European Electric Vehicle Congress Brussels, Belgium, 3rd – 5th December 2014
Classification of Electric modelling and Characterization methods of Lithium-ion Batteries for Vehicle Applications Alexandros Nikolian1, Joris de Hoog1, Karel Fleurbay1, Jean-Marc Timmermans1, Omar Noshin1, Peter Van de Bossche1, Joeri Van Mierlo 1 1
Vrije Universiteit Brussel, Pleinlaan 2 Brussels 1050, Belgium
Abstract In this paper an extensive overview of different state-of-the arts models, created to simulate the behaviour of lithium ion batteries, will be presented. A new classification system for different types of battery models is proposed, which includes models ranging from electrochemical, electrical, thermal and mechanical point of view. The new proposed classification system, distinguishes in a structured way between the large variety of available battery models based on the method used to relate the inputs to the outputs (i.e. empirical, semi-empirical and physical modelling). Further, a distinction is made based on the timescale of the modelling. In this way, it is clear if the model in casu is suitable to give information on the short-term behaviour or on the long-term behaviour of the battery. Finally, the different electrical models, suitable for lithium ion batteries, will be discussed and compared with special attention to the performance of the different models for simulating the dynamic behaviour of the batteries. Keywords: Lithium battery, Equivalent Circuit Models, Characterization Techniques, Battery
Simulation, Testing Standards
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Introduction
Academic research and applications of lithiumion batteries have seen an increasing interest during the past decade [1]–[19]. This is mainly due to the increase use of electric applications ranging from small to high energy and power demanding systems [4]. The automotive industry is investing in the research and development of electric vehicles (EV) based on new batteries and driveline technologies to transition their market from fully ICE to a more environmental and efficient fleet of Battery, Hybrid and Plug-in electric vehicle technologies (BEV, PEV, HEV)
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[1]–[3]. Thus to understand and control the behaviour of the battery in terms of chemical, electrical and thermal aspects during the different operational conditions is of very high importance.
1.1
Modelling of Lithium-ion batteries
Lithium ion batteries have an excellent volumetric energy density, exhibit no memory effect, and experience low self-discharge when not in use [3]. Thus lithium-ion are very interesting technologies for the use in EV systems. The development of lithium ion batteries models to simulate and understand the inner processes and states of the
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battery plays a very important role in the development and optimisation of these systems. 1.1.1
Classification of Lithium ion battery models Investigating the scientific literature regarding the modelling of lithium ion batteries behaviour it is found that different models have been already created and used for the different interdisciplinary sciences that a battery system operation is based on. The different types of models existing can be separated mainly by the different issues and phenomena the model should investigate. In Table 1 the different model types have been separated in:
-
Electrochemical models Electrical models Thermal models Mechanical/Fatigue models Interdisciplinary models
The electrochemical and electrical models will be discussed further in this paper, giving a special attention to the electrical models. Thermal models are used to investigate the thermal behaviour of the battery during different states. They are mainly compose of Equivalent Circuit Models using thermal electrical components to simulate the thermal behaviour of the battery while there is also pure thermal models that are based solely of theoretical and mathematical knowledge. Mechanical/Fatigue models are used to investigate the real physical constrains that the battery is undergoing during its usage. Interdisciplinary models are models that combine the different main modelling categories to simulate a wide range of phenomena e.g. thermoelectrochemical, Thermo-Mechanical. The latter category of models are combinations of models thus creating additional parameters and results to be investigate which increases the accuracy while the simulation time of the model. When modelling the behaviour of a physical system it is possible to identify three main general model categories. Depending on the method how the inputs are related to the outputs of the model they can be categorize in: empirical, physical and semi-empirical models [20]. In Table 1 the different models existing for the each model types are classified based on this exact approach..
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Empirical models are based on the “black box” approach, where the inner (physical) behaviour of the system is unknown and the relations between the inputs and outputs of the model are based on experimental results and relations only. An example of empirical model is the Neural Network model which are models that can capture the dynamic behaviour of the battery and learn the relationship of the inputs to the outputs only through experimental data found prior to the creation of the model. Another example of empirical modelling of batteries is the analytical model called Peukert’s model where it can be used to simulate the time needed to discharge the battery. The main constants of the mathematical equation governing the Peukert’s model have to be defined with the use of experimental activities [21]. More information will be provided further regarding the Peukert model. Physical models are based solely on theoretical and physical knowledge of the system under investigation. No experimental activities regarding the relation between the inputs and outputs of the system have to be performed in order to determine the behaviour of your system. Depending on the knowledge of the specific inner characteristics and physical processes of your system you can create a model to simulate the performance of your system. An example of a physical model of a lithium ion battery is the pure Electro-Chemical model. Depending on the knowledge of the specific material composition, chemical reactions and energy transfer, a set of physical equations can be created to describe the behaviour of the battery. The fact that the model equations are based on physical relations, which describe real physical effects taking place in the battery, includes the pure Electro-Chemical model in the category of physical modelling. Finally semi-empirical models lies between the physical and the empirical models. This category is a hybrid modelling category. The system under investigation is to a certain extend treated as a black box where the relation of the inputs to your outputs and inner behaviour of your system is investigated through experimental methods, as performed for empirical modelling. The difference being that, a link with some of the real physical effects inside your system can be implemented in your model. Examples of semi-empirical models are Equivalent Circuit Models (e,g. Dual Polarization, PNGV) that
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Model
Electro Chemical
Pure Electro-Chemical ECM Electro-Chemical Analytical
Model Type
ECM
Electrical
Freq.
Peukert's model Rakhmatov and Vrudhula Sheperd other iterations
Empirical Semi-Empirical Physical ✓ ✓ ✓ ✓ ✓ ✓ ✓
State-Space Simple Rint Enhance Rint RC PNGV / FreedomCAR 1st order (Thevenin Model) Dual Polarization (2nd order) Enhance PNGV (2nd order) Noshin Model Neural Nets
✓
Frequency domain
✓
✓ ✓
Thermal
Analytical Thermal ECM Thermal
✓
Mechanical/ Fatigue
Fatigue/Mechanical
✓
✓
✓ ✓ ✓
✓
Electro-Thermal Thermo-electrochemical Thermo-Mechanical Table 1: Classification of different lithium-ion battery models Combined Models
can be linked to in this case the polarization effect, the different behaviour during charging and discharging process.
1.1.2
✓ ✓ ✓ ✓ ✓ ✓ ✓
Importance of battery models
Electric applications using a battery as their primary energy and power source, will be typically accompanied by a battery management system (BMS). This is mostly implemented in vehicle applications where the need to manage the battery performance, control internal parameters of the battery and inform the user of vital battery information is needed. The accurate prediction of State of Charge, State of Heath and other characteristics (Temperature, Voltage, and Current) are the main needed information to be calculated by a BMS. In addition the proper management of the charging and discharging behaviour of the battery by the BMS, will help to maintain for a longer period the rated capacity of the battery and increase its life time. This will keep the battery in good healthy condition for a longer period. Thus it is very important for the BMS software to be based on a battery model which can calculate efficiently and accurate the battery states and characteristics and can run with low computational power and time.
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✓
Electrochemical Models
Electrochemical models can be physical models or semi-empirical models. Pure electrochemical models are physical models based solely on theory and simulates the electrochemical behaviour of a battery. They consist of non-linear differential equations that can predict the “electrochemical kinetics and transport phenomena” of ions [3], the power generation mechanism and communicate the “macroscopic (battery voltage and current) and microscopic (e.g. concentration distribution) information” of the battery [4]. Electrochemical models are potentially most complete because it incorporates most of the physical processes taking place inside the battery. Taking the electrochemical model taking into consideration is a robust and complete model of the system investigating. Due to the amount, of inputs to simulate the wide range of physical and chemical reactions and output information generated, the simulation process of electrochemical models is demanding in computational power and time consuming [1]. Thus these kinds of models are least suitable to be used in applications that need fast access of vital information and characteristics of a battery such as a Battery Management System (BMS).
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3
Electrical Models
Models that describe the electrical behaviour of the battery have been extensively studied and develop in the academia[19], [22]–[25] . There exist multiple models that can be used to describe the electrical response of the battery and those have been categorized as follow in this study: -
Analytical Models Electrical ECM Models Frequency Domain Models
Mainly Electrical Models are semi-empirical models where characterization techniques have to be performing to identify the different parameters of you battery. Those characterization techniques have been extensively described in different standardization documents [26]–[29]and they are generally composed of: -
-
-
-
3.1
Capacity Test,: Defining the Discharge/Charge Capacity of the battery OCV vs SoC test,: Relating the different State of Charge levels with the Open Circuit Voltage of the battery HPPC test: To define the internal resistances and State of Charge of the battery Impedance Spectroscopy Test (EIS).: Define the internal resistance & impendences of the battery
Analytical models
Investigating the scientific literature regarding lithium ion electrical battery models a clear distinction can be found regarding mathematical models [3], [5], [6] . In this study the main Mathematical model category of lithium ion batteries will be called Analytical modelling. The reason being that all models for batteries are based on mathematical equations and a distinction has to be made between the models found under the Mathematical category in literature and all the other mathematical equations related with modelling of lithium ion batteries. Analytical models are based on stochastic approaches and empirical equations to describe the basic electrochemical and performance characteristics of the battery. Two main equations
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dominates this category, the Peukert’s equation and the Shepherd equation. The basic Peukert’s model can predict the time to discharge a battery depending of the discharge current, the capacity of the battery and the Peukert constant which depends on the type of battery under investigation (e.g k = 1.35 for typical lead-acid batteries). The two later parameters have to be specified through experimental activities. In eq. 1 the Peukert’s equation is presented. An extension of the Peukert’s equation exist, named Rakhmatov & Vrudhula. They take into consideration effects and physical process inside the battery (e.g. diffusion process, relaxation effect) thus are more accurate models than its predecessor. The link with the physical effects and processes, classifies according to the above mentioned classification system the Rakhmatov & Vrudhula equation as a semiempirical model. 𝑡 =
𝐶𝑝 𝐼𝑘
(1)
where t = time to discharge (hours) Cp = Capacity of the battery I = discharge current (A) k = Peukert’s constant The Shepherd model and other iterations (Unnewehr Universal model, Nerst Model, Combine model) describes the electrochemical behaviour of the battery in terms of voltage and current. The accuracy of these models lies between 5% to 20% thus cannot predict very accurately the voltage response of a battery. The Shepherd model is classified as a semi-empirical model because it takes into consideration the polarization resistance [30] and in this way makes a link with the physical effect of polarisation. The Unnewehr Universal model is based on a simplified Shepherd model and attempts to simulate the variation in resistance to respect to SoC. The Nernst model is also based on the Shepherd model but attempts to simulate the SoC with the use of exponential functions.
3.2
Electrical Equivalent Circuit Models
We have identified five main electrical ECM models, that will be discussed in more detail in this paper. -
Rint model RC model
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-
Thevenin model PNGV model Dual polarisation
Additional interesting electrical ECM models will be discuss (e.g. Noshin Model) but not all the models found in the literature have been included in this paper. Electrical Equivalent Circuit Models (ECM) are models based on electrical components (e.g. ideal voltage sources, resistors, capacitors etc.) to simulate the behaviour of a battery. Most of ECM models are semi-empirical models where the process of calculating your final outputs is based on two distinctive activities. The first activity is called characterization where your initial states and values (e.g. Energy, Capacity, voltage response, and OCV) of you system are calculated, followed by the second activity, the determination of your model parameters. The design of ECM models is easily achieved and they can vary greatly in composition depending on the output and accuracy it is foreseen to obtain. The outputs of a battery ECM model ensembles the main vital battery characteristics and information (e.g. Voltage performance, Internal Resistance, SoC – OCV relations, SoH, and T). In addition the simulation time and computational power needed to simulate different steady or transient performances of the battery is lower than the electrochemical models. This aspect of ECM models makes them more appropriate for fast calculations, with acceptable accuracy and lower needed computational power. Thus making them perfect to be used and implemented in a BMS system. [1], [2], [4], [5]. The common aspects of all the ECM lithium ion battery models can be summarized in the following points:
The use of electrical components to represent the electrical, and/or chemical behaviour of the battery The use of characterization methods to identify the (initial) values and states of the battery. The Open Circuit Voltage (OCV) and the battery voltage are the main values used to simulate the State of Charge[1].
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3.2.1
Thevenin Theorem
The Thevenin theorem is the main basic theorem that ECM modelling of batteries are based on. The theorem states that any linear electric circuit can be replaced by a black box and approximate the steadystate behaviour of the circuit with a single voltage source U and an internal resistance mostly denoted as Rint. The value of U corresponds with the open circuit voltage at the terminals and the internal resistance corresponds with the steady state current that flows through the circuit divided by the close circuit voltage Ucc. When an AC current is passed through the circuit the internal resistance is represented by an impedance Z while in the case of DC current by a resistance R. Any model that uses this theorem to simulate lithium ion batteries will be an empirical model as your system under investigation is considered as a black box, without any detailed knowledge of the physics of the system. 3.2.2
Rint Model
The basic equivalent circuit model can be seen in Figure 1. It is based on the Thevenin theorem and it is composed of an ideal voltage source Uoc and an internal resistance Rint. When no current is applied at the terminals of the battery the UL equals to the OCV. The current IL takes a positive value when the battery is discharging and negative when charging. The terminal voltage of circuit is represented by UL. Eq. 2 represents the relation of the terminal voltage, open circuit voltage, current and internal resistance of the battery for the Rint model. The basic Rint model describes a linear behaviour of a battery without knowing any information regarding the inner composition and processes taking place in the battery. This aspect of the model classifies it as an empirical model. An extension of the Rint model can be achieve by simulating the ideal voltage source and the internal resistance as a function of the State of Charge (SoC) and temperature [9], [31]. This can be achieve with the use of lookup tables and experimental activities to identify the different values of the open circuit voltage and internal resistance for different SoC and temperatures. This aspect of the enhance Rint model classifies it as a semi-empirical model.
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Figure 1: Schematic representation of the Rint model 𝑈𝑏𝑎𝑡 = 𝑈𝑜𝑐 − 𝐼𝑏𝑎𝑡 𝑅𝑖𝑛𝑡
(2)
Where:
circuit is to calculate the amount of current the battery can deliver depending on a time-constant, based on the diffusion materials and chemical reactions of the battery. The Re resistance, named “end resistor”, is combined in series with the capacitor Cb. The Rt resistance, named the “terminal resistor”, represent the resistances from the connection of the two previous RC circuits. The RC model in one hand takes into consideration common physical aspects of a battery but at the same time is considering the battery as a black box. Combining this two aspects of the RC model, can classified the model as a semi-empirical with a strong link with pure physical modelling.
Ubat = voltage across the terminals of the battery (V) Uoc = ideal voltage source (V) Ibat = battery current (A) Rint = the ohmic internal resistance (Ω)
This model was firstly implemented in 1994 in the ADVISOR simulation software [8]. The basic and enhance Rint model are simple models of the battery and are not suitable to simulate the dynamical behaviour of a battery. But in the other hand they have small simulation run-time and can provide adequate information regarding the battery performance with an acceptable accuracy. Thus it is easily integrated in a simple BMS system. 3.2.3
RC Model
To tackle some of the drawbacks of the Rint model, in 2000 SAFT Battery Company provided the National Renewable Energy Laboratory (NREL) with a battery electric battery model called the RC Model[8]. It has also been included in the ADVISOR simulation software and it is more preferred for automotive simulations than the Rint model [8][9]. The model is composed of two capacitors (C c, Cb) and three resistors (Rc, Re, Rt) as seen in Figure 2 [10], [11], [32]. The capacitor Cb is called the “bulk capacitor” and it represents the relation to the energy capacity of the battery to store charge chemically. The value of the bulk capacitor has a very high value. The capacitor C c is called the “surface capacitor” and it represents the surface effects of the battery and has a low value. The C c capacitor in combination with the R c resistance, which is called the “capacitor resistance”, they create an RC circuit. The function of the RC
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Figure 2: Schematic representation of the RC model The electrical behaviour of the RC model is expressed with eq. 3 and eq. 4. They are a state space equation which can calculate the voltages across the capacitors (Ub and Uc) and the whole circuit (Ubat). The SoC is calculated by using the voltage on the bulk capacitor. It should be noted that the components of the circuit are fixed and do not vary with the SoC and temperature of the battery. In [12] enhancements of the model were performed to include such dependencies. The obtained model is called hereafter the enhanced RC model which shows an improved accuracy over the Rint model.
𝑈̇ [ 𝑏] = 𝑈̇𝑐
−1 1 𝐶𝑏 (𝑅𝑒 + 𝑅𝑐 ) 𝐶𝑏 (𝑅𝑒 + 𝑅𝑐)
[
1 −1 𝐶𝐶 (𝑅𝑒 + 𝑅𝐶 ) 𝐶𝐶 (𝑅𝑒 + 𝑅𝑐 )
]
𝑈 [ 𝑏] + 𝑈𝑐
−𝑅𝑐 𝐶𝑏 (𝑅𝑒 + 𝑅𝑐 )
[
−𝑅𝑒 𝐶𝑐(𝑅𝑒 + 𝑅𝑐)
[𝐼𝑏𝑎𝑡 ] ]
(3) 𝑅𝑐 𝑅𝑒 𝑈 [𝑈𝑏𝑎𝑡 ] = [ ] [ 𝑏] (𝑅𝑒 + 𝑅𝑐 ) (𝑅𝑒 + 𝑅𝑐 ) 𝑈𝑐 𝑅𝑒 𝑅𝑐 + [−𝑅𝑡 − ] [𝐼 ] (𝑅𝑒 + 𝑅𝑐 ) 𝑏𝑎𝑡
(4) Where: Re = the resistance in series with the capacitor Cb (Ω)
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Rc = the resistance in series with the capacitor Cc (Ω) Rt = the resistance between the two RC circuits (Ω) Cb = the bulk capacitor (F) Cc = the surface capacitor (F) Ibat = battery current (A) Ub = voltage across the capacitor Cb (V) Uc = voltage across the capacitor Cc (V) Ubat = voltage across the terminals of the battery (V) 3.2.4
First Order Model (Thevenin Model)
The first order battery model, often called in literature the Thevenin model, consist of a RC circuit in series with a resistance and it is based on the behaviour of the Rint model and the Thevenin theorem. As seen in Figure 3 the model is composed of the ohmic resistance Rint, a polarization RC circuit represented by Cth and Rth and a voltage source Uoc which equals to the opencircuit voltage OCV when no load is applied. The total internal resistance of the model is composed by the ohmic resistance Rint which is due to the contacts, electrodes and electrolyte of the battery and the polarization resistance Rth which is due to chemical reactions in the electrodes during charging and discharging. The RC circuit of the model has a voltage Uth across it’s terminals with an outflow current Ith and it describes the effect of the chemical reactions in the electrode surface and ion mass transfer. The response of the RC circuit during charging and discharging can simulate the dynamic behaviour of the battery.
Figure 3: Schematic representation of the first order battery model often called Thevenin model The model assumes that the OCV has a constant relationship with the SoC and the ohmic resistance doesn’t change during charging and discharging.
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The electrical behaviour of the model is described by the eq. 5. {
𝑈 𝐼 𝑈̇𝑡ℎ = − 𝑅 𝑡ℎ + 𝐶𝑏𝑎𝑡 𝐶 𝑡ℎ 𝑡ℎ
𝑡ℎ
𝑈𝑏𝑎𝑡 = 𝑈𝑜𝑐 − 𝑈𝑡ℎ − 𝐼𝑏𝑎𝑡 𝑅𝑜
(5)
Where: Ro = the ohmic internal resistance (Ω) Rth = the polarization resistance (Ω) Cth = the polarization capacitor (F) Cc = the surface capacitor (F) Ith = capacitory Cth current (A) Ibat= battery current (A) Uth = voltage across the capacitor Cth (V) Ubat = voltage across the terminals of the battery (V) These two previous characteristics of the model makes the simple Thevenin Model not an appropriate contender for the simulation of the dynamic performance of the battery. The resistances should vary with the SoC and Temperature. To be able to implement this, different parameterization methods have to be used. There exist two distinctive methods to do this. The first is with the use of look-up tables where you can relate you different values of resistance and capacitances with the SoC dependencies and temperatures. The second parameterization is called linear dependencies parameterization where you relate linearly your SoC and temperature with the capacitance and resistance of the model. In [33] and [13] a Thevenin model is used to simulate a lithium-ion battery. In [33] the temperature, current amplitude and current shape were not taken into account. The different OCV values were calculated linearly for different SoC and the resistances and capacitors of the model were related to the SoC by linear interpolation. It was found that the model will simulate the voltage of the battery 1.5% below the measured voltage. In [13] both of the parameterization methods described above has been used to calculate the battery parameters of three ECM battery models for the same battery. The three models are the Rint, Thevenin and Dual Polarization models which the later will be described in the next chapter. It was found that the linear parameterization of the SoC with the resistance and capacitors requires less time to be completed but cannot calculate the values as accurate as the look-up table parameterization method. The look-up table method has to
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investigate each parameter individually of each model by applying each time a current pulse to obtain the capacity and resistance values. Rather than the linear dependencies parameterization of the SoC with the capacity and resistances can be done once and apply to all the models. The reason for the higher accuracy of the look-up tables is that the SoC and temperature dependencies in reality are not related linearly to the resistances and capacitances but more as a second order polynomial thus making the look-up table values closer to the real relation of the parameters. The trade-off between complexity of the model which will increase its accuracy but also the simulation time is one of the main aspects of the Thevenin model. 3.2.5
Second Order Model Polarization Model)
(Dual
The Thevenin model can represent the ohmic polarization and concentration polarization (chemical behaviour) of the battery. In reality a third polarization effect, the activation polarization related with the electrochemical reactions at the electrode surface has to be taken into consideration. To implement this latter, a second order ECM model called the Dual Polarization Model has been established and used in the industry and academia. The model can be seen in Figure 4 and it is identical as the Thevenin model with an additional RC circuit attached in series with the first RC circuit. In this model the total internal resistance is composed of the internal ohmic resistance Rint, concentration polarization resistance Rpc and the activation polarization resistance Rpa. The capacitors Cpc and Cpa are used to simulate the behaviour of the battery during transient states of discharging and charging. The electrical behaviour of the model is described by eq. 6.
𝑈 𝐼 𝑈̇𝑝𝑎 = − 𝑅 𝑝𝑎 + 𝐶𝐿 𝐶 𝑝𝑎 𝑝𝑎
𝑝𝑎
𝑈𝑝𝑐 𝐼 𝑈̇𝑝𝑐 = − 𝑅 𝐶 + 𝐶 𝐿 𝑝𝑐 𝑝𝑐
(6)
𝑝𝑐
{𝑈𝐿 = 𝑈𝑜𝑐 − 𝑈𝑝𝑎 − 𝑈𝑝𝑐 − 𝐼𝐿 𝑅𝑜 Where: Rint = internal ohmic resistance (Ω) Rpa = the activation resistance with the capacitor Cpa (Ω) Rpc = the concentration resistance with the capacitor Cpc (Ω) Cpa = (F) Cpc = (F) Ipa = capacitor Cpa current (A) Ipc = capacitor Cpc current (A) Ibat = battery current (A) Uoc = open circuit voltage (V) Upa = voltage across the capacitor Cpa (V) Upc = voltage across the capacitor Cpc (V) Ubat = voltage across the terminals of the battery (V) In [14] a dual polarization model was used to simulate the behaviour of a lithium ion battery. The parameters were estimated for different SoC, temperatures and C-rates using a built in tool in /Simulink®. It was found that the dual polarization model when testing the battery with an HPPC test, will have higher accuracy than the Thevenin or the PNGV model, with an error of 0.1V. In [15] the dual polarization model is investigated but the identification of the parameters of the model was performed with the use of empirical testing and the Extended Kalman Filter (EKF) recursive method. The Extended Kalman Filter is an extension of the Kalman Filter that can be applied for nonlinear systems. It provides a method for estimating states of a process by minimizing the error calculated during the process [16]. In this model the open circuit voltage Uoc is composed with the equilibrium potential Ue and a hysteresis voltage as you can see in Figure 5. A DST driving cycle was applied to validate the dynamical behaviour of the model which showed that it can effectively estimate the voltage behaviour of the real battery with an error of 3%.
Figure 4: Schematic representation of the Dual Polarization Model
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1⁄ ′ = the fictive capacitor (F) 𝑈𝑜𝑐 Ipn = capacitor Cpn current (A) Ibat = battery current (A) Uoc = open circuit voltage (V) Ud = voltage across the capacitor 1⁄𝑈 ′ (V) 𝑜𝑐
Upn = voltage acros the capacitor C pn (V) Ubat = voltage across the terminals of the battery (V) Figure 5: Schematic representation of the Dual Polarization model [15] 3.2.6
PNGV/FreedomCar Model
The US Department of Energy has published different manuals related with the testing of batteries for (Hybrid & Plug-in) Electric Vehicles. From the FreedomCar battery testing manuals [17], [18] the FreedomCar battery model or otherwise called Partnership for a New Generation of Vehicles (PNGV) model was created.
Figure 6: Schematic representation of the PNGV model The model can been see in Figure 6. It is composed of an RC circuit (polarization resistance Rpn and capacitor Cpn), an internal resistance Rint representing the ohmic resistance, an ideal voltage source providing just the OCV value of the battery and a second fictive capacitor to represent the changing OCV during dynamic cycles with a rate of (1/OCV’). The behaviour of the model is described in eq. 7. ′ 𝑈̇𝑑 = 𝑈𝑜𝑐 𝐼𝑏𝑎𝑡
{
𝑈𝑝𝑛 𝐼 𝑈̇𝑝𝑛 = − 𝑅 𝐶 + 𝐶𝑏𝑎𝑡 𝑝𝑛 𝑝𝑛
𝑝𝑛
(7)
𝑈𝑏𝑎𝑡 = 𝑈𝑜𝑐 − 𝑈𝑑 − 𝑈𝑝𝑛 − 𝐼𝑏𝑎𝑡 𝑅𝑜 Where: Rint = the ohmic internal resistance (Ω) Rpn = the polarization resistance (Ω) Cpn = the polarization capacitor (F)
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The normal procedure to calculate the parameters of the model is to use the standard PNGV battery parameter estimation spreadsheet or do the standard HPPC test [18]. The standard HPPC test can calculate more accurately the parameters of the model than the PNGV spreadsheet. In [9] the normal HPPC test method is used to run a PNGV model and compare it to other ECM lithium-ion battery models. It is found that the PNGV model cannot simulate the dynamic behaviour of the battery as accurate as the Thevenin or the Dual Polarization models, even if it can simulate the polarization behaviour of the battery. In [14] two parameterization methods are used to simulate a lithium ion battery with a PNGV model. The parameters are calculated through Matlab/Simulink® parameter estimation tool and the PNGV battery parameter estimation spreadsheet. It is found that the Simulink method is simpler, more accurate and faster than then PNGV battery parameter estimation speadsheet method and “is valid for any battery model” [14]. When using the Simulink parameter estimation method and comparing the simulated voltage across the battery with the real voltage profile, the PNGV model (error 0.68%) is found to be more accurate than the Thevenin model (error 1.2%) and less accurate than the Dual Polarization model (error 0.27%). 3.2.7
Advanced PNGV Model
The PNGV model can face some drawbacks because it doesn’t take into account the number of cycles and the C-rate effects on the battery [19]. In addition it can only simulate a total polarization effect without making the distinction between activation and concentration polarization and it only accounts the variation of the OCV with a time integral of the current passing through. This will cause a cumulative integration voltage problem which decrease the accuracy of the PNGV model. In [5] a comparison of the two main ECM models (Thevenin and PNGV) and an improved PNGV was
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performed. The models are implemented in Matlab/Simulink® and the standard HPPC test is conducted to identify the parameters of the models. The improved PNGV model consist of an additional RC circuit to describe the charge and discharge characteristics of the battery. All three of the models gave an acceptable accuracy regarding the simulated voltage with the Thevenin model having the larger error. The improved PNGV model is able to simulate more accurately the voltage in the beginning of test but merges to the same values as the PNGV model at the end of the test. In [19] an extended PNGV model is created and implemented in Matlab/Simulink®. The model has improved the basic PNGV model to add the Peukert constant, self-discharge effect, State of Health (SoH) and efficiency calculations. In figure 7 the schematic representation of the model is presented. The improvements are implemented by adding two parallel RC circuits to have a more accurate response of the OCV for different currents and a self-discharge resistance to represent the effect when no load is applied to the battery. In addition the ohmic resistance is separated to two parallel resistances to have two separate values for the ohmic resistance during charging and discharging. The SoC values of the battery are calculated by taking into account the Peukert constant and efficiency during charging. An extended HPPC test is created based on the standard HPPC test with higher C-rates and lower relaxation time. Comparing the simulated and measured voltages of the PNGV and the extended PNGV models using the extended HPPC test it is found that the extended PNGV model has lower accuracy errors than the PNGV model. The reason being that the PNGV model cannot accurately simulate the higher C-rates of the extended HPPC test. It should be noted that the PNGV, improved PNGV of [5] and the extended PNGV of [19] do not make the distinction between the effect of the electrochemical reactions at the electrode surface (activation polarization) and the chemical reactions in the electrodes during charging and discharging (concentration polarization).
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Figure 7: Schematic representation of the extended PNGV model.
3.2.8
Additional models and combinations
In [4] a ECM model for NiMH and polymer Li-ion batteries is proposed and implemented in Cadence simulation environment. It consist of two parts, the first is a RC circuit to simulate the usable capacity of the battery which depends on the number of cycles, discharge current, storage time and temperature. The second part of the model is a second order RC circuit which can simulate the I-V characteristics of the battery. The paper mentions that all the parameters are normally a function of SoC, current, temperature and cycle number but some of them have been simplified e.g. the resistance of the first RC circuit which characterize the self-discharge losses of the battery can be simplified to a linear function or even ignore. The model can accurately predict for both chemistries the runtime with an error in the range of 0.4% and voltage accuracy within 30 mV. The model simulates more accurately the runtime for the polymer Li-ion battery (2%) and the voltage response for the NiMH battery (15mV). It should be noted that the simplification of the model is clearly a drawback and future improvements should take into account the effects of battery cycles, temperature, and storage time. In [1] twelve different lithium-ion batteries found in the literature were compared. Two lithium ion batteries were simulated, an NMC (nickelmagnanese-cobalt-oxide LiNMC) and an LFP (lithium iron phosphate LiFePO4). Characterization test were conducted at 10 °C, 22 °C and 33 °C. The test ran included a static capacity test, hybrid pulse test (combining standard HPPC and self-designed discharging and charging profiles), dc resistance test, DST test and FUDS test. The model that displayed the highest accuracy throughout all the tests performed was the first order RC circuit. There is some cases were adding a second RC circuit and
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a one-state hysteresis will increase the accuracy of the model but it creates a more complicate characterization and validation process which will increase your simulation time and complexity of the model. The simulation of the NMC chemistry was more accurate under the first order RC model but the LFP chemistry show a greater accuracy under the one-state hysteresis first order RC model. In [8] additionally to the ECM models, a neural network model is proposed for a lead acid battery. The inputs of the model are the SoC and the power requested to calculate the I-V response of the battery. The model was implemented in ADVISOR and was operated for constant temperature of 25 °C. The advantages of the model is that “any test data can be used to characterize the model”. Under the driving cycle US06 the model show an accuracy within of 5% for the simulated voltage. The drawbacks of the model is that is only valid for a range of data (27 – 74% SoC and 1200 W discharge, 750 W charge). It should be noted that no other temperature inputs were taken into account. In [24] the Noshin and the extended Noshin battery models are proposed. The purpose of the models is to try to incorporate the hysteresis effect and the non-linearity of battery modelling. The simple Noshin model has the OCV as a variable parameter, different ohmic resistances for charging and discharging when a load is imposed and different ohmic resistances for charging and discharging when the load decreases to zero. The parameters of this model are been estimated with the use of the PNGV vehicle spreadsheet. The “extended Noshin battery model” has additional RC branches to simulate the behaviour of the battery more accurately. Two additional branches exist for the simulation of the charging and discharging transition states of the battery, while two RC circuits have also be integrated to simulate the different polarization resistances during discharge and charge. The values of the parameters have been calculated using a dedicated logical algorithm. Comparing the “Noshin model” to other ECM battery models (e.g Rint, RC, second and third order) it was found that it can simulate more accurately the performance of lithium-ion batteries. The accuracy of the models will change, depending on the depth of discharge (DoD)
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window in which the test was conducted. For low DoD values (0-5%), the “Noshin battery model” is more accurate than the second and third order PNGV model and the errors lies between 2% and 2.5%. For the DoD range between 5% and 90 %, the highest accuracy was for the basic “Rint model”. The “RC model” had quite an acceptable error (in the range of 2 – 5 %), which is due to the voltage linearity present in this DoD window. The RC circuit assumes the voltage performance of the battery will be linear, which is the case of the voltage in this DoD range, thus simulating the voltage quite accurately. For the DoD range between 90 – 100 % the “RC model” has the worst accuracy performance and the “Noshin model” shows the best accuracy performance.
3.3
Lifetime modeling, short term and long term behaviour
Throughout the life of a battery different vital parameters and characteristics can be identify that are affected by different battery behaviours. These behaviours can be categorize in:
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Instantaneous Short term Long term
The instantaneous behaviour of a lithium ion battery is during it’s the first second’s and minutes of its lifetime. Two distinctive behaviours starts to take effect during this period. The electric double layer effect between the liquid and solid phases (electrode –electrolyte) of the battery [34]. The second effect that starts to take place is the mass transport effects where the diffusion and migration of ions are taking place [35]. During the instantaneous behaviours the SoC of the battery remains pretty constant. The short term behaviour of a lithium ion a battery is during the first hours and days of its lifetime. There the battery has started to cycle and provide energy to the load attached. The effect taking place during that period can be summarize in cycling and SoC effect. During the first discharge and charge of the battery the SoC will change thus also the voltage of its terminals. Additional effects that take place during cycling is the generation of heat which is affected by the C-rates that are applied during discharge and charge[35]. The long term behaviours of a lithium ion battery will start to take place during the first month and
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years of its lifetime. The effects described previously are still taking place during the discharge or charge of the battery but with additional effects. Now due to the extended period that the battery is being used the State of Health of the battery will be affected. The result of this will be the increase of internal resistance throughout the battery lifetime thus providing less power the more you use it and the capacity fading effect which where the rated capacity of the battery will decrease during its usage[35]. The simulation of the instantaneous and short term effects can be simulated with the use of Electrical Equivalent circuit’s models and Analytical models. The simulation of the long term effects falls in the category of lifetime modelling. In this category the use of models based on equivalent circuit modeling techniques which can be separated in time domain models (resistance) and frequency domain models (impedance). An additional model category that is being used to simulate the long term behaviour are the electrochemical models described in the beginning of this paper.
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behaviour of the battery (e.g. dependency of open source voltage of the battery and of ohmic voltage drop of the environmental temperature and of the state of charge of the battery) and the separation of the charging and discharging process will increase the accuracy of the model but also its complexity. This will lead to an increased simulation time. Depending on the purpose of the simulation, on the application that is considered, the appropriate topology of electrical components have to be chosen to represent the behaviour of the real battery have to be chosen.
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Conclusion
The main aspects of the most important ECM battery models reviewed in this study can be summarized in the following points:
Discussion
Equivalent Electric Circuit Models can vary in complexity, accuracy and simulation times. When comparing all the models reviewed in this state of the art, it is revealed that depending on the effects and outputs it simulates (electrical ECM, thermal ECM or electrochemical ECM), the model will use additional electric circuit modules (e.g. second RC circuit, diodes, additional resistances, combined electric models). The integration of physical reactions such as the activation, concentration and ohmic polarization will increase the complexity of the model but will allow to simulate more accurately the I-V characteristics of the battery and as stated in [1], some models will be more suitable for specific chemistries, depending on their respective behaviour and on the operational conditions of the application (temperature range, current rate, state of charge window). To choose an appropriate ECM model to simulate lithium-ion batteries the three main aspects (the simulation time, complexity and accuracy) have to be considered. The simulation time of the model which depends on the complexity of you model, The integration of different physical effects (e.g. polarization & hysteresis effect), the nonlinear
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The Rint model is too basic to simulate the dynamic behaviour of the battery but can be used for fast calculations of the battery performances with some acceptable accuracies for certain applications. The RC circuit can simulate quite accurately the performance of the battery if one assumes that the voltage of the battery decreases or increases linearly The simple Thevenin model doesn’t take into account the relation of the OCV and internal resistance with the SoC and Temperature. To enhance the model different parameterization techniques have to be used that will increase the simulation run-time.. The dual polarization model (second order ECM), the extended PNGV model (second order ECM) and the Noshin model have the best simulation accuracies. The PNGV and RC model can have low simulation time but they are not accurate enough to represent the real behaviour of the battery. Noshin model is the most accurate and complete model to simulate the behaviour of lithium ion batteries, in particular for dynamic load conditions such as automotive applications (1)
Acknowledgments We acknowledge IWT - Agency for Innovation by Science and Technology for the support of the SBO project BATTLE. Also we acknowledge the „SOC
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an Experimental Approach,” Energies, vol. 4, no. 12, pp. 582–598, Mar. 2011.
maakindustrie” for the support to our research team..
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Authors Ir. Alexandros Nikolian Vrije Universiteit Brussel Email:
[email protected] Alexandros Nikolian graduated at the Reading University in the UK as Renewable Energy Engineer. He has experience in vehicle simulation & emissions, developed during his activities in the Joint Research Center of the European Union and Hexagon Studio in Turkey. He started as a PhD student in January 2014 at VUB mainly working on IWT BATTLE project where an interdisciplinary lithium ion battery model will be developed.
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dr. ir. Jean-Marc Timmermans Vrije Universiteit Brussel Email:
[email protected] Jean-Marc Timmermans graduated in 2003 as an Electromechanical Engineer at the Vrije Universiteit Brussel. As an academic assistant of the department of Electrical Engineering and Energy Techno-logy (ETEC), he was involved in several projects related to clean vehicle technologies. In 2010 he obtained a PhD at the Vrije Universiteit Brussel. Currently he is a post-doctoral researcher in the field of electrical energy storage systems and project manager in the Battery Innovation center of the MOBI research group at the Vrije Universiteit Brussel. Ir. Joris de Hoog Vrije Universiteit Brussel Email:
[email protected] Joris de Hoog obtained his M.S. degree in Electronics and ICT in 2013 at the Vrije Universiteit Brussel. He is currently pursuing a PhD degree in the department of Electrical Engineering and Energy Technology (ETEC) at VUB. His current research deals with the aging of Lithium-Ion batteries, and modelling of aging phenomena during the lifetime of a Lithium-Ion battery. Ir. Karel Fleurbaey Vrije Universiteit Brussel Email:
[email protected] Karel Fleurbaey obtained his M.S degree in electromechanical engineering in 2013 at the Vrije Universiteit Brussel (VUB). He is currently pursuing the PhD degree in the department of Electrical Engineering and Energy Technology (ETEC) at VUB. His current research focusses on the characterization and modelling of lithium ion batteries and lithium ion capacitors.
HEV’s and PHEV’s. He is also active in several international standardization committees such as IEC TC21/22. He is the author of more than 70 scientific publications. Prof. Dr. ir. Peter Van den Bossche Vrije Universiteit Brussel Email:
[email protected] Peter Van den Bossche graduated as civil mechanical - electrotechnical engineer from the Vrije Universiteit Brussel and defended his PhD at the same institution with the thesis "The Electric Vehicle: raising the standards". He is currently lecturer at the engineering faculties of the Vrije Universiteit Brussel, and in charge of coordinating research and demonstration projects for electric vehicles in collaboration with the international associations CITELEC and AVERE. His main research interest is electric vehicle standardization, in which quality he is involved in international standards committees such as IEC TC69, of which he is Secretary, and ISO TC22 SC21. Prof. Dr. ir. Joeri Van Mierlo Email:
[email protected] Prof. Dr. ir. Joeri Van Mierlo is a fulltime professor at the Vrije Universiteit Brussel, where he leads the MOBI – Mobility, Logistics and automotive technology research centre (http://mobi.vub.ac.be). A multidisciplinary and growing team of 60 staff members. He is expert in the field of Electric and Hybrid vehicles (batteries, power converters, energy management simulations) as well as to the environmental and economical comparison of vehicles with different drive trains and fuels (LCA, TCO).
Prof. Dr. Eng. Omar Noshin Vrije Universiteit Brussel Email:
[email protected] Noshin Omar was born in Kurdistan, in 1982. He obtained the M.S. degree in Electronics and Mechanics from Erasmus University College Brussels. He is currently the head of Battery Innovation Center of MOBI research group at Vrije Universitit Brussel, Belgium. His research interests include applications of electrical double-later capacitors and batteries in BEV’s,
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