YXIONG Weiwei, et al: Series-parallel Hybrid Vehicle Control Strategy Design and Optimization
YUsingYReal-valued
in an Isothermal
Genetic
Tank
Algorithm
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Table 2.
where X At , X Bt —Pair of old populations before crossover
operation,
t+1
t+1
X A , X B —Pair of new populations after crossover
operation,
σ —Random number controling the variance
of each crossover operations.
Bounds of the decision variables
Parameter
SOC interval ∆S/%
Optimal torque ratio to
maximum torque φ
Series-parallel switch speed
vCLU/(km•h–1)
Lower bound
5.0
Upper bound
20.0
0.5
1.0
12.0
20.0
5.3 Fitness function
In this case, the objective function value is transformed
into a measure of relative fitness to solve a minimization
problem by the non-linear ranking method.
5.4 Selection operator
Stochastic universal sampling ensures a selection of
offspring, which is closer to what is deserved than roulette
wheel selection. The stochastic universal sampling
selection method is adopted here to decide whether a
chromosome can survive to the next generation. The
chromosomes that survive to the next generation are placed
into a matting pool for crossover and mutation operations.
5.5 Crossover operator
Once a pair of chromosomes has been selected for
crossover, one or more randomly selected positions are
assigned to the to-be-crossed chromosomes. The newly
crossed chromosomes are then combined with the rest of
the chromosomes to generate a new population.
An arithmetic crossover operator is used, which is a
linear combination of two chromosomes. This method can
be formulated as follows:
5.6 Mutation operator
After the crossover operation, the mutation operation
determines if a chromosome should be mutated in the next
generation, which plays the roles of recovering the lost
genetic materials as well as randomly disturbing genetic
information. With real-valued representations, mutation is
achieved by either perturbing the gene values or random
selection of new values within the allowed range. In this
study, uniform mutation method is applied:
⎧ X t = {x1t , x2t , ⋅⋅⋅, xkt , ⋅⋅⋅, xnt },
⎪⎪ t+1
⎨ xk = Lk + r (U k − Lk ),
⎪ t+1
t
t
t+1
t
⎪⎩ X = {x1 , x2 , ⋅⋅⋅, xk , ⋅⋅⋅, xn },
where X t —Population before mutation operation,
X t+1 —Population after mutation operation,
n —Number of variables,
k —Position of the mutation,
r —Random number between 0 and 1,
Lk, Uk —Lower and upper bounds on the variables at
location k.
6
⎧⎪ X At+1
=σ
+ (1 − σ
⎨ t+1
t
t
⎪⎩ X B = σ X A + (1 − σ ) X B ,
X Bt
) X At ,
(10)
Fig. 6.
(11)
Numerical Experiment Case
As mentioned in section 4, SPSP shown as Fig. 6 is
used to perform the optimizations.
Interface of SPSP
CHINESE JOURNAL OF MECHANICAL ENGINEERING
SPSP is forward simulation tool for series-parallel
evaluation on fuel economy, emission and other
performance. In this tool, the quasi-static model of the
engine as well as the electric motors, and an internal
resistance typed battery model are used. The vehicle is
considered as a moving mass subjected to the traction force.
The road load includes the aerodynamic drag force, the
rolling resistance of the tires and the gravitational force.
Computational simulations works were carried out on the
Chinese Transit Bus City Driving Cycle which are shown
in Fig. 7. The following parameters are configured to
perform the GA for the application under consideration.
(1) Max number of generations: 40;
(2) No. of individuals in a population: 25;
(3) No. of variables: 3;
(4) Survival selection: stochastic universal sampling;
(5) Crossover (recombination) method: arithmetic crossover;
(6) Mutation method: uniform mutation;
(7) Mutation rate: 0.025;
(8) Penalty factor α: 1 000;
(9) Initial battery state of charge: Si= Sd=0.55.
Fig. 7.
parameters are set to the optimal values, and the vehicle is
loaded 3.5 t. We use an on-board monitor system based on
controller area network(CAN) to guide the tracing of the
driving schedule. The vehicle parameters including the
vehicle speed, the transient SOC and the fuel consumption
are collected by this system.
Table 3.
Optimized parameters and results
Parameter
SOC interval ∆S/%
Optimal torque ratio to maximum torque φ
Series-parallel switch speed vCLU/(km•h–1)
Fuel consumption C/(L•100 km–1)
Value
18.12
0.62
13.15
32.29
As shown in Fig. 9, the dot line is the actual speed,
and the real line is the corresponding desired speed. The
transient SOC is presented in Fig. 9, and the fuel
consumption with the index time is shown in Fig. 10. The
data shows that the optimal fuel economy as well as the
optimal final SOC can be achieved using the optimal
control parameters. Because some tracing is missed during
a real road test, the absolute fuel economy is incomparable;
the specific fuel consumption in liters per 100 km is used to
evaluate the optimal fuel economy and actual fuel economy.
Table 4 shows that the actual results are similar to the
optimal results, which validate the optimization is effective.
Chinese Transit Bus City Driving Cycle
Fig. 8 shows the optimization process history for the
driving cycles. In this optimization case, the final SOC is
sustained to the initial (desired) value after a driving cycle,
which means that the minimum objective value equals to
the optimal fuel consumption. In addition, the optimized
results are shown in Table 3.
Fig. 9.
Simulated and actual battery state of charge
Fig. 10.
Table 4.
Simulated and actual fuel consumptions
Comparison on simulation and road test results
Parameter
Fig. 8.
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Optimization process history of RGA
Distance
d/km
Initial SOC
7 Road Test Validation
Final SOC
Si/%
Sf/%
Fuel consumption C/mL
A road test is carried out to validate the optimization
parameter’s performance. During the test, the control
Specific fuel consumption
C1/((L•100 km–1)
Simulation
Road test
Pessimistic
5.87
5.74
5.36
55.0
55.0
55.0
55.0
54.7
54.75
1 894.4
1 903.5
1 826.5
32.29
33.16
34.08
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YXIONG Weiwei, et al: Series-parallel Hybrid Vehicle Control Strategy Design and Optimization
YUsingYReal-valued
in an Isothermal
Genetic
Tank
Algorithm
Y
Y
Conclusions
(1) Series-parallel electric vehicle control parameters
need to be optimized to meet the requirements on fuel
economy as well as to prevent the depletion while
satisfying the driver’s intention.
(2) HEVs’ multi-objective nonlinear optimization can be
transferred to a single-objective optimization problem using
penalty method. For the sake of reducing the computational
cost, it is necessary to cut down the number of optimization
parameters.
(3) Real-valued genetic algorithm is a feasible approach
to optimize the parameters for an “optimal line” typed
control strategy; road test results validate its effectiveness.
(4) Intelligent control can improve strategies’
adaptability and flexibility, but such strategies also increase
the computational cost. The future work is located on
developing an engineering intelligent strategy as well as the
optimization of it.
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Biographical notes
XIONG Weiwei is currently a doctoral candidate in Institute of
Automotive Engineering, Shanghai Jiao Tong University, China.
He received his master’s degree from School of Mechanical
Engineering, Shanghai Jiao Tong University, China, in 2005. His
research interest is in advanced hybrid electric vehicle control and
optimization.
E-mail: [email protected]
YIN Chengliang is currently a professor in Institute of
Automotive Engineering, Shanghai Jiao Tong University, China.
He received his PhD degree from Jilin University, China. His
research interests include hybrid electric vehicle, vehicle
electronics, advanced transmission system, etc.
E-mail: [email protected]
ZHANG Yong is currently a post-doctorate in Institute of
Automotive Engineering, Shanghai Jiao Tong University, China.
He received his PhD degree from School of Mechanical
Engineering, Shanghai Jiao Tong University, China, in 2006. His
research interests include hybrid vehicle electronics, ESP.
E-mail: [email protected]
ZHANG Jianlong is currently a post-doctorate in Institute of
Automotive Engineering, Shanghai Jiao Tong University, China.
He received his PhD degree from School of Mechanical
Engineering, Shanghai Jiao Tong University, China, in 2008. His
research interests include hybrid vehicle regenerative brake
control, ABS.