VEDOUCÍ PRÁCE prof. Ing. FRANTIŠEK ZEZULKA, CSc.

VYSOKÉ UČENÍ TECHNICKÉ V BRNĚ

BRNO UNIVERSITY OF TECHNOLOGY

FAKULTA ELEKTROTECHNIKY A KOMUNIKAČNÍCH TECHNOLOGIÍ

ÚSTAV AUTOMATIZACE A MĚŘICÍ TECHNIKY

FACULTY OF ELECTRICAL ENGINEERING AND COMMUNICATION DEPARTMENT OF CONTROL AND INSTRUMENTATION

ALGORITMY ŘÍZENÍ ELEKTROMOBILU

CONTROL ALGORITHMS FOR E-CAR

DIPLOMOVÁ PRÁCE

MASTER'S THESIS

AUTOR PRÁCE Bc. ADAM HRAZDIRA

AUTHOR

VEDOUCÍ PRÁCE prof. Ing. FRANTIŠEK ZEZULKA, CSc.

SUPERVISOR

BRNO UNIVERSITY OF TECHNOLOGY

Faculty of Electrical Engineering and Communication

Department of Control and Instrumentation

Master's thesis

master's study field

Cybernetics, control and Measurements

Student: Bc. Adam Hrazdira ID: 73024

Year of study: 2 Academic year: 2010/2011

TITLE OF THESIS:

Control algorithms for e-car

INSTRUCTION:

The task is to design and test algorithms for energetically optimal control of electric vehicle. Use model of the vehicle discussed in the semestral project. Analyze existing dynamic programming based

optimization algorithm and design necessary improvements and modifications in order to obtain suitable results. Design your own optimization algorithm and compare simulations results of both algorithms on the given model situations. Perform simulations in Matlab. Based on the simulations results analysis, choose the most appropriate algorithm and implement it in Java programming language.

REFERENCE:

J.-Ch. Culili: Introduction a l'Optimisation. Grand Ecoles Medcine, Paris 1994

S. Boyd - L. Vandenberghe : Convex Optimisation. Cambridge University Press, 2004 Levine W.S.: The Control Handbook. CRC Press, London, N. York, 1996

Termín zadání: 7.2.2011 Termín odevzdání: 23.5.2011

Head of thesis: prof. Ing. František Zezulka, CSc.

prof. Ing. Pavel Jura, CSc.

Předseda oborové rady

WARNING:

The author of the master's thesis claims that by creating this thesis he/she did not infringe the rights of third persons and the personal and/or property rights of third persons were not subjected to derogatory treatment. The author is

ABSTRACT

The aim of this work is to design and implement energy consumption optimization control algorithms for electric vehicle. The main objective is to optimize the power-split-ratio between the main power source (batteries) and the super-capacitors during the driving cycle. The driving power profile is estimated and predicted using 3D geographic data and vehicle model. In the first part, vehicle components modelling is introduced. Then, moving average based algorithm and dynamic programming algorithm are presented.

Simulations and analysis are provided to show algorithms’ benefits. In the last part, Java implementation and also Android operating system application are described.

KEYWORDS

Electric vehicle, energy optimization, control algorithms, static optimization, batteries, super-capacitors, dynamic programming.

ABSTRAKT

Cílem práce byl návrh a implementace řídicích algoritmů pro optimalizaci spotřeby energie elektrického vozidla. Hlavním úkolem byla optimalizace rozložení energie mezi hlavním zdrojem energie (bateriemi) a super-kapacitory v průběhu jízdního cyklu. Jízdní výkonový profil je odhadován a předpovězen na základě 3D geografických souřadnic a matematick- ého modelu vozidla. V první části jsou uvedeny komponenty vozidla a jejich modely. Poté jsou představeny algoritmy na základě klouzavého průměru a dynamického programování.

Byly provedeny simulace a analýzy pro demostraci přínosů algoritmů. V poslední části je popsána Java implementace algoritmů a také aplikace pro operační systém Android.

KLÍČOVÁ SLOVA

Elektrické vozidlo, elektromobil, energetická optimalizace, řídicí algoritmy, statická opti- malizace, baterie, super-kapacitory, dynamické programování.

HRAZDIRA, AdamControl algorithms for e-car: master’s thesis. Brno: Brno University of Technology, Faculty of Electrical Engineering and Communication, Department of Con- trol and Instrumentation, 2011. 101 p. Supervised by prof. Ing. František Zezulka, CSc.

DECLARATION

I declare that I have elaborated my master’s thesis on the theme of “Control algorithms for e-car” independently, under the supervision of the master’s thesis supervisor and with the use of technical literature and other sources of information which are all quoted in the thesis and detailed in the list of literature at the end of the thesis.

As the author of the master’s thesis I furthermore declare that, concerning the creation of this master’s thesis, master’s thesis, I have not infringed any copyright. In particular, I have not unlawfully encroached on anyone’s personal copyright and I am fully aware of the consequences in the case of breaking Regulation S11 and the following of the Copyright Act No 121/2000 Vol., including the possible consequences of criminal law resulted from Regulation S152 of Criminal Act No 140/1961 Vol.

Brno . . . . (author’s signature)

ACKNOWLEDGEMENTS

I am heartily thankful to my professor, František Zezulka, whose support from the initial to the final level enabled me to work on my master’s thesis at foreign university, ESIEE Paris.

This thesis would not have been possible without the kind support, guidance and remarkable patience of my supervisor, Arben Cela, and his colleagues, Abdellatif Réama and Rhédha Hamouche, from Department of Embeded Systems at ESIEE Paris.

I would also like to thank to my family for their encouragement and absolute confidence in me and to my girlfriend for her love and continuous support.

Brno . . . . (author’s signature)

CONTENTS

1 Introduction 12

1.1 Motivation . . . 12

1.2 Objectives . . . 12

2 Full Electric Car Modeling 14 2.1 General Model Description . . . 14

2.1.1 Bicycle Model . . . 14

2.1.2 Longitudinal Model . . . 15

2.2 Components . . . 17

2.2.1 Topology of HEV Energy System . . . 17

2.2.2 Batteries . . . 19

2.2.3 Supercapacitors . . . 21

2.2.4 DC/DC Converter . . . 23

2.2.5 Electric Motor . . . 24

2.3 Simulation Methods and Tools . . . 26

3 Energy Management Optimization 28 3.1 Optimization Problems . . . 28

3.2 Optimization Methods . . . 28

3.2.1 Dynamic Programming (DP) . . . 29

3.2.2 Analytical Optimization Methods . . . 30

3.3 Moving Average Real-time Optimization Algorithm . . . 32

3.3.1 Power Transfer Efficiency . . . 34

3.3.2 Simulation Results and Analysis . . . 37

3.3.3 Conclusions . . . 46

3.4 Demanded Power Filter Algorithm . . . 46

3.5 Predictive Optimization Power Management Algorithm (POEM) . . . 49

3.5.1 Energy-based SOC Definition . . . 50

3.5.2 Position-based power calculation . . . 51

3.5.3 SOC prediction at the end of look-ahead horizon . . . 51

3.5.4 Cost Function . . . 54

3.5.5 Implementation of POEM algorithm . . . 55

3.5.6 Simulation and Analysis of POEM . . . 57

3.5.7 Conclusion and Future Work . . . 63

3.6 Algorithms Comparison . . . 64

4 Java Implementation 72

4.1 Code Structure . . . 72

4.1.1 Interface . . . 73

4.2 XML Input Data Format . . . 75

4.3 Code Example . . . 77

4.4 Execution Time Optimization . . . 78

4.5 Modeling Implementation . . . 80

4.5.1 Power Profile Calculation . . . 80

4.5.2 Conversion between Power and Energy . . . 80

4.5.3 Battery and SC Energy Calculation . . . 81

4.5.4 State-of-Charge Discretization Interval Determination . . . 81

4.5.5 Interpolation . . . 81

4.6 Simulations and Analysis . . . 82

5 Android Implementation 88 5.1 Application Structure and Description . . . 89

5.1.1 WebView and JavaScript . . . 89

5.1.2 Flot Graph Library . . . 90

5.1.3 Localization . . . 90

5.1.4 CycleView Activity . . . 91

5.2 Resources . . . 92

5.2.1 Replacing Configuration File . . . 92

5.3 Google Maps JavaScript API V3 . . . 93

5.3.1 Directions . . . 93

5.3.2 Elevations . . . 95

5.3.3 Traffic . . . 95

5.4 Altitude and Power Sampling . . . 96

6 Conclusion 97 6.1 Future Work . . . 97

Bibliography 99

LIST OF FIGURES

2.1 Forces acting on a vehicle moving uphill . . . 14

2.2 Conceptual illustration of a general HEV configuration [1] . . . 18

2.3 Topology of battery and SC in parallel . . . 18

2.4 Two kinds of topology with different connections of DC/DC converter 19 2.5 Topology of EV system . . . 19

2.6 Equivalent circuit model of Li battery . . . 20

2.7 Characteristic map of a Li battery efficiency . . . 21

2.8 Equivalent circuit model of SC . . . 22

2.9 Characteristic map of a SC efficiency . . . 23

2.10 Region diagram of energy and power characteristics of different com- ponents . . . 24

2.11 DC/DC converter power efficiency map . . . 25

2.12 Electric motor efficiency map [9] . . . 26

3.1 Schematic diagram of moving average algorithm . . . 33

3.2 Moving average algorithm flow chart . . . 35

3.3 Schematic diagram of SC control in moving average algorithm . . . . 36

3.4 Demanded power for complete driving cycle . . . 39

3.5 Battery and SC power demand for complete driving cycle . . . 41

3.6 Battery and SC SoC for complete driving cycle . . . 41

3.7 Battery and SC demanded power - moving average algorithm (look- ahead horizon is all the route) . . . 42

3.8 Battery and SC SoC - moving average algorithm (look-ahead horizon is all the route) . . . 43

3.9 Energy save improvement compared to battery only source without energy recuperation . . . 45

3.10 Filtered demanded power profile and additional battery power needed to recharge SC . . . 48

3.11 Battery and SC demanded power - demanded power filter algorithm . 48 3.12 Battery and SC SoC - demanded power filter algorithm . . . 49

3.13 Schematic diagram of POEM algorithm [9] . . . 52

3.14 Flow diagram to implement POEM algorithm [9] . . . 57

3.15 Test vehicle . . . 59

3.16 Demanded power for complete driving cycle . . . 60

3.17 Battery and SC SoC and power obtained by dynamic programming algorithm (p=269, 𝑆𝑜𝐶_{𝑏𝑖𝑛𝑖𝑡} = 30 %) . . . 62

3.18 Battery and SC SoC and power obtained by dynamic programming algorithm (p=30, ) . . . 62

3.19 Battery and SC SoC and power obtained by dynamic programming algorithm (p=10,𝑆𝑜𝐶_{𝑏𝑖𝑛𝑖𝑡} = 30 %) . . . 63 3.20 Demanded power for complete driving cycle case 1 . . . 66 3.21 Battery and SC SoC and power obtained by dynamic programming

algorithm (profile case 1) . . . 66 3.22 Battery and SC SoC and power obtained by moving average algorithm

(profile case 1) . . . 67 3.23 Demanded power for complete driving cycle case 2 . . . 68 3.24 Battery and SC SoC and power obtained by dynamic programming

algorithm (profile case 2) . . . 68 3.25 Battery and SC SoC and power obtained by moving average algorithm

(profile case 2) . . . 69 3.26 Demanded power for complete driving cycle case 3 . . . 70 3.27 Battery and SC SoC and power obtained by dynamic programming

algorithm (constant profile case 3) . . . 70 3.28 Battery and SC SoC and power obtained by moving average algorithm

(constant profile case 3) . . . 71 4.1 Energy management class structure. . . 73 4.2 Interface implementation inheritance graph. . . 74 4.3 EVMA (Moving Average) and EVDP (Dynamic Programming) class

inheritance graph. . . 74 4.4 Possible transitions in the SoC grid. . . 79 4.5 Velocity, road slope and power profile of the driving cycle. . . 82 4.6 Moving Average algorithm SoCs and power demands (power to energy

conversion coefficient is calculated from average velocity). . . 85 4.7 Moving Average algorithm SoCs and power demands (power to energy

conversion coefficient is calculated from instant velocity). . . 85 4.8 Dynamic Programming algorithm SoCs and power demands (power

to energy conversion coefficient is calculated from average velocity).

Grid discretization is 30 kW. . . 86 4.9 Dynamic Programming algorithm SoCs and power demands (power

to energy conversion coefficient is calculated from instant velocity).

Grid discretization is 30 kW. . . 86 4.10 Dynamic Programming algorithm SoCs and power demands (power

to energy conversion coefficient is calculated from average velocity).

Grid discretization is 10 kW. . . 87 4.11 Dynamic Programming algorithm SoCs and power demands (power

to energy conversion coefficient is calculated from instant velocity).

Grid discretization is 10 kW. . . 87

5.1 Application user graphic interface displaying route, battery and super- capacitors actual and final states-of-charge embedded in Samsung Galaxy Tab device. . . 88 5.2 Android application structure and parameters passing. . . 89 5.3 CycleView activity call graph. . . 92 5.4 Distances of route’s legs (route from ESIEE Paris to Noisy-le-Grand). 94 5.5 Durations of route’s legs (route from ESIEE Paris to Noisy-le-Grand). 94 5.6 Altitude samples within the route (sample every 20 meters, route

from ESIEE Paris to Noisy-le-Grand). . . 95

LIST OF TABLES

3.1 Parameters of test vehicle . . . 37 3.2 Simulation parameters . . . 38 3.3 Battery only power source without energy recuperation simulation

results . . . 38 3.4 Battery only power source with energy recuperation simulation results 39 3.5 Moving average algorithm simulation results with different parameters 40 3.6 Parameters of test vehicle . . . 58 3.7 Simulation parameters . . . 61 3.8 Battery only power source without energy recuperation simulation

results . . . 61 3.9 POEM algorithm simulation results for different look-ahead horizons 61 3.10 Algorithms comparison for profile 1 . . . 65 3.11 Algorithms comparison for profile 2 . . . 67 3.12 Algorithms comparison for profile 3 . . . 69 4.1 Algorithms comparison (power to energy coefficient calculated from

instant velocity). . . 84 4.2 Algorithms comparison (power to energy coefficient calculated from

average velocity). . . 84

1 INTRODUCTION 1.1 Motivation

Nowadays the number of personal cars is still growing and the most used internal combustion engines (ICE) cause serious problems for the environment and hydro- carbon resources. One of the biggest recent deals is thus to develop vehicles with alternative power sources.

A variety of different Hybrid Electric Vehicles (HEV) was introduced and even incorporated to the market. Even though these solutions succeeded to decrease no- tably the fuel consumption, the ICE still plays the main power source role in these systems. The demands are higher and higher and that is why the full electric vehicle (EV) is being developed.

The EV has many advantages over the conventional internal combustion en- gine vehicle, such as absence of actual emissions, high efficiency, independence from petroleum, and quiet and smooth operation. Especially the ecological aspects moti- vate the EV development. In the case of higher market share by EV in the future, the electricity making process should be examined to accomplish the pollution reduction goal.

The development of new batteries slowed down in the last years and even though some new technologies appeared, the specific energy and power are not as high as foreseen. The battery is one of the most important parts of EV and acts as the primary energy source. That is why it is very important to develop a sophisticated energy management system allowing the optimal energy consumption and recuper- ation.

1.2 Objectives

In the past decades, a vehicle modelling was studied in detail so the mathematical models and approximations can be found easily. The next step in the automotive industry was to improve the vehicle driving capabilities using a special control sys- tems usually embedded in micro-controllers which developed very rapidly during the past years. Also, the new processors calculation power enables the use of real-time control and optimization algorithms.

Even though many optimization algorithms were already examined, this work introduces new technologies and new approaches to the energy optimization. It is proposed to use super-capacitors in addition to batteries to support them and re- cuperate energy from regenerative breaking. The goal of energy management is to

optimise the power-split-ratio (PSR) between batteries and super-capacitors, be- cause the super-capacitors can mostly provide energy with higher efficiency, but can not store enough of it.

The energy management is based on the idea described in [9]. In the first time, the geographic 3D data of the driving cycle are obtained and depending on the predicted velocity profile, the driving power profile is predicted. Finally, the PSR is optimised for this power profile using either dynamic programming algorithm introduced in [9]

or our self-made algorithm. This algorithms were developed to be independent on a concrete vehicle and components parameters so they could be used in any EV with batteries and super-capacitors.

In the first part, this work summarises vehicle general model description and in- troduces a formula for vehicle power calculation. Different EV topologies are shown.

Also the EV components and their mathematical models are presented. In the next section, some energy optimization methods and problems are discussed and opti- mization algorithms principles, simulations and comparisons are shown. Further- more, the Java implementation of this algorithms is clarified. In the last part, the prototype of EV energy optimization application for Android operating systems is presented.

2 FULL ELECTRIC CAR MODELING 2.1 General Model Description

2.1.1 Bicycle Model

In the first time the discussion of vehicle fundamentals will be restricted to one- dimensional movement (bicycle model). The movement behaviour of a vehicle along its moving direction is completely determined by all the forces acting on it in this direction.

According to the Newton’s second law, vehicle acceleration can be written as 𝑑𝑉

𝑑𝑡 =

∑︀𝐹_𝑡−∑︀

𝐹_𝑟

𝛿𝑀 (2.1)

where V is the speed of the vehicle,∑︀

𝐹𝑡is the total traction effort of the vehicle,

∑︀𝐹𝑟 is the total resistance, M is the total mass of the vehicle, and𝛿𝑀 is the mass factor that equivalently converts the rotational inertias of rotating components into translational mass.

Fig. 2.1: Forces acting on a vehicle moving uphill

As shown in figure 2.1, the total resistance is composed mainly from rolling re- sistance 𝐹_𝑟 (which combines the torques 𝑇 𝑟_𝑓 and 𝑇 𝑟_𝑟), wind resistance 𝐹_𝑤, and climbing resistance𝐹_𝑐(the term𝑀 𝑔sin𝛼). In the opposite direction acts total trac- tion effort 𝐹_𝑡 which is composed from the front and rear tires efforts 𝐹_𝑡𝑓 and 𝐹_𝑡𝑟 generated by the prime movers¹ and minus all friction losses in the powertrain. By developing the equation above, we obtain the dynamic equation it the form:

𝑀𝑑𝑉

𝑑𝑡 =𝐹_𝑡−(𝐹_𝑟+𝐹_𝑤+𝐹_𝑐) (2.2)

Using the dynamic equation, we can express the maximal traction effort for both front and rear wheels. Then we can also examine the tire-ground adhesion which is connected with the maximal traction effort. The detailed description of the characteristics summarized in this chapter is presented in [4].

2.1.2 Longitudinal Model

The vehicular model of longitudinal dynamics is constructed based on the theory of vehicle multi-body dynamics as seen before.

Wind Resistance

The wind resistance is caused generally by two facts: the viscous friction of the surrounding air on the vehicle surface and the losses by the pressure difference between the front and the rear of the vehicle, generated by a separation of the air flow.

The resistance expression can be usually simplified by considering a vehicle as a prismatic body with a frontal area𝐴_𝑓. The pressure difference force can by multiplied by an aerodynamic drag coefficient𝐶_𝑑also known as Reynold’s coefficient (estimated by simulation or experiment in wind tunnel) so the wind resistance can be written as

𝐹_𝑤(𝑣) = 1

2 ·𝜌·𝐴_𝑓 ·𝐶_𝑑·𝑣² (2.3) where 𝑣 is the vehicle speed and 𝜌 is the density of the ambient air.

Tire Rolling Resistance

The tire rolling resistance can be expressed as

𝐹𝑟(𝑣, 𝑝, ...) = 𝜇𝑟(𝑣, 𝑝, ...)·𝑀 ·𝑔·cos(Θ), 𝑣 >0 (2.4) where M is the vehicle mass, g the acceleration due to gravity, term cos(Θ) is road slope influence and 𝜇_𝑟 is the rolling friction coefficient.

The rolling friction coefficient depends on many variables. Especially vehicle speed𝑣, tire pressure 𝑝, and road surface conditions.

Climbing Resistance

The climbing resistance is conservative force induced by gravity and considerably influences the vehicle behaviour.

𝐹_𝑐(Θ) =𝑀 ·𝑔· sin(Θ) (2.5)

Acceleration Resistance

The acceleration resistance due to the inertia of the vehicle and of all rotating parts inside the vehicle causes frictious (d’Alembert) forces. The rotating parts are here represented by

𝐹_𝑎( ˙𝑣) = 𝑀(1 +𝛿_𝑒𝑞𝑚)· 𝑑𝑣

𝑑𝑡 (2.6)

where 𝛿𝑒𝑞𝑚 is the vehicle equivalent moment inertia representing the rotating parts such as wheels and powertrain inertia.

According to an analysis of the summation of performing forces acting on the vehicle body in the longitudinal direction, the power balance for the controlled vehicle is governed by:

𝑃𝐷(𝑡) =𝑓𝑃_𝐷(𝑣,𝑣, 𝑀,˙ Θ) = (𝐹𝑤+𝐹𝑟+𝐹𝑐+𝐹𝑎)𝑣

=[︁𝜌

2𝐴_𝑓𝐶_𝑑𝑣³+𝑀 𝑔(𝜇_𝑟+ cos Θ + sin Θ)𝑣]︁

+𝑀(1 +𝛿_𝑒𝑞𝑚) ˙𝑣𝑣 (2.7) And the following relationships are satisfied (for the topology in figure 2.5):

𝑃_𝐷 =𝑃_𝐶𝑉 +𝑃_𝐵, 𝑃_𝑚 = 𝑃_𝐷 𝜀𝑚

𝑇_𝑚 = (𝐹_𝑤+𝐹_𝑟+𝐹_𝑐+𝐹_𝑎)𝑟

𝑖₀𝑖_𝑠 (2.8)

𝜔_𝑚 = 𝑣𝑖0𝑖𝑠

𝑟_𝑡

Where 𝑃_𝐷 is the demanded power, 𝑃_𝐶𝑉 is the power delivered by DC/DC con- verter, 𝑃_𝐵 is the power delivered by battery, 𝑃_𝑚 is the motor demanded power, 𝜀_𝑚 is the motor efficiency, 𝑇_𝑚 is the motor traction force, 𝜔_𝑚 is the motor’s rotational speed, 𝐹_𝑤 is the wind resistance, 𝐹_𝑟 is the tire rolling resistance, 𝐹_𝑐 is the climbing resistance, 𝐹_𝑎 is the acceleration resistance,𝜌 is the air density, 𝐴_𝑓 is the windward area for the vehicle, 𝐶_𝑑 is the Reynolds coefficient, 𝑔 = 9.8𝑚/𝑠², 𝜇_𝑟 is the rolling resistance coefficient,𝑣 is the velocity,𝑣˙ is the acceleration,𝑀 is the mass, Θis the road grade, 𝛿_𝑒𝑞𝑚 is the vehicle equivalent moment inertia, 𝑖₀ is the final reduction ratio, 𝑟_𝑡 is the effective tire radius, is (𝑠= 1, ...,6)is the gear position ratio.

Position-based Power Calculation

As an important parameter in equation (2.7), the road grade may change frequently at the actual road environment, especially in the mountain terrain, and has become

record the road grade by GPS and 3D-map is dependent on position rather than time.

Therefore, the time-based equation (2.7) is not suitable for the purpose of control algorithm design, and a power calculation depended on position is preferable. Using the transformation

𝑣 = 𝑑𝑠

𝑑𝑡 (2.9)

𝑑𝑣 𝑑𝑠 = 𝑑𝑡

𝑑𝑠 𝑑𝑣 𝑑𝑡 = 1

𝑣 𝑑𝑣

𝑑𝑡, 𝑣 ̸= 0 (2.10)

equation (2.7) can be transferred into a position-based form 𝑃𝐷(𝑠) = [︀_𝜌

2𝐴𝑓𝐶𝑑𝑣²+𝑀 𝑔(𝜇𝑟cos𝜃+ sin𝜃)]︀

+𝑀(1 +𝛿𝑒𝑞𝑚)𝑣^𝑑𝑣_𝑑𝑠 (2.11)

2.2 Components

HEV uses an electric motor for traction, and chemical batteries, fuel cells, ultra capacitors, and/or flywheels for their corresponding energy sources. In figure 2.2 is shown the illustration of a general HEV divided into three parts (electric propulsion, energy source and auxiliary subsystem). The electronic power converter regulates the power flow between the electric motor and energy source on the base of two control inputs - brake and accelerator pedals.

The backward power flow is due to the regenerative braking of the HEV and this regenerated energy can be restored into the energy source, provided the energy source is receptive. Most HEV batteries as well as ultra capacitors are supported to accept regenerative energy.

2.2.1 Topology of HEV Energy System

The basic topology of HEV energy system in combining a SC system with a battery system as a power supplement device is to simply connect both systems in parallel as shows figure 2.3.

After embedding the DC/DC converter, in this way, two kinds of topologies are proposed. The first type has the SC connected directly across the DC bus and the battery connected through a bi-directional DC/DC converter. The second configu- ration has the battery on the main DC bus instead. Two configurations are shown in figure 2.4.

Previous research has verified that having the SC connected to the bus cable through DC/DC converter as shown in figure 2.4 (b) is likely to yield high efficiency.

Notable, in the configuration of figure 2.4 (a), the entire battery power has to be

Fig. 2.2: Conceptual illustration of a general HEV configuration [1]

Fig. 2.3: Topology of battery and SC in parallel

transferred through the DC/DC converter and hence lowering the total efficiency of the battery pack.

Detailed topology is shown in figure 2.5. The main source composed by a battery pack and an auxiliary source implemented with a bi-directional DC/DC converter and SC bank. The battery pack connected directly across DC bus, and the SC bank connected through DC/DC converter. The output power of SC bank can be regulated by the energy management system (EMS), which acts on DC/DC converter by the way of the current control signal. The energy management algorithm takes into account multiple route information, current, voltage and state of charge (SoC) of battery and SC. They suffer from different energy loss and efficiency issues while the power transmits among them.

Fig. 2.4: Two kinds of topology with different connections of DC/DC converter

Fig. 2.5: Topology of EV system

2.2.2 Batteries

Electrochemical batteries are a key component of electric vehicles. Batteries are de- vices that transform chemical energy into electrical energy and vice versa. They represent a reversible electrical energy storage system. For HEV applications, the first consideration is the specific energy of a traction battery, because it limits the vehicle range. Other desirable attributes are high specific power, long calendar and cycle life, low initial and replacement costs, high reliability, and high robustness.

Among other current technical challenges, a key point is developing accurate tech- niques to determine the capacity or the state of charge (SoC) of batteries during their operation.

SoC is defined as the ratio of remaining capacity to fully charged capacity and can be expressed as:

𝑆𝑜𝐶 =𝑆𝑜𝐶₀−

∫︁ 𝑖

𝑄(𝑖)𝑑𝑡 (2.12)

where𝑄(𝑖)is the ampere-hour capacity of the battery or SC at current rate𝑖and 𝑆𝑜𝐶₀ is the initial value of the SoC. For discharging, 𝑖is positive, and for charging, 𝑖 is negative.

The energy capacity is considered to be more important than the coulometric capacity (ampere-hours), because it is directly associated with vehicle operation and the coulometric capacity usually depends on different discharging current rates [4].

The energy delivered from the battery can be expressed as:

𝐸_𝑐=

∫︁ 𝑡 0

𝑉(𝑖, 𝑆𝑜𝐶)𝑖(𝑡)𝑑𝑡 (2.13)

where 𝑉(𝑖, 𝑆𝑜𝐶) is the voltage at the battery terminals, which is a function of battery current and SoC.

The basic equivalent circuit model (Thevenin model) of a Li battery is shown in figure 2.6. It is represented by an ideal open circuit voltage source (𝑉_𝑜𝑐) and a series internal resistance (𝑅_𝑖𝑛𝑡).

Fig. 2.6: Equivalent circuit model of Li battery

The equivalent circuit loop holds true to Kirchhoff’s voltage law to produce a terminal voltage expressed as:

𝑉𝐵 =𝑉𝑜𝑐−𝐼𝐵𝑅𝑖𝑛𝑡 (2.14)

𝑉_𝑜𝑐 =𝑓_𝑣𝑜𝑐(𝑆𝑜𝐶_𝑄𝑏, 𝐼_𝐵) (2.15) where 𝑆𝑜𝐶_𝑄𝑏 is state of charge, 𝐼_𝐵 is battery current, 𝑅_𝑖𝑛𝑡 is internal resistance, 𝑉_𝑜𝑐 is open circuit voltage and 𝑉_𝐵 is terminal voltage.

The state variable of 𝑆𝑜𝐶_𝑄𝑏 can be defined as:

𝑆𝑜𝐶_𝑄𝑏(𝑡) = 𝑄(𝑡)

𝑄₀ (2.16)

where𝑄is the remaining battery charge,𝑄₀is the total charge for a fully charged battery.

Both 𝑉_𝑜𝑐 and 𝑅_𝑖𝑛𝑡 are dependent upon the battery instantaneous 𝑆𝑜𝐶_𝑄𝑏. The open circuit voltage 𝑉_𝑜𝑐 can be obtained from Nernst equations [8] or by empirical methods. The internal resistance𝑅_𝑖𝑛𝑡 can be expressed as a function of the battery 𝑆𝑜𝐶_𝑄𝑏, operating temperature as well as the charge and discharge currents.

To proceed modelling and simulations, it is necessary to know precise parameters of the given battery, namely capacity, voltage, energy and internal resistance of the

The key to minimize the energy consumption for the batteries manage system is the efficiency of the battery charge/discharge. If we let the Faradic efficiency be 1, we can express the battery efficiency as energy efficiency which is defined as a ratio of electrical energy delivered by a battery from a particular 𝑆𝑜𝐶_𝑄𝑏 to the electrical energy required to return the battery to the same 𝑆𝑜𝐶_𝑄𝑏. It can be written as:

𝜂_𝐵𝐸 =𝑓_𝜂𝐵𝐸(𝑆𝑜𝐶, 𝑃_𝐸) (2.17)

𝑃_𝐵 =𝐼_𝐵𝑉_𝐵 (2.18)

where 𝑃_𝐵 is battery power.

Although the battery efficiency is not a straightforward parameter to quantify the performance of a battery, it is effective as a comparative measure of the various power and energy system strategies. That is why, for the purpose of energy consumption optimization, it is necessary to know the characteristic map of battery efficiency. In the figure 2.7 is shown an example of characteristic map of Li battery efficiency.

Fig. 2.7: Characteristic map of a Li battery efficiency

2.2.3 Supercapacitors

The energy source, mainly batteries and fuel cells, has high specific energy, whereas the power source has high specific power. The power source that has received wide

attention is the SC. SC can be recharged from the energy source, which is in our case battery, during less demanding driving power or during regenerative braking.

The SC is characterized by a much higher specific power but a much lower specific energy compared to batteries so it is difficult to use SC alone as energy storage. One promising application is the so-called battery and SC hybrid energy storage system for HEVs. Specific energy and specific power requirements can be decoupled, thus affording an opportunity to design a battery that is optimized for specific energy and cycle life with little attention being paid to specific power. Due to the load levelling effect of the SC, the high current discharging from the battery and the high current charging to the battery by regenerative braking are minimized so that available energy, endurance, and life of the battery can be significantly increased. Compared to the batteries, the SC can be charged and discharged in order of milliseconds and the number of charging cycles capabilities at 80 % DoD (Depth of Discharge) can be more than 10⁶ cycles, while in the case of batteries it is only around 10³ cycles.

Of course, by increasing the endurance of battery, the whole system cost and used battery replacement expenses decrease.

The SC can be modelled by an ideal capacitance and an equivalent series resis- tance (ESR), as shown in figure 2.8.

Fig. 2.8: Equivalent circuit model of SC

The equivalent circuit loop holds true to Kirchhoff’s voltage law to produce a terminal voltage expressed as:

𝑉_𝑆𝐶 =𝑉_𝑜𝑐−𝐼_𝑆𝐶𝑅_𝑖𝑛𝑡 (2.19)

𝑉_𝑜𝑐=𝑓_𝑣𝑜𝑐(𝑆𝑜𝐶_𝑄𝑆𝐶, 𝐼_𝑆𝐶) (2.20) where 𝐼_𝑆𝐶 is SC current and 𝑉_𝑆𝐶 is terminal voltage.

The ESR accounts for resistive losses in the dielectric, plate material, and elec- trolytic solution. The actual capacitance and ESR are dependent on terminal volt- age, voltage charge rate, current, and temperature. However within the capacitor’s

Again, for the purpose of energy consumption optimization, it is necessary to know the characteristic map of SC efficiency and SC parameters - capacity, voltage and internal resistance. In the figure 2.9 is shown an example of characteristic map of a SC efficiency.

Fig. 2.9: Characteristic map of a SC efficiency

From figure 2.10 is visible, that battery is high energy component (thus it is used to provide long duration electric energy) and SC is high power component (thus it is used to provide high frequent jerk power and absorb brake regeneration energy).

Compared to the Li battery, the terminal voltage of the SC has smaller variation during charge and discharge at a fixed 𝑆𝑂𝐶_𝑄𝑆𝐶. However the SC has a much larger voltage variation when the𝑆𝑂𝐶_𝑄𝑆𝐶 varies. The SC has a higher efficiency than the Li battery, generally above 82% if the𝑆𝑂𝐶_𝑄𝑆𝐶 is higher than 60%. Also, the SC has a very rapid dynamic response and low charging time.

2.2.4 DC/DC Converter

To connect a SC to an external power system, it is necessary to boost the SC voltage or to increase the number of SC. The role of the DC/DC converter is to regulate the voltage to control the SC power. The transmission efficiency of the DC/DC converter can be influenced from multiple factors, like flow power, current and so

Fig. 2.10: Region diagram of energy and power characteristics of different compo- nents

on. For simplifying the algorithm, the power efficiency of DC/DC converter is defined as a function of the load power. It can be written as:

𝜀𝐶𝑉 =𝜂𝐶𝑉(𝑃𝐶𝑉) (2.21)

where 𝜀_𝐶𝑉 and 𝑃_𝐶𝑉 are the efficiency and the load power of DC/DC converter.

We can notice that

𝑃_𝐶𝑉 =𝑃_𝑆𝐶𝜀_𝐶𝑉 (2.22)

For the purpose of energy consumption optimization, it is necessary to know the DC/DC converter power efficiency map. Example is shown in figure 2.11.

2.2.5 Electric Motor

The electric motor characteristics are based on the efficiency data as shown in fig- ure 2.12, which is a non-linear function of the electric motor torque and the rotational

Fig. 2.11: DC/DC converter power efficiency map

speed

𝜀_𝑚 =𝜂_𝑚(𝑇_𝑚, 𝜔_𝑚) (2.23)

Then, the electric motor demanded power is 𝑃_𝑚 = 𝑇_𝑚, 𝜔_𝑚

𝜀_𝑚 (2.24)

where, 𝑇_𝑚 ∈ [𝑇_{𝑚𝑚𝑖𝑛}, 𝑇_{𝑚𝑚𝑎𝑥}], 𝜔_𝑚 ∈ [𝜔_{𝑚𝑚𝑖𝑛}, 𝜔_{𝑚𝑚𝑎𝑥}], 𝜀_𝑚 and 𝑃_𝑚 are the output torque (Unit: 𝑁.𝑚), output rotational speed (Unit: 𝑟𝑎𝑑/𝑠), efficiency and the de- manded power (Unit:𝑘𝑊) of the electric motor.𝑇_{𝑚𝑚𝑖𝑛},𝑇_{𝑚𝑚𝑎𝑥},𝜔_{𝑚𝑚𝑖𝑛}and𝜔_{𝑚𝑚𝑎𝑥}are the minimal and the maximum values of torque and rotational speed of the electric motor respectively.

The efficiency map of electric motor is given by manufacturer, and shown as the solid lines in figure 2.12. The dashed line in figure 2.12 is the distribution of the optimal efficiency operating points corresponding to the given output powers.

They can be obtained via interpolation method, and used to determine the optimal transmission ratio.

Fig. 2.12: Electric motor efficiency map [9]

2.3 Simulation Methods and Tools

While performing simulations, more approaches can be utilized. One of them are quasistatic simulations, where the input variables are the speed𝑣 and the accelera- tion𝑎 of the vehicle as well as the grade angle𝛼 of the road. With this information, the force 𝐹𝑡 is computed that has to be acting on the wheels to drive the chosen profile for a vehicle described by its main parameters {𝐴𝑓 ·𝑐𝑑, 𝑐𝑟, 𝑚𝑣}. In this step the vehicle is assumed to run at constant speed𝑣, acceleration 𝑎, and grade 𝛼 for a (short) time periodℎ. Once 𝐹𝑡 is known, the losses of the powertrain are considered by a power balance. The quasistatic method is well suited to the minimization of the fuel consumption of complex powertrain structures. With this approach it is possible to design supervisory control systems that optimize the power flows in the propulsion system. The influence of the driving pattern can be included in these calculations. The main drawback of this method is that the physical causality is not respected and the driving profile that has to be followed has to be known a priori. Therefore, this method is not able to handle feedback control problems or to correctly deal with state events.

Another possible approach is the dynamic approach, which is based on a “cor- rect” mathematical description of the system which is usually formulated by sets of ordinary differential equations in the state space form. That is the way how it can be described many dynamic effects in powertrains, which may or may not be rele- vant for fuel consumption. The description is very versatile. For example the design of feedback control systems or the detection and correct handling of state events in optimization problems can be solved using this method. Usual drawback of this method is high computational burden. This method is used only if other simpler methods are not available or sufficient.

For the reasons of simulations, efficient and powerful simulation software must be available. The software should fulfil basic requirements such a possibility of in- terconnection of different powertrain components, their scaling and parametrizing and visualization and numerical optimization integration. Such available often used software is for example ADVISOR or QSS Toolbox for Matlab/Simulink.

3 ENERGY MANAGEMENT OPTIMIZATION 3.1 Optimization Problems

In general vehicle propulsion design systems are in general at least three different optimization problems:

• structural optimization where the best powertrain structure is examined;

• parametric optimization where the best parameters for a fixed powertrain structure are examined;

• control system optimization where the goal is to find the best possible super- visory control algorithms.

Unfortunately these three elements are not independent and in the presence, there is no optimization method which would deal with all aspects simultaneously.

The control algorithms results are influenced by the chosen driving profile and especially by their causal or non-causal design. In the first case, the optimization is based only on the past and present data. In the second case, the supervisory control algorithm also utilizes future driving profile information to determine the optimal driving policy. In general, this information is obtained with trip planning instruments such as GPS and on-line traffic situation information.

The difference between casual and non-casual solutions can show the quality of control. Usually, if the casual solution achieves 95 % of non-casual solutin quality, there is not much ways how to do better [1].

3.2 Optimization Methods

In general terms, optimization means to find an optimal solution of a given problem.

The main objective of energy optimization is to decrease the overall energy use of the vehicle for a given route. The task is usually restricted by some constraints i.e.

drivability or components characteristics.

In the simplest case of a real function, the optimal solution is the maximal or the minimal value. In more complicated problems, we try to find the best available set of decision values which maximize or minimize the cost function under other system constraints.

There is a variety of methods which are adapted for different conditions and situations. The most intuitive and rather simple to implement are heuristic methods based on Boolean or fuzzy rules. These techniques can provide good results when properly tuned. Unfortunately, their control quality strongly depends on the chosen threshold, which can vary continuously during the driving cycle. These facts were the

main reasons to develop model-based methods that optimize energy consumption.

Two available approaches are static and dynamic optimization methods.

Speaking about the first one, only duty-cycle operations can be performed to ensure good performance. One mission usually needs thousands of seconds and dur- ing this period of time optimal control values have to be evaluated by means of optimization algorithms constituting a very high calculation complexity.

According to the latest published case studies [1], the most frequent energy opti- mization methods are the dynamic programming and the minimum principle based methods.

3.2.1 Dynamic Programming (DP)

Dynamic programming is widely used optimization method for a given time period.

This method is particularly adapted to sequential optimization problems, which means that we try to minimize a cost function in separated time intervals. This implies that the method requires griding of state and time variables, thus the optimal trajectory can be computed only for discretized values.

The main idea of this method is based on Bellman’s principle of optimality which says, that: “An optimal policy has the property that whatever the initial state and initial decision are, the remaining decisions must constitute an optimal policy with regard to the state resulting from the first decision” [6].

Advantageous fact is, that the computational time increases linearly with the final time 𝑡_𝑓. On the other hand, the computational burden depends exponentially on the number of state variables. In the case of reasonably long drive missions it is possible to use dynamic programming methods if the number of state variables is small. One other property of DP algorithm is that it calculate the optimal decisions backward in time or state beginning from final to initial state.

This implies that the method consists of a backward optimization process which is able to determine an approximation of the cost function V - solution of Hamilton- Jacobi-Bellman equation.

So the dynamic programming principle is defined by:

𝑉_𝑡(𝑥_𝑡) = min

𝑢𝑡

{𝐿(𝑥_𝑡, 𝑢_𝑡) +𝑉_𝑡+1(𝑥_𝑡+1, 𝑢_𝑡+1)} (3.1) where 𝑉_𝑡(𝑥_𝑡) is the cost function in the actual step, 𝐿(𝑥_𝑡) is the function to minimize in the actual step,𝑉_𝑡+1(𝑥_𝑡+1)is the cost function in the previous steps and 𝑥 is the state variable.

Due to the discretization, there may be some parasitic effects introduced. The values have to be interpolated or approximated by the nearest neighbor. This can cause i.e. an artificial increase or decrease of battery energy calculated over the

optimal trajectory. The amount of parasitic effect must be examined to decide if the state-space discretization is acceptable or if it is necessary to increase the number of grid points. [1]

Improved algorithms with reduced computational time are available such as the iterative dynamic programming algorithm based on the receding horizon. At each iteration, the state space is selected as a small fraction of the entire space, cantered around the optimal trajectory evaluated in the previous iteration [7].

Also, to reduce computational burden, we can try to simplify the original opti- mization problem, for example by linearizing the cost function and then by using classic simplex algorithm. In this case, we recede from the optimal solution and we must evaluate, if the solution is still suitable or not.

Matlab/Simulink will be used as modelling and simulation tool. While perform- ing simulation tests, we must be aware, that Matlab is an interpreted programming language so its time performance is much lower compared to C/C++ and other.

In addition, particularly in dynamic programming, we need to use loop operations due to the recursive character of the method. Matlab language is not optimized to execute for-loops and it is much more eligible to implement the loops as matrix operations. Thus to obtain proper results and computational time limits, we must tune well the algorithms [1].

3.2.2 Analytical Optimization Methods

One of the ways to decrease computational time is analytical optimization method based on minimum principle. It was proved that a necessary condition for solving the optimal control problem is that the control should be chosen so as to minimize the Hamiltonian. For that purpose the Lagrange method is used to transform the con- straint optimization problem to an unconstraint optimization problem [27]. Thereby we must introduce the Lagrange multipliers and so the Hamiltonian is defined as

𝐻(𝑥, 𝑢, 𝑡) =𝐿(𝑥, 𝑢, 𝑡) +𝜆^𝑇(𝑡)𝑓(𝑥, 𝑢, 𝑡) (3.2) where 𝐿(𝑥, 𝑢, 𝑡) is the performance index, 𝜆^𝑇(𝑡) are the Lagrange multipliers, 𝑓(𝑥, 𝑢, 𝑡) are the constraints, 𝑥is the state variable, 𝑢 is the command variable and 𝑡 is time.

The original optimization problem and the Hamiltonian formulation are equiva- lent. For an inequality optimization problem, this condition follows

𝜕𝐻

𝜕𝑢 = 𝜕𝐿

𝜕𝑢 +𝜆^𝑇𝜕𝑓

𝜕𝑢 = 0 (3.3)

where

𝜆≥0 if 𝑓(𝑥, 𝑢, 𝑡) = 0 (active constraint) 𝜆= 0 if 𝑓(𝑥, 𝑢, 𝑡)<0 (inactive constraint)

Thus, in the subspace in which the constraints are not active, a stationary point will be sought in these directions. Where the constraints are active, since the sign of the multipliers is given, a special optimization problem with equality constraints will be solved.

In real applications, the minimization problem is very complex and constrained so the computational burden can be very high. That is why we try to simplify the problem by approximations. For example, in [1] is proposed to approximate the SoC and to simplify the internal battery parameters by i.e. neglecting the internal resistance. This assumption may not be valid so it is necessary to examine each case. Otherwise the optimization problem can be reduced to searching for a constant parameter 𝜆 that approximates𝜆 (𝑡) for a given mission.

This optimization problem is straightforward. For every time t the Hamiltonian must be minimized with respect to the control variable𝑢(𝑡). A further simplification is possible when the Hamiltonian can be expressed as an explicit function of the control variable.

In some special applications, the Hamiltonian turns out to be an affine function of the control variable. In this case, the minimum principle states that the optimal control variable is found at its extreme values, depending on the sign of the switching function 𝜕 𝐻/𝜕 𝑢. When the switching function is zero, determining the optimal trajectory requires additional information, typically the second derivative of the Hamiltonian with respect to the variable𝑢.

In [2], the introduced approach is a simplified parametrization of the problem by division in separates zones. The number of parameters is reduced and so the main task is how to find the appropriate parameters to define command value by a simple fashion. We can try to find limits and thresholds when some parameters become constant and create different functionality zones. Then we can optimize the problem according to the zones and not only to the time, so we may define different optimization strategies for different zones. This should notably simplify the problem because we need to work only with a reduced number of parameters. Of course the resulting strategy will be sub-optimal.

3.3 Moving Average Real-time Optimization Algo- rithm

Even thought some complex sophisticated algorithms and methods were developed and introduced, their computational complexity may be too high with respect to a cheap HW architecture used in real applications. Thus some methods based on simple decisions and computations should be studied.

The main idea of our presented method is to compute the moving average of the demanded power (𝑃𝐷) within a given look-ahead horizon. In other words, we try to smooth the demanded power so that the power delivered by the batteries doesn’t change rapidly. The quick power changes are then provided by SC.

As we can see from the expression (2.11) of instantaneous power demand depends on the position and not on the time. It is the reason that the algorithm uses future traffic information and GPS data to predict the power demand. The SoC of batteries and SC are then calculated using the power profile of the route, the positioning information and the different efficiency maps and interpolation operated on them.

Some basic rules have to be formulated:

• if 𝑃_𝐷 represents slow variation of demanded power, the whole power will be taken over by the battery;

• if 𝑃_𝐷 represents rapid variation of demanded power, the average value will be taken in charge by battery and the rapid variation will be compensated by the SC;

• if 𝑆𝑜𝐶_𝑆𝐶 < 25 % and 𝑃_𝑆𝐶 > 0 (discharge), stop to provide energy from the SC; In this case all the demanded power and the SC charging power will be supplied by the battery;

• if 𝑆𝑜𝐶_𝑆𝐶 >100 % and 𝑃_𝑆𝐶 <0 (charge), stop the charge of SC and activate the SC for energy supply.

In the first step, we must be able to determine the demanded power and the demanded energy of longitudinal vehicle motion as a position-based forms which is done according to the expression (2.11). After that it is possible to discretize the look-ahead horizon and the route profile into proper segments with an equal length

∆𝑠 respectively. In our algorithm, ∆𝑠 = 20 𝑚.

In figure 3.1 is shown the schematic diagram of moving average algorithm. In the first step, the demanded power can be optionally divided into smaller parts.

Then the algorithm computes for each part the moving average < 𝑃_𝐷 > of future demanded power. After that, we can express the SC’s power demand as:

𝑃_𝑆𝐶 =𝑃_𝐷−< 𝑃_𝐷 > (3.4)

Fig. 3.1: Schematic diagram of moving average algorithm

In ideal case, the mean value of 𝑃𝑆𝐶 should approximately equal zero which would mean, that all the energy delivered from SC will be equally recuperated and restored into them. In other words, the final energy stored in the SC at the end of the driving cycle would be the same as the initial energy at the beginning of the driving cycle. However this is not true in real cases, because the SC can provide power with some efficiency and in the same way can be recharged with some efficiency so it is not possible to recuperate the same amount of energy as the amount of energy that was used. This means, some energy will be lost while transmitting the power.

Moreover, the distribution of power demand may not be regular, and the positive power demand may be to high, so the SC cannot deliver enough energy and the battery must be used. Whereas the negative power demand may be also too high to be recuperated by the SC.

That is why, the future estimated SC power demand is examined within a look- ahead horizon to determine moving average of power demand and corresponding amount of energy. If the average value is positive, it means, that the SC should provide more energy than he may recuperate back afterwards and we receive the additional battery energy needed to recharge the SC. If the value is negative, we receive the amount of energy which won’t be probably possible to recuperate, be- cause the SC will be fully charged. The main objective is to eliminate situations, when the SC are completely discharged so they cannot compensate quick power demand variations which has then to be compensated by battery. Also, this is the way how we can ensure, that the final 𝑆𝑜𝐶𝑆𝐶 will be 100 %. The opposite case are the situations, when the SC are fully charged and we don’t want to lose the remaining braking energy. For that purpose, future SC power demand analysis was also introduced. Within a look-ahead horizon, the next positive and negative power

demands are compared so the battery power demand can be eventualy decreased and compensated by SC in order to decharge SC enough to be able to recuperate all the available braking energy afterwards.

To summarize, the provided battery power is expressed as:

𝑃_𝐵 =< 𝑃_𝐷 >+𝑃_𝐴𝑑𝑑 (3.5) where < 𝑃_𝐷 > is moving average of demanded power and 𝑃_𝐴𝑑𝑑 is actual addi- tional power demand when SC cannot provide enough power or cannot recuperate all the instantaneous power.

After a brief description of the algorithm, we can conclude, that the method is divided into two main parts:

1. the total power demand smoothing within a look-ahead horizon and determin- ing the battery power demand; and

2. the SC recharge energy prediction and determination within a look-ahead hori- zon.

In figure 3.2 you can see the flow chart of moving average algorithm. In figure 3.3 is a detailed diagram of SC discharge and recharge control block from figure 3.2.

3.3.1 Power Transfer Efficiency

For determining the SoC of battery and SC, we must respect the energy losses during the power transmission between different components. For the calculation, efficiency maps are used in combination with interpolation methods. Different methods were examined while they were giving approximately the same results. After the efficiency values are determined, we can express the actual power demands as:

𝑃_𝐵𝑎= 𝑃_𝐵

𝜂_𝐵... for 𝑃_𝐵>0(discharge) 𝑃_𝐵𝑎=𝑃_𝐵𝜂_𝐵... for 𝑃_𝐵<0(charge) 𝑃_𝑆𝐶𝑎= 𝑃_𝑆𝐶

𝜂𝑆𝐶... for 𝑃_𝑆𝐶 >0(discharge) (3.6) 𝑃_𝑆𝐶𝑎=𝑃_𝑆𝐶𝜂_𝑆𝐶... for 𝑃_𝑆𝐶 <0(charge)

where𝑃_𝐵𝑎 ,𝑃_𝑆𝐶𝑎 are the battery and SC actual power demands and 𝜂_𝐵, 𝜂_𝑆𝐶 are the battery and SC efficiencies respectively.

Initialize input and output variables

Calculate energy demand Ed in every point of the

profile For every point of

power profile

Start from the actual point and calculate the moving

average of the power demand <P>

Calculate SC power demand Psc = Pd - <P>

SC discharge and recharge control

Battery power demand calculation from average

value and SC control results Get the power profile

Calculate SoCb and SoCsc in the next step.

END

Fig. 3.2: Moving average algorithm flow chart

If the first power demand is positive

SC is charged enough to cover the power demand Examine future positive

and negative SC power demands

Calculate battery additional energy to recharge the SC

Examine SoCsc after providing the positive

power demand

SC will be discharged enough to recuperate all the energy in the

next step

Decrease battery power demand and provide it by

SC Calculate SC power

demand Psc = Pd - <P>

SC discharge and recharge control

Battery power demand calculation from average

value and SC control results YES

YES

YES NO

NO

NO

Calculate exact SC power demand with respect of

efficiency

Calculate the negative recuperation energy within

the horizon

Is the recuperation energy sufficient to fully recharge the SC

at the end of the horizon?

Calculate the average value of battery power to

recharge the SC NO

YES

3.3.2 Simulation Results and Analysis

Simulation Conditions

The vehicle powered by the HE system is a medium passenger bus, which is the prototype vehicle to carry out the simulation. The power sources are compounded of 200 series connection SCs and a branch of 45 series connection 130 Ah Li batteries. A 6-speed automatic gearbox is installed between electric motor and wheels. It allows high level torques to ensure accelerations and to improve vehicle efficiency. The parameters of the prototype vehicle are listed in table 3.1.

Parameters Value

𝑀 (nominal mass) 11800 kg

𝑀 (total mass) 15000 kg

𝐿𝑉 (Total length) 9312 mm

𝑟𝑡 (Tire radius) 480 mm

𝐶𝑑(reynolds coefficient) 0.382 kg/m³ 𝐴𝑓 (windward area) 6.1 m² 𝜇𝑟 (rolling resistance coefficient) 0.016

𝜌 (air density) 1.25 kg/m³

𝛿𝑒𝑞𝑚 (equivalent moment inertia) 3.18 kg·m² 𝑖𝑠 (gear ratio) 𝑠=1,2,3,4,5,6 Power of electric motor (nominal) 105 kW

DC bus voltage 540 V

SC bank 200 series connection SCs

Battery pack 45 series connection batteries Single SC (2 series connection) 5200 F, 2.7 V

Single battery 130 Ah, 12.8 V

Tab. 3.1: Parameters of test vehicle

A corresponding demanded power profile (shown in figure 3.4) has been calcu- lated by using equation (2.7) and transferred into the position-based profile by using equation (2.11).

Our simulations were performed by mathematical and simulation environment Matlab. For each simulation, the parameters from table 3.1 were used. In order to demonstrate the algorithm properties, the moving average algorithm was executed with different look-ahead horizons and with different initial battery SoCs. In ad- dition, the simulations with battery only power source with and without braking energy recuperation were examined so we can compare the results with the first method simulations.

In table 3.2 are listed the parameters used in these particular simulations. The results for average moving algorithm and different look-ahead horizons are summa- rized in table 3.5. For comparison, table 3.4 contains results for battery only power source with braking energy recuperation and finally table 3.3 results for battery only power source without braking energy recuperation.

In order to settle the improvements of different cases, the reference energy is the energy consumed during the driving cycle by the battery only power source system without energy recuperation. Battery SoC difference from table 3.3 is then considered as reference quantity and as 100 % of consumption. To calculate the improvement, we subtract from this value the battery SoC difference of another method wich gives us the absolute improvement value. It is then easy to calculate relative values.

Parameters Value

∆ s 20 m

n (=L/∆ s) 270

Route distance L 5400 m Total energy demand 1,72E+04 kW Total braking energy -1,28E+03 kW Braking energy percentage 7.5 %

Minimal battery SoC 10 %

Minimal SC SoC 25 %

Tab. 3.2: Simulation parameters

Initial battery SoC [%] 100 80 60 40 30

Final battery SoC [%] 90.3 69.4 48.5 27.5 16.9

𝑆𝑜𝐶_𝐵 difference [%] 9.7 10.6 11.5 12.5 13.1

Average C-rate [ℎ⁻¹] 0.78 0.86 0.93 1.01 1.07

Maximal C-rate [ℎ⁻¹] 13.18 14.87 16.57 18.73 20.05 C-rate standard deviation [ℎ⁻¹] 1.12 1.28 1.44 1.65 1.78 Tab. 3.3: Battery only power source without energy recuperation simulation results

In figure 3.5 is shown a battery and SC power demands calculated by moving average algorithm with horizon settings stated in the first part of table 3.5 for driving cycle shown in figure 3.4. As we can see, the battery power demand is kept around mean value and the rapid variations are eliminated. These rapid variations are compensated by SC power demand, which varies a lot. In figure 3.6 is shown the

Initial battery SoC [%] 100 80 60 40 30

Final battery SoC [%] 90.7 69.7 48.9 27.9 17.3

𝑆𝑜𝐶_𝐵 difference [%] 9.3 10.3 11.1 12.1 12.7

Average C-rate [ℎ⁻¹] 0.81 0.89 0.96 1.04 1.09

Maximal C-rate [ℎ⁻¹] 13.17 14.86 16.56 18.72 20.03 C-rate standard deviation [ℎ⁻¹] 1.14 1.30 1.46 1.67 1.80

Improvement^a [%] 3.9 3.6 3.2 2.8 2.6

aCompared to the battery only power source

Tab. 3.4: Battery only power source with energy recuperation simulation results

Fig. 3.4: Demanded power for complete driving cycle

guarantee low battery power demand variations, the battery cannot be recharged and delivers almost constant power. That is why the SoC of battery decreases constantly to the value 92.4 %. In contrast, the SCs are discharged and charged rapidly, so the SCs SoC varies. We can see, that at the end of the driving cycle, the SCs are fully recharged. Also, their SoC never reaches the minimal value of 25 % which means, that the battery doesn’t have to be used to compensate the power demand and there is not so many energy losses.

Battery power look-ahead horizon 110 SC recharge power look-ahead horizon 80 Total route look-ahead horizon 270

Initial battery SoC [%] 100 80 60 40 30

Final battery SoC [%] 92.4 72.0 51.6 31.3 21.0

𝑆𝑜𝐶_𝐵 difference [%] 7.6 8.0 8.4 8.7 9.0

Average C-rate [ℎ⁻¹] 0.61 0.64 0.67 0.70 0.72

Maximal C-rate [ℎ⁻¹] 0.86 0.91 0.96 1.01 1.05 C-rate standard deviation [ℎ⁻¹] 0.12 0.13 0.14 0.15 0.16 Improvement^a [%] 22.2 24.9 27.4 29.9 31.4 Maximal computational time [s] 0.0037 0.0039 0.0037 0.0036 0.0037 Battery power look-ahead horizon 270

SC recharge power look-ahead horizon 270 Total route look-ahead horizon 270

Initial battery SoC [%] 100 80 60 40 30

Final battery SoC [%] 91.8 71.2 50.8 30.2 19.9

𝑆𝑜𝐶_𝐵 difference [%] 8.2 8.8 9.2 9.8 10.1

Average C-rate [ℎ⁻¹] 0.66 0.71 0.74 0.79 0.81

Maximal C-rate [ℎ⁻¹] 9.74 11.26 12.76 14.71 15.93 C-rate standard deviation [ℎ⁻¹] 0.60 0.70 0.79 0.91 0.99

Improvement [%] 15.1 17.5 19.6 21.7 22.9

Maximal computational time [s] 0.0043 0.0038 0.0044 0.0050 0.0040 Battery power look-ahead horizon 50

SC recharge power look-ahead horizon 20 Total route look-ahead horizon 100

Initial battery SoC [%] 100 80 60 40 30

Final battery SoC [%] 91.3 70.7 50.2 29.6 19.3

𝑆𝑜𝐶_𝐵 difference [%] 8.7 9.3 9.8 10.4 10.7

Average C-rate [ℎ⁻¹] 0.70 0.75 0.79 0.84 0.86

Maximal C-rate [ℎ⁻¹] 5.92 7.00 8.13 9.71 10.76 C-rate standard deviation [ℎ⁻¹] 0.40 0.46 0.53 0.63 0.69

Improvement [%] 10.4 12.6 14.7 16.7 17.9

Maximal computational time [s] 0.0035 0.0036 0.0035 0.0036 0.0040

aCompared to the battery only power source

Tab. 3.5: Moving average algorithm simulation results with different parameters

Impact of Look-ahead Horizons’ Parameters

The simulations with different look-ahead horizons were performed. In table 3.5 are

Fig. 3.5: Battery and SC power demand for complete driving cycle

Fig. 3.6: Battery and SC SoC for complete driving cycle

multiple parts and moving average is computed for look-ahead horizon size around one third of the cycle. In the second part, the driving cycle is not divided either and the average of all cycle is computed. Lastly, the driving cycle is divided into smaller