Download Institutionen för systemteknik Department of Electrical Engineering Electric Vehicles

Institutionen för systemteknik
Department of Electrical Engineering
Examensarbete
DC Charging of Heavy Commercial Plug-in Hybrid
Electric Vehicles
Examensarbete utfört i datorteknik
vid Tekniska högskolan vid Linköpings universitet
av
Oscar Hällman
LITH-ISY-EX--15/4878--SE
Södertälje 2015
Department of Electrical Engineering
Linköpings universitet
SE-581 83 Linköping, Sweden
Linköpings tekniska högskola
Linköpings universitet
581 83 Linköping
DC Charging of Heavy Commercial Plug-in Hybrid
Electric Vehicles
Examensarbete utfört i datorteknik
vid Tekniska högskolan vid Linköpings universitet
av
Oscar Hällman
LITH-ISY-EX--15/4878--SE
Handledare:
Robert Sjödin
Scania CV AB
Kent Palmkvist
isy, Linköpings universitet
Examinator:
Mattias Krysander
isy, Linköpings universitet
Södertälje, 22 juni 2015
Avdelning, Institution
Division, Department
Datum
Date
Computer Engineering
Department of Electrical Engineering
SE-581 83 Linköping
2015-06-22
Språk
Language
Rapporttyp
Report category
ISBN
Svenska/Swedish
Licentiatavhandling
ISRN
Engelska/English
Examensarbete
C-uppsats
D-uppsats
—
LITH-ISY-EX--15/4878--SE
Serietitel och serienummer
Title of series, numbering
Övrig rapport
ISSN
—
URL för elektronisk version
http://www.ep.liu.se
Titel
Title
DC-laddning av tunga kommersiella plug-in-hybridfordon
Författare
Author
Oscar Hällman
DC Charging of Heavy Commercial Plug-in Hybrid Electric Vehicles
Sammanfattning
Abstract
En lösning för att kunna minska avgasutsläpp från tunga fordon är att helt eller delvis framföra fordonet helelektriskt. Detta innebär att en betydande elektrisk energikälla måste finnas
ombord på fordonet. På grund av den stora energikapacitet som källan måste ha så kommer
fordonet antingen behöva avvaras en stor del av dess nyttotid för att ladda upp källan alternativt ladda med en högre effekt till kostnad av högre förlusteffekter och livslängd på energikällan. Detta arbete innehåller en förstudie på högeffektslikströmsladdning av hybridbatterier från befintlig infrastruktur anpassad till elektriska hybridbilar. Delar av arbetet
innefattar: modellering av batteripack och likspänningsomvandlare, formulering av mpcregulator till batteripack, analysering av laddningsstrategier och batterirestriktioner genom
simulering. Arbetet påvisar att en längre laddtid ökar energieffektiviteten och minskar batteridegraderingen. Arbetet har även visat att en laddningsstrategi med liknande egenskaper
som konstant-ström/-spännings-laddning bör användas för att ladda upp ett batteri från
tomt till fullt.
Nyckelord
Keywords
PHEV, DC-Charge, Heavy Trucks, Battery Modeling, Half Bridge Converter Modeling
Abstract
A solution to reduce exhaust emissions from heavy commercial vehicles are to
haul the vehicles completely or partially electric. This means that the vehicle
must contain a significant electric energy source. The large capacity of the energy source causes the vehicle to either sacrifice a large part of its up time to
charge the source or apply a higher charge power at the cost of power losses and
lifetime of the energy source. This thesis contains a pre-study of high-power dccharge of hybrid batteries from existing infrastructure suited to electric hybrid
cars. Following parts are included in the thesis: modeling of a battery pack and
a dc-dc converter, formulation of a mpc controller for the battery pack, analysis
of charging strategies and battery restrictions through simulations. The thesis
results shows that a longer charging time increases the energy efficiency and reduces the degradation in the battery. It also shows that a charging strategy similar
to constant-current-constant-voltage charging should be used for a full charge of
an empty battery.
iii
Contents
Notation
1 Introduction
1.1 Background
1.2 Objective . .
1.3 Limitations .
1.4 Outline . . .
vii
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
1
1
2
2
3
2 Theory
2.1 Charge Equipment . . . . . . . . .
2.1.1 Charging Station . . . . . .
2.1.2 DC-DC Converter . . . . . .
2.1.3 Battery Junction Box . . . .
2.1.4 Communication Module . .
2.1.5 Battery Management System
2.1.6 Battery Pack . . . . . . . . .
2.1.7 Auxiliary Sources . . . . . .
2.2 Control Theory . . . . . . . . . . . .
2.2.1 Model Predictive Control . .
2.2.2 Quadratic Programming . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
5
5
6
8
10
10
10
11
12
12
13
14
3 Method
3.1 Modeling . . . . . . . . . . . . .
3.1.1 Battery Pack . . . . . . .
3.1.2 DC-DC Converter . . . .
3.2 Control Formulation . . . . . .
3.2.1 Control Construction . .
3.2.2 Charge References . . .
3.2.3 Voltage Reference . . . .
3.3 Simulation . . . . . . . . . . . .
3.3.1 Evaluation Environment
3.3.2 Charge Time . . . . . . .
3.3.3 Voltage Control . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
15
15
15
16
17
18
21
22
22
23
23
24
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
v
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
vi
Contents
3.3.4 Current Restriction . . . . . . . . . . . . . . . . . . . . . . .
3.4 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Converter Measurements . . . . . . . . . . . . . . . . . . . .
4 Results
4.1 Modeling Results . . . . . .
4.1.1 Battery Pack . . . . .
4.1.2 DC-DC Converter . .
4.2 Simulation Results . . . . . .
4.2.1 Charge Time . . . . .
4.2.2 Voltage Control . . .
4.2.3 Current Restriction .
4.3 Implementation Results . .
4.3.1 Measurement Results
4.4 Discussion . . . . . . . . . .
24
24
24
.
.
.
.
.
.
.
.
.
.
27
27
27
29
30
30
32
33
34
35
36
5 Closure
5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
37
38
Bibliography
41
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Notation
Symbols and abbreviated terms
Abbreviation
ac
bev
bjb
bms
cc-cv
ccs
can
dc
evse
hv
mpc
ocv
phev
plc
pwm
soc
soh
res
v2g
Signification
Alternating Current
Battery Electric Vehicle
Battery Junction Box
Battery Management System
Constant Current Constant Voltage
Combined Charging System
Controller Area Network
Direct Current
Electric Vehicle Supply Equipment
High Voltage
Model Predictive Control
Open Circuit Voltage
Plug-in Hybrid Electric Vehicle
Power Line Communication
Pulse Width Modulation
State Of Charge
State Of Health
Rechargeable Energy storage System
Vehicle to Grid
vii
1
Introduction
This chapter introduces the thesis with a short background, objective and the
limitations for the thesis.
1.1
Background
The solution to quick charging of phevs (Plug-in Hybrid Electric Vehicles) and
bevs (Battery Electric Vehicles) are high power dc-chargers (Direct Current). The
reason why dc-charging is preferred instead of ac-charging (Alternating Current) is because the ac requires a rectifier in the vehicle to be able to store the
charged energy and a high power input requires a heavier and more expensive
rectifier. The gain in time with this way of charging has the drawbacks of efficiency loss and greater impact in battery life time [1]. By studying the charging
process of a high power dc-charger and modeling the electric characteristics of
the battery pack, an energy efficient control strategy can be implemented. The
aim of the control strategy is mainly to prevent damage on the battery due to
violation of its safety restrictions and reduce the efficiency loss due to the high
power, but also consider the ageing effects applied to the battery cells during the
charge. Charging scenarios can differ a lot depending on factors like initial soc
(State Of Charge) , total battery capacity, battery characteristics and charge time
available.
1
2
1
1.2
Introduction
Objective
The objective of this thesis is to pre-study high power hv (High Voltage) dccharging of heavy commercial phevs. Things to evaluate in the study are:
• How does different charging times affect the efficiency and the ageing of the
charging equipment?
• Can safety restrictions such as current, voltage and soc of the battery be ensured with an automatic control of the power drained from the evse (Electric Vehicle Supply Equipment)?
The work will be studied through simulations of models designed and adapted
to measurements and parameters of crucial charge equipments obtained from
technical specifications.
1.3
Limitations
Limitations done in this thesis will be stated below with explanations and motivations.
• The battery model will not include an explicit soh (State Of Health) , only
the most dependent factors will be mentioned in the theory. The motivation
for this is to keep the thesis within a reasonable framework. An explicit
model of soh would require years of research.
• The formulation of the control strategy will assume that the maximum
charging time and final soc is given by the user (i.e. not solved in the
optimisation). To solve these two inputs in the total optimisation would
require even further more inputs to be able to find the optimal charging
formulation.
• If the final soc cannot be reached at the given time (due to limitations in
battery, charge equipment etc.), the charge strategy should charge as much
as possible because it cannot exceed the physical boundaries.
• The strategy will not consider options like v2g (Vehicle to Grid) . v2g
uses the storage capacity in the vehicles batteries to achieve financial gains
depending on the current energy price [2].
• The temperature of components during charging is assumed to be constant
T0 . Due to T0 , all parts will be modeled to this specific temperature. Most
of the components have a non-linear temperature dependency and a combination with the heat transfers result in a very complex system that would
exceed the framework of the thesis.
1.4
Outline
3
• The internal battery impedances are assumed to be constant and not dependent of soc. As with the temperature, this parameters will change depending on the soc but to get a decent explanation of this behaviour needs lots
of work.
• Physical values of the battery pack has been censored in the tables and
graphs of the thesis.
1.4
Outline
The thesis contains five chapters and the contents of each chapter are stated below.
Chapter 1: Introduces the thesis.
Chapter 2: Explains the general theories used in the thesis.
Chapter 3: Applies the theory mentioned in the previous chapter with the specific methods for this thesis.
Chapter 4: Contains all results of the work done according to the previous chapter.
Chapter 5: Summarise the thesis with conclusions made and the remaining work
to be done in the subject.
2
Theory
This chapter presents the theory applied to the thesis. The first part contains an
overview of the charge equipment followed by a deeper description of each component displayed in the overview. The second part contains the control theory
and calculation method for the automatic control.
2.1
Charge Equipment
This section contains theory and information of the charging equipment. An
overview of all charging parts and with which interface they are connected to
each other can be seen in Figure 2.1. The different communication interfaces in
the overview are: plc (Power Line Communication), can (Controller Area Network) and Con which is a summation of logical detections and signals. Table 2.1
contains a list of all components shown in Figure 2.1 with a short description and
which section the component is further described.
Table 2.1: Components shown in the overview of Figure 2.1.
Abbreviation
Description
Section
evse
Combo2
Com Unit
bms
dc/dc
bjb
res
Charging station
Contact
Communication unit
Battery Management System
Converter
Connection box
Battery pack
2.1.1
2.1.1
2.1.4
2.1.5
2.1.2
2.1.3
2.1.6
5
6
2
PLC
Con
CAN
HV
EVSE
Com
Unit
Combo2
Auxiliary
Source
DC/DC
Charging station
BJB
Theory
BMS
RES
Vehicle
Figure 2.1: Overview of the dc-charging components and how they are connected to each other.
2.1.1
Charging Station
The evse that will be used is defined as a type 2 mode 4 dc-charging according
to [3]. It is a dc-charging station with specifications shown in Table 2.2. The
charging standard used will be ccs (Combined Charging System), which are used
by car brands like: BMW, Volkswagen, GM, Porsche and Audi [4].
Table 2.2: Charging station parameters.
Output parameter
Value
Voltage range
Current max
Power max
50 − 500V
125A
50kW
The contact to be used with the evse is a Combo2 contact [5]. Contact pins can
be seen in Figure 2.2 and pin descriptions with mode 4 dc-charging in Table 2.3
2.1
7
Charge Equipment
PP
L1
CP
PE
L2
N
L3
DC−
DC+
Figure 2.2: Pin layout of a Combo2 contact.
Table 2.3: Pin configuration of the Combo2 contact in mode 4 dc-charging.
Pin
Max U/I
Description
PP
30V/2A
CP
30V/2A
PE
850V/125A
DC+
850V/125A
DC-
850V/125A
N
L1-L3
480V/20A
480V/20A
Detects connection between evse and
bev/phev.
Communicates between evse and
bev/phev using plc.
Ground used in all charging modes used
through the contact.
Positive charging input used with dccharging.
Negative charging input used with dccharging.
Not used.
Not used.
8
2.1.2
2
Theory
DC-DC Converter
Because the evse infrastructure mostly applies to the car industry, which use
lower battery voltage [4], a dc-dc converter is needed to be able to charge the
truck battery with a car evse. Useful parameters of the dc-dc converter used [6],
can be seen in Table 2.4 where the over voltages shows at which value (even at no
operation) the converter will break down.
Table 2.4: dc-dc converter parameters.
Output parameter
Value
Voltage range
Over voltage
Max continuous power
150 − 750V
800V
120kW
Input parameter
Value
Voltage range
Over voltage
Current max
50 − 430V
445V
400A
Control parameter
Value
Voltage range
Switching frequency
Efficiency typical
9 − 16V
39kHz
98%
The dc-dc converter has a half bridge topology. A basic schematic of this topology can be seen in Figure 2.3. The converter converts the dc-input through
switches (transistors, thyristors etc. [7]) to a high frequency ac signal. This ac
signal is transformed through the transformer and rectified to the dc-output.
+
Vin
Iin
IT
N1
N2
−
+
VT
−
Figure 2.3: Schematic of a half bridge converter (without filters).
The relation between the input Vin and output VT can be described with [7]
VT
N
= 2D
Vin
N1
(2.1)
2.1
9
Charge Equipment
where N1 and N2 defines the coil turns and D = ton /tperiod where ton , tperiod is
the time when the switches at the input side is on respectively the time of the
switching period.
The power losses of a half bridge dc-dc converter can be divided into semiconductor and transformer losses. The semiconductor losses comes from non-ideal
components whom contributes with power losses Psw at switching points because
the semiconductor current must increase before the potential in the semiconductor can decrease and vice versa. These losses depend on the current while the
semiconductors are conducting, the semiconductor voltage while not conducting,
semiconductor characteristics and the switching frequency. The semiconductors
also contributes with losses Pcond while they are conducting due to small voltages
in the semiconductors Vsc . The conduction losses depend on the semiconductor
currents, characteristics and the conduction time. Assuming that the semiconductor voltages are equal in each semiconductor and that the efficiency is ideal
gives Pcond ≈ Vsc Iin (1 + Vin /VT )D where D is defined as in equation (2.1). An
example of these losses can be seen in Figure 2.4 where Psw is the sum of Pon and
Pof f .
on
u
ton
U
off
I
0
Ploss
0
P
cond
0
Pon
Poff
tperiod
Figure 2.4: Example of power losses in semiconductors.
The transformer losses consists of magnetic losses in the core Pcore and resistive
losses from the coils PR . The core losses comes from hysteresis in the transformer
core and mainly depends on switching frequency, magnetic flux density, temperature and core geometrics. The resistive losses occur due to resistances in the
lines (mostly from the transformer coils) and it mainly depends of length and
resistivity of the coils.
10
2.1.3
2
Theory
Battery Junction Box
The bjb (Battery Junction Box) connects all hv-components, i.e. master res
(Rechargeable Energy storage System) unit, dc-dc converter, auxiliary energy
sources and extra slave res units.
2.1.4
Communication Module
The Communication unit is the link between the bms (Battery Management System) and the other dc-charging components. The Communication unit also contains plc interface, since this standard is used by ccs to communicate with the
evse [8]. The Power Line Communication uses a high frequency serial communication on a low frequency power signal. In the ccs standard, the power signal is
a 1 kHz pwm (Pulse Width Modulation) signal with 5% duty cycle [9], an example of this can be seen in Figure 2.5 where a high frequency signal is applied to a
1kHz pwm signal.
PLC example
7
1
6
0
Voltage [V]
5
0.7
0.95
4
3
2
1
0
0
1
2
3
4
5
Time [ms]
Figure 2.5: An example of how a plc signal can look like.
The module also controls the connector lock in the Combo2 contact, to make
sure that the connection cannot be disrupted while high power is applied on the
connectors.
2.1.5
Battery Management System
The bms observe and controls the res and components that affect the res, like
cooling systems and charging units. Future control strategy for dc-charging will
be done here, or at least parameter estimations like soc. The communication
interface used by the bms is can, as also seen in the overview in Figure 2.1.
2.1
11
Charge Equipment
2.1.6
Battery Pack
The battery pack or res used in this thesis is Lithium-Ion cell type. In this prestudy the battery temperature is assumed to be constant at 25o C, since it has
quite complex dependency of its temperature and would require loads of work
to describe it with decent accuracy. General battery restrictions can be seen in
Figure 2.6. The restrictions prevent the risk of hot spots in the Battery cells [10].
The decreasing charge and discharge currents at high and low soc occurs due to
high electron density at the anode and cathode.
Voltage [V]
Current [A]
Power [kW]
Battery restrictions
0
0
700
0
50
100
State of Charge [%]
Figure 2.6: Battery restrictions at 25o C, allowed area is marked grey.
The ocv (Open Circuit Voltage) of the battery pack can be seen in Figure 2.7 and
it is slightly different depending on if the battery is being charged or discharged.
Both the restrictions and ocv is based on data given from the cell manufacturer.
To study the soh qualitative, the battery pack ageing can be divided in calendar
ageing and cycle ageing. Calendar ageing is a very slow process mostly dependent
of soc and time. It can therefore be neglected in studies of charging processes.
The primary factor of cycle ageing is the charging currents where higher currents
degrade the battery faster [1; 11].
12
2
Theory
Open Circuit Voltage
Charge
Discharge
VOCV [V]
700
0
0
50
100
State of Charge [%]
Figure 2.7: Open Circuit Voltage at 25o C.
2.1.7
Auxiliary Sources
As seen in Figure 2.1, there is also an ability to add auxiliary energy sources.
Two examples of auxiliary sources are inductive charging from road pick-ups
and pantograph charging. An example of this can be seen in Figure 2.8.
Pantograph
Inductive Pickup
Figure 2.8: Auxiliary charging equipment attached on a vehicle.
2.2
Control Theory
This section contains the theory of the automatic control applied to the simulations used in the thesis.
2.2
13
Control Theory
2.2.1
Model Predictive Control
A mpc (Model Predictive Control) is a time discrete mathematical controller that
predicts the model states x up to the number of total predictions N at the current
time k (in other terms x̂(k) to x̂(k + N − 1)). From this prediction it estimates the
optimal value for the upcoming control signal u(k) that minimizes a function z
that is desirable to control. This operation is done on-line and is repeated at each
time update [12]. Since it is using a mathematical optimisation, boundaries and
restrictions can be added explicitly. A mathematical explanation of an algorithm
using mpc with reference signal (r) and integral action [13] is described as
min
N
−1
X
λmin ≤λ≤λmax
||z(k + j) − r(k + j)||2Q1 + ||u(k + j) − u(k + j − 1)||2Q2
(2.2)
j=0
with the a state space model formulated as
x(k + 1) = Fx(k) + Gu(k)
(2.3a)
z(k) = Mx(k)
(2.3b)
The λ in equation (2.2) describes the restrictions of the system with the boundaries λmin and λmax . Calibration parameters in the mpc are the weight matrices
Q1 , Q2 and prediction length N . The matrix Q1 sets the weight of difference
between the signal z and reference value r and the matrix Q2 sets the weight of
differences in the control signal u. The sum notation in equation (2.2) can be
formulated in matrix form as
(MX − R)T Q1 (MX − R) + (ΩU − δ)T Q2 (ΩU − δ)
with the individual matrices and vectors described as






r(k)
x(k)
u(k)






 r(k + 1) 
 x(k + 1) 
 u(k + 1) 








U = 
 , R = 
 , X = 
.
.
.

.
.
.






.
.
.






r(k + N − 1)
x(k + N − 1)
u(k + N − 1)
X = F x(k) + GU




0
0 · · · 0
 0
 I 
 G
 F 
0
0 · · · 0






F =  .  , G =  .
.. 
..
..
..
 ..
 .. 
.
.
.
. 




F N −1
F N −2 G · · · FG G 0




Q1

Q2







Q2
Q1








Q1 = 
 , Q2 = 
..
..




.
.







Q2
Q1
(2.4)
(2.5a)
(2.5b)
(2.5c)
(2.5d)
14
2

M


M = 


2.2.2
M
..
.
M




 ,




 I
−I

Ω = 


I
..
.
..
.
−I
I




 ,





u(k − 1)
 0 


δ = 

..


.


0
Theory
(2.5e)
Quadratic Programming
To solve the mpc algorithm explained in the Section 2.2.1, quadratic programming [14] can be applied. Quadratic programming determines the control signal
vector U that minimizes the function
1
min U T H U + Γ T U
U 2
(2.6)
The mpc formulation in equation (2.4) can be converted to the quadratic form in
equation (2.6), this gives the values of Γ and H as
H = G T MT Q1 MG + ΩT Q2 Ω
(2.7a)
Γ = G T MT Q1 MF x(k) − G T MT Q1 R − ΩT Q2 δ
(2.7b)
with the matrix and vector elements as in equation (2.5).
3
Method
In this chapter, methods used in the thesis are presented. The first part describes
the methods used for modeling the charge equipment. It is followed by methods
for constructing the control system and simulation environment. The last part in
this chapter contains the implementations done for the converter measurements.
3.1
Modeling
This section contains the modeling methods for the charge equipment. The first
part contains the modeling of the res while the last part describes the converter.
3.1.1
Battery Pack
In [15], a model of ideal analogue circuit elements were applied to an automotive
battery pack with successful results. This model is usually used for modeling
battery cells. A similar model was applied to the battery pack used in this thesis
and the circuit elements with the current and voltages of the model can be seen
in Figure 3.1. The model is based on: the filter parameters R1 , C1 , R2 and C2 that
describes the dynamic voltages V1 and V2 , the parameter Vocv that models the
ocv, the internal resistance Rs and the terminal voltage and current VT and IT .
15
16
3
R1
Rs
−
Method
R2
V1
+
V2
−
+
IT
+
C
VOCV
C
1
2
VT
−
Figure 3.1: Schematic of the res model.
VT in Figure 3.1 is described with
VT = Vocv (soc) + Rs IT + V1 + V2
(3.1)
where the potentials V1 and V2 have the dynamic behaviour described with
  −1

 V̇1   R1 C1
 

 V̇2  =  0
 

˙
soc
0
0
−1
R2 C2
0

 
0  V1  
 
 
0  V2  + 
 
 
0 soc
1 
C1 


1 
C2 
 IT
1 
Qtot
(3.2)
Equation (3.2) also contains the dynamic behaviour of the soc where Qtot is the
total capacity of the battery pack. The internal resistance Rs was defined from
manufacturer data at the temperature 25o C. Since the model will be used to evaluate charging, it might be a good choice to use the charge curve in Figure 2.7 for
the Vocv . But because the remaining parameters were estimated towards both
charging and discharging currents and the small deviation between the curves in
Figure 2.7, Vocv was set as the mean of the two curves. The remaining parameters
R1 , C1 , R2 and C2 were determined through the least square algorithm
min f (IT ,meas ) =
ZV
X
2
V1+2,meas − V1,model (IT ,meas ) + V2,model (IT ,meas )
ZV = R1
C1
R2
C2
T
V1+2,meas = VT ,meas − Rs IT ,meas − Vocv (socmeas )
(3.3a)
(3.3b)
(3.3c)
with measured data of the res. The measurements were done at different soc:
0, 0.25, 0.5, 0.75 and 1, where soc is defined as the battery pack window used.
The mean value of ZV from equation (3.3) with these measurements became the
final values for the model. Results of this model can be seen in the results Section
4.1.1.
3.1.2
DC-DC Converter
To make sure how much power that is required and what voltage/current demands to transmit to the evse [16], a decent model of the dc-dc converter efficiency ηdc is needed. As mentioned in [17], this model can be described with
3.2
17
Control Formulation
PT
Pin
(3.4a)
PT = VT IT
(3.4b)
Pin = Vin Iin
(3.4c)
ηdc =
With the voltages and currents VT , Vin , IT and Iin defined as in Figure 2.3.
To parametrise this model, the behaviour of efficiency ηdc needs to be captured.
To get a model of the converter efficiency, the power losses were studied. The
total power losses can be summarized as
PT = Pin − Ploss
(3.5)
Ploss = Psw + Pcond + Pcore + PR
(3.6)
where
and contains the losses described in Section 2.1.2. From Figure 2.4 and the theory
mentioned in Section 2.1.2, it can be seen that each power loss is proportional to
Iin , Vin and VT as
!
VT
2
(3.7)
+ 1 Iin PR ∝ Iin
Pcore ∝ 1 Psw ∝ Vin Iin Pcond ∝
Vin
since the switching frequency, temperature and component characteristics can be
approximated as constant or negligible. With equations (3.6) and (3.7), a model
of the power losses can be defined as
2
Ploss,model = kP 1 + kP 2 Iin + kP 3 Iin
+ kP 4 Vin Iin + kP 5 VT Iin /Vin
(3.8)
where the values kP i , i = 1, . . . , 5 describes the proportional behaviour of equation (3.7). The parameters in equation (3.8) gets defined through least square
approximations
X
2
min f (ZP ,meas ) =
Ploss,meas − Ploss,model (ZP ,meas )
(3.9a)
Zk
T
Zk = kP 1 kP 2 . . . kP 5
T
ZP ,meas = Iin,meas Vin,meas VT ,meas
Ploss,meas = Vin,meas Iin,meas − VT ,meas IT ,meas
(3.9b)
(3.9c)
(3.9d)
applied to the converter measurement described in Section 3.4.1.
3.2
Control Formulation
The construction and calibration of the battery controller is shown in the beginning of this section. Different charge and voltage references are found at the end
of this section.
18
3.2.1
3
Method
Control Construction
A mpc controller was applied with the structure described with equation (2.2) in
T
T
the theory Section 2.2.1, where z = VT soc , u = IT and x = V1 V2 soc ocv .
The state space system for the mpc was defined as an extension of the VT model
and state space model in equations (3.1) and (3.2), but here the ocv is added too
through the constant kocv . The mpc model was applied as




  −1
  1 
0
0
0




C
V̇
V
1
 1   R1 C1
  1   1  −1
 V̇2   0
  V2   C2 
0
0

 = 
 
 +  1  IT
R2 C 2
(3.10a)
 soc
 
0
0 0  soc   Qtot 
 ˙   0




 kocv 
˙
ocv
0
0
0 0 ocv
Q
tot
!
VT
1
=
soc
0
1
0
0
1


!  V1 
!
1  V2 
R 
 + s IT
0
0  soc 


ocv
(3.10b)
which was discretised with zero order hold. The kocv is taken as the mean of ∂ocv
∂soc
at 0 ≤ soc ≤ 1, which can be found in Figure 3.2. The small deviation in Figure
3.2 occur because of the non-linear behaviour as seen in Figure 2.7. To ensure
that the safety limitations of the battery pack seen in Figure 2.6 were held and
the soc were kept in its defined range, the restrictions to the mpc system were
set as
soc ≤ 1
(3.11a)
(3.11b)
VT ≤ VT ,max
(
IT ≤
IT ,max
IT ,max + kI,max (socb − soc)
soc < socb
soc ≥ socb
(3.11c)
where kI,max > 0 defines the first linear decrease of current that occurs at the
higher soc, socb as seen in Figure 2.6.
3.2
19
Control Formulation
Partial derivative of OCV
∂OCV/∂SOC
+50%
k
−50%
0
0.25
0.5
0.75
1
SOC
Figure 3.2:
∂ocv
∂soc
as a function of soc.
With a sample time tsample of 1 second, the number of prediction steps N were set
to approximately one minute to make sure that upcoming restrictions could be
managed smoothly. The Q1 weight matrix of difference between the output values of z and reference signal r were set significantly low for the battery voltage
VT , because it does not follow a special reference in a charging scenario. Rest of
the weights: Q2 input u difference and the weight between output and reference
for soc were set equal. All calibration parameters can be seen in Table 3.1.
Table 3.1: mpc calibration parameters.
Parameter
Value
N
50
10−10
0
100
Q1
Q2
0
100
!
The step response of the system from socmin to socmax can be seen in Figure 3.3
and the lowest charging time defined as t0,min . The limits of the charge time depends of the voltage and current restrictions, which can be seen in Figure 3.4. As
seen in Figure 3.3, the response time t0 can be divided into a linear region where
the restrictions are constant and a settling part tsettle where the restrictions are
harder, which can be seen in Figure 3.4.
20
3
Step response
1
SOC
tsettle
Linear region
t
0,min
0
time
Figure 3.3: Response of a step from socmin to socmax .
Restrictions
VT
Max
IT
Max
actual value
restriction
0
b
1
SOC
Figure 3.4: Restrictions of a step from socmin to socmax .
Method
3.2
21
Control Formulation
Since the prediction horizon is significantly lower than the rise time of the system (N tsample t0,min ), any time dependent restrictions cannot be applied in
the mpc algorithm. This occur because the mpc must be able to predict the final
time and value to apply it in the optimisation and thereby ensure that the time
dependent restriction is held. The solution to apply different charging times is
solved with N tsample > t0 . This criterion can be fulfilled with increasing either
the number of predictions N or the sampling time tsample . Drawbacks due to a
larger N is the computational time in each iteration and a larger tsample increases
the risk that restrictions are violated between the samples. Therefore none of
this solutions were applied to this thesis and N tsample remained smaller than the
charging time t0 .
3.2.2
Charge References
Modifying the reference signal depending on charging time t0 , charging intervals socinit to soc0 and the step response behaviour, results in a charging that
minimizes power consumptions. The modified reference r(t) is described as
r(t) = socinit +
soc0 − socinit
t
t0
(3.12a)
r(t) = socinit + (soc0 − socinit )(1 − e−t/τ0 + e−α )
(
r(t) =
socb −socinit
t
t0 β
socinit +
socb + (soc0 − socb )(1 − e−(t−t0 β)/τ0 (1−β) + e−α )
(3.12b)
t ≤ t0 β
t > t0 β
(3.12c)
which contains three different reference solutions: equation (3.12a) for linear,
equation (3.12b) exponential and equation (3.12c) as a compound of both. The
definition of τ0 is τ0 = t0 /α where α > 0 and the term e−α is added to equations
(3.12b) and (3.12c) to make sure that the reference reaches soc0 . This makes the
reference to not start at socinit but for higher values of α, this phenomena can
be neglected. The β is defined as 0 < β < 1 and sets how much of the charging
time t0 that will apply the linear reference in the compound strategy in equation
(3.12c).
˙ = IT /Qtot gives that
The relation soc
IT (soc) = Qtot ṙ(t)
(3.13)
which gives the control signals assumed that no restrictions are active as
IT (soc) =
IT (soc) =




IT (soc) = 


Qtot
(soc0 − socinit )
t0
(3.14a)
Qtot socinit − soc + (soc0 − socinit )(1 + e−α )
τ0
Qtot
− socinit )
t0 β (soc
b
Qtot
socb − soc + (soc0
τ0 (1−β)
(3.14b)
soc ≤ socb
− socb )(1 +
e−α )
soc > socb
(3.14c)
22
3
Method
with equation (3.14a) for the linear, equation (3.14b) for the exponential and
equation (3.14c) for the compound reference. To get continuity of IT (soc) in
equation (3.14c), α must be defined as
α(1 + e−α ) =
1 − β socb − socinit
β
soc0 − socb
(3.15)
which can be solved easily with the approximation e−α ≈ 0. A visual example of
the references in equation (3.12) with control currents in equation (3.14) can be
seen in Figure 3.5, where the tuning parameter β of the compound is 0.4.
Reference examples
1
SOC(t)
b
rlin
rexp
r
com
0
0
Beta
1
IT(SOC)
t/t0
0
b
1
SOC
Figure 3.5: Reference examples as described with equations (3.12) and
(3.14).
3.2.3
Voltage Reference
For some applications, a manageable battery voltage can be desired. Examples
of this can be connection of hv equipment to the battery pack or connections of
slave res’s to the master res for a parallel charge of the battery packs. To control
the voltage of a battery pack, the penalty matrix Q1 in equation (2.2) needs to be
modified.
3.3
Simulation
This section describes the configurations of the simulations done in this thesis. It
begins with a description of the simulation environment followed by the three
methods used in simulation evaluation.
3.3
23
Simulation
3.3.1
Evaluation Environment
The res model from Section 3.1.1 and control formulation in Section 3.2 were
evaluated through simulations. The simulation environment can be seen in Figure 3.6 and the simulation outputs in Figure 3.7. An implementation of this control system would require observers for the dynamic voltages V1 , V2 , the charge
soc and an interpolation to achieve an estimation of Vocv . These values has to
be estimated since they are not measurable on a physical battery pack.
V_T
SOC
V_1
V_2
OCV
I_T
x' = Ax+Bu
y = Cx+Du
RES_model
OCV(SOC)
1-D T(u)
WorkspaceOutput
u
x
MPC Controller
Figure 3.6: Simulation model used for evaluation of reference signals in
equation (3.12).
Clock
Display
1
V_T
2
SOC
3
V_1
4
I^2
V2I
V1I
5
Scope
VI
V_2
Rs
-K-
|u|
simout
Abs
To Workspace
OCV
6
I_T
Figure 3.7: WorkspaceOutput block of Figure 3.6.
3.3.2
Charge Time
To evaluate how the charging time affects the total charging efficiency, the mean
value of the battery efficiency was defined as
η̄P = 1 −
P¯loss
P¯in
(3.16)
where P¯loss is defined as the mean value of the approximated power losses in the
model of Figure 3.1
Ploss = (Rs IT + V1 + V2 )IT
(3.17)
24
3
Method
and P¯in defined as the average input power
Pin = VT IT
(3.18)
The power losses in the resistances R1 and R2 were approximated through the
voltages V1 and V2 in equation (3.17) since these are near to constant for the
charging scenarios. Simulations were done at different charging times t0 with the
reference signals as equation (3.12).
A study in how each reference signal affects the degradation due to high current
IT was done by defining the current usage ability 0 ≤ ζ ≤ 1 according to
ζ=
IT ,restriction − IT
IT ,restriction
(3.19)
where IT ,restriction represents the restriction of equation (3.11). A higher ζ-value
represents a better soh due to slower cycling ageing from terminal currents IT .
3.3.3
Voltage Control
The possibility to use the mpc controller with a voltage reference was evaluated
through simulations. The parameters of the penalty matrix Q1 in equation (2.2)
were set to
!
100
0
(3.20)
Q1 =
0
10−10
for these simulations.
3.3.4
Current Restriction
A theoretical sensitivity analysis of how charging times could decrease with relaxed restrictions of current IT were done through simulated steps from socmin
to socmax with different restriction IT ,max .
3.4
Implementation
Implementations done in the thesis are described in this section. This section
contains the method for implementation to achieve the converter measurements.
3.4.1
Converter Measurements
To parametrise the dc-dc converter model (see Section 3.1.2) measurements were
needed. The converter temperature was kept constant to keep consistency during
the measurements, which was solved by connecting it with radiator hoses to cooling equipment. Other parts connected to the converter can be seen in Figure 3.8.
With the converter connected to laboratory power equipment, measurements of
Vin , Iin , VT and IT were made with the rig parameters as shown in Table 3.2.
3.4
25
Implementation
Table 3.2: dc-dc converter rig parameters.
Parameter
Value
Vin
Iin
VT
300 − 430V
0 − 125A
600 − 690V
Power Equipment
Iin
CAN
HV
Hose
V
+
in
−
Cooling
IT
+
DC/DC
−
V
T
Control
Unit
Figure 3.8: Rig configuration for dc-dc converter.
4
Results
This chapter contains the results according to the methods described in Chapter
3: The modeling, simulations and implementations. The chapter ends with a
discussion of the results achieved in the thesis.
4.1
Modeling Results
This section shows the validation results of the battery and converter model made
in this thesis.
4.1.1
Battery Pack
The results of the battery model mentioned in Section 3.1.1 can be seen in Figure
4.1, with the model parameters as in Table 4.1. Table 4.1 also shows the estimated
parameter values for each specific measurement and here it is seen that these
impedances differs a bit based on the current soc, but a decent representation of
the parameters can be the mean values. The modeled VT in Figure 4.1 (dark grey)
follows the dynamics of the measured VT (light grey) at soc = 0.5 well but there
is a small bias between these, probably because of uncertainty in the estimated
soc or the confidence of ocv in Figure 2.7. The relative bias error is low and it
should be allowed to neglect its effects on the overall system.
27
28
4
Table 4.1: res model parameters.
Parameter
Value
Set [soc]
mean 0
0.25
0.5
0.75
1
R1 [mΩ]
R2 [Ω]
C1 [F]
C2 [kF]
140
35.5
235
1.34
135
30.0
239
1.54
113
29.0
286
1.54
158
47.0
251
0.81
144
26.9
211
1.72
149
43.7
189
1.08
VT [V]
Model Voltage
650
EV,T [%]
3
0
IT [A]
−3
0
0
500
1000
Time [s]
Figure 4.1: A comparison between the measured and modelled VT .
Results
4.1
29
Modeling Results
4.1.2
DC-DC Converter
In Table 4.2, the estimated model parameters for equation (3.8) can be seen.
The converter efficiency model in Section 3.1.2 was derived with equation (3.4a)
where the power loss model of equation (3.8) was applied to equation (3.5). A
comparison between the model values with measurement inputs and the mean
values of measurements done according to Section 3.4.1 can be seen in Figure 4.2.
Figure 4.3 contains a map of the modeled efficiency. Here it is observed that the
efficiency decreases hugely at lower input currents because the losses mentioned
in the theory Section 2.1.2 gets relatively higher compared to the total power in
to the converter due to losses in the transformer.
Table 4.2: dc-dc converter model parameters.
Parameter
Value
kP 1
kP 2
kP 3
kP 4
kP 5
639W
−106V
9.50mΩ
15.9 × 10−3
29.2V−1
Converter Efficiency
ηDC [−]
1
0.75
0.5
VT: 600V
5
45
85
125
ηDC [−]
1
0.75
0.5
VT: 630V
5
25
50
70
ηDC [−]
1
0.75
0.5
V : 660V
T
5
30
55
ηDC [−]
1
0.75
0.5
VT: 690V
5
15
25
35
Iin [A]
Figure 4.2: A comparison between the measured (dark) and modeled (light)
ηdc .
30
4
Results
Efficiency Map
1
ηDC [−]
0.75
0.5
0.25
0
690
660
630
VT [V]
600
0
25
50
75
100
125
Iin [A]
Figure 4.3: The modeled efficiency map of ηdc .
4.2
Simulation Results
Results from the three simulation evaluations in Section 3.3 are presented in this
section.
4.2.1
Charge Time
Results from Section 3.3.2 can be seen below. Figure 4.4 shows how the final soc
at t0 , η̄P as defined in equation (3.16) and the maximal terminal voltage, VT depends on the charge time t0 . The three different results in Figure 4.4 evaluates the
three different reference signals described with equation (3.12) in Section 3.2.2.
Here it is seen that the efficiency is slightly higher with the linear reference signal although it requires that t0 ≥ 2.7t0,min to reach the final soc with the same
signal. The exponential reference signal has the lowest efficiency but reaches the
final soc at lower t0 and ends up in a lower maximum terminal voltage VT than
the other reference signals. It can reach a lower voltage since VT ,max > Vocv at
soc = 1. The balance between the linear and exponential reference signal is the
compound signal, that has its characteristics in between the linear and exponential references.
31
Simulation Results
SOC(t0)
4.2
rlin
1
rexp
rcom
ηP,mean
0.98
0.97
0.96
0.95
VT,max
1
0.99
1
2
3
4
t0/t0,min
Figure 4.4: Simulation results of different reference signals at different t0 .
The mean value of unused current capacity ζ behaviour of charge time t0 can
be seen in Figure 4.5 for the three different charge references. From Figure 4.5
it can be seen that the references are equal in a point of soh and that a longer
charging time is better for the battery pack. They are equal since the gain in the
linear case at lower charge times comes from the lack of charge as seen Figure 4.4.
Distance to restriction
ζmean
0.9
0.65
lin
exp
com
0.4
1
2
3
4
t0/t0,min
Figure 4.5: Simulation results of ζ̄(t0 ) for the three reference signals.
32
4
Results
Figure 4.6 shows how ζ in equation (3.19), depends of soc for the three different
reference signals in equation (3.12). The different lines in the graphs of Figure
4.6 represents different charge times where the brighter lines shows the results
for lower charging times. Here it is seen that higher charging times contributes to
better ζ-values and the best values are received with linear reference signal while
soc ≤ socb and the same reference contributes with the worst values if soc is
near 1 since the currents is near IT ,max here. The ζ-value of the exponential reference signal has the opposite characteristics compared to the linear case and the
compound shows an overall balance of the other references. The overshoot in the
beginning of the graphs in Figure 4.6 comes from the initial input values in the
simulations which were set to IT ,max .
Distance to restriction
1
ζlin
0.75
0.5
0.25
0
1
ζexp
0.75
0.5
0.25
0
ζcom
1
0.75
0.5
0.25
0
0
b
1
SOC
Figure 4.6: Simulation results of ζ(soc), darker lines represents higher t0 .
4.2.2
Voltage Control
In Figure 4.7, the reference tracking of VT with Q1 as described in Section 3.3.3
can be seen. Here it is seen that the voltage has a small overshoot from the
dynamics of V1 and V2 but converges to the right value. The current also converges to zero here, which is desirable because zero current and equal potentials
is the ideal condition at connections of electrical equipment. The low weight on
soc in the matrix Q1 makes it float and eventually end up in a value that fulfils
VT ,ref = Vocv (soc).
4.2
33
Simulation Results
VT control
VT,max
1
actual value
reference
SOC
1
0
IT,max
1
0
0
time
Figure 4.7: Simulation with reference on VT .
4.2.3
Current Restriction
Simulation results of how relaxations of the current restrictions in Section 3.3.4
could decrease the charging time t0 can be seen in Figure 4.8. The figure shows
the results of five different current restrictions from 1 × IT ,max to 5 × IT ,max . Here
it is seen that the time to fully charge the res is quite similar and near t0,min due
to the restrictions of VT , as can be observed in Figure 4.9.
Step response
SOC
1
5×IT,max
4×I
T,max
3×IT,max
2×I
T,max
1×IT,max
0
0
0.5
1
t/t0,min
Figure 4.8: Response of a step from socmin to socmax with relaxed IT ,max .
34
4
Results
Restrictions
VT,max
1
actual value
restriction
5
IT,max
4
3
2
1
0
0
b
1
SOC
Figure 4.9: Restrictions of a step from socmin to socmax with relaxed IT ,max .
Some interesting parameters from the simulations above can be seen in Table
4.3 and here it is shown that the efficiency decreases, similar to the results in Figure 4.4. Here t0.5soc and t0.9soc is defined as the time it takes to reach 0.5/0.9
soc. The gain of lower charge times appears to be higher in the beginning of a
relaxation (2 × IT ,max ) than in the end (5 × IT ,max ). This occurs mainly because of
the increasing significance of the voltage restrictions VT ,max .
Table 4.3: Simulation results of current relaxation.
Parameter
×It,max
ηP [%]
t0.5soc
[%]
t
1
95.0
26.8
2
93.2
13.4
3
92.0
8.9
4
91.1
6.9
5
90.6
6.2
[%]
50.9
27.9
22.5
20.5
19.9
0,min
t0.9soc
t0,min
4.3
Value
Implementation Results
This section contains a summary of the physical implementation of the converter
to achieve measurements for the converter model parameterisation.
4.3
35
Implementation Results
4.3.1
Measurement Results
The Figure 4.10 shows the results of the converter measurements described in
Section 3.4.1. The measurements seems plausible since the current IT is lower
than Iin and that the power Pin in equation (3.4c) is higher than PT in equation
(3.4b) at all samples. The distortion in outputs VT and IT comes from the internal
switching of the dc-dc converter and depends mainly on the voltage ratio VT /Vin .
The temperature differs slightly from the reference value of 25o C but it can be
approximated as constant because the small deviation can be neglected.
I [A]
V [V]
Converter Measurements
725
600
475
350
225
100
50
0
P [kW]
55
35
20
0
T [oC]
26
25
in
T
24
23
0
100
200
300
400
500
600
700
Time [s]
Figure 4.10: Measurement results of the dc-dc pre-implementation.
36
4.4
4
Results
Discussion
The parameter kocv in Section 3.2.1 is far from constant as assumed in the model
equation (3.10). The variance of kocv can be seen in Figure 3.2. Since kocv only
appears in the mpc model, its only used in the predictions of the mpc algorithm.
As long as the prediction horizon is relatively low, the error occurred with the
constant kocv might be negligible. This assumption with its dependence should
be kept in mind for future calibrations and modifications of the model.
The results shown in Figure 3.3 and 3.4 shows a cc-cv [11] behaviour which
is commonly used in charging applications of Li-ion cells [18]. This might have
occurred because cc-cv is close to the ideal charging strategy or that the manufacturer have set the restrictions according to this charging strategy.
The measured mean efficiency in Figure 4.2 deviates from the model at some
operating points, mainly at Iin = 30 − 50A. Several factors can cause this phenomena such as: measurement distortion as seen in Figure 4.10, synchronisation
deviation at the sampling of input/output values Vin , Iin , Pin , VT , IT and PT since
these were collected in different computers or that the converter has a more complex circuitry than the one described with Figure 2.3 in theory Section 2.1.2.
As seen in Figure 4.10, the input voltage Vin raises to a higher voltage at higher
current inputs Iin . It is desirable to keep this voltage constant to get consequent
evaluation but since this is controlled with the internal logic and the supply
equipment was set for delivering constant current, it was not manageable at the
time.
The behavioural in the results of Figure 4.8 and 4.9 correspond well to the results at different charging rates in [11]. This similarity might attest the model
characterization.
5
Closure
This chapter summarizes the report with conclusions from the results in Chapter
4 and future work in the subject.
5.1
Conclusions
A well-tuned mpc controller combined with a useful model can ensure that linear
restriction is kept. But the mpc controller cannot manage different time restriction if it is later than the prediction horizon of the controller. For easier charging
scenarios, a simple cc-cv logic could be applied and solve the same problem.
To reduce the charging time of the battery pack, lowering the final soc has a
great impact! As observed in Figure 3.3, it takes about 0.5t0,min to receive the last
1/8 of soc.
Conclusions that can be made from Section 4.2.1 is that the main reason to aim
for a higher charging time would be to increase life time of the battery pack rather
than reduce energy losses since the slow increase of ηP with higher charging time
seen in Figure 4.4 can be neglected.
It can be noticed from the efficiency behaviour seen in Figure 4.4 and Table 4.3
that the efficiency ηP would be significantly lower for lower charging times t0 .
To accomplish this, t0,min must be lower and therefore the restrictions like IT ,max
needs to get relaxed which also would accelerate the ageing of the battery.
37
38
5
Closure
For optimisation of the efficiency for the whole charging chain (dc-dc and res),
it is seen in Figure 4.3 that higher efficiency is received at higher currents for the
converter and in Figure 4.4 that higher efficiency is received at lower currents
for the battery pack. Therefore the final current will be weighted to the optimal
value, max (ηP × ηdc ).
Figure 4.6 in Section 4.2.1 shows that in a point of soh, a compound reference
signal is the best choice if it is intended to fully charge an empty battery pack
since it has low currents at high soc and high currents has higher impact in the
ageing at a high soc than a low soc [1].
Another way to both shorten the charging time and increase the life time of the
battery packs is to add more battery packs to the vehicle, this would increase the
possible total input power and lower the terminal currents for each pack but also
add weight to the vehicle and increase investment costs.
5.2
Future Work
The res model designed in Section 3.1.1 of this thesis does not depend on temperature variations. The model parameters behaviour can be studied and adapted to
get a model that depends on temperature.
The res restrictions in equation (3.11) has the main purpose to prevent rapid
temperature increases in the cells of the battery pack [19]. A study of how the
cell temperature increases as a function of current could relax the res restrictions
and instead depend on a reliable temperature estimation.
Battery restrictions used in this thesis are based on continuous scenarios and by
adding time dependent restrictions the charging scenario could be boosted for a
short while [20].
The efficiency model shown in Figure 4.3 is quite decent for the measurements
done, but since the converter can handle higher powers as seen in Table 2.4 it can
be applied in other applications too. To apply the converter model to higher powers, new measurements and parameters done in Sections 3.4.1 and 3.1.2 should
be redone at the new operating points.
The converter topology might be more complex than the topology used for deriving the model in Section 2.1.2. It can for example contain multiple converters
connected in parallel and only uses one or a few of them at low converter loads.
To model behaviours like this requires more measurements at different operating
points for estimations of when converters are added or removed.
5.2
Future Work
39
Expansion of the simulation environment with extra slave res models and a
model for the bjb can through simulations evaluate and increase the knowledge
of high power dc-charging of multiple batteries.
The knowledge about how much power losses that is generated while charging
can be used in a real time feedforward to the cooling system.
A more explicit description of the battery degradation could be added to easier
weight each factor of the problem formulation.
Larger vehicle fleets off duty could also be charged/discharged based on the actual energy price (v2g). To make sure that this tactics will ensure profitable, the
explicit soh estimation mentioned above must be confident since the "buy and
sell" of energy will increase the battery degradation.
The restrictions of the electric infrastructure must also be taken into account if
the vehicle fleet is significantly large and a fleet network is needed to make sure
that all vehicles gets charged in time.
Since fast charging of hybrid battery packs degrade the soh significantly, a useful
method to recycle Li-Ion battery cells [21] could decrease the cost of new batteries and contribute with a healthier environment.
40
5
Closure
Bibliography
[1] Jens Groot. State-of-Health Estimation of Li-ion Batteries: Ageing Models.
PhD thesis, Chalmers University Of Technology, 2014.
[2] Alexander Schuller, et al. Charging Strategies for Battery Electric Vehicles:
Economic Benchmark and V2G Potential. IEEE Transactions on Power Systems, 29(5), 2014.
[3] Electric vehicle conductive charging system-Part 1: General requirements.
IEC, 2011. IEC 61851-1.
[4] Electric Vehicle Charging Infrastructure Terra multi-standard DC charging
station 53. ABB, 2014. Product leaflet.
[5] Combined ACDC Vehicle Inlet Type 2 - 3ACDC. Phoenix Contact, 2014.
Datasheet.
[6] BDC546 - Bidirectional 750V DC/DC-Converter. BRUSA Elektronik AG,
2014. Datasheet.
[7] Ned Mohan, Tore M. Undeland, and William P. Robbins. Power Electronics:
Converters, Applications, and Design. WILEY, third edition, 2003.
[8] Electric vehicle conductive charging system-Part 24: Digital communication
between a d.c. EV charging station and an electric vehicle for control of d.c.
charging. IEC, 2014. IEC 61851-24.
[9] Road vehicles - Vehicle-to-Grid Communication Interface-Part 1: General
information and use case definition, 2013. ISO 15118-1.
[10] Nader Javani, et al. Heat transfer and thermal management with PCMs in
a Li-ion battery cell for electric vehicles. International Journal of Heat and
Mass Transfer, 72:690–703, 2014.
[11] Lian-xing Li, et al. CC-CV charge protocol based on spherical diffusion
model. Journal of Central South University of Technology, 18:319–322,
2011.
41
42
Bibliography
[12] Torkel Glad and Lennart Ljung. Reglerteori - Flervariabla och olinjära
metoder. Studentlitteratur AB, second edition, 2003.
[13] Martin Enqvist, et al. Industriell reglerteknik - Kurskompendium. Liutryck, 2014.
[14] Jan Lundgren, Peter Värbrand, and Mikael Rönnqvist. Optimeringslära. Studentlitteratur AB, third edition, 2008.
[15] Jianwei Li and Michael S. Mazzola. Accurate battery pack modeling for
automotive applications. Journal of Power Sources, 237:215–228, 2013.
[16] Road vehicles - Vehicle-to-Grid Communication Interface-Part 2: Network
and application protocol requirements, 2014. ISO 15118-2.
[17] Virgilio Valdivia, et al. Black-Box Behavioral Modeling and Identification of
DC–DC Converters With Input Current Control for Fuel Cell Power Conditioning. IEEE Transactions on Industrial Electronics, 61(5), 2014.
[18] Yusof Yushaizad, et al. Li-ion Battery Pack Charging Process and Monitoring
in Electric Vehicle. Applied Mechanics and Materials, 663:504–509, 2014.
[19] Hossein Maleki, et al. Li-Ion polymer cells thermal property changes as a
function of cycle-life. Journal of Power Sources, 263:223–230, 2014.
[20] Peter H.L. Notten, J.H.G. Op het Veld, and J.R.G. van Beek. Boostcharging Liion batteries: A challenging new charging concept. Journal of Power Sources,
145:89–94, 2005.
[21] Zhu Shu-guang, et al. Recovery of Co and Li from spent lithium-ion batteries by combination method of acid leaching and chemical precipitation.
Transactions of Nonferrous Metals Society of China, 22:2274–2281, 2012.
Upphovsrätt
Detta dokument hålls tillgängligt på Internet — eller dess framtida ersättare —
under 25 år från publiceringsdatum under förutsättning att inga extraordinära
omständigheter uppstår.
Tillgång till dokumentet innebär tillstånd för var och en att läsa, ladda ner,
skriva ut enstaka kopior för enskilt bruk och att använda det oförändrat för ickekommersiell forskning och för undervisning. Överföring av upphovsrätten vid
en senare tidpunkt kan inte upphäva detta tillstånd. All annan användning av
dokumentet kräver upphovsmannens medgivande. För att garantera äktheten,
säkerheten och tillgängligheten finns det lösningar av teknisk och administrativ
art.
Upphovsmannens ideella rätt innefattar rätt att bli nämnd som upphovsman
i den omfattning som god sed kräver vid användning av dokumentet på ovan
beskrivna sätt samt skydd mot att dokumentet ändras eller presenteras i sådan
form eller i sådant sammanhang som är kränkande för upphovsmannens litterära
eller konstnärliga anseende eller egenart.
För ytterligare information om Linköping University Electronic Press se förlagets hemsida http://www.ep.liu.se/
Copyright
The publishers will keep this document online on the Internet — or its possible replacement — for a period of 25 years from the date of publication barring
exceptional circumstances.
The online availability of the document implies a permanent permission for
anyone to read, to download, to print out single copies for his/her own use and
to use it unchanged for any non-commercial research and educational purpose.
Subsequent transfers of copyright cannot revoke this permission. All other uses
of the document are conditional on the consent of the copyright owner. The
publisher has taken technical and administrative measures to assure authenticity,
security and accessibility.
According to intellectual property law the author has the right to be mentioned when his/her work is accessed as described above and to be protected
against infringement.
For additional information about the Linköping University Electronic Press
and its procedures for publication and for assurance of document integrity, please
refer to its www home page: http://www.ep.liu.se/
© Oscar Hällman