Systems and methods for impedance measurement of a battery cell
A system is disclosed for determining complex impedance characteristics of one or more battery cells based on the charge signal applied, or to be applied, to the battery cell. Implementations may include measuring the impedance of a battery cell to, in some instances, determine a frequency component or harmonic that defines, at least a portion, of a waveform shape for charging the battery cell. In one implementation, the impedance at the battery cell may be measured or estimated from a discrete charge period being applied to the battery cell or from multiple discrete charge periods applied to the battery cell. The measured differences between the amplitude and time components of the voltage and current waveforms may be used to determine or estimate the magnitude, phase shift, real, and/or imaginary values of the impedance at the battery cell.
1 . A method for monitoring an electrochemical device comprising:
obtaining, via a processing device, a plurality of measurements comprising a plurality of voltage amplitudes and a plurality of current amplitudes of a charge waveform applied to an electrochemical device, the charge waveform comprising a plurality of pulses each comprising a plurality of distinct portions of differing shapes;
calculating a plurality of impedance ratios, wherein each of the plurality of impedance ratios comprise a one of the plurality of voltage amplitude measurements and a one of the plurality of current amplitude measurements, wherein the one of the plurality of voltage amplitude measurements and the one of the plurality of current amplitude measurements are measured during the same distinct portion of the same pulse of the charge waveform;
obtaining complex impedance characteristics of the electrochemical device by summing at least a first impedance ratio and a second impedance ratio of the subset of the plurality of impedance ratios, wherein:
the first impedance ratio of the subset of the plurality of impedance ratios comprises a first voltage amplitude measurement and a first current amplitude measurement obtained during a first distinct portion of a first pulse of the charge waveform; and
the second impedance ratio of the subset of the plurality of impedance ratios comprises a second voltage amplitude measurement and a second current amplitude measurement obtained during a second distinct portion of the a second pulse of the charge waveform, wherein the first distinct portion of the first pulse is the same portion of the plurality of distinct portions as the second distinct portion of the second pulse; and
altering an attribute of the charge waveform based on the obtained complex impedance characteristics of the electrochemical device.
2 . The method of claim 1 , wherein the complex impedance characteristics comprise at least one of a real impedance value, an imaginary impedance value, a magnitude impedance value, or a phase shift impedance value.
3 . The method of claim 1 , wherein the distinct portions of the charge waveform comprises a sinusoidal leading edge portion and a body portion, different than the leading edge portion, following the leading edge portion.
4 . The method of claim 3 further comprising:
estimating a real impedance value of the leading edge portion of the charge waveform by summing the subset of the plurality of impedance ratios corresponding to the leading edge portion.
5 . The method of claim 4 , wherein the real impedance value corresponds to a voltage amplitude measurement at the electrochemical device obtained at a first time and a current amplitude measurement through the electrochemical device obtained at a second time later than the first time.
6 . The method of claim 5 further comprising:
estimating the second time based on a determined inflection point of a current component of the leading edge portion of the charge waveform.
7 . The method of claim 3 further comprising:
estimating an imaginary impedance value corresponding to the leading edge portion of the charge waveform, the imaginary impedance determined from a difference of the first time and the second time.
8 . The method of claim 3 further comprising:
estimating a real impedance value corresponding to the body portion of the charge waveform by summing the subset of the plurality of impedance ratios corresponding to the body portion.
9 . The method of claim 3 further comprising
determining, based on the plurality of measurements of the voltage amplitude, a first transition a voltage component within the charge waveform from the leading edge portion to the body portion.
10 . The method of claim 9 further comprising:
determining, based on the plurality of measurements of the current amplitude, a second transition a current component within the charge waveform from the leading edge portion to the body portion, the second transition occurring after the first transition.
11 . The method of claim 3 further comprising:
calculating a centroid of the leading edge portion of the charge waveform, the complex impedance characteristics of the electrochemical device further based on the calculated centroid of the leading edge portion.
12 . The method of claim 3 further comprising:
calculating a centroid of the body portion of the charge waveform, the complex impedance characteristics of the electrochemical device further based on the calculated centroid of the body portion.
13 . The method of claim 1 , wherein the charge waveform comprises one or more discrete charge periods, the measurements of the charge waveform obtained from a first discrete charge period and a second discrete charge period different than the first discrete charge period.
14 . A method of charging an electrochemical device comprising:
for a charge waveform for charging an electrochemical device, the charge waveform comprising a plurality of pulses each comprising a plurality of distinct portions of differing shapes:
obtaining a representative value indicative of a flow of current to the electrochemical device responsive to the charge waveform, the obtained representative value based on a sum of at least a first impedance ratio and a second impedance ratio of a subset of a plurality of impedance ratios determined from of a subset of the plurality of pulses of the charge waveform, wherein:
the first impedance ratio of the subset of the plurality of impedance ratios comprises a first voltage amplitude measurement and a first current amplitude measurement obtained during a first distinct portion of a first pulse of the plurality of pulses of the charge waveform; and
the second impedance ratio of the subset of the plurality of impedance ratios comprises a second voltage amplitude measurement and a second current amplitude measurement obtained during a second distinct portion of a second pulse of the plurality of pulses of the charge waveform, wherein the first distinct portion of the first pulse is the same portion of the plurality of distinct portions as the second distinct portion of the second pulse; and
altering an attribute of the charge waveform based on the representative value.
15 . The method of claim 14 wherein the representative value is at least one of impedance, admittance, and power.
16 . The method of claim 14 wherein the charge waveform includes a shaped leading edge.
17 . The method of claim 16 wherein the representative value is impedance, the shaped leading edge is associated with a frequency defined based on a relationship between the frequency and the impedance of the electrochemical device to the frequency of the shaped leading edge of the charge waveform.
18 . The method of claim 17 wherein the representative value is based on the impedance of the frequency, and wherein altering the attribute comprises altering a frequency attribute of a shaped leading edge to reduce the impedance of the electrochemical device to the charge waveform.
19 . The method of claim 14 wherein the representative value is impedance, the charge waveform defines a body portion, the impedance associated with the body portion, and altering an attribute of the charge waveform comprises altering a period of the body portion based on the impedance.
20 . The method of claim 19 wherein the altered period of the body portion is based on maintaining the impedance of the body portion within a threshold.
21 . The method of claim 14 wherein the representative value is impedance, the charge waveform defines a body portion, the impedance associated with the body portion, and altering an attribute of the charge waveform comprises altering a frequency of a leading edge harmonic to reduce the impedance associated with the body portion.
22 . The method of claim 14 wherein the charge waveform defines a trailing edge with a voltage component and a current component, a following charge waveform applied after the current component of the charge waveform reaches zero.
23 . The method of claim 14 wherein obtaining a representative value indicative of the flow of current to the electrochemical device responsive to the charge waveform comprises obtaining a ratio between a voltage component and a current component of the charge waveform to determine a real component of an impedance.
24 . The method of claim 23 wherein the ratio is associated with a peak value of a leading edge harmonic of the voltage component of the charge waveform.
25 . The method of claim 23 wherein the ratio is associated with a value of a body portion of the charge waveform.
26 . The method of claim 23 further comprising:
obtaining the ratio at a point of the harmonic of the voltage component of the charge waveform; and
determining an imaginary component of the impedance based on a time difference between the point of the harmonic of the voltage component and a related point of the current component.