Battery monitoring system
A battery monitoring system includes a current sensor and a voltage sensor coupled to a battery cell. It also includes a microcontroller that opportunistically computes many estimates of the cell's ohmic resistance and filters these estimates to arrive at a stable value. Each estimate is traditionally computed from a delta change in voltage divided by delta change in current measured before and after a significant change in current magnitude. An improvement in accuracy of each resistance estimate is achieved by only computing an estimate if the rate of change of voltage and the rate of change of current exhibited by the values making up the delta voltage and delta current are tightly consistent and of the same polarity. This approach significantly minimizes errors induced in estimates not preselected in this manner by the different and also asynchronous sample rates of the cell's voltage and current.
1. A battery monitoring system, comprising:
a current sensor electrically coupled in series with a battery cell;
a voltage sensor electrically coupled in parallel to the battery cell;
a microcontroller obtaining cell current values of a cell current flowing through the battery cell from the current sensor at a first update frequency of M times per second;
the microcontroller obtaining cell voltage values of the battery cell from the voltage sensor, in parallel to the obtaining of the cell current values, with respect to electrical ground, at a second update frequency of N times per second, wherein M>=N;
at a third update frequency of R times per second, where R<M and R<N,
the microcontroller determining a rate of change of cell current utilizing two cell current values of the cell current values;
the microcontroller determining a rate of change of cell voltage utilizing two cell voltage values of the cell voltage values; and
the microcontroller determining a filtered ohmic resistance value based on the rate of change of cell voltage, the rate of change of cell current, and a prior filtered ohmic resistance value, if a numerical sign of the rate of change of cell voltage being identical to a numerical sign of the rate of change of cell current, and the rate of change of cell voltage being less than or equal to an upper threshold of allowable rates of cell voltage change, and the rate of change of cell voltage being greater than or equal to a lower threshold of allowable rates of cell voltage change.
2. The battery monitoring system of claim 1 , wherein:
the microcontroller determining the filtered ohmic resistance value utilizing a prior filtered ohmic resistance value, if the numerical sign of the rate of change of cell voltage is not identical to the numerical sign of the rate of change of cell current, or the rate of change of cell voltage is not less than or equal to the upper threshold of allowable rates of cell voltage change, or the rate of change of cell voltage is not greater than or equal to the lower threshold of allowable rates of cell voltage change.
3. The battery monitoring system of claim 1 , wherein:
a symbol j is a reference to a current operational cycle associated with the third update frequency, and j−1 refers to a previous operational cycle associated with the third update frequency.
4. The battery monitoring system of claim 3 , wherein:
the microcontroller determining the rate of change of cell current utilizing a following equation:
di/dt=I j −I j-1 /t j - t j-1
wherein:
di/dt is the rate of change of cell current corresponding to a first derivative of cell current with respect to time;
I j is a value of a last sampled current value prior to an execution of the current operational cycle associated with the third update frequency;
I j-1 is a value of a last sampled cell current value prior to an execution of an operational cycle previous to the current operational cycle associated with the third update frequency;
t j is an elapsed time since system startup that is recorded at a start of execution of the current operational cycle associated with the third update frequency;
t j-1 is an elapsed time since the system startup that is recorded at a start of execution of the operational cycle previous to the current operational cycle associated with the third update frequency.
5. The battery monitoring system of claim 3 , wherein:
the microcontroller determining the rate of change of cell voltage utilizing a following equation:
dv/dt=V j −V j-1 /t j −t j-1
wherein:
dv/dt is the rate of change of cell voltage corresponding to a calculation of a first derivative of cell voltage with respect to time;
V j is a value of a last sampled cell voltage value prior to an execution of the current operational cycle associated with the third update frequency;
V j-1 is a value of a last sampled cell voltage value prior to an execution of the operational cycle previous to the current operational cycle associated with the third update frequency;
t j is an elapsed time since a system startup that is recorded at a start of execution of the current operational cycle associated with the third update frequency;
t j-1 is an elapsed time since the system startup that is recorded at a start of execution of the operational cycle previous to the current operational cycle associated with the third update frequency.
6. The battery monitoring system of claim 3 , wherein:
the microcontroller determining the upper threshold of allowable rates of cell voltage change utilizing a following equation:
UpperThresholdV RofC =(abs( di/dt )*Filtered R 0 j-1 )+ x %*(abs( di/dt )*Filtered R 0 j-1 )
wherein:
UpperThresholdV RofC is the upper threshold of allowable rates of cell voltage change;
abs(di/dt) is an absolute value of the rate of change of cell current;
FilteredR0 j-1 is a result of a filtered value of cell resistance R 0 computed during the operational cycle previous to the current operational cycle associated with the third update frequency;
x % is a calibrateable percentage of (abs(di/dt)*FilteredR0 j-1 )) that defines an upper threshold of acceptable dv/dt values to be selected for use in a calculation of the FilteredR0 j for the current operational cycle associated with the third update frequency.
7. The battery monitoring system of claim 3 , wherein:
the microcontroller determining the lower threshold of allowable rates of cell voltage change utilizing a following equation:
LowerThreshold V RofC =(abs( di/dt )*Filtered R 0 j-1 )− y %*(abs( di/dt )*Filtered R 0 j-1 )
wherein:
LowerThresholdV RofC is the lower threshold of allowable rates of cell voltage change;
abs(di/dt) is an absolute value of the rate of change of cell current;
FilteredR0 j-1 is a result of a filtered value of cell resistance R 0 computed during the operational cycle previous to the current operational cycle associated with the third update frequency;
y % is a calibrateable percentage of (abs(di/dt)*FilteredR0 j-1 )) that defines a lower threshold of acceptable dv/dt values to be selected for use in a calculation of the FilteredR0 j for the current operational cycle associated with the third update frequency.
8. The battery monitoring system of claim 3 , wherein:
the microcontroller determining the filtered ohmic resistance value if the numerical sign of the rate of change of cell voltage is identical to the numerical sign of the rate of change of cell current, and the rate of change of cell voltage is less than or equal to the upper threshold of allowable rates of cell voltage change, and the rate of change of cell voltage is greater than or equal to the lower threshold of allowable rates of cell voltage change, utilizing a following equation:
Filtered R 0 j =smoothingFilterFunction(NewRaw R 0Estimate,Filtered R 0 j-1 ),
wherein:
FilteredR0 j is the filtered ohmic resistance value;
NewRaw R 0Estimate= dv/di;
dv/di is a first derivative of cell voltage with respect to cell current and is equal to a (V j -V j-1 ) calculation divided by a (I j -I j-1 ) calculation; and V j is a value of a last sampled cell voltage value prior to an execution of the current operational cycle associated with the third update frequency, and V j-1 is a value of a last sampled cell voltage value prior to the execution of the operational cycle previous to the current operational cycle associated with the third update frequency; I j is a value of a last sampled cell current value prior to an execution of the current operational cycle associated with the third update frequency, and I j-1 is a value of a last sampled cell current value prior to the execution of the operational cycle previous to the current operational cycle associated with the third update frequency; and smoothingFilterFunction( ) is a recursive smoothing filter.
9. The battery monitoring system of claim 8 , wherein:
the recursive smoothing filter is a first order lag filter, or a single exponential smoothing filter, or a double exponential smoothing filter.