# Advanced Electrochemical Impedance Spectroscopy of Industrial Ni-Cd Batteries

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}, reflecting high intrinsic rates of the redox electron transfer processes in Ni-Cd cells.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Ni-Cd Cells and Block Arrangements

#### 2.2. Electrochemical Impedance Spectroscopy (EIS) and Calibration Method

_{sig}is swept within a defined frequency range and the signals are then transformed into the frequency domain by a discrete Fourier transform (DFT) process. The resulting complex signals I(ω) and V(ω) are then used to compute the complex raw impedance Z(ω)

_{raw}= V(ω)/I(ω).

_{ser}and the gain error term G

_{e}. The measured impedance Z

_{M}is given by the following equation:

_{T}is the true impedance, and Z

_{ser}and G

_{e}are the error coefficients. The two error coefficients Z

_{ser}and G

_{e}are determined in a calibration process where at least two different known calibration standards are measured. Here, we use one short and one 10 mΩ shunt standard. Once the error coefficients are known, the true impedance can be calculated by transforming Equation (1) into the following form:

_{sol}and the charge transfer resistance R

_{ct}. The double-layer capacitance C

_{dl}is derived from the constant phase reactance CPE

_{dl}as follows [21,22]:

_{diff}is obtained from the Warburg impedance Z

_{diff}by the following relation:

^{2}/D, L is the length of the diffusion, D is the diffusion coefficient, and the fractional-order P is set as 0.5.

#### 2.3. Electromagnetic Finite Element Method (FEM) Modeling

## 3. Results and Discussion

#### 3.1. EIS Calibration Method

_{T}) is obtained by Equation (2).

#### 3.2. Calibrated EIS versus SoC

#### 3.3. Equivalent Electric Circuit Model and Fit Parameters

_{L}], a solution resistance element R

_{sol}, a ZARC element [R

_{ct}/CPE

_{dl}], and a Warburg diffusion element (W

_{diff}). The constant phase element (CPE) is used because of the porous nature of the electrodes and adsorption capacitances [31,32], while the inductive element is included to model the physical arrangement of the cell plates and connectors. From this Randles circuit, the following equation is used to obtain the impedance of the “battery under test” (BUT), Z

_{BUT}:

_{c}is the characteristic angular frequency of the CPE, α is the fractional order of the CPE, L is the inductance, and Z

_{diff}is the impedance of the Warburg diffusion.

_{sol}as identified by the intersection point of the impedance curve with the x-axis. At intermediate frequencies, the charge transfer resistance and the double-layer capacitance are shown as a depressed semi-circle. At low frequencies, the diffusion tail is obtained on the right part of the Nyquist plot.

_{sol}shows very similar values for the three cells, with an average of R

_{sol}= 1.433 mΩ. Due to the depressed semi-circle and the corresponding fit errors, the charge transfer resistance R

_{ct}values differ significantly. An average value of R

_{ct}= 0.042 mΩ is obtained, with a significantly higher value for Cell 3, which is sourced from Block 2, while Cell 1 and Cell 2 are from Block 1. Similarly, the diffusion resistances R

_{diff}of Cell 1 and Cell 2 are very similar, while R

_{diff}of Cell 3 is higher, which can be, for instance, due to small differences in the SoC leading to faster electrode kinetics [33]. Lastly, the inductance values L are very similar for all three cells because the inductance is related to the geometry of the cell and electrode plates, which is very similar for Block 1 and Block 2. Thereby, it is noted that the imaginary part of the impedance is dominated by the diffusion resistance, whereas the internal resistance is dominated by the resistance of the solution resistance, which agrees with literature observations [13].

#### 3.4. EIS Comparison of Cells and Blocks

#### 3.5. Electrochemical Interpretation

_{sol}, R

_{ct}, and C

_{dl}in relation to the principal components of a Ni-Cd cell. The electrochemical redox reactions (reduction and oxidation) include the discharge where Ni

^{3+}is reduced to Ni

^{2+}and the hydroxide ions (OH

^{−}) are transferred to the cadmium anode, where the oxidation occurs from Cd

^{0}to Cd

^{2+}. The main electrochemical model parameter describing the redox reaction is the charge transfer resistance R

_{ct}, reflecting the exchange between the ions and the electrons at the electrode interfaces. R

_{ct}is related to the reaction kinetics described by the Butler–Vomer equation for a charge-transfer controlled electrochemical reaction with an inverse relation to the exchange current density, R

_{ct}= R ×T/(n × F × i

_{0}), where i

_{0}is the exchange current density, R is the gas constant, T is the temperature, n is the number of electrons in the redox reaction, and F is the Faraday constant [34]. Considering Cell 3 with an R

_{ct}of 0.079 mΩ obtained at 296 K, and a two-electron charge transfer process, then the exchange current density is equal to i

_{0}= 0.23 A·cm

^{−2}, which corresponds to 162 A per cell with an electrode surface area of 700 cm

^{2}. The exchange current density reflects intrinsic rates of electron transfer between electrodes, and provides insights into the nature of the electrodes, their structure, as well as their physical parameters such as surface roughness [35]. The larger the exchange current density, the faster the redox reactions. Compared to Li-ion batteries which show typical i

_{0}values of around 5 mA·cm

^{−2}[36], the Ni-Cd current density is significantly larger. For instance, this is apparent by the fact that higher C-rates can be obtained from Ni-Cd batteries, which are typically required in uninterruptible power supply (UPS) applications. Such applications require mixed high and low discharge rates for electrical loads between 30 min and 3 h [37]. The highly conductive ionic solution in the Ni-Cd cell is represented in the model by a purely resistive element R

_{sol}. The solution resistance depends on the ionic concentrations, temperature, and geometry of the area in which the current is flowing. The conductivity k of the ionic solution, in units of [S/m], is obtained from the solution resistance R

_{sol}by the following relation, k = L

_{n}/(R

_{sol}× A), where A is the surface area, and L

_{n}is the length of the charge path. Considering Cell 3 with an R

_{sol}= 1.43 mΩ and based on the geometrical dimensions of the Ni-Cd cell, we obtain conductivity values around 1 S·cm

^{−1}, which compare very well with the conductivity of bulk KOH solution found in literature [38]. The deposition of ion charges at the electrode interface is countered by electronic charges at the electrode interface, creating a double-layer capacitance CPE

_{dl}. Whereas the ion diffusion process inside the electrode particles of the positive Ni active material is represented by a Warburg impedance, which is a solid-state physical diffusion process [39].

## 4. Conclusions

_{sol}, R

_{ct}, and C

_{dl}were described in relation to the principal components of a Ni-Cd cell and the electrochemical redox reactions. Based on the modelled parameters, intrinsic properties were estimated such as the solution conductivity and the exchange current density, reflecting high intrinsic rates of the redox electron transfer processes in Ni-Cd cells compared to LiBs.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Kasim, R.; Abdullah, A.R.; Selamat, N.A.; Basir, M.S.S.M.; Ramli, M.Z. Nickel-Cadmium battery analysis using spectrogram. ARPN J. Eng. Appl.Sci.
**2016**, 11, 3975–3979. [Google Scholar] - Mcdermott, P.; Halpert, G.; Ekpanyaskun, S.; Nche, P. Secondary aerospace batteries and battery materials: A bibliography, 1969–1974. Bibliography
**1976**, 7044, 1923–1968. [Google Scholar] - Nilsson, A.O. Nickel cadmium batteries in UPS design features. In Proceedings of the 10th International Telecommunications Energy Conference, San Diego, CA, USA, 30 October–2 November 1988; pp. 388–393. [Google Scholar] [CrossRef]
- Dirani, H.C.; Semaan, E.; Moubayed, N. Impact of the current and the temperature variation on the Ni-Cd battery functioning. In Proceedings of the 2013 The International Conference on Technological Advances in Electrical, Electronics and Computer Engineering (TAEECE), Konya, Turkey, 9–11 May 2013; pp. 339–343. [Google Scholar] [CrossRef]
- Jeyaseelan, C.; Jain, A.; Khurana, P.; Kumar, D.; Thatai, S. Ni-Cd Batteries. In Rechargeable Batteries; Boddula, R., Inamuddin, R.P., Asiri, A.M., Eds.; John Wiley & Sons, Ltd.: Hoboken, NJ, USA, 2020; pp. 177–194. [Google Scholar] [CrossRef]
- Mottard, J.-M.; Hannay, C.; Winandy, E.L. Experimental study of the thermal behavior of a water cooled Ni–Cd battery. J. Power Sources
**2003**, 117, 212–222. [Google Scholar] [CrossRef] - Crescentini, M.; De Angelis, A.; Ramilli, R.; De Angelis, G.; Tartagni, M.; Moschitta, A.; Traverso, P.A.; Carbone, P. Online EIS and Diagnostics on Lithium-Ion Batteries by Means of Low-Power Integrated Sensing and Parametric Modeling. IEEE Trans. Instrum. Meas.
**2020**, 70, 1–11. [Google Scholar] [CrossRef] - Babaeiyazdi, I.; Rezaei-Zare, A.; Shokrzadeh, S. State of charge prediction of EV Li-ion batteries using EIS: A machine learning approach. Energy
**2021**, 223, 120116. [Google Scholar] [CrossRef] - Chevalier, S.; Auvity, B.; Olivier, J.C.; Josset, C.; Trichet, D.; Machmoum, M. Detection of Cells State-of-Health in PEM Fuel Cell Stack Using EIS Measurements Coupled with Multiphysics Modeling. Fuel Cells
**2014**, 14, 416–429. [Google Scholar] [CrossRef] - Jungst, R.G.; Nagasubramanian, G.; Case, H.L.; Liaw, B.Y.; Urbina, A.; Paez, T.L.; Doughty, D.H. Accelerated calendar and pulse life analysis of lithium-ion cells. J. Power Sources
**2003**, 119, 870–873. [Google Scholar] [CrossRef] - Stanciu, T.; Stroe, D.-I.; Teodorescu, R.; Swierczynski, M. Extensive EIS characterization of commercially available lithium polymer battery cell for performance modelling. In Proceedings of the 2015 17th European Conference on Power Electronics and Applications (EPE’15 ECCE-Europe), Geneva, Switzerland, 8–10 September 2015; pp. 1–10. [Google Scholar] [CrossRef]
- Windarko, N.A.; Choi, J.-H. SOC Estimation Based on OCV for NiMH Batteries Using an Improved Takacs Model. J. Power Electron.
**2010**, 10, 181–186. [Google Scholar] [CrossRef] - Sathyanarayana, S.; Venugopalan, S.; Gopikanth, M.L. Impedance parameters and the state-of charge. I. Nickel-cadmium battery. J. Appl. Electrochem.
**1979**, 9, 125–139. [Google Scholar] [CrossRef] - Bundy, K.; Karlsson, M.; Lindbergh, G.; Lundqvist, A. An electrochemical impedance spectroscopy method for prediction of the state of charge of a nickel-metal hydride battery at open circuit and during discharge. J. Power Sources
**1998**, 72, 118–125. [Google Scholar] [CrossRef] - Karkuzhali, V.; Rangarajan, P.; Tamilselvi, V.; Kavitha, P. Analysis of battery management system issues in electric vehicles. IOP Conf. Ser. Mater. Sci. Eng.
**2020**, 994, 012013. [Google Scholar] [CrossRef] - Hammouche, A.; Karden, E.; De Doncker, R.W. Monitoring state-of-charge of Ni–MH and Ni–Cd batteries using impedance spectroscopy. J. Power Sources
**2004**, 127, 105–111. [Google Scholar] [CrossRef] - Olarte, J.; de Ilarduya, J.M.; Zulueta, E.; Ferret, R.; Kurt, E.; Lopez-Guede, J.M. Estimating State of Charge and State of Health of Vented NiCd Batteries with Evolution of Electrochemical Parameters. JOM
**2021**, 73, 4085–4090. [Google Scholar] [CrossRef] - Reid, M.A. Impedance studies of nickel/cadmium and nickel/hydrogen cells using the cell case as a reference electrode. J. Power Sources
**1990**, 29, 467–476. [Google Scholar] [CrossRef] - Blanchard, P. Electrochemical impedance spectroscopy of small Ni-Cd sealed batteries: Application to state of charge determinations. J. Appl. Electrochem.
**1992**, 22, 1121–1128. [Google Scholar] [CrossRef] - Meddings, N.; Heinrich, M.; Overney, F.; Lee, J.-S.; Ruiz, V.; Napolitano, E.; Seitz, S.; Hinds, G.; Raccichini, R.; Gaberšček, M.; et al. Application of electrochemical impedance spectroscopy to commercial Li-ion cells: A review. J. Power Sources
**2020**, 480, 228742. [Google Scholar] [CrossRef] - Mauracher, P.; Karden, E. Dynamic modelling of lead/acid batteries using impedance spectroscopy for parameter identification. J. Power Sources
**1997**, 67, 69–84. [Google Scholar] [CrossRef] - Dai, H.; Jiang, B.; Wei, X. Impedance Characterization and Modeling of Lithium-Ion Batteries Considering the Internal Temperature Gradient. Energies
**2018**, 11, 220. [Google Scholar] [CrossRef][Green Version] - R-Smith, N.A.-Z.; Ragulskis, M.; Kasper, M.; Wagner, S.; Pumsleitner, J.; Zollo, B.; Groebmeyer, A.; Kienberger, F. Multiplexed 16 × 16 Li-Ion Cell Measurements Including Internal Resistance for Quality Inspection and Classification. IEEE Trans. Instrum. Meas.
**2021**, 70, 1–9. [Google Scholar] [CrossRef] - Tuca, S.-S.; Badino, G.; Gramse, G.; Brinciotti, E.; Kasper, M.; Oh, Y.J.; Zhu, R.; Rankl, C.; Hinterdorfer, P.; Kienberger, F. Calibrated complex impedance of CHO cells andE.colibacteria at GHz frequencies using scanning microwave microscopy. Nanotechnology
**2016**, 27, 135702. [Google Scholar] [CrossRef] - Piatek, Z.; Baron, B. Exact Closed Form Formula for Self Inductance of Conductor of Rectangular Cross Section. Prog. Electromagn. Res. M
**2012**, 26, 225–236. [Google Scholar] [CrossRef][Green Version] - Kasper, M.; Leike, A.; Thielmann, J.; Winkler, C.; R-Smith, N.A.-Z.; Kienberger, F. Electrochemical impedance spectroscopy error analysis and round robin on dummy cells and lithium-ion-batteries. J. Power Sources
**2022**, 536, 231407. [Google Scholar] [CrossRef] - Qiao, S.; Hu, M.; Fu, C.; Qin, D.; Zhou, A.; Wang, P.; Lin, F. Experimental Study on Storage and Maintenance Method of Ni-MH Battery Modules for Hybrid Electric Vehicles. Appl. Sci.
**2014**, 9, 1742. [Google Scholar] [CrossRef][Green Version] - Cruz-Manzo, S.; Greenwood, P.; Chen, R. An Impedance Model for EIS Analysis of Nickel Metal Hydride Batteries. J. Electrochem. Soc.
**2017**, 164, A1446. [Google Scholar] [CrossRef][Green Version] - Cheng, S.; Zhang, J.; Zhao, M.; Cao, C. Electrochemical impedance spectroscopy study of Ni/MH batteries. J. Alloys Compd.
**1999**, 293–295, 814–820. [Google Scholar] [CrossRef] - Wang, H.; Tahan, M.; Hu, T. Effects of rest time on equivalent circuit model for a li-ion battery. In Proceedings of the 2016 American Control Conference (ACC), Boston, MA, USA, 6–8 July 2016; pp. 3101–3106. [Google Scholar] [CrossRef]
- Łosiewicz, B.; Budniok, A.; Rówiński, E.; Łągiewka, E.; Lasia, A. The structure, morphology and electrochemical impedance study of the hydrogen evolution reaction on the modified nickel electrodes. Int. J. Hydrogen Energy
**2004**, 29, 145–157. [Google Scholar] [CrossRef] - Agudelo, B.O.; Zamboni, W.; Monmasson, E. A Comparison of Time-Domain Implementation Methods for Fractional-Order Battery Impedance Models. Energies
**2021**, 14, 4415. [Google Scholar] [CrossRef] - Chayambuka, K.; Mulder, G.; Danilov, D.L.; Notten, P.H. Determination of state-of-charge dependent diffusion coefficients and kinetic rate constants of phase changing electrode materials using physics-based models. J. Power Sources Adv.
**2021**, 9, 100056. [Google Scholar] [CrossRef] - Krauskopf, T.; Mogwitz, B.; Hartmann, H.; Singh, D.K.; Zeier, W.G.; Janek, J. The Fast Charge Transfer Kinetics of the Lithium Metal Anode on the Garnet-Type Solid Electrolyte Li6.25Al0.25La3Zr2O12. Adv. Energy Mater.
**2020**, 10, 2000945. [Google Scholar] [CrossRef] - Bard, A.J.; Faulkner, L.R. Electrochemical Methods; Wiley & Sons: New York, NY, USA, 1980. [Google Scholar]
- Amin, R.; Belharouak, I. Part-II: Exchange current density and ionic diffusivity studies on the ordered and disordered spinel LiNi0.5Mn1.5O4 cathode. J. Power Sources
**2017**, 348, 318–325. [Google Scholar] [CrossRef] - KPL KPM KPH Ni-Cd Batteries. Saft Batteries|We Energize the World. 22 October 2020. Available online: https://www.saftbatteries.com/products-solutions/products/kpl-kpm-kph-ni-cd-batteries (accessed on 22 December 2021).
- Allebrod, F.; Chatzichristodoulou, C.; Mollerup, P.L.; Mogensen, M.B. Electrical conductivity measurements of aqueous and immobilized potassium hydroxide. Int. J. Hydrogen Energy
**2012**, 37, 16505–16514. [Google Scholar] [CrossRef] - De Vidts, P.; White, R.E. Mathematical Modeling of a Nickel-Cadmium Cell: Proton Diffusion in the Nickel Electrode. J. Electrochem. Soc.
**1995**, 142, 1509. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**(

**a**) A sketch of the Ni-Cd block showing the two cells connected in series with a bar connector, and the respective cell electrode terminals. (

**b**) Two Ni-Cd blocks (Block 1, Block 2) consisting of two cells per block connected in series with a bar connector. (

**c**) EIS measurement setup consisting of a power analyzer containing two source measure units (SMUs), a PC with EIS control and visualization software, and the calibration standards and fixture. (

**d**) EIS measurement modelled by combining an ideal impedance meter with the series error impedance Z

_{ser}and a gain error term G

_{e}. The true impedance Z

_{T}is computed from the measured and error-affected impedance Z

_{M}.

**Figure 2.**(

**a**) The 3-D electromagnetic computer-aided design (CAD) model of the Ni-Cd battery block containing two cells connected in series and the cable fixture. A four-wire connection scheme for force and sense is considered, and a metallic cell connector is used to connect both cells. (

**b**) The 3-D EMPro simulation of the cell fixture and contacts, including a planar view of the magnetic H-filed distribution around the wires. (

**c**) Simulated real impedance (upper panel) and imaginary impedance (lower panel) across the frequency range of 10 Hz to 1 kHz. The geometry and model dimensions are based on the original Ni-Cd block (SAFT SBM112) and the EIS setup.

**Figure 3.**EIS calibration (upper row) and correction process (lower row) using printed circuit board (PCB) shunt standard. The shunt standard is measured at the BUT measurement plane and the short is measured at the BUT negative terminal (upper right). The calibration raw data (upper left) are used together with the standard definition data to obtain the error coefficients which are forwarded to the correction process. The raw BUT data (lower left) and the calibrated data (lower right) are shown for a Ni-Cd single cell with 112 Ah measured at 23 °C.

**Figure 4.**(

**a**) Calibrated EIS results shown as the real impedance (resistance) and imaginary impedance (reactance), across the measurement frequency of 10 mHz to 500 Hz. The results are shown for Ni-Cd Cell 1 at six SoC charging levels, from 0% to 90%, and measured at 23 °C. The high, intermediate, and low SoC curve transitions are indicated in the graphs. (

**b**) The corresponding EIS results shown in a Nyquist plot.

**Figure 5.**Equivalent electric circuit model of a Ni-Cd cell. (

**a**) Randles model with four elements. (

**b**) Comparison of experimental impedance spectra and simulation for Cell 1, (

**c**) Cell 2, and (

**d**) Cell 3 at 10% SoC and 23 °C. (

**e**) Interpretation of the electrochemical processes in the Nyquist plot at different frequencies from 100 mHz to 500 Hz.

**Figure 6.**Calibrated EIS spectra of three cells and the extracted electrochemical parameters. (

**a**) Nyquist plot of the impedance spectra of the three cells. (

**b**) Extracted electrochemical parameters from the fitted EIS results for Cell 1, Cell 2, and Cell 3, simulated using Z-view software. The spectra were obtained in the frequency range of 100 mHz to 500 Hz.

**Figure 7.**Nyquist plot of the impedance spectra of the single cells, Cell 1, Cell 2, Cell 3, and Cell 4, compared to the block impedance for Block 1 (

**a**) and Block 2 (

**b**). The cells are at 20% SoC and the EIS measurements are performed using 3 A excitation current across the frequency range of 10 mHz to 2 kHz at 23 °C.

**Figure 8.**Electrochemical model parameters and principal components of a Ni-Cd cell. During discharge, the cathode (Ni

^{3+}O

^{2−}-OH

^{−}) reacts with water to produce Ni

^{2+}(OH)

_{2}and hydroxide ions (OH

^{−}) are transferred to the cadmium anode. The main electrochemical processes during discharge are described, including equivalent circuit model elements, such as R

_{ct}, R

_{sol}, and C

_{dl}(left and right panels).

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**MDPI and ACS Style**

Al-Zubaidi R-Smith, N.; Kasper, M.; Kumar, P.; Nilsson, D.; Mårlid, B.; Kienberger, F. Advanced Electrochemical Impedance Spectroscopy of Industrial Ni-Cd Batteries. *Batteries* **2022**, *8*, 50.
https://doi.org/10.3390/batteries8060050

**AMA Style**

Al-Zubaidi R-Smith N, Kasper M, Kumar P, Nilsson D, Mårlid B, Kienberger F. Advanced Electrochemical Impedance Spectroscopy of Industrial Ni-Cd Batteries. *Batteries*. 2022; 8(6):50.
https://doi.org/10.3390/batteries8060050

**Chicago/Turabian Style**

Al-Zubaidi R-Smith, Nawfal, Manuel Kasper, Peeyush Kumar, Daniel Nilsson, Björn Mårlid, and Ferry Kienberger. 2022. "Advanced Electrochemical Impedance Spectroscopy of Industrial Ni-Cd Batteries" *Batteries* 8, no. 6: 50.
https://doi.org/10.3390/batteries8060050