# State-of-Charge Monitoring and Battery Diagnosis of Different Lithium Ion Chemistries Using Impedance Spectroscopy

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

_{1-x}FePO

_{4}. The material is readily available, strategically uncritical and almost not harmful. Unfortunately, the cell voltage of 3.6 V is lower than the 4.2 V of most other lithium technologies. The capacity is prone to degradation if long periods of time are operated either in the upper or lower potential range and at low temperatures [9,10,11].

#### 1.1. Battery State Indicators

_{N}that is stored by a new battery under defined conditions. The state-of-charge (SOC) [13] describes the relationship between the currently available capacity, Q(t) = α·β·Q

_{N}, and the total capacity Q

_{0}at the previous full charge. α = 1 (100% SOC) represents the full charge, and α = 0 (0% SOC) is the empty battery. However, lithium-ion batteries are not allowed to be discharged below the cut-off voltage.

_{0}in relation to the nominal capacity Q

_{N}of the new battery.

#### 1.2. State-of-Health Indicators

_{S}= Re Z(ω → ∞), the intersection on the real axis, does not decrease strictly linearly with rising temperature. Eddahech et al. [24] suggest the real part at 0.1 Hz for the estimation of remaining life. As well, Galeotti et al. [25] correlate the available capacity and the SOH with the ohmic resistance. Howey et al. [26] evaluate the range between 1 Hz and 2 kHz with both multisine and noise excitation signals. M. Spielbauer et al. [27] studied the mechanical deformations using computer tomography; internal short circuits cause a drop in ohmic resistance at frequencies above 100 Hz.

#### 1.3. Pseudocapacitance and Pseudocharge

_{S}of the interface. The ohmic resistance of the electrolyte solution, R

_{S}= Re Z(ω → ∞), is found as the intersection of the complex plane plot with the real axis. The approximation in Equation (5) holds for high frequencies, when the polarization resistance of the battery is negligible [30]. This is true when the DC resistance of the battery is not much greater than the electrolyte resistance R

_{S}.

## 2. Experimental Setup

- A.
- VoltSolar: 18,650 type, 3.2 V, 1.4–1.5 Ah, charge max. 3.65 V, cut-off voltage 2.0 V.
- B.
- Sony: US18650FT cylindrical, 3.2 V, 1.05–1.1 Ah,
- C.
- LithiumWerks (formerly A123) 26,650 cell, ANR26650M1B: 3.3 V, 2.6 Ah.

#### 2.1. Test Procedure

- Capacity determination by coulomb-counting: Each cell was first charged at 1 C rate (CC) to the upper cutoff voltage, then at constant voltage (CV) until the current dropped below 0.1 A. The discharge took place at 25 °C and 1 C rate under a constant current load until the cut-off voltage was reached. Q is the withdrawn electrical charge. Then the battery was recharged as above.
- Impedance measurements were taken 20 min after each constant-current discharge step, from SOC 100%, 98%, 96%, down to 30%. The VoltSolar cell was tested down to 50% SOC. The EIS measurement took 80 s for six values per frequency decade in the frequency range from 1 kHz to 0.1 Hz. The measuring arrangement is schematically shown in Figure 2.

#### 2.2. Measurement Parameters

## 3. Results and Discussion

#### 3.1. Frequency Response of Pseudocapacitance

#### 3.2. Correlation of Pseudocapacitance and Battery Capacity

_{S}is corrected in Equation (6). Overcharging disrupts the linear trend between capacity and SOC. The abrupt increase in capacity at SOC = 1, however, could be used to indicate that the battery is fully charged before there is a risk of overcharging.

#### 3.3. Verification and Validation of the Pseudocapacitance Model

^{2}= 99.3%). The linear trend gets better if the SOC range is considered up to 98% (instead of 100%), because overcharge phenomena occur at full charge. The prediction error is less than 1% for the quadratic model (average ± 0.4%), and less than 36% for the linear model.

#### 3.4. Properties of Pseudocharge

#### 3.5. Conversion of Impedance Data to Energy and Power

#### 3.6. Impact of Cell Chemistry

- Electrolyte and solid-electrolyte interface (SEI) at high frequencies;
- Charge-transfer at medium frequencies;
- Pore diffusion and intercalation at frequencies below 0.01 Hz.

^{2}), are calculated. The shape of diffusion impedance at low frequencies depends on whether the lithium-ion are mobile in linear channels (Li

_{1-x}FePO

_{4}), in areas of the layer lattice (Li

_{1-x}CoO

_{2}, NMC) or in the void spaces of a spinel (Li

_{1-x}Mn

_{2}O

_{4}, LMO).

_{0}is the capacity of the fully charged battery, which is determined by Ah counting.

#### 3.7. Impact of Aging

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Conflicts of Interest

## List of Symbols and Abbreviations

C | pseudocapacitance (F) |

f | frequency (Hz) |

Q | electric charge, battery capacity (Ah) |

Q_{0} | capacity of a fully charged battery (Ah) |

R | ohmic resistance, real part of impedance (Ω) |

R_{S} | electrolyte resistance (Ω) |

U | cell voltage (V) |

Y | complex admittance: Y = Z^{–1} (Ω^{–1}) |

Z | complex impedance (Ω) |

ω | angular frequency: ω = 2πf (s^{–1}) |

Ah | Ampere hour: 1 Ah = 3600 C |

j | imaginary operator: $\sqrt{-1}$ |

LCO | lithium cobalt oxide |

LMO | lithium manganese spinel |

LFP | lithium iron phosphate |

N | subscript: nominal value |

NCA | nickel cobalt aluminum |

NMC | nickel manganese cobalt |

SOC, α | state-of-charge |

SOH, β | state-of-health |

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**Figure 1.**Lithium iron phosphate battery (LithiumWerks 2.6 Ah): (

**a**) Charge at constant current and constant voltage. (

**b**) Flat discharge profile. EIS measurements were performed from 100% to 30% state-of-charge (SOC) in 2% steps.

**Figure 2.**(

**a**) Schematic measurement setup: Impedance spectrometer BIM2 (BRS GmbH, Stuttgart, Germany), data logger (Agilent 34972A), electronic load (ET Systems ELP/DCM 9712C), DC power source (Elektro-Automatik EA-PS 2342-10B), and relay box reside in a climatic chamber (Vötsch VT7021). Data acquisition: Labview. (

**b**) Basic model assumption and data evaluation.

**Figure 3.**Frequency response of impedance of the cell

**C**LithiumWerks (2.6 Ah). The electrolyte resistance R

_{S}= R(333 Hz) was subtracted. Capacitance versus frequency: ${C}_{\mathrm{S}}=-1/\left(\omega X\right),$including leakage: ${C}_{\mathrm{P}}=-X/\left[\omega \left({R}^{2}+{X}^{2}\right)\right]$, and corrected by the electrolyte resistance: ${C}_{\mathrm{PR}}=-X/\left[\omega \left({\left(R-{R}_{\mathrm{S}}\right)}^{2}+{X}^{2}\right)\right]$ according to Equation (4). Imaginary part of impedance: X = Im Z(ω).

**Figure 4.**SOC monitoring by impedance spectroscopy of lithium iron phosphate (LFP) batteries at rest: (

**A**) VoltSolar (1.5 Ah), (

**B**) Sony (1.1 Ah), (

**C**) LithiumWerks (2.6 Ah). Pseudocapacitance C(ω) according to Equation (4), where the electrolyte resistance R

_{S}= R(333 Hz) was subtracted from the real parts of impedance. Frequency range 0.1 Hz to 1 kHz. Regions:

**1**Electrolyte resistance,

**2**Charge transfer,

**3**mass transport.

**Figure 5.**(

**a**) State-of-charge monitoring of a VoltSolar LFP cell (1.5 Ah) using capacitance at selected frequencies. Example: C/F = 0.1925·SOC + 11.64 at 0.15 Hz. SOC = Q/Q

_{0}is based on Ah counting. EIS measurements were performed from 100% to 50% SOC in 2% steps. (

**b**) Linear relationship between capacitance and battery capacity: C = 14.65⋅Q + 11.64 (fit quality: 95.3%).

**Figure 6.**VoltSolar LFP battery. (

**a**) Pseudocharge Q(0.15 Hz) = C(0.15 Hz)⋅U and cell voltage U versus the “true” state-of-charge Q measured by Ah counting. (

**b**) Linear correlation between pseudocharge Q(ω) and “true” battery capacity at different discharge states. Example: Q/As = 66.92⋅Q(0.15 Hz) − 2226. LPF batteries from different manufacturers show qualitatively the same results.

**Figure 7.**(

**a**) Energy W of three types of LFP cells determined by the pseudocharge Q = C U at 0.15 Hz against the real part of impedance (ohmic resistance) at 0.15 Hz. A VoltSolar 3.2 V/1.4 Ah, B Sony 3.2 V/1.1 Ah, C LithiumWerks 3.3 V/2.6 Ah. (

**b**) For comparison: Peukert diagram of true energy versus C rate, (

**c**) Ragone plot: true energy versus power (measured by current and voltage).

**Figure 8.**Impedance spectra of different lithium-ion chemistries at rest in defined charge states. NMC as measured to show the influence of SOC on electrolyte resistance. LCO and NCA are shifted on the real axis to the electrolyte resistance of SOC = 1. Frequency range 0.1 Hz to 1 kHz.

**Figure 9.**(

**a**) NMC battery #8: Normalized pseudocapacitance and pseudocharge at 0.1 Hz (reference: 589 F and 2470 As at SOC = 100%) versus “true” SOC from Ah counting. (

**b**) Cell voltage of different cell chemistries versus state-of-charge from Ah counting. Batteries under test see Table 1.

**Figure 10.**Aging of an LCO battery at the same state-of-charge (Panasonic UR18650 FK). (

**a**) Impedance spectra of fully charged batteries during aging by a thousand charge-discharge cycles. (

**b**) Pseudocapacitance correlates linearly with the actual battery capacity determined by Ah counting: C = 141⋅Q + 191. Fit quality 0.92. (

**c**) Increase of electrolyte resistance in time.

**Table 1.**Lithium-ion batteries in this study. Nominal data according to manufacturers’ data sheets. Approximate slope of the voltage-SOC curve (see Section 3.6). Cubic and linear approximation of the capacitance-capacity curve (see Section 3.2).

Chemistry | Cell | Voltage U (V) | Capacity Q (Ah) | C Rate Charge and Discharge | $\frac{\mathbf{\Delta}\mathit{U}}{\mathbf{\Delta}\mathit{S}\mathit{O}\mathit{C}}$ V per 100 % | Correlation of Pseudocapacitance (in F) and Capacity (in Ah) ${\mathit{C}}_{\mathbf{S}}=\mathit{a}{\mathit{Q}}^{3}+\mathit{b}{\mathit{Q}}^{2}+\mathit{c}\mathit{Q}+\mathit{d}$ | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

1 | LTO | BE Power 18,650 (Li_{4}Ti_{5}O_{12)} | 2.8 … 1.5 | 1.3 | 6 | 1.5 | – | – | – | – | – |

2 | LFP | SONY US18650 FTC | 3.6 … 2 | 1.1 | 1.1 | 30 | 0.21 | – | – | – | – |

3 | LithiumWerks ANR26650M1B | 3.6 … 2 | 2.6 | 4 | 70 | 0.18 | – | – | – | – | |

4 | VoltSolar 18,650 IFR | 3.6 … 2 | 1.4 | – | 3 | – | – | – | – | – | |

5 | LMO | Samsung INR18650-20R (LiNiCoMnO_{2}) | 4.2 … 2.5 | 2 | 4 | 20 | 1.15 | 2.73 – | −12.5 – | 19.3 302 | −9.34 6.2 |

6 | NMC | Samsung ICR18650-22P (MnNi) | 4.2 … 2.5 | 2.15 | 2.15 | 10 | – | – | – | – | – |

7 | Samsung INR18650-25R (NiMn) | 4.2 … 2.5 | 2.5 | 4 | 20 | – | – | – | – | – | |

8 | LG ICR18650HE2 (Ni Mn Co) | 4.2 … 2.0 | 2.5 | 4 | 20 | 1.0 | 1018 – | −5798 – | 11,032 182 | −6540 132 | |

9 | LG 18650-HG2 (Co Ni Mn) | 4.2 … 2.5 | 3 | 4 | 20 | – | – | – | – | – | |

10 | LCO | Panasonic UR18650 FK | 4.2 … 2.5 | 2.5 | 1.75 | 5 | 0.81 | 516 – | −2644 – | 4599 231 | −2349 −59 |

11 | NCA | SONY US18650VTC5 | 4.2 … 2.5 | 2.6 | 2.5 | 20 | 1.0 | – | – | – | – |

12 | LG INR18650MH1 | 4.2 … 2.5 | 3.2 | 3.1 | 10 | – | – | – | – | – | |

13 | Panasonic NCR18650GA | 4.2 … 2.5 | 3.3 | 10 | 10 | 0.93 | – | – | – | – | |

14 | Samsung INR18650-35E LiNiCoAlO_{2} | 4.2 … 2.65 | 3.35 | 2 | 8 | – | – | – | – | – | |

15 | Panasonic NCR18650 B | 4.2 … 2.5 | 3.4 | 1.62 | 3.4 | – | – | – | – | – |

**Table 2.**Validation of the linear correlation between state-of-charge and pseudocapacitance for three lithium-iron phosphate batteries of the same manufacturer.

Battery | Battery 1 | Battery 2 | Battery 3 | ||||||
---|---|---|---|---|---|---|---|---|---|

Measurement | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 |

Repeatability of | 1.42 | 1.37 | 1.36 | 1.48 | 1.15 | 1.36 | 1.56 | 1.35 | 1.34 |

slope ΔSOC/ΔC | 1.38 ± 0.02 | 1.33 ± 0.13 | 1.41 ± 0.09 | ||||||

Linear model | SOC = 1.412⋅C − 220.4 or C = 0.6995⋅SOC − 152.8 for SOC in % and C in F. | ||||||||

Quadratic model | SOC = −0.01120⋅C^{2} + 5.877⋅C − 657.6or C = 0.003748⋅SOC ^{2} + 0.2198⋅SOC + 166.6 |

**Table 3.**Qualitative changes in the impedance spectrum in different state-of-charge areas: R resistance of the high-frequency arc, X reactance at 0.1 Hz, C capacitance at 0.1 Hz.

Cell # | Full Charge SOC > 0.9 | Medium State-of-Charge SOC ≈ 0.5 | Low State-of-Charge SOC < 0.5 | ||
---|---|---|---|---|---|

5 | LMO | No significant impact on resistance. C ∼ SOC | R < 40 mΩ drops slightly. Reactance increases: X ∼ SOC. | R ≈ 40 mΩ drops slightly. X(0.1 Hz) = constant. | |

10 | LCO | No significant impact on resistance | R and X are slightly higher when SOC is lower. | R and X are high when SOC is low. Steeper U(Q) curve. | |

1113 | NCA | Resistance and impedance increase: R ∼ SOC | R and X are slightly higher when SOC is lower. | R and X are high when SOC is low. Steeper U(Q) curve. |

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**MDPI and ACS Style**

Kurzweil, P.; Scheuerpflug, W.
State-of-Charge Monitoring and Battery Diagnosis of Different Lithium Ion Chemistries Using Impedance Spectroscopy. *Batteries* **2021**, *7*, 17.
https://doi.org/10.3390/batteries7010017

**AMA Style**

Kurzweil P, Scheuerpflug W.
State-of-Charge Monitoring and Battery Diagnosis of Different Lithium Ion Chemistries Using Impedance Spectroscopy. *Batteries*. 2021; 7(1):17.
https://doi.org/10.3390/batteries7010017

**Chicago/Turabian Style**

Kurzweil, Peter, and Wolfgang Scheuerpflug.
2021. "State-of-Charge Monitoring and Battery Diagnosis of Different Lithium Ion Chemistries Using Impedance Spectroscopy" *Batteries* 7, no. 1: 17.
https://doi.org/10.3390/batteries7010017