Battery state estimation device and method

Abstract

The present invention has an advantage that the battery state can be more accurately estimated by adding system noise to a recursive filter used to estimate the battery state. According to an embodiment of the present invention, the parameters used in the extended Kalman filter are corrected taking into account the offset and variance of the current sensor and the voltage sensor, so that the battery state can be more accurately estimated.

Description

[Technical Field]

[0001] This application claims priority based on Korean Patent Application No. 10-2022-0001089, filed on January 4, 2022, the entire contents of which are incorporated herein by reference in their entirety in the specification and drawings thereof.

[0002] The present invention relates to an apparatus and method for estimating a battery state, and more particularly to an apparatus and method for estimating a battery state that can estimate the battery state more accurately by adding system noise to a recursive filter used to estimate the battery state. [Background technology]

[0003] In recent years, as demand for portable electronic products such as laptops, video cameras, and mobile phones has grown rapidly and development of electric vehicles, energy storage batteries, robots, and satellites has gained momentum, active research has been conducted into high-performance batteries that can be repeatedly charged and discharged.

[0004] Currently, commercially available secondary batteries include nickel-cadmium batteries, nickel-metal hydride batteries, nickel-zinc batteries, and lithium batteries. Of these, lithium batteries are attracting attention due to their advantages of being able to be freely charged and discharged since they have almost no memory effect compared to nickel-based batteries, as well as their extremely low self-discharge rate and high energy density.

[0005] Generally, battery status information such as the state of charge (SOC) and state of health (SOH) can be estimated based on measurable voltage, current, temperature, etc. For example, the SOC and SOH of a battery can be estimated using an extended Kalman filter, a type of recursive filter. Here, SOC refers to the current state of charge of a battery. Also, SOH refers to the remaining life of a battery, and may refer to the current life of a battery due to degradation when the initial life of the battery at the beginning of life (BOL) is assumed to be 100%.

[0006] Furthermore, research is progressing on a dual adaptive extended Kalman filter, which complements the extended Kalman filter, in order to estimate battery state information more accurately (Non-Patent Document 1).

[0007] Fig. 1 is a flowchart of a conventional dual adaptive extended Kalman filter. Specifically, Fig. 1 is a flowchart of Non-Patent Document 1, and "Eq." in Fig. 1 refers to the equation in Non-Patent Document 1.

[0008] Referring to Equation 12 and Equation 13 in Non-Patent Document 1, Q is used as process noise (system noise). However, Non-Patent Document 1 uses the multivariate normal distribution W k It only uses ∼N(0,Q) noise and does not consider offsets and variances of the current and voltage sensors that may affect system noise.

[0009] That is, in the process of estimating the SOC and SOH, Non-Patent Document 1 is unable to reflect the offset of the current sensor that is arranged in the charge / discharge path of the battery and measures the discharge current and / or charge current of the battery and the voltage sensor that measures the voltage of the battery, and therefore there is a problem that the accuracy of the estimated SOC and SOH may be low. [Prior art documents] [Non-patent literature]

[0010] [Non-Patent Document 1] SOC Estimation of Lithium Battery Based on Dual Adaptive Extended Kalman Filter (IMMAEE 2019, Yongliang Zheng et al., 2019) Summary of the Invention [Problem to be solved by the invention]

[0011] The present invention has been devised to solve the above problems, and aims to provide a battery state estimation device and method that more accurately estimates the battery state by taking into account the offset and dispersion of the current sensor and the voltage sensor.

[0012] Other objects and advantages of the present invention will become apparent from the following description and the embodiments of the present invention, and it will be readily apparent that the objects and advantages of the present invention can be realized by the means and combinations thereof set forth in the claims. [Means for solving the problem]

[0013] According to an aspect of the present invention, an apparatus for estimating a state of a battery may include: an offset and variance calculation unit configured to calculate a voltage offset and a voltage variance based on voltage values ​​of a battery acquired during a predetermined period, and to calculate a current offset and a current variance based on current values ​​of the battery acquired during the predetermined period; a system noise calculation unit configured to calculate an offset noise matrix and a variance noise matrix based on the voltage offset, the voltage variance, preset voltage measurement specifications, the current offset, the current variance, and preset current measurement specifications, and to calculate system noise from the offset noise matrix and the variance noise matrix; and a battery state estimation unit configured to estimate state information of the battery by applying the system noise to a preset recursive filter.

[0014] The offset noise matrix may be composed of a matrix including a first offset component and a second offset component, and the system noise calculation unit may be configured to calculate the first offset component based on the current offset and the current measurement specification, and to calculate the second offset component based on the voltage offset and the voltage measurement specification.

[0015] The system noise calculation unit is configured to calculate the first offset component using the following Equation 1:

[0016]

number

[0017] where w1 is the first offset component, and w 1_min is the minimum value of the first offset component that is set in advance, and w 1_max is the maximum value of the first offset component that is set in advance, and offset c is the current offset, and range c is the maximum measurable current in the current measurement specifications, and accuracy cmay be the current measurement error in the current measurement specifications.

[0018] The system noise calculation unit is configured to calculate the second offset component using the following Equation 2:

[0019]

number

[0020] where w2 is the second offset component, and w 2_min is the preset minimum value of the second offset component, and w 2_max is the maximum value of the second offset component that is set in advance, and offset v is the voltage offset, and range v is the maximum measurable voltage in the voltage measurement specifications, and accuracy v may be the voltage measurement error in the voltage measurement specifications.

[0021] The variance noise matrix may be composed of a matrix including a first variance component and a second variance component, and the system noise calculation unit may be configured to calculate the first variance component based on the current variance and the current measurement specification, and to calculate the second variance component based on the voltage offset and the voltage measurement specification.

[0022] The system noise calculation unit is configured to calculate the first variance component using the following Equation 3:

[0023]

number

[0024] where q 11 is the first variance component, and q 11_min is the minimum value of the first variance component set in advance, and q 11_max is the maximum value of the first variance component set in advance, and varc is the current dispersion, and range c is the maximum measurable current in the current measurement specifications, and accuracy c may be the current measurement error in the current measurement specifications.

[0025] The system noise calculation unit is configured to calculate the second variance component using the following Equation 4:

[0026]

number

[0027] where q 22 is the second variance component, and q 22_min is the minimum value of the second variance component that is set in advance, and q 22_max is the maximum value of the second variance component set in advance, and var v is the voltage variance, and range v is the maximum measurable voltage in the voltage measurement specifications, and accuracy v may be the voltage measurement error in the voltage measurement specifications.

[0028] The system noise calculation unit may be configured to calculate the system noise by calculating an inner product of the offset noise matrix, the variance noise matrix, and a transpose of the offset noise matrix.

[0029] The system noise calculation unit is configured to calculate the system noise using the following Equation 5:

[0030]

number

[0031] where:

[0032]

number

[0033] is the system noise, W is the offset noise matrix, and W T may be the transpose of the offset noise matrix, and Q may be the variance noise matrix.

[0034] The recursive filter may be comprised of a dual adaptive extended Kalman filter including a first extended Kalman filter that predicts and corrects the battery's SOC and SOC covariance and a second extended Kalman filter that predicts and corrects the battery's SOH and SOH covariance.

[0035] The first extended Kalman filter may be configured to predict an SOC for a current cycle based on the SOC of the battery estimated in a previous cycle and the offset noise matrix, predict an SOC covariance for the current cycle based on the SOC covariance of the battery estimated in the previous cycle and the system noise, and estimate the SOC and SOC covariance of the battery in the current cycle based on the predicted SOC, the predicted SOC covariance, and the SOH predicted by the second extended Kalman filter.

[0036] The second extended Kalman filter may be configured to predict a SOH for a current cycle based on the SOH of the battery estimated in a previous cycle, predict a SOH covariance for a current cycle based on the SOH covariance of the battery estimated in the previous cycle and the variance noise matrix, and estimate the SOH and SOH covariance of the battery in the current cycle based on the predicted SOH, the predicted SOH covariance, and the SOC predicted by the first extended Kalman filter.

[0037] A battery pack according to another aspect of the present invention may include the battery state estimation device according to one aspect of the present invention.

[0038] An energy storage system according to yet another aspect of the present invention may include the battery state estimating device according to the aspect of the present invention.

[0039] According to yet another aspect of the present invention, a battery state estimation method may include: a voltage and current acquiring step of acquiring voltage values ​​and current values ​​of a battery; an offset and variance calculating step of calculating a voltage offset and a voltage variance based on voltage values ​​of the battery acquired during a predetermined period and calculating a current offset and a current variance based on current values ​​of the battery acquired during the predetermined period; a noise matrix calculating step of calculating an offset noise matrix and a variance noise matrix based on the voltage offset, the voltage variance, preset voltage measurement specifications, the current offset, the current variance, and preset current measurement specifications; a system noise calculating step of calculating system noise from the offset noise matrix and the variance noise matrix; and a battery state information estimating step of estimating state information of the battery by applying the system noise to a preset recursive filter. [Effects of the Invention]

[0040] According to one aspect of the present invention, the parameters used in the extended Kalman filter can be corrected taking into account the offset and variance of the current sensor and the voltage sensor, thereby providing an advantage in that the state of the battery can be estimated more accurately.

[0041] The effects of the present invention are not limited to those described above, and other effects not mentioned will be clearly understood by those skilled in the art from the claims.

[0042] The following drawings attached to this specification are intended to facilitate a further understanding of the technical concepts of the present invention together with the detailed description of the invention to be given later, and therefore the present invention should not be interpreted as being limited to the matters depicted in the drawings. [Brief explanation of the drawings]

[0043] [Figure 1] FIG. 1 is a flowchart of a conventional dual adaptive extended Kalman filter. [Figure 2] 1 is a diagram illustrating a battery state estimation device according to an embodiment of the present invention; [Figure 3] FIG. 10 is a diagram schematically illustrating an exemplary configuration of a battery pack according to another embodiment of the present invention. [Figure 4] 10 is a diagram illustrating a battery state estimation method according to another embodiment of the present invention; DETAILED DESCRIPTION OF THE INVENTION

[0044] Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. Prior to this, the terms and words used in the specification and claims should not be construed as being limited to their ordinary or dictionary meanings, but should be construed as having meanings and concepts corresponding to the technical ideas of the present invention, in accordance with the principle that the inventors themselves can appropriately define the concepts of terms in order to best explain the invention.

[0045] Therefore, it should be understood that the embodiments described in this specification and the configurations shown in the drawings are merely the most preferred embodiments of the present invention and do not represent the entire technical idea of ​​the present invention, and that there may be various equivalents and modifications that can be substituted therefor at the time of this application.

[0046] Furthermore, in describing the present invention, if it is recognized that a specific description of related publicly known techniques may obscure the gist of the present invention, the detailed description will be omitted.

[0047] Terms including ordinal numbers such as first, second, etc. are used to distinguish one of various components from the other components, and are not used to limit the components by these terms.

[0048] Throughout this specification, when a part is said to "comprise" a certain element, this does not mean that it may further include other elements, unless otherwise specified.

[0049] Incidentally, throughout the specification, when a part is said to be "connected" to another part, this includes not only the case where it is "directly connected" but also the case where it is "indirectly connected" via another element in between.

[0050] DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0051] FIG. 2 is a diagram schematically illustrating a battery state estimating device 100 according to an embodiment of the present invention.

[0052] Referring to FIG. 2, the battery state estimation device 100 may include an offset and variance calculation unit 110, a system noise calculation unit 120, and a battery state estimation unit .

[0053] The offset and variance calculation unit 110 may be configured to calculate a voltage offset and a voltage variance based on voltage values ​​of the battery acquired during a predetermined period.

[0054] Here, a battery refers to a physically separable, independent cell that has a negative terminal and a positive terminal. For example, a lithium-ion battery or a lithium polymer battery may be considered a battery. A battery may also refer to a battery module in which multiple cells are connected in series and / or parallel.

[0055] Preferably, the battery may be in an unloaded state, and more preferably, the battery may be in an unloaded state for a predetermined period of time, and the open circuit voltage (OCV) may be measurable.

[0056] For example, the offset and variance calculation unit 110 may be communicatively connected to a voltage measurement unit that measures the voltage of the battery. The offset and variance calculation unit 110 may receive battery voltage values ​​measured during a predetermined period from the voltage measurement unit. Here, the battery voltage values ​​received by the offset and variance calculation unit 110 may be a plurality of voltage values ​​measured by the voltage measurement unit during a predetermined period according to a voltage measurement cycle.

[0057] For example, assume that the predetermined period is T1, the voltage measurement period is T2, and T1 is greater than T2. ​​The offset and variance calculation unit 110 may acquire multiple voltage values ​​measured over a period T2 during the period T1. The offset and variance calculation unit 110 may then calculate the difference between each of the multiple voltage values ​​measured over the period T2 and the corresponding predicted value to calculate multiple offsets for the voltage measurement unit over the period T1. The offset and variance calculation unit 110 may also calculate the variance of the calculated multiple offsets as the voltage variance.

[0058] In general, the offset of the voltage measurement unit may follow a normal distribution based on 0. That is, in the normal case, the offset is 0 [V], and when the measured value of the voltage measurement unit and the predicted value of the offset and variance calculation unit 110 differ from each other, the offset may be calculated as a value exceeding 0 [V].

[0059] For example, the offset and variance calculation unit 110 may calculate an offset for each of a plurality of voltage values ​​acquired during a predetermined period and determine the largest value of the calculated offsets as the voltage offset. As another example, the offset and variance calculation unit 110 may determine an average value of the calculated offsets as the voltage offset. Preferably, the offset and variance calculation unit 110 may determine the average value of the plurality of offsets as the voltage offset in order to determine a representative offset of the voltage measurement unit for a predetermined period as the voltage offset.

[0060] Then, the offset and variance calculation section 110 can calculate the variance of the calculated offsets to calculate the voltage variance.

[0061] For example, assume that the predetermined period is one hour and the voltage measurement period is one minute. The offset and variance calculation unit 110 may acquire a total of 60 voltage values ​​during the predetermined period (one hour). The offset and variance calculation unit 110 may calculate an offset for each of the 60 voltage values ​​to calculate a total of 60 offsets. Then, the offset and variance calculation unit 110 may determine the maximum or average value of the 60 offsets as the voltage offset. Finally, the offset and variance calculation unit 110 may calculate the variance of the 60 offsets to determine the voltage variance.

[0062] The offset and variance calculation unit 110 may be configured to calculate a current offset and a current variance based on the current values ​​of the battery acquired during a predetermined period.

[0063] For example, the offset and variance calculation unit 110 may be communicatively connected to a current measurement unit that measures the current of the battery. The offset and variance calculation unit 110 may receive current values ​​of the battery measured for a predetermined period from the current measurement unit. Here, the current values ​​of the battery received by the offset and variance calculation unit 110 may be a plurality of current values ​​measured by the current measurement unit for a predetermined period based on a current measurement cycle.

[0064] For example, assume that the predetermined period is T1, the current measurement period is T2, and T1 is greater than T2. ​​The offset and variance calculation unit 110 may acquire multiple current values ​​measured over a period T2 during the period T1. The offset and variance calculation unit 110 may then calculate multiple offsets for the current measurement unit over the period T1 by calculating the difference between each of the multiple current values ​​measured over the period T2 and the corresponding predicted value. The offset and variance calculation unit 110 may also calculate the variance of the calculated multiple offsets as the current variance.

[0065] In general, the offset of the current measurement unit may follow a normal distribution with 0 as the base. That is, in a normal case, the offset is 0 [mA]. ​​When the measured value of the current measurement unit and the predicted value of the offset and variance calculation unit 110 differ from each other, the offset may be calculated as a value exceeding 0 [mA]. ​​For example, when the battery is in an unloaded state, the predicted current value may be 0 [mA]. ​​However, when leakage current occurs or a defect occurs in the current measurement unit, the measured current value may exceed 0 [mA]. ​​In such a case, the offset for the current measurement unit calculated by the offset and variance calculation unit 110 may exceed 0 [mA].

[0066] For example, the offset and variance calculation unit 110 may calculate an offset for each of a plurality of current values ​​acquired during a predetermined period and determine the largest value of the calculated offsets as the current offset. As another example, the offset and variance calculation unit 110 may determine an average value of the calculated offsets as the current offset. Preferably, the offset and variance calculation unit 110 may determine the average value of the plurality of offsets as the current offset in order to determine a representative offset of the current measurement unit for a predetermined period as the current offset.

[0067] Then, the offset and variance calculation section 110 can calculate the variance of the calculated offsets to calculate the current variance.

[0068] For example, assume that the predetermined period is 60 minutes and the current measurement period is 1 minute. The offset and variance calculation unit 110 may acquire a total of 60 current values ​​during the 60 minutes. The offset and variance calculation unit 110 may calculate an offset for each of the 60 current values ​​to calculate a total of 60 offsets. Then, the offset and variance calculation unit 110 may determine the maximum or average value of the 60 offsets as the current offset. Finally, the offset and variance calculation unit 110 may calculate the variance of the 60 offsets to determine the current variance.

[0069] The system noise calculation unit 120 may be configured to calculate an offset noise matrix and a variance noise matrix based on the voltage offset, the voltage variance, the preset voltage measurement specifications, the current offset, the current variance, and the preset current measurement specifications.

[0070] Here, the preset voltage measurement specifications may include the maximum voltage that the voltage measurement unit can measure and the voltage measurement error of the voltage measurement unit, for example, the maximum voltage that the voltage measurement unit can measure may be 5V, and the voltage measurement error of the voltage measurement unit may be 5%.

[0071] Finally, the preset current measurement specifications may include a maximum current that the current measurement unit can measure and a current measurement error of the current measurement unit. For example, the maximum current that the current measurement unit can measure may be 100 A, and the current measurement error of the current measurement unit may be 5%.

[0072] The offset noise matrix may be composed of a matrix including a first offset component and a second offset component.

[0073] For example, the offset noise matrix may be a matrix having the following structure:

[0074]

number

[0075] where W may be an offset noise matrix, w1 may be the first offset component, and w2 may be the second offset component.

[0076] Specifically, the system noise calculation unit 120 may be configured to calculate a first offset component based on a current offset and a current measurement specification. The system noise calculation unit 120 may also be configured to calculate a second offset component based on a voltage offset and a voltage measurement specification. Specific formulas used by the system noise calculation unit 120 to calculate the first offset component and the second offset component will be described later.

[0077] The variance noise matrix may be composed of a matrix including a first variance component and a second variance component.

[0078] For example, the variance noise matrix may be a matrix having the following structure:

[0079]

number

[0080] where Q is a variance noise matrix, q11 may be the first variance component, and q22 may be the second variance component. In general, q12 and q21 may have a value of 0.

[0081] The system noise calculation unit 120 may be configured to calculate a first variance component based on the current variance and the current measurement specification, and to calculate a second variance component based on the voltage offset and the voltage measurement specification. Specific formulas used by the system noise calculation unit 120 to calculate the first variance component and the second variance component will be described later.

[0082] The system noise calculation unit 120 may be configured to calculate the system noise from the offset noise matrix and the variance noise matrix.

[0083] For example, the system noise may be calculated by calculating the dot product of an offset noise matrix and a variance noise matrix. A specific formula used by the system noise calculation unit 120 to calculate the system noise will be described later.

[0084] In other words, the system noise used in the process of estimating the battery's SOC and SOH is calculated based on the voltage offset, voltage variance, preset voltage measurement specifications, current offset, current variance, and preset current measurement specifications, thereby more accurately reflecting the noise caused by the voltage measurement unit and the current measurement unit.

[0085] The battery state estimator 130 may be configured to apply a pre-defined recursive filter to the system noise to estimate the battery state information.

[0086] For example, the recursive filter may be composed of a dual extended adaptive Kalman filter including a first extended Kalman filter that predicts and corrects the battery's SOC and SOC covariance and a second extended Kalman filter that predicts and corrects the battery's SOH and SOH covariance.

[0087] Specifically, the first extended Kalman filter may be configured to predict the SOC of the current cycle based on the battery SOC and offset noise matrix estimated in the previous cycle, predict the SOC covariance of the current cycle based on the battery SOC covariance and system noise estimated in the previous cycle, and estimate the battery SOC and SOC covariance in the current cycle based on the predicted SOC, the predicted SOC covariance, and the SOH predicted by the second extended Kalman filter.

[0088] The second extended Kalman filter may also be configured to predict the SOH of the battery in the current cycle based on the SOH of the battery estimated in the previous cycle, predict the SOH covariance of the battery in the current cycle based on the SOH covariance and variance noise matrix of the battery estimated in the previous cycle, and estimate the SOH and SOH covariance of the battery in the current cycle based on the predicted SOH, the predicted SOH covariance, and the SOC predicted by the first extended Kalman filter.

[0089] The details of the dual adaptive extended Kalman filter are explained in Non-Patent Document 1, and therefore a detailed explanation thereof will be omitted.

[0090] The battery state estimation unit 130 may estimate the battery state information by taking into account system noise corresponding to the noise of the voltage measurement unit and the current measurement unit.

[0091] Therefore, the battery state estimation device 100 according to an embodiment of the present invention has the advantage of being able to more accurately estimate the current state of the battery using system noise calculated based on voltage and current values ​​acquired during a predetermined period, rather than simply applying arbitrary noise values ​​that follow a multivariate normal distribution.

[0092] Meanwhile, the offset and variance calculation unit 110, the system noise calculation unit 120, and the battery state estimation unit 130 provided in the battery state estimation device 100 may optionally include a processor, an application specific integrated circuit (ASIC), other chipsets, logic circuits, registers, a communication modem, a data processing device, etc., known in the art for running various control logics performed in the present invention. Furthermore, when the control logic is implemented in software, the offset and variance calculation unit 110, the system noise calculation unit 120, and the battery state estimation unit 130 may be implemented as a collection of program modules. In this case, the program modules are stored in memory and can be executed by the offset and variance calculation unit 110, the system noise calculation unit 120, and the battery state estimation unit 130. The memory may be located inside or outside the offset and variance calculation unit 110, the system noise calculation unit 120, and the battery state estimation unit 130, and may be connected to the well-known offset and variance calculation unit 110, the system noise calculation unit 120, and the battery state estimation unit 130.

[0093] The battery state estimation device 100 may further include a memory unit 140. The memory unit 140 may store data and programs required for each component of the battery state estimation device 100 to operate and function, or data generated during the operation and function. The memory unit 140 may be any known information storage means known to be capable of recording, erasing, updating, and reading data. For example, the information storage means may include a random access memory (RAM), a flash memory, a read-only memory (ROM), an electrically erasable programmable read-only memory (EEPROM), a register, etc. The memory unit 140 may also store program code defining processes that can be activated by the offset and variance calculation unit 110, the system noise calculation unit 120, and the battery state estimation unit 130.

[0094] For example, the storage unit 140 may store the voltage and current values ​​of the battery acquired during a predetermined period, as well as the SOC and SOH of the previous period derived by a recursive filter.

[0095] The calculation of the offset component, variance component, and system noise by the system noise calculation unit 120 will be described in detail below.

[0096] The system noise calculation unit 120 may be configured to calculate the first offset component using Equation 1 below.

[0097]

number

[0098] where w1 is the first offset component and w 1_min is the minimum value of the preset first offset component, and w 1_maxis the maximum value of the first offset component that is set in advance, and offset c is the current offset, and range c is the maximum measurable current in the current measurement specifications, and accuracy c may be the current measurement error within the current measurement specifications.

[0099] For example, the minimum value of the first offset component (w 1_min ) is 1, and the maximum value of the first offset component (w 1_max ) is 10, and the maximum measurable current (range c ) is 100A, and the current measurement error (accuracy c ) is assumed to be 5%.

[0100] If a current offset of 1 A occurs during a predetermined period, the first offset component may be calculated as 2.8. Specifically, the system noise calculation unit 120 may calculate the first offset component as 2.8 by using the formula "1 + {1 ÷ (100 × 0.05) × (10 −1)}."

[0101] The system noise calculation unit 120 may be configured to calculate the second offset component using Equation 2 below.

[0102]

number

[0103] where w2 is the second offset component, and w 2_min is the minimum value of the preset second offset component, and w 2_max is the maximum value of the second offset component that is set in advance, and offset v is the voltage offset, and range v is the maximum voltage that can be measured in the voltage measurement specifications, and accuracy v may be the voltage measurement error in the voltage measurement specifications.

[0104] For example, the minimum value of the second offset component (w 2_min ) is 1, and the maximum value of the second offset component (w 2_max ) is 10, and the maximum measurable voltage (range v ) is 5V, and the voltage measurement error (accuracy v ) is assumed to be 5%.

[0105] If a voltage offset of 0.03 V occurs during a predetermined period, the second offset component may be calculated as 2.08. Specifically, the system noise calculation unit 120 may calculate the second offset component as 2.08 by using the formula "1 + {0.03 ÷ (5 × 0.05) × (10 −1)}."

[0106] The system noise calculation unit 120 may be configured to calculate the first variance component using Equation 3 below.

[0107]

number

[0108] where q 11 is the first variance component, and q 11_min is the minimum value of the first variance component, and q 11_max is the maximum value of the first variance component, and var c is the current dispersion, and range c is the maximum measurable current in the current measurement specifications, and accuracy c may be the current measurement error within the current measurement specifications.

[0109] For example, the minimum value of the first variance component (q 11_min ) is 0.01, and the maximum value of the first variance component (q 11_max ) is 0.1, and the maximum measurable current (range c ) is 100A, and the current measurement error (accuracy c ) is assumed to be 5%.

[0110] If the current variance is 1 for a predetermined period of time, the first variance component may be calculated as 0.0136. Specifically, the system noise calculation unit 120 may calculate the first variance component as 0.0136 by subtracting 0.01 from 100×0.05. 2 ×(0.1-0.01)}" formula can be calculated to calculate the first variance component as 0.0136.

[0111] The system noise calculation unit 120 may be configured to calculate the second variance component using Equation 4 below.

[0112]

number

[0113] where q 22 is the second variance component, and q 22_min is the minimum value of the second variance component, and q 22_max is the maximum value of the second variance component, and var v is the voltage dispersion, and range v is the maximum voltage that can be measured in the voltage measurement specifications, and accuracy v may be the voltage measurement error in the voltage measurement specifications.

[0114] For example, the minimum value of the second variance component (q 22_min ) is 0.01, and the maximum value of the second variance component (q 22_max ) is 0.1, and the maximum measurable voltage (range v ) is 5V, and the voltage measurement error (accuracy v ) is assumed to be 5%.

[0115] If the voltage variance during a predetermined period is 0.03, the second variance component may be calculated as 0.0532. Specifically, the system noise calculation unit 120 may calculate the second variance component as 0.01 + {0.03 ÷ (5 × 0.05)} 2 ×(0.1-0.01)}" can be calculated to calculate the second variance component as 0.0532.

[0116] The system noise calculation unit 120 may be configured to calculate the system noise by calculating the inner product of the offset noise matrix, the variance noise matrix, and the transpose of the offset noise matrix.

[0117] Specifically, the system noise calculation unit 120 may be configured to calculate the system noise using Equation 5 below.

[0118]

number

[0119] where:

[0120]

number

[0121] is the system noise, W is the offset noise matrix, and W T is the transpose of the offset noise matrix, and Q may be the variance noise matrix.

[0122] For example, as in the above embodiment, the first offset component (w1) is 2.8, the second offset component (w2) is 2.08, and the first dispersion component (q 11 ) is 0.0136, and the second variance component (q 22 ) is 0.0532. The system noise calculation unit 120 may calculate the system noise as 0.33678848 by calculating the inner product of the offset noise matrix, the variance noise matrix, and the transpose of the offset noise matrix.

[0123] The battery state estimating device 100 according to an embodiment of the present invention calculates the system noise (

[0124]

number

[0125] ), there is an advantage that the accuracy of estimating the battery state (SOC and SOH) using a recursive filter can be dramatically improved.

[0126] Hereinafter, an embodiment in which the battery state estimation unit 130 applies the offset noise matrix, the variance noise matrix, and the system noise to the recursive filter will be described in detail.

[0127] First, the dual adaptive extended Kalman filter includes a first extended Kalman filter and a second extended Kalman filter. The first extended Kalman filter is a recursive filter that can predict SOC and SOC covariance in a time update step and correct the predicted SOC and the predicted SOC covariance in a measurement update step. The second extended Kalman filter is a recursive filter that can predict SOH and SOH covariance in a time update step and correct the predicted SOH and the predicted SOH covariance in a measurement update step.

[0128] Also, in the following, "^hat" means an estimated value, "-" means a value predicted in the time update step, and "+" means a value corrected in the measurement update step.

[0129] However, the parameters (P, x, u, A, θ, and k) included in the following Equations 6 to 8 are defined in Non-Patent Document 1, and these parameters are widely used in the extended Kalman filter or dual adaptive extended Kalman filter. Therefore, detailed explanation of the parameters (P, x, u, A, θ, and k) will be omitted below.

[0130] The battery state estimation unit 130 may predict the SOH covariance of the battery in the second extended Kalman filter using Equation 6 below.

[0131]

number

[0132] Here, Equation 6 corresponds to Equation 12 in Non-Patent Document 1, and Q k is the variance noise matrix calculated by the system noise calculation unit 120 at time point k.

[0133] The battery state estimation unit 130 uses the second extended Kalman filter to calculate the SOH covariance determined at time point k (the SOH covariance after time update and measurement update at time point k,

[0134]

number

[0135] The variance noise matrix (Q k ) is added to obtain the SOH covariance (

[0136]

number

[0137] ) can be predicted.

[0138] After this, the SOH covariance (

[0139]

number

[0140] can be corrected according to Equation 16 in Non-Patent Document 1. Specifically, the predicted SOH covariance (

[0141]

number

[0142] is corrected according to Equation 16 in Non-Patent Document 1 to obtain the SOH covariance (

[0143]

number

[0144] can be determined.

[0145] That is, the battery state estimation unit 130 calculates the variance noise matrix (Q k ) is further considered to determine the SOH covariance (

[0146]

number

[0147] ) and thus the predicted SOH covariance (

[0148]

number

[0149] ) allows the noise of the voltage measurement unit and the current measurement unit to be reflected.

[0150] Therefore, referring to Equation 16 in Non-Patent Document 1, the predicted SOH covariance (

[0151]

number

[0152] ) based on the corrected SOH(

[0153]

number

[0154] ) can give a more accurate SOH for the battery.

[0155] The battery state estimation unit 130 may predict the SOC of the battery in a first extended Kalman filter using Equation 7 below.

[0156]

number

[0157] Here, Equation 7 corresponds to Equation 13 in Non-Patent Document 1, and W k is the offset noise matrix calculated by the system noise calculation unit 120 at time point k.

[0158] The battery state estimation unit 130 uses the first extended Kalman filter to calculate the SOC determined at time k (the SOC after time update and measurement update at time k,

[0159]

number

[0160] ) is added to the offset noise matrix (W k ) is added to obtain the SOC at time k+1.

[0161]

number

[0162] can be predicted.

[0163] After this, the SOC (

[0164]

number

[0165] ) can be corrected according to Equation 14 in Non-Patent Document 1. Specifically, the predicted SOC (

[0166]

number

[0167] ) is corrected according to Equation 14 of Non-Patent Document 1 to obtain the SOC (

[0168]

number

[0169] ) can be determined.

[0170] That is, the battery state estimation unit 130 calculates the offset noise matrix (W k ) and further consider SOC(

[0171]

number

[0172] ) and predicted SOC (

[0173]

number

[0174] ) allows the noise of the voltage measurement unit and the current measurement unit to be reflected.

[0175] Furthermore, referring to Equation 14 in Non-Patent Document 1, the predicted SOC (

[0176]

number

[0177] ) is the predicted SOC covariance (

[0178]

number

[0179] ) can be corrected by taking into account the corrected SOC (

[0180]

number

[0181] ) can give a more accurate SOC for the battery.

[0182] The battery state estimation unit 130 may predict the SOC covariance of the battery in the first extended Kalman filter using Equation 8 below.

[0183]

number

[0184] Here, Equation 8 corresponds to Equation 13 in Non-Patent Document 1,

[0185]

number

[0186] is the system noise calculated by the system noise calculation unit 120 at time point k.

[0187] The battery state estimation unit 130 uses the first extended Kalman filter to calculate the SOC covariance determined at time k (the SOC covariance after time update and measurement update at time k,

[0188]

number

[0189] ) plus the system noise (

[0190]

number

[0191] ) is added to obtain the SOC covariance (

[0192]

number

[0193] ) can be predicted.

[0194] After this, the SOC covariance (

[0195]

number

[0196] ) can be corrected according to Equation 14 in Non-Patent Document 1. Specifically, the predicted SOC covariance (

[0197]

number

[0198] ) is corrected according to Equation 14 of Non-Patent Document 1 to obtain the SOC covariance (

[0199]

number

[0200] ) can be determined.

[0201] That is, the battery state estimation unit 130 calculates the system noise (

[0202]

number

[0203] ) is further considered to determine the SOC covariance (

[0204]

number

[0205] ) and thus predicted SOC covariance (

[0206]

number

[0207] ) allows the noise of the voltage measurement unit and the current measurement unit to be reflected.

[0208] Therefore, referring to Equation 14 in Non-Patent Document 1, the predicted SOC covariance (

[0209]

number

[0210] ) based on the corrected SOC (

[0211]

number

[0212] ) can give a more accurate SOC for the battery.

[0213] The battery state estimating device 100 according to the present invention may be applied to a battery management system (BMS). That is, the BMS according to the present invention may include the battery state estimating device 100 described above. In such a configuration, at least some of the components of the battery state estimating device 100 may be realized by complementing or adding functions of components included in a conventional BMS. For example, the components of the battery state estimating device 100 may be realized as components of the BMS.

[0214] The battery state estimating device 100 according to the present invention may be installed in a battery pack. That is, the battery pack according to the present invention may include the above-described battery state estimating device 100 and one or more battery cells. The battery pack may further include electrical components (relays, fuses, etc.), a case, etc.

[0215] FIG. 3 is a diagram schematically illustrating an exemplary configuration of a battery pack according to another embodiment of the present invention.

[0216] Referring to FIG. 3, the battery pack 1 may include a battery B, a voltage measurement unit 10, a current measurement unit 20, and a battery state estimation device 100.

[0217] The positive terminal of battery B may be connected to the positive terminal P+ of battery pack 1, and the negative terminal of battery B may be connected to the negative terminal P- of battery pack 1.

[0218] The voltage measuring unit 10 may be connected to the first sensing line SL1 and the second sensing line SL2.

[0219] Specifically, the voltage measurement unit 10 may be connected to the positive terminal of battery B via a first sensing line SL1 and to the negative terminal of battery B via a second sensing line SL2. The voltage measurement unit 10 may measure the voltage of battery B based on the voltages measured on the first sensing line SL1 and the second sensing line SL2.

[0220] The current measuring unit 20 may be connected to the third sensing line SL3.

[0221] The current measuring unit 20 may be connected to the current measuring unit A via a third sensing line SL3. For example, the current measuring unit A may be an ammeter or a shunt resistor that is disposed on a charge / discharge path of the battery B and can measure the current of the charge / discharge path. The current measuring unit 20 may measure the current of the battery B using the third sensing line SL3.

[0222] The offset and variance calculation unit 110 may receive the voltage value of battery B from the voltage measurement unit 10. The offset and variance calculation unit 110 may also receive the current value of battery B from the current measurement unit 20.

[0223] In addition, the first offset component (w1) in Equation 1 and the first dispersion component (q 11 The maximum measurable current (range) of the current measurement specifications used to calculate c ) may be the maximum current value that the current measuring unit 20 can measure. For example, the maximum current value that the current measuring unit 20 can measure may be 100 A. In addition, the current measurement accuracy ( c ) may be the current measurement error of the current measuring unit 20. For example, the current measurement error of the current measuring unit 20 may be 5%.

[0224] In addition, the second offset component (w2) in Equation 2 and the second dispersion component (q 22 The maximum measurable voltage (range) of the voltage measurement specifications used to calculate v ) may be the maximum voltage value that the voltage measuring unit 10 can measure. For example, the maximum voltage value that the voltage measuring unit 10 can measure may be 5 V. In addition, the voltage measurement accuracy ( v ) may be the voltage measurement error of the voltage measurement unit 10. For example, the voltage measurement error of the voltage measurement unit 10 may be 5%.

[0225] 3, the voltage value measured by the voltage measuring unit 10 and the current value measured by the current measuring unit 20 may be directly transmitted by the offset and variance calculating unit 110 or may be stored in the storage unit 140. When the voltage value and the current value are stored in the storage unit 140, the offset and variance calculating unit 110 may access the storage unit 140 to obtain the voltage value and the current value for a predetermined period of time.

[0226] An energy storage system (ESS) according to yet another embodiment of the present invention may include the battery state estimating device 100 according to an embodiment of the present invention.

[0227] The energy storage system may include a plurality of battery racks, each of which may include a plurality of battery packs, each of which may be made up of a plurality of battery modules, each of which may be made up of a plurality of battery cells.

[0228] The battery state estimation device 100 can be installed in each battery rack and / or battery pack that constitutes the energy storage system.

[0229] For example, the battery state estimation device 100 may be installed in each battery rack constituting an energy storage system and calculate the system noise for the corresponding battery rack. Then, the battery state estimation device 100 may estimate the state of the battery pack using a recursive filter and the calculated system noise (which is commonly applied to multiple battery packs included in the battery rack).

[0230] As another example, the battery state estimation device 100 may be provided for each battery pack constituting a battery rack, calculate the system noise for the corresponding battery pack, and estimate the state of the battery pack using a recursive filter and the calculated system noise (applied to each battery pack).

[0231] Preferably, when the battery state estimation device 100 calculates the system noise for each battery cell, which is the smallest unit constituting an energy storage system, the states of the battery cells, battery modules, battery packs, and battery racks can be estimated more accurately. However, since it is practically impossible to install the battery state estimation device 100 in every battery cell constituting an energy storage system, the battery state estimation device 100 may be installed in each battery rack or battery pack to estimate the state of the battery pack.

[0232] In the above, due to the practical problem that it is not possible to install the battery state estimating device 100 in all battery cells constituting an energy storage system, an embodiment in which the battery state estimating device 100 is installed in a battery rack and / or a battery pack has been described. However, it should be noted that this description does not limit the embodiment in any way in which the battery state estimating device 100 is installed for each battery cell or each battery module.

[0233] FIG. 4 is a diagram illustrating a battery state estimation method according to still another embodiment of the present invention.

[0234] Preferably, each step of the battery state estimation method can be performed by the battery state estimation device 100. In the following, the contents that overlap with the contents described above will be briefly explained or omitted.

[0235] Referring to FIG. 4, the battery state estimation method may include a voltage and current acquisition step (S100), an offset and variance calculation step (S200), a noise matrix calculation step (S300), a system noise calculation step (S400), and a battery state information estimation step (S500).

[0236] The voltage and current acquisition step (S100) is a step of acquiring the voltage and current values ​​of the battery, and can be performed by the offset and variance calculation unit 110.

[0237] Here, the voltage and current acquired by the offset and variance calculation unit 110 may be the voltage and current values ​​of the battery in an unloaded state.

[0238] For example, in the embodiment of FIG. 3, the offset and variance calculation unit 110 may receive the voltage value of battery B from the voltage measurement unit 10 and the current value of battery B from the current measurement unit 20.

[0239] 3, the memory unit 140 may receive and store the voltage value of battery B from the voltage measurement unit 10, and may receive and store the current value of battery B from the current measurement unit 20. The offset and variance calculation unit 110 may also access the memory unit 140 to obtain the voltage value and current value of battery B.

[0240] The offset and variance calculation step (S200) is a step of calculating a voltage offset and a voltage variance based on the voltage values ​​of the battery acquired during a predetermined period, and calculating a current offset and a current variance based on the current values ​​of the battery acquired during a predetermined period, and can be performed by the offset and variance calculation unit 110.

[0241] 3, the offset and variance calculation unit 110 may calculate the offset of the voltage measurement unit 10 based on multiple voltage values ​​measured by the voltage measurement unit 10 during a predetermined period. The offset and variance calculation unit 110 may then calculate the maximum or average value of the multiple calculated offsets as the voltage offset. The offset and variance calculation unit 110 may also calculate the variance of the multiple calculated offsets as the voltage variance.

[0242] 3, the offset and variance calculation unit 110 may calculate the offset of the current measurement unit 20 based on a plurality of current values ​​measured by the current measurement unit 20 during a predetermined period. The offset and variance calculation unit 110 may then calculate the maximum or average value of the calculated plurality of offsets as the current offset. The offset and variance calculation unit 110 may also calculate the variance of the calculated plurality of offsets as the current variance.

[0243] The noise matrix calculation step (S300) is a step of calculating an offset noise matrix and a variance noise matrix based on the voltage offset, voltage variance, preset voltage measurement specifications, current offset, current variance, and preset current measurement specifications, and can be performed by the system noise calculation unit 120.

[0244] For example, the system noise calculation unit 120 may calculate a current offset according to Equation 1 and a first offset component (w1) based on the current variance and current measurement specifications. The system noise calculation unit 120 may also calculate a voltage offset according to Equation 2 and a second offset component (w2) based on the voltage variance and voltage measurement specifications. Then, the system noise calculation unit 120 may determine an offset noise matrix (W) including the first offset component (w1) and the second offset component (w2).

[0245] Furthermore, the system noise calculation unit 120 calculates the current offset according to Equation 3 and calculates the first variance component (q 11 ) according to Equation 4. The system noise calculation unit 120 may also calculate the voltage offset according to Equation 4, and the second variance component (q 22 ) can be calculated. Then, the system noise calculation unit 120 calculates the first variance component (q 11 ) and the second variance component (q 22 ) may be determined.

[0246] The system noise calculation step (S400) is a step of calculating the system noise from the offset noise matrix and the variance noise matrix, and can be performed by the system noise calculation unit 120.

[0247] For example, the system noise calculation unit 120 calculates the offset noise matrix (W), the variance noise matrix (Q), and the transpose matrix (W) of the offset noise matrix (W) according to Equation 5. T ) to calculate the dot product of the system noise (

[0248]

number

[0249] ) can be calculated.

[0250] The battery state information estimating step (S500) is a step of estimating battery state information by applying system noise to a preset recursive filter, and can be performed by the battery state estimating unit 130.

[0251] For example, the battery state estimation unit 130 may further add an offset noise matrix (W) to the SOC prediction process of the first extended Kalman filter.

[0252] In addition, the battery state estimation unit 130 includes system noise (

[0253]

number

[0254] ) may be further added.

[0255] Furthermore, the battery state estimation unit 130 may further add a variance noise matrix (Q) to the SOH covariance prediction process of the second extended Kalman filter.

[0256] The battery state estimation unit 130 calculates the offset noise matrix (W), the variance noise matrix (Q), and the system noise (

[0257]

number

[0258] ) has the advantage of being able to estimate the SOC and SOH of the battery more accurately.

[0259] The above-described embodiments of the present invention can be realized not only by the apparatus and method but also by a program that realizes the functions corresponding to the configurations of the embodiments of the present invention or a recording medium on which the program is recorded. Such realization can be easily achieved by a person skilled in the technical field to which the present invention pertains from the description of the above-described embodiments.

[0260] Although the present invention has been described above using limited embodiments and drawings, the present invention is not limited to these, and it goes without saying that various modifications and variations can be made by a person having ordinary knowledge in the technical field to which the present invention pertains within the technical spirit of the present invention and the scope of equivalents of the claims.

[0261] Furthermore, the present invention described above is susceptible to various substitutions, modifications, and alterations by a person having ordinary knowledge in the technical field to which the present invention pertains, within the scope of the technical concept of the present invention. Therefore, the present invention is not limited to the above-described embodiments and the accompanying drawings, but may be configured by selectively combining all or part of each embodiment for various modifications. [Explanation of symbols]

[0262] 1 battery pack 10 Voltage measurement section 20 Current measurement section 100 Battery state estimation device 110 Offset and variance calculation unit 120 System noise calculation unit 130 Battery state estimation unit 140 Storage section

Claims

1. an offset and variance calculation unit configured to calculate a voltage offset and a voltage variance based on voltage values ​​of the battery acquired during a predetermined period, and to calculate a current offset and a current variance based on current values ​​of the battery acquired during the predetermined period; A first offset component is calculated using the following Equation 1: Calculate the second offset component using the following Equation 2: The first variance component is calculated using the following Equation 3: The second variance component is calculated using the following Equation 4: calculating an offset noise matrix and a variance noise matrix based on the first offset component, the second offset component, the first variance component, and the second variance component; Calculating the system noise from the offset noise matrix and the variance noise matrix a system noise calculation unit configured as follows: a battery state estimation unit configured to estimate state information of the battery by applying the system noise to a preset recursive filter; Including, [Equation 1] where w 1 is the first offset component, w 1 _ min is a preset minimum value of the first offset component, w 1 _ max is a preset maximum value of the first offset component, offset c is the current offset, range c is a measurable maximum current in preset current measurement specifications, and accuracy c is a current measurement error in the current measurement specifications. [Equation 2] where w 2 is the second offset component, w 2 _ min is a preset minimum value of the second offset component, w 2 _ max is a preset maximum value of the second offset component, offset v is the voltage offset, range v is a measurable maximum voltage in the preset voltage measurement specifications, and accuracy v is a voltage measurement error in the voltage measurement specifications. [Equation 3] where q 11 is the first variance component, q 11 — min is a preset minimum value of the first variance component, q 11 — max is a preset maximum value of the first variance component, var c is the current variance, range c is a measurable maximum current in the current measurement specifications, and accuracy c is a current measurement error in the current measurement specifications. [Equation 4] where q 22 is the second variance component, q 22 — min is a preset minimum value of the second variance component, q 22 — max is a preset maximum value of the second variance component, var v is the voltage variance, range v is a measurable maximum voltage in the voltage measurement specifications, and accuracy v is a voltage measurement error in the voltage measurement specifications. Battery state estimator.

2. The system noise calculation unit The battery state estimation device according to claim 1 , configured to calculate the system noise by calculating an inner product of the offset noise matrix, the variance noise matrix, and a transpose of the offset noise matrix.

3. The system noise calculation unit The system noise is calculated using Equation 5: [Equation 5] where: [Equation 6] The battery state estimation device according to claim 2 , wherein W is the system noise, W is the offset noise matrix, W T is the transpose of the offset noise matrix, and Q is the variance noise matrix.

4. The recursive filter 2. The battery state estimation device of claim 1, configured as a dual adaptive extended Kalman filter including a first extended Kalman filter that predicts and corrects the SOC and SOC covariance of the battery and a second extended Kalman filter that predicts and corrects the SOH and SOH covariance of the battery.

5. The first extended Kalman filter is 5. The battery state estimation device of claim 4, configured to predict an SOC for a current cycle based on an SOC of the battery estimated in a previous cycle and the offset noise matrix, predict an SOC covariance for the current cycle based on an SOC covariance of the battery estimated in the previous cycle and the system noise, and estimate an SOC and SOC covariance of the battery in the current cycle based on the predicted SOC, the predicted SOC covariance, and an SOH predicted by the second extended Kalman filter.

6. The second extended Kalman filter is 5. The battery state estimation device of claim 4, configured to predict an SOH for a current period based on an SOH of the battery estimated in a previous period, predict an SOH covariance for the current period based on an SOH covariance of the battery estimated in the previous period and the variance noise matrix, and estimate the SOH and SOH covariance of the battery in the current period based on the predicted SOH, the predicted SOH covariance, and an SOC predicted by the first extended Kalman filter.

7. A battery pack comprising the battery state estimating device according to any one of claims 1 to 6.

8. An energy storage system comprising the battery state estimating device according to any one of claims 1 to 6.

9. a voltage and current acquisition step of acquiring a voltage value and a current value of the battery; an offset and variance calculation step of calculating a voltage offset and a voltage variance based on voltage values ​​of the battery acquired during a predetermined period, and calculating a current offset and a current variance based on current values ​​of the battery acquired during the predetermined period; Calculate the first offset component using the following Equation 7: Calculate the second offset component using the following Equation 8: The first variance component is calculated using the following Equation 9: The second variance component is calculated using the following Equation 10: a noise matrix calculation step of calculating an offset noise matrix and a variance noise matrix based on the first offset component, the second offset component, the first variance component, and the second variance component; a system noise calculation step of calculating a system noise from the offset noise matrix and the variance noise matrix; a battery state information estimating step of estimating state information of the battery by applying the system noise to a preset recursive filter; Including, [Equation 7] where w 1 is the first offset component, w 1 _ min is a preset minimum value of the first offset component, w 1 _ max is a preset maximum value of the first offset component, offset c is the current offset, range c is a measurable maximum current in preset current measurement specifications, and accuracy c is a current measurement error in the current measurement specifications. [Equation 8] where w 2 is the second offset component, w 2 _ min is a preset minimum value of the second offset component, w 2 _ max is a preset maximum value of the second offset component, offset v is the voltage offset, range v is a measurable maximum voltage in the preset voltage measurement specifications, and accuracy v is a voltage measurement error in the voltage measurement specifications. [Equation 9] where q 11 is the first variance component, q 11 — min is a preset minimum value of the first variance component, q 11 — max is a preset maximum value of the first variance component, var c is the current variance, range c is a measurable maximum current in the current measurement specifications, and accuracy c is a current measurement error in the current measurement specifications. [Equation 10] where q 22 is the second variance component, q 22 — min is a preset minimum value of the second variance component, q 22 — max is a preset maximum value of the second variance component, var v is the voltage variance, range v is a measurable maximum voltage in the voltage measurement specifications, and accuracy v is a voltage measurement error in the voltage measurement specifications. Battery state estimation method.

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