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MODELING AND SIMULATION OF HYBRID ELECTRIC VEHICLES
Conference Paper · May 2014
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Proceedings of the 16th Int. AMME Conference, 27-29 May, 2014 AE 1
| 15th International Conference on Applied Mechanics and Mechanical Engineering. |
Military Technical College Kobry El-Kobbah, Cairo, Egypt. |
MODELLING AND SIMULATION OF HYBRID ELECTRIC VEHICLES
M. Ali *, H. Kamel*, A. M. Sharaf *, and S. A. Hegazy*
ABSTRACT
This paper presents a detailed Hybrid Electric Vehicle (HEV) modelling method
based on a multi-physics approach. The model is introduced in order to provide
design engineers with the capability to investigate effects of component selection and
to develop control systems and automatic optimization processes for HEV vehicles. A
full drivetrain system of a series/parallel HEV is developed including the internal
combustion engine (ICE), the motor generator (MG) and the power split device (PSD)
along with the vehicle longitudinal dynamics. All aspects of rotational inertial
dynamics, friction, damping and stiffness properties are considered. The interaction
between all these modules is implemented in the MATLAB/Simulink/Simscape
blockset environment. The concepts of modularity, flexibility, and user-friendly
interface are emphasized during the model development. The numerical simulation
results are compared with the analytical results of the same hybrid power train. The
convergence between the results makes the model convenient for the future
optimization techniques on HEV.
KEY WORDS
Hybrid vehicles, MATLAB/SIMULINK, modelling, simulation, PSD
INTRODUCTION
Over the past decade, the lack of petroleum resources and the increased emission
rates have stimulated the automotive research all over the world to find more
sustainable and clean energy resources. While the limited fossil fuel reserves are
being continuously depleted, both the demand and the production rates are growing
rapidly [1-2]. Hybrid Electric Vehicle (HEV) has been considered as a short term
solution to not only improve the fuel economy but also reduce its harmful emissions
[3]. It is wildly known that, HEV combines two sources of energy namely; the
conventional ICE and the electric propulsion systems which in turn reduce the
dependency on petroleum fuels. Furthermore, the concept of having dual power
sources enables the engine downsizing, load leveling and range extending. Proper
engine sizing enables running the engine near to its economic conditions, regardless
of the vehicle’s required power and accordingly less emission levels [4].
*
Egyptian Armed Forces.
Proceedings of the 16th Int. AMME Conference, 27-29 May, 2014
| AE | 2 |
Generally, according to the architecture of hybrid propulsion, there are three basic
layouts of HEVs namely; series, parallel and series/parallel HEVs. In series HEV, the
mechanical energy is produced by the engine and converted to electric energy
through the generator. This electric energy is stored in the battery back and again is
converted to mechanical energy via the electric motors to propel the vehicle as
illustrated in Figure 1-a. Ease of both installation and operation are the main features
of this type but double energy conversion represents its major disadvantages. Also,
the series power flow reduces the powertrain redundancy. In parallel HEV, both the
mechanical power from the engine and electric power from the motor are combined
to drive the vehicle as shown in Figure 1-b. While this layout provides more choices
of operation, it is practically complex to implement in the drivetrain. Series/parallel
HEV layout joins the advantages of the aforementioned layouts and provides the
choice of utilizing both the mechanical and electric energies either sequentially or
simultaneously. Additionally, regenerative brakes can be applied to transform the
vehicle kinetic energy into potential electric one. Nevertheless, the construction
complexity is one of its main drawbacks as shown in Figure 1-c.
| (a) The Architecture of A Series HEV | (b) The Architecture of a Parallel HEV |
| (c) The Architectures of a Series/Parallel HEV Fig. 1 Hybrid Vehicle Topologies |
Accurate modelling and simulation of HEVs enables better understanding and control
of their operation. Among the well-known published literature, Khan developed a
model for ‘Honda Integrated Motor Assist’ (IMA) in MATLAB/Simulink environment
[5]. Three parameters were considered and compared during two different standard
drive cycles; these are fuel consumption, regenerated energy and consumed energy.
Peng and Liu introduced an optimization algorithm for the series/parallel ‘Toyota
Hybrid System’ (THS) [1, 6]. Later, they discussed the argument between
improvements of component sizing or powertrain architecture for ‘Toyota Hybrid
System’ (THSII) considering rule based optimization [7-9]. Peng et al. developed
another control algorithm for the model of parallel HEV considering adaptive energy
management control system [10]. Stein et al. introduced a MATLAB/ Simulink model
to apply a dynamic programming algorithm [11]. Using ADVISOR, Wipke et al.
Proceedings of the 16th Int. AMME Conference, 27-29 May, 2014
| AE | 3 |
developed a simulator to simulate the full HEV powertrain [12]. While, the reviewed
work has contributed to the state of the art in HEV, it should be noted that, most of
them were either dedicated to a certain hybrid topology [1, 5, 6] or constrained to
limited access simulator [9]. However, there is a need to develop more generic
models, yet adequate to represent HEV performance accurately. A simplified model
is presented in this paper with a code such that it is accessible to modify its subsystems and subjected for further optimization techniques. Particular attention is
paid to the modelling of series/parallel HEV due its wide application in modern
vehicles.
THE MODEL DISCRIPTION
The core of the series/parallel HEV is a power split device which combines the power
from the engine and the electric motor generator (MG). The output power from PSD
is then delivered to the wheels through transmission elements such as propeller
shaft, open differential and back axle as shown in Figure 2.
Power Split Device
Torque Carrier Gear
Engine Converter
Motor /
Battery Back Generator Sun Gear
Ring Gear
Brake
Band
Brake
Switch Band
Control System Throttle Position Signal
Fig. 2 The Main Layout of the HEV Model
These elements are modeled and implemented using Simscape blockset library
including SimDriveline, SimElectronics and SimPowerSystems toolboxes [17].
Simscape blockset is part of Simulink physical modelling, encompassing the
modelling and design of systems according to basic physical principles. Physical
modelling runs within the Simulink environment and interfaces seamlessly with the
rest of Simulink and with MATLAB. Unlike other Simulink blocks, which represent
mathematical operations, physical modelling blocks represent physical components
or relationships directly such that, it is possible to represent a HEV drivetrain system
with a connected block diagram.
The engine characteristics are included in the model as a look-up table of engine
torque versus engine speed and throttle position, see Figure 3. Rotational motion can
be initiated and maintained in a driveline with actuators while measuring, via sensors,
the motions of driveline elements and the torques acting on them. The torque
converter is modelled with the physical characteristics shown in Figure 4.
Proceedings of the 16th Int. AMME Conference, 27-29 May, 2014
| AE | 4 |
0 1000 2000 3000 4000 5000 6000 7000
Engine Speed (rpm)
0
20
40
60
80
100
120
140
160
180
Engine Power (kw)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Speed Ratio
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
Torque Ratio
10
15
20
25
30
35
40
45
50
Capacity Factor
Torque Ratio
Capacity Factor
| Fig. 3 Engine Characteristics | Fig. 4 Torque Converter Characteristics |
The model of the DC motor’s equivalent circuit is represented by the armature
resistanceR. For the steady-state torque-speed relationship the inductance L is
assumed to have no effect. Considering the motor inertia J and damping , the
generated torque by the DC motor T is proportional to the armature current, the
strength of the magnetic field and rotational speed as follows:
v
t
Armature Current
V k
T k J
R
| (1) |
Where, k k t v , are the torque and back emf constants, kv is the induced back
voltage in the armature.
The battery model implements a generic dynamic model parameterized to represent
most popular types of rechargeable batteries. The battery is modeled as a series
resistor with a charge-dependent voltage source whose voltage is given as a function
of charge of the following reciprocal relationship. For a given battery nominal
voltageVo , the voltage across the battery terminals V is calculated as follows:
1
1
o 1 1
x
V V
x
| (2) |
Where x is the ratio of the ampere-hours left to the rated ampere-hours of the
battery, , are empirical constants. The initial and maximum states of charge of
the battery are mentioned in table1.
The power split device (PSD) is a key component that directly controls the power flow
among the engine and electric motor. The model of PSD considers a single-row
planetary gear mechanism consisting of three basic components; a sun gear which is
connected to the MG, a planet carrier equipped with planetary gear which is
connected to the ICE and a ring gear which resembles the output to rear axle.
Proceedings of the 16th Int. AMME Conference, 27-29 May, 2014
| AE | 5 |
Depending on which shaft is driving, driven, or fixed, the planetary gear train can
achieve a variety of speed reduction ratios. These ratios are a function of the sun and
ring radiiRS R S / R R , and therefore of their tooth numbers. The planetary gear
imposes two kinematic and two geometric constraints on the three connected axes
and the fourth constraint; the internal wheel (planet):
R R R C C S S P P
| (3) |
| (4) |
| (5) |
| (6) |
R R R R R C C P P R R R C S P R R R R C P
| The key effective kinematic constraint is given as: |
1 RS C S RS R
| (7) |
The power split device is controlled by two actuators of brake band type. Each of
them represents frictional brake with a flexible band that wraps around the periphery
of a rotating drum to produce a braking action. A positive actuating force causes the
band to tighten around the rotating drum and it places the friction surfaces in contact.
The model employs a simple parameterization with readily accessible brake
geometry and friction parameters according to the following relationship:
in d 1 tanh 4
th
T F e r
| (8) |
The braking torque T is calculated according to required tension forceFin and is
restricted by the contact friction coefficient, wrap angle and the drum
radiusrd . Where , thare the shaft angular and threshold speeds respectively.
The control system monitors the throttle valve position signal and accordingly
switches the motor/generator and outputs the brake band signals as given in Table 1.
The brake bands are controlled via a slider gain that feed the input brake force to the
model. The motor/generator switch either electrifies or ground the motor generator
circuit. The model behaves instantaneously with parameters change, which enables
the user to apply, and monitor changes in the model dynamics in real time. The
controllers are joined together in a guide user interface (GUI) to provide a user
friendly environment to control, monitor and judge the behavior of the system.
The vehicle body is assumed to be rigid with a lumped mass m which is
concentrated at it center of gravity CG. The vehicle body has single degree of
freedom which describes the vehicle longitudinal dynamics in x-direction. All forces
affecting the vehicle body are shown in Figure 5-a, this includes gravity forcemg,
front and rear tire forcesF F xf xr , , force due to road inclination and aerodynamic
Proceedings of the 16th Int. AMME Conference, 27-29 May, 2014 AE 6
dragFd . According to Newton’s second law, the equation of motion in longitudinal
direction is given as follows:
m V F F C A V V m g x xf xr d x D 12 2 sin
| (9) |
The generated tire forces are calculated according to Newton’s second law as follows
I M F r w d x d
| (10) |
The tire force Fx is calculated according to the following tire slip ratio, Figure 5-b
= d x
d
r V
slip ratio
r
| (11) |
| (a) Vehicle Body Forces | (b) Tire Forces |
| Fig. 5 Vehicle Body Longitudinal Dynamics |
Table1: Modes of operation and control for the proposed model of HEV
| Mode | Brake Band Sun |
Brake Band Ring |
Description |
| Charging | OFF | ON | Power is delivered from ICE to the carrier and then to the sun gear. The MG is driven to generate electric energy which is stored in the battery back. |
| ICE only | ON | OFF | Power is delivered from ICE to the carrier and then to the ring gear. While the MG is off, ICE power drives the vehicle back axle. |
| Synergy | OFF | OFF | Power is delivered from ICE to the carrier and then to the ring gear. While the MG is on, power from both ICE and MG drive the vehicle back axle. |
Proceedings of the 16th Int. AMME Conference, 27-29 May, 2014
| AE | 7 |
RESULTS AND ANALYSIS
Engine Drive Mode:
In this state, the engine is drives the vehicle without the synergy of the MG output
power. The MG switch is turned off and the brake band of the sun side BB2 is
applied to prevent the engine power from leaking to the MG. the throttle is set to
30%. Figure 5 shows the engine speed accelerating from its idle speed at 800rpm to
1500rpm while the vehicle accelerating to its final speed.
MG Recharging Mode:
The MG is driven by the engine in order to function as a generator. The vehicle is
stopped and the whole engine output is used to drive the MG to charge the batteries.
The brake band of the ring side BB1 is activated and that of the sun side BB2 is
deactivated. The throttle valve is set to be 5% as expected in similar idle condition of
the engine. Figure 6 shows the engine speed accelerating from its idle speed at
800rpm to 1100rpm which is the limit of the idle range, and the MG speed reaches
3850 rpm. The batteries initial state of charge are set to be 50%.
ICE-MG Synergy Mode:
In this mode, both the ICE output and the MG output are used to empower the
vehicle. Both brake bands of the sun and ring sides are deactivated so that they can
deliver power to the vehicle at the same time. The throttle valve in this mode is set to
30% as in Engine Drive Mode, so the consumed power in both states can be
compared. Figure 7 shows the engine accelerating to 1500rpm and the vehicle
accelerating to 28.54m/s. A negative value of the MG rpm, which indicates its
rotational direction to be opposite to those of ICE and Vehicle’s propeller shaft.
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0
Time (s)
800
900
1000
1100
1200
1300
1400
1500
Engine Speed (rpm)
0
10
20
30
40
50
60
70
80
90
100
Vehicle Speed (km/h)
Engine Speed
Vehicle Speed
Fig. 6 Engine Drive Mode
Proceedings of the 16th Int. AMME Conference, 27-29 May, 2014
| AE | 8 |
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0
Time (s)
700
800
900
1000
1100
1200
1300
Engine Speed (rpm)
0
500
1000
1500
2000
2500
3000
3500
4000
Motor / Generator Speed (rpm)
Engine Speed
Motor / Generator Speed
Fig. 7 Battery Recharging Mode
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0
Time (s)
-3000
-2000
-1000
0
1000
2000
Engine , MG Speed (rpm)
0
20
40
60
80
100
120
Vehicle Speed (km/h)
Engine Speed
Vehicle Speed
MG Speed
Fig. 8 Synergy Mode
A fairly compression is carried out during the engine drive and synergy modes of
operation. It is clear that, during the synergy mode, both fuel economy and driven
mileage are improved as shown in Table 2.
Table2: Fuel economy during the engine drive and synergy modes
| Mode | Engine drive mode | Synergy mode |
| Fuel Consumption (G/kW.Hr) | 370.339 | 313.504 |
| Mileage (Km/Liter) | 11.676 | 16.653 |
Proceedings of the 16th Int. AMME Conference, 27-29 May, 2014
| AE | 9 |
CONCLUSIONS
Hybrid Electric Vehicles are one of the promising challenges in energy management
applications. Exact simulation and control of the possible states of hybrid power train
can achieve many numerous virtues such as fuel consumption optimization and
emissions reduction. The proposed model in this work shows some promising results
for the different modes of operation matching the real case. As the model behaved in
an accepted matter, many optimization and control methods can be applied on the
model to experience their effect on the overall vehicle’s efficiency.
Appendix A: Vehicle and Simulation Parameters
| The Vehicle | The Engine | ||
| Vehicle gross mass (kg) | 1200 | Max. power (kw@rpm) | 175@5000 |
| No. of Driving Axles | 2 | Max. torque (N.m@rpm) | 200@4000 |
| Frontal Area (m²) | 3 | Idle speed (rpm) | 800 |
| Wheel base (m) | 3 | Max. speed (rpm) | 7000 |
| Dynamic radius (m) | 0.3 | ||
| Drag Coefficient | 0.4 | ||
| Rolling res. coefficient | 0.02 | ||
| Power Split Devise | The Electric System | ||
| Type of planetary GB | Single row | Rated motor speed (rpm) | 2000 |
| Control Actuators | Brake bands | Rated motor power (kw) | 25 |
| Ring to sun ration | 2 | Rated DC voltage (v) | 192 |
| Battery voltage (v) | 192 |
LIST OF SYMBOLS:
A
| Frontal area of the vehicle |
| Air drag coefficient |
| Required tension force |
| Tractive effort of the vehicle at front and rear axle respectivelly |
| Batteries current |
| Tire mass moment of inertia |
| Motor inertia |
| Driving moment |
| Carrier, sun and ring gear radii respectivelly |
| Motor or braking torque |
| Battery or applied voltage |
Cd Fin F F xf xr , Ib w
I J Md R R R c s r , , T V
Proceedings of the 16th Int. AMME Conference, 27-29 May, 2014
| AE | 10 |
Vb
| Batteries voltage |
| Air velocity |
| Initial battery charge |
| Vehicle longitudinal speed |
| The ratio of the ampere-hours left to the rated ampere-hours |
| Rolling resistance coefficient |
| Torque and back emf constants |
| Vehicle mass |
| Dynamic radius of the vehicle |
| Ring to sun gear ration of the PSD |
| empirical constants |
| Ground surface inclination |
| Tire rotational speed |
| Ring, sun and carrier gear speed (rpm) respectivelly |
| Angular velocity threshold |
| Air density |
| Motor damping |
| contact friction coefficient |
| wrap angle |
VD Vo
x
V X f k k t v , m rd RS , c s r , , th REFERENCES
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Proceedings of the 16th Int. AMME Conference, 27-29 May, 2014
| AE | 11 |
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