WO2007024093A1 - System and method for estimating a state vector associated with a battery - Google Patents
System and method for estimating a state vector associated with a battery Download PDFInfo
- Publication number
- WO2007024093A1 WO2007024093A1 PCT/KR2006/003305 KR2006003305W WO2007024093A1 WO 2007024093 A1 WO2007024093 A1 WO 2007024093A1 KR 2006003305 W KR2006003305 W KR 2006003305W WO 2007024093 A1 WO2007024093 A1 WO 2007024093A1
- Authority
- WO
- WIPO (PCT)
- Prior art keywords
- battery
- state vector
- computer
- time interval
- voltage
- Prior art date
Links
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
- G01R31/382—Arrangements for monitoring battery or accumulator variables, e.g. SoC
- G01R31/3835—Arrangements for monitoring battery or accumulator variables, e.g. SoC involving only voltage measurements
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
- G01R31/367—Software therefor, e.g. for battery testing using modelling or look-up tables
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/36—Arrangements for testing, measuring or monitoring the electrical condition of accumulators or electric batteries, e.g. capacity or state of charge [SoC]
- G01R31/382—Arrangements for monitoring battery or accumulator variables, e.g. SoC
- G01R31/3842—Arrangements for monitoring battery or accumulator variables, e.g. SoC combining voltage and current measurements
Definitions
- the present invention relates to system and method for estimating a state vector associated with a battery.
- Batteries are used in a wide variety of electronic and electrical devices. It is desirable to be able to estimate the internal state of a battery, including state-of-charge (SOC).
- SOC is a value that indicates the present available capacity of the battery that may be used to do work.
- a battery monitoring system may measure a history of electrical current input to a battery and an output voltage from the battery to provide an estimate of a battery state.
- a battery generally discharges over a time interval when it is electrically unloaded and a state of the battery changes during this time interval.
- a battery monitoring system interrupts its history of measurements and calculations during this time interval.
- a disadvantage of this system is that it cannot accurately determine the state of the battery at a time when a battery is electrically coupled to a load circuit after it has been electrically decoupled from the load circuit for the time interval.
- the inventor herein has recognized a need for a system and a method for estimating a state vector associated with a battery at a time when a battery is electrically coupled to a load circuit, after it has been electrically decoupled from the load circuit for the time interval.
- a method for estimating a state vector associated with a battery in accordance with an exemplary embodiment includes determining a time interval that the battery has been electrically decoupled from a load circuit. The time interval starts at a first time. The method further includes obtaining a first state vector associated with the battery from a memory. The first state vector is determined prior to the first time. The method further includes calculating a second predicted state vector associated with the battery based on the first state vector and the time interval. The method further includes measuring a battery voltage output from the battery to obtain a first battery voltage value after the first time interval when the battery is electrically re- coupled to the load circuit. The method further includes estimating a second battery voltage value associated with the battery based on the second predicted state vector. The method further includes calculating a voltage error value based on the first battery voltage value and the second battery voltage value. The method further includes calculating a third estimated state vector associated with the battery based on the second predicted state vector and the voltage error value.
- a system for estimating a state vector associated with a battery in accordance with another exemplary embodiment includes a voltage sensor configured to measure a voltage output from the battery.
- the system further includes a computer operably coupled to the voltage sensor.
- the computer is configured to determine a time interval that the battery has been electrically decoupled from a load circuit. The time interval starts at a first time.
- the computer is further configured to obtain a first state vector associated with the battery from a memory. The first state vector is determined prior to the first time.
- the computer is further configured to calculate a second predicted state vector associated with the battery based on the first state vector and the time interval.
- the computer is further configured to induce the voltage sensor to measure the voltage output from the battery to obtain a first battery voltage value after the first time interval when the battery is electrically coupled to the load circuit.
- the computer is further configured to estimate a second battery voltage value associated with the battery based on the second predicted state vector.
- the computer is further configured to calculate a voltage error value based on the first battery voltage value and the second battery voltage value.
- the computer is further configured to calculate a third estimated state vector associated with the battery based on the second predicted state vector and the voltage error value.
- the article of manufacture includes a computer storage medium having a computer program encoded therein for estimating a state vector associated with a battery.
- the computer storage medium includes code for determining a time interval that the battery has been electrically decoupled from a load circuit. The time interval starts at a first time.
- the computer storage medium further includes code for obtaining a first state vector associated with the battery from a memory. The first state vector is determined prior to the first time.
- the computer storage medium further includes code for calculating a second predicted state vector associated with the battery based on the first state vector and the time interval.
- the computer storage medium further includes code for measuring a battery voltage output from the battery to obtain a first battery voltage value after the first time interval when the battery is electrically coupled to the load circuit.
- the computer storage medium further includes code for estimating a second battery voltage value associated with the battery based on the second predicted state vector.
- the computer storage medium further includes code for calculating a voltage error value based on the first battery voltage value and the second battery voltage value.
- the computer storage medium further includes code for calculating a third estimated state vector associated with the battery based on the second predicted state vector and the voltage error value.
- Figure 1 is a schematic of a system for estimating a state vector associated with a battery in accordance with an exemplary embodiment
- Figures 2-3 are flowcharts of a method for estimating a state vector associated with a battery in accordance with another exemplary embodiment.
- Figures 4-5 are flowcharts of a method for estimating a state vector associated with a battery in accordance with another exemplary embodiment.
- the battery 12 includes at least a battery cell 14. Of course, the battery 12 can include a plurality of additional battery cells.
- the system 10 includes one or more voltage sensors 20, a load circuit 26, and a computational unit such as a computer 28, and may also include one or more of a temperature sensor 22, and a current sensor 24.
- the voltage sensor 20 is provided to generate a first output signal indicative of the voltage produced by one or more of the battery cells of the battery 12.
- the voltage sensor 20 is electrically coupled between the I/O interface 46 of the computer 28 and the battery 12.
- the voltage sensor 20 transfers the first output signal to the computer 28.
- a single voltage sensor will be described herein. However, it should be noted that in an alternate embodiment of system 10 a plurality of voltage sensors (e.g., one voltage sensor per battery cell) are utilized in system 10.
- the temperature sensor 22 is provided to generate a second output signal indicative of one or more temperatures of the battery 12.
- the temperature sensor 22 is disposed proximate the battery 12 and is electrically coupled to the I/O interface 46 of the computer 28.
- the temperature sensor 22 transfers the second output signal to the computer 28.
- a single temperature sensor will be described herein. However, it should be noted that in an alternate embodiment of system 10 a plurality of temperature sensors (e.g., one temperature sensor per battery cell) are utilized in system 10.
- the current sensor 24 is provided to generate a third output signal indicative of a current sourced or sunk by the battery cells of the battery 12.
- the current sensor 24 is electrically coupled between the battery 12 and the load circuit 26.
- the current sensor 24 is further electrically coupled to the I/O interface 46 of the computer 28.
- the current sensor 24 transfers the third output signal to the computer 28.
- the load circuit 26 is electrically coupled to the current sensor 24 and sinks or sources a current from the battery 12.
- the load circuit 26 comprises any electrical device that can be electrically coupled to the battery 12.
- the computer 28 is provided for determining a state vector associated with the battery 12, as will be explained in greater detail below.
- the computer 28 includes a central processing unit (CPU) 40, a read-only memory (ROM) 44, a volatile memory such as a random access memory (RAM) 45 and an input/output (I/O) interface 46.
- CPU central processing unit
- ROM read-only memory
- RAM random access memory
- I/O input/output
- CPU 40 operably communicates with the ROM 44, the RAM 45, and the I/O interface 46.
- the CPU 40 includes a clock 42.
- the computer readable media including the ROM 44 and the RAM 45 may be implemented using any of a number of known memory devices such as PROMs, EPROMs, EEPROMS 3 flash memory or any other electric, magnetic, optical or combination memory device capable of storing data, some of which represent executable instructions used by the CPU 40.
- the state vector includes at least a state of charge (SOC) value associated with the battery 12.
- SOC value is a value from 0 to 100 percent, that indicates a present available capacity of the battery 12 that may be used to do work.
- the estimated state vector is determined when the load circuit 26 is energized utilizing the following parameters: (i) measured battery voltage (ii) a stored prior estimated state vector (including an SOC value); and (iii) a time interval that the load circuit 12 was de-energized or electrically de-coupled from the battery 12.
- the duration of time that the device was de-energized may be measured using the clock 42 of the computer 28.
- the state equation utilized to determine the state vector associated with the battery 12 is as follows:
- X k is the state vector associated with the battery 12 at time index k;
- U k is a variable representing a known/deterministic input to the battery 12;
- Wk is a process noise or disturbance that models some unmeasured input which affects the state of the system; and J(xk- ⁇ , u k- ⁇ ,Wfc-i ,k—l ,k) is a state transition function.
- the state vector X k includes a SOC value therein. Further, the known/deterministic input U k includes at least one of: (i) an electrical current presently sourced or sunk by the battery 12, and (ii) a temperature of the battery 12.
- Vk is sensor noise that affects the measurement of the output of the battery 12 in a memory-less mode, but does not affect the state vector of the battery 12.
- a frequently used estimator is the conditional mean:
- R x ⁇ is the range of X k
- E[ ] is the statistical expectation operator.
- the foregoing equation computes a posterior probability density pix k ⁇ Y k ) recursively. Because the foregoing equation is difficult to solve, numerical methods have been utilized to approximate the equation to calculate the estimated state vector x k , as will be explained in greater detail below.
- the circumflex symbol indicates an estimated quantity (e.g., x indicates an estimate of the true quantity x).
- the superscript symbol "-" indicates an a priori estimate (i.e., a prediction of a quantity's present value based on past data).
- the superscript symbol "+” indicates an a posteriori estimate (e.g., x k is the estimate of true quantity x at time index k based on all measurements taken up to and including time k).
- ⁇ * indicates the same quantity as ⁇ xx .
- the superscript "T" is a matrix/vector transpose operator.
- the computer 28 determines a time interval that the battery 12 has been electrically decoupled from the load circuit 26.
- the time interval starts at a first time.
- the computer 28 obtains a first state vector x k _ ⁇ associated with the battery 12 from a memory 46.
- the first state vector x 4 _ is determined prior to the first time.
- the computer 28 calculates a first covariance value ⁇ jjt associated with the second predicted state vector x k ⁇ , utilizing the equation:
- the computer 28 induces a voltage sensor 20 to measure a battery voltage output from the battery 12 to obtain a first battery voltage value after the first time interval when the battery 12 is electrically coupled to the load circuit 26.
- the computer 28 calculates a voltage error value based on the first battery voltage value and the second battery voltage value.
- the third predicted state vector is the most accurate estimate of the true state of the battery 12 produced by the foregoing method.
- the computer 28 calculates a second covariance value ⁇ k associated with the third predicted state vector Jc ⁇ , utilizing the equation:
- step 76 the method is exited.
- the computer 28 determines a time interval that a battery 12 has been electrically decoupled from a load circuit 26.
- the time interval starts at a first time.
- the computer 28 obtains a first state vector .££_, associated with the battery 12 from the memory 46.
- the first state vector £££ . is determined prior to the first time.
- the computer 28 calculates a second predicted state vector x k ⁇ associated with the battery 12 based on the first state vector and the time interval, utilizing the equation: x k - f ⁇ xl_ ⁇ ,u k _ x ,yv k _ x ,k - ⁇ k).
- the computer 28 calculates a first covariance value ⁇ k associated with the second predicted state vector Jc ⁇ , utilizing the equation: ⁇ - ⁇ VA'-. +i ⁇ / H .
- the computer 28 induces the voltage sensor 20 to measure a battery voltage output from the battery 12 to obtain a first battery voltage value after the first time interval when the battery 12 is electrically coupled to the load circuit 26.
- the computer 28 estimates a second battery voltage value associated with the battery 12 based on the second predicted state vector x k , utilizing the equation:
- the computer 28 calculates a voltage error value based on the first battery voltage value and the second battery voltage value.
- the computer 28 calculates a third predicted state vector x k associated with the battery 12 based on the second predicted state vector x k ⁇ and the voltage error value, utilizing the equation: * ⁇ - x k ⁇ +L k [y k - y k ].
- the estimated state vector x k of the battery 12 can be calculated utilizing a linear Kalman filter, a nonlinear sigma-point Kalman filter, a square-root linear Kalman filter, a square-root extended Kalman filter, a square-root sigma-point Kalman filter, a particle filter, and the like.
- the system and methods for estimating a state vector associated with a battery provide a substantial advantage over other systems and methods.
- the system and methods provide a technical effect of accurately estimating a state vector associated with the battery at a time when a battery is electrically coupled to a load circuit, after it has been electrically decoupled from the load circuit for the time interval.
- the above-described methods can also be embodied in the form of computer program code, for example, whether stored in a storage medium, loaded into and/or executed by a computer, or transmitted over some transmission medium, loaded into and/or executed by a computer, or transmitted over some transmission medium, such as over electrical wiring or cabling, through fiber optics, or via electromagnetic radiation, wherein, when the computer program code is loaded into an executed by a computer, the computer becomes an apparatus for practicing the methods.
- the computer program code segments configure the microprocessor to create specific logic circuits.
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Secondary Cells (AREA)
- Charge And Discharge Circuits For Batteries Or The Like (AREA)
- Tests Of Electric Status Of Batteries (AREA)
Abstract
A system and a method for estimating a state vector associated with a battery are provided. The method includes determining a time interval that the battery has been electrically decoupled from a load circuit. The time interval starts at a first time. The method further includes obtaining a first state vector associated with the battery from a memory. The first state vector is determined prior to the first time. The method further includes calculating a second predicted state vector associated with the battery based on the first state vector and the time interval.
Description
SYSTEM AND METHOD FOR ESTIMATING A STATE VECTOR ASSOCIATED WITH A BATTERY
Technical Field
The present invention relates to system and method for estimating a state vector associated with a battery.
Background Art
Batteries are used in a wide variety of electronic and electrical devices. It is desirable to be able to estimate the internal state of a battery, including state-of-charge (SOC). The SOC is a value that indicates the present available capacity of the battery that may be used to do work. A battery monitoring system may measure a history of electrical current input to a battery and an output voltage from the battery to provide an estimate of a battery state.
A battery generally discharges over a time interval when it is electrically unloaded and a state of the battery changes during this time interval. A battery monitoring system, however, interrupts its history of measurements and calculations during this time interval. A disadvantage of this system is that it cannot accurately determine the state of the battery at a time when a battery is electrically coupled to a load circuit after it has been electrically decoupled from the load circuit for the time interval.
Thus, the inventor herein has recognized a need for a system and a method for estimating a state vector associated with a battery at a time when a battery is electrically
coupled to a load circuit, after it has been electrically decoupled from the load circuit for the time interval.
Disclosure of the Invention A method for estimating a state vector associated with a battery in accordance with an exemplary embodiment is provided. The method includes determining a time interval that the battery has been electrically decoupled from a load circuit. The time interval starts at a first time. The method further includes obtaining a first state vector associated with the battery from a memory. The first state vector is determined prior to the first time. The method further includes calculating a second predicted state vector associated with the battery based on the first state vector and the time interval. The method further includes measuring a battery voltage output from the battery to obtain a first battery voltage value after the first time interval when the battery is electrically re- coupled to the load circuit. The method further includes estimating a second battery voltage value associated with the battery based on the second predicted state vector. The method further includes calculating a voltage error value based on the first battery voltage value and the second battery voltage value. The method further includes calculating a third estimated state vector associated with the battery based on the second predicted state vector and the voltage error value.
A system for estimating a state vector associated with a battery in accordance with another exemplary embodiment is provided. The system includes a voltage sensor configured to measure a voltage output from the battery. The system further includes a computer operably coupled to the voltage sensor. The computer is configured to determine a time interval that the battery has been electrically decoupled from a load
circuit. The time interval starts at a first time. The computer is further configured to obtain a first state vector associated with the battery from a memory. The first state vector is determined prior to the first time. The computer is further configured to calculate a second predicted state vector associated with the battery based on the first state vector and the time interval. The computer is further configured to induce the voltage sensor to measure the voltage output from the battery to obtain a first battery voltage value after the first time interval when the battery is electrically coupled to the load circuit. The computer is further configured to estimate a second battery voltage value associated with the battery based on the second predicted state vector. The computer is further configured to calculate a voltage error value based on the first battery voltage value and the second battery voltage value. The computer is further configured to calculate a third estimated state vector associated with the battery based on the second predicted state vector and the voltage error value.
An article of manufacture in accordance with still another exemplary embodiment is provided. The article of manufacture includes a computer storage medium having a computer program encoded therein for estimating a state vector associated with a battery. The computer storage medium includes code for determining a time interval that the battery has been electrically decoupled from a load circuit. The time interval starts at a first time. The computer storage medium further includes code for obtaining a first state vector associated with the battery from a memory. The first state vector is determined prior to the first time. The computer storage medium further includes code for calculating a second predicted state vector associated with the battery based on the first state vector and the time interval. The computer storage medium further includes code for measuring a battery voltage output from the battery to obtain a first battery voltage value
after the first time interval when the battery is electrically coupled to the load circuit. The computer storage medium further includes code for estimating a second battery voltage value associated with the battery based on the second predicted state vector. The computer storage medium further includes code for calculating a voltage error value based on the first battery voltage value and the second battery voltage value. The computer storage medium further includes code for calculating a third estimated state vector associated with the battery based on the second predicted state vector and the voltage error value.
Other systems and/or methods according to the embodiments will become or are apparent to one with skill in the art upon review of the following drawings and detailed description. It is intended that all such additional systems and methods be within the scope of the present invention, and be protected by the accompanying claims.
BRIEF DESCRIPTION OF THE DRAWINGS Figure 1 is a schematic of a system for estimating a state vector associated with a battery in accordance with an exemplary embodiment;
Figures 2-3 are flowcharts of a method for estimating a state vector associated with a battery in accordance with another exemplary embodiment; and
Figures 4-5 are flowcharts of a method for estimating a state vector associated with a battery in accordance with another exemplary embodiment.
Mode for Carrying Out the Invention
Referring to Figure 1, a system 10 for estimating a state vector associated with a battery 12 is illustrated. The battery 12 includes at least a battery cell 14. Of course, the battery 12 can include a plurality of additional battery cells. The system 10 includes one
or more voltage sensors 20, a load circuit 26, and a computational unit such as a computer 28, and may also include one or more of a temperature sensor 22, and a current sensor 24.
The voltage sensor 20 is provided to generate a first output signal indicative of the voltage produced by one or more of the battery cells of the battery 12. The voltage sensor 20 is electrically coupled between the I/O interface 46 of the computer 28 and the battery 12. The voltage sensor 20 transfers the first output signal to the computer 28. For clarity of presentation, a single voltage sensor will be described herein. However, it should be noted that in an alternate embodiment of system 10 a plurality of voltage sensors (e.g., one voltage sensor per battery cell) are utilized in system 10.
The temperature sensor 22 is provided to generate a second output signal indicative of one or more temperatures of the battery 12. The temperature sensor 22 is disposed proximate the battery 12 and is electrically coupled to the I/O interface 46 of the computer 28. The temperature sensor 22 transfers the second output signal to the computer 28. For clarity of presentation, a single temperature sensor will be described herein. However, it should be noted that in an alternate embodiment of system 10 a plurality of temperature sensors (e.g., one temperature sensor per battery cell) are utilized in system 10.
The current sensor 24 is provided to generate a third output signal indicative of a current sourced or sunk by the battery cells of the battery 12. The current sensor 24 is electrically coupled between the battery 12 and the load circuit 26. The current sensor 24 is further electrically coupled to the I/O interface 46 of the computer 28. The current sensor 24 transfers the third output signal to the computer 28.
The load circuit 26 is electrically coupled to the current sensor 24 and sinks or sources a current from the battery 12. The load circuit 26 comprises any electrical device that can be electrically coupled to the battery 12.
The computer 28 is provided for determining a state vector associated with the battery 12, as will be explained in greater detail below. The computer 28 includes a central processing unit (CPU) 40, a read-only memory (ROM) 44, a volatile memory such as a random access memory (RAM) 45 and an input/output (I/O) interface 46. The
CPU 40 operably communicates with the ROM 44, the RAM 45, and the I/O interface 46.
The CPU 40 includes a clock 42. The computer readable media including the ROM 44 and the RAM 45 may be implemented using any of a number of known memory devices such as PROMs, EPROMs, EEPROMS3 flash memory or any other electric, magnetic, optical or combination memory device capable of storing data, some of which represent executable instructions used by the CPU 40.
Before providing a detailed discussion of the methodologies for determining a state vector associated with the battery 12, a general overview will be provided. The state vector includes at least a state of charge (SOC) value associated with the battery 12. The SOC value is a value from 0 to 100 percent, that indicates a present available capacity of the battery 12 that may be used to do work. The estimated state vector is determined when the load circuit 26 is energized utilizing the following parameters: (i) measured battery voltage (ii) a stored prior estimated state vector (including an SOC value); and (iii) a time interval that the load circuit 12 was de-energized or electrically de-coupled from the battery 12. These parameters are utilized in a mathematical model of battery cell behavior in order to compute an improved estimate of the state vector of the battery 12 including possibly compensation for hysteresis effects, voltage polarization
effects, and self-discharge. The duration of time that the device was de-energized may be measured using the clock 42 of the computer 28.
It is assumed that a mathematical model of the battery cell dynamics is known, and may be expressed by using a discrete-time state-space model including a state equation and an output equation, as will be described below.
The state equation utilized to determine the state vector associated with the battery 12 is as follows:
wherein,
Xk is the state vector associated with the battery 12 at time index k;
Uk is a variable representing a known/deterministic input to the battery 12;
Wk is a process noise or disturbance that models some unmeasured input which affects the state of the system; and J(xk-ι ,uk-\ ,Wfc-i ,k—l ,k) is a state transition function.
The state vector Xk includes a SOC value therein. Further, the known/deterministic input Uk includes at least one of: (i) an electrical current presently sourced or sunk by the battery 12, and (ii) a temperature of the battery 12.
An output vector associated with the battery 12 is determined utilizing the following equation: yk = h(xk,uk,vk,k)
wherein, h(xk,Uk,Vk,k) is a measurement function; and
Vk is sensor noise that affects the measurement of the output of the battery 12 in a memory-less mode, but does not affect the state vector of the battery 12.
The following system utilizes probabilistic inference to determine an estimated state vector xk of the state vector xk given all observations Yt ={yo, yι,'",yk}- A frequently used estimator is the conditional mean:
= Eiχ k 1 γJ = [ χ kp(χk \ γk )^k
where Rx^ is the range of Xk, and E[ ] is the statistical expectation operator. The foregoing equation computes a posterior probability density pixk \ Yk) recursively. Because the foregoing equation is difficult to solve, numerical methods have been utilized to approximate the equation to calculate the estimated state vector xk, as will be explained in greater detail below.
For purposes of understanding, the notation utilized in the equations of the following methods will be described. The circumflex symbol indicates an estimated quantity (e.g., x indicates an estimate of the true quantity x). The superscript symbol "-" indicates an a priori estimate (i.e., a prediction of a quantity's present value based on past data). The superscript symbol "+" indicates an a posteriori estimate (e.g., xk is the estimate of true quantity x at time index k based on all measurements taken up to and including time k). The tilde symbol indicates the error of an estimated quantity (e.g., xk = xk -Xj and xk - xk ~xk ). The symbol ∑xy=E[xyτ] indicates the correlation or cross correlation of the variables in its subscript (the quantities described herein are zero-
mean, so the correlations are identical to co variances). The symbol ∑* indicates the same quantity as ∑ xx. The superscript "T" is a matrix/vector transpose operator.
Referring to Figures 2-3, a method for calculating the estimated state vector xk utilizing a general sequential probabilistic inference methodology will be explained.
At step 60, the computer 28 determines a time interval that the battery 12 has been electrically decoupled from the load circuit 26. The time interval starts at a first time.
At step 62, the computer 28 obtains a first state vector xk_λ associated with the battery 12 from a memory 46. The first state vector x4_, is determined prior to the first time.
At step 64, the computer 28 calculates a second predicted state vector xk ~ associated with the battery 12 based on the first state vector xk_x and the time interval, utilizing the equation: x~ =
, wA_, ,k -l) \ YA_, }
At step 66, the computer 28 calculates a first covariance value ∑~jjt associated with the second predicted state vector xk ~ , utilizing the equation:
At step 68, the computer 28 induces a voltage sensor 20 to measure a battery voltage output from the battery 12 to obtain a first battery voltage value after the first time interval when the battery 12 is electrically coupled to the load circuit 26.
At step 70, the computer 28 estimates a second battery voltage value associated with the battery 12 based on the second predicted state vector xk , utilizing the equation: yk = E[h(xk ,uk,vk,k) \ Yk].
At step 72, the computer 28 calculates a voltage error value based on the first battery voltage value and the second battery voltage value.
At step 74, the computer 28 calculates a third predicted state vector xk + associated with the battery 12 based on the second predicted state vector £jT and the voltage error value yk —yk , utilizing the equation: xk = xj +Lt[yk — yk]- where the value Lk is determined by utilizing the equation:
The third predicted state vector
is the most accurate estimate of the true state of the battery 12 produced by the foregoing method.
At step 76, the computer 28 calculates a second covariance value Σ~ k associated with the third predicted state vector Jc^ , utilizing the equation:
Σ~ )(l = YT- k ~LkΣy<kLτ k . After step 76, the method is exited.
It should be noted that there are many methods for approximating the third predicted state vector xk + , described above. For example, one method utilizes a linear Kalman filter, another method utilizes a nonlinear extended Kalman filter, another method utilizes a nonlinear sigma-point Kalman filter. These methods utilize different
levels of computational effort and produce different degrees of accuracy in the resulting state vector.
For example, referring to Figures 4-5, a method for calculating the estimated state vector xk utilizing a non-linear extended Kalman filter will be explained. The following definitions are utilized in the equations of the method:
A _ dh(xk,uk,vk,k) * __ dh(xk,uk,vk,k) dx,. dvt
At step 80, the computer 28 determines a time interval that a battery 12 has been electrically decoupled from a load circuit 26. The time interval starts at a first time.
At step 82, the computer 28 obtains a first state vector .££_, associated with the battery 12 from the memory 46. The first state vector ££., is determined prior to the first time.
At step 84, the computer 28 calculates a second predicted state vector xk ~ associated with the battery 12 based on the first state vector
and the time interval, utilizing the equation: xk - f{xl_λ ,uk_x,yvk_x,k -\k).
At step 86, the computer 28 calculates a first covariance value Σ~ k associated with the second predicted state vector Jc^ , utilizing the equation: Λ-ΛVA'-. +i∑/H.
At step 88, the computer 28 induces the voltage sensor 20 to measure a battery voltage output from the battery 12 to obtain a first battery voltage value after the first time interval when the battery 12 is electrically coupled to the load circuit 26.
At step 90, the computer 28 estimates a second battery voltage value associated with the battery 12 based on the second predicted state vector xk , utilizing the equation:
At step 92, the computer 28 calculates a voltage error value based on the first battery voltage value and the second battery voltage value.
At step 94, the computer 28 calculates a third predicted state vector xk associated with the battery 12 based on the second predicted state vector xk ~ and the voltage error value, utilizing the equation: *^ - xk ~ +Lk[yk - yk]. where the value Lk is determined utilizing the equation: h = ∑~,kCk τ[Ck∑ZtkCk τ +DkΣvDk τr.
At step 96, the computer 28 calculates a second covariance value Σ~ k associated with the third predicted state vector xk , utilizing the equation: Σ~ tk = (I- LkCk )∑zk . After step 96, the method is exited.
It should be noted that in alternate embodiments, the estimated state vector xk of the battery 12 can be calculated utilizing a linear Kalman filter, a nonlinear sigma-point Kalman filter, a square-root linear Kalman filter, a square-root extended Kalman filter, a square-root sigma-point Kalman filter, a particle filter, and the like.
The system and methods for estimating a state vector associated with a battery provide a substantial advantage over other systems and methods. In particular, the system and methods provide a technical effect of accurately estimating a state vector associated with the battery at a time when a battery is electrically coupled to a load circuit, after it has been electrically decoupled from the load circuit for the time interval.
The above-described methods can be embodied in the form of computer program code containing instructions embodied in tangible media, such as floppy diskettes, CD ROMs, hard drives, or any other computer-readable storage medium, wherein, when the computer program code is loaded into and executed by a computer, the computer becomes an apparatus for practicing the invention. The above-described methods can also be embodied in the form of computer program code, for example, whether stored in a storage medium, loaded into and/or executed by a computer, or transmitted over some transmission medium, loaded into and/or executed by a computer, or transmitted over some transmission medium, such as over electrical wiring or cabling, through fiber optics, or via electromagnetic radiation, wherein, when the computer program code is loaded into an executed by a computer, the computer becomes an apparatus for practicing the methods. When implemented on a general-purpose microprocessor, the computer program code segments configure the microprocessor to create specific logic circuits.
While the invention is described with reference to the exemplary embodiments, it will be understood by those skilled in the art that various changes may be made an equivalence may be substituted for elements thereof without departing from the scope of the invention. In addition, many modifications may be made to the teachings of the
invention to adapt to a particular situation without departing from the scope thereof. Therefore, is intended that the invention not be limited the embodiment disclosed for carrying out this invention, but that the invention includes all embodiments falling with the scope of the intended claims. Moreover, the use of the term's first, second, etc. does not denote any order of importance, but rather the term's first, second, etc. are used to distinguish one element from another.
Claims
1. A method for estimating a state vector associated with a battery, the method comprising the steps of: determining a time interval that the battery has been electrically decoupled from a load circuit, the time interval starting at a first time; obtaining a first state vector associated with the battery from a memory, the first state vector being determined prior to the first time; calculating a second predicted state vector associated with the battery based on the first state vector and the time interval; measuring a battery voltage output from the battery to obtain a first battery voltage value after the first time interval when the battery is electrically re-coupled to the load circuit; estimating a second battery voltage value associated with the battery based on the second predicted state vector; calculating a voltage error value based on the first battery voltage value and the second battery voltage value; and calculating a third estimated state vector associated with the battery based on the second predicted state vector and the voltage error value.
2. The method of claim 1, further comprising calculating a covariance value associated with the third estimated state vector.
3. The method of claim 1, wherein the step of calculating the second predicted state vector comprises calculating the second predicted state vector associated with the battery based on the first state vector and the time interval utilizing at least one of a Kalman filter, an extended Kalman filter, a sigma-point Kalman filter, a square-root sigma-point Kalman filter, and a particle filter.
4. The method of claim 1, wherein the step of calculating the third estimated state vector comprises calculating the third estimate state vector associated with the battery based on the second predicted state vector and the voltage error value interval utilizing at least one of a Kalman filter, an extended Kalman filter, a sigma-point Kalman filter, a square-root sigma-point Kalman filter, and a particle filter.
5. The method of claim 1, wherein the second predicted state vector is indicative of at least a predicted state-of-charge of the battery.
6. The method of claim 1, wherein the third predicted state vector is indicative of at least a predicted state-of-charge of the battery.
7. A system for estimating a state vector associated with a battery, the system comprising: a voltage sensor configured to measure a voltage output from the battery; and a computer operably coupled to the voltage sensor, the computer configured to implement the steps according to any of claims 1 to 6.
8. A computer storage medium having a computer program encoded therein for estimating a state vector associated with a battery, the computer storage medium comprising a program implementing the method as claimed in any of claims 1 to 6.
Priority Applications (3)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN2006800308815A CN101248365B (en) | 2005-08-23 | 2006-08-23 | System and method for estimating a state vector associated with a battery |
EP06783700.5A EP1917536B1 (en) | 2005-08-23 | 2006-08-23 | System and method for estimating a state vector associated with a battery |
JP2008527845A JP4772871B2 (en) | 2005-08-23 | 2006-08-23 | System and method for estimating a state vector associated with a battery |
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US11/209,453 US7589532B2 (en) | 2005-08-23 | 2005-08-23 | System and method for estimating a state vector associated with a battery |
US11/209,453 | 2005-08-23 |
Publications (1)
Publication Number | Publication Date |
---|---|
WO2007024093A1 true WO2007024093A1 (en) | 2007-03-01 |
Family
ID=37771801
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
PCT/KR2006/003305 WO2007024093A1 (en) | 2005-08-23 | 2006-08-23 | System and method for estimating a state vector associated with a battery |
Country Status (7)
Country | Link |
---|---|
US (2) | US7589532B2 (en) |
EP (1) | EP1917536B1 (en) |
JP (1) | JP4772871B2 (en) |
KR (1) | KR100952049B1 (en) |
CN (1) | CN101248365B (en) |
TW (1) | TWI320610B (en) |
WO (1) | WO2007024093A1 (en) |
Cited By (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US7965059B2 (en) | 2005-11-30 | 2011-06-21 | Lg Chem, Ltd. | System, method, and article of manufacture for determining an estimated battery parameter vector |
US20120270077A1 (en) * | 2011-04-25 | 2012-10-25 | Lg Chem, Ltd. | Battery system and method for increasing an operational life of a battery cell |
ITBO20110697A1 (en) * | 2011-12-07 | 2013-06-08 | Magneti Marelli Spa | ESTIMATION METHOD OF THE CAPACITY OF A STORAGE SYSTEM INCLUDING A NUMBER OF ELECTROCHEMICAL CELLS IN A HYBRID OR ELECTRIC TRACTION VEHICLE |
Families Citing this family (57)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US7321220B2 (en) * | 2003-11-20 | 2008-01-22 | Lg Chem, Ltd. | Method for calculating power capability of battery packs using advanced cell model predictive techniques |
US8264203B2 (en) * | 2006-03-31 | 2012-09-11 | Valence Technology, Inc. | Monitoring state of charge of a battery |
JP4703593B2 (en) * | 2007-03-23 | 2011-06-15 | 株式会社豊田中央研究所 | Secondary battery state estimation device |
US8628872B2 (en) * | 2008-01-18 | 2014-01-14 | Lg Chem, Ltd. | Battery cell assembly and method for assembling the battery cell assembly |
US7994755B2 (en) * | 2008-01-30 | 2011-08-09 | Lg Chem, Ltd. | System, method, and article of manufacture for determining an estimated battery cell module state |
US8426050B2 (en) * | 2008-06-30 | 2013-04-23 | Lg Chem, Ltd. | Battery module having cooling manifold and method for cooling battery module |
US8067111B2 (en) * | 2008-06-30 | 2011-11-29 | Lg Chem, Ltd. | Battery module having battery cell assembly with heat exchanger |
US9759495B2 (en) | 2008-06-30 | 2017-09-12 | Lg Chem, Ltd. | Battery cell assembly having heat exchanger with serpentine flow path |
US9140501B2 (en) * | 2008-06-30 | 2015-09-22 | Lg Chem, Ltd. | Battery module having a rubber cooling manifold |
US7883793B2 (en) * | 2008-06-30 | 2011-02-08 | Lg Chem, Ltd. | Battery module having battery cell assemblies with alignment-coupling features |
JP5073601B2 (en) * | 2008-07-10 | 2012-11-14 | 株式会社オートネットワーク技術研究所 | Battery state estimation method and power supply device |
US8202645B2 (en) | 2008-10-06 | 2012-06-19 | Lg Chem, Ltd. | Battery cell assembly and method for assembling the battery cell assembly |
US9337456B2 (en) * | 2009-04-20 | 2016-05-10 | Lg Chem, Ltd. | Frame member, frame assembly and battery cell assembly made therefrom and methods of making the same |
US8663829B2 (en) | 2009-04-30 | 2014-03-04 | Lg Chem, Ltd. | Battery systems, battery modules, and method for cooling a battery module |
US8663828B2 (en) | 2009-04-30 | 2014-03-04 | Lg Chem, Ltd. | Battery systems, battery module, and method for cooling the battery module |
US8403030B2 (en) | 2009-04-30 | 2013-03-26 | Lg Chem, Ltd. | Cooling manifold |
US8852778B2 (en) | 2009-04-30 | 2014-10-07 | Lg Chem, Ltd. | Battery systems, battery modules, and method for cooling a battery module |
US8399118B2 (en) * | 2009-07-29 | 2013-03-19 | Lg Chem, Ltd. | Battery module and method for cooling the battery module |
US8703318B2 (en) * | 2009-07-29 | 2014-04-22 | Lg Chem, Ltd. | Battery module and method for cooling the battery module |
US8399119B2 (en) * | 2009-08-28 | 2013-03-19 | Lg Chem, Ltd. | Battery module and method for cooling the battery module |
US8427105B2 (en) * | 2009-12-02 | 2013-04-23 | Gregory L. Plett | System and method for equalizing a battery pack during a battery pack charging process |
US8041522B2 (en) * | 2009-12-02 | 2011-10-18 | American Electric Vehicles, Ind. | System and method for recursively estimating battery cell total capacity |
US8918299B2 (en) * | 2009-12-02 | 2014-12-23 | American Electric Vehicles, Inc. | System and method for maximizing a battery pack total energy metric |
US10422824B1 (en) * | 2010-02-19 | 2019-09-24 | Nikola Llc | System and method for efficient adaptive joint estimation of battery cell state-of-charge, resistance, and available energy |
US8341449B2 (en) | 2010-04-16 | 2012-12-25 | Lg Chem, Ltd. | Battery management system and method for transferring data within the battery management system |
US9147916B2 (en) | 2010-04-17 | 2015-09-29 | Lg Chem, Ltd. | Battery cell assemblies |
KR101215037B1 (en) | 2010-04-20 | 2012-12-24 | 에스티엘 테크놀로지 컴퍼니 리미티드 | Battery monitoring system |
US8353315B2 (en) | 2010-08-23 | 2013-01-15 | Lg Chem, Ltd. | End cap |
US8758922B2 (en) | 2010-08-23 | 2014-06-24 | Lg Chem, Ltd. | Battery system and manifold assembly with two manifold members removably coupled together |
US8920956B2 (en) | 2010-08-23 | 2014-12-30 | Lg Chem, Ltd. | Battery system and manifold assembly having a manifold member and a connecting fitting |
US8469404B2 (en) | 2010-08-23 | 2013-06-25 | Lg Chem, Ltd. | Connecting assembly |
US9005799B2 (en) | 2010-08-25 | 2015-04-14 | Lg Chem, Ltd. | Battery module and methods for bonding cell terminals of battery cells together |
US8662153B2 (en) | 2010-10-04 | 2014-03-04 | Lg Chem, Ltd. | Battery cell assembly, heat exchanger, and method for manufacturing the heat exchanger |
KR101199978B1 (en) | 2011-02-09 | 2012-11-12 | 대양전기공업 주식회사 | Batterys state monitoring and power controls equipment |
US8288031B1 (en) | 2011-03-28 | 2012-10-16 | Lg Chem, Ltd. | Battery disconnect unit and method of assembling the battery disconnect unit |
US9178192B2 (en) | 2011-05-13 | 2015-11-03 | Lg Chem, Ltd. | Battery module and method for manufacturing the battery module |
CN102169168B (en) * | 2011-05-17 | 2013-04-24 | 杭州电子科技大学 | Battery dump energy estimation method based on particle filtering |
US8993136B2 (en) | 2011-06-30 | 2015-03-31 | Lg Chem, Ltd. | Heating system for a battery module and method of heating the battery module |
US8974928B2 (en) | 2011-06-30 | 2015-03-10 | Lg Chem, Ltd. | Heating system for a battery module and method of heating the battery module |
US8859119B2 (en) | 2011-06-30 | 2014-10-14 | Lg Chem, Ltd. | Heating system for a battery module and method of heating the battery module |
US8974929B2 (en) | 2011-06-30 | 2015-03-10 | Lg Chem, Ltd. | Heating system for a battery module and method of heating the battery module |
US9496544B2 (en) | 2011-07-28 | 2016-11-15 | Lg Chem. Ltd. | Battery modules having interconnect members with vibration dampening portions |
US8922217B2 (en) * | 2012-05-08 | 2014-12-30 | GM Global Technology Operations LLC | Battery state-of-charge observer |
CN103033761B (en) * | 2012-12-17 | 2014-12-10 | 哈尔滨工业大学 | Lithium ion battery residual life forecasting method of dynamic gray related vector machine |
JP6168813B2 (en) * | 2013-03-29 | 2017-07-26 | 株式会社ケーヒン | Voltage detector |
WO2015056964A1 (en) * | 2013-10-14 | 2015-04-23 | 주식회사 엘지화학 | Apparatus for estimating state of hybrid secondary battery and method therefor |
KR101650415B1 (en) | 2013-10-14 | 2016-08-23 | 주식회사 엘지화학 | Apparatus for estimating voltage of hybrid secondary battery and Method thereof |
WO2015056962A1 (en) * | 2013-10-14 | 2015-04-23 | 주식회사 엘지화학 | Apparatus for estimating voltage of hybrid secondary battery and method therefor |
WO2015056963A1 (en) * | 2013-10-14 | 2015-04-23 | 주식회사 엘지화학 | Apparatus for estimating state of secondary battery including blended positive electrode material, and method therefor |
KR101632351B1 (en) * | 2013-10-14 | 2016-06-21 | 주식회사 엘지화학 | Apparatus for estimating state of hybrid secondary battery and Method thereof |
KR101708885B1 (en) * | 2013-10-14 | 2017-02-21 | 주식회사 엘지화학 | Apparatus for estimating state of secondary battery including blended cathode material and Method thereof |
US9381823B2 (en) * | 2014-07-17 | 2016-07-05 | Ford Global Technologies, Llc | Real-time battery estimation |
KR101798201B1 (en) | 2014-10-01 | 2017-11-15 | 주식회사 엘지화학 | Method and Apparatus for estimating discharge power of secondary battery |
FR3029315B1 (en) * | 2014-11-28 | 2016-12-09 | Renault Sa | AUTOMATIC METHOD OF ESTIMATING THE CAPACITY OF A CELL OF A BATTERY |
KR101846642B1 (en) | 2015-02-02 | 2018-04-06 | 주식회사 엘지화학 | Method for determining resistance factor of secondary battery, and Apparatus and Method for estimating charging power of secondary battery using determined resistance factor |
US9846110B2 (en) * | 2015-06-02 | 2017-12-19 | GM Global Technology Operations LLC | Particulate matter sensor diagnostic system and method |
CN112965001B (en) * | 2021-02-09 | 2024-06-21 | 重庆大学 | Power battery pack fault diagnosis method based on real vehicle data |
Citations (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US6441586B1 (en) | 2001-03-23 | 2002-08-27 | General Motors Corporation | State of charge prediction method and apparatus for a battery |
US6534954B1 (en) | 2002-01-10 | 2003-03-18 | Compact Power Inc. | Method and apparatus for a battery state of charge estimator |
US20050046388A1 (en) | 2003-08-28 | 2005-03-03 | Tate Edward D. | Simple optimal estimator for PbA state of charge |
US6876175B2 (en) * | 2001-06-29 | 2005-04-05 | Robert Bosch Gmbh | Methods for determining the charge state and/or the power capacity of charge store |
Family Cites Families (13)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JP3262253B2 (en) * | 1995-02-22 | 2002-03-04 | 株式会社日立製作所 | Drive control device and control method for electric vehicle |
US5694335A (en) * | 1996-03-12 | 1997-12-02 | Hollenberg; Dennis D. | Secure personal applications network |
US7688074B2 (en) * | 1997-11-03 | 2010-03-30 | Midtronics, Inc. | Energy management system for automotive vehicle |
CN1199050C (en) * | 1998-05-28 | 2005-04-27 | 丰田自动车株式会社 | Means for estimating charged state of battery and method for estimating degraded state of battery |
JPH11346444A (en) * | 1998-06-02 | 1999-12-14 | Toyota Motor Corp | Estimating method of battery charged condition |
DE19960761C1 (en) * | 1999-12-16 | 2001-05-23 | Daimler Chrysler Ag | Battery residual charge monitoring method uses difference between minimum current and current at intersection point between current/voltage curve and minimum voltage threshold of battery |
JP2001272444A (en) * | 2000-03-27 | 2001-10-05 | Hitachi Maxell Ltd | Estimating device for remaining capacity of secondary battery |
EP1160953B1 (en) * | 2000-05-29 | 2009-12-02 | Panasonic Corporation | Method for charging battery |
FI114048B (en) * | 2001-12-03 | 2004-07-30 | Teknillinen Korkeakoulu | Method and apparatus for utilizing programmed meters to characterize accumulators |
US6727708B1 (en) * | 2001-12-06 | 2004-04-27 | Johnson Controls Technology Company | Battery monitoring system |
US20050100786A1 (en) | 2003-09-19 | 2005-05-12 | Ryu Duk H. | Nonaqueous lithium secondary battery with cyclability and/or high temperature safety improved |
US20050127874A1 (en) | 2003-12-12 | 2005-06-16 | Myoungho Lim | Method and apparatus for multiple battery cell management |
US7212006B2 (en) * | 2004-07-02 | 2007-05-01 | Bppower, Inc. | Method and apparatus for monitoring the condition of a battery by measuring its internal resistance |
-
2005
- 2005-08-23 US US11/209,453 patent/US7589532B2/en active Active
-
2006
- 2006-08-23 CN CN2006800308815A patent/CN101248365B/en active Active
- 2006-08-23 TW TW095130978A patent/TWI320610B/en active
- 2006-08-23 EP EP06783700.5A patent/EP1917536B1/en active Active
- 2006-08-23 KR KR1020087006165A patent/KR100952049B1/en active IP Right Grant
- 2006-08-23 WO PCT/KR2006/003305 patent/WO2007024093A1/en active Application Filing
- 2006-08-23 JP JP2008527845A patent/JP4772871B2/en active Active
-
2009
- 2009-06-29 US US12/493,787 patent/US7800375B2/en active Active
Patent Citations (5)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US6441586B1 (en) | 2001-03-23 | 2002-08-27 | General Motors Corporation | State of charge prediction method and apparatus for a battery |
US6876175B2 (en) * | 2001-06-29 | 2005-04-05 | Robert Bosch Gmbh | Methods for determining the charge state and/or the power capacity of charge store |
US6534954B1 (en) | 2002-01-10 | 2003-03-18 | Compact Power Inc. | Method and apparatus for a battery state of charge estimator |
US20050046388A1 (en) | 2003-08-28 | 2005-03-03 | Tate Edward D. | Simple optimal estimator for PbA state of charge |
DE102004036302A1 (en) * | 2003-08-28 | 2005-03-31 | General Motors Corp. (N.D.Ges.D. Staates Delaware), Detroit | Simple optimum value estimator for the state of charge of a lead power source |
Non-Patent Citations (2)
Title |
---|
B. S. BHANGU ET AL.: "Nonlinear Observers for Predicting State-of-Charge and State-of-Health of Lead-Acid Batteries for Hybrid-Electric Vehicles", IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, vol. 54, no. 3, 2005, pages 783 - 794, XP011132633, DOI: doi:10.1109/TVT.2004.842461 |
GREGORY L. PLETT: "Extended Kalman filtering for battery management systems of LiPB-based HEV battery packs", J. OF POWER SOURCES, vol. 134, no. 2, 2004, pages 277 - 292, XP055218097, DOI: doi:10.1016/j.jpowsour.2004.02.033 |
Cited By (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
US7965059B2 (en) | 2005-11-30 | 2011-06-21 | Lg Chem, Ltd. | System, method, and article of manufacture for determining an estimated battery parameter vector |
US20120270077A1 (en) * | 2011-04-25 | 2012-10-25 | Lg Chem, Ltd. | Battery system and method for increasing an operational life of a battery cell |
KR101412769B1 (en) * | 2011-04-25 | 2014-07-02 | 주식회사 엘지화학 | Battery system and method for increasing an operational life of a battery cell |
ITBO20110697A1 (en) * | 2011-12-07 | 2013-06-08 | Magneti Marelli Spa | ESTIMATION METHOD OF THE CAPACITY OF A STORAGE SYSTEM INCLUDING A NUMBER OF ELECTROCHEMICAL CELLS IN A HYBRID OR ELECTRIC TRACTION VEHICLE |
Also Published As
Publication number | Publication date |
---|---|
JP4772871B2 (en) | 2011-09-14 |
CN101248365A (en) | 2008-08-20 |
KR100952049B1 (en) | 2010-04-07 |
US7800375B2 (en) | 2010-09-21 |
TW200711210A (en) | 2007-03-16 |
EP1917536B1 (en) | 2018-08-08 |
CN101248365B (en) | 2010-11-10 |
JP2009506317A (en) | 2009-02-12 |
EP1917536A1 (en) | 2008-05-07 |
KR20080041702A (en) | 2008-05-13 |
US7589532B2 (en) | 2009-09-15 |
EP1917536A4 (en) | 2017-08-23 |
TWI320610B (en) | 2010-02-11 |
US20090261837A1 (en) | 2009-10-22 |
US20070046292A1 (en) | 2007-03-01 |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
US7589532B2 (en) | System and method for estimating a state vector associated with a battery | |
US7656123B2 (en) | System, method, and article of manufacture for determining an estimated battery state vector | |
US8035345B2 (en) | System, method, and article of manufacture for determining an estimated combined battery state-parameter vector | |
KR101355958B1 (en) | System, method and article of manufacture for determining an estimated battery parameter vector | |
KR101355959B1 (en) | System and method for determining both an estimated battery state vector and an estimated battery parameter vector |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
WWE | Wipo information: entry into national phase |
Ref document number: 200680030881.5 Country of ref document: CN |
|
121 | Ep: the epo has been informed by wipo that ep was designated in this application | ||
WWE | Wipo information: entry into national phase |
Ref document number: 2006783700 Country of ref document: EP |
|
WWE | Wipo information: entry into national phase |
Ref document number: 2008527845 Country of ref document: JP |
|
NENP | Non-entry into the national phase |
Ref country code: DE |
|
WWE | Wipo information: entry into national phase |
Ref document number: 1020087006165 Country of ref document: KR |