RELAXATION MODEL IN REAL-TIME ESTIMATION OF STATE-OF-CHARGE IN LITHIUM POLYMER BATTERIES
Relaxation time constants give valuable information about a lithium polymer battery cell's state-of-charge. Moreover, determination of these time constants can be performed in real time by fitting exponential functions to transient voltage or current patterns.
1 . A method of determining the state of charge for a battery cell comprising:
measuring voltage and current as a function of time while the battery cell is operating;
recording in a memory location the voltage as a function of time over periods in which the current, expressed in terms of C-rate, is stable to within +/−0.01 C;
fitting, using a computer processor, the recorded voltage as a function of time to a pre-defined function that has three or more fit parameters, wherein the three or more fit parameters are selected to generate a fit of the recorded voltage as a function of time; and
determining the state of charge of the battery cell by comparing, using a computer processor, the three or more fit parameters to a previously-populated look-up table in a memory location, wherein the look-up table correlates the fit parameters to state-of-charge values.
2 . The method of claim 1 wherein the battery cell comprises lithium metal as an anode, lithium iron phosphate as a cathode, and a polymer electrolyte as a separator.
3 . The method of claim 1 wherein the pre-defined function has a single exponential term and has the form.
OCV
(
t
fit
)
=
k
0
+
k
1
-
t
τ
1
4 . The method of claim 1 wherein the pre-defined function has two exponential terms and has the form:
OCV
(
t
fit
)
=
k
0
+
k
1
-
t
τ
1
+
k
2
-
t
τ
2
5 . The method of claim 1 wherein the method is performed in real time on an operating battery.
6 . A computer-readable medium comprising code which, upon execution by a computer processor implements a method, the method comprising:
measuring voltage and current as a function of time while the battery cell is operating;
recording in a memory location the voltage as a function of time over periods in which the current, expressed in terms of C-rate, is stable to within +/−0.01 C;
fitting, using a computer processor, the recorded voltage as a function of time to a pre-defined function that has three or more fit parameters, wherein the three or more fit parameters are selected to generate a fit of the recorded voltage as a function of time; and
determining the state of charge of the battery cell by comparing, using a computer processor, the three or more fit parameters to a previously-populated look-up table in a memory location, wherein the look-up table correlates the fit parameters to state-of-charge values.
7 . The computer-readable medium of claim 6 wherein the battery cell comprises lithium metal as an anode, lithium iron phosphate as a cathode, and a polymer electrolyte as a separator.
8 . The computer-readable medium of claim 6 wherein the pre-defined function has a single exponential term and has the form.
OCV
(
t
fit
)
=
k
0
+
k
1
-
t
τ
1
9 . The computer-readable medium of claim 6 wherein the pre-defined function has two exponential terms and has the form:
OCV
(
t
fit
)
=
k
0
+
k
1
-
t
τ
1
+
k
2
-
t
τ
2
10 . The computer-readable medium of claim 6 wherein the method is performed in real time on an operating battery.