Comprehensive review on battery capacity estimation methods by DNV AS

Development of a Proposed Performance Standard for a Battery Storage System connected to a Domestic/ Small Commercial Solar PV system

A Comprehensive Review on Battery Capacity Estimation Methods

Report Number: PP198127-AUME-MS02-TEC-05-R-01-A

Project Partners

Funding Partners

Revision History: Revision No 1 2

Date

Authored by

Reviewed by

Approved by

03/12/2018 Dr. Sajeeb Saha

Dr Shama Islam Dr Md Enamul Haque

Dr Md Enamul Haque

18/12/2019 Dr. Sajeeb Saha

Dr Shama Islam Dr Md Enamul Haque

Dr Md Enamul Haque

DNV GL Approval

Approved 22/01/2020

The views expressed herein are not necessarily the views of the Australian Government, and the Australian Government does not accept responsibility for any information or advice contained herein. 2

DEAKIN UNIVERSITY

Deakin University CRICOS Provider Code: 00113B

Table of Contents Table of Figures ....................................................................................................................................... 5 List of Abbreviation ................................................................................................................................. 6 Executive Summary................................................................................................................................. 7 1.

Battery Capacity and State of Charge ............................................................................................. 8 1.1

Introduction ............................................................................................................................ 8

1.2

Battery Capacity Definitions ................................................................................................. 10

1.3

SoC and Its Relationship with Battery Capacity .................................................................... 11

1.4

Necessity of battery SoC Estimation in a PV-Battery System ............................................... 12

Battery Capacity Estimation Techniques ...................................................................................... 14 2.1

Introduction .......................................................................................................................... 14

2.2

Direct Measurement Approaches ......................................................................................... 14

2.1.1

Direct Measurement Method using OCV...................................................................... 14

2.2.2

Direct Measurement Method Using Battery Impedance ............................................. 17

2.3

Book Keeping Approach ........................................................................................................ 20

2.3.1

Coulomb Counting approach ........................................................................................ 20

2.3.2

Enhanced Coulomb Counting approach ....................................................................... 22

2.4

Model Based Approach ......................................................................................................... 22

2.4.1

Equivalent circuit model (ECM)..................................................................................... 23

2.4.2

Empirical model (EM) .................................................................................................... 26

2.4.3

Data Driven Learning model ......................................................................................... 27

2.4.4

Battery SoC Estimation using State Estimation Filters:................................................. 28

2.4.5

Performance of Model Based SoC Estimation .............................................................. 34

2.5

Learning Algorithm Based Approach .................................................................................... 35

2.6

Combined Approach ............................................................................................................. 38

2.7

Discussion and Conclusion .................................................................................................... 38

Table of Figures Figure 1: Charging and discharging of the battery bank depending on the availability of solar energy and load demand. [1]............................................................................................................................... 8 Figure 2: A conceptual diagram showing battery capacity. .................................................................. 10 Figure 3: Relationship between battery SoC and the battery capacity.................................................. 11 Figure 4: Schematic diagram of a small-scale hybrid PV-Battery system............................................ 12 Figure 5: Operating Region of Battery State of Charge (SoC). ............................................................ 12 Figure 6: Capacity fade of Li-ion battery cycling at a varying charge and discharge bandwidths. [3] 13 Figure 7: OCV vs SoC of a Li ion battery. [4] ...................................................................................... 15 Figure 8: Battery OCV after being charged to different SOC. [5] ........................................................ 15 Figure 9: Battery OCV-SOC under varying temperature and charging conditions. ............................. 16 Figure 10: LiFePO4 Battery OCV-SoC curve [9]. ................................................................................ 17 Figure 11: Nyquist plot of Li-ion battery impedance spectrum.[10] .................................................... 18 Figure 12: Equivalent circuit of a battery cell....................................................................................... 19 Figure 13: (a) Change in RHF of a 6 V. 2.6 A h lead-acid battery with SoC, (b) Rt Cdl vs SoC of a leadacid battery, where Rt Cdl is measured at the frequency corresponding to the peak of mid-frequency range. (c) Lead Acid cell impedance characteristics (modulus |Z|, real part Re(Z), imaginary part Im(Z)) vs SoC at 0.1 Hz. (d) AC impedance phase angle vs SoC of lead acid battery cell. [11] ......... 19 Figure 14: Enhanced Coulomb counting method proposed in [30]. ..................................................... 21 Figure 15: Battery Thevenin equivalent circuit model. ........................................................................ 23 Figure 16: Battery Rint equivalent circuit model.................................................................................. 23 Figure 17: Battery PNGV equivalent circuit model.............................................................................. 24 Figure 18: Battery DP equivalent circuit model. .................................................................................. 24 Figure 19: Piecewise linear approximation of OCV vs SoC [37]. ........................................................ 24 Figure 20: Schematic diagram of establishment of data driven model using machine learning algorithm. .............................................................................................................................................. 28 Figure 21: Schematic diagram of KF method. ...................................................................................... 30 Figure 22: Schematic diagram of the EKF method............................................................................... 31 Figure 23: Schematic diagram of AEKF method.................................................................................. 32 Figure 24: Schematic diagram of Observer based battery SoC estimation technique for batteries used alongside a PV system. ......................................................................................................................... 34 Figure 25: Schematic diagram of machine learning algorithm based battery SoC estimation. ............ 35

List of Abbreviation ABPS

Australian Battery Performance Standard

Ampere Hour

ANN

Artificial Neural Network

ARENA

Australian Renewable Energy Agency

BMS

Battery Management System

DoD

Depth of discharge

DST

Dynamic stress test

EMS

Energy Management System

ECM

Equivalent circuit model

Empirical model

DDM

Data driven model

ITP

IT Power (Australia) Pty Ltd, trading as ITP Renewables

Kilowatt

kWh

Kilowatt hour

Kalman Filter

EKF

Extended Kalman Filter

OCV

Open circuit voltage

SoC

State of Charge

Executive Summary Battery capacity is regarded as the most important parameter of a battery, precise knowledge of which is imperative for battery operation and optimal energy management in a PV-battery system and to ensure lifetime longevity for the battery. However, there are no reported battery capacity estimation techniques available in the literature that can estimate capacity of batteries with different chemistries under different operating conditions with good accuracy. Therefore, it is essential to include a generic battery capacity estimation methodology which is chemistry agnostic and performs well under wide spectrum of operating conditions. As capacity is widely regarded as one of the key performance criteria of a battery, inclusion of a generic battery capacity estimation methodology in the Australian Battery Performance Standard project (ABPS) is essential to generalise the standard for all commonly used batteries that are used in conjunction with PV systems. The generic battery capacity estimation methodology will be released as part of the ABPS project. In the context of battery technology, it is common practice to represent battery capacity in terms of its state of charge (SoC), and most of the existing techniques estimate battery capacity in the form of SoC. This report presents a comprehensive review on the commonly used battery capacity estimation methods, which includes a detailed description of each of the methods and highlights the advantages and disadvantages of the methods in terms of real-time application, accuracy and computational costs. Finally, a summary of the existing capacity estimation techniques has been presented. This report will be used as a guideline for developing a capacity estimation technique for battery energy storage systems connected to domestic/small commercial solar PV systems. The developed capacity estimation technique will be validated using battery system charge/discharge data from IT Power renewables battery testing program and experimental data generated as part of the ABPS project at CSIRO laboratories.

1.Battery Capacity and State of Charge 1.1

Introduction

In this report, a review of the existing methodology for battery capacity estimation has been outlined. Battery capacity is an important factor to aid consumersâ&#x20AC;&#x2122; decision making for battery selection. This battery capacity depends on different factors ranging from temperature, charging and discharging conditions, as well as life cycle. Thus, developing a generic method for estimating battery capacity is essential for benchmarking battery performance. In this regard, the report elaborates a range of capacity estimation methods and performs critical evaluation based on their suitability against different system variables, as well as operating conditions. Advancement of the battery technology plays a pivotal role in maximising the utilisation of solar energy. Nowadays, battery systems have become integral parts of small, medium and large-scale PV systems. Typical coordinated operation of the batteries with solar PV in relation to a â&#x20AC;&#x153;demand managementâ&#x20AC;? application is shown in Figure 1. The Energy Management System (EMS) and Battery Management System (BMS) in a PV-battery system control the charging and discharging of the battery to ensure maximum utilisation of the solar energy and the battery energy.

Figure 1: Charging and discharging of the battery bank depending on the availability of solar energy and load demand. [1]

Battery capacity is considered as one of the most important parameters of a battery, which is a representation of the amount of charge stored in the battery. The commonly used measure of battery capacity are watt-hours (Wh), kilowatt-hours (kWh), or ampere-hours (Ah). Among the available measures, Ah is the most commonly used measure of battery capacity, which is 8

defined as the number of hours a battery can provide a constant current equal to the discharge rate. The unit Ah is commonly used while working with a battery system where the battery voltage varies throughout the charging or discharging cycle. The unit Wh or kWh is a representation of the amount of energy a battery can store. For example, a 48 V, 100 Ah battery allows an energy storage of 100 Ah X 48 V = 4800 Wh or 4.8 kWh. Accurate and precise knowledge about battery capacity is imperative for optimum and efficient energy management of battery energy storage for residential solar PV systems, as well as to ensure a longer lifetime of the battery. However, it has been found that there is no available generic battery capacity estimation methodology that can be used for different battery chemistries and operating conditions such as temperature, aging, charging and discharging rates. Battery capacity is very closely related with battery state of charge (SoC). Battery SoC represents the current portion of available energy as compared to the nominal capacity (available energy) of a battery. The amount of energy a battery is able to deliver over its lifetime largely depends on the SoC. The energy management system (EMS) in a PV-battery system requires precise knowledge about the battery SoC, in order to ensure optimum and efficient operation of the PV-battery system, as well as a longer life cycle of the battery. Furthermore, capacity retention of a battery depends on how battery SoC is maintained during the charging and discharging cycle of the battery. Thus, an accurate technique to estimate battery capacity is highly important to the battery industry for testing and evaluation purposes. As a part of Australian Battery Performance Standard (ABPS) development, it is essential to include a generic battery capacity estimation methodology that can accurately estimate battery SoC regardless of the battery chemistry and operating conditions. The generic battery capacity estimation methodology will be released as part of the ABPS project. In this report, a detailed review of the battery capacity estimation methodology has been presented, which will be later used as the basis for development of a generic battery capacity estimation methodology. The developed battery capacity estimation methodology will be validate through the use of ITP test data and data obtained from the battery testing carried out by CSIRO.

1.2

Battery Capacity Definitions

Battery capacity is the measure of amount of extractable charge from a fully charged battery until its cut off discharge voltage is reached. However, it is worth noting that the battery capacity is not a constant parameter and it varies over battery lifetime due to internal aging of the battery. The factors that affect battery-aging process is charging and discharge current, operating temperature, battery depth of discharge (DoD), no of charging and discharging cycles etc. Unfortunately, there are no available consistent definition of battery capacity. However, the following definitions are commonly used in the literature [2]: a) Nominal Capacity (C Nominal ) : It is the defined capacity of a battery in the data sheet by the manufacturer for operation under nominal conditions, including nominal temperature (e.g., 25o C), nominal discharge current (e.g., one hour discharge rate (1C) ) and being fully discharged from fully charged condition. Nominal capacity is the capacity promised by the manufacturer. b) Available Capacity (C available ): This refers to the highest amount of charge that can be extracted from a battery in its actual aged state starting from a fully charged condition. Under nominal operating conditions, the available capacity of a new battery is the same as the nominal capacity of the battery.

Figure 2: A conceptual diagram showing battery capacity.

c) Dynamic Capacity (C dynamic ): Dynamic capacity of a battery refers to the amount of stored energy at any instant of time in the battery. The dynamic capacity varies with the charging and discharging of the battery as the stored energy varies in the battery.

A conceptual diagram of a battery showing the nominal, actual and dynamic capacity of a battery is shown in Figure 2. In the figure, the capacity fade section represents the loss of battery capacity due to aging and battery operating conditions.

1.3

SoC and Its Relationship with Battery Capacity

SoC is an indication of remaining energy in the battery relative to its energy when it was fully charged. The SoC gives the user an indication of the remaining time the battery will continue to perform before it needs recharging. In other word, the SoC is a measure of the short-term capacity of a battery. Usually, the SoC is termed as the fuel gauge of a battery, as it indicates how full the battery is. The SoC of a battery is commonly expressed in percentage, and defined as the dynamic capacity of the battery at any instant of time relative to nominal capacity, as shown below:

()

= SoC t

C Dynamic t () C Nominal

Ă&#x2014; 100%

(1)

In the equation (1), C Dynamic : capacity of the battery under consideration and C Nominal : Nominal capacity of the battery. A schematic diagram showing the relationship between battery capacity and its SoC is shown in Figure 3.

Figure 3: Relationship between battery SoC and the battery capacity.

For example, if a battery of 100 Ah nominal capacity possesses 80% SoC, it will imply that the battery has 80 Ah energy (remaining capacity) left before it is fully discharged. In other words, the SoC of a battery at any point in time provides knowledge about the remaining energy (capacity) that can be extracted from the battery at that instant. 11

1.4

Necessity of battery SoC Estimation in a PV-Battery System

Batteries have emerged as integral parts of residential and small-scale PV systems, as they provide the users a mean to better utilize the harvested PV power, and reduces dependencies on the grid power. A schematic diagram of a small-scale solar PV system with battery energy storage is shown in Figure 4. Appropriate functioning of the energy management system in a PV-Battery is essential to ensure optimum, efficient and economic operation of the PV system.

Figure 4: Schematic diagram of a small-scale hybrid PV-Battery system

Figure 5: Operating Region of Battery State of Charge (SoC).

The energy management in the PV-Battery system typically ensures charging and discharging of the battery in such a manner that the best cycle life of the battery is achieved. This is accomplished by ensuring battery SoC remains in the recommended region, i.e. SoC is

(

maintained between its maximum SoC max

)

(

)

and minimum SoC min values as shown in

Figure 5. This in turn avoids over charging and discharging of batteries. Moreover, studies show that the capacity-fading process of a battery depends on how SoC of the battery is maintained during the charging and discharging process. Figure 6 shows the dynamic stress test (DST) results of a Li-ion battery, which shows the capacity retention of the battery when it is cycled at varying charging and discharging levels. It can be clearly seen from the figure that retention of battery capacity depends largely on how the battery SoC is maintained during the charging and discharging cycles.

Figure 6: Capacity fade of Li-ion battery cycling at a varying charge and discharge bandwidths. [3]

Furthermore, most of the existing research on the monitoring for battery health is based on estimated SoC as it provides precise knowledge about the battery capacity. Therefore, accurate estimation of battery SoC, which in turn provides an estimation of remaining battery capacity of a battery is of paramount importance for monitoring and maintaining battery health, efficient energy management in a hybrid PV-battery system and ensuring longer life cycle of the battery.

2. Battery Capacity Estimation Techniques 2.1

Introduction

The existing techniques available in literature commonly estimates battery capacity in the form of SoC, as it provides the knowledge of the remaining capacity of a battery at any instant of time with respect to the available capacity of the battery. In the quest for accurate and online battery-capacity estimation, several techniques have emerged over the years, which are classified as below based on the methodologies adopted in those approaches. (a) Direct measurement approach. (b) Bookkeeping approach. (c) Model based approach. (d) Learning Algorithm based approach. (e) Combined approach. In the following sections, these approaches are explained in detail.

2.2

Direct Measurement Approaches

It is well studied that battery SoC has a distinct relationship between measurable battery quantities of batteries such as open circuit voltage (OCV ), terminal voltage (Vt ), internal impedance etc. That means

( )

SOC = y x

(2)

where, x = OCV ,Vt ,Z . Indirect measurement method, the function y â&#x2C6;&#x2019;1 : x ď Ą SOC

is approximated from the

experimental or historical data of the battery using lookup tables, curve fitting methods, machine learning methods etc. In the following, we first study the direct measurement method using battery OCV.

2.1.1

Direct Measurement Method using OCV

The relationship between open circuit voltage (OCV) of a Li-ion battery with SOC acquired from experimental study is shown in Figure 7, which shows that battery OCV is a monotonically increasing function of its SOC. This type of monotonically increasing 14

relationship also exists for other type of batteries such as Lead-Acid, Nickel Manganese Cobalt etc.

Figure 7: OCV vs SoC of a Li ion battery. [4]

Figure 8: Battery OCV after being charged to different SOC. [5]

In this method, the battery OCV vs SoC relationship is utilised to determine the SoC. Using this well-known mapping between OCV and SoC, a measured OCV value at any instance allows the corresponding SoC to be estimated. In the existing OCV based SoC estimation approaches, the OCV-SoC mapping function is implemented using a lookup table, mathematical expressions [5-7], linear (piece wise linearization) [4], and nonlinear curve fitting techniques [8, 9]. As OCV possesses a precise relationship to the SoC, this OCV vs SoC relationship is widely adopted in the literature for SoC estimation. However, there are some inherent issues in this approach, which makes this approach unsuitable for online SoC estimation techniques. In the following, these drawbacks are explained in detail. (a) Real-time measurement: The main hindrance in using OCV based SoC estimation approach for online application is that OCV voltage cannot be directly measured if there is no sufficient rest time. Figure 8 shows battery OCV after being charged to different 15

SoC. It can be seen from the figure that once the battery is disconnected from the system, the OCV requires a significant amount of time to reach its steady state. This makes OCV based SoC estimation technique unsuitable for online SoC estimation. (b) Varying OCV-SoC characteristics under different C-rate and temperature: It can be seen from Figure 9 (a) and (b) that battery OCV-SoC relationship varies for different temperature and C-rate condition. From the figure, it is evident that for the same open circuit voltage under different temperature or charging rates, the SoC can be significantly different. Therefore, the temperature and charging rate is required to be taken into account while implementing the mapping between OCV-SoC to ensure the accuracy of this method, which can significantly complicate the implementation of this approach.

( )

OCV (V)

(b)

SOC

1/5 C

SOC (%)

Figure 9: Battery OCV-SOC under varying temperature and charging conditions.

(c) Flat region in the OCV-SoC curve and battery-aging factor: For some battery types, for example, LiFePO4 battery, there exists a prominent flat region in the OCV-SoC curve. As can be seen from Figure 10 that in the region between 20% - 80% SoC the variation in OCV is very small, which makes it difficult to derive a mapping between OCV and SoC in this region. Another concern with this approach is the battery-aging, as with the aging of a battery the OCV-SoC relationship varies from its nominal relationship. Therefore, an aging factor is required to be included into consideration to yield accurate SoC estimation using this approach as the battery ages. This requires carrying out a large number of experiments under different cycling conditions in order get a family curve that represents OCV-SoC relationship. 16

Figure 10: LiFePO4 Battery OCV-SoC curve [9].

The OCV based approaches are commonly used as a supporting tool and adopted in conjunction with other approaches. These methods will be discussed later when describing the combined SoC estimation technique.

2.2.2 Direct Measurement Method Using Battery Impedance In the context of batteries, impedance is commonly referred to as electrochemical impedance. This is defined as the transfer function between battery potential and current. The battery electrochemical impedance is a complex quantity and usually measured using a frequency response analyser. The interests in battery impedance measurement stems from the fact that different components of a battery impedance have distinct relationships with the battery SoC. The method of determining battery impedance is commonly known as impedance spectroscopy. This is based on characterising battery dynamic behaviour by exciting the battery using small amplitude voltage or current signals

(

)

(

= D V V= I max sin 2p ft max sin 2p ft or D I

)

(3)

imposed with the battery terminal voltage or charging/discharging current at different frequencies and corresponding yielding voltage or current response:

(

D= I I max sin 2p ft + f

)

(

or D V= Vmax sin 2p ft + f

)

(4)

From (3) and (4), battery impedance is expressed as

( )

Z f=

Vmax −i q e = I max

( )

Z ∠−q = Real Z + j Imaginary Z

(5)

where q is the phase angle difference between current and voltage.

Figure 11: Nyquist plot of Li-ion battery impedance spectrum.[10]

The impedance response of the battery under different frequency can be plotted in a bode plane (impedance magnitude vs frequency or phase angle vs frequency) or, more frequently in Nyquist plane (imaginary part vs real part). The Nyquist plot of the complex impedance of a Li-ion battery under different frequencies is shown Figure 11, which shows that the impedance spectrum can be divided into three sections depending on the frequency of the excitation signal. The high-frequency tail in the Nyquist plot is interpreted as the effect of the ohmic resistance of the inductive battery components, such as current collectors and test cables. The lowfrequency straight line is due to the electrochemical double-layer and charge-transfer reactions, while the mid-frequency semi ellipse corresponds to ion diffusion in the electrolyte and the pores of the electrodes. A commonly used electrical circuit that represents the complex nature of the battery cell impedance is shown in Figure 12, where subscripts p and n are related to positive and negative electrodes of a battery. In the equivalent circuit, Lp and Ln are the inductances related to the imaginary part of a battery complex impedance Z(f) at high frequency as shown in the Nyquist plot in Figure 11, the resistance RHF represents the battery resistance at high frequency. The resistances Rt,p and Rt,n are the equivalent resistances of the charge transfer at the electrodes, while the capacitances Cdl,p and Cdl,n are the capacitances due to space charge distribution in the electrochemical double layer. The resistances (Rt,p and Rt,n) and the capacitances Cdl,p and Cdl,n are the real and imaginary parts of the battery impedance at the low-frequency straight line in the Nyquist plot in Figure 11. The battery impedance in the mid-frequency semi-ellipse 18

of the Nyquist plot is represented in battery equivalent circuit by ZW,p, and ZW,n and are commonly termed as Warburg impedance.

Figure 12: Equivalent circuit of a battery cell.

Figure 13: (a) Change in RHF of a 6 V. 2.6 A h lead-acid battery with SoC, (b) Rt Cdl vs SoC of a lead-acid battery, where Rt Cdl is measured at the frequency corresponding to the peak of mid-frequency range. (c) Lead Acid cell impedance characteristics (modulus |Z|, real part Re(Z), imaginary part Im(Z)) vs SoC at 0.1 Hz. (d) AC impedance phase angle vs SoC of lead acid battery cell. [11]

Over the years, extensive studies have been carried out to determine the relationship with the aforementioned parameters with the battery SoC and distinct relationships have been identified. Figure 13 (a) - (c) show relationships between lead acid battery cell ac impedance with the SoC of the battery. Similar relationship between ac impedance vs SoC for other batteries cells, such as Nickel Cadmium, Nickel metal Hydride, Lithum Ion etc. have been reported in literature. Since the ac impedance of a battery has distinctive relationships with the battery SoC, these relationships are used as indicators of battery SoC over the years. For example, in [12] the relationship between battery ac impedance and SoC has been mapped using recurrent neural network to estimate Li-ion battery SoC estimation. In [13], impedance spectroscopy and extremum machine learning algorithm has been used to estimate battery SoC. A new relationship between high frequency battery resistance with the remaining battery capacity of Lithium Polymer batteries has been identified through experimentation in reference [14], which is mathematically formulated using theory of evidence [15] to estimated battery SoC and SoH. In reference [16], relationships between equivalent series resistance (Rs) and capacitance (Cs) 19

corresponding to battery ac impedance (Zf) with SoC at low frequency spectrum for Li-ion battery have been introduced and are used to estimate Li-ion battery SoC. A detailed review on the ac impedance based battery SoC estimation has been detailed in reference [17]. Due to the proven relationships between battery ac impedance and SoC, impedance based dynamic models of batteries [18-20], which are determined using impedance spectroscopy are widely used for model based approaches for determination of battery SoC. However, online implementation of impedance based SoC estimation technique is not easy as: (a) Impedance spectroscopy requires additional circuitry to inject high frequency ac signals to determine ac impedance of a battery [11]. Therefore, online implementation of this test is complex. (b) It has been identified in literature that the relationships between battery ac impedance parameters and SoC are greatly affected by temperature variation [21]. Therefore, this approach of SoC estimation is best suited under controlled laboratory conditions, which makes the implementation very expensive. Nonetheless, the impedance-based approach still is deemed as one of the powerful tools for analysing the battery internal dynamics and estimating battery SoC. For this reason, continued effort has been made over the years for online measurement of ac impedance of the battery [2225]. The progress of online impedance spectroscopy methods for online SoC estimation techniques using battery ac impedance has been reported in the literature (for example references [26, 27]). However, further research development is required before the impedancebased techniques can be adopted for online SoC estimation techniques in practical systems.

2.3 Book Keeping Approach

The book keeping approaches for battery SoC estimation is established using the definition of electric charge and by keeping a track of the battery charging or discharging current. There are two types of book keeping approaches reported in the literature: (a) Coulomb counting approach and (b) Enhanced Coulomb counting approach.

2.3.1 Coulomb Counting approach The coulomb counting approach, which is also known as Ampere-hour Integral method is regarded as the most commonly used battery SoC estimation method, because of its simplicity and ease of implementation [21, 28]. Most of the battery energy management systems in real world devices such as computers, mobile phones etc. use this approach for the associated 20

battery SoC estimation. In this approach, charging and discharging current of a battery is monitored using corresponding measurement device(s) to determine the amount of charge received or given by the battery during a period between time t0 and t1, then calculate the battery state of charge as follows [29]. 1

= SoC SoC 0 + Qref

â&#x2C6;Ť hcI L dt

(6) where SoC 0 are battery state of charge at the beginning of the period, hc is Columbic efficiency and Qref is reference capacity, as highlighted earlier this can be either rated capacity or battery available capacity.

Figure 14: Enhanced Coulomb counting method proposed in [30].

The main concerns associated with the Coulomb counting methods include: (a) Accumulated errors due to measurement error: Since integral operation is carried out on the measured charging and discharging currents, any error and/or noise in the measurement will accumulate and cause SoC estimation error. 21

(b) Initial value error: A precise knowledge about initial SoC value is imperative for accurate SoC estimation using this approach. Any error in the initial SoC will accumulate due to the integral action in the estimation process. (c) Difficulty in determining Coulombic efficiency, h [31]:

Since the Coulombic

efficiency is affected by charging/discharging rate, SoC range, temperature and aging, it is a difficult task to estimate Coulombic efficiency accurately. The aforementioned issues related to the coulomb counting method have initiated development of approaches that aim to enhance the Coulomb counting method; these approaches has been categorised as enhanced Coulomb counting approach.

2.3.2 Enhanced Coulomb Counting approach Despite the issues related to Coulomb counting approach, it is regarded as one of the most suitable SoC estimation technique that can be implemented practically. A lot of research has been carried out with a view to overcome the issues related to Coulomb counting method [30, 32-34]. For example in reference [32], in order to overcome the SoC initial value error, battery temperature and terminal voltage are continuously monitored alongside the current. Using the measured terminal voltage, temperature, currents and battery equivalent circuit model [35] the battery OCV is approximated. This is followed by the use of battery OCV vs SoC relationship from a look-up table to determine battery initial SoC required for coulomb counting method. In [33], in order to overcome the issue related to coulombic efficiency, modified Puekert relationship that includes current rate parameters are included along with the Coulomb counting method. In reference [30], using the battery depth of discharge (DoD) information, correction factors are proposed for charging, discharging and self-discharge modes to account for varying Coulombic efficiency of the battery in Coulomb counting method to enhance the accuracy of battery SoC estimation. An schematic diagram of the enhanced Coulomb counting method proposed in [30] is presented in Figure 14. Similar to the aforementioned approaches, there are several other approaches available in the literature [4, 31, 36], which proposes correction methods that enhances the accuracy of Coulomb counting method.

2.4 Model Based Approach The difficulties of online implementation of the direct approaches and the adverse effects of measurement error on the coulomb counting approaches for battery SoC estimation have motivated the emergence of model-based approaches. The model-based approaches, which utilise a mathematical model of a battery alongside advanced estimation algorithms are 22

reported to possess better accuracy and robustness against measurement error. Based on the model used for SoC estimation, this approach can be subdivided into three categories: (a) Equivalent circuit model, (b) Empirical model, and (c) Data driven learning model. In the following, these models are described briefly.

2.4.1 Equivalent circuit model (ECM) Commonly used battery equivalent circuit model used in the model based approach for battery SoC estimation is the Thevenin equivalent circuit model [35], which is shown in Figure 15. In the model R0 and Rth represent the ohmic and polarization resistances of the battery. The capacitance Cth is included in the model to describe the transient response of the battery during the charging and discharging process. Vth I Vth = − + L RthCth Cth

(7)

Vt = VOCV − I L R0 − Vth

(8)

. Figure 15: Battery Thevenin equivalent circuit model.

Figure 16: Battery Rint equivalent circuit model.

Figure 17: Battery PNGV equivalent circuit model.

Figure 18: Battery DP equivalent circuit model.

Figure 19: Piecewise linear approximation of OCV vs SoC [37].

Equations (7) and (8), describe the dynamics of the battery Thevenin equivalent circuit model shown in Figure 15. The other types of existing equivalent circuit models that are used for SoC estimation are Rint, PNGV and DP model, which are shown in Figure 16 - Figure 18 [38]. The equations related to the Rint, PNGV and DP models can be found in [35]. These models possess varying degrees of accuracy and complexity and are used for battery SoC estimation depending on the accuracy requirement and application. The parameters of the battery models are usually determined through rigorous experimental studies and there are several methods for battery parameter estimation reported in the literature, for example [7, 39-41]. A review on the existing methods for estimation of parameters related to the battery equivalent circuit models shown in Figure 15 - Figure 18 can be found in [42]. It should be noted that 24

the battery OCV (VOCV ) is not an online measureable quantity. However, as the battery OCV is a function of SoC and it can be approximated by regression models described as follows: (i)

Linear regression model [37, 43]: Using the OCV vs SoC relationship, piecewise linear regression models are used to represent VOCV in terms of SoC. In reference [37], the following piecewise linear approximation is used to represent each segments of the OCV vs SoC relationship shown in Figure 19.

(

)

VOCV SoC= A0,n + A1,n SoC n

(9)

where n is the number of linear segments in the approximation of OCV vs SoC curve, in reference [37], n has been chosen to be 9 as shown in Figure 19. The coefficients A0,n and

A1,n are usually computed using curve fitting technique. (ii)

Polynomial regression model [38, 44, 45]: In this model battery OCV vs SoC relationship is approximated using an n th order polynomial regression model as shown below:

(

)

VOCV SoC = A0 + A1SoC + A2SoC 2 + .... + An SoC n

(10)

Order of the polynomial is chosen based on the accuracy requirement of the SoC estimation. The coefficients of the polynomial in (10) is determined using curve fitting techniques on the experimental data related to the battery. (iii)

Nonlinear regression model [46-53]: Most commonly used regression model that is used to approximate the monotonically increasing relationship as below:

(

)

VOCV SoC = K 0 + K 1SoC + K 2SoC 2 + K 3SoC 3 + .... + K n SoC n K + n +1 + K n +2 loge SoC + K n + 3 1 â&#x2C6;&#x2019; loge SoC SoC (11)

(

)

(

))

where OCV is approximated as sum of polynomial, inverse and logarithmic functions of SoC in order to represent the OCV vs SoC relationship. The coefficients of the nonlinear regression model in (11), i.e., K 0,K 1,....,K n +1,K n +2,K n + 3 are commonly approximated using polynomial curve fitting on experimental battery data. Since the battery OCV vs SoC relationship is affected with variations in temperature, in order to include the temperature effect in the SoC estimation in reference [54], the least square regression method

the

battery

experimental

data

used

determine

coefficients

K 0,K 1,....,K n +1,K n +2,K n + 3 as polynomial functions of temperature.

(

)

Combining (6) - (8) and VOCV SoC approximation model ((9) or (10) or (11)) in discrete time, the following state space model [37, 43, 46, 47] is achieved:

(

)

= xk +1 fECM xk,uk , qk + wk = yk gECM xk,uk , qk + J k

(

)

(12)

= V SoC  ,yk Vt ,k and uk = I L,k are state vector outputs and inputs of the where xk =  th,k k  system, qk is a vector containing time varying model parameters; wk and J k process and measurement noise and uncertainties respectively.

2.4.2 Empirical model (EM) In empirical modesl, terminal voltage of a battery is represented as a mathematical function of battery SoC and its charging and discharging current. Classical empirical models that are widely adopted for mathematically representing battery terminal voltage are as follows: (i)

Shepherd model [55]: In this model the terminal voltage of a battery is mathematically represented as a function of battery charging/discharging current as follows:

C Vt SoC = VOCV − Rint i L − 1 0 SoC

(

)

(13)

where VOCV is battery OCV when it is fully charged, Rint is the battery internal resistance 0

and C1 represents a constant. The unknown parameters of the model are either identified offline using regression techniques using laboratory test data, or they are co-estimated online while estimating the battery SoC. (ii)

Unnewehr universal model [56]: Battery terminal voltage in this model is represented mathematically as follows:

(

)

(14)

Vt SoC = VOCV − Rint i L − C1SoC 0 (iii)

Nernst model [57]: The following mathematical expression is used in this model for representing the battery terminal voltage as a function of battery SoC and its charging and discharging current.

C Vt SoC = VOCV − Rint i L − 1 − C 2SoC + C 3 loge SoC 0 SoC +C 4 loge 1 − SoC

(

)

(

)

(15)

In (15), C1 − C 4 are model constants, which are commonly identified offline using regression techniques carried out on the experimental data set of the battery. The accuracy of the aforementioned model in expressing battery terminal has been compared in [58], which shows that the Nernst model has better accuracy compared to other two models. However, this model does not include the battery hysteresis effect and therefore suffers from inaccuracy during relaxation period [59]. In order to increase the accuracy of the empirical model, advanced models are derived by including more parameters in the model. Examples of empirical models with greater accuracy as compared to the classical models can be found in [60, 61]. The discrete time state space equation corresponding to the empirical model [9, 52, 62, 63] in the standard form yields by combining the SoC equation in (6) with the battery empirical model ((13) or (14) or (15)) as follows:

( (

) )

= xk +1 fEM xk,uk , qk + wk = yk gEM xk,uk , qk + J k

(16)

The state variable in the state space equation in (16) is xk = SoC , the input and output variables

uk = I L,k and yk = Vt ,k .

2.4.3 Data Driven Learning model The complexity of determining the battery equivalent circuit model parameter and limited capability of empirical model in describing battery hystersis and relaxation phenomena combined with the emergence of data mining methods in the machine learning area have motivated the development of data driven learning battery models. The main benefit in this model is that it does not require prior knowledge about the battery. In this model, a mapping function x : I L,k 

SoCk Tk   Vt relates the battery terminal voltage with the battery 

SoC, charging/discharging current and the temperature as follows:

(

Vt = x I L ,SoC ,T

)

(17)

Figure 20: Schematic diagram of establishment of data driven model using machine learning algorithm.

The mapping function x is determined by harnessing the knowledge inherent in the historical measurement data using machine learning algorithms such as artificial neural network (ANN) [64], support vector machine (SVM) [65], extreme learning machine (ELM) [66] etc. A simplified schematic of estimation of mapping function is shown in Figure 20. The discrete time state space equation related to the data driven model yields by combining (6) and (17) as follows:

( (

) )

= xk +1 fDDM xk,uk , qk + wk yk gDDM xk,uk , qk + J k =

(18)

The state variable in the state space equation in (18) is xk = SoC , the input and output variables uk = I L,k and yk = Vt ,k . The state space models (12) , (17) and (18), corresponding to equivalent circuit model, empirical model and data driven learning model respectively, are used by state estimation techniques battery SoC estimation. The broad group of state estimation techniques can be categorised into two main groups: (a) State estimation filters, and (b) state estimation observers.

2.4.4 Battery SoC Estimation using State Estimation Filters: State estimation filters such as Kalman filters, advanced Kalman filters and particle filters are widely used for estimation of battery SoC. In the following, we briefly detail the filtering techniques that are commonly used for battery SoC estimations. Kalman filter: Kalman filter (KF) which is regarded as the optimal state estimator has

(i)

been widely used as an on-line tool for estimating SoC of a battery. The main feature of the KF is that it allows to recursively estimate internal states (unmeasurable) of a system, which is SoC for the case of a battery, using prior knowledge, prediction from system models and noisy measurement. The advantage of KF approach lies in the fact that this approach initially estimates current system state using the estimation of earlier state and then updates it according to the available measurement of the system. A schematic representation of KF used for battery SoC estimation is shown in Figure 21. The steps carried out in KF are briefly explained as follows. â&#x20AC;˘

Prediction Steps: 28

(i) System state vector is predicted first using previous time step state vector estimation x̂k−+1 using the discrete time linearized system model as shown in equation (a) in

Figure 21. In the case of a battery system, one of the models among the available models ((12), (16) and (18)) are commonly used after linearizing it around initial operating condition. As explained earlier in the description of battery models, the state vector of the battery model contains battery SoC and the voltage across the internal capacitor if ECMs are chosen; else, for the other two battery models (EM and DDM) the battery SoC is the only state. − (ii) This is followed by a prediction of error covariance matrix Px,k +1 and computation

of Kalman gain K k +1 using equations (b) and (c) as shown in Figure 21. (iii) Then using x̂k−+1 and the output equation in the discrete time linearized system model, system output ŷk +1 is predicted as shown in equation (d) of Figure 21. In the context of battery, as can be seen from the battery model, this step estimates terminal voltage of the battery. •

Correction Steps: (i) Estimated system output ŷk +1 (estimated battery terminal voltage) is compared with the measured system output yk +1 (measured battery terminal voltage) as shown in Figure 21. (ii) The error ey,k +1 is used to correct the state prediction as shown in equation (e) in the figure.

However, the main drawback of the KF method is that it requires a linearized system model, but the battery models are nonlinear as described earlier. Therefore, in order to use the KF for SoC estimation, the battery model is required to be linearized around an operating point of the battery. The linearized model will not accurately describe the battery behaviour when the battery operating condition deviates far from the operating point around which the battery model is linearized.

Figure 21: Schematic diagram of KF method.

(ii)

Extended Kalman filter: The extended Kalman filter (EKF) overcomes the issues of KF related to linearization by slightly modifying the steps in KF to include the nonlinear system model in the prediction and correction steps [6, 19, 67-70]. As can be seen from Figure 22, the state and output are predicted using a nonlinear system (battery) models (equations (a) and (d) in the figure). However, in every time step k+1, the nonlinear system (battery) model is linearized around the predicted system state x̂k+ to get system matrices Ak ,Bk and C k , which are used while computing and updating the state − + estimation error covariance matrix ( Px̂,K +1 and Px̂,K +1 ) and the Kalman gain ( K k +1 ).

‘

Figure 22: Schematic diagram of the EKF method.

Since the EKF uses nonlinear system model, this approach can estimate system states over the complete horizon of system operating conditions. For this reason, the EKF filter is very widely adopted for battery SoC estimation. However, in the case of a highly nonlinear system (the accurate battery models can be highly nonlinear), linearization around every predicted system state may even fail to represent the corresponding nonlinear system accurately. This is due to the fact that the linearization process (for example Taylor series expansion) usually neglects the higher order terms in the approximation of nonlinearities, which in turn may cause loss of complete essence of the nonlinear function. Keeping the effectiveness of the EKF in estimating nonlinear system states under consideration, there has been a great deal of research carried out to improve the EKF to accurately estimate battery SoC. For example, in reference [71], a dual EFK is used to incorporate battery OCV-SoC relationship to accurately estimate battery SoC. In references [72, 73], the equivalent circuit and empirical models of batteries are improved by incorporating more parameters, then EKFs are developed using these improved models to accurately estimate the battery SoC. Improvements in EKF methods are proposed in [74] and [75] to enhance the estimation accuracy of EKF.

Figure 23: Schematic diagram of AEKF method.

(iii)

Adaptive Extended Kalman filter:

To incorporate the varying uncertainty in system model and measurement noise, further improvement in EKF have been proposed, which is commonly known as adaptive extended Kalman filter (AEKF). The schematic diagram of AEKF is shown in Figure 23 (highlighted in blue in the figure), at every time step k+1, using N subsequent time samples (including N-1 previous time samples), estimate the measurement noises { J k +1 â&#x2C6;&#x2019;N ,....,J k ,J k +1} and ( )

Ë&#x2020; Ë&#x2020; update the process and measurement noise variance matrices Q v,k +1 and Rw,k +1 . This improves the EKF to incorporate the varying system and measurement uncertainties. This feature of AEKF has motivated researchers to adopt AEKF to ensure enhancement of battery SoC estimation accuracy during varying charging and discharging, temperature and aging, as well as measurement noise conditions [44, 53, 63, 76, 77]. (iv)

Other State Estimation Filters:

Besides, KF, EKF and AEKF, other state estimation filters have also been adopted to enhance battery SoC estimation. These approaches are developed to enhance certain features of battery 32

SoC estimation such as accuracy, implementation complexity, computational burden, variations in system operating conditions etc. For example, in the Unscented Kalman filter (UKF), to overcome the inaccuracies due to linearization process of nonlinear systems the Unscented transformation has been adopted, and it has been well documented that while estimating states of highly nonlinear systems, the UKF outperforms the KF, EKF and AEKF [78]. The feature of handling highly nonlinear system with less computational cost and greater efficiency has resulted in the UKF being very widely used for estimating battery SoC [79-82]. Other extensions of the Kalman filter, such as the Sigma point Kalman filter [83-85], fading Kalman filter [86], etc have also been used. Other than Kalman filters and their extensions, particle filter [9, 87] and H â&#x2C6;&#x17E; filter [88] are also reported to be used for battery SoC estimation. (v)

Observer based State Estimation:

In observer-based state estimation techniques, instead of stochastic models related to batteries incorporating measurement and process noise distribution, deterministic models of batteries are considered. In observer-based approaches, it is assumed that the parameters of a battery equivalent circuit model are predetermined from experimental data and measurement noise is not significant. A basic diagram of observer-based battery SoC estimation technique is presented in the Figure 24. Different types of state estimation observers are reported in the literature that are used for battery SoC estimation. For example in [89], a modified linear Luenburger observer is used to estimate battery SoC by linearizing the battery equivalent circuit model at every time step. A P-I observer, which is developed using a linear approximated battery model, has also been adopted for battery SoC estimation in [89]. In order to adaptively tune the observer gains to incorporate the variation in battery models due to change in operating conditions such as aging, temperature and charging/discharging rates etc, adaptive observers are used in [90] and [91] . Nonlinear observers that can deal with nonlinearities in a battery model are adopted in [92-94]. Apart from the aforementioned observers, sliding mode observers, due to their robustness against modelling uncertainties, have also been widely adopted for battery SoC estimation [9597].

Figure 24: Schematic diagram of Observer based battery SoC estimation technique for batteries used alongside a PV system.

2.4.5 Performance of Model Based SoC Estimation So far, the battery models and the estimation algorithms used for model-based battery SoC estimation algorithm have been explained in detail. Let us discuss the performance of modelbased approaches used for battery SoC estimation. It should be evident from the discussions so far that the model-based approaches take estimation error into consideration by comparing estimated terminal voltages form the estimated battery state with the measured terminal voltage and corrects that estimation. This feedback loop in the estimation approach enhances the accuracy of model based SoC estimation techniques [98-100]. However, the model based approaches require precise battery models, which requires significant effort in terms of experimentation and model parameter identification [100, 101]. Though there are estimation algorithms reported in the literature that are capable of adaptively accounting for model parameter variations, or estimate the parameters online alongside battery SoC estimation, these approaches are reported to be computationally expensive and complex in terms of their implementation [21].

2.5 Learning Algorithm Based Approach The evolution of machine learning and data mining techniques, as well the great advancements in computational algorithms have motivated researchers to formulate the battery SoC estimation problem as a machine learning regression problem. In this approach, SoC of a battery is estimated using predetermined nonlinear relationship between battery SoC and measurable battery parameters such as voltage, current and temperature, etc.

Figure 25: Schematic diagram of machine learning algorithm based battery SoC estimation.

The nonlinear relationship between a battery measureable quantity and its SoC is estimated by a nonlinear function

f̂

that maps battery measurable quantities and SoC, i.e.,

= f̂ : x = V ,T ,I ,etc.  y SoC . The function f̂ is approximated by learning the inherent

knowledge embedded in historical or experimental battery data. The learning process is commonly known as training which is carried out on a set of pre-processed training data. Once the training process approximates = f̂ : x = V ,T ,I ,etc.  y SoC , the function is ready to be used online and estimate battery SoC as shown in Figure 25. There are many different machine learning algorithms that have been used over the years for estimation of battery SoC. Artificial Neural Network (ANN) [8, 64, 102-104] is one of the most commonly used machine learning techniques for battery SoC estimation. In reference [105], multi hidden layer Wavelet neural network optimized using Levenberg – Marquardt algorithm to estimate battery SoC is described, using battery terminal voltage, current and ambient temperature measurements. A dual neural network fusion battery model has been proposed in [8] to utilize battery OCV vs SoC relationship for SoC estimation. A load classifying neural network based battery SoC

estimation technique has been proposed in [106]. However, the ANN based estimation algorithms are reported to suffer from following issues: i)

Convergence to local instead of global minima.

ii)

Over fitting issues and low generalization capability.

iii)

Measurement noise in data can significantly affect the training process and hence the estimation accuracy.

iv)

No well-defined approach to determine number of hidden layers and size of data set to accurately approximate the mapping function.

Computational complexity could be high depending on the number of inputs and hidden layers.

Fuzzy logic based learning methods have also widely adopted for battery SoC estimation [107109]. This approach formulates a linguistic set of rules using experimental or historical set of data related to batteries that relates battery measured quantities with battery SoC. The linguistic rules reduce the impact of measurement rules and uncertainties related to battery model parameters. However, with regards to fuzzy inference-based algorithms, it is well known that there is no systematic method to determine the rule set and the input and output membership function; these are usually determined intuitively. Combination of ANN and fuzzy inference based Adaptive Neuro Fuzzy Inference system (ANFIS) have also been reported to be used for battery SoC estimation [110, 111]. Compared to ANN and fuzzy inference systems, support vector machine (SVM) are considered to have better generalization properties. These are based on the Structural Risk Minimization (SRM) technique, which minimizes the upper bound on the expected risk principle while the ANN and Fuzzy algorithms use Empirical Risk Minimization (ERM), which minimize the least square error on the training set. Some of the SVM based SoC estimation approach include [112115]. Like other learning approaches, SVM based approaches also require sufficiently large sets of data to generalize the relationship between battery measureable quantities such as voltage, current, temperature, charging rate etc. Therefore, the accuracy of SVM approach under different operating conditions, like any other learning algorithm based approaches, depends largely on how well the training data set related to a battery is constructed through experimentation under different temperature and charging/discharging conditions.

Table 1: A summary of existing battery capacity (in terms of SoC) estimation approaches Approach

Direct Measurement based Approach

OCV based approach

Impedance measurement based approach

Coulomb Counting method

Advantages

Issues related to the approach

Uses SoC vs OCV relationship

Can provide SoC estimation with good accuracy.

Uses the relationship between battery ac impedance and SoC. Battery ac Impedance is determined using spectroscopy test.

Can provide SoC estimation with good accuracy.

Offline approach. On line SoC estimation is not possible, as measurement of OCV requires a long rest time. Impedance spectroscopy is an offline test that requires additional complex set up. In addition, it has been reported that this test yields accurate battery impedance measurements only in a controlled environment in a laboratory.

In this approach, the amount of charge received or given by the battery during a period is determined from measured battery current to estimate as below: = SoC SoC 0 + Q

â&#x2C6;Ť hcI L dt

Most commonly used method for practical applications for its simplicity and ease of implementation

Affected by current measurement error and error in initial SoC value. Difficulty in determining Columbic efficiency in real time.

ref t 0

Book keeping approach Enhanced Coulomb Counting method

Model based approach

Methodology

Equivalent circuit model (ECM) based approach Empirical model (EM) based approach Data driven model (DDM) based approach

Learning algorithm based approach

Coulomb counting method is improved by including battery OCV vs SoC relationship, depth of discharge (DoD) information and correction factors for charging, discharging and self-discharge modes in order to update columbic efficiency online. Uses one of the models (ECM, EM and DDM) to derive stochastic filter (Kalman filter, Extended Kalman filter, Unscented Kalman filter, Particle filter or H infinity filter) or observer to determine battery SoC in real-time.

In this approach SoC of a battery is estimated using predetermined nonlinear relationship between battery SoC and measurable battery parameters such as voltage, current and temperature, etc. The nonlinear relationship function is approximated by learning the inherent knowledge embedded in historical or experimental battery data. Commonly used learning algorithms include ANN, SVM, Extreme learning machine, Fuzzy logic, Genetic algorithm etc.

Overcomes issues with coulomb counting method by including correction factors to overcome current measurement error and inaccuracy due to error in initial SoC value.

Has the ability to determine battery SoC in real-time with good accuracy.

Added layer of complexity in coulomb counting method, which complicates the real-time implementation.

It is difficult to determine battery model parameters accurately. It requires prior laboratory experiment to determine the battery model parameters. These approaches are usually computationally expensive.

Large data set is required. Affected by errors/noise in training data set. Difficulty in determining large data set that include data under different battery operating condition. Computationally expensive.

2.6 Combined Approach

So far, a detailed review of existing approaches for battery capacity (in terms of SoC) estimation has been presented. It is quite evident from the review that each approach has its merits and demerits. In order to include virtues of different approaches, hybrid approaches that combine two capacity estimation techniques have evolved. These hybrid approaches not only increases the reliability and accuracy of capacity estimation, but also reduces cost of the battery management system. For example, in [116] an approach that incorporates EKF and Coulomb counting has been presented, which is reported to overcome the issue of initial SoC value error inherent in the coulomb counting method. Another approach including adaptive unscented Kalman filter with least square support vector machine has been reported in [65].

2.7 Discussion and Conclusion

Remaining capacity is one of the key parameters of a battery, which is required to be estimated with good accuracy to ensure efficient and optimum operation of a battery. It is a common practice in the battery industry to represent the battery capacity in terms of SoC and there exists numerous techniques in the literature to estimate battery capacity in terms of SoC. All of these techniques have varying degrees of accuracy, applicability and computational requirements. In Table 1, pros and cons of each of the SoC (battery capacity) estimation technique are highlighted, which may be used as a rough guideline for choosing SoC estimation technique for a PV-battery system. With the knowledge gained from the literature review carried out in this report, in the next stage of the project, a generic capacity estimation method will be developed which should possess reasonable computation complexity, easy to implement and guarantees good accuracy across a range of battery chemistries and under a range of operating conditions. The developed capacity estimation method will be validated through test data and the experimental data obtained from CSIRO throughout this project.

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