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Writing—original draft preparation, review and editing, P.K. and W.S. All authors have read and agreed to the published version of the manuscript.
Figure 1. (a) Qualitative discharge characteristics of a nickel–cadmium battery suffering the memory effect. (b) End-of-charge determination by minus-delta-U cutoff.
U
= voltage in volts.Figure 1. (a) Qualitative discharge characteristics of a nickel–cadmium battery suffering the memory effect. (b) End-of-charge determination by minus-delta-U cutoff.
U
= voltage in volts.
Figure 2. Impedance spectra of a nickel-cadmium (NiCd) battery (cell #5, new: State-of-health (SOH) 100% = 1.7 Ah, aged: SOH 71% = 1.21 Ah) at full charge (state-of-charge (SOC) = 100%, solid line) and 80% state-of-charge (dashed): (a) complex plane plot of impedance
Z
, so-called Nyquist plot, (b) admittanceY
= 1/Z
in the complex plane, (c) complex capacitanceC
=Y
/(jω
), (d) frequency response of modulus |Z
|(ω
), part of Bode diagram. Reactance ImZ
, susceptance ImY
, and pseudocapacitance ReC
reflect the state-of-charge more clearly than the ohmic resistance ReZ
, conductance ImY
, and the phase angle ϕ (not shown here).Figure 2. Impedance spectra of a nickel-cadmium (NiCd) battery (cell #5, new: State-of-health (SOH) 100% = 1.7 Ah, aged: SOH 71% = 1.21 Ah) at full charge (state-of-charge (SOC) = 100%, solid line) and 80% state-of-charge (dashed): (a) complex plane plot of impedance
Z
, so-called Nyquist plot, (b) admittanceY
= 1/Z
in the complex plane, (c) complex capacitanceC
=Y
/(jω
), (d) frequency response of modulus |Z
|(ω
), part of Bode diagram. Reactance ImZ
, susceptance ImY
, and pseudocapacitance ReC
reflect the state-of-charge more clearly than the ohmic resistance ReZ
, conductance ImY
, and the phase angle ϕ (not shown here).
Figure 3. Voltage during continuous cycle testing at 50 °C (NiCd, 1.7 Ah, 0.5C) for 1200 cycles.
Figure 3. Voltage during continuous cycle testing at 50 °C (NiCd, 1.7 Ah, 0.5C) for 1200 cycles.
Figure 4. SOC monitoring by impedance spectroscopy of a used NiCd battery (cell 5 of pack #3 of 2017). (a) Reactance
X
= ImZ
at different frequencies versus state-of-charge. (b) Pseudo-capacitanceC
and (c) calculated residual electric pseudo-chargeQ
(t
) =C
U
(t
) at the momentary voltageU
(SOC).Figure 4. SOC monitoring by impedance spectroscopy of a used NiCd battery (cell 5 of pack #3 of 2017). (a) Reactance
X
= ImZ
at different frequencies versus state-of-charge. (b) Pseudo-capacitanceC
and (c) calculated residual electric pseudo-chargeQ
(t
) =C
U
(t
) at the momentary voltageU
(SOC).
Figure 5. State-of-health monitoring (SOH) by impedance spectroscopy of NiCd batteries. (a) Reactance Im
Z
(1 Hz) during 1200 charge–discharge cycles (cell of new pack #6, C/2, 50 °C). (b) Rapid method with 0.19 mAh discharge and capacity measurement by ampere-hour counting (cell of new pack #5). (c) ImZ
(1 Hz) of fully charged battery packs versus SOH. (d) Cell 5 of pack #1 after 400 pre-cycles. The state-of-health SOH =Q
0/Q
N (ratio of actual and rated available capacityQ
) correlates quite well with the reactance ImZ
.Figure 5. State-of-health monitoring (SOH) by impedance spectroscopy of NiCd batteries. (a) Reactance Im
Z
(1 Hz) during 1200 charge–discharge cycles (cell of new pack #6, C/2, 50 °C). (b) Rapid method with 0.19 mAh discharge and capacity measurement by ampere-hour counting (cell of new pack #5). (c) ImZ
(1 Hz) of fully charged battery packs versus SOH. (d) Cell 5 of pack #1 after 400 pre-cycles. The state-of-health SOH =Q
0/Q
N (ratio of actual and rated available capacityQ
) correlates quite well with the reactance ImZ
.
Figure 6. Capacitance-based state-of-health monitoring with respect to terminal voltage
U
/U
0 at (a) 0.1 Hz and (b) 1 Hz. BoL = beginning of life (1.7 Ah), EoL = end of life (1.2 Ah) of cell #5 of pack #6. Solid:C
= ImY
/(jω
), according to Equation (4). Dashed: ApproximationC
D =C
(ω
→∞).Figure 6. Capacitance-based state-of-health monitoring with respect to terminal voltage
U
/U
0 at (a) 0.1 Hz and (b) 1 Hz. BoL = beginning of life (1.7 Ah), EoL = end of life (1.2 Ah) of cell #5 of pack #6. Solid:C
= ImY
/(jω
), according to Equation (4). Dashed: ApproximationC
D =C
(ω
→∞).
Figure 7. Aging study. Relative pseudo-charge
Q
(ω
) =C
(ω
)⋅U
(SOC) of an aged 1.7 Ah battery (pack #6, EoL = end of life) with regard to the new battery (BoL = beginning of life). (a) Impedance measurements at selected frequencies versus the actual state-of-charge SOC =Q
/Q
0 received by genuine Ah counting. (b) Frequency response of relative pseudo-charge, which is determined by the internal resistance of the battery below 1 Hz, and the surface capacitance above 1 Hz.Figure 7. Aging study. Relative pseudo-charge
Q
(ω
) =C
(ω
)⋅U
(SOC) of an aged 1.7 Ah battery (pack #6, EoL = end of life) with regard to the new battery (BoL = beginning of life). (a) Impedance measurements at selected frequencies versus the actual state-of-charge SOC =Q
/Q
0 received by genuine Ah counting. (b) Frequency response of relative pseudo-charge, which is determined by the internal resistance of the battery below 1 Hz, and the surface capacitance above 1 Hz.Figure 8. The impact of aging. Ratio of the available electric pseudo-charge
Q
0(t
) of used NiCd batteries with respect to the rated value of the new batteryQ
N (pack #5 and pack #6). Data are taken fromQ
0 =C
(1 Hz)U
(divided by the rated capacityQ
N) correlates well with the true SOH values from Ah measurements.The impact of aging. Ratio of the available electric pseudo-charge) of used NiCd batteries with respect to the rated value of the new battery(pack #5 and pack #6). Data are taken from Figure 5 . Impedance-based pseudo-charge(1 Hz)(divided by the rated capacity) correlates well with the true SOH values from Ah measurements.
Figure 8. The impact of aging. Ratio of the available electric pseudo-chargeQ
0(t
) of used NiCd batteries with respect to the rated value of the new batteryQ
N (pack #5 and pack #6). Data are taken fromQ
0 =C
(1 Hz)U
(divided by the rated capacityQ
N) correlates well with the true SOH values from Ah measurements.The impact of aging. Ratio of the available electric pseudo-charge) of used NiCd batteries with respect to the rated value of the new battery(pack #5 and pack #6). Data are taken from Figure 5 . Impedance-based pseudo-charge(1 Hz)(divided by the rated capacity) correlates well with the true SOH values from Ah measurements.
Figure 9. Aging characteristics of NiCd cell #5 of pack #6 (new: 1.7 Ah, aged: 1.3 Ah, SOH = 76%) in the plot of pseudo-capacitance C(
ω
) and pseudo-chargeQ
(ω
) =C
(ω
)U
versus the internal resistance (real part of impedance).U
(SOC) = actual cell voltage at the time of measurement.Figure 9. Aging characteristics of NiCd cell #5 of pack #6 (new: 1.7 Ah, aged: 1.3 Ah, SOH = 76%) in the plot of pseudo-capacitance C(
ω
) and pseudo-chargeQ
(ω
) =C
(ω
)U
versus the internal resistance (real part of impedance).U
(SOC) = actual cell voltage at the time of measurement.
Figure 10. Aging characteristics of a NiCd battery (cell #5 of pack #6). (a) Different normalized state-of-charge quantities with respect to voltage
U
/U
0, pseudo-capacitanceC
/C
0 at 0.22 Hz, imaginary part of impedance at 0.22 Hz, and relative time constant τ/τ0 at 0.22 Hz against the actual state-of-charge received from Ah counting. (b) Relative time constant between the old battery τ =R
(1 kHz)⋅C
(0.1 Hz) and the new battery τ0 at different frequencies according to Equation (6).Figure 10. Aging characteristics of a NiCd battery (cell #5 of pack #6). (a) Different normalized state-of-charge quantities with respect to voltage
U
/U
0, pseudo-capacitanceC
/C
0 at 0.22 Hz, imaginary part of impedance at 0.22 Hz, and relative time constant τ/τ0 at 0.22 Hz against the actual state-of-charge received from Ah counting. (b) Relative time constant between the old battery τ =R
(1 kHz)⋅C
(0.1 Hz) and the new battery τ0 at different frequencies according to Equation (6).
Table 1. Overview of experiments.
Table 1. Overview of experiments.
Test MethodBattery Pack: 7.5 V, 1.7 Ah, 5 Single CellsA. Cycling (SOC) at 50 °CB. Impedance Measurements During Discharge (SOC 1 → 0.7) After 400, 800, 1200 CyclesC. Capacity After Full 0.5C Charge (Ah Counting)1 Full discharge(a) old (#1)If you have any questions on Ni-MH Battery. We will give the professional answers to your questions.