Modeling the Impedance Characterization of Prismatic Lithium-Ion Batteries

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Procedia Manufacturing 32 (2019) 762–767 Procedia Manufacturing 00 (2017) 000–000 www.elsevier.com/locate/procedia

The The 12th 12th International International Conference Conference Interdisciplinarity Interdisciplinarity in in Engineering Engineering

Modeling Modeling the the Impedance Impedance Characterization Characterization of of Prismatic Prismatic LithiumLithiumIon Batteries Manufacturing Engineering Society International Conference 2017, MESIC 2017, 28-30 June Ion Batteries 2017, Vigo (Pontevedra), Spain a b, Maryam Maryam Ghalkhani Ghalkhania,, Moein Moein Mehrtash Mehrtashb, **

Costing models for capacity optimization in Industry 4.0: Trade-off Department of Electrical and Computer Engineering, University of Windsor, 401 Sunset Ave., Windsor, ON, Canada N9B 3P4 Department of Electrical and Computer Engineering, University of Windsor, 401 Sunset Ave., Windsor, ON, Canada N9B 3P4 W Booth School of Engineering Practice and Technology, MARC-273, McMaster Automotive Resource Center (MARC) W Booth School of Engineering Practice and Technology, MARC-273, McMaster Automotive Resource Center (MARC) between used capacity and operational efficiency 200 Longwood Road South, Hamilton, ON, Canada L8P 0A6 0F

0F

a a

b b

200 Longwood Road South, Hamilton, ON, Canada L8P 0A6

A. Santanaa, P. Afonsoa,*, A. Zaninb, R. Wernkeb Abstract Abstract

a

University of Minho, 4800-058 Guimarães, Portugal b Unochapecó, 89809-000 Chapecó, SC, Brazil

The internal battery resistance can be measured using any one of the three available methods; conductance, impedance, or The internal battery resistance can be measured using any one of the three available methods; conductance, impedance, or resistance measurements. An experimentally validated modeling technique using COMSOL multiphysics software has been resistance measurements. An experimentally validated modeling technique using COMSOL multiphysics software has been developed to explain the importance of electrochemical impedance spectroscopy (EIS) modeling. The influence of the design developed to explain the importance of electrochemical impedance spectroscopy (EIS) modeling. The influence of the design Abstract parameters on the cell impedance in a wide frequency range has been investigated. Some of the defined properties studied in this parameters on the cell impedance in a wide frequency range has been investigated. Some of the defined properties studied in this work may have a significant role in the design of battery management system (BMS) for EVs and HEVs. The verification results work may a significant role in the4.0", design of battery management will system (BMS) for EVs HEVs. The verification results Under thehave concept of "Industry production pushed to and beand increasingly have shown the dependency of the impedance calculation processes on active materialbe particle radius the current rate,interconnected, especially at the have shown the dependency of the impedance calculation on active material particle radius and the current rate, especially at the information based on a real time basis and, necessarily, much more efficient. In this context, capacity optimization positive electrode. positive electrode.

goes beyond the traditional aim of capacity maximization, contributing also for organization’s profitability and value. © 2018 2019 The Authors. Published by Ltd. Indeed, lean management continuous © 2018 The Authors. Publishedand by Elsevier Elsevier Ltd. improvement approaches suggest capacity optimization instead of This is an open access articleof under the CCoptimization BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) maximization. The study capacity and costing models is an important research topic that deserves This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering. contributions from both the practical and theoretical perspectives. This paper presents and discusses a mathematical Selection and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering. model for capacity management based on different costing models (ABC and TDABC). A generic model has been Keywords: Lithium-ion batteries; Simulation models; Impedance Characterization; Electrochemical impedance spectroscopy; Electric vehicles Keywords: Lithium-ion Impedance Electrochemical spectroscopy;of Electric vehicles developed and it wasbatteries; used toSimulation analyze models; idle capacity andCharacterization; to design strategies towardsimpedance the maximization organization’s value. The trade-off capacity maximization vs operational efficiency is highlighted and it is shown that capacity optimization might hide operational inefficiency. 1. Introduction 1. 2017 Introduction © The Authors. Published by Elsevier B.V.

Peer-review under responsibility of the scientific committee of the Manufacturing Engineering Society International Conference The Lithium-ion batteries (LIBs) have attracted a lot of research interest in recent years, due to their high 2017. The Lithium-ion batteries (LIBs) have attracted a lot of research interest in recent years, due to their high

potential as compared to the conventional aqueous-based batteries, high gravimetric and volumetric energy density, potential as compared to the conventional aqueous-based batteries, high gravimetric and volumetric energy density,

Keywords: Cost Models; ABC; TDABC; Capacity Management; Idle Capacity; Operational Efficiency

1. Introduction * Corresponding author. * The Corresponding author. cost of idle capacity is a fundamental information for companies and their management of extreme importance E-mail address: [email protected] E-mail address: [email protected]

in modern production systems. In general, it is defined as unused capacity or production potential and can be measured 2351-9789 2018 The Authors. Published by Elsevier Ltd.hours of manufacturing, etc. The management of the idle capacity in several©ways: tons of production, available 2351-9789 © 2018 The Authors. Published by Elsevier Ltd. This is an Afonso. open access under the761; CC BY-NC-ND (https://creativecommons.org/licenses/by-nc-nd/4.0/) * Paulo Tel.:article +351 253 510 +351 253license 604 741 This is an open access article under the CC fax: BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering. E-mail address: [email protected] Selection and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering.

2351-9789 © 2017 The Authors. Published by Elsevier B.V. Peer-review under of the scientificbycommittee the Manufacturing Engineering Society International Conference 2017. 2351-9789 © 2019responsibility The Authors. Published Elsevier of Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of the 12th International Conference Interdisciplinarity in Engineering. 10.1016/j.promfg.2019.02.283



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and high-power capability. Additionally, LIBs are offering further advantages such as capability of rapid charging, and very low self-discharge. Therefore, these traits are quickly developing LIBs as the preferred rechargeable battery and maintain the dynamism of EVs [1-4]. However, Li-ion batteries suffer from high self-heating, particularly during high power applications and fast charging, which confines their lifetime and cause safety, reliability and environmental concerns. The flowing of the discharge current through the battery produce the impedance or the internal resistance. It is very challenging to assign a unique value to the battery impedance due to its dynamic nature by respect to current and time, which is possible using the electrochemical impedance spectroscopy (EIS) and the measurement of a voltage response after a DC pulse. Thus, different processes in the cell can be observed and interpreted with the aim to get an improved understanding of lithium-ion cells [5,6]. EIS is a modern technique widely used to enable the characterization of the electrochemical systems. Generally, the EIS method is measuring the characteristic response of an applied sinusoidal signal from a cell that can either be current or voltage and depends on the cell impedance. Since the solid electrolyte interphase (SEI) film composed of Li salts has a week flexibility, it might break due to an increase in particle volume during the charge/discharge process. Accordingly, a small reaction happens between the exposed electrode particles and the electrolyte solution which increase the surface impedance with cycling. Furthermore, this process can define the major increase of the electrode impedance at higher temperatures [7,8]. Many studies have been carried out over the last two decades on EIS-based temperature estimation methods and expansions or improvements of these methods [9-11]. The impedance response provides an understanding of some battery properties and processes wherever potential perturbations are applied on an electrode at varying frequency. The dependence of the power-delivery capability of lithium-ion cells on the cell’s state-of-charge (SOC) is due to the variation of the positive electrode’s impedance with the oxide’s lithium content [12,13]. Later, Andre et al. [14] were found the non-linear correlation between temperature and impedance due to temperature and SOC on LIBs. Furthermore, to estimate the battery’s internal temperature and determine the thermal model parameters battery impedance has been employed [14-16]. High-power battery positive nickel cobalt aluminium oxide (NCA) composite porous electrodes are recognized to be the key source of impedance increase in batteries. The ohmic resistance decrease as the temperature increases and inductive characteristics barely change at different temperatures [17]. The electrochemical reactions, capacitance, and local resistances affect the impedance at high frequencies while the diffusion in the electrolyte and active material particles changes the impedance at low frequencies. 2. Mathematical Modeling This study demonstrates a model using COMSOL Multiphysics software to predict and optimize the electrochemical impedance behavior of lithium-ion batteries. A 1D model with three domains of different thickness with double-layer capacitances on the active electrode materials and on the electronic conductor in the positive electrode has been used. The general model includes electronic current conduction in the electrodes, ionic charge transport in the pores of the electrodes and separator, material transport in the electrolyte to include the effects of lithium-ion concentration on ionic conductivity and concentration overpotential. Fick’s Law governs the material transport within the spherical intercalating particles that form the electrodes, and the Butler-Volmer equation directs the charge transport in the electrode for the electrode kinetics. The charge and mass transport equations are used to describe the spatial and time-dependent variation of the potential and the lithium-ion concentration in the solid electrodes and the liquid electrolyte phases. In this work, it is presumed that the lithium ion migrates through a film that prevents the transport of ions on the surface of the active particle in the porous electrodes to react electrochemically with the active material that causes an increase in resistance. This extra layer resembles the existence of the SEI layer on the electrodes. The consequence of insufficient contact between the electronically conducting diluent phase and the active material phase also increases overall cell internal resistance. Both effects are modeled as a single film resistance (R_film) [1, 6, 13].

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The local charge transfer current density, 𝑖𝑖𝑙𝑙𝑙𝑙𝑙𝑙 , in the electrode is defined by the Butler-Volmer kinetic expression given below [15]: 𝑖𝑖𝑙𝑙𝑙𝑙𝑙𝑙 = 𝑖𝑖0 �𝑒𝑒𝑒𝑒𝑒𝑒 �

𝛼𝛼𝑎𝑎 𝐹𝐹𝜂𝜂 𝑅𝑅𝑅𝑅

� − 𝑒𝑒𝑒𝑒𝑒𝑒 �

−𝛼𝛼𝑐𝑐 𝐹𝐹𝜂𝜂 𝑅𝑅𝑅𝑅

��

(1)

The exchange current density 𝑖𝑖0 and the magnitude of electrode potential polarization η that denotes the voltage loss during discharge of the cell at various rates are given as [15], 𝛼𝛼

𝑎𝑎 𝑖𝑖0 = 𝐹𝐹(𝑘𝑘𝑐𝑐 )𝛼𝛼𝑎𝑎 (𝑘𝑘𝑎𝑎 )𝛼𝛼𝑐𝑐 �𝑐𝑐𝑠𝑠,𝑚𝑚𝑚𝑚𝑚𝑚 − 𝑐𝑐𝑠𝑠 � (𝑐𝑐𝑠𝑠 )𝛼𝛼𝑎𝑎𝑎𝑎 �

𝜂𝜂 = ∅𝑠𝑠 − ∅𝑙𝑙 − ∆∅𝑠𝑠,𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 − 𝑉𝑉𝑜𝑜𝑜𝑜

𝑐𝑐𝑙𝑙

𝑐𝑐𝑙𝑙,𝑟𝑟𝑟𝑟𝑟𝑟

𝛼𝛼𝑎𝑎

�

(2) (3)

where 𝛼𝛼𝑎𝑎 and 𝛼𝛼𝑐𝑐 are the anodic and cathodic charge transfer coefficients, 𝐹𝐹 is the Faraday’s constant, 𝑘𝑘𝑐𝑐 and 𝑘𝑘𝑎𝑎 are cathodic and anodic rate constants respectively, 𝑐𝑐𝑠𝑠,𝑚𝑚𝑚𝑚𝑚𝑚 is the maximum lithium concentration at the in the solid phase, 𝑐𝑐𝑠𝑠 is the concentration of lithium in the active material particle, 𝑐𝑐𝑙𝑙 is the lithium ion concentration in the liquid electrolyte phase, 𝑐𝑐𝑙𝑙,𝑟𝑟𝑟𝑟𝑟𝑟 is the electrolyte reference concentration on the surface of the active particles before application of current load, ∅𝑠𝑠 is the solid phase potential, ∅𝑙𝑙 is the electrolyte phase potential. The total electrode reaction current density, 𝑖𝑖𝑣𝑣,𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 , is a summation of the electrode reaction current density 𝑖𝑖𝑣𝑣,𝑚𝑚 and double layer current source, 𝑖𝑖𝑣𝑣,𝑑𝑑𝑑𝑑 , given by the following equations: 𝑖𝑖𝑣𝑣,𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = ∑𝑚𝑚 𝑖𝑖𝑣𝑣,𝑚𝑚 + 𝑖𝑖𝑣𝑣,𝑑𝑑𝑑𝑑

(4)

𝑖𝑖𝑣𝑣,𝑑𝑑𝑑𝑑 = 𝑎𝑎𝑣𝑣,𝑑𝑑𝑑𝑑 𝑖𝑖𝑑𝑑𝑑𝑑

(6)

(5)

𝑖𝑖𝑣𝑣,𝑚𝑚 = 𝑎𝑎𝑣𝑣 𝑖𝑖𝑙𝑙𝑙𝑙𝑙𝑙

where 𝑎𝑎𝑣𝑣 is the active specific surface, 𝑎𝑎𝑣𝑣 =

3𝜀𝜀𝑠𝑠 𝑟𝑟𝑝𝑝

; 𝜀𝜀𝑠𝑠 is the electrode volume fraction, and 𝑟𝑟𝑝𝑝 is the particle size, 𝑖𝑖𝑑𝑑𝑑𝑑

is the double layer current density, 𝑖𝑖𝑑𝑑𝑑𝑑 = 𝑖𝑖𝑖𝑖�∅𝑠𝑠 − ∅𝑙𝑙 − ∆∅𝑠𝑠,𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 �𝐶𝐶𝑑𝑑𝑑𝑑 ; 𝜔𝜔 is the frequency, ∆∅𝑠𝑠,𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 is the solid phase film potential, ∆∅𝑠𝑠,𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 = 𝑅𝑅𝑓𝑓𝑓𝑓𝑙𝑙𝑙𝑙 𝑖𝑖𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 ; 𝐶𝐶𝑑𝑑𝑑𝑑 is the electrical double layer capacitance, and 𝑎𝑎𝑣𝑣,𝑑𝑑𝑑𝑑 is the double layer particle based area. The total interface current density 𝑖𝑖𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 is the summation of, 𝑖𝑖𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 = ∑𝑚𝑚 𝑖𝑖𝑙𝑙𝑙𝑙𝑙𝑙,𝑚𝑚 + 𝑖𝑖𝑑𝑑𝑑𝑑

(7)

To demonstrate experimental EIS spectra on NCA electrodes, an additional double-layer at the electronic conductor has been used. The experimental EIS spectra measurement has been borrowed from the observations by Abraham et [16]. The problem solved by an AC Stationary Impedance study while all variables are displaced from being time-dependent to frequency dependent on the following equations: � 𝑒𝑒 2𝜋𝜋𝜋𝜋.𝑖𝑖𝑖𝑖 } 𝑛𝑛 = 𝑛𝑛0 + 𝑅𝑅𝑅𝑅{𝑛𝑛.

(8)

where 𝑛𝑛 is the variable, and subscript 0 signifies the initial value around which the perturbation takes place, 𝑖𝑖 is the imaginary unit, 𝑓𝑓 the frequency in Hz, and t the time. A sinusoidal perturbation applied to the positive electrode current-collector and the negative electrode current-collector determined as ground that fixed to 0 V. The cell impedance, 𝑍𝑍� at the boundary of the positive electrode’s current collector is calculated according to:



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� 𝑠𝑠 = ∅𝑠𝑠,𝑏𝑏𝑏𝑏𝑏𝑏 + ∆∅𝑠𝑠 𝑒𝑒𝑒𝑒𝑒𝑒(−𝑖𝑖𝑖𝑖𝑖𝑖) ∅

(9)

−𝑛𝑛. 𝐼𝐼̃𝑠𝑠 = 𝑖𝑖𝑛𝑛,𝑠𝑠 + ∆𝑖𝑖𝑛𝑛,𝑠𝑠 𝑒𝑒𝑒𝑒𝑒𝑒(−𝑖𝑖𝑖𝑖𝑖𝑖)

𝑍𝑍� =

(10)

� 𝑠𝑠 ∅ �𝒏𝒏.𝑰𝑰�𝑠𝑠 �

(11)

where, 𝒏𝒏 is the normal vector to the boundary, and 𝐼𝐼𝑠𝑠 the current density in the current collector or current feeder, ∅𝑠𝑠,𝑏𝑏𝑏𝑏𝑏𝑏 is the boundary electric potential at the boundary of the positive electrode current-collector, ∆∅𝑠𝑠 is the amplitude of potential perturbation, 𝑖𝑖𝑛𝑛,𝑠𝑠 is the normal electrode current density , ∆𝑖𝑖𝑛𝑛,𝑠𝑠 is the amplitude of current perturbation induced by the voltage perturbation. To decrease any deviations from experimental interference the model is computed for frequencies between 10 mHz and 1 kHz [17]. Table 1. Model parameter in different regions. Parameters Density, 𝝆𝝆𝝆𝝆 (kg m-3)

Anode 2660

Separator 492

Cathode 4770

1437.4

1978

1172

Electrode volume fraction, ε

0.3

0.4

Maximum Li concentration in solid, 𝒄𝒄𝒄𝒄𝒔𝒔𝒔𝒔,𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎𝒎 (mol m-3)

28688.77

Specific heat capacity, 𝒄𝒄𝒄𝒄𝒑𝒑𝒑𝒑 (J kg-1 K-1)

0.2 20950

Initial electrolyte concentration, cl (mol m-3)

1000

1000

1000

Solid phase electronic conductivity, σ (S m-1)

2.0

0

0.01

Bruggeman exponent

1.5

1.5

1.5

Double-layer capacitance (Fm-2)

0.6

Volumetric double-layer capacitance positive electronic conductor(Fm-3)

895000

Film resistance (Ωm2)

0.00028

Anodic/Cathodic transfer coefficient, αa, αc Faraday’s constant, 𝑭𝑭𝑭𝑭 (C mol-1)

0.5

0.5 96487.0

3. Results and Discussion The Variation of the internal resistance of the cell against the time at different current rates presented in Figure 1. In fact, the temperature is a critical factor to be considered for internal resistance calculation, since the resistance of the electrolyte component is highly sensitive to the temperature variation.

Fig 1. Variation of the internal resistance at different current rates.

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The results of measuring the impedance at two different current rates (C-rate) are shown in Figure 2. The cell impedance at higher C-rate has a smaller depressed semicircle. The simulation shows one large semi-circle and an indication of another semi-circle at high frequencies. The difference between simulations at different C-rates is most noticeable in the semicircle frequency region, comparing to mid-high frequencies. Therefore, the exchange current density for electrode kinetics has a greater impact on the size of the semicircle at the lower C-rate process than for a very fast process at higher C-rate.

Fig 2. Simulated cell Impedance at different c-rates compared Impedance at positive electrode.

Figure 3 presents the simulated and experimental Nyquist spectra in the NCA positive electrode to overlap well, considering the main contribution to the cell impedance is in the positive electrode [17]. An adjustable parameter must be applied in simulation to achieve a good agreement with the measured data. Therefore, the optimization procedure using a parametric sweep has been considered to vary parameters such as exchange current density NCA, double-layer capacitance NCA, film resistance NCA, volumetric double-layer capacitance positive electronic conductor. Furthermore, the difference of the radius of the positive electrode material particles comprised in the model which affects the large time-scale process of diffusion in the particles. The result is compatible with the measurements by Abraham et al. [16].

Fig 3. Simulated and experimental Nyquist spectra for 10 mHz to 1 kHz at positive electrode.

Conclusions This work provides the insights into impedance response of several battery properties and processes by applying potential perturbations of varying frequency on an electrode. The simulated and experimental spectra for the positive electrode is observed to overlap well. The short time-scale processes such as electrochemical reactions and local resistances affect the impedance at high frequencies, while the diffusion in the electrolyte and active material particles influence the impedance at low frequencies.



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