JP2008522152A - Battery state and parameter estimation system and method - Google Patents

Abstract

A method and system for estimating a value indicating a current operating condition of a battery includes a step of estimating SOC in a battery in which SOC (State Of Charge) constitutes one of internal states, and SOH (State Of Health). Estimating SOH in the battery constituting one of the parameters. In particular, a method for estimating SOC in a battery includes a step of predicting an internal state of the battery in which the SOC is one of internal states, and a step of predicting uncertainty of the prediction of the internal state. Applying an algorithm that repeats the step of correcting the prediction of the internal state and the prediction of the uncertainty, the step of predicting the internal state, the step of predicting the uncertainty, and the correction step Then, an estimation performed on the SOC and a step of calculating uncertainty with respect to the SOC estimation are included.
A method and system for estimating a current parameter of an electrochemical cell system includes the steps of predicting the internal parameter of the cell, predicting the uncertainty of the prediction of the internal parameter, Uncertainty for prediction and parameter prediction by applying the algorithm that repeats the prediction and the prediction of uncertainty and applying the algorithm for predicting the internal parameter, predicting the uncertainty and correcting the uncertainty Calculating sex.

Description

  The present invention relates to an apparatus and method for estimating the state and parameters of a battery pack system using digital filtering techniques, in particular Kalman filtering and extended Kalman filtering. The battery management system in the battery pack should estimate a value indicating the current operating condition of the battery pack. The current operating state includes SOC (State Of Charge), power reduction (power-fade), capacity reduction (capacity-fade), and immediately available power. The power reduction and the capacity reduction are mainly handled as expressions of SOH (State Of Health). The present invention provides an improved method and apparatus for estimating a value indicative of the current operating conditions of a pack including batteries SOC and SOH.

  Batteries are widely used in electronic and electrical devices. It is useful and necessary to measure how much charge remains in the battery in each application. Such a measurement is referred to as a state of charge (SOC). For example, it is useful to know how long a cell phone user can speak on his telephone. Note that the recharging device needs to know how much charge is present in the battery in order to prevent overcharging. Various batteries are sensitive not only to overcharging, but also to undercharging. Overcharging and undercharging can reduce battery efficiency and even damage it.

  There are currently many techniques for measuring the remaining charge of a battery. Each such SOC determination technique has drawbacks. Techniques such as Ampere-hour counting are sensitive to measurement errors, and those such as Coup de foot operate only with one battery type. Other techniques, such as Impedance Spectroscopy, are still limited to battery conditions such as rapidly changing temperatures. Also, many techniques do not provide an uncertain range for SOC estimation. The range of uncertainty associated with SOC measurement in applications such as HEV and EV is very important. If the range of uncertainty is not known and the battery is accidentally undercharged, the transport means can lose power on the road and pose a danger. If the range of uncertainty is known, this can be prevented. For example, if the battery SOC is determined to be within 10% of the minimum charge critical value and the uncertainty range is known to be 15%, then the system knows that the battery should be charged. This is because the uncertainty range is larger than the critical value interval.

A schematic for the existing technologies existing technologies and their disadvantages will be described. One method called discharge testing is an exact form of testing. This requires the battery to be fully discharged to determine the SOC under controlled conditions. However, the requirement for full discharge makes this test impractical for real life applications. This takes too much time and interrupts the system function while the test is performed.

Another SOC determination technique is called ampere-hour-counting. This is the most common technique for determining the SOC because it can be easily performed. This measures the battery current and uses the above measurements to determine the SOC. Amp-hour-counting uses the following formula:

In the above equation (1), C _n is an estimated capacity of the battery. I _batt is the battery current, and I _loss is the current consumed by the loss reactions. The above equation (equation) determines the SOC based on the initial value SOC ₀ that is the starting point. Ampere-hour-counting is an inherently misleading "open loop" scheme. Measurement errors accumulate and degrade the accuracy of the SOC determination over time. There are ways to improve current measurements, but they are quite expensive.

  Electrolyte measurement is yet another common technique. For example, in lead-acid batteries, the electrolyte is involved in the reaction between charge and discharge. Therefore, a linear relationship exists between the change in acid density and the SOC. Therefore, if the electrolyte density is measured, the estimated SOC value can be calculated. The density is measured directly or indirectly by ion concentration, conductivity, refractive index, viscosity, and the like. In addition, it is susceptible to acid stratification in the battery, moisture loss, and long term instability of the sensor.

  An open circuit voltage measurement can be made to the battery SOC test. Despite the non-linear relationship between open circuit voltage and SOC, it can be determined through laboratory tests. Once the relationship is determined, the SOC can be determined by measuring the open circuit voltage. However, measurements and estimates are only accurate when the battery is in a steady state that can only be made after a long period of inactivity. This makes the open circuit voltage technique impractical for dynamic real time applications.

  Impedance spectroscopy is another technique used to determine SOC. Impedance spectroscopy has a wide variety of applications in determining various characteristics of batteries. Impedance spectroscopy takes advantage of the relationship between battery model parameters and SOC derived from impedance spectroscopy measurements. However, the disadvantage of this technique is that the impedance curve is strongly affected by the temperature effect. Therefore, this application example is limited to an application example in a temperature stable environment.

  Internal resistance is a technique related to impedance spectroscopy. The internal resistance is calculated by the voltage drop divided by the current change during the same time interval. The selected time interval is important because all time intervals longer than 10 ms result in more complex resistance measurements. The measurement of internal resistance is very sensitive to measurement accuracy. Such a requirement is particularly difficult to achieve in application examples of hybrid electric vehicles (HEV) and electric vehicles (EV).

  One technique uses nonlinear modeling to estimate SOC directly from measurements. One example is artificial neural networks. Artificial neural network networks work in any system to predict the relationship between input and output. The network should be iteratively trained to improve its estimation. Since the accuracy of the data is based on a training program for the neckwork, it is difficult to determine the error associated with the SOC prediction given by the artificial neural network network.

  There is another group of SOC estimation techniques called interpretive techniques. Interpretation techniques do not provide SOC directly, but they use electrical discharge and charge characteristics to determine SOC. As such, the SOC should be inferred from the calculated value. One such technique is called “Cup de fouet”. “Whipping” refers to a short voltage drop region that occurs at the beginning of the discharge following the full charge of the lead acid battery. The SOC can be inferred using a special correlation between the voltage parameters generated in this “whipping” region. One limitation to the “whipping” is that it only works with lead acid batteries. Furthermore, this is only effective if full charging is done frequently during battery operation.

Kalman filter (The Kalman Filter)
One SOC determination technique involves mathematically modeling battery behavior and predicting SOC based on the model. One model is the Kalman filter. It has a mathematical basis in statistics, probability and system modeling. The main purpose of the Kalman filter is to recursively predict the internal state of a dynamic system using only the output value of the system. This is quite useful in many instances because the internal state of the system is unknown and cannot be measured directly. As such, the Kalman filter can work with all types of batteries, addressing many of the technology limitations mentioned.

  The Kalman filter has several advantages over many other similar mathematical system models and is widely used in fields such as aeronautics and computer graphics. In particular, the Kalman filter considers both measurement uncertainty and estimation uncertainty when updating the estimation in successive steps. The Kalman filter corrects for two uncertainties based on new measurements received from the sensor. This is very important for two reasons. First, the sensor often has an uncertainty or noise component associated with its measurement. If not corrected, the measurement uncertainty can accumulate over time. Second, the estimation itself is inherently uncertain in any model system. This is because the internal dynamic state of the system can change over time. Since the system may change internally and behave too little to fit the model, the estimation of one time step may be less accurate than the next. The correction mechanism of the Kalman filter can minimize such uncertainties at each time step to prevent a decrease in accuracy over time.

  FIG. 1 shows the basic operation of the Kalman filter. The Kalman filter has two main components: a predictive component 101 and a correct component 102. First, a series of initial parameters are input to the prediction component 101. The prediction component 101 uses a series of input parameters to predict the internal state of the system at a particular point in time. In addition to predicting internal conditions, it also provides prediction uncertainty. As shown in FIG. 1, the two outputs of the prediction component 101 are the predicted internal state vector (including the internal state) and its uncertainty.

  The role of the correction component 102 is to correct the predicted internal state and uncertainty received from the prediction component 101. The correction is made by comparing the predicted internal state and the predicted uncertainty with a new measurement received from the sensor. The result is a corrected internal state and a corrected uncertainty, and both are then fed back as parameters to the prediction component 101 for the next iteration again. In the next iteration, the cycle is repeated again.

Mathematical Basis of Kalman Filter FIGS. 1A and 1B show mathematical formulas used in both the Kalman filter prediction and correction components. To understand the root of the formula used, consider a dynamic process represented by the following form of n-th order difference equation: n-th order difference equation.

In the above (2), _{u k} is zero-mean white random process noise (zero-mean whiterandom process noise) . Under some basic conditions, the difference equation can be re-expressed as follows:

は、以前状態（ｐｒｅｖｉｏｕｓ ｓｔａｔｅ）の

と入力ｕ_ｋの線形的組み合わせによってモデルされた新しい状態（ｎｅｗ ｓｔａｔｅ）を示す。マトリックスＡとＢの表記法に注目すると、これは状態空間（ｓｔａｔｅ‐ｓｐａｃｅ）モデルを誘導する。

In the above equation (3),

Is the previous state (previous state)

Indicate the new state of being model (new new state) by a linear combination of the input _{u k} and. Focusing on the notation of matrices A and B, this leads to a state-space model.

Or, as a more general form,

  The above formula is the basis for many linear estimation models. Equations (3) through (5) show a system with a single input and a single output, while B has multiple columns and C has multiple rows. For example, the equations (6), (7) and the following equations allow multiple inputs and multiple outputs.

Based on the equations (6) and (7), the Kalman filter is operated by the following equation.
x _k = Ax _k-1 + Bu _k-1 + w _k-1 (8)
y _k = Cx _k + Du _k + v _k (9)

Although D is sometimes assumed to be 0, equation (9) is a more general form. The matrices A and B in the equation (8) are related to the matrices A _k and B _{k in the} equation (6), respectively. The matrices C and D in equation (9) are related to C _k and D _{k in} equation (7). Equation (8) is called a process function in order to operate estimation of a dynamic system process. Random variables w _k and v _k added in equations (8) and (9) indicate process noise and measurement noise, respectively. Their contribution to the estimation is represented in FIGS. 1A and 1B by their covariance matrices Σω and Σν.

で表現されたベクターである、次の時間段階（ｎｅｘｔ ｔｉｍｅ ｓｔｅｐ）におけるシステムの内的状態を予測する。負数表示はベクターが上記予測コンポーネントの結果であることを示す。正数表示はベクターが上記補正コンポーネントの結果であることを示す。（１５１）式において、現在時間段階で補正コンポーネントの結果は次の時間段階の結果を予測するために用いられる。（１５２）式は、不確定性を予測するのに用いられ、これはまた誤差共分散（ｅｒｒｏｒ ｃｏｖａｒｉａｎｃｅ）として参照される。（１５２）式において、マトリックスΣωはプロセスノイズ共分散マトリックス（ｐｒｏｃｅｓｓ ｎｏｉｓｅ ｃｏｖａｒｉａｎｃｅ ｍａｔｒｉｘ）である。 Also, referring to FIG. 1A (showing mathematical formulas in the prediction component 101), formula (151) is based on formula (8), and formula (152) is based on part of formula (9). Equation (151) is very similar to the form of equation (8), but the steps necessary to convert equation (9) to the form shown in equation (152) are not shown here. Equation (151) uses parameters from the current time step.

The internal state of the system in the next time step, which is a vector expressed by A negative number display indicates that the vector is the result of the prediction component. A positive number indication indicates that the vector is the result of the correction component. In equation (151), the result of the correction component at the current time stage is used to predict the result of the next time stage. Equation (152) is used to predict uncertainty, which is also referred to as error covariance. In the equation (152), the matrix Σω is a process noise covariance matrix.

間に加重値を付与するために用いられる。（１６１）式に示したように、マトリックスΣν、実際の測定ノイズ共分散（ａｃｔｕａｌ ｍｅａｓｕｒｅｍｅｎｔ ｎｏｉｓｅ ｃｏｖａｒｉａｎｃｅ）はカルマン利得係数Ｌ_ｋと逆比例になる。Σνの減るほどＬ_ｋは増加し、実際の測定値ｙ_ｋにさらに大きい加重値を提供する。しかし、予測された不確定性であるマトリックス

が減少したらＬ_ｋは減少し、予測された測定値

にさらに大きい加重値を提供する。そのため、カルマン利得係数はさらに小さい不確定性を有する測定形態に依存する実際の測定値または予測された測定値を選好する。 FIG. 1B shows the mathematical formula within the correction component 102. These three mathematical expressions are performed continuously. First, Equation (161) determines a Kalman gain factor. The Kalman gain coefficient is used to correct the correction in the equations (162) and (163). In the equation (161), the matrix C is derived from the equation (9), which relates the state and the measured value y _k . In the equation (162), the Kalman gain coefficient is an actual measured value y _k and a predicted measured value.

It is used to give a weight value between them. As shown in the equation (161), the matrix Σν and the actual measurement noise covariance are inversely proportional to the Kalman gain coefficient L _k . As Σν decreases, L _k increases, providing a greater weight to the actual measurement y _k . However, the matrix that is the predicted uncertainty

If _k decreases, L _k decreases, and the predicted measurement

Provides a greater weight. Therefore, the Kalman gain factor prefers actual or predicted measurements that depend on a measurement configuration with even less uncertainty.

（予測コンポーネント１０１から）、新しい測定値ｙ_ｋ及び予測された測定値

に基づいて、補正された内的状態ベクター

を演算する。結局、補正コンポーネント１０２の最後の数式において（１６３）式は、上記予測された不確定性または状態‐誤差共分散（ｓｔａｔｅ‐ｅｒｒｏｒ ｃｏｖａｒｉａｎｃｅ）を補正する。（１６３）式において、マトリックスＩは、単位行列を意味する。（１６２）式及び（１６３）式の出力は次の反復のために予測コンポーネント１０１に入力される。さらに具体的に、（１６２）式において上記計算された値

は次の反復のために（１５１）式に交替され、（１６３）式において上記計算された値

は次の反復のために（１５２）式に交替される。それでカルマンフィルターは内的状態とこれと関連した不確定性を反復的に予測し補正する。実際に、Ａ、Ｂ、Ｃ、Ｄ、Σω及びΣνは、各時間段階で変更されることができるということに注目すべきである。 Using this method of assigning weights, equation (162) is used to predict the predicted internal state vector

(From prediction component 101) new measurement y _k and predicted measurement

Corrected internal state vector based on

Is calculated. Eventually, in the last equation of the correction component 102, equation (163) corrects the predicted uncertainty or state-error covariance. In the equation (163), matrix I means a unit matrix. The outputs of equations (162) and (163) are input to the prediction component 101 for the next iteration. More specifically, the value calculated above in equation (162).

Is replaced by (151) for the next iteration, and the value calculated above in (163)

Is replaced by equation (152) for the next iteration. So the Kalman filter iteratively predicts and corrects the internal state and the associated uncertainty. In fact, it should be noted that A, B, C, D, Σω and Σν can be changed at each time step.

Extended Kalman filter (Extended Kalman Filter)
While Kalman filters use linear functions in their models, extended Kalman filters have been developed to model systems with nonlinear functions. Apart from this distinction, the mathematical basis or operation of the extended Kalman filter is essentially the same as the Kalman filter. The extended Kalman filter uses an approximate value model similar to Taylor series that linearizes a function to obtain an estimate. The above linearization is accomplished by taking the basis for two equations in the partial derivatives with current non-linear processes, measurement functions and prediction components.

The extended Kalman filter is operated by the following formula.
_{x k + 1 = f (x} k, u k, w k) (10)
And y _{k + 1} = h (x _k , u _k , v _k ) (11)

In the above equation, the variables w _k and v _k mean process noise and measurement noise, respectively. In equation (10), the non-linear function f associates the state vector x _k at the current stage k with the internal state vector x _{k + 1} at the next time stage k + 1. The function f further includes a driving function u _k and a process noise w _k as parameters. In equation (11), the nonlinear function h associates the internal state vector x _k and the input u _k with the measured value y _k .

  2A and 2B show mathematical formulas of the extended Kalman filter. The operation sequence is the same as that of the Kalman filter. Again, there are two components: a prediction component 201 and a correction component 202. The formula is slightly different. Specifically, the matrices A and C currently have a time-step subscript (sub-script) k in the sense that each time-step changes. This change is necessary because the function is currently non-linear. No further assumption can be made that the matrix is constant as in the case of the Kalman filter. In order to approximate them, a Jacobian matrix is calculated by taking partial derivatives of the functions f and h at each time stage. The Jacobian matrix is listed below.

A is a Jacobian matrix calculated by taking an eccentric function of f with respect to x. That is,

C is a Jacobian matrix calculated by taking a partial derivative of h with respect to x. That is,

  Apart from this additional step of taking the partial derivative of the function, the operation of the extended Kalman filter is essentially the same as the Kalman filter.

Use of the Kalman filter to determine the SOC in the battery The Kalman filter has the advantage that it can work in all forms of battery systems, including dynamic applications such as HEV and EV, because it only needs to measure the battery output. Have There are existing applications that use Kalman filters to determine the SOC of a battery. However, none of them use SOC as the internal state of the model. Therefore, the uncertainty associated with SOC estimation cannot be determined. The above disadvantages are particularly important in HEVs and EVs where an indeterminate range is necessary to prevent power loss of the vehicle or undercharging of the battery. Also, none of the existing methods uses an extended Kalman filter to model the battery SOC nonlinearly.

  It is important to note that the Kalman filter is only treated as a general model. Each application of the Kalman filter still needs to use a good specific battery model and initial parameters that can accurately indicate battery drive to estimate the SOC. For example, in order to measure SOC as an internal state using a Kalman filter, the filter needs to have a specific mathematical formula indicating a method of SOC transition from one time stage to the next stage. The determination of such a formula is important.

Use of the Kalman filter to determine SOH in the battery In addition, it is not possible to directly measure in the technical field of rechargeable battery packs, but it is possible to estimate the quantitative factors that currently indicate the battery pack conditions Is desirable in certain applications. Some of these quantitative factors, such as pack state of charge, that traverse the entire range within minutes can change rapidly and are typically 10 years or more Others such as cell capacity, which can change in as little as 20% range, will change very gradually. Quantitative elements that tend to change rapidly constitute the “state” of the system, and quantitative elements that tend to change slowly constitute the time varying parameters of the system.

  Battery system field, for example, hybrid electric vehicle (HEV), battery electric vehicle (BEV), laptop computer battery, movable equipment battery pack, etc. In particular, information on slowly changing parameters (eg total volume) determines the pack health and includes the SOC calculation, such as those that need to operate as long as possible without affecting It's useful for other operations.

  There are various existing methods for estimating the SOH (State Of Health) of a cell, but these involve estimating two quantitative factors: power degradation and capacity degradation (both slowly varying). The power reduction can be calculated if the current and initial pack electrical resistances are known, and the capacity reduction can be calculated if the total capacity of the current and initial packs is known, for example, although other methods are used.

  Power and capacity decline can usually be expressed in terms of health status. Other information can be inferred using values of variables such as the maximum power available from the pack at a given time. Additional parameters may also be required for specific applications, and individual algorithms will typically be required to know each one.

  The prior art uses the following other approaches to SOH estimation: discharge testing, chemistry-dependent methods, ohmic tests, and partial discharge. The discharge test completely discharges a fully charged cell to determine the overall capacity of the cell. This test disrupts system function and wastes cell energy. The chemical dependent method involves measuring the level of corrosion, electrolyte density of the plate. “Whipping” is used for lead acid batteries. Ohmic testing includes resistance, conductance, impedance testing, but is optionally coordinated with a fuzzy-logic algorithm and / or neural network. Such a method requires invasive measurements. Partial discharge and other methods compare the experimental cell to a good quality cell or a good quality cell model.

  What is needed is a way to continually estimate cell parameters such as cell resistance and capacity. In addition, tests that do not interrupt system functions and do not waste energy, methods that allow general applications (eg, other types of cell electrochemistry, other applications), invasive measurements and very harsh access A method that is not required is needed. What is needed is a way to operate on other configurations of parallel and / or series cells in a battery pack.

Summary of the Invention

  The present invention relates to estimation of values indicative of the current operating conditions of the pack including battery state of charge (SOC) and health (SOH) for battery power applications. The battery can be a primary type or a secondary (rechargeable) type. Furthermore, the present invention can be applied to any battery chemistry field. It addresses issues associated with existing implementations such as high error uncertainty, limited application range (eg, only one battery type) and sensitivity to temperature changes.

  The embodiment of the present invention uses a Kalman filter, a linear algorithm as a battery model having SOC as an internal system state. The embodiment of the present invention uses an extended Kalman filter and a nonlinear algorithm as a battery model having SOC as an internal system state. Having SOC as an internal state allows the present invention to provide uncertainty associated with SOC estimation. Embodiments of the present invention do not take battery temperature as a parameter in SOC estimation. Another embodiment of the invention uses battery temperature as a parameter to adjust the SOC estimate. It is important to maintain the accuracy of the SOC estimation because it is affected by the changing temperature.

  One embodiment allows highly dynamic batteries used in hybrid electric vehicles and electric vehicles that were previously difficult to implement to accommodate different modeling parameters during battery operation. Have a choice.

  Furthermore, the present invention relates to an apparatus and method for estimating parameters of an electrochemical cell, more specifically, for example, a parameter value of a cell.

  A method for estimating a current parameter of an electrochemical cell according to still another aspect of the present invention includes a step of predicting an internal parameter of a cell, a step of predicting uncertainty of prediction of an internal parameter, The estimation of the parameters and the parameter Calculating uncertainty for the prediction.

  An apparatus configured to estimate a current parameter of an electrochemical cell according to yet another aspect of the present invention includes a component configured to perform prediction of the internal parameter of the cell, and a failure to predict the internal parameter. A component configured to perform deterministic prediction, a component configured to correct the internal parameter prediction and the uncertainty prediction, and a internal parameter prediction Repeat the steps performed by the component, the component configured to perform uncertainty prediction and the component configured to correct, to calculate the uncertainty to estimate and the parameter prediction to perform on the parameter And a component configured as described above.

  Further, the system for estimating the current parameters of an electrochemical cell disclosed herein as an example comprises a means for predicting the internal parameters of the cell and a prediction of the uncertainty of the prediction of the internal parameters. A means for performing, a means for correcting the prediction of the internal parameter and a prediction of the uncertainty, a prediction of the internal parameter, a prediction of the uncertainty, and the correction. And applying means for repeating the algorithm to predicting the parameter and calculating uncertainties for the parameter prediction.

  Further disclosed in another embodiment is a storage medium encoded with computer program code recognizable by a machine that includes instructions for causing a computer to perform the above method for estimating current parameters of an electrochemical cell. Is done.

  Furthermore, other embodiments for computer data signals embodied as computer recognizable media are disclosed. The computer data signal includes code configured to cause the computer to perform the method of estimating the current parameters of the electrochemical cell.

  The various features, forms and advantages of the present invention will be more clearly understood through the detailed description of the invention and the appended claims and drawings. In the drawings, the same reference numerals mean the same components.

BEST MODE FOR CARRYING OUT THE INVENTION

Implementation of Battery State of Charge (SOC) Estimation Embodiments of the present invention relate to implementation of a battery SOC estimator for all battery power applications.

  The present invention can be applied to primary or secondary (rechargeable) type batteries, and the present invention can be applied to any battery chemistry field. Embodiments of the present invention operate on hybrid electric transportation means and dynamic batteries used in the electric transportation means, which were difficult to implement before. It has the advantage of providing both SOC estimation and SOC estimation uncertainty. It addresses issues associated with existing implementations such as high error uncertainty, limited application range and sensitivity to temperature changes.

Temperature-Independent Model (Temperature-Independent Model)
FIG. 3A shows the components of the SOC estimator according to one embodiment of the present invention. The battery 301 is connected to the load circuit 305. For example, the load circuit 305 can be an electric transportation means or a motor of a hybrid transportation means. The battery terminal voltage is measured by a voltmeter 302. The battery current is measured by an ammeter 303. The voltage and current measurement values are processed by an arithmetic circuit 304 that estimates the SOC. It should be understood that no means are required to measure from the battery's intrinsic chemical composition.

  It should also be noted that all measurements are non-invasive. That is, no signal that can interfere with the normal operation of the load circuit 305 is introduced into the system.

  The arithmetic circuit 304 uses a mathematical model of the battery including the battery SOC as a model state. In one embodiment of the present invention, a discrete-time model is used, and in another embodiment, a continuous-time model is used.

In one embodiment, the model formula is as follows:
_{xk + 1} = f ( _xk , _ik , _wk ) (12)
And y _{k + 1} = h (x _k , i _k , v _k ) (13)

In the above equation, x _k is the model state at the time index k (x _k can be a scalar quantity or a vector). i _k is the battery current at time index k, and w _k is the disturbance input at time index k. The function f (x _k , i _k , w _k ) associates the model state at the time index k and the model state at the time index k + 1 and can be a linear or nonlinear function. Examples of the present invention has a battery SOC as an element of a model state vector x _k.

In equation (13), the variable v _k is the measurement noise at the time index k, and y _k is the prediction of the battery terminal voltage model at the time index k. The function h (x _k , i _k , w _k ) relates the model state, current and measurement noise to the predicted terminal voltage at time index k. This function can be linear or non-linear. The period that elapses between the time indices may be fixed, although the measurement of the present invention may be omitted from time to time.

Temperature-Dependent Model (Temperature-Dependent Model)
FIG. 3B shows the components of the SOC estimator according to another embodiment of the present invention. The battery 351 is connected to the load circuit 355. For example, the load circuit 355 can be an electric transportation means or a motor of a hybrid transportation means. The battery terminal voltage is measured with a voltmeter 352. The battery current is measured by an ammeter 353. Battery temperature is measured by temperature sensor 356. The measured values of voltage, current, and temperature are processed by an arithmetic circuit 354 that estimates the SOC.

The arithmetic circuit 354 uses a battery temperature-dependent mathematical model including the battery SOC as a model state. In one embodiment of the invention, a discrete time model is used. In other embodiments, a continuous time model is used. In one embodiment, the model formula is as follows:
_{xk + 1} = f ( _xk , _ik , _Tk , _wk ) (14)
And y _{k + 1} = f (x _k , i _k , T _k , v _k ) (15)

In the above equation, x _k is the model state at the time index k (x _k can be a scalar quantity or a vector). T _k is the battery temperature measured at one or more points in the battery pack at time index k, and w _k is the disturbance input at time index k. As a dependent parameter, the use of battery temperature is important to maintain the accuracy of the SOC estimation since it is affected by changing temperature. The function f (x _k , i _k , T _k , w _k ) associates the model state at the time index k with the model state at the time index k + 1 and can be a linear or nonlinear function. Examples of the present invention has a battery SOC as an element of a model state vector x _k.

In equation (15), the variable v _k is the measurement noise at the time index k, and y _k is the prediction of the battery terminal voltage model at the time index k. The function h (x _k , i _k , T _k , w _k ) associates model state, current and measurement noise with the predicted terminal voltage at time index k. This function can be linear or non-linear. The period of time between the time indexes is fixed, although the measurement of the above invention is sometimes omitted.

Application of the above model to the Kalman filter and the extended Kalman filter In one embodiment of the present invention, the mathematical model of the temperature-independent battery of Equations (12) and (13) determines the battery SOC when the system operates. Used as a basis for the Kalman filter to estimate. In this embodiment, the functions f and h are linear. In another embodiment of the present invention, the mathematical model of the temperature-dependent battery of equations (14) and (15) is used as a basis for the Kalman filter to estimate the battery SOC when the system is operating. In this embodiment, the functions f and h are both linear.

  In another embodiment of the invention, the above temperature-independent mathematical model of equations (12) and (13) is used as the basis for the extended Kalman filter. The functions f and h are non-linear in this embodiment. In another embodiment of the invention, the above temperature-dependent mathematical model of equations (14) and (15) is used as the basis for the extended Kalman filter. In this embodiment, both functions f and h are non-linear. Those skilled in the art will recognize that other variations of the Kalman filter can be used, as well as certain Luenberger-like observers.

は、バッテリーの内的状態を示す予測されたベクターを現在示している反面、

は、上記予測された状態‐誤差共分散（不確定性）を現在示している。関数ｆとｈは、（１２）式と（１３）式で示されたものと同様である。補正コンポーネント４０２の（４６２）式における実際の測定項目は現在ｍ_ｋとして表現されると理解すべきである。 Operation of Extended Kalman Filter FIGS. 4A and 4B show an embodiment for an extended Kalman filter. In this example, equations (12) and (13) from the temperature-independent model are used as the basis for the extended Kalman filter. The equations in both prediction and correction components in both drawings have the general form of an extended Kalman filter, as shown in FIG. However, there are some changes in the names of the variables in this embodiment. This difference reflects the variables used for battery SOC measurement and the use of equations (12) and (13).

Is currently showing a predicted vector indicating the internal state of the battery,

Currently shows the predicted state-error covariance (uncertainty). The functions f and h are the same as those shown in the equations (12) and (13). It should be understood that the actual measurement item in equation (462) of the correction component 402 is now expressed as m _k .

5A and 5B show another embodiment for an extended Kalman filter. In this example, equations (14) and (15) from the temperature-dependent model are used as the basis for the extended Kalman filter. All formulas therewith in FIGS. 4A and 4B, are identical except that has (551) and (562) below an additional temperature fields T _k current. Thus, in this embodiment, the battery temperature is used to determine an estimate for each iteration of the extended Kalman filter. Since battery capacity is sometimes affected by temperature, this additional item allows the formula to model the battery more accurately.

の以前推定値（ｐｒｉｏｒ ｅｓｔｉｍａｔｅｓ）に初期化される。

は、（１２）式の関数ｆから由来する反面、

は、（１３）式の関数ｈから由来する。ブロック６００の完了後、

の推定値をもって上記アルゴリズムは拡張カルマンフィルターの補正コンポーネントを開始する。

の推定値は補正コンポーネントによって要求された予測コンポーネントからの出力の役割を果たす。ブロック６０１において、ｘに対する数式ｈの偏道関数が演算され、マトリックスＣを算出する。ブロック６０２においては、カルマンゲイン（Ｋａｌｍａｎ ｇａｉｎ）Ｌ_ｋがマトリックスＣ、

を用いて演算される。これは、図４Ｂにおける補正コンポーネント４０２の一番目の数式（（４６１）式）に対応する。ブロック６０３において、予測された内的状態ベクター、カルマンゲインＬ_ｋと端子電圧の測定値ｍ_ｋは補正された状態ベクター

を計算するのに用いられる。これは、拡張カルマンフィルターにおける補正コンポーネントの二番目の数式に対応する。ブロック６０４においては、上記予測された状態‐誤差共分散

が補正された状態‐誤差共分散

を演算するために用いられる。これは、補正コンポーネントの三番目の数式に対応する。 FIG. 6 illustrates the operation of an extended Kalman filter according to one embodiment of the present invention using a temperature-independent model. In block 600, the algorithm is

Is initialized to prior estimates.

Is derived from the function f in equation (12),

Is derived from the function h in equation (13). After completion of block 600,

The above algorithm starts the correction component of the extended Kalman filter.

The estimated value serves as the output from the prediction component requested by the correction component. In block 601, the eccentric function of equation h with respect to x is calculated to calculate matrix C. In block 602, Kalman gain L _k is matrix C,

Is calculated using. This corresponds to the first mathematical expression (formula (461)) of the correction component 402 in FIG. 4B. In block 603, the predicted internal state vector, the Kalman gain L _k and the terminal voltage measurement m _k are corrected.

Used to calculate This corresponds to the second formula of the correction component in the extended Kalman filter. In block 604, the predicted state-error covariance.

Corrected state-error covariance

Is used to calculate This corresponds to the third formula of the correction component.

が演算される。ブロック６０６において、時間指標ｋは増加し動作はブロック６０１でまた次の時間段階として始まる。 In block 605, all of the prediction component formulas are computed. Matrix A is computed by taking the partial derivative of the function f with respect to x, and the predicted value for the next iteration, i.e.

Is calculated. At block 606, the time index k is incremented and operation begins at block 601 and as the next time step.

の以前推定値に初期化される。

は、（１４）式の関数ｆから由来する反面、

は（１５）式の関数ｈから由来する。ブロック７００の完了後、

の推定値をもって上記アルゴリズムは拡張カルマンフィルターの補正コンポーネントを開始する。

の推定値は補正コンポーネントによって要求された予測コンポーネントからの出力の役割を果たす。ブロック７０１において、ｘに対する数式ｈの偏道関数が演算され、マトリックスＣを算出する。ブロック７０２においては、カルマンゲインＬ_ｋがマトリックスＣ、

を用いて演算される。これは、図５Ｂにおいて補正コンポーネント５０２の一番目の数式（（５６１）式）に対応する。その次にブロック７０３において、予測された内的状態ベクター

およびカルマンゲインＬ_ｋ及び端子電圧の測定値ｍ_ｋが補正された状態ベクター

を計算するのに用いられる。これは、拡張カルマンフィルターで補正コンポーネントの二番目の数式に対応する。ブロック７０４においては、上記予測された状態‐誤差共分散

が補正された状態‐誤差共分散

を演算するために用いられる。これは、補正コンポーネントの三番目の数式に対応する。 FIG. 7 illustrates the operation of an extended Kalman filter according to yet another embodiment of the present invention using a temperature-dependent model. In block 700, the algorithm is

Is initialized to the previous estimate of.

Is derived from the function f in equation (14),

Is derived from the function h in equation (15). After completion of block 700,

The above algorithm starts the correction component of the extended Kalman filter.

The estimated value serves as the output from the prediction component requested by the correction component. In block 701, the deviating function of equation h for x is computed to calculate matrix C. In block 702, the Kalman gain L _k is the matrix C,

Is calculated using. This corresponds to the first formula (formula (561)) of the correction component 502 in FIG. 5B. Then, in block 703, the predicted internal state vector

And a state vector in which the Kalman gain L _k and the measured value m _{k of the} terminal voltage are corrected

Used to calculate This corresponds to the second formula of the correction component in the extended Kalman filter. In block 704, the predicted state-error covariance.

Corrected state-error covariance

Is used to calculate This corresponds to the third formula of the correction component.

が演算される。ブロック７０６において、時間指標ｋは増加し動作はブロック７０１でまた次の時間段階として始まる。 At block 705, all of the prediction component formulas are computed. Matrix A is computed by taking the partial derivative of the function f with respect to x, and the predicted value for the next iteration, i.e.

Is calculated. At block 706, the time index k is incremented and operation begins at block 701 and as the next time step.

は、バッテリーの内的状態を示す予測されたベクターを現在示している反面、

は、上記予測された状態‐誤差共分散（不確定性）を現在示している。補正コンポーネント８０２の（８６２）式における実際の測定項目は現在ｍ_ｋに表現されると理解すべきである。 Operation of Kalman Filter FIGS. 8A and 8B show an embodiment for the Kalman filter. Equations (12) and (13) from the temperature-independent model are used as the basis for the Kalman filter. In another embodiment, equations (14) and (15) from the temperature-dependent model are used. In the drawings, the equations in both the prediction component and the correction component have a general form of an extended Kalman filter as shown in FIG. However, there are some changes in the names of the variables in this embodiment. In one embodiment, the difference reflects the use of the variables used to measure the battery SOC, equations (12) and (13). In another embodiment, the difference reflects the use of variables (14) and (15) used for battery SOC measurement.

Is currently showing a predicted vector indicating the internal state of the battery,

Currently shows the predicted state-error covariance (uncertainty). It should be understood that the actual measurement item in equation (862) of the correction component 802 is now expressed in m _k .

の以前推定値に初期化される。一つの実施例において、

は（１２）式の関数ｆから由来する反面、

は（１３）式の関数ｈから由来する。この実施例は、温度‐独立的である。他の実施例において、

は、（１４）式の関数ｆから由来する反面、

は、（１５）式の関数ｈから由来する。この実施例は、温度‐従属的である。ブロック９００の完了後、

の推定値をもって上記アルゴリズムは拡張カルマンフィルターの補正コンポーネントを開始する。

の推定値は補正コンポーネントによって要求された予測コンポーネントからの出力の役割を果たす。ブロック９０１において、カルマンゲインＬ_ｋがマトリックスＣ、

を用いて演算される。これは、図８Ｂにおいて、補正コンポーネント８０２の一番目の数式（（８６１）式）に対応する。それから、ブロック９０２において、予測された内的状態ベクター

およびカルマンゲインＬ_ｋ及び端子電圧の測定値ｍ_ｋが補正された状態ベクター

を計算するのに用いられる。これは、拡張カルマンフィルターで補正コンポーネントの二番目の数式に対応する。ブロック９０３においては、上記予測された状態‐誤差共分散

が補正された状態‐誤差共分散

を演算するために用いられる。これは、補正コンポーネントの三番目の数式に対応する。ブロック９０４において、上記予測コンポーネントの両数式が演算される。次の反復のための予測値、すなわち、

が演算される。ブロック９０５において、時間指標ｋは増加し動作はブロック９０１でまた次の時間段階として始まる。 FIG. 9 illustrates the operation of the Kalman filter according to an embodiment of the present invention. In block 900, the algorithm is

Is initialized to the previous estimate of. In one embodiment,

Is derived from the function f in equation (12),

Is derived from the function h in equation (13). This example is temperature-independent. In other embodiments,

Is derived from the function f in equation (14),

Is derived from the function h in the equation (15). This embodiment is temperature-dependent. After completion of block 900,

The above algorithm starts the correction component of the extended Kalman filter.

The estimated value serves as the output from the prediction component requested by the correction component. In block 901, the Kalman gain L _k is the matrix C,

Is calculated using. This corresponds to the first mathematical expression (formula (861)) of the correction component 802 in FIG. 8B. Then, in block 902, the predicted internal state vector

And a state vector in which the Kalman gain L _k and the measured value m _{k of the} terminal voltage are corrected

Used to calculate This corresponds to the second formula of the correction component in the extended Kalman filter. In block 903, the predicted state-error covariance

Corrected state-error covariance

Is used to calculate This corresponds to the third formula of the correction component. At block 904, both equations for the prediction component are computed. The predicted value for the next iteration, i.e.

Is calculated. At block 905, the time index k is incremented and operation begins at block 901 and as the next time step.

Specific Formula In one embodiment, the following specific form for function f is used. The internal state vector x _k is

And the governing equation for each state is

The battery SOC is the first element of the state vector. The above variables are defined as follows: I _k is the instantaneous current, Δt is the instantaneous time interval, and C _p (temp...) Is the temperature-dependent battery “poicart” capacity (“Peukert”) "Capacity), and n is the Poicart exponent associated with the poi cart. The capacity and η (I _k ) are the coulomb efficiency of the battery as a function of current. The state variables FILT and IF are filter states that capture most of the dynamic state of flat and slow batteries.

In one embodiment, the following specific form for function h is used.

In the above formula, y _k is a terminal voltage. All other variables (k ₀ , k _1, etc.) are model coefficients, can be a priori determined from laboratory tests, using mechanisms not discussed here Can be adjusted during system operation. Such a coefficient varies in the present invention such that a coefficient used for an instantaneous discharge of 10 Amps is different from a coefficient used for an instantaneous charge of 5 Amps. This allows the present invention to model the current-dependency of the model more accurately.

In another embodiment, the following form of function f is used. The internal state vector x _k is

Where SOC _k is the current SOC estimate, SOC _k−1 is the previous SOC estimate (etc.), i _k is the current current measurement (etc.), y _k−1 Is the previous battery voltage estimate. α, β, γ are positive constants and are chosen to create an acceptable model with the state variable's persimmon number. The governing equation for the SOC state is as follows.

In the above embodiment, a specific form of the function h is used.
y _k = h (x _k , T _k )

  In the above formula, h is embodied as a non-linear function that matches the measured data. For example, h can be implemented using a neural network.

  In one embodiment, the neural network can be used to estimate the internal state of the battery. The difference between this embodiment and a conventional neural network is as follows. The SOC estimated in the conventional neural network is the output of the neural network. This embodiment measures SOC indirectly by first modeling of the battery cell with a neural network having SOC as one of the states. Thereafter, a Kalman filter is used with a neural network to estimate the SOC. Such an approach has two main advantages. First, it can be trained online during operation, and second, error bounds for the estimation can be computed.

Changing Parameters FIG. 10 illustrates the operation of one embodiment of the present invention that dynamically changes the modeling formula for the battery SOC. In this embodiment, the arithmetic circuit can adapt the changing behavior of the battery using different parameters for different time intervals. In block 1000, a change in battery current level is sensed. For example, in a hybrid electric vehicle, a sudden drain of battery power is triggered by the vehicle being uphill. The above sudden change with the situation triggers the arithmetic circuit to use a different set of modeling formulas to more accurately estimate the SOC under new conditions. At block 1010, a new set of modeling formulas is used. At block 1020, the new formula is used to determine the SOC. This adaptive modeling behavior is useful in highly dynamic applications such as hybrid electric vehicles and electric vehicles.

  Further, various embodiments for methods, systems and apparatus for estimating electrochemical cell parameters using filtering are disclosed herein. Referring to FIGS. 11 and 12, the following drawings, a number of specific details, are used to further understand the present invention. Although exemplary embodiments have been described with reference to battery cells, various electrochemical cells, referred to below as cells, include batteries, battery packs, ultra-high capacity capacitors, capacitor banks, fuel cells, electrolysis It should be understood that not only batteries but also combinations including at least one of those described above can be used without limitation. Further, it should be understood that a battery or battery pack can include a plurality of cells, and the exemplary embodiments disclosed herein are applicable to the plurality of one or more cells.

  One or more exemplary embodiments of the present invention estimate cell parameter values using a filtering method. One or more exemplary embodiments of the present invention estimate cell parameter values using Kalman filtering. Some embodiments of the present invention estimate cell parameter values using extended Kalman filtering. One embodiment estimates the overall capacity of the cell. Some embodiments estimate other time-varying parameter values. Although the term filtering is employed for the description and illustration of the exemplary embodiment, the terminology is a recursive prediction that is generally expressed as filtering, including without limitation Kalman filtering and / or extended Kalman filtering. It should be understood that it is intended to include a methodology for amendments.

Implementation of Battery State of Health (SOH) Estimation FIG. 11 illustrates components of a parameter estimator system 10 according to one embodiment of the present invention. An electrochemical cell pack 20 (for example, a battery) including a plurality of cells 22 is connected to a load circuit 30. For example, the load circuit 30 can be an electric transportation means or a motor of a hybrid transportation means. An apparatus for measuring various cell characteristics and attributes is provided at reference numeral 40. The measuring device 40 can include a device for measuring a cell terminal voltage such as a voltage sensor 42 (for example, a voltmeter) without limitation. On the other hand, the cell current is measured by a current sensing device 44 (for example, an ammeter). Optionally, the temperature of the cell is measured by a temperature sensor 46 (eg, a thermometer). Additional cell characteristics such as internal pressure or impedance can be measured, for example, with the pressure sensor and / or impedance sensor 48 and can be employed for the selected cell type. Various sensors necessary for evaluating cell characteristics and attributes can be employed. Voltage, current, and optionally temperature and cell-attribute measurements are made by the arithmetic circuit 50 (eg, processor, computer), which estimates cell state and parameters. The system may include a storage medium 52 including a computer usable storage medium known to those having ordinary skill in the art to which the present invention pertains. The storage medium is in a state where it can communicate with the arithmetic circuit 50 by employing various means including the radio signal 54 without limitation. It should be understood that any means for measurement from the underlying chemical components of the cell 12 can be used in the present invention, but is not essential. All measurements are also non-invasive. In other words, it should be understood that no signals that can interfere with the normal operation of the load circuit 30 are introduced into the system.

  In order to perform the above defined functions and desirable processing and operations, the arithmetic circuit 50 includes a processor, a gate array, custom logic, a computer, a memory, a storage medium, a register, a timing, an interrupt, a communication interface, and an input / output signal interface. And the combination which consists of at least 1 or more mentioned above can be included without a restriction | limiting. Arithmetic circuit 50 can include input and input signal filtering to perform signal acquisition, conversion, and accurate sampling from the communication interface and input d. Additional features and processor of the arithmetic circuit 50 will be described later.

  One or more embodiments of the present invention may be implemented by newly updated firmware and software executed by the arithmetic circuit 50 and / or other processing control means. The software function includes firmware without limitation, and can be implemented by hardware, software, or a combination thereof. Thus, a significant advantage of the present invention is that it can be realized by utilizing current and / or new processing systems for charging and controlling electrochemical cells.

In the exemplary embodiment, arithmetic circuit 50 employs a mathematical model of cell 22 that includes dynamic system state indicators. In one embodiment of the invention, a discrete time model is used. An exemplary model (preferably non-linear) in discrete time state space has the following form:

In the above equation, _{x k} is the state of the system, θ _k is, a set of time-varying model parameters, _{u k} is input from the outside, _{y k,} the output of the system, _{w k} and _{v k} is, "noise" Input. All quantitative elements can be scalars or vectors. f (.,.,.) and g (.,.,.) are functions defined by the model used. Non-time-varying numerical values required by the model can be incorporated in f (•, •, •) and g (•, •, •) but are not included in θ _k .

The system state x _k contains a minimal amount of information along with at least the mathematical model of the cell and the current input needed to predict the current output. In the case of cell 22, the state (eg, SOC) includes a polarization voltage level and a hysteresis level for different time constants. The input u _k from outside the system includes the minimum value of the current cell current i _k and can optionally include the cell temperature (if the temperature change itself is not modeled in the state). The system parameter θ _k is a value that varies slowly over time in that it cannot be determined directly by knowing the system measured inputs and outputs. Such things include cell capacity, resistance, polarization voltage time constant, polarization voltage harmonic factor, hysteresis harmonic factor, hysteresis rate constant, efficiency factor, and the like. The model output y _k corresponds to a physically measurable quantitative element of the cell or one that can be calculated directly from the quantitative element measured at the minimum value (eg load cell voltage).

  There are many existing methods for estimating the state of a cell that includes without limitation the state of charge of the cell 22. The SOC is typically a percentage value and refers to the portion of the cell capacity that is currently operational. Many approaches have been employed to measure the SOC. Discharge test, ampere-hour-counting (coulomb counting), electrolyte measurement, open circuit voltage measurement, linear / nonlinear circuit modeling, impedance spectrometer, internal resistance measurement, Cup de fouet and some of Kalman filtering This form corresponds to this. Each such method has advantages as well as limitations.

  According to the above embodiment of the present invention relating to the implementation of the battery state (SOC) estimator, the filter, preferably the Kalman filter, is used by adopting a known mathematical model of cell dynamics and cell voltage, current and temperature measurement. It is done. Preferably, the method directly estimates the state value for the cell when the SOC is at least one of the above states. However, it should be understood that there are a variety of known methodologies for computing SOC.

In FIG. 12, a mathematical model of dynamic parameters is also utilized. An exemplary model has the following form:

One th equation, parameter is essentially the constant shows that slow variations can over time in the example modeled by a pseudo noise process displayed in r _k. The output value d _k is a function of the optimal dynamic parameter modeled by g (,) taking into account the estimation error e _k , which is the system state x _k , the external input u _k and a series of time-varying parameters θk. Is a function of

で表されるパラメーターの推定値を実際（ｔｒｕｅ）パラメーターの最上の推測値（ｔｈｅ ｂｅｓｔ ｇｕｅｓｓ）、例えば、

に設定することで初期化される。状態推定が要求されるか定義されないが、

で表される上記状態推定値はセル状態の最上の推定値、例えば、

に設定され得る。推定‐誤差共分散マトリックス

も初期化される。例えば、状態、特にＳＯＣの初期化は、ルックアップテーブルにおけるセル電圧またはバッテリーパック／セルが最後に電力ダウンされたときに以前に貯蔵された情報に基づくか／推定され得る。他の例は電力ダウンなどからバッテリーシステムが休止された（ｒｅｓｔｅｄ）時間の長さを統合することができる。 In one embodiment, the filtering process is applied to a model of the cell system, dynamic state requirements and defined dynamic parameters. Once again, alternatively, a dual Kalman filter or a dual extended Kalman filter can be employed. Table 1 illustrates an exemplary implementation of a system and method that utilizes an extended Kalman filter 1100. Although estimation model of the cell model and parameters employing the state x _k of the cell 22, the state is to be understood once again need not be always predicted as part of the process of estimating parameters. For example, in one exemplary embodiment, the state x _k of the cell 22 is computed by other processes with the resulting state information supplied to the parameter model. Following the exemplary implementation of Table 1, the above process is

An estimate of the parameter represented by the the best guess of the true parameter, eg,

It is initialized by setting to. Although state estimation is required or not defined,

The state estimate represented by is the best estimate of the cell state, for example,

Can be set to Estimation-error covariance matrix

Is also initialized. For example, the initialization of the state, particularly the SOC, may be based / estimated based on the cell voltage in the lookup table or information previously stored when the battery pack / cell was last powered down. Another example may integrate the length of time that the battery system was rested, such as from power down.

Table 1: Extended Kalman filter for parameter update

であり、パラメーター誤差不確定性は時間の流れ（駆動ノイズｒ_ｋによりモデルに適応された）のためより大きい。パラメーター不確定性の推定のアップデートに対する多くの可能性が存在し、上記テーブルは説明的な例を提供する。セル出力の測定がなされ、状態推定値

（推定されるか提供され得るが）とパラメーターの推定値

に基づいて上記予測された出力値と比較される。この差は

の値をアップデートするのに用いられる。また、状態推定値

は、パラメーターの推定値によって前に進むか上述のように外部手段を介して供給されることもできる。

は、下記の循環関係を用いて演算され得る。

In this example, various stages are performed at each measurement interval. First, the previous parameter estimate advances in time. The new parameter estimate is identical to the previous parameter estimate, i.e.

, And the larger because of a parameter error uncertainty time flow (adapted to the model by driving noise r _k). There are many possibilities for updating parameter uncertainty estimates, and the above table provides an illustrative example. Cell output is measured and state estimate

Parameter estimates (although they can be estimated or provided)

Based on the predicted output value. This difference is

Used to update the value of. In addition, state estimate

Can be advanced by parameter estimates or supplied via external means as described above.

Can be computed using the following circular relationship:

The differential calculation is essentially recursive and evolves over time as the state x _k is expanded. If the side information does not calculate a better estimate of that value, the dx ₀ / dθ term is initialized to zero. It should be understood that the steps shown in the table can be performed in various orders. Although the above table lists an exemplary order for illustrative purposes, one of ordinary skill in the art will be able to ascertain many equivalent sequences of formulas.

を適応させる。上記フィルターは、時間アップデートまたは予測１１００の側面と測定アップデートまたは補正１１０４の側面を有する。パラメーター時間アップデート／予測ブロック１１０３は、入力として以前の外部入力ｕ_ｋ−１、以前の時変パラメーター予測値

及び補正されたパラメーター不確定性の推定値

を受信する。パラメーター時間アップデート／予測ブロック１１０３は、予測されたパラメーター

と予測されたパラメーター不確定性

をパラメーター測定アップデート／補正ブロック１１０４に出力する。 Referring also to FIG. 12, an exemplary implementation of an exemplary embodiment of the present invention is shown. The recursive filter 1100 is an estimate of the above parameters

Adapt. The filter has a time update or prediction 1100 aspect and a measurement update or correction 1104 aspect. The parameter time update / prediction block 1103 has the previous external input u _k−1 as input, the previous time-varying parameter predicted value

And corrected parameter uncertainty estimates

Receive. The parameter time update / prediction block 1103 is a predicted parameter

Predicted parameter uncertainty

Is output to the parameter measurement update / correction block 1104.

とパラメーター不確定性推定値

を提供するパラメーター測定アップデート／補正ブロック１１０４は、上記予測されたパラメーター

と予測されたパラメーター不確定性

のみならず外部入力ｕ_ｋとモデリングされたシステム出力ｙ_ｋを受信する。マイナス表記はベクターが上記フィルター１１００の上記予測コンポーネント１１０３の結果であることを意味する反面、プラス表記はベクターが上記フィルター１１００の上記補正コンポーネント１１０４の結果であることを意味すると理解すべきである。 Current parameter estimate

And parameter uncertainty estimates

The parameter measurement update / correction block 1104 providing the predicted parameter

Predicted parameter uncertainty

As well as the external input u _k and the modeled system output y _k . A minus notation means that the vector is the result of the prediction component 1103 of the filter 1100, while a plus notation means that the vector is the result of the correction component 1104 of the filter 1100.

Embodiments of the present invention require a mathematical model of cell state and dynamic output for specific applications. In the above embodiment, this is accomplished by defining specific functions for f (,,) and g (,,) to facilitate the reception or estimation of various states and estimates of many parameters of interest. it can. One embodiment uses a cell model that includes the effects of one or more of an open circuit voltage (OCV), internal resistance, voltage polarization time constant, and hysteresis level of the cell. Although this structure and the method presented here are general and applicable to other electrochemistry, for illustrative purposes, the parameter values are the same for modeling the dynamics of a high power LiPB (Lithium-ion Polymer Battery) cell. Adapted to the model structure. For example, in one embodiment, the state and parameter of interest are contained in f (,,) and g (,,). An example is as follows.

は分極電圧時定数、

は、分極電圧調和ファクター、
Ｒ_ｋは、セルの抵抗、
Ｍ_ｋは、ヒステリシス調和ファクター及び
ｒ_ｋは、ヒステリシス率定数である。 Where η _{i, k} is an efficiency factor such as Coulomb efficiency,
C _k is the cell capacity,

Is the polarization voltage time constant,

Is the polarization voltage harmonic factor,
R _k is the cell resistance,
M _k is the hysteresis conditioning factor and r _k are hysteresis rate constant.

In this example, the SOC is obtained by one state of the model as part of the function f (.,.,.). This formula is as follows.

Where Δt means the period (in seconds) between samples, C _k indicates the cell capacity (in ampere-seconds), Z _k is the cell SOC at time index k, and i _k is , Cell current, and η _{i, k} is the Coulomb efficiency of the cell at current level i _k .

In this example, the polarization voltage level is obtained by a number of filter states. Assuming there is a n _f polarization voltage time constants,

は、実数値（ｒｅａｌ‐ｖａｌｕｅｄ）分極電圧時定数

を有した単位行列であり得る。そうであれば、全てのエントリーが１より小さい値を持てばシステムは安定的である。上記ベクター

は、単にｎ_ｆ「１」に決めることができる。Ｂ_ｆのエントリーは、それらが０でない限り臨界的ではない。Ａ_ｆマトリックスでｎ_ｆエントリー値は、モデルパラメーターを測定されたセルデータに最も合わせるシステムの同定過程の一部として選択できる。上記Ａ_ｆとＢ_ｆマトリックスは、時間と現在のバッテリーパック動作条件に関連した他のファクターによって変わり得る。 Matrix above

Is the real-valued polarization voltage time constant

Can be a unit matrix. If so, the system is stable if all entries have a value less than one. The above vector

Can simply be determined to be n _f “1”. Entries in _Bf are not critical unless they are zero. The n _f entry values in the A _f matrix can be selected as part of the system identification process that best fits the model parameters to the measured cell data. The A _f and B _f matrices may vary depending on time and other factors related to current battery pack operating conditions.

In this example, the hysteresis level is obtained by a single state.

In the above formula, r _k is the hysteresis rate constant determined again by system identification.

In other embodiments, the overall model state is a combination of the above examples as follows.

  In the above formula, other orders of states are possible.

In this example, the output formula combining the state values that predict the cell voltage is as follows:

は、出力において上記分極電圧状態をともに調和させる分極電圧調和ファクター

のベクターであり、Ｒ_ｋは、セルの抵抗である（他の値は放電／充電に用いることができる）。そして、Ｍ_ｋは、ヒステリシス調和ファクターである。Ｇ_ｋは、ｉ_ｋからＧ_ｋｆ_ｋまでのｄｃゲインが０になるように強制されることができ、これはＲ_ｋの推定値が正確になるようにする。 In the above formula,

Is a polarization voltage harmony factor that harmonizes the polarization voltage states together in the output

Where R _k is the resistance of the cell (other values can be used for discharging / charging). M _k is a hysteresis harmonic factor. G _k can be forced so that the dc gain from i _k to G _k f _k is zero, which _{ensures that} the estimate of R _k is accurate.

は、実数値分極電圧時定数

を有した単位行列である）において分極電圧時定数に対する項を含むことができる。このような時定数は、ａ_ｉ，k＝ｔａｎｈ（α_ｉ，k）により演算することができ、上記数式において、上記モデルのパラメーターベクターはα_ｉ，kを含むが直接的にａ_ｉ，kを含まない。上記ｔａｎｈ（ ）関数はａ_ｉ，kがα_ｉ，kの値に関係なく常に±１以内（すなわち、安定的）になるように保障する。 Certain embodiments of the invention can include a method for forcing the parameters of the model to be a stable system. In one embodiment, the state equation is of the form f _{k + 1} = A _f f _k + B _f i _k where the matrix,

Is the real-valued polarization voltage time constant

A unit matrix with a term for the polarization voltage time constant. Such a time constant can be calculated by a _{i, k} = tanh (α _{i, k} ). In the above formula, the parameter vector of the model includes α _{i, k} , but directly a _{i, k} Not included. The tanh () function ensures that a _{i, k} is always within ± 1 (ie, stable) regardless of the value of α _{i, k} .

を用いてＧ_ｋの最後の要素が演算されるように強制することでなされる。これはまた

に関わる

の要素を演算する場合、さらに注意が必要である。もしａ_ｉ，k値が常に±１以内（例えば、以前の段落に記述された方法を用いて）なら、微分演算で０で除される問題は絶対に生じない。 Certain embodiments of the invention include constraints on the model to ensure convergence of the parameter to its exact value. One embodiment using the model shown here forces G _k such that the dc gain from i _k to G _k f _k is zero, which _{ensures that} the estimate of R _k is accurate. This is the other factor of G _k and the polarization voltage time constant

Is used to force the last element of G _k to be computed. This is also

Involved in

Further care must be taken when computing the elements of. If a _{i, k} values are always within ± 1 (eg, using the method described in the previous paragraph), the problem of being divided by zero in the differential operation never occurs.

  Another embodiment includes a method for estimating important aspects of SOH without employing a full filter 1100. The full filter 1100 method is computationally intensive. Other methods that are potentially less complex or less computationally intensive can be used unless exact values for the full set of cell model parameters are required. An exemplary method uses a filtering method to determine cell capacity and resistance. The change in capacity and resistance from the nominal “new cell” value provides capacity and power reduction, which is the most commonly used indicator for cell SOH.

In this example, the model is formulated as follows to estimate cell resistance using a filtering mechanism.

In the above equation, R _k is the cell resistance and is modeled as a constant along with a pseudo noise process r _k that allows modification. y _k is an estimate of the cell voltage, i _k models the cell current, and e _k models the estimation error. If an estimate of _Zk generated and supplied externally is employed, filter 1100 can be applied to this model to estimate cell resistance. In the standard filter 110, the model prediction of y _k is compared with the actually measured cell voltage. Any difference generated by the comparator is also used similar adapt the R _k.

It should be noted that the model mentioned above can be extended to handle different resistance values for various conditions of the cell 22 (eg, differences based on charge and discharge, different SOCs, different temperatures). The scalar R _k can consist of a vector containing all the resistance values to be modified, and the appropriate elements from the vector can be used at each time step of the filter during the calculation process.

In this example, in order to estimate the cell capacity using the filter 1100, the cell model is formulated as follows:

  Also, a filter is formulated that uses this model to calculate the capacity estimate. As the filter 1100 is applied, the operation of the second equation is compared to 0, and the difference is used to update the capacity estimate. It should be noted that a good quality estimation of the current and previous SOC is required from the filter that estimates the SOC if possible. The estimated capacity can be made a function such as temperature by adopting a capacity vector, if desired, and appropriate elements are used at each time step during the calculation process from the capacity vector.

  Thus, a method for cell parameter estimation has been described with many specific examples. One or more embodiments use a Kalman filter. One embodiment uses an extended Kalman filter 1100. Further, some embodiments include a mechanism that enforces convergence of one or more parameters. One or more embodiments include a simplified parameter filter to estimate resistance, while some embodiments include a simplified parameter filter to estimate overall capacity. The present invention is applicable to a wide range of applications and cell electrochemistry.

  The disclosed method can be embodied in the form of a computer-implemented process or an apparatus for performing the process. The above method can also be realized in the form of computer program code, including instruction words, embodied / shaped in a tangible medium 52 such as a floppy disk, CD-ROM, hard disk or computer readable storage medium. Here, the computer program code is loaded into a computer and executed by the computer, and the computer becomes an apparatus capable of executing the method. The method may be in the form of a computer program, eg, stored in a storage medium, loaded and / or executed by a computer, modulated carrier wave, transmission medium, electrical wiring or cable, optical fiber, electromagnetic It can also be realized in the form of a data signal 54 transmitted in the form of radiation or the like. Here, the computer program code is loaded into the computer and executed by the computer. When implemented on a general-purpose microprocessor, the computer program code segments are configured such that the microprocessor creates specific logic circuits.

  The use of the first, second or other similar names to indicate similar configurations should not be intended to imply or include a particular order unless otherwise noted.

  Although the present invention has been described with reference to one embodiment, it is within the technical field to which the present invention pertains that equivalent components can be substituted and various changes can be made without departing from the scope of the present invention. The merchant will understand. In addition, many modifications may be made to the particular situation and content of the teachings of the invention without departing from the essential scope thereof. Accordingly, the present invention is not limited to the specific embodiment disclosed as the most preferred embodiment contemplated for practicing the invention, but includes all embodiments that fall within the scope of the appended claims.

FIG. 1 is a diagram illustrating the operation of a general Kalman filter. FIG. 1A is a diagram illustrating a mathematical expression of a prediction component of a general Kalman filter. FIG. 1B is a diagram illustrating mathematical expressions of a correction component of a general Kalman filter. FIG. 2A is a diagram illustrating a mathematical expression of a prediction component of a general extended Kalman filter. FIG. 2B is a diagram illustrating a mathematical expression of a correction component of a general extended Kalman filter. FIG. 3A is a diagram illustrating components of an SOC estimator according to an embodiment of the present invention. FIG. 3B is a diagram illustrating components of an SOC estimator according to still another embodiment of the present invention. FIG. 4A is a diagram illustrating a mathematical expression of a prediction component of an extended Kalman filter implemented according to an embodiment of the present invention. FIG. 4B is a diagram illustrating a mathematical expression of a correction component of an extended Kalman filter implemented according to an embodiment of the present invention. FIG. 5A is a diagram illustrating a mathematical expression of a prediction component of an extended Kalman filter implemented according to still another embodiment of the present invention. FIG. 5B is a diagram illustrating a mathematical expression of a correction component of an extended Kalman filter implemented according to still another embodiment of the present invention. FIG. 6 is a diagram illustrating an operation of the extended Kalman filter according to an embodiment of the present invention. FIG. 7 is a diagram illustrating an operation of an extended Kalman filter according to another embodiment of the present invention. FIG. 8A illustrates a mathematical expression of a prediction component of a Kalman filter implemented according to an embodiment of the present invention. FIG. 8B illustrates a mathematical expression of a Kalman filter correction component implemented according to an embodiment of the present invention. FIG. 9 is a diagram illustrating an operation of a Kalman filter implemented according to an embodiment of the present invention. FIG. 10 is a diagram illustrating the operation of an embodiment of the present invention that dynamically changes the modeling formula for the battery SOC. FIG. 11 is a block diagram illustrating an exemplary system for parameter estimation according to one embodiment of the present invention. FIG. 12 is a block diagram illustrating a filtering method for parameter estimation according to an embodiment of the present invention.

Claims (40)

Estimating SOC in a battery in which SOC (State Of Charge) constitutes one of internal states;
Estimating SOH in a battery in which SOH (State Of Health) constitutes one of the internal parameters;
A method for estimating a value indicative of a current operating condition of a battery, comprising: The step of estimating the SOC in the battery includes
Predicting the internal state of the battery in which the SOC is one of the internal states;
Predicting the uncertainty of the internal state prediction,
Correcting the internal state prediction and the uncertainty prediction;
Applying an algorithm that repeats the step of predicting the internal state, the step of predicting the uncertainty, and the step of correcting, and calculating the estimation performed on the SOC and the uncertainty relative to the SOC estimation And the stage of
The method of estimating a value indicative of a current operating condition of the battery according to claim 1, comprising: The stage of predicting the internal state is as follows:
Determining a current measurement;
Determining a voltage measurement; and
Predicting the internal state using the current measurement and the voltage measurement in a mathematical model;
The method for estimating a value indicating a current operating condition of the battery according to claim 2, comprising: The stage of predicting uncertainty is
4. The method for estimating a value indicating a current operating condition of a battery according to claim 3, further comprising the step of predicting the uncertainty using the current measurement value and the voltage measurement value in a mathematical model. . The correction step is as follows:
Calculating a gain factor;
Calculating an internal state prediction corrected using the gain factor, the voltage measurement, and the internal state prediction;
Computing an uncertainty prediction corrected using the gain factor and the uncertainty prediction;
The method of estimating a value indicating a current operating condition of the battery according to claim 4, comprising: The application step is
6. The method of claim 5, comprising using the corrected internal state prediction and the corrected uncertainty prediction to obtain a prediction for the next time step in which the algorithm is repeated again. A method for estimating a value indicating a current operating condition of the battery described in 1. The above algorithm is
The method of estimating a value indicating a current operating condition of the battery according to claim 6, wherein the value is a Kalman filter. The above algorithm is
The method of estimating a value indicating a current operating condition of the battery according to claim 6, wherein the value is an extended Kalman filter. The stage of predicting the internal state is as follows:
The method of claim 8, further comprising using another mathematical model for prediction based on changing battery conditions. The stage of predicting uncertainty is
The method of claim 8, further comprising using another mathematical model for prediction based on changing battery conditions. The stage of predicting the internal state is as follows:
Determining the temperature; and
A mathematical model for predicting the internal state using the temperature measurement, the current measurement and the voltage measurement;
The method of estimating a value indicative of a current operating condition of the battery according to claim 3, further comprising: The stage of predicting uncertainty is
The battery operating condition according to claim 11, wherein the mathematical model includes a step of predicting the uncertainty using the temperature measurement value, the current measurement value, and the voltage measurement value. A method for estimating the indicated value. A component configured to estimate an SOC in a battery for which the SOC constitutes one of the internal states;
A component configured to estimate SOH in a battery where SOH constitutes one of the internal parameters;
A device for estimating a value indicating a current operating condition of a battery including The component configured to estimate the SOC in the battery is:
A component configured to predict an internal state of the battery in which the SOC is one of the internal states;
A component configured to predict uncertainty of the internal state prediction;
A component configured to correct the internal state prediction and the uncertainty prediction;
Apply to the SOC by applying a component configured to predict the internal state, a component configured to predict the uncertainty, and an algorithm that repeats the correction step A component configured to calculate an uncertainty for the estimate and the SOC estimate;
The apparatus for estimating a value indicating a current operating condition of the battery according to claim 13. The component configured to perform the internal state prediction is
A component configured to determine a current measurement;
A component configured to determine a voltage measurement;
A component configured to predict the internal state using the current measurement and the voltage measurement in a mathematical model;
The apparatus for estimating a value indicating a current operating condition of the battery according to claim 14, comprising: The components configured to correct above are:
A component configured to compute a gain factor;
A component configured to compute a predicted internal state corrected using the gain factor, the voltage measurement, and the internal state prediction;
A component configured to compute an uncertainty prediction corrected using the gain factor and the uncertainty prediction;
The apparatus for estimating a value indicating a current operating condition of the battery according to claim 15, comprising: The component configured to perform the internal state prediction is
A component configured to determine a temperature measurement; and
A mathematical model that predicts the internal state using the temperature measurement, the current measurement, and the voltage measurement;
The apparatus for estimating a value indicating a current operating condition of the battery according to claim 15, further comprising: Predicting the internal parameters of the cell;
Predicting the uncertainty of the internal parameter prediction,
Correcting the internal parameter prediction and the uncertainty prediction;
Applying an algorithm that repeats the step of predicting the internal parameter, the step of predicting the uncertainty, and the step of correcting the above, the uncertainty for the parameter estimation and parameter prediction is applied. Calculating the stage;
A method for estimating a current parameter of an electrochemical cell system comprising: The stage of predicting the internal parameters is as follows:
Receiving a state estimate; and
Determining a current measurement;
Determining a voltage measurement; and
Predicting the internal parameter using the mathematical model with the state estimate, the current measurement, and the voltage measurement;
The method of estimating a current parameter of an electrochemical cell system according to claim 18, comprising: The stage of predicting uncertainty is
The current model of the electrochemical cell system according to claim 19, wherein the mathematical model includes a step of predicting the uncertainty by using the state estimation value, the current measurement value, and the voltage measurement value. How to estimate parameters. The correction step is as follows:
Calculating a gain factor;
Calculating a corrected internal parameter prediction using the gain factor, the voltage measurement, and the internal parameter prediction;
Computing an uncertainty prediction corrected using the gain factor and the uncertainty prediction;
21. A method for estimating a current parameter of an electrochemical cell system according to claim 20, comprising: The application step is
The method of claim 21, comprising obtaining a prediction for a next time step in which the algorithm is repeated using the corrected internal parameter prediction and the corrected uncertainty prediction. Method for estimating the current parameters of the described electrochemical cell system. The above algorithm is
The method for estimating a current parameter of an electrochemical cell system according to claim 22, wherein the current parameter is at least one of a Kalman filter and an extended Kalman filter. The internal parameters are
The current parameter of the electrochemical cell system according to claim 23, comprising at least one of resistance, capacity, polarization voltage time constant, polarization voltage harmonic constant, hysteresis harmonic factor, hysteresis rate constant, and efficiency factor. How to estimate. The stage of predicting uncertainty is
Receiving a state estimate; and
Determining a current measurement;
Determining a voltage measurement; and
A mathematical model for predicting the uncertainty using the state estimate, the current measurement, and the voltage measurement;
The method of estimating a current parameter of an electrochemical cell system according to claim 18, comprising: The stage of predicting uncertainty is
Further comprising determining a temperature measurement;
The stage of predicting uncertainty is
26. Estimating a current parameter of an electrochemical cell system according to claim 25, including using the state prediction value, the current measurement value, the voltage measurement value, and the temperature measurement value in a mathematical model. Method. The stage of predicting the internal parameters is as follows:
Determining a temperature measurement;
A mathematical model for predicting the internal parameter using the state measurement, the temperature measurement, the current measurement and the voltage measurement;
The method of estimating current parameters of an electrochemical cell system according to claim 19 further comprising:   The method of estimating current parameters of an electrochemical cell system according to claim 18, further comprising ensuring convergence of one or more parameters for each physical value. The guarantee stage is
30. The method of estimating current parameters of an electrochemical cell system according to claim 28, comprising forcing the dc gain of the voltage polarization filter to be zero.   The method for estimating current parameters of an electrochemical cell system according to claim 18, comprising ensuring the safety of cell model dynamics. The guarantee stage is
32. The method of estimating current parameters of an electrochemical cell system according to claim 30, comprising forcing filter poles to have a value less than one.   31. The method of estimating current parameters of an electrochemical cell system according to claim 30, wherein the filter pole is calculated using a tanh function to ensure that the size of the filter pole is less than one.   The method of estimating current parameters of an electrochemical cell system according to claim 18, comprising receiving initial state values and initial parameter values associated with the electrochemical cell. The component configured to estimate the current parameters of the battery is
A component configured to predict the internal parameters of the cell;
A component configured to predict the uncertainty of the internal parameter prediction;
A component configured to correct the prediction of the internal parameter and the prediction of the uncertainty;
Repeat the steps performed by the component configured to predict the internal parameter, the component configured to predict the uncertainty, and the component configured to correct A value indicative of a current operating condition of the battery according to claim 13, comprising: a component configured to calculate an estimate for the parameter and to calculate an uncertainty for the parameter estimate. Device to estimate. The components configured to make predictions of the internal parameters are
A component configured to receive a state estimate;
A component configured to determine a current measurement;
A component configured to determine a voltage measurement;
A component configured to predict the internal parameter using the state estimate, the current measurement, and the voltage measurement in a mathematical model;
35. The apparatus for estimating a value indicating a current operating condition of a battery according to claim 34. The components configured to correct above are:
A component configured to compute a gain factor;
A component configured to compute a predicted internal parameter corrected using the gain factor, the voltage measurement, and the internal parameter prediction;
A component configured to compute an uncertainty prediction corrected using the gain factor and the uncertainty prediction;
36. The apparatus for estimating a value indicative of a current operating condition of a battery according to claim 35. The components configured to perform the uncertainty prediction are:
A component configured to receive a state estimate;
A component configured to determine a current measurement;
A component configured to determine a voltage measurement;
A component configured to determine a temperature measurement; and
A component configured to predict the uncertainty using the state estimate, the temperature measurement, the current measurement, and the voltage measurement in a mathematical model;
35. The apparatus for estimating a value indicating a current operating condition of a battery according to claim 34. The components configured to make predictions of the internal parameters are
A component configured to determine the temperature;
A component configured to predict the internal parameter using a mathematical model using the state estimate, the temperature measurement, the current measurement, and the voltage measurement;
36. The apparatus for estimating a value indicative of a current operating condition of a battery according to claim 35, further comprising: Means for predicting the internal parameters of the cell;
Means for predicting the uncertainty of the internal parameter prediction;
Means for correcting the internal parameter prediction and the uncertainty prediction;
Means for applying an algorithm that repeats the prediction of the internal parameter, the prediction of the uncertainty and the correction to calculate an estimation performed on the parameter and the uncertainty of the parameter prediction;
A system for estimating the current parameters of an electrochemical cell system including: Predicting the internal parameters of the cell;
Predicting the uncertainty of the internal parameter prediction,
Correcting the internal parameter prediction and the uncertainty prediction;
Applying an algorithm that repeats the step of predicting the internal parameter, the step of predicting the uncertainty, and the step of correcting, to make an estimate for the parameter and an uncertainty for the prediction of the parameter Calculating gender,
A storage medium encoded with computer program code recognizable by a machine, including instructions that cause a computer to perform a method for estimating a current parameter of an electrochemical cell comprising:

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