Modeling and Simulation of a Hybrid...

IN DEGREE PROJECT VEHICLE ENGINEERING,SECOND CYCLE, 30 CREDITS

, STOCKHOLM SWEDEN 2018

Modeling and Simulation of a Hybrid Powertrain

MARTIN HEDON

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE

TRITA TRITA-EECS-EX-2018:145

www.kth.se

Modeling and Simulation of a Hybrid

Powertrain

by:

Martin Hedon

Master Thesis in Electrical Machines and Drives

KTH Royal Institute of Technology

School of Electrical Engineering and Computer Science

Department of Electrical Power and Energy Systems

Supervisor:

Allassane Seydou, Altran

Examiner:

Oskar Wallmark, Associate Professor, KTH

Stockholm, Sweden, 2018

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Abstract

Hybrid powertrains represent the current trend on passenger cars. The purpose of this

report is to create a basic model of a hybrid powertrain in Matlab/Simulink

environment and study their performance over certification driving cycle. Three

commonly used architectures are modeled and discussed in Simulink. Hence, the basic

components of a powertrain – battery, electric machine and combustion engine – are

studied and basic models are realized. A Thevenin equivalent circuit is used to simulate

the behavior of the battery, and the combustion engine is modeled after a Willans

model. The electric machine model is based on a known efficiency map. Then, the

architectures are created as well as their control strategies. The control strategies are

created through state diagrams, and implemented into the Simulink model via

Stateflow charts. A validation procedure is presented in order to study the consistency

of the models.

Keywords:

Automotive, control strategy, hybrid powertrain, Matlab/Simulink, stateflow, Thevenin

equivalent circuit, Willans model.

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Sammanfattning

Hybrid drivlinor representerar en central personbilstrend. Syftet med rapporten är att

presentera en grundläggande modell för en hybrid drivlina i Matlab/Simulink. Tre

arkitekturer behandlas och har implementerats i Simulink. Sedan studeras de

grundläggande komponenterna i ett drivaggregat (batteri, elmaskin och

förbränningsmotor). En Thevenin-ekvivalent krets används för att simulera batteriets

beteende. Förbränningsmotorn är modellerad efter en Willans-modell.

Elmaskinmodellen är baserad på en känd verkningsgradsmapp. De tillhörande

styrstrategierna med hjälp av tillståndsdiagram. De implementeras i Simulink-

modellen med hjälp av Stateflow-diagram. Ett valideringsförfarande presenteras och

visar modellernas konsistens.

Nyckelord:

Bil, hybrid drivlina, kontrollstrategi, Matlab/Simulink, stateflow, Thévenin-ekvivalent krets,

Willans modell.

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Acknowledgements

To begin with, I would like to express my sincere gratitude to my school supervisor Dr.

Oskar WALLMARK and to my company supervisor Dr. Allassane SEYDOU, for their

continuous support, patience, motivation and immense knowledge during the

internship.

I would like to thank my Research & Innovation Responsible, Dr. Alberto NAI OLEARI

for allowing me to do this internship with his team, and also for his help during the

snow panic in Paris.

For all the table football games we played, I would like to thank the first generation of

interns, Mathieu POYARD, Yohan “Tonio” SAMSON, Adrien ECOUE, Lucas

MARLIERE, Quentin DE SAVIGNY, Alexis CORNET, and for the good moments we

shared.

I would like to thank the second generation of interns, Bao PHAN, Valentin BLANC,

Guillaume SAULNIER, Raphael MONTEIL, and all the others for all the intense

discussions we had and for all the funny ones.

I would like to thank all the colleagues that I have not mentioned from team

ECOCKPIT, HYPOT, CITIZEN and CITY TWIZ for their help and their cheerfulness all

along the internship.

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Contents

1 Introduction ............................................................ 11

2 Architecture of a Hybrid Vehicle ............................ 13

2.1 Definition ................................................................................ 13

2.2 Architectures ........................................................................... 14

Series architecture ..................................................................... 14 Parallel architecture ................................................................... 15 Series-parallel architecture (complex architecture) .................. 16

3 Basic components of Hybrid Vehicles and modelling17

3.1 Battery ...................................................................................... 17

Definition ................................................................................... 17 Technologies .............................................................................. 18 Model ........................................................................................ 20

3.2 Electric machine ..................................................................... 28

Definition .................................................................................. 28 Technologies ............................................................................. 29 Electric Machine Model ............................................................. 31

3.3 Engine ..................................................................................... 37

Definition ................................................................................... 37 Technologies ............................................................................. 38 Engine Model ............................................................................ 39

3.4 Transmission .......................................................................... 47

Planetary gear set ....................................................................... 47 Other transmission components .............................................. 49

4 Hybrid Vehicle system modelling ........................... 50

4.1 Global model framework ........................................................ 50

Control strategy ........................................................................ 50 Driving cycle .............................................................................. 52 Vehicle model............................................................................. 53

4.1 Series hybrid architecture ...................................................... 54

System model ............................................................................. 54 Control strategy ......................................................................... 55

4.2 Parallel hybrid architecture .................................................... 60

System model ............................................................................ 60 Control system ........................................................................... 61

4.3 Series-parallel hybrid architecture ........................................ 62

System model ............................................................................ 62

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Control strategy ........................................................................ 64

5 Results ................................................................... 65

5.1 First validation part: test cycles ............................................. 65

5.2 Second validation part: driving cycle ..................................... 67

Series architecture .................................................................... 68 Parallel architecture .................................................................. 70 Series-Parallel architecture ....................................................... 71

5.3 Conclusion .............................................................................. 73

6 Conclusion and future work ................................... 74

6.1 Conclusion .............................................................................. 74

6.2 Future work ............................................................................ 75

Bibliography ............................................................... 76

Appendixes ................................................................. 78

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List of Figures

Figure 1: Group Altran's Work Portfolio ......................................................................... 11

Figure 2: Series architecture ........................................................................................... 14

Figure 3: Parallel architecture ......................................................................................... 15

Figure 4: Series-parallel architecture .............................................................................. 16

Figure 5: Ragone diagram [14] ........................................................................................ 18

Figure 6: Battery diagram, charge and discharge [15] .................................................... 19

Figure 7: Example of a simple battery equivalent circuit model [5] .............................. 22

Figure 8: Thévenin equivalent circuit of the battery ...................................................... 23

Figure 9: Reference parameters expressed as a function of the SOC for charge (blue)

and discharge (red) conditions ............................................................................... 25

Figure 10: Simulink model of the battery ....................................................................... 25

Figure 11: Simulink model of the Thévenin equivalent circuit ....................................... 26

Figure 12: Simulink model of RC block for the determination of U1 ............................. 26

Figure 13: Simulink model of the SOC determination .................................................... 27

Figure 14: Pulse charge test: voltage response from the experiment (in blue) and

simulation (in red) for the current (in black), experimental data extracted from [11]

.................................................................................................................................. 27

Figure 15: Pulse discharge test: voltage response from the experiment (in blue) and

simulation (in red) for the current (in black), experimental data extracted from [11]

................................................................................................................................. 28

Figure 16: Example of an electric machine characteristic [12] ...................................... 29

Figure 17: Reference efficiency map of the Electric Machine ........................................ 32

Figure 18: Original efficiency map compared to the efficiency map created by the model

................................................................................................................................. 33

Figure 19: Error in % between the two efficiency maps ................................................. 33

Figure 20: 75 kW AC induction motor, original efficiency map compared to the

efficiency map created one by the model ................................................................ 34

Figure 21: Error in % between the two efficiency maps ..................................................35

Figure 22: Algebraic flows of power in the electric part................................................. 36

Figure 23: Simulink model of the electric machine ........................................................ 37

Figure 24: Reference map and parameters [10] .............................................................. 41

Figure 25: Toyota Prius original efficiency maps compared to the efficiency map from

the model ................................................................................................................. 44

Figure 26: Error (%) between the Toyota Prius real efficiency map and the efficiency

map extracted from Willans model ......................................................................... 45

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Figure 27: Honda Insight original efficiency maps compared to the efficiency map from

the model ................................................................................................................. 45

Figure 28: Error (%) between the Honda Insight real efficiency map and the efficiency

map extracted from Willans model ......................................................................... 46

Figure 29: Simulink model of Willans model .................................................................. 47

Figure 30: Planetary gear set .......................................................................................... 48

Figure 31: Algebraic flows in the Simulink model .......................................................... 50

Figure 32: NEDC driving cycle ....................................................................................... 52

Figure 33: WLTC3 driving cycle ......................................................................................53

Figure 34: Vehicle dynamics ...........................................................................................53

Figure 35: Series architecture......................................................................................... 54

Figure 36: Simulink model of the Series architecture ..................................................... 55

Figure 37: Stateflow chart implemented into the Simulink model ................................ 56

Figure 38: Power transfer in the model .......................................................................... 57

Figure 39: Optimization of operating point (blue dots) as a function of output power

(black dotted lines) ................................................................................................... 57

Figure 40: Comparison of the two-optimization process, blue dots represent the

optimization on the engine, green dots represent the optimization on the system

“ICE-Generator” ...................................................................................................... 60

Figure 41: Parallel hybrid architecture [16] ................................................................... 60

Figure 42: Simulink model of the Parallel architecture .................................................. 61

Figure 43: Series-Parallel architecture ........................................................................... 63

Figure 44: Simulink model of the Series-Parallel architecture ...................................... 64

Figure 45: Operation mode and SOC results for the braking test for the parallel

architecture ............................................................................................................. 66

Figure 46: Power, Torque and speed expected and obtained at the wheels, engine and

electric machine ....................................................................................................... 67

Figure 47: WLTC3 cycle (in blue) with the operation mode (in red) for the Series

architecture in normal conditions........................................................................... 68

Figure 48: WLTC3 cycle (blue) and operation mode (red) of the Series architecture in

the reduced time window ........................................................................................ 69

Figure 49: Power distribution Series architecture in the reduced time window ........... 69

Figure 50: Energy consumption of the Series architecture in the reduced time window

................................................................................................................................. 70

Figure 51: WLTC3 cycle (blue) and operation mode (red) of the Parallel architecture in

the reduced time window ........................................................................................ 70

Figure 52: Power distribution Parallel architecture in the reduced time window .......... 71

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Figure 53: Energy consumption of the Parallel architecture in the reduced time window

.................................................................................................................................. 71

Figure 54: WLTC3 cycle (blue) and operation mode (red) of the Series-Parallel

architecture in the reduced time window ................................................................ 72

Figure 55: Power distribution Series-Parallel architecture in the reduced time window

.................................................................................................................................. 72

Figure 56: Energy consumption of the Series-Parallel architecture in the reduced time

window ..................................................................................................................... 73

Figure 57: Real part of a real battery impedance as a function of the inverse of its

imaginary part ......................................................................................................... 78

Figure 58: Nyquist and bode plots from the battery model ............................................ 79

Figure 59: WLTC3 cycle (blue) and operation mode (red) of the Series architecture in

the reduced time window, low SOC ........................................................................ 85

Figure 60: Energy consumption of the Series architecture in the reduced time window,

low SOC ................................................................................................................... 86

Figure 61: Power distribution Series architecture in the reduced time window, low SOC

................................................................................................................................. 86

Figure 62: WLTC3 cycle (blue) and operation mode (red) of the Series-Parallel

architecture in the reduced time window, low SOC ................................................ 87

Figure 63: Energy consumption of the Series-Parallel architecture in the reduced time

window, low SOC .................................................................................................... 87

Figure 64: Power distribution Series-Parallel architecture in the reduced time window,

low SOC ................................................................................................................... 88

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List of Tables

Table 1: Reference battery parameters ........................................................................... 24

Table 2: Reference electric machine characteristics ....................................................... 31

Table 3: Reference electric machine characteristics ...................................................... 32

Table 4: Reference electric machine characteristics ...................................................... 34

Table 5: Reference engine characteristics ....................................................................... 41

Table 6: Willans parameters ........................................................................................... 42

Table 7: Engine data needed for the determination of the maximum torque limitation 43

Table 8: Operation modes and conditions of activation or deactivation, Series hybrid

case ........................................................................................................................... 55

Table 9: Operation modes and conditions of activation or deactivation, Parallel hybrid

case ........................................................................................................................... 61

Table 10: States of the clutches ...................................................................................... 62

Table 11: Operation modes and conditions of activation or deactivation, Series-parallel

case .......................................................................................................................... 64

Table 12: Braking mode verifications ............................................................................. 66

Table 13: Energy consumption results for each architecture in the reduced time window

.................................................................................................................................. 73

List of Appendices

Appendix 1: Frequency analysis ..................................................................................... 78

Appendix 2: Stateflow chart Parallel architecture ......................................................... 80

Appendix 3: Stateflow chart Series-Parallel architecture ............................................... 81

Appendix 4: Vehicle parameter inputs ........................................................................... 82

Appendix 5: Validation procedure results ...................................................................... 85

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1 Introduction

Altran Technologies, SA is a global innovation and engineering consulting firm founded

in 1982 in France by Alexis Kniazeff and Hubert Martigny. Altran operates primarily in high

technology and innovation consultancy, which account for nearly 75% of its sales turnover.

Administrative and information consultancy accounts for 20% of its sales turnover with

strategy and management consulting making up the rest. The firm is active in most

engineering domains, particularly electronics and IT technology (see Figure 1). In 2015,

Altran generated €1.945 billion in revenues and employed over 25,000 people around the

world. Since June 18, 2015, Altran has been led by CEO Dominique Cerutti.

Figure 1: Group Altran's Work Portfolio

E-cockpit project was started in January 2014 under the Research and Innovation Division

of Altran created 2009. Their projects aim at showcasing the competencies of Altran Group

in the field of research and innovation. E-cockpit project was established to showcase the

skills of Altran Group in the field of Automobile and its capacities to innovate and anticipate

the future with the advancement in the technologies.

The E-cockpit project is a concept of innovative and modular vehicle designed to be

economic, ecologic and to suggest new technical solutions with the idea of ‘Sustainable

Mobility’. The basic idea behind initiating this project was to provide an innovative and

sustainable solution of mobility for the future.

The powertrain activities within E-Cockpit project migrated to the Hybrid Powertrain project

(HYPOT), created in the beginning of 2018. Its purpose is to realize a modeling platform to

simulate the performances of several powertrains. The asset of the platform is that it is

adaptable and it gives the possibility to design a powertrain very easily. Also, several

powertrain technologies should be available be modeled allowing comparisons. The hybrid

powertrain is one of these technologies.

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For this project, the purpose of the proposed master thesis was to create a first Simulink of a

hybrid powertrain. It aims at giving a first approach of the systems to model, with an initial

basic model. This Simulink model should be used to access the global performances of a

hybrid powertrain, provided that the basic characteristics of the components are known.

Later on, the model will be improved with more detailed models for every component, going

deeper into the simulation and hence being more accurate.

In this report, a quick introduction on the definition of a hybrid vehicle is given section 1,

with a description of the three main architectures of a hybrid powertrain. Then in section 2,

the basic components of a hybrid powertrain are described. This should give the reader the

very basic knowledge on which technologies present and most used on the market

technologies. Section 3 introduces and explains the different component models. Discussions

on their validation are made, as well as conclusions. The global architecture models and the

way they were created are then presented in section 4, with the control strategies and the

optimization process. Finally, the final validation procedure and the results are shown and

discussed in section 5.

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2 Architecture of a Hybrid Vehicle

2.1 Definition

A hybrid vehicle is by definition a vehicle with two or more power sources. Both of

them can take part into propelling the vehicle, either together or independently. Also, one

system needs to be reversible [1].

Several technologies of hybrid powertrain exist, mostly coupling an internal combustion

engine (ICE) with a reversible system, such as the fuel cell technology or the hydrogen

combustion engine for instance. The most common technology is the combination of a

combustion engine with one or more electric machines, due to an easy access to electricity

through the power grid system.

Several hybridization levels exist, and enable to classify the vehicles [1-3]:

- Micro-hybrid: it concerns conventional vehicles with the Start&Stop technology. It

allows the engine to stop when small stops are made (at a stop sign or a red light) and

to start again fast enough so that the user does not feel it. This technology is based on

a starter-generator that helps the engine while restarting. Sometimes, this system

enables the energy regeneration during braking phases.

- Mild-Hybrid: an electric assistance is available for the vehicle. It can assist the

combustion engine with a boost mode, added to the Start&Stop system and the

regenerative braking. The Honda Insight and Civic as well as the Mercedes S400

Hybrid are examples of such hybrid vehicles [1].

- Full-Hybrid: more efficient and powerful electric components equip the vehicle

increasing its electric power. For example, it is possible to drive in a full electric mode

for short periods. This hybridization level is the one of the Toyota Prius, first large

scale hybrid vehicle commercialized in 1997, and lately of the Peugeot 3008 Hybrid,

the Audi Q5 and the BMW ActiveHybrid 5 [1].

- Plug-in-Hybrid (PHEV): a full-hybrid vehicle that can be charged from an external

source. The electric range is thus improved and it imposes different strategies for the

battery use. Indeed, either the battery is used as much as it can – the Charge

Depleting mode- or the battery is saved and the state of charge of the battery kept

almost constant - the Charge Sustaining mode.

- Extended Range Electric Vehicle (EREV): final level before the full electric

vehicle, an EREV uses the combustion engine as energy source, in other words to

charge the battery, but does not take a direct part in the vehicle traction per say. The

purpose of those vehicles is to use a small power combustion engine at its best

operating point, so that engine best efficiency is obtained.

From Mild-Hybrid to EREV, the control strategy of the electric part is very important in

order to reduce the fuel consumption and improve the global vehicle efficiency. Several

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operation modes can be selected regarding the driving situation, with full electric driving

phases for example.

The hybridization level of a car is also influenced by the way the different components are

assembled spatially. Indeed, the connection between the two energy systems can be done in

different manners. A connection solution, associated with a specific spatial disposition of the

components, defines an architecture.

2.2 Architectures

The architecture of a hybrid vehicle represents the way the components (combustion engine,

electric machine) are connected and spatially arranged in the vehicle. Three main hybrid

architectures can be distinguished on the market: series architecture, parallel architecture,

and complex or series-parallel architecture. For each architecture, several options of linking

the two energy sources are possible.

Series architecture

In this type of architecture, the mechanical connection with the wheels is entirely made with

the driving electric machine (EM). The combustion engine (ICE) is linked to a second electric

machine that processes as a generator, and converts the mechanical energy into electrical

energy. This energy either goes to the first electric machine to propel the vehicle, or helps

charging the battery.

The series architecture is represented schematically Figure 2 below.

Figure 2: Series architecture

One of the advantages of this architecture is that it gives the possibility to define/control the

combustion engine operating mode so that it can operate in an optimal efficiency region.

However, the two electric machines increase the price and the weight of this architecture as

well as the occupied volume. Also, the architecture global efficiency is lowered because of

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many energy conversions between the combustion engine and the wheels. Indeed, the

conversion of the energy from mechanic to electric and then back to mechanic decreases the

efficiency of the overall system, and thus the interest of this architecture.

The series architecture is interesting while operating in cities [3], thanks to the ability of the

electric system to deal with speed variations and stops, but not well suited for highway uses

with high power demands [1].

The Chevrolet Volt and the Opel Ampera [2] are examples of vehicles with a hybrid series

architecture.

Parallel architecture

In the parallel architecture the two systems are mechanically connected to the wheels and can

both propel the vehicle either together or separately. As shown in Figure 3, only one electric

machine is needed, which represents an advantage in terms of volume, weight and price.

Figure 3: Parallel architecture

The power coupling is here more complex than for the series architecture.

Two types of mechanical coupling systems exist, the speed coupling systems and the torque

coupling systems [1]:

- Speed coupling can be made possible through a planetary gear set. The technology is described in detail in Section 3.4.1.

- Torque coupling is the most common coupling system used in this architecture (Honda Insight, Peugeot 3008 Hybrid, Porsche Panamera S-E Hybrid [1]). Three major coupling techniques can be determined: pre-transmission coupling, post-transmission coupling and coupling through the road. Pre-transmission coupling consists in using the traction electric machine before the transmission system (gear box, CVT for instance), either by a belt pulley (low power type Start&Stop), or by sprockets for example. A post-coupling is made possible by integrating the electric machine after the transmission. Finally, coupling through the road consists in connecting the two energy systems on different wheel axles, for example used by the Peugeot 3008 [2].

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The advantages of the parallel architecture come from the fact that this architecture is very

close to a conventional vehicle one. The gain in volume, weight and price are significant.

However, the combustion engine is directly connected to the wheels which make it more

complex to control in order to target its optimal operating area. This kind of architecture is

mostly used in low hybridized vehicles (Micro or Mild-hybrid) as an electric boost to help the

combustion engine.

Series-parallel architecture (complex architecture)

The complex architecture is a combination of parallel and series architectures. Indeed, the

two power coupling systems are used. This method gives access to a better control over the

engine and the battery, combining the advantages of each architecture.

The architecture outline is presented in Figure 4.

Figure 4: Series-parallel architecture

Although it takes all benefits from the two architectures, some drawbacks remain. This

system, with two electric machines and two coupling systems, is heavy in terms of volume

and weight. It is also more complex to control than the previous architectures, but gives a

better engine control [2].

The first generation of the Toyota Prius uses this architecture with the Toyota Hybrid System

(THS) lately replaced by the Hybrid Synergy Drive (HSD) [3].

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3 Basic components of Hybrid Vehicles and

modelling

As previously shown, a hybrid powertrain is composed of several basic components,

such as a battery, one or two electric machines, a combustion engine and a transmission

system. Also, depending on the architecture used, the transmission can slightly differ. In this

part, the basic components forming a hybrid powertrain are described, giving knowledge of

the technologies used by car manufacturers. It also helps justifying the choice of the

technologies to model. Then the Simulink models of each component are presented and

discussed. A validation method is proposed and applied to the model. Each model results are

presented and their relevance is discussed.

3.1 Battery

Definition

One of the most important components of a hybrid powertrain is the battery, as it is the most

limiting one. Its challenging constraint makes it one of the most researched technologies as

major investments are made in USA, Japan, China [4] and Europe. The two most used

battery technologies are discussed here: Nickel-Metal batteries and Lithium-Ion batteries.

Obviously, many other types of batteries exist, but those two technologies globally represent

the market of power batteries in the automobile sector.

The objective of the battery is to store a sufficient amount of energy to ensure an important

range, as well as having the ability to give a high power during short periods. The acceleration

characteristics depend directly on how the battery deals with those short high power

demands.

The weight and volume of the battery are also key parameters. Its capacities of energy

absorption and dissipation have a great influence on its use to support fast charging or

discharging phases that may occur. Another important issue to be mentioned is the ageing

properties of the battery since a car is generally designed to be in service for several years or

even one or more decades.

What a battery is called in everyday life should actually be called a battery pack. A battery

pack is composed of several modules, and a module is an assembly of cells. The cells number

and organization in a module determine the basic characteristics of the battery pack. Several

cells can be placed in series and/or in parallel to form a module. A higher voltage can be

obtained by the use of cells in series branches while parallel branches aim at increasing the

output current.

These choices of organization or architecture of a module is the main difference between high

power batteries and high energy batteries. High power batteries are capable of receiving high

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power during charging and discharging phases, which can be the case during high

accelerations or decelerations (important braking phase). High energy batteries tend to

optimize the energy storage so that the vehicle range is increased.

A battery can be characterized by several factors [4], the most important ones to know are:

- The State Of Charge (SOC) of the battery. Usually expressed in percentage, the SOC

gives the level of energy left in the battery compared to its maximum energy storage

capacity. Further explanations on the SOC are given Section 3.1.3.

- The Depth Of Discharge (DOD) represents how close to being discharge the battery is.

It is equal to 1 − 𝑆𝑂𝐶.

- Its life cycle that corresponds to the number of charging-discharging cycles the

battery can endure at a certain DOD before not being able to meet the performance

objectives anymore.

- The calendar life that represents the life expectancy of the battery under periodic

storage or cycle conditions.

A Ragone [14] diagram is shown in Figure 5. It allows the comparison between the different

energy storage systems by taking into consideration the specific energy and power.

Figure 5: Ragone diagram [14]

The Ragone diagram points out clearly the high efficiency of the Li-ion technology compared

to the other ones.

Technologies

A battery cell consists of two dissimilar electrodes, separated from each other by an

electrolyte. An electrolyte is an ionic conductor and electronic insulator. One electrode is

called the anode and the other is the cathode. While charging, the anode is where the

19

reduction takes place (gain of electrons), and the oxidation (loss of electrons) takes place at

the cathode. Positively-charged ions are called “cations”, and negative ions are referred as

“anions”. An electrolyte is an ionic conductor and enables the transfer of the ions.

A sketch of a battery is shown in Figure 6 with the basic principle for charge and discharge

scenario.

Figure 6: Battery diagram, charge and discharge [15]

Nickel-Metal battery

The Nickel-Metal (NiMH) technology equipped the first generation of hybrid vehicles. This

type of batteries is then well known in terms of ageing and safety. Toyota has always used this

technology in its models. The Ragone diagram in Figure 5 indicates that this solution is one

of the most interesting one. One of its benefits is that NiMH batteries require a simple air-

cooling system, which represents an advantage in terms of weight, volume and cost.

However, the limits in terms of specific energy provide those batteries from being used in

high-hybridized vehicles like PHEV and EREV [1].

New development efforts have been recently made by BASF (Badische Anilin- & Soda-

Fabrik), world leader in the chemical industry. BASF claims that the storage capacity of

NiMH batteries could be multiplied by eight. With its competitive price compared to the

other batteries, this breakthrough could completely modify the current trend in the battery

market [13].

Lithium-Ion battery

Lithium-ion batteries (Li-ion) concern a large group of batteries. Ions can come from

different materials with varying properties. This causes variations in the resulting battery

calendar life, price and power [3]. Although Li-ion batteries are more expensive than NiMH

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batteries, they are mostly used by car manufacturers in their latest models, like Tesla,

Chevrolet and Nissan [1].

Lithium is a highly reducing metal with an important mass capacity. Its potential is then

interesting as it gives access to a high specific energy.

However, Li-ion batteries suffer from a short calendar life. To counteract this effect, batteries

need to be oversized. Also, for safety reasons, the input power is limited to prevent from Li-

dendrite formation [13]. This phenomenon is the Lithium accumulating between the cathode

and the anode which creates a reduction in the performances, short-cuts, overheating, or

thermic run-aways that can even cause explosions.

The cooling system is more complex than the one needed for NiMH batteries. A liquid

cooling system is indeed required to avoid batteries to overheat, and foremost for safety

reasons [1].

Such a cooling system adds weight and complexity compared to the NiMH technology.

Other solutions exist and are not described here. For example, supercapacitors are more and

more used for their ability to quickly store and give back the energy. In that sense,

supercapacitors represent a viable additional storing system for high power demands

(Start&Stop uses for instance).

Conclusion on the battery technology

More interesting than NiMH batteries at first sight, Li-ion batteries present the best energy

and power characteristics. However, the technology is more expensive and requires a

complex cooling system. Those aspects explain why some car manufacturers still use NiMH

batteries, when the others are ready to invest in a more efficient yet more expensive solution.

For this project, the choice was made to use Li-ion batteries, for their global best

performances compared to NiMH batteries.

Model

Developing a realistic model of a battery is quite complex due to its dynamic behavior and the

numerous interactions that take place within it. The electrochemical reactions, the intern

resistance, the state of charge, the temperature, the charge and discharge current or the use

history are all parameters that impact the behavior of a battery [5].

Different types of models exist: electrochemical models, electrical equivalent circuit models,

and black box models for example. Electrochemical models represent the chemical effects

and reactions in the battery. The electrical equivalent circuit models are basic electric circuits

composed of resistors and capacitors that aim at reproducing the battery behavior. The black

21

box models are based on experimental data. Then fitting techniques are used to derive the

model of the battery behavior [10].

In this project, a precise model of the chemical reactions is not required, only the global

behavior of the battery is needed. So the equivalent circuit models seem to be appropriate to

meet the objective of the internship.

Several models exist, for different level of model accuracy. The equivalent circuit models are

mostly used as they make an interesting compromise between precision, complexity and

calculation time. Obviously, a simple model will not take all the previously introduced

parameters into account. The parameters to be taken into account must be determined before

the model is chosen and implemented.

In this project, only the influence of the SOC and the operation mode of the battery (charging

or discharging) are represented. The limits of this strategy are described at the end of this

section.

Before introducing a few examples of battery models, it seems important to introduce further

knowledge on the State Of Charge (SOC).

The State Of Charge is defined as the ratio of the remaining quantity of electricity at a certain

time 𝑡 in the battery (𝑄(𝑡)), and the battery nominal capacity (𝑄0 in Ah). 𝑄0 represents the

total amount of energy that can be discharged from the battery when fully charged. Equation

(1) below shows the determination of the State Of Charge in percent. The SOC is expected to

be given by the program, as it is the information given to the driver.

𝑆𝑂𝐶(𝑡) =

𝑄(𝑡0) − 𝑄(𝑡)

𝑄0⋅ 100 (1)

Finally, the SOC expressed in percentage is determined by Equation (2) as a function of the

battery current 𝑖𝑏𝑎𝑡𝑡 (A).

𝑆𝑂𝐶(𝑡) = 𝑆𝑂𝐶(𝑡0) −

100

3600∫𝑖𝑏𝑎𝑡𝑡(𝑡)

𝑄0𝑑𝑡

𝑡

𝑡0

(2)

The estimation of the State Of Charge is more complex but is of a capital importance for the

battery usage strategy. It enables to keep the battery sound and so safe for the user, as well as

optimizing its use.

Conventionally, a battery is used in the range 10%-90% of SOC. Over 90% and below 10%,

unwanted chemical reactions can happen, and cause long-term damages for the battery. Also,

the major variations of battery voltage happen below 10% and over 90%.

22

Simple battery model

The first level of battery modeling with an equivalent circuit is presented in Figure 7. A

generator of a perfect voltage 𝐸𝐵 is associated with a resistance 𝑅𝐵 in serial configuration.

Figure 7: Example of a simple battery equivalent circuit model [5]

The global voltage is given by Equation (3) below with 𝑈𝐵 in V, 𝑅𝐵 in 𝛺 and 𝐼𝐵 in A.

𝑈𝐵 = 𝐸𝑏 − 𝑅𝐵 ⋅ 𝐼𝐵 (3)

Many hypotheses are made in this model:

- The open circuit voltage 𝐸𝑏 and the internal resistance 𝑅𝐵 are independent of the

battery SOC.

- The influence of the temperature is neglected.

- The discharging current has no influence on the battery capacity, so the Peukert law is

not taken into account. This law stipulates that a high discharge current causes a

diminution in the battery capacity.

Those hypotheses are too restrictive. Thus, a more developed model is studied: the Thévenin

equivalent circuit model.

Thévenin Equivalent circuit

A Thévenin equivalent circuit (or Dual-polarization) is used to model the battery. It consists

of several RC blocks to approximate the kinematic of the battery as shown in Figure 8.

The advantage of the Thévenin equivalent model is that it is a good trade-off between

simulation accuracy, computational complexity and parametrization effort.

The automotive field requires light and efficient models which must not sacrifice accuracy,

both for system-level simulation (e.g. drivetrain electrification) and for real-time applications

(e.g. Battery Management System). The Thévenin based electrical equivalent circuit models

represent the best choice.

Two effects are represented by the RC blocks:

- Activation polarization or charge-transfer polarization: represents the voltage involved in increasing the rate of the chemical reactions, or in other words, the voltage needed to overcome the activation barrier: this phenomenon is the fastest

23

between the two and thus fitted by the smaller time constant RC block. In the model, the RC block 1 schematizes this effect.

- Diffusion polarization or mass-transport polarization represents the voltage involved

in the electrolyte: this represents the slowest between the two phenomena and is thus

fitted by the largest time constant RC block. The RC block 2 represents this effect.

𝑅0 represents the ohmic resistance of the battery cell, which is made up by different

contributions belonging to the cell connectors, the current collectors, the electrolyte and the

active materials.

Figure 8: Thévenin equivalent circuit of the battery

The parameters of the equivalent electric circuit mostly depend on the SOC, the amplitude

and the sign of the current (which indicates whether the battery is charging or discharging),

the temperature and the ageing of the battery.

Due to the lack of data, the influence of the temperature is not taken into account here, as

well as the amplitude of the current.

So, in the model, the parameters 𝑉𝑂𝐶, 𝑅0, 𝑅1, 𝑅2, 𝐶1 and 𝐶2 depend only on the SOC and the

sign of the current. 𝑉𝑂𝐶 and all voltages are expressed in V, the resistances in 𝛺 and the

capacitors in F.

For a given RC block 𝑘, the equation of 𝑢𝑘 is given by Equation (4).

𝑅𝑘 ⋅ 𝑖𝑏𝑎𝑡 = 𝑢𝑘 + 𝑅𝑘𝐶𝑘 ⋅

𝑑𝑢𝑘𝑑𝑡

(4)

And the voltage of the battery is given by:

𝑈 = 𝑉𝑜𝑐 − 𝑅0 ⋅ 𝑖𝑏𝑎𝑡 − 𝑢1 − 𝑢2 (5)

The RC parallel blocks correspond to transient response of battery voltage.

By using the Laplace transform, Equation (4) gives in the s-domain:

𝑖𝑏𝑎𝑡 =𝑢𝑘𝑅𝑘+ 𝑠𝐶𝑘𝑢𝑘 (6)

24

And finally:

𝑢𝑘 = (

1

𝑠) [𝐼

𝐶𝑘−

𝑢𝑘𝑅𝑘𝐶𝑘

] (7)

This model is adapted to the project demand, as it allows having an accurate model that is

easily computable. However, a lot of data is needed in order to run the model. These data can

be obtained from experimental results. In this project, the data were extracted from [11].

Then, the created model was compared to the experimental results on which the paper based

its model in order to validate the battery model.

One difficulty was to find data that were adapted to the project objectives. Indeed, the

behavior of the battery has to be consistent for tests lasting around 20 to 30 minutes. So, the

very fast responding effects (less than a second) and very slow responding effects (more than

an hour) are neglected, and the focus was made on this limited scale. This approximation

introduces an error and corresponds to a first limit of the model that will be further

discussed.

Extraction of the parameters

The parameters used are presented in Figure 9. Those parameters concern a Li-ion battery

with a nominal capacity of 40 Ah. Those characteristics, presented in Table 1, are in

accordance with the cell characteristics of usual hybrid car batteries.

In the paper [11] where the parameters were extracted, the tests were made on a module of

seven cells connected in series.

Table 1: Reference battery parameters

Parameter Cell Module

Nominal capacity (𝐴ℎ) 40 40

Cell nominal voltage (𝑉) 3.7 25.9

25

Figure 9: Reference parameters expressed as a function of the SOC for charge (blue) and discharge (red) conditions

Extracted from [11] and presented in Figure 9, these parameters of a Li-ion module depict the

variation of the different parameters depending on the SOC for charge and discharge

configurations respectively. The Simulink model as well as the validation of the battery model

discussed later based on those values.

Implementation in Simulink

In Simulink the variation of the parameters 𝑉𝑂𝐶, 𝑅0, 𝑅1, 𝑅2, 𝐶1 and 𝐶2 as a function of the SOC

is possible through look-up tables. The sign of the power gives the information if the battery

is in charging (P negative) or in discharging (P positive) phase.

The Simulink model of the battery, shown in Figure 10, is made of two parts:

- The equivalent circuit subsystem that calculates 𝑈𝑏𝑎𝑡𝑡 from 𝐼𝑏𝑎𝑡𝑡 and the SOC, - The SOC determination subsystem that gives the SOC.

Figure 10: Simulink model of the battery

The two subsystems are described below.

26

Equivalent circuit subsystem

The Thévenin equivalent circuit model in Simulink is shown in Figure 11. Its architecture follows Equation (5) that determines 𝑈𝑏𝑎𝑡𝑡.

Figure 11: Simulink model of the Thévenin equivalent circuit

The RC blocks are made as shown below for the RC block 1. The two RC blocks are similar

and calculates U1 and U2 respectively.

It follows Equation (7) given previously. The subsystems “Subsystem R1” and “Subsystem C1”

are composed of look up tables respectively for 𝑅1 and for 𝐶1 as a function of the state of

charge. It also takes into account the fact that the battery is in charging or discharging phase.

The sign of the battery power defined as positive for discharging phases, and negative for

charging phases gives this information.

Figure 12: Simulink model of RC block for the determination of U1

RC block that calculates 𝑈2 is similar to that for 𝑈1, and is obtained from the same procedure

as for 𝑈1 determination.

SOC determination subsystem

27

The determination of the state of charge is simply following Equation (2). The Simulink SOC

block is shown in Figure 13.

Figure 13: Simulink model of the SOC determination

Validation of the model

The validation of the battery model is made through a comparison with experimental data

during charge and discharge tests. The principle is to apply a constant current during a

certain period of time and have a rest period. That way, at the end of the rest period, all the

modeled effects are ended and the charging or discharging cycle is performed.

“The method is based on the analysis of voltage-relaxation characteristics of pulse discharge

and pulse charge experiments. It can be used for both discharge and charge operation with

any number of parallel resistor-capacitor branches” [11].

First, a comparison with the results of a battery performing a charge test is made with pulses

of 200s duration and amplitude of 80A, and a rest period of 1800s (30min). The results are

shown in Figure 14.

Figure 14: Pulse charge test: voltage response from the experiment (in blue) and simulation (in red) for the current (in black), experimental data extracted from [11]

28

Then, in the same way a comparison with a discharge test is realized. The test is made of cycle

with 360s duration of discharge at 40A of current amplitude, followed by rest periods of

1800s. The results are presented in Figure 15.

Figure 15: Pulse discharge test: voltage response from the experiment (in blue) and simulation (in red) for the current (in black), experimental data extracted from [11]

The behavior of the model appears to be consistent with the experimental data. The only

major difference at the very end of the test is due to the fact that the battery was almost

empty. Thus, it could not follow the discharge test as expected. Also, as mentioned before, the

dynamic effects for extremely low SOC are more complex and explain this error in the results.

To conclude, the simulation results (red color plots) show the same behavior as the

experimental data in both charge and discharge cases. These uncertainties detected can be

explained by the extraction of the data (data extrapolated from [11]), and by the small error

introduced by the model itself.

A frequency analysis of the model can also validate the battery model as well as show its

limits. Indeed, this method points out the choice of time constants used in the model

compared to a real battery, showing the limits of the model. As said previously, modeling

only two effects enable to have a good approximation of the behavior for the chosen testing

conditions, but cannot be representative for other usage cases.

3.2 Electric machine

In this section, the electric machine is presented. A first approach of the different

technologies is given, before introducing the model used and its implementation is Simulink.

The results are then discussed.

Definition

29

Several types of electric machines exist and can be distinguished by their type of alimentation

and their rotational speed characteristics [1]. Three types of electric machines are described

in this report [7]:

- DC machines: direct current machines

- AC machines: synchronous alternative current machines

- Induction machines: asynchronous alternative current machines

The global characteristics response of an electric machine is presented in Figure 16 below.

Figure 16: Example of an electric machine characteristic [12]

Two regions of operation appear:

- At constant torque: the counter-electromotor force increases linearly with the

rotational speed until it reaches a certain limit. The same behavior is observed for the

maximum power as well. This limit is usually imposed by the electronic supply system

and its maximum voltage.

- At constant power the counter-electromotor force is kept to its maximum value by

diminishing the excitation magnetic field in the machine. This process is called field-

weakening.

The rotational speed setting the limit between the constant torque and constant power zones

is called base speed or rated speed. It varies with the injected current, so that when the

current increases (and so does the torque), the basic speed decreases.

Technologies

DC Machines

Direct current machines were used in the very first hybrid models in the 1900s [6]. Those

machines benefit from an easy control and met the requirements at the time.

30

Very easily to miniaturize, DC machines are adapted to very low speed and low voltage. The

torque control can be precise. Its power supply is very simple.

However, in today’s application, DC machines appear to be limited in terms of performances,

which reduces their use in vehicles. Fragile and expensive, they also suffer from an important

wear at the metallic collectors for example that limits their life expectancy.

Synchronous or AC machines

In synchronous machines, the rotational speed is directly proportional to the power supply

frequency of its stator. Those machines are reversible and can create an alternative voltage of

frequency proportional to the rotational speed. Many systems use synchronous machines as

they give great performances, and are reliable compared to other types of machines.

The major technology found on the market is permanent magnets machines, even if wound

rotor machines are also used.

Permanent magnets machines present the best performances in terms of efficiency, torque

and mass power [2,6]. Low maintenance is required and the control is relatively easy.

However, those machines suffer from very low efficiencies at high speeds due to the field-

weakening method. Also, the maximum speed is sometimes limited in order to prevent the

magnets from being wrenched off.

Permanent magnets machines are widely used in hybrid vehicles such as in the Toyota Prius

and the Chevrolet Volt for example [1].

The field-weakening zone can be better controlled in wound rotor machines, by acting

directly on the rotor current. It also avoids reducing the machine efficiency at high speeds.

However, the global efficiency is still lower than for permanent magnets machines.

The Renault Fluence ZE is an example of a vehicle using wound rotor machines [1].

Asynchronous or Induction machines

In an asynchronous machine, a difference exists between the synchronous speed and the

operating speed. This speed difference, expressed in percentage, is called slip. The main

difference between synchronous and asynchronous machines is the rotor. For an

asynchronous machine, it is either made of a metallic cylinder, a squirrel cage, or other

technologies. Squirrel cage machines are the most used in the industry as their control

system is in constant progress for variable-torque applications.

This type of machines is well known as this technology requires little maintenance compared

to DC motors for example. Also, it benefits from low fabrication costs as it is standardized. In

terms of performances, a large scale of speed is available, with a good efficiency even at

maximum power and maximum speed [8].

31

However, it efficiency is below the one from a permanent magnets synchronous machine, as

it suffers from high Joule losses particularly in the rotor. Also, asynchronous machines are

heavier than synchronous machines in general.

Asynchronous machines are widely used, with a large scale of available power, from

household electrical goods to electric propulsion in high-speed trains [7].

Conclusion on the electric machine

Asynchronous machines show the most important margin of progress and many car

manufacturers are betting on it for the future. Therefore, the electric machine considered in

our work is an asynchronous machine.

Electric Machine Model

An electric machine is a complex system to model. As for the battery, hypotheses need to be

made in order to come with a simpler model. The best compromise between accuracy and

calculating time is to use a model based on an efficiency map. That way, even though the

computation of the efficiency map takes time, it is done only once at the very beginning of the

program. Then the results are implemented and used in the Simulink model. This technique

gives a quite accurate model with a good computation time.

An efficiency map of an induction machine has been chosen to be the reference. The

characteristics of the reference electric machine are presented in Table 2. This efficiency map

is presented in Figure 17.

The purpose of the program is to adapt that efficiency map to the parameters given by the

users, and to verify that this model gives accurate results.

Table 2: Reference electric machine characteristics

Parameter Values

Maximum power (𝑘𝑊) 40

Maximum speed

(𝑡𝑟/𝑚𝑖𝑛)

7 000

Maximum torque (𝑁𝑚) 300

32

Figure 17: Reference efficiency map of the Electric Machine

In order to make the simulation scalable, this electric machine efficiency map is taken as the

reference and will be adapted in order to estimate the efficiency map of other induction

machine.

Little information is required from the electric machine that needs to be modeled: maximum

power, maximum torque, and maximum rotational speed. The torque limitation envelope is

then determined, while the efficiency is simply adapted to the new data with a scaling

coefficient.

This method is not completely accurate, but gives a good approximation of the machine

behavior, with its own limits. Also, the computation time to adapt the map is almost

instantaneous, which makes this method interesting for the wanted model in this case.


Two engine efficiency maps were used in order to validate the model.

First, a 30 kW induction asynchronous machine was tested. Based on the maximum speed,

maximum torque and maximum power given by the electric machine characteristics, the

previously explained model is able to adapt the efficiency map. The results are presented

Figure 18.


Parameter Values


Maximum speed


9 000


33

a) Original efficiency map b) Efficiency map created by the model

Figure 18: Original efficiency map compared to the efficiency map created by the model

The percentage of deviation of the model from the real efficiency map gives a better

understanding of the accuracy of the model. The results are presented in Figure 19 below.

Two indications emerge from it. First, the efficiency map that serves as reference is close to

the one from the 30 kW machine. The percentages of deviation are under 10% in most of the

map.

Secondly, the limiting torque envelopes are quite close, as the plain line represents the real

torque envelope, while the dotted line is the modeled one.

Figure 19: Error in % between the two efficiency maps

In the same way, a comparison is made with a 75 kW AC induction motor, to see if the scaling

method is well suited for higher power machines. The original and modeled efficiency maps

34

are shown in Figure 20. The global characteristic seems to be consistent. The interesting

areas are quite close to each other, the behavior at very low speeds and very low torques are

regions that are complicated to model, and are areas to avoid. So those little deviations are

not problematic.


Parameter Values


Maximum speed


10 000



Figure 20: 75 kW AC induction motor, original efficiency map compared to the efficiency map created one by the model

The percentage of deviation of the modeled efficiency map is represented in Figure 21. Those

results are consistent with the previous remarks, and enable to conclude that in the majority

of the efficiency map, the deviation is between -5 and 5%.

35

Figure 21: Error in % between the two efficiency maps

Other comparisons with electric machines (Based on spec sheet for AC-150 motor/controller,

prototype or small-production 62 kW, AC induction motor/controller, prototype or small-

production 59 kW, AC induction motor/controller) confirm the results expressed.

Limits

Scaling an efficiency map in order to match other electric machines characteristics is not an

accurate method. Though the global behavior of the electric machine is conserved, the maps

extracted from the model show high discrepancies in some regions.

However, if the comparison only concerns the operating points that are used (therefore not

taking the low speeds and low torques operating points), the model appears to be a good first

approximation. Unfortunately, as expressed later on, the choice of the operating point of the

electrical machine is often imposed by the expected performances at the wheels or for the

ICE.

The validation procedure has also its limits. The original data are taken from papers with a

low precision, as it is possible to see in Figure 18 and Figure 20.

Conclusion on the scaling of the electric machine

This method represents an easy and quite accurate model. It has proven itself to be adaptable

for low power machines as well as high power ones with good results in the operating region

that is mostly used.

However, the dynamic effects are not represented in this model.

36

Simulink model

The input torque and rotational speed are given by the vehicle model. The look-up table of

the efficiency map gives the efficiency of the electric machine for this operational point,

which can be used to determine the power needed from the battery. Figure 22 shows the

convention chosen for the sign of the power flows. It is based on the fact that at the

transmission, the sum of all the powers is equal to 0.

Figure 22: Algebraic flows of power in the electric part

So, when the power demand at the wheels is negative (acceleration phase for example), the

electric machine gives a positive power. In this case, the relation between the battery power

𝑃𝑏𝑎𝑡𝑡 and the electric machine power 𝑃𝑒𝑚 is given by Equation (8).

𝑃𝑏𝑎𝑡𝑡 =

𝑃𝑒𝑚𝜂𝑒𝑚

(8)

On the other hand, when the power from the wheels is positive, the system is acting as a

generator, and the battery is then being charged. So 𝑃𝑏𝑎𝑡𝑡 is determined by Equation (9).

𝑃𝑏𝑎𝑡𝑡 = 𝜂𝑒𝑚 ⋅ 𝑃𝑒𝑚 (9)

The Simulink model of the electric machine is shown in Figure 23 below.

The torque limitation subsystem represents the torque envelope on the efficiency map. The

𝑃𝑒𝑚−> 𝑃𝑏𝑎𝑡𝑡 subsystem calculates the power of the battery depending on charging or

discharging phases as shown in Equation (8) and Equation (9).

37

Figure 23: Simulink model of the electric machine

Limits of the model

The efficiency map differs from one machine to another, which is not taken into account in

the model. However, in this model, the approximation gives positive estimated results.

Further work can be done to optimize the use of the electric machine by targeting the

maximum efficiency zone of the efficiency map.

3.3 Engine

All the way through the 20th century, combustion engine has been the technology used to

propel vehicles. The technology is well known, and has been continuously improved over the

years. Today, two types of combustion engines are commonly used: spark ignited engines (SI

engines, also called Otto engines) and Diesel engines. The basic principle of a combustion

engine is presented in this section, as well as further description of the SI and Diesel engines.

Then, the modeling of the engine is presented and discussed.

Definition

ICE engines are commonly two stroke engines and four stroke engines, but only four stroke

engines are used in the automobile industry. Two stroke engines are used for smaller power

demand, in some motorbike or in chainsaw for example.

As mentioned above, two types of engines are widely used: SI engines and Diesel engines.

The basic principle of those engines is the same, but they differ in the combustible used,

injection in the combustion chamber, combustion type, pollutant emissions and functional

characteristics [9].

In a general manner, combustion engines are known for their limits in terms of torque and

rotational speed [1]:

38

- At low engine speeds, the engine suffers from a functioning instability due to the variability in the mean torque from one cycle to another. Also, high torque variations inside a cycle are present.

- At high engine speeds, an efficiency drop happens due to the increase in the friction losses, as well as constraints of mechanical integrity for the engine components, that becomes limiting.

- The maximum torque is limited by the air quantity available in the combustion chamber and by the degradation of the combustion.

- The engine brake torque, which corresponds to the behavior of the engine when no fuel is injected. It is only due to the friction losses and the pumping losses.

Also, there is an increase in the friction at cold starts and the depollution systems tend to

increase the fuel consumption.

Several systems have been created in order to improve the engine performances or fuel

consumption:

- Downsizing: reducing the engine size for the same output power reduces the friction losses and the low regime operating points. This technology has lately been questioned in recent scandals.

- Compressor: increase of air pressure at the admission via a turbine. It is called a turbocharger when it is using the exhaust gas and a turbine to drive the compressor.

Other systems exist but are not presented in this report. For example, the exhaust gas

recirculation (EGR) lowers the NOx emissions, which could be seen as an efficiency

improvement in terms of emissions.

Technologies

Spark ignited engines are used in a majority of hybrid vehicles. It is mostly due to the

antipollution norms that are stricter for Diesel engines than SI engines.

An advantage of those engines is that they can be rapidly and easily turned on and off, which

facilitates its management in a hybrid vehicle. For instance, the Start&Stop feature benefits

from those characteristics.

However, it suffers from a poor efficiency, usually between 25 to 30% [9]. It can be partly

explained by the combustible used (fuel) that has lower calorific power value than gasoil.

Diesel engines on the other hand have a better efficiency, between 30 to 45% [9]. Compared

to SI engines, they require heavier structure for the same power. This is explained by the

difference in the combustion process. Indeed, the combustion is made by self-ignition of the

fuel during the compression stroke. This means that stronger materials are required to

ensure holding higher pressures levels in the combustion chamber.

Also, this combustion type releases more 𝐶𝑂2 than SI engines, as well as other pollutants like

particulate matter and nitrogen oxides (𝑁𝑂𝑥). Furthermore, ever since the Volkswagen

scandal in 2015, anti-Diesel engines incentives have been discussed in major cities all over

the world.

39

Conclusion

Although some car manufacturers are betting on Diesel hybrid vehicles, like Peugeot with the

HYbrid2 and HYbrid4 technologies, SI engines seem to be the solution that will be even more

generalized in the future. Indeed, Diesel engines are already more expensive than SI engines.

The hybrid technology increasing the price of a vehicle, having both Hybrid and Diesel

represent the most expensive option that may be not covered by the smaller diesel

consumption during the life of the vehicle.

Furthermore, depending on the hybrid architecture, the vehicle performances are not so

dependent on the thermial power source. SI engines can achieve performances close to Diesel

engines.

Engine Model

Initially, the idea was to use an efficiency map of an engine, and to try to adapt it with the

desired vehicle engine data. After some research, it occurred that it is difficult to adapt an

efficiency map in order to match another one.

A different method was chosen to approximate the efficiency map: Willans model. The model

is described in Section 3.3.3.1.

Also, it is a quite simple yet close to the reality method, which is possible to adapt.

The limits of this model are that it is based on the approximation of the chemical efficiency

and of the mean pressure losses, and sometimes underestimate them. Thus, the obtained

efficiency map of the engine is better than in reality.

Normalized engine variables: the engine torque 𝑇𝑒 and rotational speed 𝜔𝑒 have a clear

physical interpretation. Unfortunately, their range depends on the specific engine that is

modeled (size, geometry, etc.). For this reason, normalized variables are introduced. Using

these variables, the engine size can be used as an optimization parameter [10].

Willans approach

A simple model of the engine can be done using Willans model. It consists in calculating the

mean pressures that occurs over a cycle in the engine in order to have simple equations to

calculate the mean-value fuel mass flow, and the engine efficiency. The mean pressures taken

into account in the model are the mean effective pressure, the mean absolute pressure and

the mean friction pressure. Further explanations over those mean pressures are presented

below.

The mean effective pressure 𝑝𝑚𝑒 (𝑃𝑎) represents the actual pressure available mechanically,

and is expressed by the relation (10).

𝑝𝑚𝑒 = 𝑇𝑒 ⋅

4 𝜋

𝑉𝑑 (10)

40

Where 𝑇𝑒 is the engine torque (𝑁𝑚), and 𝑉𝑑 the engine’s displaced volume (𝑚3).

The mean absolute pressure 𝑝𝑚𝑎 characterizes the mean pressure that would be available if

all the chemical energy was transformed in mechanical energy. It is defined by:

𝑝𝑚𝑎 = 𝐻𝐿𝑉 ⋅

�̇� ⋅ 4𝜋

𝜔𝑒 ⋅ 𝑉𝑑 (11)

Where 𝐻𝐿𝑉 is the low heating value of the fuel (𝑘𝑊ℎ/𝑘𝑔), and 𝜔𝑒 the engine speed (𝑟𝑎𝑑/𝑠).

The mean friction pressure 𝑝𝑚𝑙𝑜𝑠𝑠 (𝑃𝑎) represents all mechanical friction and pumping losses

in the engine.

The global idea of the Willans model is to approximate the mean effective pressure and the

mean friction pressure losses with quadratic functions of the engine speed or the mean piston

speed defined below in Equation (14). In term of work, it can be explained as:

𝑊𝑜𝑢𝑡 = 𝑒0 ⋅ 𝑊𝑖𝑛 −𝑊𝑙𝑜𝑠𝑠 (12)

Where 𝑊𝑜𝑢𝑡 is the output work of the engine, 𝑊𝑖𝑛 is the work available if the chemical work

were completely transformed into mechanical work, and 𝑊𝑙𝑜𝑠𝑠 is the friction work loss. 𝑒0 is

the efficiency coefficient that describes the thermodynamic properties of the engine [10].

It can also be rewritten in terms of torque, as shown in Equation (13).

𝑇𝑒 = 𝑒0 ⋅ 𝐻𝐿𝑉 ⋅

�̇�

𝜔− 𝑇𝑙𝑜𝑠𝑠 = 𝑒0 ⋅ 𝑇𝑎 − 𝑇𝑙𝑜𝑠𝑠 (13)

Introduced in Equation (14), the mean piston speed 𝑐𝑚 is usually used as an input of the

Willans model. Indeed, it makes the model easier to scale, and the model created is

independent of the engine characteristics.

𝑐𝑚 =𝑆

𝜋⋅ 𝜔

(14)

Where 𝑆 is the engine stroke (𝑚) and 𝜔 the engine speed (𝑟𝑎𝑑/𝑠).

In the formulation, the efficiency coefficient 𝑒0 and 𝑝𝑚𝑙𝑜𝑠𝑠 models the friction and gas-

exchange losses. The formulation is given by the following equation:

𝑝𝑚𝑒(𝑐𝑚) = 𝑒0(𝑐𝑚) ⋅ 𝑝𝑚𝑎 − 𝑝𝑚𝑙𝑜𝑠𝑠(𝑐𝑚) (15)

41

The efficiency coefficient and 𝑝𝑚𝑙𝑜𝑠𝑠 are expressed as quadratic function of the engine angular

velocity, as expressed in the following equation.

{

𝑒0(𝑐𝑚) = 𝑒00 + 𝑒01 ⋅ 𝑐𝑚 + 𝑒02 ⋅ 𝑐𝑚2

𝑝𝑚𝑙𝑜𝑠𝑠(𝑐𝑚) = 𝑝𝑚𝑙𝑜𝑠𝑠0 + 𝑝𝑚𝑙𝑜𝑠𝑠1 ⋅ 𝑐𝑚 + 𝑝𝑚𝑙𝑜𝑠𝑠2 ⋅ 𝑐𝑚2 (16)

The parameters used are extracted from [10]. The reference engine is a naturally aspirated SI

engine. The engine parameters are expressed in Table 5. In the Willans model used, only the

displaced volume and the stroke are needed.

Table 5: Reference engine characteristics

Parameter Values

Displaced volume 𝑉𝑑

(𝑚3)

710 ⋅ 10−6

Bore 𝐵 (𝑚) 0.067

Stroke 𝑆 (𝑚) 0.067

Compression ratio 𝜖 12

Figure 24 shows the efficiency map and the evolution of Willans parameters of the reference

engine.

Figure 24: Reference map and parameters [10]

After treatment of the data, the Willans parameters were extracted and are presented in

Table 6. 𝑝𝑚𝑙𝑜𝑠𝑠 is expressed as −𝑝𝑚𝑒0.

42

Table 6: Willans parameters

Parameter Values Units

𝑒00 0.3528 [ ]

𝑒01 0.0108 [𝑠/𝑚]

𝑒02 −4.4487

⋅ 10−4

[𝑠2/𝑚2]

𝑝𝑚𝑙𝑜𝑠𝑠0 1.3 ⋅ 105 [𝑃𝑎]

𝑝𝑚𝑙𝑜𝑠𝑠1 −351.3 [𝑃𝑎 ⋅ 𝑠/𝑚]

𝑝𝑚𝑙𝑜𝑠𝑠2 822.5 [𝑃𝑎

⋅ 𝑠2/𝑚2]

And so from Equation (15), 𝑝𝑚𝑎 is given by:

𝑝𝑚𝑎 =

𝑝𝑚𝑒 + 𝑝𝑚𝑙𝑜𝑠𝑠𝑒0

(17)

Finally, the mean-value fuel mass flow is:

�̇� =

1

𝑒0⋅𝜔𝑒 ⋅ 𝑉𝑑4𝜋 ⋅ 𝐻𝐿𝑉

⋅ (𝑇𝑒 ⋅4𝜋

𝑉𝑑+ 𝑝𝑚𝑙𝑜𝑠𝑠) (18)

The engine efficiency is given by Equation (19).

𝜂𝑒𝑛𝑔 =

𝑃𝑚𝑒𝑐ℎ𝑃𝑐ℎ𝑒𝑚

=𝑇𝑒𝑛𝑔 ⋅ 𝜔𝑒𝑛𝑔

�̇� ⋅ 𝐻𝐿𝑉 (19)

Scaling

In order to be able to make an approximation of the consumption for different engine, a

scaling method is used.

Determination of the maximum torque

The Willans model gives an estimation of the efficiency map but does not take the power limit

of the engine into consideration. An approximation of the maximum torque limitation needs

to be found from the engine power characteristics. In general, the engine data available is

resumed Table 7. Based on those information, the only approximation of the maximum

torque curve is a quadratic function of the engine speed 𝜔𝑒𝑛𝑔.

43

Table 7: Engine data needed for the determination of the maximum torque limitation

Parameter Units

Maximum Power [𝑊]

Engine speed at maximum

power

[𝑟𝑎𝑑/𝑠]

Maximum torque [𝑁𝑚]

Engine speed at maximum

torque

[𝑟𝑎𝑑/𝑠]

With the few data available, three equations are needed to determine the coefficients 𝑎, 𝑏 and

𝑐 of the quadratic function expressed in Equation (20).

𝑇𝑚𝑎𝑥(𝜔𝑒) = 𝑎 ⋅ 𝜔𝑒(𝑃𝑚𝑎𝑥)2 + 𝑏 ⋅ 𝜔𝑒(𝑃𝑚𝑎𝑥) + 𝑐 (20)

The equations in (21) are the expression of the torque at maximum power, the maximum

torque at the corresponding engine speed, and the derivative at the maximum torque.

{

𝑇𝑚𝑎𝑥

(𝜔𝑒)|𝑃max = 𝑎 ⋅ 𝜔𝑒|𝑃max2 + 𝑏 ⋅ 𝜔𝑒|𝑃max + 𝑐

𝑇𝑚𝑎𝑥(𝜔𝑒)|𝑇max = 𝑎 ⋅ 𝜔𝑒|𝑇max2 + 𝑏 ⋅ 𝜔𝑒|𝑇max + 𝑐

𝑑𝑇𝑚𝑎𝑥(𝜔𝑒)

𝑑𝜔𝑒|𝑇max = 0 = 2𝑎 ⋅ 𝜔𝑒|𝑇max + 𝑏

(21)

Finally, the expressions for the parameters 𝑎, 𝑏 and 𝑐 are expressed Equations (22).

{

𝑎 =

𝑇𝑚𝑎𝑥(𝑇𝑚𝑎𝑥) − 𝑇𝑚𝑎𝑥(𝑃𝑚𝑎𝑥)

𝜔𝑒(𝑇𝑀𝑎𝑥)2 −𝜔𝑒(𝑃𝑚𝑎𝑥)2 − 2 𝜔𝑒(𝑇𝑚𝑎𝑥) ⋅ (𝜔𝑒(𝑇𝑚𝑎𝑥) − 𝜔𝑒(𝑃𝑚𝑎𝑥))

𝑏 = −2 𝜔𝑒(𝑇𝑚𝑎𝑥) ⋅ 𝑎

𝑐 = 𝑇𝑚𝑎𝑥(𝑃𝑚𝑎𝑥) − 𝑎 ⋅ 𝜔𝑒(𝑃𝑚𝑎𝑥)2 − 𝑏 ⋅ 𝜔𝑒(𝑃𝑚𝑎𝑥)

(22)

The parameters 𝑎, 𝑏 and 𝑐 are calculated in the main program, and give the maximum torque

available that is then used in a look-up table in Simulink.

Willans model adaptation

The scaling mostly concerns the adaptation of the mean piston speed 𝑐𝑚 and of the mean

effective pressure 𝑝𝑚𝑒. The main equations are the same (Equations (11)(15)(16)(17)(18)) but

the determination of 𝑐𝑚 and 𝑝𝑚𝑒 takes the actual engine data into consideration. The Willans

parameters are kept the same.

44


The validation of the model results are made through the comparison of a known efficiency

map with the efficiency map obtained for the same engine.

In order to study how well the Willans model is modeling the efficiency map, several engine

efficiency maps are compared with the extracted ones from the model. The comparison

between the two efficiency maps indicates the quality of the model.

First, the engine of the first-generation Toyota Prius is tested. It is a 1.5L Spark Ignited

engine. The two efficiency maps are presented in Figure 25.


Figure 25: Toyota Prius original efficiency maps compared to the efficiency map from the model

The general behavior is consistent, with the iso-efficiency lines close from one efficiency map

to another. However, the values are quite different, as shown in Figure 26 with the error

between the two maps plotted in percentage.

45

Figure 26: Error (%) between the Toyota Prius real efficiency map and the efficiency map extracted from Willans model

The resulting errors vary from 12% to 20%. These values represent an important gap and can

induce high discrepancies in the results.

In the same manner, the engine of the Honda Insight first generation is being tested. The

engine is a 1.0L Sparked Ignited engine. The results are shown in Figure 27.


Figure 27: Honda Insight original efficiency maps compared to the efficiency map from the model

Again, the global behavior is conserved. However, the singularity of the original efficiency

map is not well approximated.

This effect points out the limit of the Willans model with quadratic approximations of the

brake mean effective pressure and the mean friction pressure losses. This limit is even clearer

in the plot of the error in percentage expressed in Figure 28.

46

Figure 28: Error (%) between the Honda Insight real efficiency map and the efficiency map extracted from Willans model

Apart from the singularity, the values are close to the original efficiency map, with errors

between -6% and 6%. In the singularity however, the error is important with a maximum of

16%.

The model appears to represent well the global efficiency behavior, but the fast-changing

zones cannot be distinguished precisely. This leads to great errors while determining the

optimized engine operating point (see after).

Limits of the model

The Willans model is usually used to model Diesel engines, as the efficiency maps are more

adapted to this model. Although the reference engine map is a SI engine that was used with a

Willans model, this study showed that the Willans model is limited in the accuracy of the

results.

Also, the reference map was extracted from a small size engine, so the mean friction pressure

is larger than in most modern engines. Yet, as this model tends to give better engine

efficiencies than the expected results, this effect is not too much of a problem.

Furthermore, the adaptation of the model is also a source of a small error, but the result is

close enough to the approximation of the engine fuel consumption and efficiency.

Conclusion

A choice has to be made between two options: either to continue with this model, or to

choose between several engines the one that will be used in the model.

47

The solution chosen was to give the possibility to the user to enter the engine characteristics

and use the Willans model, especially when testing Diesel engines, or to use an existing

engine map.

On Simulink, the model uses a look-up table on the consumption map of the engine. Since

the model needs data of preexisting maps or from Willans model, it is the best alternative.

The Engine subsystem on Simulink is shown in Figure 29.

Figure 29: Simulink model of Willans model

The torque limitation subsystem implements the limitation calculated before. The saturation

on the engine rotational speed avoids having a requested speed that is over the maximum

speed fixed for the engine.

Estimation of the fuel consumption

Since the consumption map is used in the look-up table, the fuel consumption is directly

available. Indeed, the consumption is given in 𝑔/𝑠, so by dividing the mass flow with the fuel

density, it gives the volume flow rate.

Therefore, it is easy to get the fuel consumption through the heating value of the fuel, as:

𝑉𝑓𝑢𝑒𝑙 =

1

𝜌𝑓𝑢𝑒𝑙⋅ ∫ �̇� 𝑑𝑡 (23)

With 𝜌𝑓𝑢𝑒𝑙 being the fuel density.

3.4 Transmission

Planetary gear set

48

For electrical hybrid vehicles, the power transmission is the link between the combustion

engine, the electric machine and the wheels. For each architecture, a different solution is

used and presented in this section. The technical solution used is dictated by the desired

control on the operation point of the engine. A control of torque and/or speed is possible

depending on the possibilities given by the architecture.

The power split device chosen is a planetary gear set that controls the speeds of the different

parts or components of the system: engine speed, motor speed and output shaft speed.

Although the mechanical link between the two power systems and the driveline is made, a

control power unit is needed in order to control how the power is being distributed between

the systems. Also, the battery management strategy of the vehicle can be determined and

applied.

A sketch of a planetary gear set is presented in Figure 30.

Figure 30: Planetary gear set

The equation that links the rotational speeds of a planetary gear is expressed in the following

equation, with 𝑠 the index of the sun gear, 𝑟 the index of the ring gear and 𝑐 the index of the

planet carrier:

𝜆 =

𝜔𝑠 −𝜔𝑐𝜔𝑟 −𝜔𝑐

= −𝑍𝑟𝑍𝑠

(24)

𝑍𝑖 represents the teeth number and 𝜔𝑖 the angular velocity (𝑟𝑎𝑑/𝑠) of component 𝑖.

And so the global relation between all the rotational speeds is:

𝜔𝑠 − 𝜆 ⋅ 𝜔𝑟 + (𝜆 − 1) ⋅ 𝜔𝑐 = 0 (25)

The torque relation is given by Equation (26).

𝑇𝑠 + 𝑇𝑟 + 𝑇𝑐 = 0 (26)

49

So, the torques are given by:

𝑇𝑐 = (1 − 𝜆) ⋅ 𝑇𝑠 =

𝜆 − 1

𝜆⋅ 𝑇𝑟

(27)

As the planetary gear losses are neglected, the power equation is given by:

∑𝑃𝑖 = 0 ⇒ 𝑇𝑠 ⋅ 𝜔𝑠 + 𝑇𝑟 ⋅ 𝜔𝑟 + 𝑇𝑐 ⋅ 𝜔𝑐 = 0 (28)

The rotational inertia of the planetary gear is negligible when compared with those of the

machines and shafts connected [10].

Other transmission components

Final drive

The final drive ratio represents the ratio between the transmission shaft and the wheels. In

the model, it is simply given as a fixed ratio, set to 1/3.

Gearbox

No actual gearbox is used, as the control of the engine demand is made by different coupling

devices and by the power control unit. This choice will limit the use of combustion engine,

which will be discussed in Section 5 when presenting the results.

The major components are modeled, so the global architecture can now be created.

50

4 Hybrid Vehicle system modelling

4.1 Global model framework

The convention with which the model has been developed on needs to be defined. This choice

of convention applies for all three architectures, and enables the model to be consistent from

one architecture to another.

A representation is shown Figure 31 with the algebraic flows.

Figure 31: Algebraic flows in the Simulink model

This representation indicates that at the transmission, the governing equation is given by

Equation (29) below. The power at the wheels is seen as a loss. So when the power at the

wheels is negative, the wheels are consuming power, which can be interpreted as the vehicle

is accelerating for example. On the contrary, when the power at the wheels is positive, the

wheels are giving power to the system, so the vehicle is in a braking phase.

𝑃𝐸𝑀 + 𝑃𝐼𝐶𝐸 + 𝑃𝑤ℎ𝑒𝑒𝑙 = 0 (29)

The modeled series, parallel and series-parallel architectures follow this global

representation at the transmission.

This vision allows having a clear idea of how each system is behaving. It also gives access to

the control strategy that is discussed in the next section, and further explained for each

architecture.

Control strategy

The control strategy is modeled thanks to Stateflow in Simulink. This tool allows creating the

control strategy under the form of a state diagram. The first step to create the control strategy

is then to define the different states that are actually driving modes.

51

Several operating modes are determined and correspond to different vehicle states:

- Hybrid drive: taken as the reference drive mode (see after), it represents the normal driving mode for a hybrid car, when both systems are propelling the vehicle.

- Regenerative braking: when the power at the wheels is positive, the wheels are giving power to the system. The electric motor can then be acting as a generator in order to charge the battery with that process.

- Full electric drive: under a certain limit of speed, the control strategy can decide to use only the electric system to propel the vehicle. In the program, the limit of the electric drive has been set to 35 km/h.

- Engine driving + battery charging: when the SOC is below a certain limit (set at 20%), the control strategy stops using the battery. In that situation, the combustion engine simultaneously propels the vehicle and charges the battery by having an output power higher than the power requested at the wheels (in terms of amplitude). The difference between the two is the power that is given to the electric system to charge the battery.

- Full ICE drive: when the power demand at the wheels is too important, the engine focuses on meeting the demand and stops charging the battery as well. Also, when the amount of fuel left is beginning to be critical (set to 4L), the engine simply propels the vehicle in order to go as far as possible. This last case can be seen as a full ICE survival mode.

- Stationary charging: at standstills, if the SOC is below the limit and enough fuel is available, the engine will charge the battery.

- Full electric survival mode: a critical mode operating when no more fuel is left in the tank. The battery can be used until an extreme SOC limit defined at 10%. This mode gives a short electric extended range.

Those different operating modes are described more thoroughly in the control strategy

section. Added to those operating mode, classic modes are created, for extreme cases. Those

normal modes are:

- Normal braking: no regenerative energy is made. This mode is needed when the battery reaches a very high SOC level, which could be dangerous if charging continues.

- Normal standstill: When the battery is not below the SOC limit, there is no need for charge, so at standstill both systems are shut down.

Thanks to the definition of all these modes, the control strategies can be created.

The idea of the control strategies of all architectures is to have a reference state (the hybrid

drive state), and to have all the activation conditions based on this reference state. The hybrid

drive mode has been taken as reference state because it represents the operation mode that

should be the most used in normal conditions.

Deactivation conditions also have to be thought off, in order to be able to switch from one

operation mode to another.

The control strategy is implemented into Simulink via a Stateflow chart. This tool is

particularly well adapted for the representation that was chosen, with the different operation

modes.

52

The last thing to consider before creating the control strategy is to choose the battery mode.

Indeed, as explained in Section 2.1, two modes can be chosen: charge depletion and charge

sustaining. In this project, the mode chosen is the charge depletion mode, particularly used

in plug-in hybrid cars. In the control strategy, it means that the activation and deactivation

conditions will be made so that the vehicle uses the electric system as much as possible.

Driving cycle

The input of the program is a speed of the vehicle, following a driving cycle. Several driving

cycles exist, the NEDC (not used anymore), the WLTC or other cycles, depending on the

legislation.

The cycles were created to compare the performances of vehicles, and are supposed to give a

first indication on the energy consumption and emissions of a car.

In Europe, between 1973 and 2017, the New European Driving Cycle (NEDC) was the driving

cycle test used to determine the fuel consumption and emissions of a vehicle. It is composed

of four urban cycles of 195 sec each and one extra-urban cycle of 400 sec. See Figure 32 for

the NEDC driving cycle.

Figure 32: NEDC driving cycle

Since September 2017, the Worldwide harmonized Light vehicles Test Procedure (WLTP) is

the new legislation that aims at creating world standardized cycles close to real driving

conditions, with three different cycles. The Worldwide harmonized Light vehicles Test Cycle

3 (WLTC3) concerns light cars with “high performances”, but it actually concerns the great

majority of cars. The WLTC3 cycle is presented in Figure 33.

53

Figure 33: WLTC3 driving cycle

The final objective of the program is to be able to give consistent results for a given test cycle.

Vehicle model

From the driving cycle, the expected power, torque and rotational speed at the wheels are

determined. In order to do so, a simple vehicle model is implemented. The vehicle model

implemented is basic; a more realistic one is present in the global vehicle model. The vehicle

dynamics equation is represented by Equation (30) and (31).

Figure 34: Vehicle dynamics

With the following notations: 𝑚 the vehicle mass (𝑘𝑔), 𝑎 the acceleration (𝑚/𝑠2), 𝐹𝑡𝑟𝑎𝑐 the

traction force needed to propel the vehicle (𝑁), 𝐹𝑎𝑒𝑟𝑜 the aerodynamic force (𝑁), 𝐹𝑟𝑜𝑙 the

rolling resistance (𝑁) and 𝐹𝑔𝑟𝑎𝑑𝑒 the force introduced by the grade (𝑁).

𝑚 ⋅ 𝑎 = 𝐹𝑡𝑟𝑎𝑐 − 𝐹𝑎𝑒𝑟𝑜 − 𝐹𝑟𝑜𝑙 − 𝐹𝑔𝑟𝑎𝑑𝑒 (30)

𝑚 ⋅ 𝑎 = 𝐹𝑡𝑟𝑎𝑐 −

1

2⋅ 𝜌 ⋅ 𝑆 ⋅ 𝐶𝑥 ⋅ 𝑣

2 −𝑚 ⋅ 𝑔 ⋅ 𝑓𝑟 −𝑚 ⋅ 𝑔 ⋅ sin(𝛼) (31)

54

Where 𝑣 is the vehicle speed (𝑚/𝑠), 𝜌 is the air density (𝑘𝑔/𝑚3), 𝑆 the frontal surface of the

vehicle (𝑚2), 𝐶𝑥 the drag coefficient, 𝑔 the gravitational constant (𝑚/𝑠2), 𝑓𝑟 the rolling

resistance coefficient, and 𝛼 the slope.

From Equation (31), it is possible to determine the last required inputs of the model: 𝑃𝑤ℎ𝑒𝑒𝑙𝑠

and 𝑇𝑤ℎ𝑒𝑒𝑙𝑠. Their expressions are given by the system of equations (32) below.

{𝑃𝑤ℎ𝑒𝑒𝑙𝑠 = 𝐹𝑡𝑟𝑎𝑐𝑡 ⋅ 𝑣

𝑇𝑤ℎ𝑒𝑒𝑙𝑠 = 𝐹𝑡𝑟𝑎𝑐𝑡 ⋅ 𝑟𝑤ℎ𝑒𝑒𝑙 (32)

With 𝑟𝑤ℎ𝑒𝑒𝑙 the wheel radius.

Some hypotheses are made. The model assumes that no slip occurs between the wheels and

the road for example.

This hypothesis lead to a small error between the vehicle speed and the requested one.

4.1 Series hybrid architecture

System model

The architecture of the series hybrid modeled is represented in Figure 35.

Figure 35: Series architecture

The power split device directly concerns the power since no mechanical link is made between

the generator and the motor. So, the power distribution is easy to access in this case.

(𝑇𝑒 , 𝜔𝑒) are directly controlled, so the power split device only concerns the power

distribution.

Two electric machines are required, one propelling directly the vehicle, and the other linked

to the combustion engine is used as a generator.

55

On Simulink, the Series architecture is modeled as presented in Figure 36. The electric

machines are directly in the “Power Control Unit Series” subsystem as an approximation of

the electric machine efficiency is needed to determine the control strategy (see after).

Figure 36: Simulink model of the Series architecture

Control strategy

In order for the system to have a consistent behavior, a control system needs to be

determined.

The purpose here is not to create the most optimized control system for a hybrid powertrain,

but to create a basic, yet robust one, that is a good start for the simulation.

The different operation modes described previously in section 4.1.1, and their activation and

deactivation conditions are expressed Table 8.

Table 8: Operation modes and conditions of activation or deactivation, Series hybrid case

In order to avoid having fast changes between two states, some conditions are slightly

modified to give the system a hysteresis behavior. For example, the activation of the full

Operation

mode SOC Pwheels v vtank SOC Pwheels v vtank

Regenerative Braking SOC < SOCmaxlim-2 P > 0 SOC >= SOCmaxlim P <= 0

Full electric SOC > SOCmin+5 P <= 0 v < vlim SOC <= SOCmin P > 0 v >= vlim

Full ICE SOC < SOCmin P <= -Pmin v > 0 vtank > 0 P > 0 vtank = 0

Stationary charging SOC <= SOCmin v = 0 vtank > vtanklim SOC >= SOCmaxlim v > 0 vtank <= vtanklim

Hybrid drive

Engine driving +

motor chargingSOC < SOCmin 0 > P > -Pmin vtank > vtanklim SOC > SOCmin+10 Pmin >= P > 0 vtank <= vtanklim

Full electric survival SOC > SOCminlim vtank = 0 SOC <= SOCminlim P > 0

Full electric forced SOC >= SOCmaxlim

Normal Braking SOC >= SOCmaxlim P > 0 SOC <= SOCmax P <= 0

Normal Standstill SOC <= SOCmin v = 0 v <= vtanklim v > 0

Dead SOC <= SOCminlim vtank = 0

Activation conditions Deactivation conditions

56

electric mode is for a SOC over 𝑆𝑂𝐶𝑚𝑖𝑛 + 5, and the deactivation condition is for a SOC below

𝑆𝑂𝐶𝑚𝑖𝑛.

The Stateflow chart used for the Series architecture is presented in Figure 37.

Figure 37: Stateflow chart implemented into the Simulink model

The logic of the Stateflow chart is to follow the control strategy imagined, with the activation

and deactivation conditions (represented by the arrows between the blocks).

The Simulink function “Generator” – that can be seen in Figure 36 – optimizes the use of the

engine. The optimization technique is explained in the next section.

Engine optimization control

A full control of the engine operating mode is available in this architecture, as no mechanical

link is present between the engine and the wheels.

Using the convention shown in Figure 38, Equations (33) gives the relation between 𝑃𝐼𝐶𝐸,

𝑃𝑔𝑒𝑛, 𝑃𝑏𝑎𝑡𝑡 and 𝑃𝐸𝑀 when 𝑃𝐼𝐶𝐸 > 0 and 𝑃𝐸𝑀 > 0.

{

𝑃𝑔𝑒𝑛 = 𝜂𝑔𝑒𝑛 ⋅ 𝑃𝐼𝐶𝐸𝑃𝐸𝑀 = 𝜂𝐸𝑀 ⋅ (𝑃𝑔𝑒𝑛 + 𝑃𝑏𝑎𝑡𝑡)

(33)

For a fixed required output power, the optimization process compares the efficiencies of all

the operating points that give access to that specified output power. The optimized engine

operating point is taken to be the one with the maximum efficiency.

57

Figure 38: Power transfer in the model

Figure 39 below shows the optimized engine operating points as a function of the needed

output power for the Geo Metro 1.0L engine. The dotted lines represent the iso-power curves.

The blue dots represent the chosen operating point that maximizes the engine efficiency for a

given power.

Figure 39: Optimization of operating point (blue dots) as a function of output power (black dotted lines)

In the Matlab initialization program, relations between the power demanded and the engine

speed and torque are created to be used in look-up tables in the Simulink. Even though it

makes the Matlab initialization model slower, this method appeared to maximize the

computation speed of the Simulink model.

The general idea of engine control is as follow: the engine should run as much as possible at a

certain engine power, defined as 𝑃𝑚𝑖𝑛 and the battery will compensate the power gap. Two

cases results:

- When a higher power than 𝑃𝑚𝑖𝑛 is demanded, the engine tries to meet the demand.

For example, in hybrid drive mode, the engine is running at 𝑃𝑚𝑖𝑛, and the battery

regulates the amount of power needed.

58

- If the power needed is less than the power given by the engine, the battery will be

charged.

The only operating modes in which the engine is propelling the vehicle on its own are the

“Full ICE mode” and the “engine propelling + battery charging” mode (see Table 8). The

“engine propelling + battery charging” mode represents when the requested power is below

𝑃𝑚𝑖𝑛, then the battery can charge with the power difference. When the requested power turns

to be over 𝑃𝑚𝑖𝑛, the engine adapts its power to match the power requested at the wheels. In

this control process, the efficiencies of the generator and the electric machine must be known

(or approximated) in order to have the engine giving the right amount of power.

In order to have the best system efficiency for the requested power at the wheels, the optimal

operating mode of the engine needs to be found. An optimization process is used to find the

best operating point for each requested power. However, the efficiency of the generator has to

be approximated in some way. The method used is described here.

The system power equation is given by Equation (34), with the notations from Figure 38.

𝑃𝐸𝑀 = 𝜂𝐸𝑀 ⋅ (𝑃𝑔𝑒𝑛 + 𝑃𝑏𝑎𝑡𝑡) (34)

And the link between the engine power and the power at the electric machine is:

𝑃𝐸𝑀 = 𝜂𝐸𝑀 ⋅ (𝜂𝑔𝑒𝑛 ⋅ 𝑃𝐼𝐶𝐸 + 𝑃𝑏𝑎𝑡𝑡) (35)

When the power demanded is higher than 𝑃𝑚𝑖𝑛 in the Full ICE mode, the battery is no longer

charging (𝑃𝑏𝑎𝑡𝑡 = 0), so the optimization needs to take the efficiencies into account since:

𝑃𝐼𝐶𝐸 =

𝑃𝐸𝑀𝜂𝐸𝑀 ⋅ 𝜂𝑔𝑒𝑛

(36)

A difficulty for the optimization is to have a proper estimation of the efficiencies 𝜂𝐸𝑀 and

𝜂𝑔𝑒𝑛so that the targeted power is met. The estimation of 𝜂𝑔𝑒𝑛is not difficult since it is given

directly by the operating point of the engine. However, the power demanded to the wheels

does not give any indications on the torque or on the rotational speed of the EM. In order to

consider it in the optimization process, the efficiency of the EM 𝜂𝐸𝑀is assumed to be equal to

𝜂𝑔𝑒𝑛 weighted with a coefficient of 0.1, as expressed Equation (37). The star indicates that the

variable is a control variable, no star represents the physical variable.

𝑃𝐼𝐶𝐸∗ =

𝑃𝐸𝑀∗

(𝜂𝑔𝑒𝑛 − 0.1)2 (37)

59

Finally, the optimization is realized on the engine efficiency, as shows in Equation (38).

𝑃𝑐ℎ𝑒𝑚 =

𝑃𝐼𝐶𝐸𝜂𝐼𝐶𝐸

(38)

Limits of the optimization method

This method is based on the engine efficiency map only, so the level of accuracy directly

depends on the accuracy of the map and the engine model used.

Several approximations were made on the optimization process also, adding an error in the

demanded ICE power.

Optimization on the “ICE-Generator” system

If the engine is clearly the most limiting components in terms of efficiency, taking the

generator into consideration could slightly modify the results. Indeed, using the engine at its

best operating point in terms of efficiency does not implicate that the efficiency of the global

system is optimal. A study of the optimization of the efficiency of the “ICE-Generator” system

for each requested power has been conducted in order to see the difference.

To do so, the same process can be done by taking the maximum efficiency of the “ICE-

Generator” system, so searching for max(𝜂𝐼𝐶𝐸 ⋅ 𝜂𝑔𝑒𝑛), since the equation to optimize is:

𝑃𝑐ℎ𝑒𝑚 =

𝑃𝑔𝑒𝑛

𝜂𝐼𝐶𝐸 ⋅ 𝜂𝑔𝑒𝑛 (39)

The results depend on the engine and the electric machine chosen. An example with the

Honda Insight engine and a generator of 57kW is expressed Figure 40. The difference

between the engine operating points is visible for three requested powers. For those

requested powers, taking the generator into consideration improves the efficiency of the

system “ICE-Generator” and influences the choice of the operating point of the engine.

60

Figure 40: Comparison of the two-optimization process, blue dots represent the optimization on the engine, green dots represent the optimization on the system “ICE-Generator”

The optimization of the “ICE-Generator” system is kept for the control of the engine. It still

suffers from the approximation of the electric machine 𝜂𝐸𝑀 which can introduce an error in

the demand.

4.2 Parallel hybrid architecture

System model

The parallel architecture modeled is shown in Figure 41. In this architecture, the mechanical

link between the systems – which is made by a planetary gear set – imposes speed and torque

relations showed section 3.4.1. Not represented in the architecture are two gear ratios for the

engine and the electric machine. Those gear ratios are adjustment variables to modify along

with the engine and electric motor used.

Figure 41: Parallel hybrid architecture [16]

61

The control of the power flows is made through clutches presented in Figure 41. In the model,

it assumed that when a clutch is “off” (see the control strategy), the concerned shaft is

blocked. That way, the clutches state can be seen as state variables, as shown later on in Table

10.

In Simulink, the Parallel architecture has been modeled as presented in Figure 42. The

components of the architecture clearly appear in the architecture. The power split device is

modeled in the “Transmission Parallel” subsystem, after first being taken into consideration

in the “Power Control Unit Parallel” subsystem.

Figure 42: Simulink model of the Parallel architecture

Control system

The control strategy is summarized in Table 9. It is close to the series control strategy in its

activation and deactivation conditions. However, the outputs are different since the clutches

are also controlled.

Table 9: Operation modes and conditions of activation or deactivation, Parallel hybrid case

Operation




Full ICE SOC <= SOCmin v > 0 vtank > 0 SOC >= SOCmin+10 P > 0 vtank = 0


Hybrid drive


Full electric forced SOC >= SOCmaxlim SOC <= SOCmax





62

The outputs of the Stateflow chart are the engine and electric machine operating points, as

well as the state of clutches expressed in Table 10. For each operation mode, the state of

clutches is different.

Table 10: States of the clutches

The whole point of the hybrid technology is to have a control over the engine operating point.

In this architecture and with the technologic choices made, the engine speed is controlled.

As the planetary gear set makes a mechanical link between the wheels and the engine, there

are some mechanical constraints.

By definition of the planetary gear set, the relation when the EM output is locked is:

{TICE = −

λ − 1

λ⋅ Twheel

ωICE =λ

λ − 1⋅ ωwheel

(40)

Equations (40) represents the minimum torque and engine speed needed by the engine if it

were propelling the vehicle on its own.

The engine control strategy implemented for the parallel architecture is as follows: in hybrid

mode, the engine speed is determined and the torque adapts itself to the demand, the electric

machine adjusting its speed in order to have a consistent transmission block. In other driving

modes, the planetary gear equations (speed and torque) define the operating mode of the

engine and in general of the systems.

This control strategy implies that no optimization on the use of the engine is made. Hence, it

does not give access to the operation mode “engine driving + motor charging” due to the fact

that the control of the engine is only made on its speed.

The Stateflow chart of this architecture is presented in Appendix 2.

4.3 Series-parallel hybrid architecture

System model

The architecture of the series-parallel hybrid is represented in Figure 43. It is based on the

same architecture as the parallel architecture with a similar power split device and clutches

Planet and Sun Ring Operation

1 2 3 Carrier ( C ) Gear ( S ) Gear ( R ) mode

Off On On Stationary Output Input Regenerative Braking

Off On On Stationary Input Output Full electric

On Off On Input Stationary Output Full ICE

On On Off Input Output Stationary Stationary charging

On On On Input Input Output Hybrid drive

State of Clutches

63

system. This time, no gear ratios are present before the two clutches for the engine shaft and

the electric motor 1 respectively. However, it might be interesting to add such gear ratios as

adjustment variables, as in the parallel architecture.

Figure 43: Series-Parallel architecture

In the same manner as seen in the series architecture, the engine operating point can be

entirely controlled in this architecture.

Similarly, an optimization of the engine efficiency for a requested power has also been made.

However, for this architecture, the optimization process is almost immediate. Indeed, the

efficiency optimization is realized on the engine only, and not on the system “ICE-EM2”, for

simplicity purposes. So, the operating point of the engine for a requested power is the one

offering the best engine efficiency.

Limits

The global system efficiency could be studied in order to be optimized, in the same way as it

has been done for the series architecture. However, this optimization is more complex than

the one realized in the series architecture since two electric machines are concerned with bi-

directional power flows (EM2 can help the engine as well as regenerate the battery, same idea

with EM1).

The Simulink model of the architecture is shown in Figure 44.

64

Figure 44: Simulink model of the Series-Parallel architecture

Control strategy

One of the great advantages of the series-parallel hybrid model is to control both speed and

torque repartition. The global idea is then to control the system by optimizing the use of the

combustion engine, which should increase the engine average efficiency, and thus improve

the fuel consumption.

The control strategy is summed up in Table 11.

Table 11: Operation modes and conditions of activation or deactivation, Series-parallel case

The Stateflow chart of this architecture is presented in Appendix 3.

Operation




Full ICE SOC < SOCmin v > 0 0 < vtank < vtanklim SOC >= SOCmin P > 0 vtank = 0


Hybrid drive

Engine driving +

motor chargingSOC < SOCmin v > 0 vtank > vtanklim SOC > SOCmin+10 P > 0 vtank <= vtanklim


Full electric forced SOC >= SOCmaxlim SOC <= SOCmax





65

5 Results

In order to validate the global behavior of the different architectures, a validation procedure

has been created. First, this procedure consists in testing the architecture in specific

situations, for several initial conditions. The results of these tests should point out the way

the system reacts to those specific conditions. Changes of operating modes can be verified, as

well as the performances in every mode. Those cycles are referred a test cycles.

Then, the architectures are tested for several driving cycles. The behavior of the systems can

then be studied in situations close to real driving conditions. In this report, only the WLTC3

driving cycle is presented.

5.1 First validation part: test cycles

In the test cycles, extreme cases are tested. It enables to identify how the system reacts in

those uncommon situations, for example when running out of fuel.

Several driving conditions are chosen in order to have a wide range of conditions tested:

- Braking: constant breaking phase from 90 𝑘𝑚/ℎ with a −0.5 𝑚/𝑠2 (this value ensures to have a positive power at the wheels)

- Low speed: constant speed under 35 𝑘𝑚/ℎ, reveals the behavior in the full electric mode.

- High speed: speed over 35 𝑘𝑚/ℎ (fixed at 90𝑘𝑚/ℎ) to see how the system reacts in normal conditions, when the SOC is critical, or when there is no more fuel left.

- Constant acceleration: an acceleration of 0.5 𝑚/𝑠2 until 150 𝑘𝑚/ℎ is applied and indicates the limits of the system either in hybrid mode, in full electric mode or full ICE mode.

- Standstill: vehicle speed=0, shows the stationary charging mode use. - Grade ability: a constant acceleration of 0.2 𝑚/𝑠2 until 130 𝑘𝑚/ℎ with a slope of 5%,

pointing out the limits in those conditions of the hybrid, the full electric and the full ICE modes.

To simulate different vehicle states, the tests are run with different initial conditions. For

example, “Normal conditions” correspond to an initial SOC of 70%, and a full fuel tank (40L).

To see the behavior of the system when no more fuel is available, the fuel left in the tank is set

to 0, and to see what happens at low SOC, the SOC is set to a low value for example.

The limits of the systems developed are shown through those driving tests that represent

every condition and for every operating mode. An example of the verification process is given

for the braking test in Table 12.

66

Table 12: Braking mode verifications

Braking Operation mode Observations on the architecture

Normal conditions Regenerative

braking

The SOC is below the maximum SOC allowed,

so the battery is charging during braking

phases.

𝑆𝑂𝐶0 = 90% Normal braking The SOC is over the maximum SOC allowed so

the battery is not charging during braking

phases.

An example is shown in Figure 45 for the braking test for the parallel architecture. The input

parameters of the vehicle for all the tests are presented in Appendix 4.

On the left, the vehicle speed is plotted in blue, and the vehicle operation mode is in red. The

first test is done in “Normal conditions” and presented on the first line. In those conditions,

the battery can be charged without endangering it. On the right, the charge of the battery is

presented in blue, and the fuel consumption is represented by the red curve.

The second test (second line) points out a situation in which the battery is initially almost

fully charged (at 90%). As explained in section 3.1.3, going above that value could endanger

the battery and even cause unwanted effects. So, the operation mode used is “Normal

braking”, and so the SOC is neither increasing nor decreasing.

Figure 45: Operation mode and SOC results for the braking test for the parallel architecture

The results in terms of torques, speeds and powers can also be compared. The information

extracted concern the wheels, then engine and the electric machine respectively. The

67

expected power, torque and speed of the wheels are also plotted in order to see if the systems

meet the target.

The results for the braking test of the parallel architecture with the normal conditions are

presented in Figure 46.

Figure 46: Power, Torque and speed expected and obtained at the wheels, engine and electric machine

Those results show that the wheels are following the expected performances. Also, the electric

machine is the one involved in the process, with a negative power. So, it is consistent with the

fact that the SOC is increasing. The engine is shut down and its power, torque and speed are

equal to zero.

Remark: In this case, the power required to brake is entirely taken by the electric machine.

Also, the values of torque and speed are extracted before the power split device for the

engine and the electric machine, and after the final drive for the wheels (“Transmission”

subsystem). For the parallel architecture, the gear ratios introduced respectively in section

4.2.1 and in section 4.3.1 are placed after the extraction of the data. Here, the values

exposed are the engine and electric machine values.

The behavior of the system is then validated through the information given in Figure 45, and

Figure 46 enables to verify that the system meets the target and is consistent with the

operation mode.

5.2 Second validation part: driving cycle

The second part of the validation process is to study the systems with a driving cycle. Since

the WLTC3 is the new driving cycle used as a reference to estimate the performances, energy

consumption and emissions of a vehicle, it is chosen to present the results. The purpose of

this second validation part is to see how the modeled system behaves for longer tests. Here,

the WLTC3 cycle lasts 1800 seconds (30 min).

68

The results for the three architectures in normal conditions –initial SOC of 70% and fuel tank

full – are given. The component parameters used are shown in Appendix 4.

Series architecture

Figure 47 shows the control behavior of the architecture (in red) over the WLTC3 cycle (in

blue). To see the results more clearly, the results shown are taken between 1000 and 1500

seconds of the cycle (black dotted rectangle in Figure 47). This reduced time window enables

to clearly see the behavior of the system.

Figure 47: WLTC3 cycle (in blue) with the operation mode (in red) for the Series architecture in normal conditions

Figure 48 shows in detail the results for the reduced time window of the WLTC3 driving

cycle. It is easier to see that the three major operating modes are “Full elec” at low speeds,

“Hybrid drive” at high speeds and “Regenerative braking” during braking phases. Those

results are consistent with the energy consumption shown in Figure 50.

69

Figure 48: WLTC3 cycle (blue) and operation mode (red) of the Series architecture in the reduced time window

Figure 49 shows the power of the engine, the electric machine, the generator and the wheels

(expected in blue and obtained with dotted plot). As presented before, those power curves

enable validating the control of the operation mode and systems.

For the Series architecture, the generator (purple curve) follows the engine (red curve). The

scale factor between the two powers is the efficiency of the generator.

The same phenomenon is happening with the electric machine power (yellow curve) and the

power at the wheels (blue curve). When the wheel power is negative the electric machine is

propelling the vehicle, so |𝑃𝐸𝑀| > |𝑃𝑏𝑎𝑡𝑡|. When the wheel power is positive, the electric

machine is regenerating the energy, so |𝑃𝐸𝑀| < |𝑃𝑏𝑎𝑡𝑡|. This behavior is consistent with the

convention defined earlier.

Figure 49: Power distribution Series architecture in the reduced time window

Figure 50 shows the energy consumption of the system. In blue is the SOC evolution in

percentage, and in red the consumed fuel in liters.

70

It is possible to see that during braking phases, the engine is shut down, and the battery is

charging. When both systems are used the SOC decreases and the fuel consumed increases as

indicated in Figure 50.

Figure 50: Energy consumption of the Series architecture in the reduced time window

Parallel architecture

The same study is conducted for the parallel architecture.

The results are shown in Figure 51, Figure 52 and Figure 53 respectively. The control strategy

is close to the control strategy of the series architecture.

Figure 51: WLTC3 cycle (blue) and operation mode (red) of the Parallel architecture in the reduced time window

Figure 52 shows a different use of the engine, helped by the electric machine, but that follows

the power demand at the wheels. This is due to the mechanical link imposed by the power

split device.

This figure shows that the power distribution is consistent with the operation mode given by

the control unit.

71

Figure 52: Power distribution Parallel architecture in the reduced time window

Figure 53: Energy consumption of the Parallel architecture in the reduced time window

Series-Parallel architecture

The same study is conducted for the series-parallel architecture.

The results are shown in Figure 54, Figure 55 and Figure 56. Once again, the control strategy

is close to the ones seen for the series and parallel architectures.

72

Figure 54: WLTC3 cycle (blue) and operation mode (red) of the Series-Parallel architecture in the reduced time window

In Figure 55, it is possible to see the use of the generator (purple curve). Its purpose is to

control the engine torque, so its power fluctuates a lot. The electric machine (yellow curve)

has approximately the use as in the parallel architecture.

Associated with the operation mode, the power represented for all the components are

consistent.

Figure 55: Power distribution Series-Parallel architecture in the reduced time window

73

Figure 56: Energy consumption of the Series-Parallel architecture in the reduced time window

5.3 Conclusion

The operation mode managements are the same for the three architectures in the reduced

time window. The activation and deactivation conditions – presented Section 4 – are close

from one another.

The energy consumption shows best the difference between the architectures. It reveals

which system (ICE or EM) is prioritized in one architecture, as presented in Table 13.

Table 13: Energy consumption results for each architecture in the reduced time window

Architecture Delta SOC Fuel consumed

Series -1 % 0.33 L

Parallel -3.3 % 0.15 L

Series-parallel -3.5 % 0.16 L

The results of the Parallel and Series-parallel architectures are close to each other, while the

series architecture gives a greater importance to the engine use.

This is a direct consequence of the control strategy, which sets the limit of the engine power

higher for the series architecture than for the parallel and series-parallel architectures.

Globally, the results are consistent for all architectures both in terms of operation mode, and

power distribution. Here, only the simulation run under the “normal conditions” are shown.

Other initial conditions also show consistent results, as was pointed out by the test cycles in

the first validation part.

Some results are shown in Appendix 5 for other initial conditions.

74

6 Conclusion and future work

6.1 Conclusion

Three architectures are modeled in Simulink, with adjustable variables. The test results show

consistent behaviors for all three architectures, for all operating conditions.

To create the architectures, the different components needed to be modeled. To do so,

models were developed for the battery, the electric machine and the engine. Then, a model

for the power transmission was created, in order to follow the technical solutions chosen for

the architectures. The final step was to establish a control strategy adapted to each one of the

architectures. A reflection on the engine use was done, in order to improve its efficiency. It

led to two optimization methods to determine the best operating point of the engine. The first

method is used in series control unit, the second in the series-parallel architecture. The

parallel control strategy is more complex and no optimization strategy was used. Once

everything was done, the global Simulink model was made.

The global Simulink model enables creating a hybrid powertrain by specifying the

architecture, and the components characteristics. Then, the model created gives a first

indication on the performances of the powertrain.

The created powertrain can be studied thanks to the validation procedure proposed. Its limits

are pointed out and the user can modify the characteristics or the architecture of the

powertrain if the initial objective is not fulfilled. Several standardized test cycles are also

available. It can be interesting to look at the fuel consumption of the created powertrain and

to compare it with another model for examples. In that sense, the objectives of the project

were accomplished.

However, the model suffers from several limits. Although the control strategies can be seen

as basic, the obtained results are interesting and consistent. The control strategy is entirely

based on the optimization of the engine use, while it could be interesting to take the global

energy consumption or the emissions into consideration.

The different models used have their own limits, discussed after the introduction of each

model. Once the components are assembled to form an architecture, structural limits appear.

For example, the control is assumed to be immediate and cannot depict transitory states.

No gearbox is used in order to simplify the model and the control strategy. However, it

restricts the engine using range, and it can also cause an increase in the fuel consumption.

From a personal point of view, this project gave me a global and transversal vision of hybrid

powertrains. From the behavior of the different components to the behavior of the global

system, I had the chance to work on several physical systems.

75

6.2 Future work

The model proposed is just a first step into the realization of a more detailed and accurate

model.

More detailed models are needed for the components in order to make a complete study on

the powertrain performances. For example, emissions could be calculated in the engine

model and so be taken into account in the control strategy.

Thermodynamic properties are not directly taken into consideration. Indeed, limits in the

operating points are given but a more precise model and monitoring is needed.

The transient behaviors would also improve the model and enable having a global idea of

how the system reacts in a more realistic manner.

An optimization on the control strategies could also improve the performances. The

efficiency of the global powertrain could be improved with a more optimized control for

example.

76

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78

Appendixes

Appendix 1: Frequency analysis

Unfortunately, the model used does not present a great frequency response as it takes only

two effects into consideration.

A slightly modified Nyquist plot is usually chosen to study the frequency analysis of the

battery. Indeed, it is usual to plot the real part of the battery impedance as a function of the

inverse of its imaginary part as shown in Figure 57. The impedance of the battery 𝑍𝑏𝑎𝑡 is

given by Equation (41).

𝑍𝑏𝑎𝑡 = 𝑅0 +

𝑅11 + 𝑗𝜔𝑅1𝐶1

+𝑅2

1 + 𝑗𝜔𝑅2𝐶2 (41)

The frequency response of a Li-ion battery is represented in Figure 57. On this figure, the

principal effects and their frequency domain of application are expressed.

Figure 57: Real part of a real battery impedance as a function of the inverse of its imaginary part

The Nyquist plot of the battery at 50% of SOC with the parameters extracted is shown in

Figure 58.

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Figure 58: Nyquist and bode plots from the battery model

For each SOC, the frequency response is slightly different, since the parameters 𝑉𝑂𝐶, 𝑅0, 𝑅1,

𝑅2, 𝐶1 and 𝐶2 vary with the SOC. Even though, the changes in the equivalent circuit do not

modify the global behavior of the battery.

The Nyquist and Bode plots reveal that the battery is not representative of a real battery from

a frequency point of view. Indeed, the general behavior and the cutting frequencies of the

system are not close. The cutting frequencies are lower than they should be as:

𝑓 =

1

2𝜋 ⋅ 𝜏 (42)

In the regard of the requirements of the project, and its use (battery model in driving cycles,

global estimation…), the effects modeled and their time constants (𝜏1 ≈ 20 𝑠 and 𝜏2 ≈ 250 𝑠)

are adapted to the need.

Limits of the model

With the choice of the equivalent circuit, it was known that the model will have some

discrepancies compared to the real physical system. The fast-chemical effects are neglected as

well as the very long wear effects. The frequency analysis results point out the limit of the

model when those effects are neglected.

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Appendix 2: Stateflow chart Parallel architecture

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Appendix 3: Stateflow chart Series-Parallel architecture

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Appendix 4: Vehicle parameter inputs

The components characteristics presented in this appendix are extracted from the excel sheet

that is read by the Simulink in order to initialize all the needed parameters. For each

component, the name of the parameter, name of the variable in Matlab, value and unit are

indicated.

The battery characteristics are defined below. It is the same battery for all the architectures.

Battery Characteristics

Name Matlab Value Unit

Cell voltage Vcell 3.7 V

Battery Voltage Vtot 345 V

Number of cell ncell 93

Minimum voltage Vtotmin 241.5 V

Battery nominal capacity Q0 40 Ah

Maximum battery power Pbatt_max 75000 W

The electric machines characteristics are presented below. For each architecture, the electric

machines are taken to be the same, based on the electric machine used in a Golf GTE.

Electric Machine Characteristics (Series)


Maximum Torque Tmax_true1 330 Nm

Maximum speed wmax_true1 7000 tr/min

Maximum power Pmax_scaled1 57000 W

Generator Characteristics (Series)




Electric Machine Characteristics (Parallel)

Maximum Torque Tmax_true 330 Nm

Maximum speed wmax_true 7000 tr/min

Maximum power Pmax_scaled 57000 W

Electric Machine Characteristics (Series-Parallel)




Generator Characteristics (Series-Parallel)




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The engine characteristics are presented in the table below. The variable “Engine choice”

enables the user to decide whether he wants to use Willans model (input is “1”), the Insight

1.5L engine (input “2”) or the Prius 1L engine (input “3”). When the Willans model is chosen,

the parameters given after are used, otherwise they are not needed, nor used. For all tests

presented in this report, the engine chosen is the one of the Honda Insight.

Engine Characteristics


Tank volume TankVol 40 L

Fuel density FuelDensity 8.94 kWh/L

Lower heating value Hlv 11.86 kWh/kg

Petrol volumic density rohfuel 753.794266 kg/m^3

Willan's parameter e00 e00 0.3528

Willan's parameter e01 e01 0.0108 1/(m/s)

Willan's parameter e02 e02 -

0.00044487 1/(m/s)^2

Willan's parameter pmloss0 pmloss0 1.3*10^5 Pa

Willan's parameter pmloss1 pmloss1 -351.3 Pa/(m/s)

Willan's parameter pmloss2 pmloss2 822.5 Pa/(m/s)^2

Engine Characteristics (Series)

Engine choice ChoiceEng1 2

Stroke St1 0.08 m

Engine's displaced volume Vd1 1.4 L

Maximum power Pmax_eng1 110000 W

Engine speed at maximum power wePmax1 5500 tr/min

Maximum torque Tmax_eng1 250 Nm Engine speed at maximum torque weTmax1 3600 tr/min

Engine Characteristics (Parallel)


Stroke St2 0.08 m





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Engine Characteristics (Series-Parallel)


Stroke St3 0.08 m





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Appendix 5: Validation procedure results

Series architecture

Test initial conditions: 𝑆𝑂𝐶0 = 10, 𝑇𝑎𝑛𝑘𝑉𝑜𝑙 = 40

The control strategy is consistent with the control strategy chosen. When the SOC is below

20% the engine is charging the battery, for example at standstill between 1000 and 1040

seconds. Then, the SOC is over 20%, so the hybrid drive mode can be used. The SOC

decreases until it reaches 20 % at 1180 sec, so the vehicle changes to full ICE mode until

regenerative braking is available in this case.

Figure 59: WLTC3 cycle (blue) and operation mode (red) of the Series architecture in the reduced time window, low SOC

The energy consumption, shown in Figure 60 is consistent with the control strategy.

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Figure 60: Energy consumption of the Series architecture in the reduced time window, low SOC

Limits of the estimation of electric machine efficiency 𝜂𝐸𝑀 are revealed in Figure 61. The

power at the wheels is close the expected power, but the estimation of 𝜂𝐸𝑀 adds an

uncertainty in the calculation.

The driver model in the global vehicle model should limit this divergence in the power, so

this error should be decreased.

Figure 61: Power distribution Series architecture in the reduced time window, low SOC

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Series-parallel architecture

Test initial conditions: 𝑆𝑂𝐶0 = 10, 𝑇𝑎𝑛𝑘𝑉𝑜𝑙 = 40

In this case, the engine is propelling the vehicle as well as charging the battery between 1150

and 1350 seconds as shown in Figure 62.

Figure 62: WLTC3 cycle (blue) and operation mode (red) of the Series-Parallel architecture in the reduced time window, low SOC

Figure 63 shows that the battery is indeed being charged during the cycle.

Figure 63: Energy consumption of the Series-Parallel architecture in the reduced time window, low SOC

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However, limits of the engine are revealed in Figure 64. The engine cannot cope with the

power demand when driving along the vehicle. When it can, it charges the battery through

the generator, but very high-power demands are not attainable.

Figure 64: Power distribution Series-Parallel architecture in the reduced time window, low SOC

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