modularized battery management systems for lithium-ion battery packs in...

IN DEGREE PROJECT ELECTRICAL ENGINEERING,SECOND CYCLE, 30 CREDITS

, STOCKHOLM SWEDEN 2016

Modularized Battery Management Systems for Lithium-Ion Battery Packs in EVs

YIZHOU ZHANG

KTH ROYAL INSTITUTE OF TECHNOLOGYSCHOOL OF ELECTRICAL ENGINEERING

Modularized Battery Management Systems for Lithium-IonBattery Packs in EVs

YIZHOU ZHANG

Master of Science Thesis in Electrical Machines and Drivesat the School of Electrical Engineering

KTH Royal Institute of TechnologyStockholm, Sweden, August 2016.

Examiner: Oskar WallmarkIndustrial Supervisor: Christian Fleischer

TRITA-EE 2016:136

Modularized Battery Management Systems for Lithium-Ion Battery Packs in EVsYIZHOU ZHANG

c© YIZHOU ZHANG, 2016.

School of Electrical EngineeringDepartment of Electrical Energy ConversionKungliga Tekniska hogskolanSE–100 44 StockholmSweden

Abstract

The (Battery management system)BMS has the task of ensuring that for the individual bat-tery cell parameters such as the allowed operating voltage window or the allowable temperaturerange are not violated. Since the battery itself is a highly distinct nonlinear electrochemical de-vice it is hard to detect its internal characteristics directly. The requirement of predicting batterypacks’ present operating condition will become one of the most important task for the BMS.Therefore, special algorithms for battery monitoring are required.

In this thesis, a model based battery state estimation technique using an adaptive filter tech-nology is investigated. Different battery models are studied in terms of complexity and accuracy.Following up with the introduction of different adaptive filter technology, the implementation ofthese methods into battery management system is decribed. Evaluations on different estimationmethods are implemented from the point of view of the dynamic performance, the requirementon the computing power and the accuracy of the estimation. Real test drive data will be used asa reference to compare the result with the estimation value. Characteristics of different moni-toring methods and models are reported in this work. Finally, the trade-offs between differentmonitor’s performance and their computational complexity are analyzed.

Key words: battery management system, electric vehicle, Kalman Filter, Li-ion battery cellmodel, state estimation.

iii

Sammanfattning

BMS (eng. battery management system) har till uppgift att se till att viktiga parametrarsasom tillspannings- och temperaturintervall uppratthalls for varje individuell battericell. Daenbattericells beteende ar icke-linjart ar det svart att bestamma cellens interna karakteristika di-rekt. Att kunna forutsaga dessa karakteristika for ett komplett batteripack kommer att en mycketviktig funktion hos framtida BMS.

I detta examensarbete har en modellbaserad tillstandsestimeringsmetod med anvandandeav adaptiv filtrering undersokts. Olika batterimodeller har studerats med avseende pakomplexitetoch noggrannhet. Efter introduktionen av olika metoder for adaptiv filtrering har dessa metoderimplementerats i en BMS modell. Utvardering av de olika metoderna for att astadkomma tillstandsestimeringhar sedan utforts med avseende padynamisk prestanda, krav paberakningskraft och noggrannhethos de resulterande estimaten. Data fran uppmatta kordata fran ett fordon har anvants som ref-erens for att jamfora de olika estimaten. Slutligen presenteras en jamforelse mellan de olikatillstandsestimeringsmetodernas prestanda nar de appliceras pade olika batterimodellerna.

Nyckelord: BMS, elbil, Kalmanfiltrering, litiumjonbatterimodell, tillstandsestimering.

v

Acknowledgements

The present thesis was carried out at National Electric Vehicle Sweden.

First, I would like to thank my industrial supervisor Dr. Christian Fleischer for giving methis opportunity by offering such an interesting and challenging topic. Second, I would like toexpress my gratitude to my examiner Dr. Oskar Wallmark for giving me feedback from time totime and guiding me in the right direction.

I would also like to thank all my collegues in NEVS for sharing their knowledge and givingfeedback on my thesis work. Furthermore, I would like to thank to all my friends for supportingme all the time and for the good time we had together during my master study period.

Yizhou ZhangTrollhattan, SwedenAugust 2016

vii

Contents

Abstract iii

Sammanfattning v

Acknowledgements vii

Contents ix

1 Introduction 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Presentation of NEVS . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.3 Battery Management System . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Motivations and Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Li-ion Battery Cell Equivalent Electric Circuit Model 5

2.1 lntroduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 The Rint Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.3 The RC Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

ix

x Contents

2.4 The PNGV Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.5 The Thevenin Model (First Order RC Model) . . . . . . . . . . . . . . . . . . 8

2.6 The DP Model (Second Order RC Model) . . . . . . . . . . . . . . . . . . . . 9

2.7 Varied-parameters’ Electric Circuit Model . . . . . . . . . . . . . . . . . . . . 10

3 Methods For the Battery State Estimation 13

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.1.1 Definition of SOC . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.1.2 Definition of pack SOC . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2 Methods for the SOC estimation . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2.1 Ampere-hour counting . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2.2 Open Circuit Voltage related SOC estimation . . . . . . . . . . . . . . 16

3.2.3 Adaptive Filter SOC estimation . . . . . . . . . . . . . . . . . . . . . 17

3.3 Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.4 Advanced Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.4.1 Extended Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.4.2 Unscented Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.4.3 Central Difference Kalman Filter . . . . . . . . . . . . . . . . . . . . 24

3.4.4 Square Root Unscented Kalman Filter . . . . . . . . . . . . . . . . . . 25

3.4.5 Square Root Central Difference Kalman Filter . . . . . . . . . . . . . . 27

3.5 Particle Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.5.1 Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.5.2 Resampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

Contents xi

4 Experiment and simulation set up 29

4.1 Experiment set up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.1.1 Test and Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . 29

4.1.2 Test run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.2 Simulation set up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5 Experiment Result and Discussion 41

5.1 Comparison between different electric models . . . . . . . . . . . . . . . . . . 41

5.1.1 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.2 Comparison between different estimation algorithms . . . . . . . . . . . . . . 47

5.2.1 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.3 Practical case with poorly initial value . . . . . . . . . . . . . . . . . . . . . . 51

5.3.1 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . 51

5.4 Multiple driving cycles estimation . . . . . . . . . . . . . . . . . . . . . . . . 54

5.4.1 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . 54

6 Conclusions and further work 57

6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

6.2 Further work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

A Matlab Battery State Estimation Graphic User Interface 59

B Kalman filter related algorithms 61

References 67

xii Contents

Chapter 1

Introduction

The background knowledge along with the motivation behind this project will be presented inthis chapter. At the same time, the goal and the expectation of the thesis outcome will also begiven

1.1 Introduction

1.1.1 Presentation of NEVS

National Elctric Vehicle Sweden (NEVS), was a relatively new car manufacture which acquiredthe main assets of SAAB Automobile in 2012. In order to tackle the global warming problemand lead to a more sustainable future, NEVS dedicated itself into electric vehicle industry withpassion and confidence. The headquarter of NEVS located in Trollhattan, Sweden, with anautomative factory and a global R&D center. Aside from that NEVS also owns a customerexperience center in Beijing, a new manufacture in Tianjin Binhai High-Tech zone which intendto have the capability to produce 100,000 cars per year and a R&D joint venture also in Tianjin.Right now the company has 800 employees in Sweden and another 500 in China.

1.1.2 Background

The global warming of the world is becoming one of the most important environmental issuesall over the world and also a key reason leveraging the large scale adoption of EV [1]. The newautomobile industry products, hybrid electric vehicles (HEVs), pure battery electric vehicles

1

2 Chapter 1. Introduction

(BEVs), and fuel cell vehicles (FCEVs) are the future direction in transportation sector, and letmost of the leading car manufactures all over the world start researching and producing suchpromising cars[2]. Road transportation contributes to nearly half of the world’s oil consumptionin 2009 and may keep increasing up to 60% in 2035 [3]. The transportation sector contribute upto 19.0% of the world’s CO2 emission making it one of the principle targets in order to mitigatethe climate change and reduce green house gas emissions [4].

The traction battery which directly provides the energy to a BEV is one of the most impor-tant components in this industry and it will definitely attract even more attention in the future.Considering the high power and energy density, good temperature characteristics, good con-sistency, no environmental pollution and reliability (long lifetime) profile of the lithium-ionbatteries which has let it become the most favorable choice for HEVs and BEVs [5] [2]. Whenwe use a Lithium-ion battery to generate traction power, a battery management system (BMS)is needed in order to track and monitor the battery condition[6]. The BMS can prevent irra-tional use of the battery and also can prevent dangerous situation happens. By using the datacollected from the sensor it can also estimate other useful information of the battery to controlthe behavior of the battery to maximize its performance and expand its lifetime [2].

1.1.3 Battery Management System

Quoting Dr. Frank Toolenaar ”Battery management involves implementing functions that ensureoptimum use of the battery in a portable device.” [7] The most fundamental tasks of a BMS isto limit overcharge and undercharge in the cells, ensure that the cells in the pack are balancedand maintain a safe operations of the pack [8]. In order to achieve these tasks, several functionscan be performed:

• Battery State Estimation. Track the battery’s internal state variable to prevent dangeroussituations to occur and use the estimated value to control the dynamic behavior of thebattery (during charging phase, control the charging strategy with practically no over-charging to expand the lifetime of the battery; during discharging phase, detect the emptycell in advance to avoid over discharging.). At the same time send the signal value tothe user as a notification. To have a full impression of the battery’s state we will expandstate estimation from SOC to state of energy, SOH, internal resistance, available power,remaining of life and so on [2][8].

• Battery Balancing. Cells in series connection naturally become unbalanced and remainso unless a balance action is taken. Since the balancing issue may have a big effect onthe battery life and remaining available power, a well designed BMS should be equippedwith an equalization function. The balancing strategy includes passive balancing, active

1.2. Motivations and Objectives 3

balancing or both. Technically, passive balancing methods use passive electrical compo-nents(resistor, capacitors and inductors) and active balancing method use active DC-DCconverters to achieve battery equalization [2][8].

• Battery Safety Management. As the most significant and fundamental requirement of theBMS, safety issue regarding to preventing over-charge, over-discharge, over-heating andover-current will be fully controlled by a central controller. Apart from that a diagnosticalarm equipped with high voltage interlock is also embedded in the system [2].

1.2 Motivations and Objectives

The BMS has the task of ensuring, that for the individual battery cell parameters such as theallowed operating voltage window, or the allowable temperature range are not violated. Be-cause that each individual battery cell of the battery pack must be connected, which results ina high cabling requirements which complicates the design and building of the pack. The modu-larization of BMS is therefore describe with the overall aim to develop easy to install units foreach cell. Various implantation options have to be evaluated regarding efforts and functionality.In order to fulfill the final goal of the project, we formulated the following subgoals. Duringthe process of finishing these sub-targets we will approach to our final destination. These havebeen formulated in such a manner that once one is completed, it should make a distinguishableprogress.

• Compare different battery models used in EVs/HEVs currently and choose a proper elec-tric circuit model which can properly represent the dynamic characteristic of the batterycell.

• According the cell thermodynamics properties, the battery cell open circuit voltage canbe a good indicator of the cell SOC need to be determined [9].

• Give the equation to describe the relationship between voltages, currents and parametersof the model.

• Compare different estimation methods in terms of computing power and computing errorto choose proper monitor approach.

• Implement a Kalman filter based method to estimate pack average SOC and simplifiedKalman filter based method for SOC determination. Draw a flow chart of the dual time-scale estimator to easily explain the procedure of the monitor.

4 Chapter 1. Introduction

• Set up a group of experiments to test and verify the feasibility and performance of thedesigned BMS.

• Analyze the experimental result and compare different scenarios.

1.3 Thesis Outline

Here is how this thesis report organized:

• Chapter 1 Introduction of THE thesis and a presentation of its background and motiva-tion.

• Chapter 2 Investigation of different battery electric circuit models.

• Chapter 3 Introduction of the core estimated algorithm and how to integrate it into theBMS system.

• Chapter 4 Introduction of the experiment and simulation set up.

• Chapter 5 Detailed description of how to estimate battery states and experimental results.

• Chapter 6 Conclusions and further work.

Chapter 2

Li-ion Battery Cell Equivalent ElectricCircuit Model

In this chapter, four different electric models to simulate a battery cell will be introduced andthe layout of the corresponding electric circuits will also be given.

2.1 lntroduction

Nowadays in order to simulate EVs, HEVs and PHEVs over whole driving cycles the need foran accurate battery model which can predict the battery characteristics fast and convenient arises[10]. The concept behind this battery model is to use measured battery values (voltage, currentand temperature) with the battery SOC employing a battery model. Based on this proposedelectric model, the battery SOC will be estimated later on. Briefly stated the accuracy and thecomplexity of the battery model will affect the estimation result of the battery SOC, capacity andSOH. Three different kinds of battery model method will be presented here: the electrochemicalmodel, the neural network model and the electric circuit model.

The electrochemical model can depict the characteristics of the battery cell which willinclude the relationship between SOC and temperature. By using such a model, an accurateterminal voltage estimate can be achieved. However the complexity of the model ask for a lotof computing power and complex the monitoring algorithms [6].

Another way to build battery models is to use neural networks, fuzzy logic, artificial neu-ronal networks, fuzzy based neural networks and support vector machines. The accuracy ofthese types of models can reach up to 3% under certain conditions [6][2]. Nevertheless, the

5

6 Chapter 2. Li-ion Battery Cell Equivalent Electric Circuit Model

computing power is quite high for these method. At the same time, it also need a large group ofdata to train the neural networks to make it more accuracy.

Electric model method is right now the most popular method to monitor the battery thanksto its simplicity and accuracy. Which only use typical electrical components to represent thebattery characteristics. Typically, the electric model is expressed in one or several equationsto correlate the input and output values and to estimate the OCV(Open Circuit Voltage) valuebased on this state space model. The estimation of SOC is incorporated in this model by itsdirect relationship with the OCV. The core of the electric model based SOC estimation is to es-timate the OCV and determine the SOC value using look-up tables. Its dynamic characteristicsand high accuracy makes this method widely used in all different kinds of electric vehicle ap-plications. However, the disadvantage of the method is that the parameter of the electric modelcan only be accurately identified for new batteries in the laboratory. Complex monitoring andestimation algorithms are needed if we want to update the parameters and this is only practicalfor simple models.

2.2 The Rint Model

The Rint model, which is depicated in Fig 2.1. Where UOC is to indicate the battery cell opencircuit voltage and R0 represent the internal resistor. However the value of the resistor will bechanged according to the battery SOC, SOH and temperature. [10].

Figure 2.1: The RINT Model [10]

2.3. The RC Model 7

UL = Uoc − ILR0 (2.2.1)

2.3 The RC Model

The RC model which is shown in Fig 2.2 was designed by the famous battery manufactureSAFT [2][10], which contains two capacitors and three resistors. The very large capacitor Cb

indicates the ample capability of the battery; the relatively small capacitor Cc is to represent thesurface effects of the battery cell; the resistance RT represent the thermal resistance; the resis-tance RE represent the cutoff resistance and the resistance RC is referred to as the capacitiveresistance. The parameters are functions of the SOC and temperature. The following equationsrepresent the electric behavior of the circuit.

Figure 2.2: The RC Model [10]

Ua =Us

Cb(Rc +Rca)− Ua

Ca(Rc +Rca)− RcItCa(Rc +Rca)

(2.3.1)

Us =Ua

Cs(Rc +Rca)− Us

Cs(Rc +Rca)− RcItCs(Rc +Rca)

(2.3.2)

Ut =RcaUa

Rc +Rca

+RcUs

Rc +Rcs

−RthIt −RcRcaItRc +Rca

(2.3.3)


2.4 The PNGV Model

The Partnership for a New Generation of Vehicles (PNGV) model shown in the following Fig2.3 which was introduced in ”Freedom CAR Battery Test Manual” in 2003 [11][2]. The re-sistance RO represents the internal resistance of the battery cell and resistance RP refer to thepolarization resistance; the capacitance CP represents the polarization capacitance, UOC is anideal voltage source. The relationship between each variables are shown below:

Figure 2.3: The PNGV Model [10]

2.5 The Thevenin Model (First Order RC Model)

The Thevenin model shown in the Fig 2.4 is one of the most wildly used model, which capturethe dynamic characteristic of the battery behavior very well. The model uses an ideal voltagesource to represent the OCV and a polarization resistance RP with an internal resistance RO. In

2.6. The DP Model (Second Order RC Model) 9

order to indicate the transient characteristics of the battery cell, an equivalent capacitance CTh

is introduced. The electric behavior of the first order RC model can be expressed as.

Figure 2.4: The First Order RC Model [10]

Uth = − Uth

RthCth

+ILCth

(2.5.1)

UL = Uoc − Uth − ILR0 (2.5.2)

2.6 The DP Model (Second Order RC Model)

Polarization effects have a big impact on the dynamic behavior of the Li-ion battery, especiallywhen the battery SOC is less than 10 or more than 80. There are actually two kinds of polar-ization effects within the battery cell. One is the concentration polarization which indicate thechange of the electrolyte concentration result from current flow. The other one is the electro-chemical polarization which indicate the transport process of the ion slow down [2]. In orderto track these two different characteristics respectively dual polarization model is introducedwhich is also know as second order RC model [10]. The model consists of a voltage sourceUOC to represent OCV value, an internal resistance RO and two RC components indicate con-centration and electrochemical polarization respectively. The model can be expressed as.


Figure 2.5: The Second Order RC Model [10]

Upa = − Upa

RpaCpa

+ILCpa

(2.6.1)

Upc = − Upc

RpcCpc

+ILCpc

(2.6.2)

UL = Uoc − Upa − Upc − UPN − ILR0 (2.6.3)

2.7 Varied-parameters’ Electric Circuit Model

Untill now the parameters of the equivalent electic circuit model have remained unchanged andobtained from a set of laboratory measurements. When we implement this method to estimatethe new battery states, it has a pretty good accuracy. However, considering the aging effect,the characteristics of the battery will change significantly [12]. This require us to update themodel parameters also during the battery operation otherwise a high inaccuracy for battery stateestimations will occur. In order to tackle this problem, we will choose a first order RC model asan example. The resistance Rth represent the internal resistance of the battery. The capacitanceC indicate the ample capability of the battery which is not a function of current. On the contrast,the resistor R0 is related to the transient response during charing or discharging which is notconstant during the battery operation phase and can be described by the Butler-Volmer equation[12][13].

R0(IL) = R0(ln(kiIL +

√(kiIL)2 + 1)

kiIL) (2.7.1)

2.7. Varied-parameters’ Electric Circuit Model 11

Where R0 is the resistance value when IL = 0, ki describe the current dependence of theresistance.

Chapter 3

Methods For the Battery State Estimation

In this part, we will discuss how to use the electrical model that we introduced in the previouschapter to monitor the battery states. The methods from control theory will be used here to helpus improve the efficiency and the dynamic performance of the model based SOC state estimationand at the same time make the estimation possible when complex models are implemented [6].By introducing this technique, closed-loop estimation can be realized wherein the deviationbetween the modeled and measured battery terminal voltage is used for the correction of theestimation states and at the same time we can minimize the estimation error within some extents.

3.1 Introduction

Since the battery is an electrochemical devices with an extremely complex behavior and itsdistinct nonlinear behavior depend on several internal and external conditions, estimating theirstates will become a challenging task. Considering the complexity and difficulties of the batterywe will choose several important data which may have big impact to the EV drivers or related tothe safety issues to do the state estimation. State of Charge (SOC) in EVs serves a similar rolein that of the petrol gauge in the traditional internal combustion car. In that case the accuracyof the estimated SOC value will have a big impact on the optimization of the vehicle control.At the same time, effectively estimating state of charge of the battery can prevent the cell fromover heating, overcharging, over-discharging, or over current which will, in turn, increase thelifetime of the battery and ensure the safety during its use.

13

14 Chapter 3. Methods For the Battery State Estimation

3.1.1 Definition of SOC

As mentioned before, the SOC of the battery in EVs can be employed as fuel gauge used inconventional vehicles. In theory, the SOC imply the ratio of the remaining capacity (Qrem) andthe nominal capacity Qnor:

SOC =Qrem

Qnom

× 100% (3.1.1)

The capacity that the battery discharges from the present state to the fully discharged state willbe called remaining capacity. In terms of the nominal capacity we will ran a test experimentlet the battery self-discharge from the full state to zero state. In practical it is hard to determinethe zero state of the battery. Here, we will use the open circuit voltage value as an indicator tojudge whether the battery is fully discharged/charged or not. In another way, the SOC can beexpressed as the following equation [14]:

SOC = SOC +η∫tt0i(τ), dτ

Cn

(3.1.2)

where i(τ) represents the value of current (defined to be positive for charging and negative fordischarging), η represents the Coulomb efficiency, Cn represents the nominal capacity.

3.1.2 Definition of pack SOC

Consider the power and energy requirements of the BEVs and HEVs, the battery pack is usuallycomposed of multiple battery cells series or parallel connected. Parallel connected battery unitscan provide higher available capacity to meet the desired settings. Since for cells connected inparallel, a self balance characteristic exist, we can simply regarded the battery module to a singlecell with a higher capacity. Just as how we define the single cell battery SOC, the pack SOC canalso be defined as the remaining available capacity of the pack as a percentage of the nominalcapacity of the pack. If we want to estimate the pack SOC, we firstly need to get to know thetopology of the battery pack and analyze into two different categories: series connection andparallel connection. When the cells are in series, we have to taken into account the differencesbetween cells and the balance strategy that the BMS provides. Three different balance strategywill be discussed below: no balance, passive balance and active balance [14][15].

No Balance

When there is no balance strategy implemented on the battery packs, the capcity of the packwill be limited by weakest battery cell [14]. When one or some of the cells is fully discharged

3.1. Introduction 15

during discharging phase, even though some of the other cells may still have some remainingcapacity but as a matter of fact the pack cannot be discharged anymore considering the safetyissues and the lifetime of the battery. Similar during charging phase, when one or some of thecells are fully charged and some of the cells still have capacity available the pack still need topause the charging. Thus, the total capacity of the pack is:

Cpack = min(Cr) + min((1− SOC)Cnom) = Cmin−r + Cmin−c (3.1.1)

Here Cpack is the pack capacity and Cr represent remaining cell capacity. SOC is the cell currentstate of charge and Cnom is the cell nominal capacity. In that case, the SOC of the pack will begiven as:

SOCpack =Cmin−r

Cmin−r + Cmin−c

(3.1.2)

Passive Balance

Generally speaking, the difference between active and passive balancing is based on how theenergy flow within the cells. In terms of passive balancing, we will add an external circuit todissipate the remaining energy of the highest SOC cells. In most of the cases a resistor is thecheapest and easiest way to dissipate this energy. Which means the designer have to choose anappropriate resistor to integrate into battery pack [7][14]. Which result in:

SOCpack = SOCcell = SOCmin−cell (3.1.3)

The advantage of passive balancing over active is that it is much cheaper, which makesit the most wildly used method in automotive applications. However, the drawback of this ap-proach is that when we using a resistor to dissipate extra energy it will transfer to heat. In thatcase we need to take in to account the increasing of the temperature do not violate the safetytemperature window. Another difficulty of the passive balancing strategy is that it needs moretime to tackle the problem than using active balancing method[7]. At the same time passivebalance control only exist during charging phase.

Active Balance

In active balancing system, the excess energy will be transfer within different cells in order toachieve the equalization. It normally needs an active switch and several capacitors to fulfill thisrequirement which of course cause more money and also need extra space within the pack [16].Another challenge is that the electronics device must also be attached to each cell or integrated


in the slave boards for a group of cells. Thus, the pack SOC is:

SOCpack =

N∑i=1

SOCiCi

N∑i=1

Ci

(3.1.4)

3.2 Methods for the SOC estimation

SOC in EVs is treated as fuel gauge used in traditional internal combustion vehicles. The de-termination of the battery SOC is always an important job for the BMS. Untill now, there are awide range of methods proposed in the literature to tackle this problem. The most and widelyused method are given below.

3.2.1 Ampere-hour counting

Ampere-hour counting method can also be denoted as Coulomb counting method which liter-ally means ”counting the charge flowing into or out of the battery” [17]. When we can get accessto the initial SOC value and the battery capacity. Simply measure the input current and do thetime integral, then we can calculate the battery SOC. Since the battery is an electrochemicaldevice and the complexity of the battery behavior, we still need some other variable to com-pensate the counter. For instance, the charging efficiency, discharging efficiency, self dischargephenomenon, capacity loss and aging effect [17]. Which not only increases the difficulty of es-timation but also decreases the accuracy of the whole method. Apart from that considering theerrors will accumulate over time in an Ampere-hour counting method, recalibration is neededfrom time to time. Which will let the driver come across a lot of inconveniences especially whenthe car indicate a relatively well enough energy, but as a matter of fact it only has limited energyleft.

3.2.2 Open Circuit Voltage related SOC estimation

The OCV (Open Circuit Voltage) has a direct relationship with the battery SOC, which is not thefunction of the battery’s temperature and age. This has been proved by several practical experi-ments [17]. In order to have an accurate SOC estimation, we need to get access the ”pure” OCVvalue which is known as EMF (Electro Motive Force). The difference between OCV and EMF

3.3. Kalman Filter 17

is: any battery voltage measured under open circuit condition is called OCV, the equilibriumbattery voltage at the end of OCV relaxation is called EMF [6]. Right now, there are actuallyseveral ways for accessing the value of EMF: voltage relaxation (after current interruption thebattery open circuit voltage will take some time to relax to the EMF. But it is really hard todetermine when the battery is fully relaxed.); Linear interpolation (using the same currents tocharge and discharge the battery to find two OCV value and the EMF is the average of thesetwo value. But in most of the real cases, this methods become impractical since the battery isnot attached to a charger all the time.); Linear extrapolation. However, all these methods maysuffer from aging of the battery since the parameters of the battery may change significantly.

3.2.3 Adaptive Filter SOC estimation

Considering the complexity and uncertainty of both battery and user behavior. We can introduceadaptive filter technology from the control theory to realize the non-linear state estimation.Battery behavior depends strongly on a lot of conditions, say: aging effect, temperature, driverbehavior and also the manufacturing process. The basic theory behind this is using availablemeasuring variables Iinput, Uterminal and Tb as input to estimate battery behavior and conditionby integrating battery model into this. The output will be the estimation value that we need totrack for example the battery SOC, available capacity or the available power. The advantage ofusing adaptive filter technology is that it can provide battery state accurately and continuouslyduring battery operation. However the main drawback that limit the use of this method is itshigh demand on computing power. But with the fast development of microprocessors whichwill make it more and more popular to implement this method into automobile application. Inthis thesis report, we will focus on this method.

3.3 Kalman Filter

The Kalman filter which was first developed by Rudolf E. Kalman in 1960 and is a well cele-brated theory using the state space formulation of a linear systems. It is an efficient way to solvelinear optimal problem recursively[18][19]. It can be used not only in stationary environmentsbut also in non stationary environments. Kalman filters provides an efficient and easy methodsfor predicting current state value of a dynamic system. Generally speaking, the state within thebattery cells is always related to the past and present inputs or outputs. So the state of the batterycan be estimated by the Kalman filter.

In order to implement a Kalman filter, a dynamic model which uses several internal statevariables of the battery is necessary to estimate the battery state. The detailed battery electric


model has already been given in Chapter 2 following with the state space equation of the model.In this chapter we will use first order RC model as an example to show how we implementKalman Filter to estimate the battery SOC. The first order RC model which consists of aninternal resistance R0 with one RC element in series. In order to determine the value of theparameter, we will implement least squares methods so as to minimize the error between themodel output and experimental outcome [20][21][22]. The following discrete time equationsdepict the relationship of the battery SOC, terminal voltage of the cell and three parameters inthe first order RC model.

Here k is the discrete time index, Vt is the terminal battery voltage, η is the Comlumbicefficiency, Cnom is the nominal capacity of the battery cell and I is the battery input current.

Normally former is called the state equation. The state equation which can represent thestability , controllability and also sensitivity to disturbance of the triggered dynamic system.Here xk ∈ Rn represent the state that we want to estimate. The input of the system is uk ∈ Rp

which in most of the case is the measured value we obtained from the sensor. yk ∈ Rm indicatethe output of the system which is also the measurement value in most of the cases to correctthe estimated value. wk ∈ Rn and vk ∈ Rn is the noise of the system, in some referencesit also called “disturbances” [20][19][18]. The matrices A ∈ Rn×n, B ∈ Rn×p, C ∈ Rm×n,D ∈ Rn×p represent the dynamics of the system. Note that in practice these matrices mightchange with each time step but in order to reduce the complexity, here we assume they remainconstant all the time. Another thing need to be mentioned here is both wk and vk are zero-meanwhite Gaussian stochastic process, and the error covariance matrices are Q and R, respectively.Actually the condition we set here is hard to met in real applications, but the experiments showsthat the Kalman filter based methods work well in battery state estimation [23].

3.3. Kalman Filter 19

Here we define x−k ∈ Rn (known as super minus) to be a priori state value priori to timestep k, and xk ∈ Rn to be a posteriori state estimate at step k using measurement value ykto update the previous estimated value. The estimate errors of the priori and posteriori can beshown as:

e−k = xk − x−kek = xk − xk

The error covariance can be represented as:

P−k = E[e−k e

−Tk ]

P−k = E[eke

Tk ]

And E[.] is defined as:

E(x) =n∑

i=1

pixi

Where x1, x2, x3...xn is the outcomes with its corresponding probabilities p1, p2, p3...pn [24].The step by step Kalman Filter algorithm can be found in the Appendix B Fig B.1.

The core of this algorithm is to predict the state value in advance and obtain feedback inthe form of measurement. As a matter of fact, Kalman filter contains two fundamental steps:time update or prediction update step and measurement update or observation update step.The first step is by using prior state estimate as calculated in the previous iteration, ˆxk−1 anderror covariance Pk−1. The calculation of this step do not need any measurement value in ad-vance. The second step is measurement update which take care of the feedback-for incorporateknowledge gained from the measurement value to improve the previous estimation. At the sametime this will also be the value that we will use to report the real state of the battery say SOC orSoH [20][24].

The initial value of the filter is according to the previous calculation or recorded informa-tion in the RAM. In most of the practical cases the initial value cannot be precisely predictedand collected. But the robustness characteristic of the Kalman filter will help us handle the poorinitial issues which will be shown in the next chapter.

x0 = E[x0]

Px,0 = E[(x0 − x0)(x0 − x0)T ]

After the initialization process, the Kalman filter will repeatedly perform two steps updateand this recursive nature makes it very appealing since the implementation becomes feasible.


The time update step calculate the estimated state value for the next measurement point.

x−k = A ˆxk−1 +Buk

Then the state error covariance will also be updated:

P−k = APk−1A

T +Q

In theory, the uncertainty (error covariance) will decrease to zero when the system is stable, butthe process noise term Q will increase the uncertainty since wk can not be measured and predictand makes it hard to analyze how it affect the result.

Then, we will come to the measurement update step in order to calculate the value ofposteriori state xk.

xk = x−k +Kk(yk − Cx−k −Duk)

As we can see from this equation, the updated state is based on the predicted state that we findin the previous step plus a weighted correction factor yk − Cx−k − Duk part is the differencebetween the real measurement value and the estimated measurement value which can be calledthe measurement innovation. If the innovation is zero this indicates that the real and estimatedvalue have no difference. The weighted factor shown in front of the innovation value is theKalman gain vector Kk which is chosen to be the corrected factor that minimizes error [25].

Kk = P−k C

T (CP−k C

T +R)−1

Finally is the measurement error covariance step:

Pk = (I −KkC)P−k

Consider there is new information coming from the measurement the state error covariancewill always decrease. Figure 3.1 below gives a detailed flow chart of how the Kalman filterrelated estimator implemented on the battery monitoring system to estimate the state of thebattery cell. In a word the Kalman filter provide a robustic, automatic and time efficient approachto estimate dynamic system’s state using limited input output. [20][26][16]. Another importantissue that needs to be addressed here is that the recursive nature and the demand for matrixoperations makes Kalman filter based technology easy to embedded on microprocessor chips.

3.4 Advanced Kalman Filter

As we mentioned before, the Kalman filter estimates the state of a dynamic system using a lineardiscrete time state space model. In order to handle more strict environment which addressed anonlinear dynamic model, the extension of the Kalman filter may become necessary.

3.4. Advanced Kalman Filter 21

Figure 3.1: Flow chart of how Kalman filter estimator estimate the state of the battery cell


3.4.1 Extended Kalman Filter

The extended Kalman filter(EKF) which using Taylor series to linearize the nonlinear statespace equation and transform the nonlinear problem to linear problem [19][20][24]. Here, wewill define the nonlinear system as:

The same as what we define in the Kalman filter, the random variables wk and vk are againzero-mean white Gaussian stochastic process and the error covariance matrices are Q and R,respectively. Instead of keeping error covariance matrices Q and R constant as what we didin the Kalman filter, we will update this matrix with the time step k in the EKF algorithm.Non-linear function f indicate the relationship between previous state and present state. Non-linear function h indicate the relationship between measurement value and state value. Here,we assume that at all operating points both f and g are differentiable in order to implement firstorder Taylor-series expansion.

Then, we can rewrite the equation (3.4.2) as:

where xk and yk represent real state and measurement value. xk represent the posterioristate at time step k. wk and vk represent process and measurement zero mean white Gaussianstochastic noise respectively. A, B, C, D is the Jacobian matrix.

The whole steps of the extended Kalman filter can be described in the Appendx B Fig B.2.


However, since the EKF use Taylor series to transform the nonlinear problem to a linerproblem which does not consider state vector x has its inherent uncertainty. Which has a largeimplications on the dynamic performance of the EKF related state estimation [27][28]. As amatter of fact the EKF is not the only possible way to solve the nonlinear dynamic system stateestimation method. In particular, sigma point Kalman filter and particle filter can also give analternative to provide even better accuracy.

3.4.2 Unscented Kalman Filter

Considering the EKF based estimation method naturally has some shortcomings. These estima-tion will result in decreasing of estimation accuracy and leading to unstable filters. In stead ofusing Taylar series linearization method. Sigma point Kalman filter will use a small fixed groupof function to linearize the nonlinear state space equation and transform the nonlinear prob-lem to linear problem [29][30]. A random variables will be carefully chosen to be the samplepoints to represent the state vectors. The requirement of these chosen sample points is that themean and error covariance of these sample points are exactly the same as the mean and errorcovariance of the priori state variable.

Before the introduction of Unscented Kalman filter, we will introduce the unscented trans-formation first. Specifically we define a function y = f(x) with an input variable x has adimension L. The mean value and error covariance of the state x are x and Px respectively.We will formulate a matrix X with 2L + 1 sigma points in order to fulfill the requirements wediscussed in the previous paragraph.

The λ = α2(L+ κ)−L is a scaling parameter. 2L+ 1 indicate the total (which is also theminimum) number of sigma points that needed to fulfill the requirement that mentioned above.Where the constant α is normally set to be a small positive number. In our application we defineα equals 1. The κ is determined by 3 − L and β normally equals to 2 [31]. Using these sigmapoints as the input of the non-linear measurement equation we find:

Here we will use a weighted posterior sample points’ mean and error covariance to approx-imately calculate the mean and error covariance of the measurement value y.


Where weights Wi are determined by

Another thing need to be addressed here is that when we derive the sigma points we haveto calculate the square root of covariance. In order to reduce the complexity of calculation wecan implement Cholesky decomposition here. Considering a matrix square root R =

√Px, if

the matrix Px is a positive defined matrix than it can be represented as P = RRT . The goodside of this method is that R is a lower triangular matrix. The whole steps of the UKF can befound in the Appendx B Fig B.3.

3.4.3 Central Difference Kalman Filter

As we mentioned before the difference between each Sigma point kalman filter (SPKF) is howthey choose the sigma points. The UKF will choose a fixed number of sample points to trans-form the nonlinear problem to linear problem. The requirement for these points are their meanand error covariance value are exactly the same as prior state variable’s. However, the centraldifference Kalman filter(CDKF) use a different method to generate the sigma points. Sterling’spolynomial interpolation method will be used here instead of using Taylor series [32]. The same


as what we did in the UKF, we will draw 2L+ 1 sigma points from the prior state variable x.

X0 = x (3.4.1)

Xi = x+ (√h2Px)i, i = 1, .....L, (3.4.2)

Xi = x− (√h2Px)i, i = L+ 1, ..., 2L, (3.4.3)

Where weights Wi is determined by

W(m)0 =

h2 − Lh2

(3.4.4)

W(m)i =

1

2h2, i = 1, ..., 2L (3.4.5)

Since the implementation of the CDKF is more or less the same as UKF, except the choice ofsample points so the detailed procedure can be found in previous UKF section. Another thingneed to be mentioned here is that the CDKF only need one extra variable to calculate the sigmapoints, step variable h, compare to the three variables (α, β, κ) that the UKF needed. And at thesame time as it shown in [33] that the CDKF literally has better dynamic performance than theUKF under some specific conditions. In terms of computation power since less extra variableare used which will increase the speed of calculation compare to the UKF algorithm. But inmost of the practical cases this difference in computation power and accuracy is not so obviouswhich indicate the SPKF has same order of accuracy and computation power. Specifically, theoptimal value for h is

√3 (for Gaussian priors) [27].

3.4.4 Square Root Unscented Kalman Filter

The reason why we want to introduce the Square root sigma point kalman filter (SRSPKF) ismainly because the normal SPKF need to calculate the matrix square root of the state errorcovariance which cost a lot of computation power and decrease the numerical stability of thewhole system. Before we introduce the SRSPKF, we will introduce three linear algebra theoriesfirst that are required to implement the SRSPKF which are QR decomposition, Cholesky factorupdating and Backsubstitution [30][27].

• QR decomposition: Assume we have a matrix A ∈ Rl×n, the QR decomposition of thismatrix can be written as:

AT = QR,

where two factors inside the equation are orthogonal matrix Q ∈ Rn×n and upper tri-angular matrixR ∈ Rn×l. Here, we assume n ≥ l and R ∈ Rl×l is the upper part of


the triangular matrix R and the Cholesky factor of P = AAT is RT , so in that caseRT R = AAT . QR decomposition can be simplified as qr. and here the return value is R.This method can be implemented in the SPKF to compute:

which can be referred as P−x,k+1 = AAT , where A =

√w

(c)i (Xx,−

k+1,i − x−k+1). Insteadof computing AAT and follow up with the Cholesky factor, we can implement the QRdecomposition ofAT here, in order to find out the R component which can help us reducethe computation complexity. And that can also applied to Py,k+1 =

∑pi=0w

(c)i (Yk+1,i −

yk+1)(Yk+1,i − yk+1)T [29][30].

• Cholesky factor updating: Assume the Cholesky factor of P = AAT is R which isa lower triangular matrix according to the Cholesky factor theory. then we can havethe Cholesky factor downdate P = P ±

√vuuT , which can be represented as R =

cholupdateS, u,±v. The algorithm that we implement here is also available in Matlabas cholupdate. The reason why we need to introduce this is because the previous methodcan not be used when w(c)

i is negative. And this can also be used in the final step to updatethe value of state error covariance.

• Backsubstitution: This was mainly used in the estimator gain matrix computation whereKk+1 = P−

xy,k+1P−1y,k+1 which can also be written as Kk+1 = P−

xy,k+1(Ry,k+1RTy,k+1)

−1.The backsubstituion is consist of two steps totally. We calculate Pxy/R

Ty and then calcu-

late Kk+1 = (Pxy/RTy )/Ry.

The initialization step for SRSPKF is the same as what we have already introduced in the stan-dard SPKF. Cholesky factor updating can be used here to reduce the computation complexity.

Xak = xak, xak + λRa

x,k, xak − λRa

x,k

During time update step, the QR decomposition is used to compute the square root priori co-variance

R−x,k+1 = qr[

√w

(c)i (Xx,−

k+1,(0:p) − x−k+1)

T ]T

Under certain conditions especially when the weight factor is negative Cholesky factor updatingwill be used instead of QR decomposition:

R−x,k+1 = cholupdateR−

x,k+1, Xak+1,0 − x−k+1, w

(c)0

3.5. Particle Filter 27

The similar two step method is applied to the calculation of the measurement error covariance,

Then the Kalman gain can simply computed by: Kk+1 = P−xy,k+1Py which can be solved

by back-substitution. The whole steps of the square root unscented Kalman filter can be foundin the Appendix B Fig B.4.

3.4.5 Square Root Central Difference Kalman Filter

Just as the difference between standard UKF and the standard CDKF, SRCDKF and SRUKFonly differs from the derivation of sigma points. What special for square root CDKF is sinceall weights are positive, Cholesky factor updating method is not necessary for CDKF. Whencompute the QR decomposition of the error covariance we only calculate in following way:

3.5 Particle Filter

When the nonlinear system is corrupted by the non- Gaussian noise or the the problem itself isnot followed Gaussian process then no matter the SPKF nor the EKF cannot worked properly.In order to tackle this problem we will introduce particle filter (PF) which based on Monte Carlosimulation and use sequential importance sampling and re-sampling to estimate the state of thedynamic system. In that case the PF can handle more strict environment than the SPKF and theEKF.


3.5.1 Monte Carlo Simulation

Before we introduce the PF, we will briefly explain the Monte Carlo Simulation first. The like-lihood of the posterior state can be calculated by a group of weighted sample points which canbe computed as:

Where δ() represent the Dirac delta function, ω(m), x(i);m = 1...N represent theweighted factor which are drawn from distribution π(x). The statistic expectation of the pre-vious likelihood can be represented by:

In that case we can rewrite the statistic expectation into:

However in most of the cases it is not practical to derive the sample points from the pos-terior likelihood. So sequential importance sampling (SIS) algorithm is needed to tackle thisproblem. Detailed explanation can be found in [32][34][27].

3.5.2 Resampling

Considering the number of sample points that we choose in the previous step will have a bigimpact on the dynamic performance of the PF. The more points that we draw the more accuracythe estimation is. However this will also cost more computing power. Re-sampling step herecan emphasize the point which has more impact on the final result and eliminate the uselessparticles. Which can be evaluated by the weighted factor w [32][34][27]. The detailed algorithmis given in the Appendix B Fig B.5.

Chapter 4

Experiment and simulation set up

In this chapter the experiment and simulation set up will be introduce and the step by stepprocedure will also be given.

4.1 Experiment set up

The real drive test is conducted at RWTH Aachen University in Germany [35]. In this thesiswork, the test data collected from these group of tests will be used. The whole test was im-plemented on a FEV eFIAT floor 500 battery electric vehicle. The measurement set up and theillustrate of the measured signals will be explained in this section. Technical data was given inthe following table 4.1.

4.1.1 Test and Measurement Setup

In order to have the real data from the vehicle, extra tools which in order to track the state of thevehicle will be added. As shown in Fig4.1. The introduction in Fig 4.1c are GPS receiver cableand USB memory stick. The explanations in Fig 4.1d are MicroAutoBox II, CAN bus coupler,IMU sensor board, connections and 5V voltage supply from left to right. Using the CAN buson the vehicle to receive the signal when the vehicle is driving. In order to locate the vehicle(monitor the driving distance and road condition) a GPS sensor is installed on top of the car. Theremaining components were housed in the trunk. For reading and storing measurement signalsMicroAutoBox II dSPICE is used. The used version here is 1401/1507 which has 4 CAN busesand two RS-232 interfaces and a USB port for storing the measured values on a USB storage

29

30 Chapter 4. Experiment and simulation set up

DriveElectric Machine Permanent Magnet Syn-

chronous MachineRated Power 45 kWMax Torque 240 NmMax rotate speed 7500 min−1

Max speed 121km/hvehicle dataWeight 1170kgTire 175/65 R14Dynamic tire radius r 0.2835mGear ratio i 6.61Cross-sectional area 2.42m2

Drag coefficient 0.325Efficiency of the the drivetrain

95.5%

BatteryManufacture of cells KokamNumber of cells 84Norminal voltage 310.8 VNorminal capacity 40 AhEnergy content 12.4 kWhUsable capacity 31.25 Ah

Table 4.1: Technical data FEV eFiat 500 [35]

device.

4.1.2 Test run

After installing the measurement hardware in the vehicle and some test drive were also imple-mented. The test drive is anonymously and totally 130 groups of data were collected with atleast 2 km route length of 51 different drivers. Overall 2547.7km covered in 103.2h. The aver-age speed of the test is around 23.37 km/h. The highest ambient temperature of the test is 24 C

and the lowest temperature of the test is 0 C. From the CAN bus we can read the news of thebattery management system, the power-train drive unit and the sensors in the low voltage. Thesampling rate is 100 ms and the memory requirements while driving is approximately 1.1 MBper minute. Table 4.2 shows the signal that the monitor will track during the experiment.

4.2. Simulation set up 31

Figure 4.1: Measurement devices set up

4.2 Simulation set up

The whole simluation work was ran on Matlab and used Recursive Bayesian Estimation Li-brary(ReBEL) toolkit to build a battery cell state estimation monitor. The ReBEL toolkit whichcontains the basic functions for state estimation, parameter estimation, joint estimation and dualestimation, we can implement a lot of applications by implemented it.

In this thesis, we will firstly build a dynamic state space model for battery cell which hasalready introduced in Chapter 2. There are totally 4 generalized state space models were builtwhich are Rint model, first order RC model, first order RC model with functional resistor andsecond order RCs model with functional resistor. The battery state estimation Matlab toolkitwas first developed by Dr. Christian Fleisher [6]. Here we will use first order RC model as anexample to introduce how the model is built.

First we have to define the dimension of the state, the observation, the parameter and soon. which can be seen in Fig 4.2:

As we can see from the previous code, in terms of first order RC model we have 5 states in


Singal Name Unit DescriptionCAN busBMS-iBatAct A current battery powerBMS-iBatChgCont A current maximum allowable charge currentBMS-iBatDchCont A current maximum allowable discharge currentBMS-rSOCAct current battery state of chargeBMS-rSOCMax maximum battery state of chargeBMS-rSOCMin minimum battery state of chargeBMS-tCellAvg C average temperature of the battery cellBMS-tCellMaxAct C maximum temperature of the battery cellBMS-tCellMinAct C Minimum temperature of the battery cellBMS-uBatAct V current battery terminal voltageBMS-uCellMaxAct V maximum battery terminal voltageBMS-uCellMinAct V minimum battery terminal voltageIPU-iAct A measured DC current of the drive unitIPU-nAct min−1 speed of the electric machineIPU-tqAct Nm torque of the electric machineIPU-uAct V measured voltage of the drive unitLV-Current A current of the low voltage networkLV-Voltage V voltage of the low voltage network

Table 4.2: Technical data FEV eFiat 500 [35]

Figure 4.2: First order RC Model variable dimension definition

total which represent the SOC, the internal resistor, polarization resistor, polarization capacitorand the voltage over capacitor. Apart from that we have one observation variable which is theterminal voltage of the batter cell. And the parameter dimension here is 3 since the modelcontains 3 parameters (internal resistor, polarization resistor and polarization capacitor). Twoinput which are the measured current value and measured terminal voltage value. Since theboth the process noise and the observation noise have the same dimension with process stateand observation state are 5 and 1,respectively. Then we need to set up the noise source forprocess and measurement which can use the default function of the ReBEL toolkit gennoiseds.Nest step is to define the non linear state space function of the battery model. The code representthe f function are given in Fig 4.3:

One thing need to be addressed here is that the we do not update the value of model


Figure 4.3: First order RC Model f function design

parameters in the SOC state estimation, so in that case we define:

R0k+1 = R0K

R1k+1 = R1K

C1k+1 = C1K

In terms of parameter, joint and dual estimation we will re-define the model which the valueof the battery parameters need to be updated. After we define the f function, we will design theh function in order to find out the difference of the estimated value and real test value. Fig 4.4shows how we design the h function.

Figure 4.4: First order RC Model h function design

Here, the function OCV = bsasoc2ocv(state(1, :)); means that we will use the relation-ship between OCV and SOC to find estimated OCV value according to the estimated SOC state.The OCV and SOC relationship that we used here is defined in the following code Fig 4.5 whichis actually a look-up tables as we can seen in figure Fig 4.6.

Figure 4.5: SOC & OCV relationship


Figure 4.6: SOC & OCV relationship

The last thing of model simulation is that we will set up the Jacobian matrix of f and hfunctions for EKF based estimation. The corresponding code is given in Fig 4.7:

Figure 4.7: First order RC Model Jacobian define

Here we only show the result of Jacobian matrix A, as a matter of fact we still need todefine the Jacobian matrix B, C and D. Until now we have almost finished build the circuitmodel.

Next, we will set up the adaptive filter algorithm in order to estimate the state of the bat-tery. Here we will take UKF as an example to show how to define and use the filter to do theestimation. First, we will define the scaling parameters of the UKF (Fig 4.8) and then set up theweighted factor for the sigma point that we will derive later on.


Figure 4.8: Unscented Kalman filter scaling parameters’ definition

Then the covariance of the noise source will be defined using Cholesky decompositionwhich is shown in Fig 4.9.

Figure 4.9: Unscented Kalman filter noise covariance set up

The sigma points will be derived according to the requirements that we mentioned in Chap-ter 3, which required these chosen sample points’ mean and error covariance match the meanand error covariance of the priori state variable. So in that case the sigma points are built ac-cording to the formula given in Chapter 3 and the corresponding code is given in Fig 4.10.

Figure 4.10: Unscented Kalman filter sigma points set up

After deriving the sigma points we will calculate predicted state mean and covariance ofthe prior state as it shown in Fig 4.11.

Until now we have already know the state mean of the prior variable. So we can take thisvalue back to h function and find out the estimated value for the measurement (In our case themeasurement value is the terminal voltage of the battery cell) the related code was shown in Fig4.12.


Figure 4.11: Unscented Kalman filter state mean and covariance calculation

Figure 4.12: Unscented Kalman filter measurement estimated value

The last step is the measurement update, where Kalman filter gain and the update statevalue will be calculate based on the difference between the estimated measurement value andreal test value. The code is given below Fig 4.13.

Figure 4.13: Unscented Kalman filter state value update

Apart from UKF which was described in this section, EKF, CDKF, SRUKF, SRCDKF andPF will also be built and used in the later validation part. Before we run the simulation we needto initialize the adaptive filter and also the state space model. Fig 4.14 and Fig 4.15 shows theintilization process.

In order to make it more easier for the user to use this tool to do some extra test or research,a graphic user interface is also developed which can be seen in the Appendix A. From the lefthand side we can choose different battery models, different estimation types (right now we onlydesign the state estimation) and filter types. In terms of the noise set up we will use the default


Figure 4.14: Initialization of the adaptive filter

noise function in the ReBEL toolkit to help us generate noise. Fig 4.16 shows how we set upthe noise for the first order RC model.

As you can see in Fig 4.16. here we will generate white mean Gaussian process noisewhich has initialized with a really small error covariance. In order to run the simulation we stillhave to upload the data of cell input current and terminal voltage. Here in order to compare theestimated SOC value with real test SOC value, we will also upload the SOC value we get fromthe real drive test to the simulation tool as well. Until now the simulation set up has finishedand we can move to the validation part.


Figure 4.15: Initialization of the state space model


Figure 4.16: Noise set up

Chapter 5

Experiment Result and Discussion

In this part of the report we will introduce how we implement EKF, SPKF and PF to estimateSOC and so on. Follow up with the simulation results and discussions.

5.1 Comparison between different electric models

In this part of the work, an Lithium-ion battery cell for electric vehicle with a nominal capacityof 40 Ah and a nominal voltage of 3.2V, is used for the comparison study of the electric modelcomparison for estimating SOC of the battery cell. More detailed information regarding to theexperiment set up was given in the previous section. In order to compare the performance ofdifferent battery electric models, several typical driving cycles will be applied. Here we willusing the data from several real driving cycles test on real city road using both aged and new cell.The first cell is a fresh new battery with real capacity 42 Ah and the cell ambient temperatureis 0 C. The test last for around 54 mins and the initial SOC value is adjusted to 100%. Thesecond experiment is implemented on an aged cell which has the real capacity reduced to 38 Ahand the cell ambient temperature is still 0 C. The second test also last 54 mins and the initialSOC value starts from 100%. The input current and terminal voltage can be found in Fig.5.1a,Fig.5.1b and Fig.5.2a, Fig.5.2b for the first and the second experiment, respectively.The samplerate for the current and voltage sensors are 10Hz during the tests[35]. The battery models thatwill be used in this section has already introduced in Chapter 2. In terms of the estimationalgorithm, square root unscented kalman filter will be used. Filter states are initialized to ratedvalue drawn from the data sheet with covariance initialized to very small values. The other thingwe have to addressed here is in all test cases, ”true” SOC we used as reference was calculatedfrom the current sensor recorded data using Coulomb counting method. So as a matter of fact

41

42 Chapter 5. Experiment Result and Discussion

the ”true” SOC is only relatively accurate since the current sensor error and the accumulatederror caused by using Ampere hour counting method[16].

5.1.1 Results and discussion

First we take a look at the result of the test which the ambient temperature is 0 C and the batteryis a fresh new battery. Fig.5.3a and Fig.5.3b show the result for the RINT model; Fig.5.5d andFig.5.3d show the results for the Thevenin model; Fig.5.3e and Fig.5.3f show the results for theThevenin model with functional R; Fig.5.3g and Fig.5.3h show the results for the DP model.Left hand side column shows the results for the SOC estimation of the simulation and right handside column shows results for the terminal voltage estimation of the test. From the pictures wecan simply conclude that the estimation error of all 4 cases is not so big and within the accept-able limits. The following table5.2 shows the results of the estimation error and the computingpower for each model. The reason why the error starts from zero is because we correctly setan initial value. The double polarization model which is usually called second order RC modeldoes a better job considering the estimation error but in terms of the computing power, it costthe most time to calculate. In terms of the computing power, here we use computing time ofone time calculation on personal computer to indicate the computing power of the estimationmethods. For estimation error or the estimation accuracy here we use root mean square methodto indicate the estimation accuracy. The formula to calculate the estimation error is given below.

SOCerror =

√1

n((SOCref (0)− SOCest(0))2 + ...+ (SOCref (T )− SOCest(T ))2) (5.1.1)

Model The RINTModel

TheTheveninmodel

TheveninModel withFunctionalR

The DPModel

ComputingPower(s)

14.08 17.02 16.45 20.19

EstimatedError(%)

2.34 2.24 2.2 1.77

Table 5.1: Comparison of Different Model using fresh new battery

5.1. Comparison between different electric models 43

Model The RINTModel

TheTheveninmodel

TheveninModel withFunctionalR

The DPModel

ComputingPower(s)

17.77 20.1 19.65 20.19

EstimatedError(%)

7.85 7.69 7.53 7.29

Table 5.2: Comparison of Different Model using aged battery

(a) Input Current of the single battery cell(new bat-tery)

(b) Terminal Voltage of the single battery cell(newbattery)

(a) Input Current of the single battery cell(aged bat-tery)

(b) Terminal Voltage of the single battery cell(agedbattery)


(a) SOC Estimation using RINT Model (b) Terminal voltage Estimation using RINT Model

(c) SOC Estimation using Thevenin Model(d) Terminal Voltage Estimation using TheveninModel

(e) SOC Estimation using TheveninModel(functional R)

(f) Terminal Voltage Estimation using TheveninModel(functional R)

5.1. Comparison between different electric models 45

(g) SOC Estimation using DP Model (h) Terminal Voltage Estimation using DP Model

Figure 5.3: Comparison of different equivalent electric circuit model state estimation using newbattery cell

Secondly, the test was implemented on an aged cell with the same ambient temperaturearound 0 C. Results for the RINT model is shown in frame Fig. 5.4a and Fig. 5.4b; resultsfor the Thevenin model is shown in frame Fig. 5.4c and Fig. 5.4d; results for the Theveninmodel with functional R is shown in frame Fig. 5.4e and Fig. 5.4f and results for the DP modelis shown in the frame Fig. 5.4g and Fig. 5.4h. In all cases, we reset the initial of the batterycapacitor to 38 instead of 42 for the new cell. But this should be done within the BMS usingonline parameter estimation to estimate the real battery capacity. Several methods has beenpresented in the literature can be generally divided into four groups [6]. The first method isbased on the change in the measured battery OCV before and after charging or discharging andthen the battery capacity is calculated based on the SOC-OCV relationship. The second methodis to estimate the OCV change from the battery voltage measured under load. The third andfourth method is to using electric circuit model to calculate the battery capacity using joint ordual estimation. In order to compare with the previous simulation result we will implement thesame estimation method and the cell is also test under the same temperature. In this model,estimation model is worse than the previous one because of the poorly capacity value. But westill can see the priority of the second order RC model has better estimation result in terms ofthe accuracy. And the linear RINT model takes the least time to calculate. From these groupsof experiment, we can easily see the aging effect will have a big effect no matter on the batteryitself but also on the monitoring accuracy.


(a) SOC Estimation using RINT Model (b) Terminal voltage Estimation using RINT Model

(c) SOC Estimation using Thevenin Model(d) Terminal Voltage Estimation using TheveninModel

(e) SOC Estimation using TheveninModel(functional R)

(f) Terminal Voltage Estimation using TheveninModel(functional R)

5.2. Comparison between different estimation algorithms 47

(g) SOC Estimation using DP Model (h) Terminal Voltage Estimation using DP Model

Figure 5.4: Comparison of different equivalent electric circuit model state estimation using agedbattery cell

5.2 Comparison between different estimation algorithms

”Estimation algorithms are mathematical techniques used to compute the optimal estimatesof states and parameters of a dynamical system” [36][9]. Here in our report we will comparesix estimation algorithms in total which are EKF, UKF, CDKF, SRUKF, SRCDKF and PF.A groups of experiments has been conducted to validate the model based state estimation andusing this estimation algorithm. First the same model of new cell will be running under differenttemperature. Secondly the same model of cell will be running at different road conditions to testthe accuracy of the monitoring method also. Another thing need to be mentioned here is that wewill implemented first order RC model here considering the modest computing power it neededand relatively good dynamic performance.

5.2.1 Results and discussion

Fig.5.5 shows the results of different estimation algorithm SOC estimation for first order RCmodel under ambient temperature 0 C, while the SOC was initialized to 100% and internalresistor R0 is 0.0005Ω, parallel resistor R1 is 0.0005Ω and the capacitor is 200 pF. Results forthe EKF is shown in the Fig.5.5a; results for the UKF is shown in the Fig:5.5b; results for theCDKF is shown in the Fig:5.5c; results for the SRUKF is shown in the Fig:5.5d; results forthe SRCDKF is shown in the Fig:5.5e; results for the PF is shown in the Fig:5.5f. The detailedinformation about the computing power and estimated error can be found in the table5.3. Fromthese figures we can conclude that existing estimation algorithms tend to either be accuratebut complex or easy but suffer from the big errors it will produced. According to this, a trade


off need to be done by the car manufacture to choose their preference. When the battery isrunning at different temperature both the estimated error and computing power will still remainthe same trend. But we can notice that in Fig.5.6b the estimated value has a jump at the endof the estimation timescale. One reason behind this is because the OCV curve for these cells isextremely flat when SOC value is between 20 to 70. A small deviation of the estimated value ofthe voltage may have a big impact on the estimated SOC value, and is worst around 50%. As wecan seen from the comparison table, the superiority of the EKF over SPKF is mainly becausethe nonlinear characteristic of the battery that we use here is mostly known. Another reasonis because the SOC of a Li-ion battery can only have one trend during a period of time(whencharging SOC increase, when discharging SOC decrease). Considering when we face a mildlynonlinear model with known noise distribution EKF will of course have some priority overSPKF . As SPKF approximates the Gaussian noise distribution instead of the state space model.The particle filter will have higher accuracy compare to the others, however will cost morecomputation power instead.

Estimation Algorithms ComputingPower(s)

EstimatedError(%)

Extended Kalman Filter 24.55 1.177Unscented Kalman Filter 15.67 2.133Central Difference Kalman Filter 18.41 1.639Square Root Unscented KalmanFilter

16.98 1.245

Square Root Central DifferenceKalman Filter

17.43 1.639

Particle Filter 31.01 0.631

Table 5.3: Comparison of Different Estimation Algorithms (ambient temperature 0 C)


EstimatedError(%)


15.9 0.86


16.87 0.89


Table 5.4: Comparison of Different Estimation Algorithms (ambient temperature 10 C)

The previous two tests are all run inside the city. The following picture shows the result

5.2. Comparison between different estimation algorithms 49

(a) SOC Estimation using Extended Kalman Filter (b) SOC Estimation using Unscented Kalman Filter

(c) SOC Estimation using Central DifferenceKalman Filter

(d) SOC Estimation using Square Root UnscentedKalman Filter

(e) SOC Estimation using Square Root Central Dif-ference Kalman Filter

(f) SOC Estimation using Particle Filter

Figure 5.5: Comparison of different Estimation Algorithms under 0 C







Figure 5.6: Comparison of different Estimation Algorithms under 10 C

5.3. Practical case with poorly initial value 51

when the car is driving on highway. Results for the EKF is shown in the Fig.5.7a; results forthe UKF is shown in the Fig:5.7b; results for the CDKF is shown in the Fig:5.7c; results forthe SRUKF is shown in the Fig:5.7d; results for the SRCDKF is shown in the Fig:5.7e; resultsfor the PF is shown in the Fig:5.7f. The detailed information about the computing power andestimated error can be found in the table5.5. The conclusion that we drew in previous paragraphis still valid.


EstimatedError(%)


10.58 4.64


11.48 1.43


Table 5.5: Comparison of Different Estimation Algorithms (ambient temperature 0 C), high-way mode

5.3 Practical case with poorly initial value

In reality, we actually have several ways to estimate the battery SOC value as what we havediscussed in chapter 3. The most widely used method is Ampere-hour counting method which iseasy to implement and relatively cheap compare to other methods. But the drawback is also quiteobvious. Poorly initial value and accumulated measurement error may cause a big deviationbetween the real and estimated value. This can be pretty annoying when a car suddenly stopsin the middle of the road whereas sufficient battery capacity is indicated. Here we will seewhether the adaptive filter technology can overcome this deficit and show some priority interms of tackling poorly initial value problem. Here we will show the example where adaptivefilter technology SOC estimation result under incorrect initialization.

5.3.1 Results and Discussions

Fig.5.8 shows the result of poorly initial value, where the filter SOC was incorrectly reset to90%, 80%, 70% and 50% respectively. As we can easily seen from the experiments’ result,







Figure 5.7: Comparison of different Estimation Algorithms under 0 C, highway mode

5.3. Practical case with poorly initial value 53




Figure 5.8: SOC estimation under poor initial value


no matter how big the deviation is, this method can eventually converge to very low estima-tion error, which shows the robustness and adaptivity of this approach. At the same time theconvergence just take several minutes to complete is also a very positive feature.

5.4 Multiple driving cycles estimation

From these set of experiments alone, it is hard for us to draw the conclusion that Kalman filterbased methods can be used for electric vehicle related applications to estimated the SOC valueof the traction battery. So in that case, we now show some practical cases to help us get afull impression about the monitoring method. In practice, the car will running through severalcharging and discharging phases and the time slot for each phase is extremely hard to predict.Since it is highly depends on the driver’s daily routine and the functionality of the car. If thedriver just go for a short trip say daily shopping then the car will experience a 5 minutes shortdischarging and then followed up with a several hours long charging. If the driver go for a longroad trip, then the car will experience a several hours long discharging and follow up with a longcharging also. In this case the robustness of the algorithm will become an important issue whenwe choose the estimation method. Here we will present several simulation results showing theperformance of the estimation methods under multiple driving cycles.

5.4.1 Results and Discussions

Fig.5.9 and Fig.5.10 shows the result of SOC estimation for multiple driving cycles, and theSOC state was reinitialized to 96% after each charging phase. The reason why we do not es-timate the charging phase is because we only have one 12V battery system in our prototypewhich is designed for start the engine. But in reality we will install more 12V back up batteriesto let the BMS working under key-off state. The cell that we use for this test is a fresh new cellwith real capacity around 42 Ah with a 3.2V nominal voltage. Here we will using SRUKF as theestimation algorithm and first order RC model to do the estimation since the modest accuratelevel and relatively low demand on computing power that we conclude from previous section.Results for a consecutive driving profile is shown in Fig.5.9 and a driving profile from one ofour test engineer is shown in Fig.5.10 which is not consecutive. We can see the robustness andadaptivity of the SRUKF method from this. Which indicate the Kalman filter based estimatorcan be used under practical cases.

5.4. Multiple driving cycles estimation 55

Figure 5.9: Multiple Driving Cycle SOC estimation using SRUKF and first order RC model(consecutive)

Figure 5.10: Multiple Driving Cycle SOC estimation using SRUKF and first order RC model(driver profile)

Chapter 6

Conclusions and further work

In this part of the report, discussion regarding to the performance of model based battery stateestimation using adaptive filter technology will be given here. Suggestions for further work andimprovements will also be given.

6.1 Conclusion

In this thesis, we mainly discussed how to utilize Kalman filter based algorithm to track thestate of the battery.

First, we introduce several existing electric battery circuit model which can predict thecharacteristics of the battery fast and convenient. The performances of different models areobtained by conducting the accuracy of SOC estimation with same Kalman filter algorithmusing real test drive data as input. By comparison, the second order RC model with functionalinternal resistor model has the best dynamic performance in terms of SOC state estimation,however, it also require large computation power to compute.

Second, six model-based algorithms are introduced to track the state of battery parameter.Which are EKF, UKF, CDKF, SRUKF, SRCDKF and PF. The performance of these algorithmare compared in terms of speed and accuracy. Simulation result shows EKF performs betterthan SPKF in most of the case is mainly because of the system itself is only a mildly nonlinearsystem. SPKF is based on an approximation of the Gaussian noise distribution rather than thestate space model like EKF. Under some special case when the system is corrupted by non-Gaussian noise the particle filter will outperforms the other algorithms. Unfortunately we alsonotice that existing estimation algorithms tend to either be accurate but complex or suffer from

57

58 Chapter 6. Conclusions and further work

worse dynamic performance but have higher calculation speed.

Third, we take a look at the robustness of the Kalman Filter based algorithm. We will givea poor initial value manually to see whether the algorithm can adjust the estimated value back tothe right outcome. The simulation result clearly shows the method can automatically convergeto a relatively small number which prove the robustness and adaptivity of this method.

Finally we implement multiple driving cycle simulation to see whether the algorithm can beused in the real practical case. The result is quite positive that the Kalman filter based algorithmcan quickly track the SOC of the battery and can converge to a small number also.

6.2 Further work

In future work, we still have a lot of tasks need to be fulfilled:

• Here we assume the parameter of the battery itself remains constant which is not the realcase. In the future we need to update the parameter of the battery model parameters at thesame time.

• Aging effect of the battery need to be tackled therefore the performance of the algorithmsover the lifetime of the battery need to be further studied and improved.

• Here we only consider a single cell state estimation, but , for electric vehicle pack state ismore important for drivers.

• The algorithms will be implemented on a BMS which indicate it need to be embeddedinto a micro processor. Which will give the requirements to choose suitable algorithmwith limited computation power but with enough accuracy.

• Real time state estimation is needed for EV applications, so the calculation speed of thealgorithm need to be analyzed

Appendix A

Matlab Battery State Estimation GraphicUser Interface

Here we show the Matlab battery state estimation graphic user interface.

59

60 Appendix A. Matlab Battery State Estimation Graphic User Interface

Figure A.1: Matlab Battery State Estimation Graphic User Interface

Appendix B

Kalman filter related algorithms

The Kalman filter related algorithm step by step flow chart is given here:

Figure B.1: Kalman filter algorithm flow chart

61

62 Appendix B. Kalman filter related algorithms

Figure B.2: Extended Kalman filter algorithm flow chart

Appendix B. Kalman filter related algorithms 63

Figure B.3: Unscented Kalman filter algorithm flow chart


Figure B.4: Square root unscented Kalman filter algorithm flow chart

Appendix B. Kalman filter related algorithms 65

Figure B.5: Particle filter algorithm flow chart

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