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

,

STOCKHOLM SWEDEN 2016

Modularized Battery Management

Systems for Lithium-Ion Battery

Packs in EVs

YIZHOU ZHANG

KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ELECTRICAL ENGINEERING

Modularized Battery Management Systems for Lithium-Ion

Battery Packs in EVs

YIZHOU ZHANG

Master of Science Thesis in Electrical Machines and Drives at the School of Electrical Engineering

KTH Royal Institute of Technology Stockholm, Sweden, August 2016.

Examiner: Oskar Wallmark Industrial Supervisor: Christian Fleischer

c

YIZHOU ZHANG, 2016.

School of Electrical Engineering

Department of Electrical Energy Conversion Kungliga Tekniska h¨ogskolan

SE–100 44 Stockholm Sweden

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 temperature range 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 battery packs’ 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 of these methods into battery management system is decribed. Evaluations on different estimation methods are implemented from the point of view of the dynamic performance, the requirement on the computing power and the accuracy of the estimation. Real test drive data will be used as a 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 different monitor’s performance and their computational complexity are analyzed.

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

Sammanfattning

BMS (eng. battery management system) har till uppgift att se till att viktiga parametrar s˚asom tillsp¨annings- och temperaturintervall uppr¨atth˚alls f¨or varje individuell battericell. D˚aen battericells beteende ¨ar icke-linj¨art ¨ar det sv˚art att best¨amma cellens interna karakteristika di-rekt. Att kunna f¨oruts¨aga dessa karakteristika f¨or ett komplett batteripack kommer att en mycket viktig funktion hos framtida BMS.

I detta examensarbete har en modellbaserad tillst˚andsestimeringsmetod med anv¨andande av adaptiv filtrering unders¨okts. Olika batterimodeller har studerats med avseende p˚akomplexitet och noggrannhet. Efter introduktionen av olika metoder f¨or adaptiv filtrering har dessa metoder

implementerats i en BMS modell. Utv¨ardering av de olika metoderna f¨or att ˚astadkomma tillst˚andsestimering har sedan utf¨orts med avseende p˚adynamisk prestanda, krav p˚aber¨akningskraft och noggrannhet

hos de resulterande estimaten. Data fr˚an uppm¨atta k¨ordata fr˚an ett fordon har anv¨ants som ref-erens f¨or att j¨amf¨ora de olika estimaten. Slutligen presenteras en j¨amf¨orelse mellan de olika tillst˚andsestimeringsmetodernas prestanda n¨ar de appliceras p˚ade olika batterimodellerna.

Nyckelord: BMS, elbil, Kalmanfiltrering, litiumjonbatterimodell, tillst˚andsestimering.

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 me this opportunity by offering such an interesting and challenging topic. Second, I would like to express my gratitude to my examiner Dr. Oskar Wallmark for giving me feedback from time to time and guiding me in the right direction.

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

Yizhou Zhang Trollh¨attan, Sweden August 2016

Contents

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

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

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

Chapter 1

Introduction

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

1.1

Introduction

1.1.1

Presentation of NEVS

National Elctric Vehicle Sweden (NEVS), was a relatively new car manufacture which acquired the main assets of SAAB Automobile in 2012. In order to tackle the global warming problem and lead to a more sustainable future, NEVS dedicated itself into electric vehicle industry with passion and confidence. The headquarter of NEVS located in Trollh¨attan, Sweden, with an automative factory and a global R&D center. Aside from that NEVS also owns a customer experience center in Beijing, a new manufacture in Tianjin Binhai High-Tech zone which intend to 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 issues all over the world and also a key reason leveraging the large scale adoption of EV [1]. The new automobile industry products, hybrid electric vehicles (HEVs), pure battery electric vehicles

(BEVs), and fuel cell vehicles (FCEVs) are the future direction in transportation sector, and let most of the leading car manufactures all over the world start researching and producing such promising cars[2]. Road transportation contributes to nearly half of the world’s oil consumption in 2009 and may keep increasing up to 60% in 2035 [3]. The transportation sector contribute up to 19.0% of the world’s CO2 emission making it one of the principle targets in order to mitigate the 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-ion batteries which has let it become the most favorable choice for HEVs and BEVs [5] [2]. When we 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 data collected from the sensor it can also estimate other useful information of the battery to control the 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 ensure optimum use of the battery in a portable device.” [7] The most fundamental tasks of a BMS is to limit overcharge and undercharge in the cells, ensure that the cells in the pack are balanced and maintain a safe operations of the pack [8]. In order to achieve these tasks, several functions can be performed:

• Battery State Estimation. Track the battery’s internal state variable to prevent dangerous situations to occur and use the estimated value to control the dynamic behavior of the battery (during charging phase, control the charging strategy with practically no over-charging to expand the lifetime of the battery; during disover-charging phase, detect the empty cell in advance to avoid over discharging.). At the same time send the signal value to the user as a notification. To have a full impression of the battery’s state we will expand state 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 remain so unless a balance action is taken. Since the balancing issue may have a big effect on the battery life and remaining available power, a well designed BMS should be equipped with 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-DC converters to achieve battery equalization [2][8].

• Battery Safety Management. As the most significant and fundamental requirement of the BMS, safety issue regarding to preventing over-charge, over-discharge, over-heating and over-current will be fully controlled by a central controller. Apart from that a diagnostic alarm 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 the allowed 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 in a 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 for each 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. During the process of finishing these sub-targets we will approach to our final destination. These have been formulated in such a manner that once one is completed, it should make a distinguishable progress.

• 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 battery cell.

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

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

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

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

• Set up a group of experiments to test and verify the feasibility and performance of the designed 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 the BMS 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 Electric

Circuit Model

In this chapter, four different electric models to simulate a battery cell will be introduced and the 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 for an 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, current and temperature) with the battery SOC employing a battery model. Based on this proposed electric model, the battery SOC will be estimated later on. Briefly stated the accuracy and the complexity of the battery model will affect the estimation result of the battery SOC, capacity and SOH. Three different kinds of battery model method will be presented here: the electrochemical model, the neural network model and the electric circuit model.

The electrochemical model can depict the characteristics of the battery cell which will include the relationship between SOC and temperature. By using such a model, an accurate terminal voltage estimate can be achieved. However the complexity of the model ask for a lot of 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 of these types of models can reach up to 3% under certain conditions [6][2]. Nevertheless, the

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

Electric model method is right now the most popular method to monitor the battery thanks to its simplicity and accuracy. Which only use typical electrical components to represent the battery characteristics. Typically, the electric model is expressed in one or several equations to correlate the input and output values and to estimate the OCV(Open Circuit Voltage) value based on this state space model. The estimation of SOC is incorporated in this model by its direct 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 characteristics and 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 model can only be accurately identified for new batteries in the laboratory. Complex monitoring and estimation algorithms are needed if we want to update the parameters and this is only practical for 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 open

circuit voltage and R0 represent the internal resistor. However the value of the resistor will be

changed according to the battery SOC, SOH and temperature. [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 manufacture SAFT [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 Ccis to represent the

surface 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 capacitive

resistance. The parameters are functions of the SOC and temperature. The following equations represent the electric behavior of the circuit.

Figure 2.2: The RC Model [10]

Ua= Us Cb(Rc+ Rca) − Ua Ca(Rc+ Rca) − RcIt Ca(Rc+ Rca) (2.3.1) Us = Ua Cs(Rc+ Rca) − Us Cs(Rc+ Rca) − RcIt Cs(Rc+ Rca) (2.3.2) Ut= RcaUa Rc+ Rca + RcUs Rc+ Rcs − RthIt− RcRcaIt Rc+ Rca (2.3.3)

2.4

The PNGV Model

The Partnership for a New Generation of Vehicles (PNGV) model shown in the following Fig 2.3 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 the

polarization resistance; the capacitance CP represents the polarization capacitance, UOC is an

ideal 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 capture the dynamic characteristic of the battery behavior very well. The model uses an ideal voltage source 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 CT h

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 + IL Cth (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, especially when 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 polarpolar-ization which indicate the change 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 order to track these two different characteristics respectively dual polarization model is introduced which is also know as second order RC model [10]. The model consists of a voltage source UOC to represent OCV value, an internal resistance RO and two RC components indicate

Figure 2.5: The Second Order RC Model [10] Upa = − Upa RpaCpa + IL Cpa (2.6.1) Upc = − Upc RpcCpc + IL Cpc (2.6.2) U L = Uoc− Upa− Upc− UP N − ILR0 (2.6.3)

2.7

Varied-parameters’ Electric Circuit Model

Untill now the parameters of the equivalent electic circuit model have remained unchanged and obtained from a set of laboratory measurements. When we implement this method to estimate the 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 the model parameters also during the battery operation otherwise a high inaccuracy for battery state estimations will occur. In order to tackle this problem, we will choose a first order RC model as an example. The resistance Rthrepresent the internal resistance of the battery. The capacitance

C 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 not

constant during the battery operation phase and can be described by the Butler-Volmer equation [12][13]. R0( ˙IL) = R0( ln(kiI˙L+ q (kiI˙L)2+ 1) kiI˙L ) (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 the

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 previous chapter to monitor the battery states. The methods from control theory will be used here to help us improve the efficiency and the dynamic performance of the model based SOC state estimation and 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 deviation between the modeled and measured battery terminal voltage is used for the correction of the estimation 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 its distinct nonlinear behavior depend on several internal and external conditions, estimating their states will become a challenging task. Considering the complexity and difficulties of the battery we will choose several important data which may have big impact to the EV drivers or related to the safety issues to do the state estimation. State of Charge (SOC) in EVs serves a similar role in that of the petrol gauge in the traditional internal combustion car. In that case the accuracy of 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 from over heating, overcharging, over-discharging, or over current which will, in turn, increase the lifetime of the battery and ensure the safety during its use.

3.1.1

Definition of SOC

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

the 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 will be called remaining capacity. In terms of the nominal capacity we will ran a test experiment let the battery self-discharge from the full state to zero state. In practical it is hard to determine the zero state of the battery. Here, we will use the open circuit voltage value as an indicator to judge whether the battery is fully discharged/charged or not. In another way, the SOC can be expressed as the following equation [14]:

SOC = SOC + η R t t 0i(τ ), dτ Cn (3.1.2)

where i(τ ) represents the value of current (defined to be positive for charging and negative for discharging), η represents the Coulomb efficiency, Cnrepresents 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 usually composed of multiple battery cells series or parallel connected. Parallel connected battery units can provide higher available capacity to meet the desired settings. Since for cells connected in parallel, a self balance characteristic exist, we can simply regarded the battery module to a single cell with a higher capacity. Just as how we define the single cell battery SOC, the pack SOC can also be defined as the remaining available capacity of the pack as a percentage of the nominal capacity of the pack. If we want to estimate the pack SOC, we firstly need to get to know the topology of the battery pack and analyze into two different categories: series connection and parallel connection. When the cells are in series, we have to taken into account the differences between cells and the balance strategy that the BMS provides. Three different balance strategy will 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 pack will 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 remaining capacity but as a matter of fact the pack cannot be discharged anymore considering the safety issues and the lifetime of the battery. Similar during charging phase, when one or some of the cells are fully charged and some of the cells still have capacity available the pack still need to pause 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 Cpackis the pack capacity and Crrepresent remaining cell capacity. SOC is the cell current

state of charge and Cnom is the cell nominal capacity. In that case, the SOC of the pack will be

given 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 the energy flow within the cells. In terms of passive balancing, we will add an external circuit to dissipate the remaining energy of the highest SOC cells. In most of the cases a resistor is the cheapest and easiest way to dissipate this energy. Which means the designer have to choose an appropriate 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 makes it 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 that case we need to take in to account the increasing of the temperature do not violate the safety temperature window. Another difficulty of the passive balancing strategy is that it needs more time to tackle the problem than using active balancing method[7]. At the same time passive balance control only exist during charging phase.

Active Balance

In active balancing system, the excess energy will be transfer within different cells in order to achieve the equalization. It normally needs an active switch and several capacitors to fulfill this requirement 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 X i=1 SOCiCi N X 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 a wide range of methods proposed in the literature to tackle this problem. The most and widely used 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 access to the initial SOC value and the battery capacity. Simply measure the input current and do the time integral, then we can calculate the battery SOC. Since the battery is an electrochemical device 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 discharge phenomenon, 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 the errors will accumulate over time in an Ampere-hour counting method, recalibration is needed from time to time. Which will let the driver come across a lot of inconveniences especially when the car indicate a relatively well enough energy, but as a matter of fact it only has limited energy left.

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 the function 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” OCV value 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 equilibrium battery voltage at the end of OCV relaxation is called EMF [6]. Right now, there are actually several ways for accessing the value of EMF: voltage relaxation (after current interruption the battery open circuit voltage will take some time to relax to the EMF. But it is really hard to determine when the battery is fully relaxed.); Linear interpolation (using the same currents to charge and discharge the battery to find two OCV value and the EMF is the average of these two value. But in most of the real cases, this methods become impractical since the battery is not attached to a charger all the time.); Linear extrapolation. However, all these methods may suffer 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 introduce adaptive 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, driver behavior and also the manufacturing process. The basic theory behind this is using available measuring variables Iinput, Uterminal and Tb as input to estimate battery behavior and condition

by integrating battery model into this. The output will be the estimation value that we need to track for example the battery SOC, available capacity or the available power. The advantage of using adaptive filter technology is that it can provide battery state accurately and continuously during battery operation. However the main drawback that limit the use of this method is its high demand on computing power. But with the fast development of microprocessors which will make it more and more popular to implement this method into automobile application. In this 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 solve linear optimal problem recursively[18][19]. It can be used not only in stationary environments but also in non stationary environments. Kalman filters provides an efficient and easy methods for predicting current state value of a dynamic system. Generally speaking, the state within the battery cells is always related to the past and present inputs or outputs. So the state of the battery can be estimated by the Kalman filter.

In order to implement a Kalman filter, a dynamic model which uses several internal state variables 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 implement Kalman Filter to estimate the battery SOC. The first order RC model which consists of an internal resistance R0 with one RC element in series. In order to determine the value of the

parameter, we will implement least squares methods so as to minimize the error between the model output and experimental outcome [20][21][22]. The following discrete time equations depict the relationship of the battery SOC, terminal voltage of the cell and three parameters in the first order RC model.

Here k is the discrete time index, Vt is the terminal battery voltage, η is the Comlumbic

efficiency, Cnomis 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 the stability , 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 ∈ Rmindicate

the output of the system which is also the measurement value in most of the cases to correct the estimated value. wk ∈ Rn and vk ∈ Rn is the noise of the system, in some references

it 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 might change with each time step but in order to reduce the complexity, here we assume they remain constant all the time. Another thing need to be mentioned here is both wkand vkare zero-mean

white 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 shows that the Kalman filter based methods work well in battery state estimation [23].

3.3. Kalman Filter 19

Here we define ˆx−_{k ∈ R}n _{(known as super minus) to be a priori state value priori to time}

step k, and ˆxk ∈ Rn to be a posteriori state estimate at step k using measurement value yk

to update the previous estimated value. The estimate errors of the priori and posteriori can be shown as:

e−_k = xk− ˆx−k

ek= xk− ˆxk

The error covariance can be represented as:

P_k−= E[e−_ke−T_k ]

P_k− = E[ekeTk]

And E[.] is defined as:

E(x) =

n

X

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 in the 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, xk−1ˆ and error 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 incorporate knowledge gained from the measurement value to improve the previous estimation. At the same time this will also be the value that we will use to report the real state of the battery say SOC or SoH [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 predicted and collected. But the robustness characteristic of the Kalman filter will help us handle the poor initial issues which will be shown in the next chapter.

ˆ

x0 = E[x0]

Px,0 = E[(x0− ˆx0)(x0− ˆx0)T]

After the initialization process, the Kalman filter will repeatedly perform two steps update and 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. ˆ

x−_k = A ˆxk−1+ Buk

Then the state error covariance will also be updated: P_k− = APk−1AT + Q

In theory, the uncertainty (error covariance) will decrease to zero when the system is stable, but the process noise term Q will increase the uncertainty since wkcan not be measured and predict

and 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 of posteriori state ˆxk.

ˆ

xk = ˆx−k + Kk(yk− C ˆx−k − Duk)

As we can see from this equation, the updated state is based on the predicted state that we find in the previous step plus a weighted correction factor yk − C ˆx−k − Duk part is the difference

between the real measurement value and the estimated measurement value which can be called the measurement innovation. If the innovation is zero this indicates that the real and estimated value have no difference. The weighted factor shown in front of the innovation value is the Kalman gain vector Kkwhich is chosen to be the corrected factor that minimizes error [25].

Kk = Pk−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 covariance will always decrease. Figure 3.1 below gives a detailed flow chart of how the Kalman filter related estimator implemented on the battery monitoring system to estimate the state of the battery cell. In a word the Kalman filter provide a robustic, automatic and time efficient approach to estimate dynamic system’s state using limited input output. [20][26][16]. Another important issue that needs to be addressed here is that the recursive nature and the demand for matrix operations 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 linear discrete time state space model. In order to handle more strict environment which addressed a nonlinear dynamic model, the extension of the Kalman filter may become necessary.

3.4. Advanced Kalman Filter 21

3.4.1

Extended Kalman Filter

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

The same as what we define in the Kalman filter, the random variables wkand vkare again

zero-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 did in the Kalman filter, we will update this matrix with the time step k in the EKF algorithm. 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 first order Taylor-series expansion.

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

where xk and yk represent real state and measurement value. ˆxk represent the posteriori

state at time step k. wk and vk represent process and measurement zero mean white Gaussian

stochastic noise respectively. A, B, C, D is the Jacobian matrix.

3.4. Advanced Kalman Filter 23

However, since the EKF use Taylor series to transform the nonlinear problem to a liner problem which does not consider state vector x has its inherent uncertainty. Which has a large implications on the dynamic performance of the EKF related state estimation [27][28]. As a matter of fact the EKF is not the only possible way to solve the nonlinear dynamic system state estimation method. In particular, sigma point Kalman filter and particle filter can also give an alternative 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 estimaestima-tion accuracy and leading to unstable filters. In stead of using Taylar series linearization method. Sigma point Kalman filter will use a small fixed group of function to linearize the nonlinear state space equation and transform the nonlinear prob-lem to linear probprob-lem [29][30]. A random variables will be carefully chosen to be the sample points to represent the state vectors. The requirement of these chosen sample points is that the mean and error covariance of these sample points are exactly the same as the mean and error covariance 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 a dimension 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 we discussed in the previous paragraph.

The λ = α2_{(L + κ) − L is a scaling parameter. 2L + 1 indicate the total (which is also the}

minimum) 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 define α equals 1. The κ is determined by 3 − L and β normally equals to 2 [31]. Using these sigma points 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 have to calculate the square root of covariance. In order to reduce the complexity of calculation we can 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 good

side of this method is that R is a lower triangular matrix. The whole steps of the UKF can be found 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 how they 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 mean and error covariance value are exactly the same as prior state variable’s. However, the central difference Kalman filter(CDKF) use a different method to generate the sigma points. Sterling’s polynomial interpolation method will be used here instead of using Taylor series [32]. The same

3.4. Advanced Kalman Filter 25

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 + ( p h2_P x)i, i = 1, ...L, (3.4.2) Xi = ¯x − ( p h2_P x)i, i = L + 1, ..., 2L, (3.4.3)

Where weights Wiis determined by

W₀(m) = h

2_{− L}

h2 (3.4.4)

W_i(m) = 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 of sample points so the detailed procedure can be found in previous UKF section. Another thing need to be mentioned here is that the CDKF only need one extra variable to calculate the sigma points, step variable h, compare to the three variables (α, β, κ) that the UKF needed. And at the same time as it shown in [33] that the CDKF literally has better dynamic performance than the UKF under some specific conditions. In terms of computation power since less extra variable are used which will increase the speed of calculation compare to the UKF algorithm. But in most of the practical cases this difference in computation power and accuracy is not so obvious which indicate the SPKF has same order of accuracy and computation power. Specifically, the optimal 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) is mainly because the normal SPKF need to calculate the matrix square root of the state error covariance which cost a lot of computation power and decrease the numerical stability of the whole system. Before we introduce the SRSPKF, we will introduce three linear algebra theories first that are required to implement the SRSPKF which are QR decomposition, Cholesky factor updatingand Backsubstitution [30][27].

• QR decomposition: Assume we have a matrix A ∈ Rl×n_{, the QR decomposition of this}

matrix can be written as:

AT = QR,

where two factors inside the equation are orthogonal matrix Q ∈ Rn×n _{and upper}

the triangular matrix R and the Cholesky factor of P = AAT _{is ˜R}T_{, so in that case}

˜

RTR = AA˜ T. 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_ˆx,k+1− = AAT, where A = q

w_i(c)(X_k+1,ix,− − ˆx−_k+1). Instead of computing AAT and follow up with the Cholesky factor, we can implement the QR decomposition of AT here, in order to find out the ˜R component which can help us reduce the computation complexity. And that can also applied to Pˆy,k+1 =

Pp i=0w (c) i (Yk+1,i− ˆ yk+1)(Yk+1,i− ˆyk+1)T [29][30].

• Cholesky factor updating: Assume the Cholesky factor of P = AAT _{is R which is}

a lower triangular matrix according to the Cholesky factor theory. then we can have the Cholesky factor downdate ˆP = P ± √vuuT_{, which can be represented as ˆR =}

cholupdate{S, u, ±v}. The algorithm that we implement here is also available in Matlab as cholupdate. The reason why we need to introduce this is because the previous method can not be used when w(c)_i is negative. And this can also be used in the final step to update the value of state error covariance.

• Backsubstitution: This was mainly used in the estimator gain matrix computation where Kk+1 = P_xˆˆ−_y,k+1P_y,k+1ˆ−1 which can also be written as Kk+1 = P_xˆˆ−_y,k+1(Ry,k+1ˆ RTy,k+1ˆ )

−1

. The backsubstituion is consist of two steps totally. We calculate Pxy/RTy and then

calcu-late Kk+1 = (Pxy/RyT)/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.

X_ka = {ˆxa_k, ˆx_ka+ λRa_x,kˆ , ˆxa_k− λRa ˆ x,k}

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

R−_x,k+1ˆ = qr{[ q

w_i(c)(X_k+1,(0:p)x,− − ˆx−_k+1)T]}T

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

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_xˆˆ−_y,k+1Pyˆwhich can be solved

by back-substitution. The whole steps of the square root unscented Kalman filter can be found in 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 SRUKF only differs from the derivation of sigma points. What special for square root CDKF is since all weights are positive, Cholesky factor updating method is not necessary for CDKF. When compute 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 is not 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 Carlo simulation and use sequential importance sampling and re-sampling to estimate the state of the dynamic system. In that case the PF can handle more strict environment than the SPKF and the EKF.

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 can be computed as:

Where δ() represent the Dirac delta function, {ω(m)_{, x}(i)_{; m = 1...N } represent the}

weighted 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 this problem. 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 big impact on the dynamic performance of the PF. The more points that we draw the more accuracy the estimation is. However this will also cost more computing power. Re-sampling step here can emphasize the point which has more impact on the final result and eliminate the useless particles. Which can be evaluated by the weighted factor w [32][34][27]. The detailed algorithm is 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 step procedure will also be given.

4.1

Experiment set up

The real drive test is conducted at RWTH Aachen University in Germany [35]. In this thesis work, 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 the illustrate of the measured signals will be explained in this section. Technical data was given in the 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 the vehicle will be added. As shown in Fig4.1. The introduction in Fig 4.1c are GPS receiver cable and 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 bus on 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. The remaining components were housed in the trunk. For reading and storing measurement signals MicroAutoBox II dSPICE is used. The used version here is 1401/1507 which has 4 CAN buses and two RS-232 interfaces and a USB port for storing the measured values on a USB storage

Drive

Electric Machine Permanent Magnet Syn-chronous Machine

Rated Power 45 kW Max Torque 240 Nm Max rotate speed 7500 min−1 Max speed 121km/h vehicle data

Weight 1170kg Tire 175/65 R14 Dynamic tire radius r 0.2835m Gear ratio i 6.61 Cross-sectional area 2.42m2 Drag coefficient 0.325 Efficiency of the the drive

train

95.5% Battery

Manufacture of cells Kokam Number of cells 84 Norminal voltage 310.8 V Norminal capacity 40 Ah Energy content 12.4 kWh Usable 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 at least 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 the battery management system, the power-train drive unit and the sensors in the low voltage. The sampling rate is 100 ms and the memory requirements while driving is approximately 1.1 MB per 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 which contains the basic functions for state estimation, parameter estimation, joint estimation and dual estimation, 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 has already introduced in Chapter 2. There are totally 4 generalized state space models were built which are Rint model, first order RC model, first order RC model with functional resistor and second order RCs model with functional resistor. The battery state estimation Matlab toolkit was first developed by Dr. Christian Fleisher [6]. Here we will use first order RC model as an example to introduce how the model is built.

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

Singal Name Unit Description CAN bus

BMS-iBatAct A current battery power

BMS-iBatChgCont A current maximum allowable charge current BMS-iBatDchCont A current maximum allowable discharge current BMS-rSOCAct current battery state of charge

BMS-rSOCMax maximum battery state of charge BMS-rSOCMin minimum battery state of charge BMS-tCellAvg ◦C average temperature of the battery cell BMS-tCellMaxAct ◦C maximum temperature of the battery cell BMS-tCellMinAct ◦C Minimum temperature of the battery cell BMS-uBatAct V current battery terminal voltage

BMS-uCellMaxAct V maximum battery terminal voltage BMS-uCellMinAct V minimum battery terminal voltage IPU-iAct A measured DC current of the drive unit IPU-nAct min−1 speed of the electric machine

IPU-tqAct Nm torque of the electric machine IPU-uAct V measured voltage of the drive unit LV-Current A current of the low voltage network LV-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 capacitor and the voltage over capacitor. Apart from that we have one observation variable which is the terminal voltage of the batter cell. And the parameter dimension here is 3 since the model contains 3 parameters (internal resistor, polarization resistor and polarization capacitor). Two input which are the measured current value and measured terminal voltage value. Since the both the process noise and the observation noise have the same dimension with process state and observation state are 5 and 1,respectively. Then we need to set up the noise source for process 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 represent the f function are given in Fig 4.3:

4.2. Simulation set up 33

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 value of the battery parameters need to be updated. After we define the f function, we will design the h function in order to find out the difference of the estimated value and real test value. Fig 4.4 shows 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 which is actually a look-up tables as we can seen in figure Fig 4.6.

Figure 4.6: SOC & OCV relationship

The last thing of model simulation is that we will set up the Jacobian matrix of f and h functions 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 to define the Jacobian matrix B, C and D. Until now we have almost finished build the circuit model.

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 the estimation. First, we will define the scaling parameters of the UKF (Fig 4.8) and then set up the weighted factor for the sigma point that we will derive later on.

4.2. Simulation set up 35

Figure 4.8: Unscented Kalman filter scaling parameters’ definition

Then the covariance of the noise source will be defined using Cholesky decomposition which 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 mean and 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 of the 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 this value back to h function and find out the estimated value for the measurement (In our case the measurement value is the terminal voltage of the battery cell) the related code was shown in Fig 4.12.

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 state value will be calculate based on the difference between the estimated measurement value and real 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 and PF will also be built and used in the later validation part. Before we run the simulation we need to initialize the adaptive filter and also the state space model. Fig 4.14 and Fig 4.15 shows the intilization 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 left hand side we can choose different battery models, different estimation types (right now we only design the state estimation) and filter types. In terms of the noise set up we will use the default

4.2. Simulation set up 37

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 up the noise for the first order RC model.

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

4.2. Simulation set up 39

Chapter 5

Experiment Result and Discussion

In this part of the report we will introduce how we implement EKF, SPKF and PF to estimate SOC 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 capacity of 40 Ah and a nominal voltage of 3.2V, is used for the comparison study of the electric model comparison for estimating SOC of the battery cell. More detailed information regarding to the experiment set up was given in the previous section. In order to compare the performance of different battery electric models, several typical driving cycles will be applied. Here we will using 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 temperature is 0◦C. The test last for around 54 mins and the initial SOC value is adjusted to 100%. The second experiment is implemented on an aged cell which has the real capacity reduced to 38 Ah and the cell ambient temperature is still 0◦C. The second test also last 54 mins and the initial SOC 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 sample rate for the current and voltage sensors are 10Hz during the tests[35]. The battery models that will be used in this section has already introduced in Chapter 2. In terms of the estimation algorithm, square root unscented kalman filter will be used. Filter states are initialized to rated value drawn from the data sheet with covariance initialized to very small values. The other thing we have to addressed here is in all test cases, ”true” SOC we used as reference was calculated from the current sensor recorded data using Coulomb counting method. So as a matter of fact

the ”true” SOC is only relatively accurate since the current sensor error and the accumulated error 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 battery is a fresh new battery. Fig.5.3a and Fig.5.3b show the result for the RINT model; Fig.5.5d and Fig.5.3d show the results for the Thevenin model; Fig.5.3e and Fig.5.3f show the results for the Thevenin 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 hand side column shows results for the terminal voltage estimation of the test. From the pictures we can simply conclude that the estimation error of all 4 cases is not so big and within the accept-able limits. The following taccept-able5.2 shows the results of the estimation error and the computing power for each model. The reason why the error starts from zero is because we correctly set an initial value. The double polarization model which is usually called second order RC model does a better job considering the estimation error but in terms of the computing power, it cost the most time to calculate. In terms of the computing power, here we use computing time of one time calculation on personal computer to indicate the computing power of the estimation methods. For estimation error or the estimation accuracy here we use root mean square method to indicate the estimation accuracy. The formula to calculate the estimation error is given below.

SOCerror =

r 1

n((SOCref(0) − SOCest(0))

2_{+ ... + (SOC}

ref(T ) − SOCest(T ))2) (5.1.1)

Model The RINT Model The Thevenin model Thevenin Model with Functional R The DP Model Computing Power(s) 14.08 17.02 16.45 20.19 Estimated Error(%) 2.34 2.24 2.2 1.77

5.1. Comparison between different electric models 43

Model The RINT Model The Thevenin model Thevenin Model with Functional R The DP Model Computing Power(s) 17.77 20.1 19.65 20.19 Estimated Error(%) 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(new battery)

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

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

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

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

(e) SOC Estimation using Thevenin Model(functional R)

(f) Terminal Voltage Estimation using Thevenin Model(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 new battery cell

Secondly, the test was implemented on an aged cell with the same ambient temperature around 0◦C. Results for the RINT model is shown in frame Fig. 5.4a and Fig. 5.4b; results for the Thevenin model is shown in frame Fig. 5.4c and Fig. 5.4d; results for the Thevenin model with functional R is shown in frame Fig. 5.4e and Fig. 5.4f and results for the DP model is shown in the frame Fig. 5.4g and Fig. 5.4h. In all cases, we reset the initial of the battery capacitor to 38 instead of 42 for the new cell. But this should be done within the BMS using online parameter estimation to estimate the real battery capacity. Several methods has been presented in the literature can be generally divided into four groups [6]. The first method is based on the change in the measured battery OCV before and after charging or discharging and then the battery capacity is calculated based on the SOC-OCV relationship. The second method is to estimate the OCV change from the battery voltage measured under load. The third and fourth method is to using electric circuit model to calculate the battery capacity using joint or dual estimation. In order to compare with the previous simulation result we will implement the same 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 we still can see the priority of the second order RC model has better estimation result in terms of the accuracy. And the linear RINT model takes the least time to calculate. From these groups of experiment, we can easily see the aging effect will have a big effect no matter on the battery itself 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 Thevenin Model

(e) SOC Estimation using Thevenin Model(functional R)

(f) Terminal Voltage Estimation using Thevenin Model(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 aged battery cell

5.2

Comparison between different estimation algorithms

”Estimation algorithms are mathematical techniques used to compute the optimal estimates of states and parameters of a dynamical system” [36][9]. Here in our report we will compare six 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 and using this estimation algorithm. First the same model of new cell will be running under different temperature. Secondly the same model of cell will be running at different road conditions to test the accuracy of the monitoring method also. Another thing need to be mentioned here is that we will implemented first order RC model here considering the modest computing power it needed and 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 RC model under ambient temperature 0◦C, while the SOC was initialized to 100% and internal resistor R0 is 0.0005Ω, parallel resistor R1 is 0.0005Ω and the capacitor is 200 pF. Results for

the EKF is shown in the Fig.5.5a; results for the UKF is shown in the Fig:5.5b; results for the CDKF is shown in the Fig:5.5c; results for the SRUKF is shown in the Fig:5.5d; results for the SRCDKF is shown in the Fig:5.5e; results for the PF is shown in the Fig:5.5f. The detailed information about the computing power and estimated error can be found in the table5.3. From these figures we can conclude that existing estimation algorithms tend to either be accurate but complex or easy but suffer from the big errors it will produced. According to this, a trade