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Model Based Approach to Supervision of Fast Charging
Master of Science in Power Engineering
SHEMSEDIN NURSEBO
Department of Energy and Environment
Division of Power Engineering
CHALMERS UNIVERSITY OF TECHNOLOGY
Göteborg, Sweden, 2010
Model Based Approach to Supervision of Fast Charging
SHEMSEDIN
NURSEBO
Performed at ABB Corporate Research
Examiner: Professor Torbjön Thiringer
Department of Energy and Environment
Division of Electric Power Engineering
Chalmers University of Technology
Supervisor: Dr. Hector Zelaya
ABB Corporate Research
Västerås, Sweden
Department of Energy and Environment
Division of Electric Power Engineering
CHALMERS UNIVERSITY OF TECHNOLOGY
Göteborg, Sweden, 2010
i
Model Based Approach to Supervision of Fast Charging
SHEMSEDIN NURSEBO
Department of Energy and Environment
Division of Electric Power Engineering
Chalmers University of Technology
Abstract
Due to various economic, political and environmental reasons, the introduction of electric vehicles
(EVs) into the streets is probable. Their introduction will require extra facilities such as the charging
stations. In order for EVs to be able to penetrate the market their recharging/ refueling time should be
comparable to conventional once. This results in charging stations supplying hundreds of amps to
EV batteries. The usual trend in charging EV batteries is that the BMS (Battery Management Sys-
tem) gives various orders and information signals and the charger acts as a slave in the system. But
this could result in a dangerous situation if the BMS happens to fail for some reason. Thus in this re-
port a supervisory algorithm is investigated. It is based on modeling the important characteristic of
the battery and then identifying suitable model parameters. Then these models are effectively used
during decision making in the battery charging process.
The results of this report show that:
Model based approach to supervision of battery fast charging provides a satisfactory result
Battery voltage monitoring through prediction could be used to avoid overvoltage on battery ter-
minals. While SOC models could be used to predict the SOC steps ahead but its use is not that
important. Similarly temperature prediction in normal situation is less important as the rate of
change of temperature in very low. But temperature prediction could be valuable when the rate of
temperature rise is high for some reason.
Temperature and state of charge models can effectively be used to validate the corresponding
readings from the BMS.
At the present state the algorithm is relatively prone to noise levels in the working environment
which could be improved in future works.
ii
Acknowledgement
After all the supports I get from the peoples around me to make this thesis a success, it is my plea-
sure to use this opportunity to acknowledge their valuable inputs. First of all, I am highly grateful to
my supervisor Hector for his interest in me to work on this thesis and for his constant guidance dur-
ing the whole project. It is also worthy of mentioning the efforts of other staffs in ABB corporate
research to make my stay at ABB enjoyable. It will be unfair not to mention the positive response,
valuable information and guidance provided by Jens Groots on batteries.
It is my pleasure to value the supports provided by my friends Mebratu, Thinley, Jemal, Khalid and
Bereket among many others during my stay at Chalmers. They really have made my stay possible as
well as enjoyable. Of course, the overall Chalmers community deserves my gratitude for its well
coordinated system. And I am always indebted to my family for their unconditional support. Thank
you God for all blessings you have bestowed on me.
Last but not least, I highly appreciate the guidance and feedback provided by my examiner Torbjön.
Shemsedin Nursebo
iii
List of abbreviations
BMS Battery Management System
HEV Hybrid Electric vehicle
EV Electric vehicle
PHEV Plug-in Hybrid Vehicle
xEV Hybrid ,plug-in hybrid and Electric vehicle,
USABC U.S. Advanced Battery Consortium
EPRI Electric Power Research Institute
MIT Sloan automotive Laboratory at Massachusetts Institute of Technology
NiMH Nickel metal Hydride
NiCd Nickel Cadmium
Li-ion Lithium ion
CC/CV Constant current/Constant voltage
LM Levenberg-Marquardt
AC Alternating current
DC Direct current
THD Total Harmonic Distortion
CCM Continuous conduction mode
DCM Discontinuous conduction mode
VSC Voltage source converter
PWM Pulse width Modulation
DSP Digital signal processor
V-I Voltage-current
RCGR Reference Current generating Routine
MCGR Minimum Current Generating Routine
TMR Temperature monitoring Routine
SOCMR State of Charge Monitoring Routine
BVMR Battery Voltage Monitoring Routine
MPIR Model Parameter Identification Routine
SA Supervisory Algorithm
iv
T
ABLE OF CONTENTS
ABSTRACT ........................................................................................................................................................ I
ACKNOWLEDGEMENT ............................................................................................................................... II
LIST OF ABBREVIATIONS ......................................................................................................................... III
TABLE OF CONTENTS ................................................................................................................................ IV
1 INTRODUCTION ...................................................................................................................................... 1
1.1 P
URPOSE
................................................................................................................................................ 1
1.2 S
COPE
.................................................................................................................................................... 2
1.3 S
TRUCTURE
........................................................................................................................................... 2
2 BATTERY TECHNOLOGIES ................................................................................................................. 4
2.1 N
ICKEL
-M
ETAL
H
YDRIDE CELL
(N
I
MH) .............................................................................................. 5
2.1.1 State of the art NiMH batteries ...................................................................................................... 5
2.1.2 Charging performance ................................................................................................................... 6
2.1.3 Charging methods .......................................................................................................................... 7
2.2 L
I
-I
ON BATTERY TECHNOLOGY
............................................................................................................. 9
2.2.1 State of the art Li-ion batteries .................................................................................................... 10
2.2.2 Charging method ......................................................................................................................... 11
2.3 S
UMMARY ON BATTERIES
................................................................................................................... 11
3 REVIEW OF BATTERY MODELS ...................................................................................................... 12
3.1 M
ODELING TIPS
................................................................................................................................... 12
3.1.1 Charge, discharge, recovery, resistive effect ............................................................................... 12
3.1.2 Capacitive effects ......................................................................................................................... 12
3.2 B
ATTERY
M
ODEL
R
EVISION
............................................................................................................... 13
3.2.1 Electrochemical or physical battery models ................................................................................ 14
3.2.2 Mathematical models ................................................................................................................... 14
3.2.3 Electrical models ......................................................................................................................... 15
3.3 E
LECTRICAL
M
ODELS USED IN THE OPTIMIZATION ALGORITHM
........................................................ 20
3.3.1 Model for voltage prediction ....................................................................................................... 20
3.3.2 Model for SOC measurement validation and prediction ............................................................. 22
3.4 B
ATTERY
T
HERMAL MODELS
.............................................................................................................. 22
3.4.1 Battery thermal model for predicting temperature rise ................................................................ 23
3.4.2 Modeling effect of temperature on charge acceptance and open circuit voltage ......................... 24
4 BATTERY SYSTEM IDENTIFICATION ............................................................................................ 26
4.1 I
NTRODUCTION
.................................................................................................................................... 26
4.2 S
YSTEM
I
DENTIFICATION BASED ON
O
PTIMIZATION APPROACH
........................................................ 27
4.2.1 Model Objective functions .......................................................................................................... 27
4.2.2 Model Parameter Identification Routine ...................................................................................... 28
4.2.3 The Levenberg-Marquardt (LM) method .................................................................................... 30
4.2.4 A Secant Version of the LM Method........................................................................................... 31
4.2.5 Constrained optimization ............................................................................................................. 31
4.3 A
UXILIARY INPUT TO THE IDENTIFICATION ALGORITHM
.................................................................... 33
4.3.1 Kalman filter ................................................................................................................................ 33
4.3.2 Kalman filter calculation ............................................................................................................. 34
5 THE CONVERTER ................................................................................................................................. 36
5.1 T
OPOLOGY
.......................................................................................................................................... 36
v
5.2 C
ONVERTER
P
ARAMETER
V
ALUES
..................................................................................................... 37
5.3 T
HE
C
ONTROL SYSTEM
....................................................................................................................... 39
5.3.1 Control of AC/DC VSC ............................................................................................................... 39
5.4 C
ONTROL OF THE
DC/DC
CONVERTER
............................................................................................... 41
5.5 R
ESULTS AND ANALYSIS
..................................................................................................................... 42
5.5.1 Low pass filter of the battery reference current ........................................................................... 42
5.5.2 Pre-charging the DC link and the DC filter capacitors ................................................................ 46
5.5.3 Reference current generation for the q component of the grid current ........................................ 53
6 THE SOLUTION: THE CHARGE SUPERVISORY ALGORITHM (CSA) .................................... 56
6.1 A
SSUMPTIONS MADE IN THE ALGORITHM
........................................................................................... 56
6.2 I
MPLEMENTATION
............................................................................................................................... 58
6.2.1 State of charge Monitoring routine .............................................................................................. 59
6.2.2 Battery Voltage Monitoring Routine (BVMR) ............................................................................ 60
6.2.3 Temperature Monitoring Routine ................................................................................................ 62
6.2.4 Minimum Current Generating Routine (MCGR) ........................................................................ 63
6.2.5 Reference current Generating Routine (RCGR) .......................................................................... 64
7 RESULTS AND ANALYSIS ................................................................................................................... 66
7.1 S
IMULATION SET UP
............................................................................................................................ 66
7.1.1 Simulation model for battery including thermal model ............................................................... 67
7.1.2 The converter simulation model .................................................................................................. 69
7.1.3 The optimization routine .............................................................................................................. 69
7.2 R
ESULTS AND
A
NALYSIS
..................................................................................................................... 69
7.2.1 Identification ................................................................................................................................ 69
7.2.2 SOC Validation and monitoring .................................................................................................. 76
7.2.3 Terminal voltage monitoring ....................................................................................................... 77
7.2.4 Temperature validation and monitoring ...................................................................................... 78
7.2.5 Minimum current Generation Routine ......................................................................................... 83
7.2.6 Output reference current coordination ......................................................................................... 83
8 CONCLUSIONS ...................................................................................................................................... 85
9 FUTURE WORK ..................................................................................................................................... 88
10 APPENDIX ........................................................................................................................................... 89
11 REFERENCES ..................................................................................................................................... 94
1
1 INTRODUCTION
1.1 Purpose
Owing to different political, economic and environmental reasons the introduction of
electric vehicles (EVs) into the streets is unavoidable. Parallel to their introduction the in-
frastructure that supports them needs considerable attention. One of the main components
of this infrastructure besides the grid is the charging station.
In order for EVs to be considered as an alternative their refueling/recharging time should
match or be near to their IC engine counter parts. This demands fast charging stations
which provide, depending on the vehicle type, hundreds of amps to vehicle batteries. Ta-
ble 1.1 below shows the power requirements in different fast charging approaches for dif-
ferent vehicle types.
Table 1.1 different fast charging power requirements [1]
Type of Charg-
ing
Charging
duration
Charges
up to
(SOC)
Charger Power Level. kW
Heavy
Duty
SUV/Sedan Small Sedan
Fast Charge 10 minutes 100% 500 250 125
Rapid Charge. 15 minutes 60% 250 125 60
Quick Charge. 60 minutes 70% 75 35 20
Plug-In Hybrid. 30 Minutes 40 20 10
As can be seen from the table the power demand is very high which needs special consid-
eration both in charging system and in safety issues. To this end, there are a couple of
companies working on charging infrastructure. Table 1.2 provides the ratings of the
charging station a few of these companies are providing (taken from their respective
sites).
Chalmers University of Technology
Model Based Approach to Supervision of Fast Charging
2
Shemsedin Nursebo August 30 2010
Table 1.2 charging station ratings as provided by their respective providers
Company
AC charging output
DC charging
ABB - 50-250KW
Aerovironment 208VAC to 240VAC @ 30A 30-250KW @480V 3-ph lines
Aker wade 16A, 32A and 63A 36 kW and 50 kW
Coulomb Technologies 230V/16A(level I)
230V/32A (3 phase)(Level II)
-
Elektromotive 240V/20Amps
-
The usual trend in off-board battery chargers, however, is a master-slave approach where
the BMS demands a current and the charger supplies the current. The BMS has of course
better knowledge and information about the battery, than for instance an off-board charg-
er. However if the BMS happens to malfunction for any reason, considering the sensitivi-
ty of the batteries to overcharging, there will be a disaster that nobody wants to undertake.
Thus the purpose of this thesis is adding intelligence to the battery chargers which insures
safe charging even if the BMS happens to malfunction. It will also act as a supervisory
system to warn or avoid accidents. These tasks require
A tangible way of finding if the BMS is working inappropriately
An internal algorithm that calculates the safe charging current and the duration of
charging if the BMS is not working properly.
Also
the supervisory algorithm needs to interact with the converter controller;
hence it is important to understand how it works. Thus some discussion on the
converter is included.
1.2 Scope
This report describes the modeling and identification the battery system based on which a
supervisory algorithm is developed. The supervisory algorithm developed for the battery
charging system works only under the assumptions described thought the report in differ-
ent places.
1.3 Structure
The report has the following structure:
Section 1: Introduction (this section) describes the purpose and scope for this report.
In section 2 a brief discussion of the battery types which could be used in EVs as well as
plug in hybrid vehicles (PHEVs) are provided. The main concern there is
Chalmers University of Technology
Model Based Approach to Supervision of Fast Charging
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Shemsedin Nursebo August 30 2010
How large batteries are required for each vehicle type?
What is the state of art batteries for EVs?
What is their characteristic in terms of charging? What is the charging strategy
recommended by their respective manufacturers?
Which are the charge monitoring techniques that are recommended for each bat-
tery type?
Answering these questions will clear the way for decisions to be taken in the algorithm to
be developed!
The core of any algorithm development is decision making. The approach used in this
thesis for decision making is model based approach. Thus in section 3 various models
which facilitate decision making are discussed. These include:
Simplified battery model for predicting battery terminal voltage steps ahead
State of charge reading validating and predicting model
Temperature reading validating and predicting model
These models will, however, be committed to their responsibility only when they are
equipped with the correct parameters. Otherwise only general information is available
about batteries. This information is far way behind to equip the model parameters with
correct values beforehand. Hence section 4 is devoted to an investigation of identification
algorithms which will be executed on line for each battery to be charged. The identifica-
tion algorithm used in the thesis is bounded Levenberg-Marquardt method.
Section 5 is added for sake of understanding how the converter is working in order to
have a clear idea how it may affect the proposed algorithm. Hence, there a typical battery
charger circuit is discussed; some analysis of a three phase AC/DC converter and buck-
boost DC/DC converter is provided.
Section 6 describes
The charge monitoring algorithm
The assumptions in selection of the algorithm
Implementation issues related with algorithm
Section 7 provides the result and analysis of the proposed algorithm in Matlab simulation
Section 8 provides the conclusion the report.
Section 9 lists future works that could be done based on this work.
Section 10 is appendix
Section 11 references specifies source material and further reading.
Chalmers University of Technology
Model Based Approach to Supervision of Fast Charging
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Shemsedin Nursebo August 30 2010
2
BATTERY TECHNOLOGIES
When we consider an intelligent charger, or charging in general, understanding the cha-
racteristic of the batteries to be charged is indispensable. Knowing the capacity of the bat-
teries to be charged also needs considerable attention. However there are comparatively
only few such cars on the road. Thus finding any tangible information on this topic is not
easy. Thus we need to find an alternative solution. To that end there are three most noti-
ceable bodies working on EV related issues. These are USABC
1
, EPRI
2
and MIT
3
. Ac-
cordingly these bodies have specifications on the battery requirements for different xEVs
type as shown in Fel! Hittar inte referenskälla.. Based on this it is possible to evaluate
currently available battery types for possible xEV use. Of course, the same is provided by
them.
Table 2.1 Battery goals for different PHEVs [2]
Vehicle as-
sumption
units USABC MIT EPRI
PHEV PHEV EV[7] PHEV PHEV PHEV EVs[3]
CD
4
range miles 10 40 30 20 60
CD Operation All
electric
All
electric
blended All
electric
All
electric
Depth of dis-
charge (DoD)
percent 70% 70% 80% 70% 80% 80%
Body type Cross.
SUV
Mid.
car
Mid. car Mid.
car
Mid.
car
Battery goals
Peak power kW 50 46 44 54 99 75-100
Peak power
density (2sec
pulse)
kW/kg 830 380 300(30
sec)
730 340 330 300-400
Total energy
capacity
kWh 6 17 40 8 6 18 25-40
energy density kWh/kg 100 140 150(@
C/3 dis-
charge
rate)
130 40 60 100-140
1
U.S. Advanced Battery Consortium (USABC)
2
Electric Power Research Institute
3
Sloan Automotive Laboratory at MIT
4
Charge depletion
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Model Based Approach to Supervision of Fast Charging
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Shemsedin Nursebo August 30 2010
From the table, EPRI’s analysis suggests the performance goals for an all-electric PHEV-
20 is achievable by current NiMH technology, the goals of the USABC and MIT are
beyond even current Li-Ion technology capabilities. In any case, it is clear that lead acid,
nickel-Cadmium (Ni-Cd) and sodium-nickel chloride (ZEBRA) technologies are not like-
ly to achieve goals for even the less ambitious PHEVs. In contrast, Li-Ion battery tech-
nologies hold promise for achieving much higher power and energy density goals [2].
Thus, it appears that while NiMH could be used for lower performance PHEV designs
(e.g. blended operation with lower CD range); only a chemistry with the energy and pow-
er density capabilities of Li-Ion can meet USABC goals for PHEVs with all-electric
range [2]. Thus in this thesis focus is given only to Li-ion and NiMH batteries. In the fol-
lowing sections we will briefly look at the state of the art NiMH and Li-ion batteries and
charging related issues.
2.1 Nickel-Metal Hydride cell (NiMH)
Compared to other battery chemistries, the primary advantage of NiMH is its proven lon-
gevity in calendar and cycle life, and overall history of safety. However, the primary
drawbacks of NiMH are limitations in energy and power density, and low prospects for
future cost reductions. As it has reached its maturity there is little room left for improve-
ment in power and energy density or cost. Thus NiMH batteries could play an interim role
in less demanding blended-mode designs, but it seems likely that falling Li-Ion battery
prices may preclude even this role [2].
2.1.1 State of the art NiMH batteries
As with any battery type, NiMH batteries are either energy or power optimized. Most of
high power NiMH batteries are intended for application in full and moderate to mild
HEVs [3]. They are not our concern here and we will focus on high energy and medium
energy/power NiMH batteries. Table 2.2 provides state of the art high energy and medium
energy/power NiMH batteries.
Table 2.2 Characteristics of currently available NiMH batteries (high energy and medium
energy/power design cells and modules) [3]
manufacturer SAFT COBASYS VARTA
Cell capacity(Ah) 100
5
85
5
43
6
45
6
25
6
Module voltage(V) 12 12 12 5(4.8) 5(4.8)
Specific energy(Wh/kg) 69 60 45 50 35
Specific power(W/Kg) 160
7
200
7
(250)
8
605
7
400 700
7
5
High energy design
6
Medium energy/power design
7
At 80% DOD
8
At 50% DOD
Chalmers University of Technology
Model Based Approach to Supervision of Fast Charging
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Shemsedin Nursebo August 30 2010
The high energy NiMH battery design of COBASYS has specific energy and specific
power characteristics which do not meet the requirements shown in Fel! Hittar inte refe-
renskälla. for a midsize EV.
The medium energy/power designs of COBASYS and VARTA were developed to have
much higher specific power levels, now meeting PHEV specific power requirements.
Their specific energies of around 45 Wh/kg are close to meeting minimum requirements
for PHEVs, implying only small (COBASYS) or modest (VARTA) weight penalties for
PHEV batteries of the required storage capacities.
Data detail on SAFT’s product sheet indicates a high probability for substantially longer
cycle life. After 1500 discharges, battery storage capacity is shown to have declined by
less than 2%, and the internal resistance (essentially the inverse of specific power) in-
creased by only 15% [3].
2.1.2 Charging performance
Figure 2-1 shows how voltage, temperature and pressure vary as charging progresses. The
voltage spike up on initial charging then continues to rise gradually through charging until
full charge is achieved. Then as the cell reaches overcharge, the voltage peaks and then
gradually trends down.
Since the charge process is exothermic, heat is being released throughout charging giving
a positive slope to the temperature curve. When the cell reaches overcharge, where the
bulk of the electrical energy input to the cell is converted to heat, the cell temperature in-
creases dramatically.
Cell pressure, which increases somewhat during the charge process, also rises dramatical-
ly in overcharge as greater quantities of gas are generated at the C rate than the cell can
recombine. Without a safety vent, uncontrolled charging at this rate could result in physi-
cal damage to the cell [4].
Chalmers University of Technology
Model Based Approach to Supervision of Fast Charging
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Shemsedin Nursebo August 30 2010
The charging performance of a NiMH cell is affected by charging temperature and rate.
Specifically charge acceptance in NiMH cell decreases monotonically with rising temper-
ature. It begins below 20°C and continues through the upper limits of normal cell opera-
tion [5]. More over the voltage profile moves down for higher charging temperature.
2.1.3 Charging methods
Unlike, the lead acid battery where voltage level is closely monitored, here current level
should be controlled. Whereas the voltage level, or change in voltage level or temperature
are used as a feedback signals.
The preferred charging method for NiMH batteries is fast charging. Fast charging is pre-
ferred since it reduces crystalline formation. Moreover, fast-charge rates serve to accen-
tuate the slope changes used to trigger both the temperature and voltage-related charge
terminations [4].
Depending on the battery type, fast charge restores almost all of the discharged capacity.
However for some this phase is followed by an intermediate timed charge which com-
pletes the charge and restores the full capacity. The fast charge (with currents in the 1C
range) is typically switched to the intermediate charge using a temperature sensing tech-
nique, which triggers at the onset of overcharge. The intermediate charge normally con-
sists of a 0.1C charge for a timed duration selected based on battery pack configuration.
But some time if the battery is excessively discharged allowing a high current may make
it impossible to sufficiently restore the battery capacity. In this case the battery is first
trickle charged at the rate of 0.2C~0.3C to the appropriate voltage level (usually 0.8V per
cell) [5]. Then it is followed by the same charging steps described above.
20 40 80 100 60
SOC (%)
Increasing
Figure 2-1 NiMH cell charging characteristic [4]
Voltage
pressure
Temperatur
Chalmers University of Technology
Model Based Approach to Supervision of Fast Charging
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Shemsedin Nursebo August 30 2010
Because of the sensitivity of cell life to overcharge history and the greater subtlety of
some of the overcharge transitions, charge termination redundancy in charger design is
recommended. This applies to both built-in redundant charge control techniques and fail-
safe charge termination techniques such as thermal fusing [4].
2.1.3.1 Overcharge Detection
Primary charge control schemes typically depend on sensing either the dramatic rise in
cell temperature or the peak in voltage. Charge control based on temperature sensing is
the most reliable approach to determining appropriate amounts of charge for the nickel-
metal hydride cell [4]. Temperature-based techniques are thus recommended over vol-
tage-sensing control techniques for the primary charge control mechanism.
Some overcharge of the battery is vital to ensure that all cells are fully charged and ba-
lanced, but maintenance of full charge currents for extended periods once the cell has
reached full charge can reduce life.
2.1.3.1.1 Temperature-Based Charge Control
Use of charge control based on the temperature rise accompanying the transition of the
cell to overcharge is generally recommended because of its reliability (when compared to
voltage peak sensing techniques) in sensing overcharge. The exothermic nature of the
nickel-metal hydride charge process results in increasing temperature throughout the
charging process. There are three ways we can use temperature sensing for overcharge de-
tection [4]:
Based on absolute temperature rise: this approach is subjected to change with
weather condition and is not reliable. Thus this approach should only be used as a
fail-safe strategy to avoid destructive heating in case of failure of the primary
switching strategy.
Based on relative temperature rise: this is the simple form of temperature based
switching where the battery temperature increment, say 20
0
c, from the start of
charging is monitored. The chosen ∆T has to account for both normal temperature
gain during charge and the spike at overcharge. Selection of the proper tempera-
ture increment can be greatly influenced by the environment surrounding the cell.
Based on slope change in temperature profile: charge switching based on the
change in slope of the temperature profile eliminates much of the influence of the
external environment and can be a very effective technique for early detection of
overcharge.
2.1.3.1.2 Voltage-Based Charge Control
Voltage –based charge control can only be used as backups to temperature-based control.
This is due to the fact that the voltage peak typically occurs later in the overcharge
process, the voltage overcharge is not as distinct as that seen with temperature and the
voltage behavior may change with cycling.
Chalmers University of Technology
Model Based Approach to Supervision of Fast Charging
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Shemsedin Nursebo August 30 2010
Similar to the temperature based control, the voltage-based control cab be approached in
three ways [4]:
Based on absolute maximum (~1.8V/cell): is relatively imprecise.
Based absolute voltage rise: can be useful if the initial charging state is known.
Based on change in voltage profile: can provide detection of early entry to over-
charge region.
Moreover, since the voltage does peak during overcharge, switching on the voltage de-
crease (5 to 10mV/cell) is feasible. This eliminates the concerns faced in both voltage and
temperature increment methods about determining the increment that ensures charge re-
turn without excessive overcharge.
2.1.3.2 Environmental Influences on Charging Strategy [4]
The discussions above are most pertinent for devices operating in the room-ambient
range. The following subsection provides the general information in extreme temperature
environment under the batteries operating range.
2.1.3.2.1 High Temperature (40 to 55
0
c)
At higher temperatures, the charge acceptance of nickel-based batteries is drastically re-
duced. Charging of nickel-metal hydride cells in high-temperature environments requires
careful attention for two reasons: (1) the selection of set points, for both temperature and
voltage-sensing systems, can be affected if the cells are already at elevated temperatures
prior to starting charge; and (2) charge duration may have to be extended due to the
charge acceptance inefficiencies.
2.1.3.2.2 Low Temperature
The charge time increases at lower temperatures so charge durations must be carefully
considered to provide adequate low-temperature charging while avoiding excessive
charge at normal temperatures. Charge rates must also be reduced at low temperatures.
An upper limit of 0.1C is recommended below 15°C. Charging below 0°C is not advisa-
ble.
As a concluding remark here is that unlike lead acid batteries where it is enough to moni-
tor voltage only, charging NiMH is a complex monitoring process where voltage and
temperature feedback signals play a major role.
2.2 Li-Ion battery technology
In contrast to NiMH, Li-Ion technology has the potential to meet the requirements of a
broader variety of PHEVs and EVs. Lithium is said to be very attractive for high energy
Chalmers University of Technology
Model Based Approach to Supervision of Fast Charging
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Shemsedin Nursebo August 30 2010
batteries due to its lightweight nature and potential for high voltage, allowing Li-Ion bat-
teries to have higher power and energy density than NiMH batteries. Also a reduction in
Li-Ion cost relative to NiMH is anticipated [2]. However, Li-Ion batteries face drawbacks
in longevity and safety which still need to be addressed for automotive applications.
2.2.1 State of the art Li-ion batteries
Unlike “NiMH”, which specifies particular battery chemistry, the term “Li-Ion” refers to
a family of battery chemistries, each of which has its own characteristics with respect to
the categories of energy, power, cost, lifetime, and safety. Specific battery chemistries are
typically named according to the material used for the positive electrode (cathode), al-
though the negative electrode (anode) material can also be a distinguishing factor.
Table provides state of the art Li-ion batteries which are likely to be used for xEVs appli-
cation.
Table 2.3 the performance characteristics of lithium-ion cells of different chemistries
from various battery developers [6]
manufac-
turer
Technology type Ah Voltage
range
Wh/Kg
(@300W/k
g)
(W/Kg)
90%eff
50% SOC
charging
tempera-
ture
K2 Iron phosphate 2.4 3.65-2 86 667
EIG Iron phosphate 10.5 3.65-2 83 708
A123 Iron phosphate 2.1 3.6-2.5 88 1146 -30~60
0
c
Lishen Iron phosphate 10.2 3.65-2 82 161 0~45
0
c
EIG Graphite/NiCoMnO2 18 4.2-3.0 140 895
GAIA Graphite/LiNiCoO2 42 4.1-3.0 94 174@70%S
OC)
0~40
0
c
Quallion Graphite/Mn spinel 1.8 4.2-3 144 491(@60%S
OC)
2.3 4.2-3.0 170 379(@
60%SOC)
Altairnano Lithium Titanate 11 2.8-1.5 70 684 -40~55
0
c
52 2.8-1.5 57 340
EIG Lithium Titanate 12 2.7-1.5 43 584
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2.2.2 Charging method
In general Li-ion, batteries are charged using constant current/constant voltage. But the
charge rate and the voltage limit differ for different batteries from different manufacturer
as shown in the Table 2.3 above.
As for the charge rate it can vary from 0.3C to 6C or more depending on the model type.
A typical constant current/constant voltage (CC/CV) is shown in Figure 2-2.
Figure 2-2 a typical constant current/constant voltage charging of Li-Ion battery [8]
2.2.2.1 Effect of temperature on charging performance
In general Li-ion batteries exhibit a good charge acceptance in wide temperature range.
But the actual charging temperature range differs with in different battery chemistries as
shown in Table 2.3 above. Some of the points mentioned in the discussion of NiMH bat-
teries concerning temperature in relation to monitoring equally apply here.
2.3 Summary on batteries
Finally as a concluding remark to this section, battery type most likely to be used for EVs
and high range PHEVs is Li-ion battery while NiMH could be used for lower perfor-
mance PHEV designs.
From the charger point of view the range of battery capacities that are likely to be charged
is between (6-40 kWh) or more. The charging current depends on the battery type and ca-
pacity. The fast charging strategy most likely to be used is constant current/constant vol-
tage. Charge monitoring is done by using voltage and temperature. While change in tem-
perature slope could be used to trigger charge termination in NiMH, this is not the case in
Li-ions.
Moreover, since in fast charging strategy batteries are not charged fully this may
not be necessary at all. However temperature increase and absolute temperature limits can
be used to insure safe charging. Charge termination will be facilitated by SOC measure-
ment from the BMS.
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3 REVIEW OF BATTERY MODELS
The charging process can be facilitated if the battery system is well defined and unders-
tood. For this reason it is essential that the battery is modeled into a system whose physi-
cal response can be simulated and analyzed. Thus in this section different battery models
discussed in literatures are reviewed and suitable models for the job at hand are selected.
The modeling is approached in two ways: electrical modeling and thermal Modeling.
Much of the discussion is devoted to electrical modeling while a brief discussion is given
on thermal modeling towards the end.
3.1 Modeling tips
In order to better understand modeling, it necessary that we have some basic understand-
ing of the underlying processes. In this subsection some basics of the underlying process
are discussed.
3.1.1 Charge, discharge, recovery, resistive effect
In every battery, there are two electrodes: positive and negative. Each electrode, in gener-
al, involves an electronic (metallic) and an ionic conductor in contact. At the surface of
separation between the metal and the solution there exists a difference in electrical poten-
tial, called the electrode potential. The electromotive force (e.m.f.) of the cell is then
equal to the algebraic sum of the two electrode potentials.
In equilibrium (no load), the species are uniformly distributed in the electrolyte. Once the
external flow of electrons is established, the electrochemical reaction results in reduction
of the number of species near the electrode. Thus, a nonzero concentration gradient is
created across the electrolyte. If a load is switched off, then the concentration near the
electrode surface will start to increase, or recover, due to diffusion, and eventually, the
concentration gradient will become zero again. In other words, electro-active species will
become uniformly distributed in the electrolyte, but their concentration level will be
smaller than the initial value. The above processes help us understand where open circuit
voltage dependence on SOC comes from. It also explains the increase in resistance at
higher discharge rate.
More resistive effect is encountered due to finite conductivities of electrodes, electrolyte,
and separators, from concentration gradients of ionic species near the electrodes and from
limited reaction rates (kinetics) at the electrode surfaces [9].
Once the concentration of near the cathode drops below a certain level, the cathode reac-
tion can no longer be sustained. Similarly, once the concentration of near the anode drops
below a certain level, the anode reaction can no longer be sustained.
3.1.2 Capacitive effects
Generally, mass transfer arises either from differences in electrical or chemical potential,
or from the movement of a volume element of the solution. The transfer of charge across
the electrode surface causes a charge separation. The excess of charge on the electrode
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surface is counterbalanced by the accumulation of ions, of opposite charge, on the solu-
tion side of the interface. The layer across which this charge separation occurs is called
the electrical double layer, and is extremely thin compared with the width of the electro-
lyte and electrodes [10].
In its simplest form the double layer is described by the Helmholtz model, which de-
scribes the double layer as a parallel plate capacitor with a small plate separation (see
Figure 3-1). This layer is referred to as the Helmholtz layer and can be described by a
constant capacitance Cdl. These differences are only expected close to the electrode sur-
face, since we assume electro-neutrality in the bulk of the solution.
More capacitive effect is introduced due to pure electrical polarization and from diffusion
limited space charges (pseudo-capacitance). Both double layer capacitance and diffusion
capacitance (pseudo capacitance) influence the transient response of the battery, especial-
ly when the rates of reactions are high [9].
Figure 3-1 Electrical double layer as a parallel plate capacitor with capacitance Cdl; the
electrode is assumed to be positively charged [9]
3.2 Battery Model Revision
The main aim of this section is to highlight the complexities involved in battery modeling
and based on this study conclude on a recommended battery model for the supervision
outlined before.
There are a wide range of battery models out there in various literatures. These battery
models can be categorized in the following groups:-
Electrochemical or physical battery models
Electrical models
Mathematical models
-
+
+
+
+
-
-
-
-
+
C
dl
Electrode Electrolyte
Helmholtz layer
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3.2.1 Electrochemical or physical battery models
Electrochemical models are the most accurate and mainly used to optimize the physical
design aspects of batteries, characterize the fundamental mechanisms of power genera-
tion. They can relate battery design parameters with macroscopic (e.g., battery voltage
and current) and microscopic (e.g., concentration distribution) information. However,
they are complex and time consuming because they involve a system of coupled time-
variant spatial partial differential equations a solution for which requires days of simula-
tion time, complex numerical algorithms, and battery-specific information that is difficult
to obtain, because of the proprietary nature of the technology [11]. Thus they will not be
discussed here.
3.2.2 Mathematical models
Mathematical models use stochastic approaches or empirical equations which can predict
runtime, efficiency, and capacity. However, these models are inaccurate (5-20% error)
and have no direct relation between model parameters and the I-V characteristics of batte-
ries. As a result, they have limited value in circuit simulation software [11]. The simplest
and popular one is Peukert’s law.
3.2.2.1 Peukert’s law
The simplest model for predicting battery lifetimes that takes into account part of the non-
linear properties of the battery is Peukert’s law. It captures the non-linear relationship be-
tween the lifetime of the battery and the rate of discharge, but without modeling the re-
covery effect [12]. According to Peukert’s law, the battery lifetime (L) can be approx-
imated by:
3-1
Where I is the discharge current, and ‘a’ and ‘b’ are constants which are obtained from
experiments. Ideally, ‘a’ would be equal to the battery capacity and b would be equal to 1.
However, in practice ‘a’ has a value close to the battery’s capacity, and ‘b’ is a number
greater than one. For most batteries the value of b lies between 1.2 and 1.7 [12].
The Peukert relationship can be written to relate the discharge current at one discharge
rate to another combination of current and discharge rate:
C
1
=C
2
(I
2
/I
1
)
(n-1)
Where
C = capacity of the battery
Subscripts 1 and 2 refer different discharge-rate states
Peukert’s formula shows an average error of 14% and a maximum error of 43%. Peu-
kert’s formula works well for light loads, but the errors will become very large at heavy
loads [12].
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Another more complex model for life time determining is the R V W’s analytical battery
model [13]. However its discussion here is unnecessary as far as our aim is concerned.
3.2.3 Electrical models
For electrical engineers, electrical models are more intuitive, useful, and easy to handle,
especially when they can be used in circuit simulators and alongside application circuits.
This group uses a combination of capacitors, resistors and voltage sources or current
sources to model behavior of a battery. A wide variety of them have been proposed in
various literatures for one or more battery chemistries. Only a few of them are discussed
below:
The simplest model is composed of a voltage source and an internal resistance as shown
in Figure 3-2
V
t
can be obtained from the open circuit measurement and R
int
can be obtained from both
the open circuit measurement and one extra measurement with load connected at the ter-
minal when the battery is fully charged. This model does not take into account the varying
characteristic of the internal impedance of the battery with the varying state of charge.
In [14] an improved representation, which takes the variation of R
int
with SOC in to ac-
count, is used while the constant voltage source is kept as it is.
3-2
Where
, state of charge(SOC)
Ro is the initial internal resistance R
int
with the battery fully charged. This value
varies as the battery ages.
C10 is the ten-hour capacity (Ah) at the reference temperature. This value also va-
ries as the battery ages.
E
R
int
V
t
Figure 3-2 Simplest battery model
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k is a coefficient that is a function of the discharge rate
In [11] a model capable of predicting runtime and I-V characteristic is provided. This
model has been verified to work for both NiMH and Li-Ion cells [11]. The equivalent cir-
cuit is given as below
Figure 3-3 a generic runtime battery model [11]
On the left, a capacitor (C
b
) and a current-controlled current source, model the capacity,
SOC, and runtime of the battery. The RC network simulates the transient response. To
bridge the SOC to open-circuit voltage, a voltage-controlled voltage source is used.
Usable capacity
The usable capacity, which is represented by C
b
, declines as cycle number, discharge cur-
rent, and/or storage time (self-discharge) increases, and/or as temperature decreases. The
voltage across C
b
varies between 0 and 1 depending on SOC. Thus voltage across C
b
represents SOC of the battery.
Self-discharge resistor R
Sd
is used to characterize the self-discharge energy loss when bat-
teries are stored for a long time. Theoretically, R
Sd
is a function of SOC, temperature, and,
frequently, cycle number. Practically, it can be simplified as a large resistor, or even ig-
nored [11].
Open circuit voltage
The nonlinear relation between the open-circuit voltage (VOC) and SOC is important to
be included in the model. Thus, voltage-controlled voltage source VOC (V
SOC
) is used to
represent this relation. The open circuit voltage is normally measured as the steady-state
open circuit terminal voltage at various SOC points. However, for each SOC point, this
measurement can take days as the different processes inside the cell have longer time con-
stant [11].
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Transient response
In a step load current event, the battery voltage responds slowly. Its response curve usual-
ly includes instantaneous and curve-dependant voltage drops. Therefore, the transient re-
sponse is characterized by the two parallel RC branches in Figure 3-3 above. The series
resistor R
int
is responsible for the instantaneous voltage drop of the step response. R
Tran-
sient_s
, C
Transient_s
, R
Transient_L
, and C
Transient_L
are responsible for short- and long-time con-
stants of the step response. Using two RC time constants, instead of one or three, is the
best tradeoff between accuracy and complexity because two RC time constants keep er-
rors to within 1 mV for all voltage curve fittings [11].
Model extraction
[11]
Theoretically, all the parameters in the proposed model are multivariable functions of
SOC, current, temperature, and cycle number. These functions make the model extraction
complex and the test process long. However, within certain error tolerance, some parame-
ters can be simplified to be independent or linear functions of some variables for specific
batteries. Thus the different parameters can be made only SOC dependent and give over-
all good result provided that it is in isothermal environment. This was of course done for
Li-polymer cell and may not hold for lead acid or other battery chemistries. As some bat-
tery chemistries depend significantly on discharge and charge rate.
The model extraction is done by curve fitting the behavior (V vs. SOC) of the battery
which is the most representative of the group. All the extracted RC parameters are ap-
proximately constant over 20%–100% SOC and change exponentially within 0%–20%
SOC caused by the electrochemical reaction inside the battery. Just to have some insight
into the problem, the following equations are the curve fit results for different parameters
of the Li-polymer cell used in [11].
VOC (SOC) = −1.031e
−35SOC
+ 3.685 + 0.2156SOC − 0.1178SOC
2
+ 0.3201SOC
3
R
Series
(SOC) = 0.1562e
−24.37SOC
+ 0.07446
R
Transient S
(SOC) = 0.3208e
−29.14SOC
+ 0.04669
C
Transient S
(SOC) = −752.9e
−13.51SOC
+ 703.6
R
Transient L
(SOC) = 6.603e
−155.2SOC
+ 0.04984
C
Transient L
(SOC) = −6056e
−27.12SOC
+ 4475.
3-3
In reference [15] an extension of [11] is provided where the transient response is com-
posed of three time constants in seconds, minutes, hours; also a rate factor is included to
model the effect of discharge rate.
Ref. [9] presents a model based on curve fitting experimentally available voltage vs. SOD
curve for various temperature and current level. The battery output voltage can be calcu-
lated due to the battery open circuit voltage, voltage drop resulting from the battery
equivalent internal impedance and the temperature correction of the battery potential. Ac-
cordingly, the battery output voltage may be expressed as
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Vbat =VOC - ibat * Zeq + ∆E(T)
3-4
In reference [16] a model having the form in Figure 3-4 is proposed
Figure 3-4 non linear battery model [16]
3-5
Where:
E = no-load voltage (V)
E0 = battery constant voltage (V)
K = polarization voltage (V)
A = exponential zone amplitude (V)
B = exponential zone time constant inverse (Ah)
−1
Vbatt = battery voltage (V)
R = internal resistance (Ω)
i = battery current (A)
Q = battery capacity (Ah)
q= current charge level in battery (Ah)
Model assumptions:
The internal resistance is supposed constant during the charge and discharge
cycles and does not vary with the amplitude of the current.
+
_
it
E
Controlled
voltage
source
Internal Resistance
V
bat
+
_
Ibat
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The model’s parameters are deduced from the discharge characteristics and as-
sumed to be the same for charging.
The capacity of the battery does not change with the amplitude of the current (No
Peukert effect).
The temperature does not affect the model’s behavior.
The self-discharge of the battery is not represented.
The battery has no memory effect
Model limitations:
The minimum no-load battery voltage is 0 V and the maximum battery voltage is
not limited.
The minimum capacity of the battery is 0 Ah and the maximum capacity is not li-
mited. Therefore, the maxi-mum SOC can be greater than 100% if the battery is
overcharged.
What is good about this modeling approach is the model parameters can easily be ex-
tracted from the manufacturers’ datasheet. The interested reader can refer to [16] for
model parameter extraction procedure.
This is actually the model which is used in Matlab to represent the battery and is available
in SimPowerSystems toolbox. Since there are no interface to real battery this model has
been used as a battery in analyzing the algorithm.
While (3-5) gives the steady state open circuit voltage for a given state of charge, it does
not model the transient behavior of the battery. Thus, in the Matlab, the equations below
(3-6 & 3-7) are used to include the transient behavior of batteries. Moreover different
models are used for charging and discharging as well as for different battery chemistries
such as Li-ion, lead acid and NiMH/NiCd batteries. The equations below show only the
charging model for Li-ion and NiMH. More information is available on the Matlab help
file for the battery model.
The charging mode for Li-ion is
3-6
And for NiMH is
3-7
Where
And i<0 for charging
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As a general conclusion on battery model revision, the battery models are usually opti-
mized for a given application. For example the one in [16] is optimized for HEV, or func-
tion such as determining life time [12 & 13], or available capacity. There are others
which can be used to determine V-I characteristic. But what is common for all is that the
accuracy of the model depends on the detail knowledge of the battery chemistry, which is
normally only available to battery manufacturers.
3.3 Electrical Models used in the optimization algorithm
The discussion above indicates that most models in literature are interested in capturing
the whole V-I characteristic of the battery i.e. from lowest SOC to highest. Even for a
given battery type it is difficult, if not impossible, to find a single equation which works
at different temperature and state of health (SOH).
Consequently, it is very difficult and time consuming for an on-line implementation. But
what we can do, based on our prior information about batteries is
Use the current and voltage measurement to build a model which can predict the voltage
of the battery steps ahead.
Use the simple knowledge we have about sate of charge and current relation to validate
the reading from the BMS; and if the measurements are found to be accurate, use it to
predict SOC steps ahead.
As long as our aim is safe and reliable charging it works perfectly. Thus what follows is
the discussion of two simple models for tasks just described.
3.3.1 Model for voltage prediction
Of course we do not need a model that predicts the voltage–current relation for the whole
range of SOC. However, what we need is a model that can predict the battery terminal
voltage accurately a minute or so ahead. This is enough as the model parameters are up-
dated every 10 sec or so by the optimization algorithm. Moreover the model should not be
battery chemistry specific.
Thus based on this understanding and the discussions we have in battery model revision
the following circuit is well suited for the job at hand.
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Figure 3-5 simple battery circuit model
Here:
R
int
-internal resistance: takes care of the instantaneous voltage boost whenever a
current step is applied. Its value for a given battery cell is usually in a mOhm
range.
R
t
C
t
-RC circuit branch: will be responsible for the transient responses occurring in
a battery with time constants in a minute range. It exact value differs from battery
to battery. Considering the low Value resistance involved in RC branch the capa-
citance Ct is in kF (kilo farad range).
The voltage over Cb: can be taken as the open circuit voltage of the battery. How-
ever it is not exactly the open circuit voltage as longer dynamics of the battery is
included in it. Actually it doesn’t matter as long as we can accurately predict the
terminal voltage of the battery 10 sec or so ahead.
There is no one value range for capacitance Cb; it is value greatly varies even for
single battery because it is not related to any single physical process in the above
model. But generally its starting value in the optimization algorithm in section IV
can be made way above Ct.
In the model formulation, we need to know the initial voltage of the different capacitors.
Considering the model formulation above it is reasonable to assume the voltage on tran-
sient RC branch to be zero and the voltage over Cb to be equal to the open circuit voltage
of the battery. That is just before charging starts.
The model equations in state space form are given as:
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3-8
Where
e is stands for any error that results from measurement and modeling
K is the Kalman gain
3.3.2 Model for SOC measurement validation and prediction
If the SOC measurement from BMS is taken at different time as charging progresses, it is
possible to calculate the capacity of the battery and any columbic inefficiency associated
with it using the following simple relation.
3-9
And in discrete form
3-10
Where
Once the model parameters are identified they can be used to validate the next SOC read-
ing. Once the SOC reading is found to be consistent the model can be used to predict the
SOC steps ahead.
3.4 Battery Thermal models
When consider of thermal model we have to able to answer the following questions:
How much does the temperature rise for a given charging current and a given cooling
power? What does the trajectory of this temperature rise looks like. This answer to this
question is determinant in understanding and validating the temperature reading from the
BMS. Moreover we need to include a thermal model in our simulation to take into ac-
count the temperature rise during the charging process.
How is the charge acceptance affected for a given charging current at different tempera-
ture? This is the same as asking, how much does the capacity of the battery vary with
temperature?
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For a given state of charge, how much does the open circuit voltage of the battery vary
with temperature?
The last two questions required only to build our simulation model. That is once we have
decided how much the temperature rise is for a given charging current we need to know
how this affects charge acceptance of the battery and the battery terminal voltage. This is
how ultimately the battery thermal model is included. If we know how much the tempera-
ture rises and but if it does not affect the characteristic of the battery. There is no need to
include the thermal model. Reference [9] provides a way on how this can be answered
from manufacturers’ data sheet.
The next subsection discusses the answer for the first question and the subsequent section
will answer the rest.
3.4.1 Battery thermal model for predicting temperature rise
Conservation of energy for a battery cell with lumped thermal capacity balances accumu-
lation, convective heat dissipation, and heat generation terms as [17]
3-11
Where
ρ density
c
p
specific heat capacity
T cell temperature
h the heat transfer coefficient for forced convection from each cell,
A
s
is the cell surface area exposed to the convective cooling medium (typically
air)
T
∞
is the free stream temperature of the cooling medium.
A electrode plate area (cm2)
q
c
ohmic heat generation rate due to contact resistance (W)
q
j
ohmic (joule) heat generation rate of solid and electrolyte phases(W)
q
r
heat generation rate of electrochemical reaction (W)
The above equation however does not suit our problem as it contains battery specific pa-
rameters. It also considers the change in heat capacity and density of the battery with
temperature [18]. An alternative is to ignore the change in heat capacity and density with
temperature and have the following circuit friendly approach for thermal model [9].
3-12
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However, we have no idea what value h and ‘As’ would be for a given vehicle. Thus it is
reasonable to assume ‘hAs’ to be constant for a given charging period; where, off course,
‘As’ is constant and then we assume constant cooling power.
is composed off voltage transients having time constants of different duration.
Thus, to simplify calculation, we can assume it to be constant based the following reason-
ing.
Voltage transients with long time constants vary slowly and they can be considered con-
stant compared to the 10 seconds time window chosen for the algorithm
Voltage transients with short time constants can be assumed constant as they will reach a
constant value after an initial transient.
The calculation results for V
tr
and R
tr
are less critical in giving the thermal generation
equivalent of the transient voltage drops.
Once again for constant charging current
is also constant for reasonably longer pe-
riod of time. Consequently, (3-12) can be reduced to
3-13
Where
P represents any thermal generation or cooling system and initial thermal state, as
represented by T
∞
.
Now, (3-13) can be solved as:
3-14
Thus given a short period of time, it is expected the temperature measurements have to fit
to this equation. Once the model parameters that fit to a given measurement data are
identified, the same model can be used for validating the subsequent data up to a given
time like 10sec. This time span could be chosen based on our understanding of parameter
variation and the computational power of the DSP.
3.4.2 Modeling effect of temperature on charge acceptance and open circuit voltage
When the temperature of a battery rises it affects the battery capacity and the open circuit
voltage. Generally for lithium ion batteries charge acceptance increase with temperature
[9] while for NIMH [4] the charge acceptance is optimum at room temperature and de-
crease more with decrease in temperature than with increase. As for the open circuit vol-
tage at a given SOC, it increases for Li-ion batteries with increase in temperature. How-
ever, NiMH batteries have higher voltage at room temperature and decreases with tem-
perature both ways; but relatively the decrease with increase in temperature is negligible.
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It is apparent that the two chemistries have different characteristic and will result in a dif-
ferent models. Since this model is required only for simulation, we have provided the
modeling for Li-ion batteries only.
According to [9] two parameters are enough to model the two temperature effects: tem-
perature factor β (T) and the temperature-dependent potential-correction term ∆E (T).
When these two terms are included the SOC equation from (3-9) and open circuit voltage
are adjusted as follows.
3-15
3-16
Where
E0 is the open circuit voltage at reference temperature for reference discharge rate
Cb and η are the capacity and columbic efficiency of the battery at reference tem-
perature. Note that, in Matlab battery model mentioned above Cb and η doesn’t
change with discharge rate.
β(T) is the factor responsible for the change in charge acceptance due to tempera-
ture. It is one at reference temperature
The way this two parameters are calculated in reference [9] results in a piecewise linear
curves.
Finally in our overall simulation model the following are true
The battery capacity and columbic efficiency doesn’t vary with discharge rate
The open circuit voltage varies both with temperature and discharge rate
The charge acceptance or capacity of the battery varies with temperature
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4 BATTERY SYSTEM IDENTIFICATION
4.1 Introduction
There are different types of systems: linear, nonlinear, time invariant, time varying. These
systems can be modeled in different model types: transfer function models, state space …
etc. Nonlinear systems have specialized model types such as Wiener and Hammerstein,
and neural network models [19].
However modeling is not the subject this chapter, it is mentioned here only to stress the
link between the model type and the identification procedure we use. Battery system
modeling is provided in chapter three. In this chapter our mission is to identify model pa-
rameters.
Model parameter identification can be approached in different ways depending system
model type. The most popular identification methods in literature are prediction error me-
thod and sub space identification method. While the former is usually used for transfer
function models the later is used for state space models. However the basic principle is
the same in either case: minimizing the prediction error. Moreover in each method there
are various ways to solve the problem; hence various algorithms are developed by differ-
ent authors and can be found in [19, 20, 21, 22, 23].
Generally, these methods are used for black box identification. Black box identification
refers to an identification procedure where the detailed knowledge of the system is not re-
quired. The system model is built from input output data alone. Knowledge of the system
order will be appreciated but not necessary. Whenever this knowledge is not available,
there are ready made identification tools, like Matlab identification toolbox, which can
decide the best model order and the model parameters based input-output data provided.
However in black box identification there is no relation between identified parameters and
the system. Besides, there is no single solution to the problem. This is clearly visible in
state space models where the similarity transform will result in the same input-output re-
lation with different state values and model parameters. The same is provided below in
(4-1& 4-2):
4-1
4-2
The concept of system identification mentioned above is an offline one. However it is al-
so possible to find their online counterparts which are well adapted to online where the
computation complexity should be reduced. They are usually discussed in literature under
recursive Identification methods [22, 24, 25]
In this thesis, however, a different approach than highlighted above is followed. This is
because
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Considerable information about the system (battery system) has already been gathered.
The model parameters are required to provide some meaningful information about the
battery, such as the internal resistance of the battery, capacity of the battery
As opposed to recursive identification methods there is no need to update model parame-
ters during each sampling interval.
The approach used in this report is usually stated as white box identification in literature.
The subsequent sections will provide detailed information about this identification proce-
dure.
4.2 System Identification based on Optimization approach
There are a wide variety of optimization algorithms, also known as non-linear least square
methods, which could be possible choices for the job at hand. They are generally iterative
processes. Some of them are: Gauss-Newton, Levenberg-Marquardt (LM) and Powell’s
Dog led method [26]. These non-linear least square methods are instrumental in finding
the minima of a given nonlinear function. In optimization problems this function is
known as objective or cost function.
So how does this relate to our problem? Well, given a model, our problem is finding the
parameters of the model that result in the minimum error between the observed and pre-
dicted data. Thus the error function between the observed and predicted data will be our
objective function. To clarify this Idea more the following subsection provide how the ob-
jective functions are developed for each model discussed in section III.
4.2.1 Model Objective functions
Objective function for battery voltage prediction
We have specified in section III that the model in Figure 3-5, provided that it has the cor-
rect parameter values, can correctly predict the battery voltage in the time range we are
working on. The same battery model in Figure 3-5 can be represented by the following
system of equation (refer to (3-8)).
4-3
Now the question remains how we can get the correct parameter for each battery model.
For this we have two tools. One is best initial guess for each parameter as it is highlighted
in section III. The second tool is the voltage measurement we have from the BMS or the
sensors in charger itself. The philosophy is that the calculated voltage using battery cur-
rent as input to the model should be equal to the measured voltage. Of course the initial
parameter values are too erroneous to result in a correct voltage prediction. Thu we need a
way to reduce this error between the measured out voltage and predicted output voltage.
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That is we have to minimize our objective function. Mathematically our objective func-
tion is
4-4
Where
is the measured voltage and
is the predicted voltage as shown in
(4-3).
The same reasoning applies for other model objective functions and they are given in (4-5
and 4-6). While the objective function for the first two cases relay on input-output relation
but the objective function for the temperature monitoring is different. It is based on know-
ing the present value of temperature and predicting its future value based on the thermal
model of the battery.
Objective function for soc monitoring (refer to (3-10))
4-5
However since this is a linear model we will use simple linear solvers to identify the pa-
rameters and there is no need to go for iterative ones.
Moreover, from numerical point of
view there is no way to distinguish the two model parameters therefore we will fix the ef-
ficiency at 100% as we calculate for the capacity of the battery.
Objective function for Thermal model (refer to (3-14))
4-6
Since one input-output data can’t give us any better result than our original parameters
thus we need a couple of data to work with. The larger the data the better but it is also
computational intensive. Besides for time varying systems like battery the older data are
less important. Thus choice of sampling time and sample data length should take these
things into account. One way or another, at the end the objective function is a vector with
length equal to the sample data length selected.
Once we know what our objective function looks like the next question is ‘how we set
about to minimize our objective function?’ The next section discusses this issue.
4.2.2 Model Parameter Identification Routine
Now that the objective functions are discussed along with approximate initial parameter
values we are left with how to adjust the parameter values. They have to be adjusted so as
to result in the parameters values which minimize our objective function. Mathematically
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given our objective function f: R
n
where n is number of unknown
model parameters and m sample data length, we want to minimize ||f(θ) ||. In nonlinear
methods mentioned above this minimization is done by minimizing the square of the ob-
jective function as given below:
4-7
Where
4-8
The index i represents a given sampling time
Adjusting the initial parameter values require to make a step vector h on the parameter
vector θ such that the following holds
That is the each step taken should result in a decent direction. The main purpose of a giv-
en nonlinear least method is thus finding h that result in reduction of the objective func-
tion faster. Mainly, that is where the different nonlinear least square methods differ.
Thus, in this thesis, the Levenberg-Marquardt method is used. For it combines the benefit
of both the steepest decent and the Gauss-Newton method. The steepest decent is good
when the solution is far from the final solution while the Gauss-Newton method works
well when we are in the neighborhood of the solution. In the next section we see some
important points related to the Levenberg-Marquardt method. But before that we need to
clarify two important terms which are common in nonlinear square methods and without
which we can’t move an inch.
Jacobean,
, is a matrix containing the derivative of the original objective func-
tion with respect to each unknown parameters along its row and for each index i:
4-9
Gradient, g, the derivative of the square of objective function (see Eq. 4-8) by each un-
known model parameter as:
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4-10
4.2.3 The Levenberg-Marquardt (LM) method
In the previous section it is stressed that the main difference between different nonlinear
square methods is the way h is calculated. In LM this step h is given as [26]
Where
hlm= is the step h to be taken in the LM method
J is the Jacobean of the objective function
I is an identity matrix
µ is the damping term
g is the gradient
4-11
Now we can manipulate the damping term µ to switch between steepest decent and gauss-
Newton method depending on how far we are from the final solution. For large values of
µ we get
4-12
This is a short step in the steepest descent direction. This is good if the current iterate is
far from the solution. If µ is very small, then
4-13
This is the gauss-Newton step and is good if we are close to the final solution as men-
tioned above.
Now the question remains: How do we select the initial value of µ? How do we know
how far from the final solution we are? And then how is µ it updated? How is the iteration
stopped? Since these issues are more mathematically involved, interested reader can refer
to appendix A. However, the following sections are understandable without these answers
in mind.
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4.2.4 A Secant Version of the LM Method
In (4-99) the Jacobean is calculated using the derivative of the cost function with respect
to each model parameters. This approach requires a function vector where the row mem-
bers are the derivative of the cost function with respect to each model parameters. During
the work it is found that providing this function vector for each model and whenever a
model changed is time consuming; specially for state space model. However a numerical
approximation of the derivatives provides as satisfactory result as the actual derivate.
Moreover a single function handles the Jacobean calculation for all model involved given
the cost function for each model. The secant version of LM is, thus, a version of LM me-
thod where the derivates in Jacobean is approximated numerically by finite difference ap-
proximation as:
4-14
Where ‘
’ is the unit vector in the j
th
coordinate direction and is an appropriately small
real number.
4.2.5 Constrained optimization
What is common for all nonlinear optimization algorithms is that they are relatively
prone, depending on the parameter set up of the cost function, to initial model parameters.
This will sometimes result in unacceptable values. For example, during simulation, it is
observed that, depending on the initial values given, the resulting model parameter con-
tain negative values. This parameters being capacitances and resistances, it is not accepta-
ble.
Moreover there can be several local minima for the objective function. And depending on
where the initial parameter values are, the solution will have different values. Therefore
for better result it is an utmost importance that the approximate values of the parameters
are known. In addition, if the bounds of these parameters are specified, better results will
be attained.
There are various approaches to solving constrained optimization problems. One way of
doing it is by using penalty function or another way can be saturating the parameter when
the limit is reach. But these methods are found to be not helpful. Yet another way could
be defining the parameter in square root or log, however this is not tried.
However in this thesis it is found that the ‘lsqlin’ Matlab optimization tool along with Le-
venberg-Marquardt (LM) method, discussed above, works well.
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4.2.5.1 The ‘lsqlin’ optimization tool
The’ lsqlin’ function solves the problem of the form in (4-15) with the given bounds.
However we are only interested at the simple bound that is
4-15
Called as (Since we are not interested in the terms in bracket, we skip them)
Where
C is a data matrix
X0 is vector of parameter whose value is to be calculated
d is a data vector
More insight into these parameters is given in the following subsection.
4.2.5.2 Levenberg-Marquardt (LM) method and ‘lsqlin’
The trick in combining the two (LM and ‘lsqlin’) is modifying the way h
lm
is calculated.
(4-11) can be rewritten as:
4-16
This can equally be defined as [27]:
4-17
Now it is easy to ’lsqlin’ function, as it is clear from the formulation (C=
, x=h
lm
,
d=
). Yet another trick is bounding the step h
lm
. The bounds for h
lm
can be adapted
from [27]:
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4-18
Since the actual computation results in
4-19
Now what is changed? Well, in the unbounded LM method we used to calculated h
lm
us-
ing (4-11) where there is no limit on the actual h
lm
calculated. However now we are calcu-
lating h
lm
using the ‘lsqlin’ with upper and lower bound as necessary. But the rest includ-
ing Jacobean calculation, µ selection and updating, iteration stopping mechanisms are in-
tact as in LM method.
This finalizes the solution for the optimization problem and the resulting parameters are
strictly bounded.
4.3 Auxiliary input to the identification algorithm
Executing the optimization algorithm during each sample interval is costly as well as un-
necessary. Considering the potential variability
of the battery parameters and computa-
tional complexity of the routine, the optimization routine will be executed after every
10sec. However, due to modeling inadequacy and measurement noises, there will be er-
rors between measured and predicted values in the mean time. To keep the model up to
date and reliable we have to take advantage of the data from each sampling interval. This
could successfully be done by using Kalman filter. Then what is Kalman filter?
4.3.1 Kalman filter
The Kalman filter is a set of mathematical equations that provides an efficient computa-
tional (recursive) means to estimate the state of a process, in a way that minimizes the
mean of the squared error [28].
The Kalman filter addresses the general problem of trying to estimate the state
of
a discrete-time controlled process that is governed by the linear stochastic difference equ-
ation
4-20
With measurement
that is
4-21
In our case
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The random variables
and represent the system disturbance additive vector
and model disturbance additive vector respectively [20]. They are assumed to be indepen-
dent (of each other), white, and with normal probability distributions:
4-22
Where Q and R are their respective covariance matrices, whose values are chosen based
on our knowledge of the system.
4.3.2 Kalman filter calculation
As highlighted above during each sampling interval we need to get the best estimation of
the states. These states will provide the basis for the correct prediction of the terminal vol-
tage (see (4-21)). Now how is this accomplished?
In setting up the solution for the Kalman filter, we begin with the goal of finding an equa-
tion that computes an a posteriori state estimate as a linear combination of a priori state
estimate and a weighted difference between an actual measurement
and a measurement
prediction
as shown below in (4-23)
4-23
The priori state estimate is the state estimated at time step k-1 as
4-24
The actual derivation of the Kalman gain ‘K’ is beyond the scope of this report; interested
reader can consult [28]. A typical expression for Kalman gain calculation is given in
(4-25) [20, 28]
4-25
The overall recursive implementation of Kalman filter is given in Figure 4-1 below [20,
28]
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Form A, B, C, and D from current
parameters and prepare
Measurement
Input
Predict state:
Calculate error covariance and
Kalman gain
Correct state prediction
Update error covariance matrix
Figure 4-1 the recursive Kalman filter implementation
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5 THE CONVERTER
In this section issues related to the converter are discussed. Since the aim the thesis is not
to design a converter, here only a general information and operating characteristic will be
presented. Interested reader can refer to the corresponding references for issues related to
designing the converter and the control system.
5.1 Topology
There are a wide variety of converter topologies which could be used for battery charger
application. To begin with the battery charger for EVs has two parts: the AC/DC and DC
/DC converters. Mainly in the AC/DC side we have a variety of options to choose from;
ranging from single phase [29] to three phases [30-34]. On the other hand the three phase
converters can also be soft switched [30, 32] or hard switched [30, 31, 34]; or two levels
[30, 31, 34] or three level [32, 33].
Choice of the best converter is a tradeoff between overall costs, efficiency, and quality of
charging as well as the simplicity of the control circuit. However, the power level re-
quirement for fast charging demands a three phase power source.
In this report, the battery charger shown in Figure 5-1 will be investigated [31].
Figure 5-1 the charger power circuit Simulink diagram
The charger circuit consists of a hard switched three phase AC/DC converter preceded by
LCL filters, and followed by a DC/DC two quadrant buck/boost converter with LCL fil-
ters. LCL filters chosen for their better filtering performance and lower inductance re-
quirement compared to first order filter (L-filter) [31].
The charger which is going to be investigated has the ratings or operating conditions
shown in Table 5.1.
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Table 5.1charger rating
parameter symbol rating
Rated power S 50KVA
Grid voltage ULL 400V±10%
Grid frequency f 50±5%
Battery voltage Vbat 96 to 600
Charging current Ibat ±150A
Dc link voltage Vdc 700V
Switching frequency f
sw
5kHz
5.2 Converter Parameter Values
Given the operating conditions as in Table 5.1, let us now focus on the values of the dif-
ferent components. The AC/DC converter has the values given in Table 5.2 for compo-
nents involved. The LCL parameters are selected based on the procedure described in
[37]. Valuable information on setting the DC link voltage can be found in [36] and [41]
provides a simple expression on selecting the value of the DC link capacitor.
Table 5.2 AC/DC converter component values
Parameter Value
DC link voltage -
Inductor (L2) 250µH
Inductor (L1) 500µH
Capacitor(C) 33µF
Capacitor(Cdc) 6800µF
Damping resistor(Rd) 0.75Ω
Equivalent resistance
of the inductors
1mΩ
Figure 5-2 shows the DC/DC Buck-Boost converter used in the charger. The correspond-
ing component values are given in Table 5.3. The equivalent resistance has not been cal-
culated; it is just chosen, its actual value could be different. The LCL filters for the
DC/DC converter are selected following the same procedure as in [41].
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Figure 5-2 DC/DC buck-boost converter
Table 5.3 component values/Ratings for DC/DC converter
Parameter value
C 33µF
L1 3.3mH
L2 120µH
f
res
2.55KHz
Equivalent resistance of
the inductors(R1,R2)
1mΩ
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5.3 The Control system
5.3.1 Control of AC/DC VSC
There are various literatures dealing with control of front end voltage source converter
(VSC) [31, 34, 38, 39,40]. Some of them [31, 38, 39] discuss VSC control with LCL fil-
ter. Here the simple control strategy which makes use of the usual PI controls in syn-
chronous frame is adopted [34, 38,40]. The synchronous frame is often used to obtain fast
current control dynamic response [37].
Moreover the dq-coordinate can be aligned either to the grid voltage (ULL) or to the vol-
tage over the capacitor bank (Uc). Here we are dealing with a control system where the
dq-coordinate is aligned to Uc. The approach used to make sure the required reactive
power is drawn from the grid is discussed at the end of this section.
The overall control diagram of the AC/DC voltage source converter (VSC) is shown in
Figure 5-3.
To get the reference angle the three phase voltage over the capacitor bank are used. They
are first transformed from 3 phase to stationary coordinate (alpha-beta). Then they are low
pass filtered at cutoff frequency of 50Hz twice to filter out noise. After which they are
normalized to get the cosine and sine of the transformation angle; mind you, they are
shifted 90 degrees while filtering.
As mentioned above, the controller is a cascaded PI controller. The values of proportional
and integral gain for the current controller and voltage regulator are given in Table 5.4
and Table 5.5 respectively. The controller also includes active damping resistor (Ra), de-
coupling, feed forward, saturation blocks and anti- windup terms. The active damping re-
sistor is used to rule out the uncertainty in equivalent resistance of the inner inductor (L1).
The appropriate manipulation of the PI output to accommodate the converter gain is also
provided.
Here the modulation technique used is pulse width modulation (PWM) with triangular
carrier wave.
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Table 5.4 Parameter values in the current control loop
parameter value
Carrier wave amplitude(Vc) 1
Active damping resistor (Ra) 0.03Ω
Proportional gain(Kp) 2.5
Integral gain(Ki)
155
Sampling time(Ts) 1e-4
Converter gain(G) 350
Uc I1
L2 L1
GRID
Cosθ
sinθ Id ref
Iq ref
αβ=>dq
3ph=>dq
Id & Iq re-
gulator
Compensations
& and PMW gene-
ration
Udc-
regulator
3ph=> αβ
LPF(fc=50Hz)
LPF(fc=50Hz)
Normalization
Figure 5-3 the overall diagram the VSC system
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Table 5.5 Voltage regulator parameters
parameter value
Proportion gain(Kp) 10
Integral gain(Ki) 500
5.4 Control of the DC/DC converter
The overall control layout of the DC/DC converter is shown in
Fel! Hittar inte referens-
källa.
and it is a cascaded PI controller as in the AC/DC case above. Similarly, the feed
forward loop trough Ra is included to remove uncertainties due to the resistance R1. Oth-
er feed forward terms as shown in
Fel! Hittar inte referenskälla.
are also used. Not
shown are the saturation blocks and the anti-windup loops. Some parameter, like the sam-
pling time and switching frequency, are similar the AC/DC converter case. Here even
though the modulation technique is PMW the carrier wave is saw tooth.
The proportional and integral gain values for the three PI controllers shown in
Fel! Hittar
inte referenskälla.
are given in Table 5.6.
DC/DC
converter
D(s)
F(s) +
+
+
+
+
-
-
+
H(s) +
+
-
Ra I
-
Figure 5-4 General block diagram the DC/DC converter control loop
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Table 5.6 DC/DC converter controller parameters
parameter value
Carrier wave amplitude(Vc)
1
Kp
D
16.5
KI
D
155
Kp
F
0.25
KI
F
5
Kp
H
0.75
KI
H
3
Ra 0.03
5.5 Results and analysis
The charger is intended to work on a constant DC link voltage of 700v while the battery
voltage and current varies considerably. We have to also make sure that unacceptable vol-
tage overshoots does not occur in the system. And the current drawn from the grid should
be maintained below within the rating of the various components. Most importantly, the
current delivered to the battery should be limited to the charge acceptance level of the bat-
tery as demanded by the BMS (battery management system).
The simulation is set up under the assumption, the DC link capacitor is pre-charged to the
DC link voltage and the filter capacitors are pre-charged to the battery voltage. Pre-
charging of the capacitors is important as will be discussed later. In the first 0.1 sec the
controller locks in with the AC side filter capacitor voltage to generate the reference an-
gle. Then the charger starts to provide power for the battery as set by the reference cur-
rent. The battery model (Li-ion) available in Matlab SimPowerSystems toolbox is used
for the analysis.
5.5.1 Low pass filter of the battery reference current
In attempt to run smoothly the two control circuits (the AC/DC and DC/DC converter
control circuits) the battery reference current is low pass filtered. This step is crucial for
the required performance of the battery charger to be met. This is due to the fact that the
two control circuits are designed separately and it happened so that one control circuit is
either slower or faster than the other. When this happens there will be over voltage or un-
der voltage on the DC link. This results in overshoot on the grid and battery current. The
larger the step change the worse the problem is; noticeably in the beginning. Figures
(Figure 5-6,Figure 5-7, Figure 5-8) below show what happens.
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As can be seen it is a disastrous situation for both the battery and the grid current, espe-
cially in the beginning. For the same step changes in battery reference current (100A) at
0.1sec and 0.5 the circuit works much worse in the beginning. Except for the small over-
shoots in the Dc link voltage, however, the circuit works well in the remaining part of the
simulation.
Figure 5-5 Battery current reference used for the simulation
Figure 5-6 The DC link response for step changes in battery reference current
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
20
40
60
80
100
120
140
Battery current reference
Time (sec)
Current(A)
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
680
690
700
710
720
730
740
750
Time (sec)
Voltage(V)
DC link Voltage
Mea sured
Reference
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Figure 5-7 Response Synchronous d component current
Figure 5-8 battery current response for step changes in reference current
The above shocking simulation results can be dealt with easily just by low pass filtering
the battery reference current. The results below show the response of the battery current,
the grid current and the Dc link voltage response when the same is done. The same step
changes in battery reference current as in Fel! Hittar inte referenskälla. are used.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-200
-100
0
100
200
300
400
500
600
Synchronous frame d-Component line current
Time (sec)
Current(A)
Mea sured
Reference
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-100
0
100
200
300
400
500
Time (sec)
Current(A)
Battery Current
Mea sured
Reference
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Figure 5-9 the DC link response for step changes in battery reference current
From the figure above we can see that the controller has managed to maintain the DC link
voltage almost constant while the battery draws highly variable current. This is just the
worst case scenario of the actual charging cycle. Moreover the ripple is higher for higher
current levels as can be expected.
Figure 5-10 Response Synchronous d component current
Contrary to the previous case the grid current drawn follows the reference current and
there is no overshot.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
696.5
697
697.5
698
698.5
699
699.5
700
700.5
701
701.5
DC Link Voltage
Time (sec)
Voltage(V)
Mea sured
Refrence
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-60
-40
-20
0
20
40
60
80
100
120
Synchronous Frame d Component Current
Time (sec)
Current(A)
measured current
reference current
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Figure 5-11 Battery voltage response for step changes in input voltage
Figure 5-12 battery current response for step changes in reference current
Here we have small overshoot (+5A) on battery current and only for short period of time
and in the beginning only. If required, this can totally be eliminated by taking reasonably
lower steps in battery reference current.
5.5.2 Pre-charging the DC link and the DC filter capacitors
It is stressed above that pre-charging of the capacitor is essential; indeed it is a disaster for
the grid if not done. The simulation result in Figure 5-13 shows what happens to the grid
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
355
360
365
370
375
380
385
Battery and Filter Capacitor Voltage
Time (sec)
Voltage(V)
Filter Capa citor voltage
Battery voltage
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-20
0
20
40
60
80
100
120
140
Battery Current
Time (sec)
Current(A)
measured
Reference
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current when the DC link voltage is initially 300V. Here one should note that the control-
ler circuit is not activated it is just the diode rectifier which is charging the capacitor. It
can be seen that the current drawn from the grid is huge and the same current flows
through the capacitor. This may even damage circuit components involved; even though
it is for short period of time.
Figure 5-13 Start up Grid Current with Low DC link voltage
But how low should the DC link voltage be to require pre-charging? Well, as far as the
grid current is concerned it is safe to work with a DC link voltage above 500V without
pre-charging. But to avoid over modulation thereby compromise the controller perfor-
mance, Pre-charging is recommended whenever the DC link capacitor voltage falls below
650V.
On other hand the filter capacitors on the DC side also need some pre-charging to the bat-
tery voltage or limiting/damping the inrush current from the battery to the filter capacitor
before the charging process starts. If charging starts before this is done, the controller will
malfunction as there is uncontrollable current oscillation between the battery and the fil-
ter. If not damped the current oscillation peak is very high. The following simulation re-
sult shows the battery current when the connection is not assisted by damping resistors.
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
-400
-300
-200
-100
0
100
200
300
400
Time (sec)
Grid Current
Grid current during Startup
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Figure 5-14 Overshoot in battery current
This overshoot in current is from the battery to the filter capacitor which is not welcomed
by a battery which needs to be charged.
Then how to charge the capacitors? The DC link voltage can easily be charged to the peak
line to line voltage using the already available diodes rectifier bridges in the VSC [34].
Using the appropriate series resistors, we can control the current level drawn from the
grid. These series resistors are to be bypassed when the circuit starts supplying power.
Alternatively, the DC link capacitor could be charged to the required level using the same
diode bridge rectifiers supplying the DC voltage through the DC/DC buck/boost conver-
ter. Here the appropriate switching mechanism should be used to make it work as per de-
sired.
The first approach is best in limiting the current from the grid but it falls short of com-
promising the controller in the beginning for large current steps. Of course which ever
approach is used the damping series resistor is necessary; and this results in power loss.
But it is very low as it lasts for a short period of time.
The following simulation results provide the comparison of the two approaches. In the
first approach the grid supply is connected to the VSC through the series resistors and left
to charge the capacitor to the peak of line to line voltage. Then the resistors are bypassed
where there is an extra inrush current. Meanwhile the DC filter capacitor is charged to
half of the DC link voltage. Next the battery is connected with the DC/DC converter and
synchronized with the filter capacitor.
In the second approach first the grid is switched in the DC/DC converter Battery side and
it charges the DC link capacitor to 700V using boost strategy (shown in Figure 5-17).
When it is done it is switched back on DC link side ready for operation. Then the battery
1.03 1.032 1.034 1.036 1.038 1.04
-20
0
20
40
60
80
100
120
Time (sec)
Current(A)
Ba tte ry Curre n t
Ba tte ry Curre n tBa tte ry Curre n t
Ba tte ry Curre n t
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is connected to appropriate terminals of the DC/DC converter where, similar to the pre-
vious case, it is synchronized with the filter capacitor, then charging starts.
Figure 5-15 Comparison of Current from the Grid
Figure 5-16 Comparison of Current from the Grid
0 0.002 0.004 0.006 0.008 0.01
-40
-20
0
20
40
Current(A)
Grid Current: Approach I
0 0.5 1 1.5
-200
-100
0
100
200
Time (sec)
Current(A)
0 0.002 0.004 0.006 0.008 0.01
-100
-50
0
50
100
Current(A)
Grid Current: Approach II
0 0.5 1 1.5 2 2.5
-100
-50
0
50
100
Time (sec)
Current(A)
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It can be clearly seen the first approach is better in limiting the current in the beginning
and results in less distorted waveforms. However, when charging starts there is an over-
shoot, if the step current is of high value, as in the simulation.
Figure 5-17 Charging the DC link Capacitor
This figure shows the process of charging the DC link Capacitor.
0 0.5 1 1.5
0
500
1000
Voltage(V)
DC Link Capacitor voltage: Approach I
0 0.5 1 1.5 2 2.5
0
500
1000
Time(sec)
Voltage(V)
DC Link Capacitor voltage: Approach II
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Figure 5-18 synchronous frame current
This is another view of the line current in synchronous frame. Here the current hits the
limit and the controller goes for over modulation for the time the current is saturated. It is
clear that the second approach is better in maintaining the current as desired by the refer-
ence value and there is no over modulation.
1.2 1.25 1.3 1.35 1.4 1.45 1.5
0
50
100
Current(A)
Synchronous fram e curre nt( Id): Approach I
Synchronous fram e curre nt( Id): Approach ISynchronous fram e curre nt( Id): Approach I
Synchronous fram e curre nt( Id): Approach I
2 2.05 2.1 2.15 2.2 2.25 2.3
0
50
100
Time(sec)
Current(A)
Synchronous fra me curre nt(Id): Approach II
Synchronous fra me curre nt(Id): Approach IISynchronous fra me curre nt(Id): Approach II
Synchronous fra me curre nt(Id): Approach II
Measured
Refrence
Measured
Reference
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Figure 5-19 Filter Capacitor and battery voltage
In the first approached the filter capacitor is charged to half the DC link voltage though
leakage currents owing to the voltage felt due to its position in the circuit. This of course
should be facilitated for two reasons one the filter capacitor needs to be charged anyway.
The second reason is that it will relieve the stress from the upper IGBT in DC/DC conver-
ter.
In the second approach the filter capacitor is directly charged. Also in the beginning the
there is an inrush current which is safe relative to the rating of the capacitor.
0 0.5 1 1.5
0
200
400
Voltage(V)
Ba tte ry a n d filte r C apa citor Voltage : Approa ch I
Ba tte ry a n d filte r C apa citor Voltage : Approa ch IBa tte ry a n d filte r C apa citor Voltage : Approa ch I
Ba tte ry a n d filte r C apa citor Voltage : Approa ch I
0 0.5 1 1.5 2 2.5
-200
0
200
400
Time(sec)
Voltage(V)
Ba tte ry a nd filte r C apa citor Voltage : Approa ch II
Ba tte ry a nd filte r C apa citor Voltage : Approa ch IIBa tte ry a nd filte r C apa citor Voltage : Approa ch II
Ba tte ry a nd filte r C apa citor Voltage : Approa ch II
Battery Vol.
Capacitor Vol.
Capacitor Vol.
Battery vol.
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Here we see that when the battery is connected to the filter capacitor there is a current
flow (at time 0.7(I) and 1.01(II)) from the battery to the filter capacitor owing to the vol-
tage difference existing there. This phase is assisted by a damping resistor in both ap-
proaches. Comparatively this current is low magnitude and highly damped. Both ap-
proaches almost result in the same performance.
In the meantime, whenever the DC link voltage is not at its set value, it is vital that we
low pass the Step from the measured Dc link voltage value to the set level to lower the
overshoot that could occur.
At the end, which approach to use is dependent on the suitability of the implementation
and the cost of the components to be used. The first approach requires a three phase series
resistors and one three phase by pass breaker while one DC breaker and one IGBT and a
resistor are enough for the second approach. The rest component requirements are similar.
5.5.3
Reference current generation for the q component of the grid current
There is a phase difference between the grid voltage and the capacitor voltage owing the
voltage drop over the filter inductance. And maintaining a zero angle difference between
the capacitor voltage and line current does not guarantee unity power factor from the grid.
Therefore to draw a load at unity power factor form the grid, the q-reference current
should be different from zero. Here the simple relation between the grid side current (I2),
0 0.5 1 1.5
-110
-80
-50
-20
10
Current(A)
Ba tte ry C urrent:Approach I
Ba tte ry C urrent:Approach IBa tte ry C urrent:Approach I
Ba tte ry C urrent:Approach I
0 0.5 1 1.5 2 2.5
-110
-80
-50
-20
10
3030
Time(sec)
Current(A)
Ba tte ry C urrent: App roa ch II
Ba tte ry C urrent: App roa ch IIBa tte ry C urrent: App roa ch II
Ba tte ry C urrent: App roa ch II
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capacitor voltage (Uc) and converter side current (I1) is exploited. This is written as fol-
lows- considering steady state
5-1
The philosophy is the ratio of synchronous frame grid current and synchronous frame grid
voltage should be equal. To maintain equality in the ratios the equation above is used
without the need to measure the grid current. The Simulink diagram of the implementa-
tion is provided below.
Figure 5-20 Simulink diagram for Iqref generating
A low pass filter is used to remove the high frequency ac component which inherent in
the measured signals.
The approach is more pronounced when low power is drawn from the grid where the
reactive power is higher at zero q-reference current. The following simulation result
shows the same when the power drawn from the grid is 10Kw. In the simulation after the
charging is started in the first 0.2 sec the q-reference is set to zero then the above algo-
rithm takes over.
From the simulation the algorithm is good as producing the reference current. The reac-
tive power drawn from the grid decreases but it does not assure zero reactive power. This
is due to the approximation inherent in the above equation.
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Figure 5-21 Synchronous frame q current
Figure 5-22 Reactive Power from the grid
2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8
-40
-30
-20
-10
0
10
20
30
40
Time (sec)
Current(A)
Synchron ous Fra m e q- C urrent
Synchron ous Fra m e q- C urrentSynchron ous Fra m e q- C urrent
Synchron ous Fra m e q- C urrent
1.8 2 2.2 2.4 2.6
-3000
-2500
-2000
-1500
-1000
-500
0
500
Reactive pow er Drawn from the Grid
Time (sec)
Reactive Power(VAr)
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6
THE SOLUTION: THE CHARGE SUPERVISORY ALGORITHM (CSA)
As mentioned in the introduction, the main aim of the thesis is to insure safe and reliable
charging in case the BMS malfunctions. In another way the work in thesis enables the
charging system to be aware of what is going on. It enables the charging system to take
decision on whether the BMS working properly or not, if not, it will take over the charg-
ing process all in all and ensure safe charging.
Thus this section, taking inputs from previous sections, describes how this is accom-
plished. However, due to versatility xEV battery system, it was necessary to make some
simplifying assumptions. Hence the section starts by stating these simplifying assump-
tions. It also explains how practical these assumptions are.
6.1
Assumptions made in the algorithm
Assumption I: this assumption deals with the maximum allowable battery terminal vol-
tage. That is, there is standardized maximum voltage limit for all batteries used in xEVs.
Or the maximum voltage limit for each vehicle type is available from the BMS.
Reasons for the assumption: To avoid damage to the battery the voltage limit of the bat-
tery should not be violated. However, in battery charging, especially fast charging envi-
ronment it is possible for battery voltage to reach the limit while the battery is not fully
charged. If an off board battery charger should participate in supervision of the battery it
is important that it should have this knowledge. Moreover it is impossible for the off
board battery charger to decide this limit in any way if it is not provided.
Practicality of the assumption: Almost every equipment has standard working voltage
but EV Batteries due to the early stages in development, standard voltages are not yet de-
cided. Thus it is possible for standard voltage limits to be set for xEV batteries. When this
is not available, it is possible to make this information available from the BMS. Such in-
formation is already available in the so called intelligent batteries [43, 45]; however it is
not clear if they are there in all xEV batteries.
Assumption II: This assumption comes into play to validate the charging current de-
manded by the BMS. That is, the current demanded by the BMS is correct unless it results
in abnormal temperature increase; like if it is found that the temperature will hit the limit
in a short period of time. Also if the BMS should demand comparatively low current, an
appropriate current will be provided keeping in check the temperature increase.
Reasons for the assumption: this is a must assumption based on the information available
to the author presently. As such there is no information available to relate the battery ca-
pacity or internal resistance to specific current revel. Someone may raise the question
‘How then are the manufacturers determining the charging capability of a given battery?’
well manufactures do specify the current rating or current capability of a battery based on:
Electrochemical characteristic consideration: such as the battery electrolyte con-
centration, electrode geometry and many other microscopic considerations. Dif-
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ferent values are given for short term and long term ratings of a battery. This ap-
pears in manufacturer’s datasheet as a pulse current of specified duration or conti-
nuous current.
Practical consideration: such as how long should the battery be used? For example
you can use a battery rated 10A for 15A provided that it conforms to condition 1
above, but it will have shorter cycle life. Moreover the limit for cycle life also de-
pends how we interpret it. For example the usual trend is the battery is at the end
of life it is 80% of the original capacity. And of course there is no a mathematical
relation which some body can use to relate cycle life with a charge or discharge
current.
Batteries are optimized for energy or power, and they could be different chemistry. Even
if they are assumed to be ,say, energy optimized and are specific chemistry, say Li-ion,
there is no information available to the author on how to determine the charging current
of the battery on the basis of information that could be available online while charging.
However there could be another way into the problem by monitoring the charging effi-
ciency; considering the inefficiency due to voltage drop over the internal resistance alone.
Consumer electronics battery charging typically results in charging efficiency of 99.9%
[44]; usually slow charging. However it clear that fast charging will be less efficient. But
presently there is no information to the author what the limiting efficiency on fast charg-
ing is.
Practicality of the assumption: Even though this assumption does not result in optimum
charging, as optimality depends on how we specify it as described earlier, it does insure a
safe charging strategy.
Assumption III: this assumption is concerned with thermal related issues. Here the as-
sumption is that there is same maximum charging temperature limit for all batteries or
they are available from the BMS. And all temperature rises while charging should be li-
mited below certain value; and this is the same for all battery types.
Reasons for the assumption: almost all batteries for xEVs release heat during charging
process. Depending on the heat released and the cooling system, this results in tempera-
ture rise. All xEV batteries do have a maximum charging temperature, if this limit should
be violated, the battery performance will deteriorate. However not only should we consid-
er the temperature limit, but also the temperature increment during charging as discussed
in section 2. This temperature limit and increments could vary from battery to battery.
Unless we are supported by ‘assumption III’ it is not possible to determine them in any-
way.
Practicality of the assumption: as mentioned above the temperature limits do vary from
battery to battery. As long as our concern is safe charging if we could take the safest tem-
perature limit. That is, among available battery types we take lowest temperature limit
available. For example for Li-ion batteries investigated in this report this temperature lim-
it is 40
0
C (refer to
Table 2.3 the performance characteristics of lithium-ion cells of differ-
ent chemistries from various battery developers [6]
Table 2.3). Moreover it is possible
that this information is available from the BMS as in intelligent batteries [43, 45].
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Assumption IV: this assumption has already been mentioned on section three in relation
thermal modeling. Here we only mention the assumption for the sake of completeness. It
is assumed that thermal generation less cooling system is constant i.e. the net heat genera-
tion is constant.
Assumption V: this of course could be considered more of an approach. Presently most
manufacturers recommend constant current/constant voltage (CC/CV) charging. However
there could be also another better way of charging the battery as in [46]. But in this thesis
CC/CV is charging strategy is followed. That is CC/CV from the BMS for all vehicles are
assumed.
Now based on these simplifying assumptions, the different optimization routines will be
discussed.
6.2
Implementation
The overall supervisory algorithm has six main routines. These are
Model Parameter Identification Routine (MPIR):-this includes every process and
procedure involved in the parameter identification, state adjustment though Kal-
man filter and so on. This is discussed in section four.
Battery Voltage Monitoring Routine(BVMR)
SOC Monitoring Routine(SOCMR)
Temperature Monitoring Routine(TMR)
Minimum Current Generating Routine(MCGR)
Reference current Generating Routine(RCGR)
The last five routines are discussed below. Before that Figure 6-1 gives the clear picture
on how the overall structure works and how the different routines interact to each other.
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As can be seen on Figure 6-1 the overall aim of the routine is calculating safe value for
reference current or issue warning. The system gets input about the battery current (Ib),
voltage (Vb), temperature (T
0
), SOC, current reference (Iref_in) from the BMS. Using
this data the supervisory algorithms executes the different routines shown in the flow
chart (see Figure 6-1) each time step. However within each routine some computation
demanding executions are done after predetermined sample intervals. These will be men-
tioned in corresponding sections.
6.2.1
State of charge Monitoring routine
As discussed earlier in section four, we have to rely on the BMS to get information about
the SOC of the battery. However these readings should be validated to check if, for some
reason, the BMS is malfunctioning. If they are found to be valid they are used for charge
monitoring purpose.
Figure 6-2 shows the SOC reading validation and monitoring routine. The routine starts
by initializing the different status report values. It also gets most recent current and SOC
reading from the data buffer and model information from the MPIR. It calculates the error
between the model predicted values and the reading. Then the necessary decisions are
taken as given in the flow chart.
Figure 6-1 the overall charge supervisory algorithm
K-length
data buffer MPIR
Measured data
Ib, Vb, SOC, T0
SOCMR
TMR
BVMR
MCGR
RCGR
Vmax,
Iref_in
SOCmax
Iref_in
Iref_0ut, end
of charge or
Warning,
Model parameter delivery line
Data delivery line
Iref2
status
Iref3
Iref1, and
status
status
T
0
max,
Iref_in
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The actual implementation is not exactly as it appears. SOC reading validation routine is
done only every 5 sec while the rest are done each sampling interval where the sampling
interval is 0.2 sec.
6.2.2
Battery Voltage Monitoring Routine (BVMR)
This routine is entitled to make sure the maximum voltage of the battery is not violated.
The following flowchart in Figure 6-33 provides an over view of how this routine
Figure 6-2 SOC reading validation routine
Soc_Rs=1(valid);
Soc_prs=0;
Soc_frs=0;
Err_tsh
Calculate: Err = g(Soc_v
– f1 (Ib_v))
K-length data
buffer
Soc_v
Ib_v
Is Err
>=err_tsh?
?
Soc_pr (present
SOC level)
NO
Soc_Rs = 0
(Invalid)
Predict SOC m sec
ahead, Soc_f =f (Iref)
Is Soc_pr >
Soc_max??
YES
f1
Is Soc_f >
Soc_max?
Soc_Rs=1(valid)
Soc_frs= ´0’
YES
YES
NO
NO Soc_Rs=1(valid)
Soc_frs= 1
Soc_Rs=1(valid)
Soc_prs= 1
Soc_Rs=1(valid)
Soc_prs= 0
MPIR
NO
Iref
Key
Soc_Rs= SOC Reading status
Soc_prs= SOC present status
Soc_frs= SOC future status
Soc_max= maximum SOC
f1 and g are model and error calculation functions
Soc_v, Ib_v SOC and current data vectors
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works
The input to this routine is the battery model and current state from the optimization rou-
tine and the current reference from the BMS. It predicts the voltage steps ahead and if the
predicted voltage is found to be equal to or greater than the limit voltage and the maxi-
mum soc level is not attained in the meantime, the current which results in the mid vol-
tage between the current battery voltage and the maximum voltage is calculated. This cur-
rent is taken as a reference. Otherwise the same reference current as given by the BMS is
taken as reference current in this routine. Finally this current level is passed to MPIR for
Vmax,
Iref_in
Predict voltage m sec ahead,
Vpd =f (Iref_in, state)
Is (Vpd >
Vmax)?
Model
state
Figure 6-3 flow chart for battery voltage monitoring routine
NO
MPIR
YES
Vb (present
battery voltage)
Is ((Vpd >
Vmax) &&
(Soc_frs==0))?
Is (Soc_Rs=1)?
Vmax_S=0;
Iref1=Iref_in
Vmax_S=1;
NO NO
YES
YES
SOCMR
Soc_Rs
Soc_Rs
K-length data
buffer
Key
Vb = battery voltage
Vmax= maximum Vb
Vmax_S= Vmax status
Vpd= predicted Vb
f is prediction function
Vmax_S=1;
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further decision making. Moreover some more issues like what if the BMS changes the
current reference a bit later is also included which is not shown in the flow chart.
6.2.3
Temperature Monitoring Routine
The overall temperature monitoring routine is shown in Fel! Hittar inte referenskälla..
The basic procedure for validation is the same as SOC reading validation routine, the dif-
ference is only the inputs i.e. the model and the data (temperature). The temperature is
predicted steps ahead and if it is going to be on or above the limit the reference current is
halved, provided the reference current is not changed from the previous step (not shown
in the flow chart). The routine also considers the BMS reference current reduction if it
happens in the next steps which are not shown as well.
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6.2.4
Minimum Current Generating Routine (MCGR)
This routine intended to give the minimum current incase the BMS provides very low
current reference for some reason. This current value is calculated based on the time it
takes to charge the battery to the desired level. Figure 6-6 shows the flow chart for
MCRG routine.
Tmax, Err-tsh
Calculate: Err = g (T
0
_v –
f (T
0
(0)))
K- length
buffer
T
0
_v
Is Err >=
Err_tsh??
YES
NO
Predict T
0
m sec ahead,
T
0
_pd =f (T
0
(0))
Is T
0
_pd
>=Tmax?
T
0
_RS=1;
Tmax_S=1;
Iref2=Iref/2;
T
0
_RS=1;
Tmax_S=0;
Iref2= Iref;
MPIR
Model
YES
NO
Key
Err = error
T
0
= temperature
T
0
_RS= T
0
Reading status
T
0
_v= T
0
data vector
Tmax= maximum T
0
Tmax_S= Tmax status
Err_tsh= error threshold
T
0
_pd= predicted T
0
f and g are model and error calcula-
tion functions
Figure 6-4 Temperature Monitoring Routine
T
0
_RS = 0
( Invalid)
Tmax_S=0
Iref2=Iref;
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6.2.5
Reference current Generating Routine (RCGR)
This routine takes current references from different routines above makes the appropriate
decision on current reference based on the available status information.
tmax
Is
Soc_Rs==1?
Soc_Rs
SOCMR
Model,
Soc_pr
Iref3= f (model,
Soc_pr, tmax)
Iref 3= Iref_in
tmax= maximum charging time
f = model function
NO
Figure 6-6 MCGR routine flow chart
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The above flow chart clearly depicts how the right current reference is chosen. In the fig-
ure ‘Iref_in’ is the reference current from the BMS and the rest signals come from the re-
spective routine shown in the Figure 6-7.
Is
T
0
_Rs==1?
Is
T
0
max_S==1
?
Is
Soc_Rs==1?
Is
Vmax_S==1
?
Iref_o = 0;
End of charge
Iref_o= min
(Iref2,Iref1)
Is
Soc_prs==1?
Iref_o = 0;
End of charge
Iref_o = Iref4
Is
Vmax_S==1
?
Iref_o= Iref1;
Iref4=Max
(Iref_in, Iref3)
YES
YES
YES
YES
YES
YES
NO
NO NO
NO
NO
NO
Figure 6-7 Reference Current Generation Routine
Iref1, Iref2,
Iref3, Iref_in
TMR
BVMR
SOCMR
Iref1,Vmax_S
Iref2, T
0
max_S,
T
0
_Rs
Soc_Rs, Soc_prs
Sources of different signals
MCGR
BMS
Iref3
Iref_in
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7
RESULTS AND ANALYSIS
This section provides an analysis of the different routines discussed in section 6 creating
some scenarios. The aim of this section then is to show the performance of the routines
and how well coordinated their response is. However, before that the following subsection
provides how the simulation is setup.
7.1 Simulation set up
Figure 7-1 shows the Matlab model of the simulation
Figure 7-1 Matlab model of the simulation setup
There are four main blocks shown in fig 7-1,
The battery model (Magenta)
The thermal model (Light blue blocks)
The controlled current source (Red)
The Optimization block (Orange)
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7.1.1
Simulation model for battery including thermal model
The battery model used is the model that comes with Matlab in SimPowerSystems tool-
box. This model is implemented using the model highlighted at the end of section 3.2.3;
but it does not include thermal model. Thus there is a need to include thermal model.
At the end of section 3 we have discussed thermal related issues of a battery. Here we
have applied the same principle to include thermal model to the given battery model. Here
is how it is done: the block in Figure 7-2 calculates the temperature rise for a given charg-
ing current. Given the initial temperature of the battery, the change in temperature is cal-
culated. Some representative model parameters are given in Table 7.1.
Figure 7-2 Simulink model for calculating the temperature rise in a battery during
charging
Table 7.1 Thermal model parameter values
Parameter definition Value
h (W m
-2
K
-1
) The heat transfer coefficient for forced con-
vection
5
A(m
2
) Battery surface area exposed to the convec-
tive cooling medium (typically air)
2.0755
M(Kg) Mass of the battery 250 [7]
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Parameter definition Value
Volume(m
3
) Volume of the battery 0.15 [7]
Cp(KJ Kg
-1
K
-1
) Specific capacity of the battery 1.0118 Fel! Hittar
inte referenskälla.
T0(
0
C) Initial battery temperature 25
Tair(
0
C) Ambient temperature 25
The heat transfer coefficient is something which is dependent on the battery cooling sys-
tem and there is no information to the author what the typical value is. But here its value
is chosen to have the effect that is required. The mass and volume of the battery is taken
from [7] (USABC battery goals for EVs). And If we take one of the Li-ion batteries in
Table 2.3 (say the one in [48]) and dimension it according to EV requirements in [7], then
we get the surface area of the battery exposed to air approximately as in Table 7.1. It is
assumed that the ambient temperature is 25
0
C and the battery temperature initially is the
same as the ambient temperature. One can assume whatever initial battery temperature as
long as it is in the operating range of the battery. The specific heat capacity of lithium ion
battery is taken from reference Fel! Hittar inte referenskälla. which is the specific heat
capacity for a typical Li-ion polymer battery used for EV application.
However these are just representative parameters for fictitious battery and not actual bat-
tery; such information is hard to find for a given battery. Moreover what is needed to see
is if the temperature monitoring system predicts future temperature correctly and how it
reacts whenever triggering events occur. In that respect the given parameters fulfill the
objective of the simulation.
As it is specified in section 3, to simplify things, it is assumed that the change in charge
acceptance and open circuit voltage are linearly related to the change in temperature. The
change in open circuit voltage (see eq. 3-16) is evaluated as shown in Figure 7-3.
Figure 7-3 Modeling effect of temperature on battery voltage
Here the gain is taken by linearizing the curve given for temperature-dependent potential-
correction term in Ref [9].
The input to optimization algorithm is ‘Vb_th’ which is considered as the measured bat-
tery terminal voltage.
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The change in charge acceptance (see eq. 3-15) is incorporated by manipulating the cur-
rent flowing into battery (see Figure 7-4).
Figure 7-4 Modeling effect of temperature on charge acceptance
Here once again the gain term is taken from reference [9] in similar procedure as men-
tioned above.
From Figure 7-4 Modeling effect of temperature on charge acceptance, for a given refer-
ence current ‘Iref_out’ the rate of change of SOC will be different depending on the tem-
perature of the battery. It is achieved by manipulating the actual current flowing into the
battery. However what the optimization algorithm knows is that the current flowing into
the battery is the same as the reference current provided by itself in the previous routine.
The approach used in the simulation set up to model the change in charge acceptance is
not completely genuine as there will a difference between the current that is assumed to
flow into the battery and what actually flows. Even though this properly models the
change in charge acceptance it could affect the current-voltage (V-I) relation of the mod-
el. The proper modeling would have been a allowing all current to flow in and then ma-
nipulating the capacity of the battery depending on the change in temperature. It is used
here this way as there is no way to manipulate the capacity once the simulation is started
with given simulation set up. But since the temperature change is very slow it has neglig-
ible effect on the V-I relationship of the battery.
7.1.2
The converter simulation model
Using the actual converter model in the simulation is very computation intensive and time
consuming. In section 5 we have discussed the converter and it is seen that, except for
starting process, it can be considered as a controlled current source. Therefore all of the
simulation results provided below use a simple controlled current source as shown in Fig-
ure 7-1. It is controlled by the reference current provided by the optimization block.
7.1.3
The optimization routine
Finally the optimization routine includes all model identification and decision making
processes discussed in section 4. It is implemented In S-function.
7.2
Results and Analysis
7.2.1
Identification
Before looking at the results, let us ask our self the question: ‘what do we want to see in
identification?’ One answer is the identified parameters must be able to predict correctly.
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The other is the identified parameter values should be nearly constant for time invariant
models, or slowly varying for time varying models. Here we have a battery model with
time varying characteristic. But the thermal model and the SOC models are nearly con-
stant. This can easily be understood from the way the model is formulated and is setup for
simulation. Let us see first their prediction capability.
7.2.1.1 Identified model prediction capability
Model for terminal voltage prediction
Figure 7-5 shows the prediction performance of the V-I relationship Battery model. It can
easily be seen that the prediction performance very good. The prediction is started once
the optimization routine has collected enough data to optimize the battery model parame-
ters. In this simulation the time it takes is 5 sec with sampling interval of 0.2sec. That is
the minimum data length used for optimization is 25 sample data.
Figure 7-5 measured and predicted voltage
Model for State of charge prediction
Similarly Figure 7-6 shows the prediction performance of the SOC model.
0 10 20 30 40 50 60
365
370
375
Time(sec)
Voltage(sec)
Battery voltage
measured
10 sec ahead prediction
30 35 40 45 50 55 60
371
372
373
374
375
Time(sec)
Voltage(sec)
Closer look
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Figure 7-6 Measured and predicted SOC
Model for temperature prediction
If the exact parameter values as in Table 7.1 are used, the thermal constant of the battery
will be around 6hr and 45 min; this is usually the case for battery thermal time constants.
However, the simulation will not show any visible result for thermal behavior of batteries
and predicting the temperature after 10 sec or even 10 minutes will give no benefit as the
temperature change is very small. Thus for batteries working under normal condition such
prediction is not necessary and the battery thermal model can be approximated by linear
model which then can be used for validating the temperature reading. However if some-
thing goes wrong and if the temperature starts to increase rapidly, assuming this tempera-
ture rise follows the model developed in section 3, the same model can be used to take ac-
tion in time. Therefore to simulate such effects and to see more clearly the prediction ca-
pability of the temperature monitoring routines the specific heat capacity of the battery is
reduced to 100. The following figure shows the same. The remaining simulation results
on temperature monitoring use the same value.
0 10 20 30 40 50 60
50
50.5
51
51.5
52
52.5
53
53.5
54
54.5
Time(sec)
SOC(sec)
State of Charge
measured
10 sec ahead prediction
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Figure 7-7 Measured and Predicted Temperature
In all of the figures above we see one fact: they all show good performance in predict-
ing 10 sec ahead.
Before concluding this subsection let us see the effect of the converter on the predic-
tion performance of the different models. Figure 7-8 shows prediction performance of
the different models when they work with the actual converter circuit instead of the
controlled current source. It can be seen that the performance is not compromised and
the decision to replace it with controlled current source is validated.
0 5 10 15 20 25 30 35 40
25
25.5
26
26.5
27
27.5
28
Time(sec)
Temperature(0C)
Battery Temperature
predicted
actual value
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Figure 7-8 prediction performance of the different models when working with the
charging circuit
7.2.1.2 Identified parameter consistency
Parameters for voltage current relation:
In parameter estimation, as specified previously, initial parameters affect the ulti-
mate result if the objective function happens to have several local minima. More-
over the larger the number of parameter the greater is the possibility to have sev-
eral local minima. In parameter estimation for V-I battery model the parameters
are relatively many. Therefore there we see parameter variation. This most visibly
seen in parameter which have less effect on V-I relation in time range we are
working in, that is Cb. The rest are comparatively constant. This is enough as far
as our aim is concerned. We only need to be able to predict the voltage correctly
that is all. Moreover there are no real capacitors or resistors in a battery to whose
value we can check.
0 5 10 15 20
359
360
361
362
363
Time(sec)
Voltage(sec)
Battery voltage
0 5 10 15 20
50
50.2
50.4
50.6
50.8
51
Time(sec)
SOC(sec)
State of Charge
0 5 10 15 20
25
25.1
25.2
25.3
25.4
25.5
Time(sec)
Temperature(0C)
Battery Temperature
predicted
actual value
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Figure 7-9 battery V-I model parameters
Figure 7-10 Battery V-I model parameters (continued)
Parameters for SOC monitoring: - here although the model parameters are two:
columbic efficiency and capacity, as seen in section 3 they are numerically indis-
tinguishable. Therefore one parameter is fixed at a given value the other is opti-
mized. Thus we fix efficiency at 1 (that is 100%) and optimize the capacity of the
0 20 40 60
0
5
10
15 x 10
4
Time(sec)
Capacitance(F)
Cb
0 20 40 60
5000
10000
15000
Time(sec)
Capacitance(F)
Closer Look(Cb)
0 20 40 60
10
20
30
40
Time(sec)
Time constant(sec)
RC
0 20 40 60
11
12
13
14
15
Time(sec)
Time constant(sec)
RC
0 20 40 60
0
0.01
0.02
0.03
0.04
Time(sec)
resistance(Ohm)
Rint
0 20 40 60
0.03
0.035
0.04
0.045
0.05
Time(sec)
resistance(Ohm)
Closer Look(Rint)
0 20 40 60
200
300
400
500
600
Time(sec)
Capacitance(F)
C
0 20 40 60
250
300
350
Time(sec)
Capacitance(F)
Closer Look(C)
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battery C
b
. Moreover since this is a linear model, linear solver is used to optimize
the parameter.
Figure 7-11 SOC model parameters
Parameters for temperature monitoring
Figure 7-12 Thermal Model Parameters
From the above figures the overall impression is the parameters are well identified. Be-
sides, lower number of parameters will result in a more or less constant value for the iden-
tified parameters.
Next an analysis of the performance each routine will be presented.
0 10 20 30 40
80
82
84
86
88
90
92
94
96
98
100
Time(sec)
eff(%)
Columbic Efficiency
0 10 20 30 40
0
0.5
1
1.5
2
2.5
3
3.5 x 10
5
Time(sec)
Capacitance(F)
Battery Capacity (Cbr)
0 5 10 15 20
4.9975
4.998
4.9985
4.999
4.9995
5
5.0005 x 10-4
Time(sec)
d(sec
-
1)
T
0
model parameter(d)
0 5 10 15 20
0
50
100
150
Time(sec)
q(0C)
T
0
model parameter(q)
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7.2.2
SOC Validation and monitoring
The first task of this routine is validating the SOC measurement values. It uses the error
between model-predicted values and measurement values to accomplish its task. The error
threshold is selected based on our expectation of the noise level. However the prediction
performance is only good at much lower noise levels. Here it has to be noted that the time
range we are working in affects the noise rejection capability of the routine. In longer
time ranges, it easier to see how the SOC trajectory is moving better than in shorter time
ranges. ´
To see the noise rejection capability of the routine a white noise is added to the measured
SOC level. Then error for various noise power levels calculated and the prediction capa-
bility of the routine is checked. Based on the way the error is calculated in the routine an
error value beyond 0.1% indicates that the routine is not appropriately predicting. The fol-
lowing figure shows the different signals for error level of around 1% (left) and 0.1%
(right).
Figure 7-13 state of charge prediction
From the figure in the left it can be seen that in a sample data taken for 5 sec or 10 sec it
is difficult to anticipate the trajectory of the SOC but in longer time ranges it could be
done. Therefore for better noise rejection capability of the routine, besides using filters, it
is recommended to increase the time window which is used by the routine.
The rest of the routines task is providing the status signals therefore it discussed in the
next subsections by creating scenarios.
0 10 20 30 40
49
49.5
50
50.5
51
51.5
52
52.5
53
Time (sec)
SOC(%)
Sta te of cha rge
Sta te of cha rgeS ta te of ch a rge
Sta te of cha rge
0 10 20 30 40
49
49.5
50
50.5
51
51.5
52
52.5
53
time(se c)
State of charge
actual SOC mea surement
noisy SOC mea surment
10 sec ahead prediction
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7.2.3
Terminal voltage monitoring
This routine is responsible for keeping in check of the battery voltage limit. For the model
we working with the voltage limit is 385V.
Scenario I: SOC measurement is correct and the voltage limit reaches while the BMS
does not take action (the BMS malfunctions)!
Figure 7-14 voltage monitoring, Scenario I
Scenario II: SOC measurement is correct and the voltage limit reaches while the BMS
does take action!
10 20 30 40 50 60
376
378
380
382
384
386
Time (sec)
Voltage(V)
Battery voltage monitoring
10 20 30 40 50 60
230
235
240
245
250
255
Time (sec)
Current(A)
Refere nce currents
Iref form optimisation routine
Iref from BMS
Mea sured voltage
predicted voltage (10 sec ahead)
10 20 30 40 50 60
225
230
235
240
245
250
Current(A)
Reference Current
10 20 30 40 50 60
375
380
385
Time(sec)
Voltage(v)
Battery voltage
Iref-BMS
Iref-optimisation routine
predicted voltage
measured voltage
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Figure 7-15 voltage monitoring, Scenario II
Scenario III: SOC measurement is correct and the voltage limit reaches while the BMS
does take action but it is a bit late!
Figure 7-16 voltage monitoring, Scenario III
In Figure 7-16 the optimization routine acts in time and reduces the current to avoid vol-
tage limit violation then the BMS reduces the reference current, then we take the mini-
mum of the two from safety consideration point of view.
Scenario IV: SOC measurement is incorrect and the voltage limit reaches: in this work it
is decided that the charging process should be ended; as there is no way to tell when the
required level of SOC is reached. Of course this more probably results in premature
charge interruption. But it is a necessary measure to avoid possible battery overcharging
and damage.
7.2.4
Temperature validation and monitoring
Similar to the SOC validation and monitoring, the prediction is reliable in almost noise
free environment. It also depends on the thermal time constant the battery system and the
time window we are working with. Figure 7-17 shows the result for noisy environment.
As it can be seen the noise level is very low but if the noise level is increased it could re-
sult in unacceptable results. Moreover the initial parameter values for the optimization
will affect the actual performance. The parameters values should be as much as possible
close to their actual value. At least we need to have an Idea on what the thermal time con-
stant could be. In addition, we can see that in length of time window we are working in a
0 10 20 30 40 50 60
0
100
200
300
time(sec)
Voltage(V)
Reference currents
0 10 20 30 40 50 60
370
375
380
385
Time(sec)
Voltage(V)
Battery voltage
predicted(10 sec ahead)
measured
BMS
Optimisation routine
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linear model with one parameter could work as accurately as the nonlinear model; and
even better, since we have to optimize only one parameter.
On the other hand, as far as validation is concerned we can decide the error threshold
based on our expectation of the noise level there, and use Kalman filter to get better tem-
perature readings.
Figure 7-17 Temperature Reading Validation
Now let us see how the routine reacts when temperature limit is reached. The temperature
limit is 45
0
C. We take the battery and ambient temperature to be initially at 42
0
C to re-
duce the simulation time.
The routine takes action based on its predicted temperature 10 sec ahead if it happens that
after 10 seconds the temperature limit will be reached the routine takes action in time;
making the charging process more safer. In this report, what is done is to halve the charg-
ing reference current to culminate the temperature rise. But if the BMS happens to reduce
the current reference, then the charging current reference will follow that of the BMS’s.
Scenario I: when temperature limit is reached and the BMS did not take action (the BMS
malfunctions)!
0 5 10 15 20 25 30 35 40
25
25.5
26
26.5
27
27.5
28
Time(sec)
Temperature(0C)
Battery Temperature
noisy measurement
predicted
actual value
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Figure 7-18 Temperature monitoring, Scenario I
We see the limit reaches twice consecutively as the result the current reference is halved
twice.
Scenario II: when temperature limit is reached and the BMS did take action a bit latter
0 10 20 30 40 50 60 70 80
42
42.5
43
43.5
44
44.5
45
45.5
Time(sec)
Temperature(0C)
Battery Temperature
predicted
actual value
0 10 20 30 40 50 60 70 80
0
50
100
150
200
Time(sec)
Current(A)
Reference Currents
from BMS
From Optimization routine
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Figure 7-19 Temperature monitoring, Scenario II
Here the temperature is reached the BMS have not taken action; the TMR decreases the
reference current. Then the BMS takes action and reduces the reference current and the
TMR follows.
Scenario III: when temperature limit is reached and the BMS did take action in time.
0 10 20 30 40 50 60 70 80
40
41
42
43
44
45
46
Time(sec)
Temperature(0C)
Battery Temperature
predicted
actual value
0 10 20 30 40 50 60 70 80
0
50
100
150
200
Time(sec)
Current(A)
Reference Currents
from BMS
From Optimization routine
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Figure 7-20 Temperature monitoring, Scenario III
0 10 20 30 40 50 60 70 80
40
41
42
43
44
45
46
Time(sec)
Temperature(0C)
Battery Temperature
predicted
actual value
0 10 20 30 40 50 60 70 80
0
50
100
150
200
Time(sec)
Current(A)
Reference Currents
from BMS
From Optimization routine
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7.2.5
Minimum current Generation Routine
Figure 7-21 Minimum Current calculation
Here the charging current from the BMS is low compared to the capacity of the battery.
And it takes unreasonably long time when fast charging is considered. Therefore the rou-
tine calculates the minimum current which results in the required charge level within the
time slot of fast charging.
7.2.6
Output reference current coordination
In this section we will see how the reference current generation routine (RCGR) will end
the charging process. It is seen above how well RCGR has coordinated the orders from
the different routines. Let us see how it handles the double event: reaching voltage limit
and end of charge. The end of charge is reached when SOC is 85%.
Figure 7-22 shows the case when first the voltage limit is reached where by the current is
reduced then the maximum SOC level is reached which ends the charging process.
0 10 20 30 40 50 60
0
20
40
60
80
100
120
Time(sec)
Current
Current reference
BMS
Optimization routine
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Figure 7-22 Voltage limit and end of Charging
0 5 10 15 20 25 30 35 40 45 50
0
100
200
current(A)
Reference Current
0 5 10 15 20 25 30 35 40 45 50
83
84
85
86
SOC(%)
State of charge
0 5 10 15 20 25 30 35 40 45 50
370
375
380
385
Time(sec)
Voltage(V)
Battery voltage
Measured
predicted
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8
CONCLUSIONS
In this thesis a charge supervisory algorithm has been developed for an off-board battery
charger. Unlike many off-board battery chargers, a charger which is equipped with this
algorithm will be able to take some crucial decisions independent of the BMS whenever it
is necessary. This results in safe and reliable charging process.
The algorithm uses three important models to facilitate its decision making:
Battery V-I characteristic model
Battery SOC model
Battery thermal model
The model parameters are identified using the data collected during the charging process.
The identification process uses for nonlinear models the LM method and linear solvers for
linear models. In case of nonlinear models, it is found that using constrained optimization
provides a better result in terms of prediction performance and consistency of the parame-
ters. The optimization routine is executed after a specified time of interval. Executing the
routine every sample interval is both computationally intensive and unnecessary as only
slow parameter variation is expected. However for better accuracy we have to make use
of each sampled data. This is accomplished through the use of the recursive Kalman filter
which is executed during each sampling interval. This will counteract errors that occur
due to modeling and measurement.
On the other hand before accepting the new optimized parameters the error of the objec-
tive function is checked and if it is above a given threshold the old parameters are main-
tained until the next routine. The convergence problem occurs when the collected data
are not well conditioned.
The supervisory algorithm works well provided that the simplifying assumptions given in
section 6 holds true. These assumptions are necessary due to the versatility of the battery
system and without those assumptions it is difficult to carry out the objective of the thesis.
All in all, the algorithm is composed of six main routines which carry out specific tasks
and communicate to each other through parameters and status information. These routines
are
Model Identification routine (MIR)
Battery Voltage Monitoring Routine(BVMR)
SOC Monitoring Routine(SOCMR)
Temperature Monitoring Routine(TMR)
Minimum Current Generating Routine(MCGR)
Reference current Generating Routine(RCGR)
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MIR is the routine which optimizes the model parameters as mentioned above. BVMR
takes care of the battery voltage limit. It ensures in no time during the charging process
the battery voltage limit is violated. It predicts the future value of battery voltage based on
the current states and battery V-I model. A Kalman filter is used to get correct current
states which will result in a correct future battery voltage prediction. During the work it is
found that the accurate parameter tuning of the Kalman filter is very important to get sa-
tisfactory battery voltage prediction.
SOCMR checks the SOC readings for correctness or consistency and predicts the future
value of SOC if they are found to be correct. Then it provides information to other rou-
tines about the present and future status of the SOC. The SOCMR checks the readings for
correctness based the error between model predicted value and measured value. If the er-
ror is found to be above a given threshold the SOC readings are said be incorrect. The er-
ror threshold is selected based on our expectation of the noise level which the algorithm is
expected to encounter.
However the SOC prediction could be corrupted in an environment where the noise level
could be considered reasonable. This happens if the time window during which the algo-
rithm is working on is short or the rate of change of SOC is relatively slow. Thus there are
two possible solutions in dealing with this problem. Filters and longer time windows
could be used to suppress noises. On the other hand predicting SOC unlike battery vol-
tage and temperature is less important. Thus it can be avoided without having any effect
on the performance of the overall algorithm. Hence the most important task of this routine
is checking if the readings are correct or not and providing the present status of the SOC
to other routines.
TMR is entitled to make sure that the temperature readings are correct and predict the
temperature a specific time ahead to avoid any possibility of reaching temperature limit. If
it is found that the temperature limit will be reached after a given time, then the charging
current is reduced in time to reduce the temperature rise.
Unlike other models, due to the scarcity of the information on this part, thermal modeling
seems to be over simplified. Similar to the SOC prediction, temperature prediction is con-
siderably affected by noise. Similar solutions as for the SOC prediction can apply. How-
ever unlike SOC prediction, temperature prediction is important.
On the other hand, in the simulation the thermal time constant of the battery appears to be
low, this is because we want to see the prediction capability and the various events more
clearly as mentioned above. However the actual time constant is much longer. And this
would have been in favor of going for longer time window to get better noise rejection.
However, the rate of rise of temperature is usually very low; the noise might make it dif-
ficult to predict the temperature trajectory. In that respect, temperature prediction is more
important whenever something goes wrong in the battery system the rate rise of the tem-
perature is noticeable. This could be that the charging current is too high or any other rea-
sons that could result in rapid temperature rise in the battery system. However, in normal
situations it is enough to validate the readings in which case a linear model with one pa-
rameter is preferable as it will have better numerical stability and less computational bur-
den.
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MCGR is responsible to for deciding the minimum current that should be delivered to the
battery at normal conditions. This routine along with other routines make sure that the
charging time will not be unreasonably long. It ensures that all batteries will be charged to
the required level in the time frame of fast charging. In this report the time taken is 30
minutes. This time could be decreased as more information on charging capability of ac-
tual EV batteries is known.
Finally the RCGR chooses the appropriate reference current from the reference currents
generated by the routines mentioned above based on the status information supplied by
them.
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9
FUTURE WORK
Various future works based on improving this work or using the same concept to apply it
for other similar areas could be proposed. To improve this work and to make it practical
the following things need to be done.
Carry out Laboratory experiments to understand and decide
Effect of measurement noise on the algorithm; both in parameter identification,
and validation and prediction
The best prediction horizon, sample time and sample length
The exact thermal time constant of the battery and the nature of temperature rise.
The routines could be improved and additional features could be added if more practical
problems that face the BMS are known. Most of the problems discussed in this thesis are
hypothetical, such as incorrect measurements values form the BMS, occurrence of low
current references from the BMS. Of course these problems could occur but there is no
practical information on them.
It will also be possible to fix the maximum current for a given battery if the worst case
charging efficiency of Batteries are known; where the inefficiency is due to the voltage
drop on the internal resistance. Or provided that a minimum charging time exists, we can
fix the maximum charging current for a particular battery.
In this thesis the optimization routine is executed every 10 sec interval but it is possible to
execute it only when the error in the objective function is above a certain value say 1e-2.
This could result in a more computationally efficient approach.
Concerning applying the same principle in other areas, for example, for a single battery as
in a BMS, actual, meaningful parameters could be determined experimentally and varia-
tion in specific parameter can be attributed to specific condition. For example, cold crank-
ing, capacity fading etc. Thus the online optimization algorithm could play an important
role in this area. This same principle is used in [10] and [20] for lead acid battery.
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10
APPENDIX
Appendix A: The LM method
How is the initial µ value selected? How is not know in the solution is far from or near to
the final solution? Then how is µ
updated?
According to [26], the initial value µ
0
is
10-1
Where
10-2
Where τ can be any value between 1 and 1e-6 depending on how far the initial parameter
values are from the final value. For good initial guess it is 1e-6 [26].
After each iteration µ is updated as follows:
Given f(x+h) as in
Fel! Hittar inte referenskälla.
, where in this case
10-3
The updating is controlled by the gain ratio which gives us an indication to how far from
the final solution we are. This is given by:
10-4
From 4-11 and 10-3
10-5
If is small (may be even negative), then L (h
lm
) is a poor approximation, and we should
increase µ with the two fold aim of getting closer to the steepest descent direction and re-
ducing the step length. In [26] the following is algorithm is used
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10-6
Any Iterative process needs stopping criteria. Then what are the stopping criteria
for this process?
Well, there are three stopping criteria [26] based on different requirements on involved
parameters.
The global minimizer should reflect that F’(x*) =g(x*) =0, therefore it is required that the
maximum in norm of g i.e. ||g||
∞
should as low as a given low value ε
1
∞
10-7
Another relevant Criterion is to stop if the change in x is small
10-8
The final stopping criterion is the number of maximum iteration
10-9
More information can be found at reference [26] and its Matlab implementation can be
downloaded from the author’s website http://www2.imm.dtu.dk/~hbn/Software/.
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APPENDIX B: MATLAB FILE DOCUMENTATION: THE INTELLIGENT CHARGER
TOOLBOX
All in all this is just a rough introduction to the role of individual functions defined in dif-
ferent M- files, for the actual implementation and further information consult the model
files and M-files where the function is defined.
The overall Matlab files can be grouped into two categories
Those involved in with the converters only; without the supervisory algorithm(Converter
related files)
Those which deal with the charging circuit along with the supervisory algorithm (SA)(SA
related files)
Let us see them one by one.
Converter Related Files
The user can use this simulation files to study the different characteristic of the converter
circuit. The files are only ‘mdl’ Matlab files, the different parameter values used in them
are defined in file > model properties > call backs > InitFcn. The files include
Buck_Boost.mdl:- which is the simulation model of the Buck-Boost converter along with
its control circuit.
VSC_BuckBoost_Approach_I.mdl:- this is a simulation model of the whole charger cir-
cuit including the VSC, Buck boost converter and their control system. In this simulation
model the starting mechanism mentioned as approach I in section 5 is used
VSC_BuckBoost_Approach_II.mdl:- is similar to the above model but the starting me-
chanism described as approach II in section 5 is implemented in this model
SA Related Files
These files simulate and can be used to study the performance of the SA algorithm. These
contain both ‘mdl’ and M- Matlab files. These files are comparatively numerous. We
have two ‘mdl’ files from where the simulation is launched:
Intelligent_Charger_CCS.mdl:-Here the controlled current source is used in place of the
charging circuit
Intelligent_Charger_Buck_Boost.mdl:- In here the buck-boost DC/DC converter is used
to simulate the charging circuit.
From the mdl files the OptMF () S-function is launched.
The Main Optimization Function (Optmf () Function)
B.3.1
General
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This is an S-function from which the different routines are called and coordinated. It sam-
ples the measured data at user specified sample interval and stores user specified sample
length data. The measured data includes battery current, voltage, temperature and SOC.
This data will be used for building the different models and making decisions whenever
necessary. It also accepts information and requests related to the battery. The information
includes the maximum voltage and temperature, and the start signal while the request is
the amount of charging current it should provide. It outputs the optimum reference current
to the battery and the different information signals to the user. This information signals
include the model parameters for each model, the predicted battery voltage, temperature
and SOC level.
Inside the S-function
The main tasks carried out inside the S-function are
Initialization
This initialization can be seen in two ways:
S-function initialization: - this includes determining the number of inputs, output and state
variables. This is done in ‘mdlInitializeSizes’ which usually the case in S-functions.
Simulation variable initialization: this includes initializing model and other parameters.
This initialization is done inside mdlUpdate function. The model parameter initialization
is carried out by calling prepare_data() function.
Model Parameter Optimization
This part is responsible for calculating the model parameters and is executed at an interval
which is set by the user. Different set of functions are involved in parameter identification
of each model.
Functions involved in parameter identification of V-I battery model:
A good approximate value of the internal resistance could easily be found whenever a
step in current occurs. Using this value, the rest of parameter identification can be done
using SMarquardt_M() function.
The ‘SMarquardt_M.m’ M-file: - this function is taken from
http://www2.imm.dtu.dk/~hbn/Software/ is slightly adapted to problem at hand. A call to
SMarquardt_M(), provided that enough data is gathered, will optimize the parameter of
the battery V-I model. This function gets the measured data, a vector which contains algo-
rithm related values and the initial values of the battery V-I model parameters. The model
parameters are passed as structure of matrices. This function uses the help of the follow-
ing functions to carry out its duty.
The ‘extract.m’ since the actual optimization works in parameter vectors rather than ma-
trixes. Thus ‘extract.m’ extracts parameter vectors that need to be optimized from the ma-
trix passed to SMarquardt_M ().
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The ‘subopt_M.m’ M-file: - this is where the objective function for V-I battery model is
defined.
‘update_mat.m’ once the parameters are optimized, the original matrices of the model are
updated using the update_mat () function.
Functions involved in parameter identification of SOC of the battery model:
The ‘soc_par.m’ M-file: - a call to soc_par () with appropriate inputs will optimize the
SOC model parameters of the battery.
Functions involved in parameter identification of thermal model of the battery:
The ‘Tdq_par.m’ M-file: - a call to Tdq_par() with appropriate inputs will optimize the
thermal model parameters of the battery. The following two functions are called within
this function to carry out the task.
temp_es(), found in temp_es M-file, is the function where the objective function for this
model is defined.
SMarquardt, found in SMarquardt M-file, uses the objective function along with other da-
ta and algorithm related inputs to solve the problem of optimizing the model parameters.
i)
Battery Voltage Monitoring
This part uses Kalman filter to adjust the current states in the model, predicts the battery
voltage, and calculates the suitable reference current whenever the predicted voltage is
found to be above the voltage limit.
For predicting the future state there by the future battery voltage it uses the function pre-
dict_st() found in predict_st.m M-file.
To calculate the suitable reference current whenever the predicted voltage goes above the
limit it uses the function cal_Iin() found in cal_Iin.m M-file.
ii)
State Of Charge Monitoring
This part of the S-function takes care of SOC related issues; checking the correctness of
the SOC provided, predicting the future value, providing the status information to other
routines. This all is accomplished by calling the function soc_routine(). Inside the
soc_routine function soc_check() is called to calculate the error between the measured
and predicted SOC values which then can be used to validate the reading.
iii)
Battery Temperature Monitoring
Here a call to temp_routine() function is made to carry out all the tasks necessary for tem-
perature monitoring. Inside the routine temp_es() is called to calculate the error in the ob-
jective function which then can be used to validate the temperature readings.
The remaining part of the mdlUpdate function contains calculates the minimum current
for a given battery as described in section 6 and produces the appropriate reference cur-
rent to the converter. Finally the different parameters computed are prepared to be output-
ted. The outputting is done by mdloutputs function which is usual the case in S-functions.
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11
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