Estimating state of charge (SOC) and uncertainty from relaxing voltage measurements in a battery
Some embodiments of the present invention provide a system that estimates a state of charge for a battery. During operation, while the battery is relaxing toward a fully rested state, the system determines if a modified state of charge of the battery is substantially consistent with a predetermined decay pattern. If so, the system estimates the state of charge of the battery as a value of the modified state of charge determined at the time when the consistency is observed. Otherwise, the system continues monitoring the modified state of charge of the battery. In one embodiment, the predetermined decay pattern is a single exponential decay. After estimating the state of charge of the battery, the system may determine an uncertainty of the estimated state of charge. More specifically, the system can estimate the uncertainty as substantially equal to a fraction of the difference between the value of the modified state of charge and the value of the voltage-based state of charge at the time when the consistency is observed.
1. A battery with a state-of-charge estimation mechanism, comprising:
a cell;
a voltage sensor that measures a voltage for the battery; and
a controller programmed to receive inputs from the voltage sensor and to generate a state-of-charge estimate;
wherein while the battery is relaxing toward a fully rested state, the controller is programmed to:
determine if a modified state of charge of the battery is substantially consistent with a predetermined decay pattern; and
if so, estimate the state of charge of the battery as a value of the modified state of charge determined at the time when the consistency is observed;
otherwise, continue monitoring the modified state of charge of the battery.
2. The battery of claim 1 , wherein the predetermined decay pattern is a single exponential decay.
3. The battery of claim 1 , wherein the controller is programmed to determines if the modified state of charge of the battery is substantially consistent with the predetermined decay pattern by:
computing a rate of change of the modified state of charge; and
determining whether the rate of change of the modified state of charge has become less than a threshold rate of change.
4. The battery of claim 3 , wherein the controller is programmed to computes the rate of change of the modified state of charge by computing both a first value of the modified state of charge at a first time and a second value of the modified state of charge at a second time, wherein the first time and the second time are associated with a predetermined time interval.
5. The battery of claim 1 , wherein the controller is programmed to derive the modified state of charge from a voltage-based state of charge of the battery.
6. The battery of claim 5 , wherein the controller is programmed to derives the modified state of charge from a voltage-based state of charge of the battery by:
determining one or more sample values of the voltage-based state of charge of the battery;
computing a first time derivative of the voltage-based state of charge;
computing a time constant associated with the predetermined decay pattern; and
determining the value of the modified state of charge based on the one or more sample values of the voltage-based state of charge, the first time derivative of the voltage-based state of charge, and the time constant.
7. The battery of claim 6 , wherein the controller is programmed to computes the time constant associated with the predetermined decay pattern by:
computing a second time derivative of the voltage-based state of charge; and
computing the time constant as the ratio of the first time derivative and the second time derivative of the voltage-based state of charge.
8. The battery of claim 6 , wherein the controller is programmed to determines the value of the voltage-based state of charge by:
measuring an open circuit voltage of the battery; and
determining the value of the voltage-based state of charge based at least on the open circuit voltage.
9. The battery of claim 6 , wherein after estimating the state of charge of the battery, the controller is programmed to computes an uncertainty of the estimated state of charge as a fraction of the difference between the value of the modified state of charge and the value of the voltage-based state of charge at the time when the consistency is observed.