# US 10,371,754 B2 · Systems and methods for real-time estimation of capacity of a rechargeable battery

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- Number: US 10,371,754 B2
- Document ID: US10371754B2
- Status: Granted
- Kind: B2
- Application number: 15/048,816
- Filed: 2016-02-19
- Published: 2017-08-24
- Granted: 2019-08-06
- Earliest claimed: 2016-02-19
- Assignees: CPS Technology Holdings LLC
- Applicants: Johnson Controls Technology Company
- Inventors: Qingzhi Guo; Christian Kuper; Timur L. Aliyev; Zhihong H. Jin
- Web page: https://patentgrep.com/patent/US10371754B2

## CPC

- G01R 31/367: Software therefor, e.g. for battery testing using modelling or look-up tables
- B60L 58/12: responding to state of charge [SoC]
- H01M 10/48: Accumulators combined with arrangements for measuring, testing or indicating the condition of cells, e.g. the level or density of the electrolyte (constructional details of current conducting connections for detecting conditions inside cells or batteries, e.g. details of voltage sensing terminals, H01M50/569)
- G01R 31/389: Measuring internal impedance, internal conductance or related variables
- Y02E 60/10: Energy storage using batteries
- Y02T 10/70: Energy storage systems for electromobility, e.g. batteries
- G01R: MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES (indicating correct tuning of resonant circuits H03J3/12)
- B60L: PROPULSION OF ELECTRICALLY-PROPELLED VEHICLES (arrangements or mounting of electrical propulsion units or of plural diverse prime-movers for mutual or common propulsion in vehicles B60K1/00, B60K6/20; arrangements or mounting of electrical gearing in vehicles B60K17/12, B60K17/14; preventing wheel slip by reducing power in rail vehicles B61C15/08; dynamo-electric machines H02K; control or regulation of electric motors H02P); SUPPLYING ELECTRIC POWER FOR AUXILIARY EQUIPMENT OF ELECTRICALLY-PROPELLED VEHICLES (electric coupling devices combined with mechanical couplings of vehicles B60D1/64; electric heating for vehicles B60H1/00); ELECTRODYNAMIC BRAKE SYSTEMS FOR VEHICLES IN GENERAL (control or regulation of electric motors H02P); MAGNETIC SUSPENSION OR LEVITATION FOR VEHICLES; MONITORING OPERATING VARIABLES OF ELECTRICALLY-PROPELLED VEHICLES; ELECTRIC SAFETY DEVICES FOR ELECTRICALLY-PROPELLED VEHICLES
- H01M: PROCESSES OR MEANS, e.g. BATTERIES, FOR THE DIRECT CONVERSION OF CHEMICAL ENERGY INTO ELECTRICAL ENERGY
- Y02E: REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
- Y02T: CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION

## Abstract

A battery system includes a battery that couples to an electrical system. The battery system also includes a battery control module that electrically couples to the battery. The battery control module monitors at least one monitored parameter of the battery, and the battery control module recursively calculates a first capacity estimation of the battery using two linear regression models based on at least an equivalent circuit model, the at least one monitored parameter, and a Kalman filter.

## Claims

### Claim 1

An automotive vehicle comprising:
a battery, wherein the battery comprises a plurality of battery cells;
an electrical system comprising an electrical generator configured to, in operation, generate electrical power and an electrical load configured to operate using electrical power;
a relay electrically coupled between the plurality of battery cells and the electrical system;
one or more sensors configured to measure a plurality of battery parameter sets during operation of the battery, wherein each battery parameter set of the plurality of battery parameter sets comprises a terminal voltage and a terminal current; and
one or more control modules communicatively coupled to the relay and the one or more sensors, wherein the one or more control modules are configured to:
determine a first Kalman filter based at least in part on a first relationship between the terminal voltage and the terminal current of the battery with an open circuit voltage of the battery, an ohmic resistance of the battery, and a charge transfer resistance of the battery;
determine a second Kalman filter based at least in part on a second relationship between capacity of the battery, a change in state of charge of the battery, and an accumulative ampere-hour throughput of the battery during the change in the state of charge;
determine a plurality of estimated open circuit voltages by executing the first Kalman filter based at least in part on each battery parameter set of the plurality of battery parameter sets;
determine a plurality of estimated states of charge each corresponding with one of the plurality of estimated open circuit voltages based at least in part on a third relationship between the state of charge and the open circuit voltage of the battery;
determine the capacity of the battery based at least in part on execution of the second Kalman filter using each estimated state of charge of the plurality of estimated states of charge; and
control charging of the battery, discharging of the battery, or both based at least in part on the capacity of the battery by:
instructing the relay to switch to, maintain, or both a connected state to enable the electrical generator to charge the battery, the battery to discharge electrical power to the electrical load, or both; and
instructing the relay to switch to, maintain, or both a disconnected state to block the electrical generator from charging the battery and the battery from discharging to the electrical load.

### Claim 2 (depends on 1)

The automotive vehicle of claim 1, wherein the plurality of battery cells comprises:
a first battery cell that uses a first battery chemistry; and
a second battery cell that uses a second battery chemistry.

### Claim 3 (depends on 1)

The automotive vehicle of claim 1, wherein the one or more control modules are configured to:
determine a plurality of estimated capacities by executing the second Kalman filter using each estimated state of charge of the plurality of estimated states of charge;
determine a mean estimated capacity of the plurality of estimated capacities;
determine an estimated capacity variance of the plurality of estimated capacities of the battery;
determine whether a ratio of the estimated capacity variance to the mean estimated capacity squared is greater than a relative error tolerance threshold; and
determine the capacity of the battery based at least in part on the plurality of estimated capacities when the ratio of the estimated capacity variance to the mean estimated capacity squared is not greater than the relative error tolerance threshold.

### Claim 4 (depends on 3)

The automotive vehicle of claim 3, wherein the one or more control modules are configured to:
determine a maximum estimated state of charge from the plurality of estimated states of charge;
determine a minimum estimated state of charge from the plurality of estimated state of charge;
determine whether a difference between the maximum estimated state of charge and the minimum estimated state of charge is greater than a swing threshold; and
determine the capacity of the battery based at least in part on the plurality of estimated capacities when the ratio of the estimated capacity variance to the mean estimated capacity squared is not greater than the relative error tolerance threshold and the difference between the maximum estimated state of charge and the minimum estimated state of charge is greater than the swing threshold.

### Claim 5 (depends on 4)

The automotive vehicle of claim 4, wherein the one or more control modules are configured to:
determine a most recent open circuit voltage of the plurality of estimated open circuit voltages by executing the first Kalman filter based at least in part on a most recent battery parameter set of the plurality of battery parameter sets;
determine a most recent estimated state of charge of the plurality of estimated states of charge by mapping the most recent open circuit voltage to the most recent estimated state of charge based at least in part on the third relationship between the state of charge and the open circuit voltage of the battery;
determine a most recent estimated capacity of the plurality of estimated capacities by executing the second Kalman filter based at least in part on the most recent estimated state of charge; and
set the capacity of the battery equal to the most recent estimate capacity when the ratio of the estimated capacity variance to the mean estimated capacity squared is not greater than the relative error tolerance threshold and the difference between the maximum estimated state of charge and the minimum estimated state of charge is greater than the swing threshold.

### Claim 6 (depends on 1)

The automotive vehicle of claim 1, wherein the one or more control modules are configured to:
determine the accumulative ampere-hour throughput of the battery based at least in part on the terminal current indicated in each battery parameter set of the plurality of battery parameter sets; and
determine the capacity of the battery based at least in part on execution of the second Kalman filter using the accumulative ampere-hour throughput of the battery.

### Claim 7 (depends on 1)

The automotive vehicle of claim 1, wherein the one or more control modules are configured to:
initialize parameters of the first Kalman filter with random values before execution of the first Kalman filter based at least in part the plurality of battery parameter sets; and
initialize parameters of the second Kalman filter with random values before execution of the second Kalman filter based at least in part on the plurality of estimated states of charge.

### Claim 8 (depends on 1)

The automotive vehicle of claim 1, wherein:
the one or more control modules are communicatively coupled to the electrical generator; and
the one or more control modules are configured to control charging of the battery, discharging of the battery, or both by controlling electrical power output by the electrical generator.

### Claim 9 (depends on 8)

The automotive vehicle of claim 8, wherein the one or more control modules comprise:
a battery control unit configured to control switching of the relay; and
a vehicle control unit configured to control electrical power output by the electrical generator.

### Claim 10

A method comprising:
receiving, using one or more processors implemented in a vehicle, a plurality of battery parameter sets measured by one or more sensors during operation of a battery implemented in the vehicle, wherein each battery parameter set of the plurality of battery parameter sets comprises a terminal voltage and a terminal current;
determining, using the one or more processors, a first Kalman filter based at least in part on a first relationship between the terminal voltage and the terminal current of the battery with an open circuit voltage of the battery, an ohmic resistance of the battery, and a charge transfer resistance of the battery;
determining, using the one or more processors, a second Kalman filter based at least in part on a second relationship between capacity of the battery, a change in state of charge of the battery, and an accumulative ampere-hour throughput of the battery during the change in the state of charge;
determining, using the one or more processors, a plurality of estimated open circuit voltages by executing the first Kalman filter based at least in part on each battery parameter set of the plurality of battery parameter sets;
determining, using the one or more processors, a plurality of estimated states of charge each corresponding with one of the plurality of estimated open circuit voltages based at least in part on a third relationship between the state of charge and the open circuit voltage of the battery;
determining, using the one or more processors, the capacity of the battery based at least in part on execution of the second Kalman filter using each estimated state of charge of the plurality of estimated states of charge; and
controlling, using the one or more processors, charging of the battery, discharging of the battery, or both based at least in part on the capacity of the battery, wherein controlling charging of the battery, discharging of the battery, or both comprises:
instructing a relay electrically coupled between the battery and an electrical system implemented in the vehicle to switch to, maintain, or both a connected state to enable the electrical system to charge the battery, the battery to discharge electrical power to the electrical system, or both; and
instructing the relay to switch to, maintain, or both a disconnected state to block the electrical system from charging the battery and the battery from discharging to the electrical system.

### Claim 11 (depends on 10)

The method of claim 10, wherein determining the capacity of the battery comprises:
determining a plurality of estimated capacities by executing the second Kalman filter using each estimated state of charge of the plurality of estimated states of charge;
determining a mean estimated capacity of the plurality of estimated capacities;
determining an estimated capacity variance of the plurality of estimated capacities of the battery;
determining whether a ratio of the estimated capacity variance to the mean estimated capacity squared is greater than a relative error tolerance threshold; and
determining the capacity of the battery based at least in part on the plurality of estimated capacities when the ratio of the estimated capacity variance to the mean estimated capacity squared is not greater than the relative error tolerance threshold.

### Claim 12 (depends on 11)

The method of claim 11, wherein determining the capacity of the battery comprises:
determining a maximum estimated state of charge from the plurality of estimated states of charge;
determining a minimum estimated state of charge from the plurality of estimated state of charge; and
determining whether a difference between the maximum estimated state of charge and the minimum estimated state of charge is greater than a swing threshold; and
determining the capacity of the battery based at least in part on the plurality of estimated capacities when the ratio of the estimated capacity variance to the mean estimated capacity squared is not greater than the relative error tolerance threshold and the difference between the maximum estimated state of charge and the minimum estimated state of charge is greater than the swing threshold.

### Claim 13 (depends on 12)

The method of claim 12, wherein determining the capacity of the battery comprises:
determining a most recent open circuit voltage of the plurality of estimated open circuit voltages by executing the first Kalman filter based at least in part on a most recent battery parameter set of the plurality of battery parameter sets;
determining a most recent estimated state of charge of the plurality of estimated states of charge by mapping the most recent open circuit voltage to the most recent estimated state of charge based at least in part on the third relationship between the state of charge and the open circuit voltage of the battery;
determining a most recent estimated capacity of the plurality of estimated capacities by executing the second Kalman filter based at least in part on the most recent estimated state of charge; and
setting the capacity of the battery equal to the most recent estimate capacity when the ratio of the estimated capacity variance to the mean estimated capacity squared is not greater than the relative error tolerance threshold and the difference between the maximum estimated state of charge and the minimum estimated state of charge is greater than the swing threshold.

### Claim 14 (depends on 10)

The method of claim 10, comprising:
initializing, using the one or more processors, parameters of the first Kalman filter with random values before execution of the first Kalman filter based at least in part the plurality of battery parameter sets; and
initializing, using the one or more processor, parameters of the second Kalman filter with random values before execution of the second Kalman filter based at east least in part on the plurality of estimated states of charge.

### Claim 15 (depends on 10)

The method of claim 10, wherein controlling charging of the battery, discharging of the battery, or both comprises controlling voltage, current, or both of electrical power output by an electrical generator implemented in the electrical system.

### Claim 16

A tangible, non-transitory, computer-readable medium storing instruction executable by one or more processors, wherein the instructions comprise instructions to:
receive, using the one or more processors, a plurality of battery parameter sets measured by one or more sensors during operation of a battery, wherein the plurality of battery parameter sets comprises:
a first battery parameter set measured at a first time, wherein the first battery parameter set comprises a first terminal voltage of the battery and a first terminal current of the battery; and
a second battery parameter set measured at a second time after the first time, wherein the second battery parameter set comprises a second terminal voltage of the battery and a second terminal current of the battery;
determine, using the one or more processors, whether the battery is relaxed at the first time based at least in part on the first battery parameter set and whether the battery is relaxed at the second time based at least in part on the second battery parameter set;
when the battery is relaxed at the first time and at the second time:
determine, using the one or more processors, a first state of charge of the battery present at the first time by mapping the first terminal voltage based on a first relationship between state of charge and open circuit voltage of the battery;
determine, using the one or more processors, a second state of charge of the battery present at the second time by mapping the second terminal voltage based on the first relationship between state of charge and open circuit voltage of the battery;
determine, using the one or more processors, an accumulative ampere-hour throughput of the battery between the first time and the second time based at least in part on one or more of the plurality of battery parameter sets measured between the first time and the second time; and
determine, using the one or more processors, capacity of the battery based at least in part on the accumulative ampere-hour throughput of the battery between the first time and the second time and a difference between the first state of charge of the battery and the second state of charge of the battery; and
control, using the one or more processors, charging of the battery, discharging of the battery, or both based at least in part on the capacity of the battery by:
instructing a relay electrically coupled between the battery and an electrical system to switch to, maintain, or both a connected state to enable the electrical system to charge the battery, the battery to discharge electrical power to the electrical system, or both; and
instructing the relay to switch to, maintain, or both a disconnected state to block the electrical system from charging the battery and the battery from discharging to the electrical system.

### Claim 17 (depends on 16)

The tangible, non-transitory, computer-readable medium of claim 16, wherein:
the instructions to determine whether the battery is relaxed at the first time comprise instructions to determine that the battery is relaxed at the first time when the first terminal current measured at the first time does not exceed a relaxation current threshold; and
the instructions to determine whether the battery is relaxed at the second time comprise instructions to determine that the battery is relaxed at the second time when the second terminal current measured at the second time does not exceed the relaxation current threshold.

### Claim 18 (depends on 16)

The tangible, non-transitory, computer-readable medium of claim 16, wherein:
the instructions to determine whether the battery is relaxed at the first time comprise instructions to:
determine a first rate of change of the open circuit voltage of the battery based at least in part on the first terminal voltage measured at the first time; and
determine that the battery is relaxed at the first time when the first rate of change of the open circuit voltage is less than a rate of change threshold; and
the instructions to determine whether the battery is relaxed at the second time comprise instructions to:
determine a second rate of change of the open circuit voltage of the battery based at least in part on the second terminal voltage measured at the second time; and
determine that the battery is relaxed at the second time when the second rate of change of the open circuit voltage is less than the rate of change threshold.

### Claim 19 (depends on 16)

The tangible, non-transitory, computer-readable medium of claim 16, comprising instructions to, when the battery is not relaxed at the first time and not relaxed at the second time:
determine, using the one or more processors, a first Kalman filter based at least in part on a second relationship between a terminal voltage of the battery, a terminal current of the battery, the open circuit voltage of the battery, an ohmic resistance of the battery, and a charge transfer resistance of the battery;
determine, using the one or more processors, a second Kalman filter based at least in part on a third relationship between the capacity of the battery, a change in the state of charge of the battery, and the an accumulative ampere-hour throughput of the battery during the change in the state of charge;
determine, using the one or more processors, a plurality of estimated open circuit voltages by executing the first Kalman filter based at least in part on each battery parameter set of the plurality of battery parameter sets;
determine, using the one or more processors, a plurality of estimated states of charge each corresponding with one of the plurality of estimated open circuit voltages based at least in part on the first relationship between the state of charge and the open circuit voltage of the battery; and
determine, using the one or more processors, the capacity of the battery based at least in part on execution of the second Kalman filter using each estimated state of charge of the plurality of estimated states of charge.

### Claim 20 (depends on 19)

The tangible, non-transitory, computer-readable medium of claim 19, comprising instructions to, when the battery is not relaxed at the first time and not relaxed at the second time:
determine, using the one or more processors, a plurality of estimated capacities by executing the second Kalman filter using each estimated state of charge of the plurality of estimated states of charge;
determine, using the one or more processors, a mean estimated capacity of the plurality of estimated capacities;
determine, using the one or more processors, an estimated capacity variance of the plurality of estimated capacities of the battery;
determine, using the one or more processors, whether a ratio of the estimated capacity variance to the mean estimated capacity squared is greater than a relative error tolerance threshold;
determine, using the one or more processors, a maximum estimated state of charge from the plurality of estimated states of charge;
determine, using the one or more processors, a minimum estimated state of charge from the plurality of estimated state of charge;
determine, using the one or more processors, whether a difference between the maximum estimated state of charge and the minimum estimated state of charge is greater than a swing threshold; and
determine the capacity of the battery based at least in part on the plurality of estimated capacities when the ratio of the estimated capacity variance to the mean estimated capacity squared is not greater than the relative error tolerance threshold and the difference between the maximum estimated state of charge and the minimum estimated state of charge is greater than the swing threshold.