KR20070074621A - Method and system for battery state and parameter estimation - Google Patents

Abstract

A system and a method for estimating the state of a battery and parameters are provided to estimate the state of a battery pack system and parameters by using kalman filtering and dual extended kalman filtering. A method for estimating the state of a battery(20) and parameters comprises a step of estimating SOC(State Of Charge) in a battery where the SOC forms one of internal states and a step of estimating SOH(State of Health) in a battery where the SOH forms one of internal parameters. The step of estimating SOC in the battery is composed of steps for predicting the internal state of the battery including SOC as one of the internal states; predicting uncertainty in predicting the internal state; correcting the prediction of the internal state and uncertainty; predicting the internal state to estimate SOC and calculate uncertainty for SOC; and applying an algorism for repeating the uncertainty predicting and correction steps.

Description

Method and system for battery state and parameter estimation

The present invention relates to an apparatus and method for estimating the status and parameters of a battery pack system using digital filtering techniques, in particular Kalman filtering and dual extended kalman filtering. The battery management system in the battery pack must estimate a value indicating the current operating condition of the battery pack. The current operating state includes a state of charge (SOC), power-fade, capacity-fade, and readily available power. The power decay and the capacity decay are treated primarily as a representation of state of health (SOH). The present application provides an improved method and apparatus for estimating values indicative of current operating conditions of a pack including battery SOC and SOH.

Batteries are widely used in electronic and electrical devices. In each application, it is useful and necessary to measure how much charge remains in the battery. Such a measurement is called a state of charge (SOC). For example, it is useful to know how long cell phone users can talk on their phones. Rechargeable devices, on the other hand, need to know how much charge is present in the battery to prevent overcharging. Many types of batteries are sensitive to overcharging as well as undercharging. Overcharging and undercharging can reduce the battery's efficiency and even damage it.

At present, there are many techniques for measuring the remaining charge of a battery. Each of these SOC determination techniques has drawbacks. Techniques such as ampere-hour counting are sensitive to measurement errors, and things like the Coup de fouet only work on one battery type. Other techniques, such as impedance spectroscopy, are still limited to battery conditions, such as rapidly changing temperatures. In addition, many techniques do not provide an uncertainty range for the estimation of SOC. In applications such as HEV and EV, the uncertainty range associated with SOC measurements is very important. If the uncertainty range is unknown and the battery is undercharged in error, vehicles can lose power on the road and pose a risk. Knowing the uncertainty range can prevent this. For example, if the battery SOC is determined to be within 10% of the minimum charge threshold, and the uncertainty range is known to be 15%, then the system can know that the battery needs to be charged. This is because the uncertainty range is larger than the interval of the threshold.

Existing Technologies

An overview of existing technologies and their shortcomings is disclosed herein. One method called discharge testing is an exact form of testing. This involves completely discharging the battery 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 to be useful and interrupts system functionality while the test is running.

Another SOC decision technique is called amp-hour counting. This is the most common technique for SOC decision making because it is easy to implement. It measures the current in the battery and uses that measurement to determine the SOC. Ampere-hour counting uses the following formula:

C _n in the above formula is the rated capacity of the battery. I _batt is the current in the battery, and I _loss is the current consumed by the loss reactions. The equation (Equation) determines the SOC based on the initial value SOC _o which is the starting point. Ampere-hour counting is essentially an "open loop" method that is easily confused. Measurement errors accumulate and deteriorate the accuracy of SOC decisions over time. There is a way to improve the current measurement, but it is expensive.

Electrolyte measurement is another common technique. For example, in lead-acid batteries, the electrolyte is involved in the reaction during charging and discharging. Therefore, a linear relationship exists between the change in acid density and the SOC. Therefore, measuring electrolyte density can yield an SOC estimate. The density is measured directly or indirectly by ion concentration (concentration), conductivity (conductivity), refractive index (refraction index), viscosity (viscosity) and the like. Moreover, it is susceptible to acid stratification, water loss, and long term instability of the sensor in the battery.

Open-circuit voltage measurements can be performed on the battery's SOC test. Although the relationship between the open circuit voltage and the SOC is non-linear, it can be determined through laboratory testing. Once the relationship is determined, the SOC can be determined by measuring the open circuit voltage. However, measurements and estimates are accurate only when the battery is in a steady state that can only be achieved after long periods 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 the determination of various characteristics of batteries. Impedance spectroscopy takes advantage of the relationship between SOC and battery model parameters derived from impedance spectroscopy measurements. However, a disadvantage of this technique is that the impedance curve is strongly influenced by the temperature effect. Therefore, its application is limited to the application under a temperature stable environment.

Internal resistance is a technique related to impedance spectroscopy. Internal resistance is calculated as the voltage drop divided by the current change over the same time interval. The selected time interval is important because all time intervals longer than 10 ms result in more complex resistance measurements. Measurement of internal resistance is very sensitive to measurement accuracy. This requirement is particularly difficult in applications of heterogeneous electric vehicles (HEVs) and electric vehicles (EVs).

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

There is another group of SOC estimation techniques called interpretive techniques. Analysis techniques do not give SOC directly. Instead, they use electrical discharge and charge characteristics to determine the SOC. As such, the SOC has to be inferred from the calculated values. One such technique is called coup de fouet. The coup de fouet represents a short voltage drop region that occurs at the beginning of the discharge following a full charge of the lead acid battery. The SOC can be inferred using a special correlation between the voltage parameters occurring in this coup de fouet region. One limitation to the coup de fouet is that it only works with lead acid batteries. Moreover, this is only effective if full charge is frequently made during battery operation.

Kalman filter ( The Kalman Filter )

One of the SOC determination techniques involves mathematically modeling the operation of a battery and predicting SOC based on the model. One such 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 of the system. In many instances this is quite useful because the internal state of the system is unknown and cannot be measured directly. By itself, Kalman filters can operate on any type of battery and address the limitations of many of the technologies mentioned.

Kalman filters are widely used in areas such as aeronautics and computer graphics because they have several advantages over many other similar mathematical system models. In particular, the Kalman filter considers both measurement uncertainty and estimation uncertainty when updating the estimate in successive steps. The Kalman filter compensates for two uncertainties based on new measurements received from the sensors. This is very important for two reasons. First, sensors often have uncertainty or noise components associated with their measurements. Over time, if not corrected, the measurement uncertainty may accumulate. Second, the estimation itself inherently uncertain in any model system. This is because the internal dynamics of the system can change over time. Estimation of one time step may be less accurate than next because the system can be changed internally to drive the model less similarly. The Kalman filter's correction mechanism minimizes these uncertainties in each time step and prevents the degradation of accuracy over time.

1 shows the basic operation of the Kalman filter. There are two major components in the Kalman filter: predict component 101 and correct component 102. In the beginning, a series of initial parameters are input into the prediction component 101. 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 the internal state, it also provides uncertainty in the prediction. Thus, as shown in FIG. 1, the two outputs of the predictive 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 predicted uncertainty with new measurements received from the sensor. The result is the corrected internal state and the corrected uncertainty, which are then both fed back as parameters to the prediction component 101 for next iteration. In the next iteration, the cycle itself is repeated again.

Mathematical Basics of Kalman Filters

1A and 1B show the equations used within both the prediction and correction components of the Kalman filter. To understand the source of the equations used, consider the dynamic process represented by the n-th order difference equation of the form:

U _k in the above equation is zero-mean white random process noise. Under some basic conditions, the above equation can be re-expressed as follows.

는 이전 상태(previous state)

와 입력 u_k의 선형적 조합에 의하여 모델된 새로운 상태(new state)를 나타낸다. 매트릭스 A와 B의 표기법에 주시하여야 한다. 이것은 상태-공간 모델(state-space)을 이끌어 낸다.In the above formula

Is the previous state

The new state is modeled by the linear combination of and the input u _k . Attention is drawn to the notations of matrices A and B. This leads to a state-space model.

Or in a more general form,

The equation is the basis of many linear estimation models. Equation 3 to Equation 5 represent a system with a single input and a single output, while B has multiple columns and C has multiple rows. Equations 6, 7 and the following equations allow multiple inputs and multiple outputs.

Based on Equations 6 and 7, the Kalman filter is operated by the following equation.

x _k = Ax _{k -1} + Bu _{k -1} + w _{k -1}

y _k = Cx _k + Du _k + v _k

및

에 의하여 표현된다.Although D is often assumed to be 0, Equation 9 is a more general form. Matrix A and B in Equation 8 are associated with matrix A _k and B _k in Equation 6, respectively. The matrixes C and D in [Equation 9] are associated with C _k and D _k in [Equation 7]. Equation 8 is called a process function because it operates an estimate of the dynamic system process. The random variables w _k and v _k added in Equations 8 and 9 represent process noise and measurement noise, respectively. Their contribution to the estimate is shown in their covarinace matrices in FIGS. 1A and 1B.

And

Is represented.

로 표현된 벡터인, 다음 시간 단계(next time step)에서의 시스템의 내적 상태를 예측한다. 음수 표시는 벡터가 상기 예측 컴퍼넌트의 결과임을 나타낸다. 양수 표시는 벡터가 상기 보정 컴퍼넌트의 결과임을 나타낸다. 수식 151에서, 현재 시간 단계에서 보정 컴퍼넌트의 결과는 다음 시간 단계의 결과를 예측하기 위하여 사용된다. 수식 152는 불확정성을 예측하는 데 사용되며, 이는 또한 오차 공분산(error covariance)으로서 참조된다. 수식 152에서 매트릭스

는 프로세스 노이즈 공분산 매트릭스(process noise covariance matrix)이다.Referring again to FIG. 1A (which represents the equation in the predictive component 101), equation 151 is based on [Equation 8], and equation 152 is based on part of [Equation 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 a parameter from a current time step.

Predict the internal state of the system at the next time step, a vector represented by. A negative notation indicates that a vector is the result of the predictive component. A positive sign indicates that the vector is the result of the correction component. In Equation 151, the result of the correction component in the current time step is used to predict the result of the next time step. Equation 152 is used to predict uncertainty, which is also referred to as error covariance. Matrix from Equation 152

Is the process noise covariance matrix.

의 사이에 가중치를 부여하기 위하여 이용된다. 수식 161에서 나타난 바와 같이 매트릭스

, 실제 측정 노이즈 공분산(actual measurement noise covariance)는 칼만 게인 팩터 L_k와 역비례 된다.

가 줄어들수록 L_k는 증가하고, 실제 측정값 y_k에게 더 많은 가중치를 제공한다. 그러나, 예측된 불확정성인 매트릭스

가 감소한다면 L_k는 감소하고, 예측된 측정값

에 더 많은 가중치를 제공한다. 그래서, 칼만 게인 팩터는 더 작은 불확정성을 가지는 측정 형태에 의존하는 실제 측정값 또는 예측된 측정값을 선호한다.1B shows the equation within the correction component 102. These three equations are performed in succession. First, Equation 161 determines the Kalman gain factor. The Kalman gain factor is used to correct the corrections in Equations 162 and 163. In Equation 161, matrix C is derived from Equation 9, which associates the state with the measured value y _k . In Equation 162, the Kalman gain factor is the actual measurement y _k and the predicted measurement

Used to weight between Matrix as shown in Equation 161

The actual measurement noise covariance is inversely proportional to the Kalman gain factor L _k .

Decreases, L _k increases, giving more weight to the actual measurement y _k . However, the matrix is the predicted uncertainty

Decreases, L _k decreases, and the predicted measured value

To give more weight. Thus, the Kalman gain factor favors actual or predicted measurements that depend on the type of measurement with less uncertainty.

(예측 컴퍼넌트(101)로부터), 새로운 측정값 y_k 및 예측된 측정값

에 기초하여, 보정된 내적 상태 벡터

를 연산한다. 결국, 보정 컴퍼넌트(102)의 마지막 수식에서 수식 163은 상기 예측된 불확정성 또는 상태-오차 공분산(state-error covariance)을 보정한다. 수식 163에서 매트릭스 I는 단위 행 렬(identity matrix)을 의미한다. 수식 162 및 163의 출력은 다음 반복을 위하여 예측 컴퍼넌트(101)에 입력된다. 더욱 구체적으로, 수식 162에서 상기 계산된 값

은 다음 반복을 위하여 수식 151로 교체되고, 수식 163에서 상기 계산된 값

은 다음 반복을 위하여 수식 152와 교체된다. 그래서 칼만 필터는 내적 상태와 이와 연관된 불확정성을 반복적으로 예측하고 보정한다. 실제적으로 A, B, C, D,

및

는 각 시간 단계에서 변경될 수 있다는 것이 주목되어야 한다.Using this method of weighting, Equation 162 uses the predicted dot product

(From predictive component 101), the new measurement y _k and the predicted measurement

Based on the corrected dot product

Calculate As a result, Equation 163 in the last equation of correction component 102 corrects the predicted uncertainty or state-error covariance. In Equation 163, the matrix I refers to an identity matrix. The outputs of equations 162 and 163 are input to prediction component 101 for the next iteration. More specifically, the calculated value in Equation 162

Is replaced by Equation 151 for the next iteration, and the calculated value in Equation 163

Is replaced by Equation 152 for the next iteration. Thus, the Kalman filter repeatedly predicts and corrects internal states and their associated uncertainties. Actually A, B, C, D,

And

It should be noted that can be changed at each time step.

Extended Kalman Filter

The Kalman filter uses linear functions in the model, while the extended Kalman filter was developed to model the system as a nonlinear function. 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 approximation model similar to the Taylor series, which linearizes the functions to obtain an estimate. The linearization is achieved by taking the basis of two equations in the partial derivatives, measurement functions, and prediction components with current nonlinear processes.

The extended Kalman filter is operated by the following equation.

x _{k +1} = f (x _k , u _k , w _k )

And

y _{k +1} = h (x _k , u _k , v _k )

In the above equations, the variables w _k and v _k mean process noise and measurement noise, respectively. Non-linear function in Equation 10] f is thus associated with the current state vector x _k at step k and internal state vector x _{k + 1} at the next time step k + 1. The function f also includes the driving function u _k and the 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 the formula of the Extended Kalman Filter. The working sequence is the same as the Kalman filter. Here too, there are two components-the predictive component 201 and the correction component 202. The equations are a bit different. Specifically, matrices A and C now have a time-step subscript k, meaning that they change with each time step. This change is necessary because the functions are now nonlinear. We can no longer assume that matrices are constant, as in the Kalman filter. To approximate them, Jacobian matrices are computed by taking the partial derivatives of the functions f and h at each time step. Jacobian is listed below.

A is a Jacobian matrix computed by taking the partial derivative of f with respect to x, i.e.

C is a Jacobian matrix computed by taking the partial derivative of h with respect to x. In other words,

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

From battery SOC The Kalman filter to determine

Since only the battery output needs to be measured, the Kalman filter has the advantage that it can work in all types of battery systems, including dynamic applications such as HEV and EV. There are existing applications using Kalman filters to determine the SOC of a battery. However, none of them use SOC as the internal state of the model. Thus, the uncertainty associated with SOC estimation cannot be determined. This drawback is particularly important in HEVs and EVs where an uncertainty range is necessary to prevent power loss in vehicles or undercharging of batteries. In addition, none of the existing methods use an extended Kalman filter to nonlinearly model the battery SOC.

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 represent the drive of the battery to estimate the SOC. For example, to measure SOC as an internal state using a Kalman filter, the filter needs to have a specific formula that describes how the SOC transitions from one time step to the next. The decision of such a formula is not trivial.

From battery SOH The Kalman filter to determine

Moreover, although not directly measurable in the rechargeable battery pack art, it is desirable in some applications to be able to estimate quantities that represent the condition of current battery packs. Some of these quantitative factors, such as the pack state of charge, which can traverse the full range in minutes, can change dramatically, with 20% of normal use over 10 years or more. Something else changes very slowly, such as cell capacity, which can change in a small range. Quantitative factors that tend to change rapidly constitute the “state” of the system, and quantitative factors that tend to change slowly constitute the time varying parameter of the system.

Battery system applications, such as heterogeneous electric vehicles (HEV), battery electric vehicles (BEV), laptop computer batteries, portable equipment battery packs, etc., adversely affect battery life In those that need to operate for as long a time as actively as possible without any information, information about slowly varying parameters (e.g. total capacity) determines the pack health of the pack, This is useful for helping with other operations, including SOC operations.

There are many existing methods for estimating the state of health (SOH) of a cell, which are related to estimating two quantitative factors: power decay and capacity decay (both full). Power decay can be calculated if the current and initial pack electrical resistance are known, and capacity decay can be calculated if the current and initial pack total capacity is known, for example, although other methods may also be used.

Power and capacity decay is often expressed in terms of state of health (SOH). Other information can be inferred using the values of these variables, such as the maximum power available from the pack at any given time. Additional parameters may also be required for a particular application, and individual algorithms will typically be required to find each one.

The prior art uses the following other approaches to the estimation of SOH: discharge tests, chemistry-dependent methods, ohmic tests and partial discharges. The discharge test completely discharges a fully charged cell to determine the total capacity of the cell. This test disrupts system functionality and wastes cell energy. Chemically dependent methods include measuring the level of plate corrosion, electrolyte density. Coup de fouet is used in lead acid batteries. Ohm tests include resistance, conductance, and impedance tests, which are optionally associated with fuzzy-logic algorithms and / or neural networks. These methods require invasive measurements. Partial discharges and other methods compare the cell under test with a model of a good cell or a good cell.

There is a need for a method of constantly estimating cell parameters such as cell resistance and capacity. Moreover, methods that do not disrupt system function, do not waste energy, enable general applications (e.g., other types of cell electrochemistry, other applications), and methods that do not require invasive measurements and fairly harsh approaches. There is a need for. There is a need for a method that can operate on other configurations of parallel and / or series cells in a battery pack.

The present invention relates to performing estimation of values indicative of current operating conditions of packs including battery state of charge (SOC) and state-of-health (SOH) for battery power applications. . The battery may be in primary form or secondary (rechargeable) form. Moreover, the present invention can be applied to any battery chemistry. It addresses issues related to existing practices such as high error uncertainty, limited application range (eg, only one battery type) and sensitivity to temperature changes.

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

One embodiment is battery operation on highly dynamic batteries used in hybrid electric vehicles (HEV) and electric vehicles (EV), where such prior implementations were difficult. Has the option to allow other modeling parameters to be adapted.

Moreover, the present invention relates to an apparatus and method for estimating the parameters of an electrochemical cell, more particularly for example the parameter values of the cell.

According to another aspect of the present invention, a method of estimating a current parameter of an electrochemical cell includes: performing internal parameter prediction of the cell; Performing uncertainty prediction of the internal parameter prediction; Correcting the internal parameter prediction and the uncertainty prediction; And applying an algorithm that repeats the internal parameter prediction, the uncertainty prediction, and the correction to calculate an ongoing estimate for the parameter and an ongoing uncertainty for the parameter prediction.

According to yet another aspect of the present invention, an apparatus configured to estimate a current parameter of an electrochemical cell includes: a component configured to perform internal parameter prediction of the cell; A component configured to perform an uncertainty prediction of the internal parameter prediction; A component configured to correct the internal parameter prediction and the uncertainty prediction; And repeating the steps taken by the component configured to perform the intrinsic parameter prediction, the component configured to perform the uncertainty prediction, and the component configured to correct to calculate the ongoing estimation for the parameter and the ongoing uncertainty for the parameter prediction. Contains components that are configured to.

In addition, a system for estimating a current parameter of an electrochemical cell disclosed herein as an embodiment includes means for predicting an internal parameter of the cell; Means for performing uncertainty prediction of the internal parameter prediction; Means for correcting the internal parameter prediction and the uncertainty prediction; And to apply an algorithm that repeats performing the internal parameter prediction, performing the uncertainty prediction, and correcting to calculate the ongoing prediction for the parameter and the ongoing uncertainty for the parameter prediction. Means;

Moreover, another embodiment discloses a storage medium encoded with machine readable computer program code that includes instructions for causing a computer to perform the method for estimating a current parameter of an electrochemical cell.

Moreover, another embodiment of a computer data signal implemented with a computer readable medium is disclosed. The computer data signal includes code configured for a computer to perform the method of estimating a current parameter of an electrochemical cell.

Various features, forms, and advantages of the invention will be more clearly understood from the following detailed description of the invention and the appended claims and drawings. In addition, the same reference numerals in the drawings means the same components.

1 is a view showing the operation of a general Kalman filter,

1A is a diagram showing a formula of a prediction component of a general Kalman filter,

1B is a diagram showing the formula of a correction component of a general Kalman filter;

2A is a diagram showing a formula of a prediction component of a general extended Kalman filter;

2B is a diagram showing the equation of a correction component of a general extended Kalman filter,

FIG. 3A illustrates components of an SOC estimator in accordance with an embodiment of the present invention; FIG.

3B illustrates a component of an SOC estimator in accordance with another embodiment of the present invention;

4A is a diagram showing the equations of a predictive component of an extended Kalman filter implementation in accordance with an embodiment of the present invention;

4B is a diagram showing the equations of a correction component of an extended Kalman filter implementation in accordance with an embodiment of the present invention;

5A is a diagram showing the formula of a predictive component of an extended Kalman filter implementation according to another embodiment of the present invention;

5B is a diagram showing the equation of a correction component of an extended Kalman filter implementation according to another embodiment of the present invention;

6 illustrates the operation of an extended Kalman filter according to an embodiment of the present invention;

7 illustrates the operation of an extended Kalman filter according to another embodiment of the present invention;

8A is a diagram showing the equation of a predictive component of performing a Kalman filter in accordance with an embodiment of the present invention;

8B is a diagram showing the formula of a correction component of performing a Kalman filter in accordance with an embodiment of the present invention;

9 is a view illustrating an operation process of a Kalman filter according to an embodiment of the present invention;

FIG. 10 is a flowchart illustrating an operation of an embodiment of the present invention for dynamically changing a modeling equation for a battery SOC. FIG.

11 is a block diagram illustrating an exemplary system for parameter estimation in accordance with an embodiment of the present invention;

12 is a block diagram illustrating a filtering method for parameter estimation according to an embodiment of the present invention.

Battery charge status ( SOC Implementation of estimation

Embodiments of the present invention relate to the implementation of a battery SOC estimator for all battery power applications.

The invention can be applied to batteries in primary or secondary (rechargeable) form, and the invention can be applicable to any battery chemistry. Embodiments of the present invention work on dynamic batteries used in hybrid electric vehicles (HEVs) and electric vehicles (EVs), which previously had difficult implementations. It has the advantage of providing both SOC estimation and uncertainty in SOC estimation. It addresses issues related to existing implementations such as high error uncertainty, limited application range and sensitivity to temperature changes.

Temperature-Independent Model

3A illustrates components of an SOC estimator in accordance with an embodiment of the present invention. The battery 301 is connected to the load circuit 305. For example, the load circuit 305 may be a motor of an electric vehicle (EV) or a heterogeneous vehicle (HEV). The measurement of the battery terminal voltage is made with a voltmeter 302. The measurement of the battery current is made with an ammeter 303. Volt and current measurements are processed by arithmetic circuit 304 estimating SOC. It should be understood that no means are required to make measurements from the intrinsic chemical composition of the battery.

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

Computation circuit 304 uses a mathematical model of the battery containing the battery SOC as the 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 equation is as follows.

x _{k +1} = f (x _k , i _k , w _k )

And

y _{k +1} = h (x _k , i _k , v _k )

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

In Equation 15, the variable v _k is measurement noise at time index k, and y _k is model prediction of battery terminal voltage at time index k. The function h (x _k , i _k , w _k ) correlates the state, current and measurement noise of the model with the predicted terminal voltage at time index k. This function can be linear or nonlinear. The period of time that elapses between the time indicators can be fixed even though the invention allows measurements to be omitted from time to time.

Temperature-Dependent Model

3B illustrates components of an SOC estimator in accordance with another embodiment of the present invention. The battery 351 is connected to the load circuit 355. For example, the load circuit 355 may be a motor of an electric vehicle (EV) or a hybrid electric vehicle (HEV). The measurement of the battery terminal voltage is made with a voltmeter 352. The measurement of the battery current is made with an ammeter 353. The battery temperature is measured by the temperature sensor 356. Voltage, current, and temperature measurements are processed by arithmetic circuit 354 estimating SOC.

The computing circuit 354 uses a temperature dependent mathematical model of the battery that includes the battery SOC as the model state. In one embodiment of the invention, a discrete time model is used. In another embodiment, a continuous time model is used. In one embodiment, the model equation is as follows.

x _{k +1} = f (x _k , i _k , T _k , w _k )

And

y _{k +1} = f (x _k , i _k , T _k , v _k )

In the above equation, x _k is the model state in time index k (x _k may 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 indicator k and w _k is the disturbance input at time indicator k. The use of battery temperature as a dependent parameter is important to maintain the accuracy of the SOC estimate from being affected by varying temperatures. The function f (x _k , i _k , T _k , w _k ) associates the model state at time index k with the model state at time index k + 1 and can be a linear or nonlinear function. An embodiment of the invention has a battery SOC as an element of the model state vector x _k .

In Equation 17, the variable v _k is measurement noise at time index k, and y _k is model prediction of battery terminal voltage at time index k. The function h (x _k , i _k , T _k , w _k ) correlates the state, current and measurement noise of the model with the predicted terminal voltage at time index k. This function can be linear or nonlinear. The period of time that elapses between the time indicators can be fixed even though the invention allows measurements to be omitted from time to time.

Applicable to Kalman filter and Extended Kalman filter of above models

In one embodiment of the present invention, the temperature-independent mathematical battery models of Equations 14 and 15 are 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 linear. In another embodiment of the present invention, the temperature-dependent mathematical battery models of Equations 16 and 17 are 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 present invention, the temperature-independent mathematical models of Equations 14 and 15 are used as the basis for the extended Kalman filter. The functions f and h are nonlinear in this embodiment. In another embodiment of the present invention, the temperature-dependent mathematical models of Equations 16 and 17 are used as the basis for the Extended Kalman Filter. In this embodiment, the functions f and h are both nonlinear. Those skilled in the art will recognize that not only certain Luenberger-like observers, but also other variations of the Kalman filter, may also be used.

Extended Kalman Filter Behavior

는 배터리의 내적 상태를 나타내는 예측된 벡터를 지금 나타내는 반면,

은 상기 예측된 상태-오차 공분산(state-error covariance)(불확정성)을 지금 나타낸다. 함수 f와 h는 [수학식 14]와 [수학식 15]에서 나타난 그것들과 동일하다. 보정 컴퍼넌트(402)의 수식 462에서 실제 측정 항목은 지금 m_k로 표현된다고 이해되어야 한다. 4A and 4B show one embodiment for an extended Kalman filter. In this embodiment, equations (14) and (15) from the temperature-independent model are used as the basis of the extended Kalman filter. In both figures, the equations in both the predictive component and the correction component retain the general form of the extended Kalman filter as shown in FIG. However, there is some variation in the variable name in this embodiment. The difference reflects the variables used in the battery SOC measurement and the use of Equations 14 and 15.

Now represents a predicted vector representing the internal state of the battery,

Now represents the predicted state-error covariance (uncertainty). The functions f and h are the same as those shown in Equations 14 and 15. It should be understood that the actual measurement item in equation 462 of the correction component 402 is now expressed in m _k .

5A and 5B illustrate another embodiment of an extended Kalman filter. In this embodiment, Equations 16 and 17 from the temperature-dependent model are used as the basis of the Extended Kalman Filter. All equations are the same except that in Figures 4A and 4B and Equations 551 and 562 now have an additional temperature item T _k . Thus, in this embodiment the temperature of the battery is used to determine the estimates for every iteration of the Extended Kalman Filter. Since battery capacity is sometimes affected by temperature, this additional entry allows equations to model the battery more accurately.

과

의 이전 추정값(prior estimates)으로 초기화된다.

는 [수학식 14]의 함수 f에서 오는 반면,

은 [수학식 15]의 함수 h에서 온다. 블록 600의 완료 후,

과

의 추정값으로 상기 알고리즘은 확장 칼만 필터의 보정 컴퍼넌트를 개시한다.

과

의 추정값은 보정 컴퍼넌트에 의하여 요구된 예측 컴퍼넌트로부터의 출력으로 역할한다. 블록 601에서, x에 대한 수식 h의 편도 함수가 연산되며, 매트릭스 C를 산출한다. 블록 602에서는, 칼만 게인(kalman gain) L_k가 매트릭스 C,

과

을 이용하여 연산된다. 이것은 도 4B에서 보정 컴퍼넌트(402)의 첫번째 수식(수식 461)에 대응한다. 블록 603에서, 예측된 내적 상태 벡터, 칼만 게인 L_k와 단자전압의 측정값 m_k는 보정된 상태 벡터

를 계산하는데 사용된다. 이것은 확장 칼만 필터에서 보정 컴퍼넌트의 두번째 수식 에 대응한다. 블록 604에서는, 상기 예측된 상태-오차 공분산

이 보정된 상태-오차 공분산

을 연산하기 위하여 이용된다. 이것은 보정 컴퍼넌트의 세번째 수식에 대응한다. 6 illustrates the operation of an extended Kalman filter according to an embodiment of the present invention using a temperature-independent model. At block 600, the algorithm is

and

It is initialized with prior estimates of.

Comes from the function f in equation (14),

Comes from the function h in (15). After completion of block 600,

and

With an estimate of, the algorithm initiates a correction component of the Extended Kalman Filter.

and

The estimated value of 으로 serves as the output from the predictive component required by the correction component. In block 601, the one-way function of equation h for x is computed, yielding matrix C. In block 602, the kalman gain L _k is the matrix C,

and

It is calculated using This corresponds to the first equation (Equation 461) of the correction component 402 in FIG. 4B. In block 603, the predicted internal state vector, Kalman gain L _k and the measured value of terminal voltage m _k are the corrected state vector

Used to calculate This corresponds to the second expression of the correction component in the Extended Kalman Filter. In block 604, the predicted state-error covariance

2 corrected state-error covariance

Is used to compute. This corresponds to the third equation of the correction component.

과

이 연산된다. 블록 606에서 시간 지표 k는 증대되고 동작과정은 블록 601에서 다시 다음 시간 단계로 시작된다. At block 605, all of the equations of the prediction component are computed. Matrix A is computed by taking the one-way function of function f with respect to x, and predicting the next iteration,

and

Is computed. At block 606 the time indicator k is incremented and the operation begins again at the next time step at block 601.

의 이전 추정값(prior estimates)으로 초기화된다.

는 [수학식 16]의 함수 f에서 오는 반면,

은 [수학식 17]의 함수 h에서 온다. 블록 700의 완료 후,

과

의 추정값으로 상기 알고리즘은 확장 칼만 필터의 보정 컴퍼넌트를 개시한다.

과

의 추정값은 보정 컴퍼넌트에 의하여 요구된 예측 컴퍼넌트로부터의 출력으로 역할한다. 블록 701에서, x에 대한 수식 h의 편도 함수가 연산되며, 매트릭스 C를 산출한다. 블록 702에서는, 칼만 게인 L_k가 매트릭스 C,

과

을 이용하여 연산된다. 이것은 도 5B에서 보정 컴퍼넌트(502)의 첫번째 수식(수식 561)에 대응한다. 그 다음에 블록 703에서, 예측된 내적 상태 벡 터

, 칼만 게인 L_k 및 단자전압의 측정값 m_k가 보정된 상태 벡터

를 계산하는데 사용된다. 이것은 확장 칼만 필터에서 보정 컴퍼넌트의 두번째 수식에 대응한다. 블록 704에서는, 상기 예측된 상태-오차 공분산

이 보정된 상태-오차 공분산

을 연산하기 위하여 이용된다. 이것은 보정 컴퍼넌트의 세번째 수식에 대응한다. 7 illustrates operation of an extended Kalman filter according to another embodiment of the present invention using a temperature-dependent model. In block 700 the algorithm is

It is initialized with prior estimates of.

Comes from the function f in equation (16),

Comes from the function h in [Equation 17]. After completion of block 700,

and

With an estimate of, the algorithm initiates a correction component of the Extended Kalman Filter.

and

The estimated value of 으로 serves as the output from the predictive component required by the correction component. At block 701, the partial derivative function of equation h for x is computed, yielding matrix C. In block 702, Kalman gain L _k is represented by matrix C,

and

It is calculated using This corresponds to the first equation (Equation 561) of the correction component 502 in FIG. 5B. Then at block 703, the predicted internal state vector

, Kalman Gain L _k State vector with measured value m _k of terminal voltage

Used to calculate This corresponds to the second equation of the correction component in the Extended Kalman Filter. At block 704, the predicted state-error covariance

2 corrected state-error covariance

Is used to compute. This corresponds to the third equation of the correction component.

과

이 연산된다. 블록 706에서 시간 지표 k는 증대되고 동작과정은 블록 701에서 다시 다음 시간 단계로 시작된다. At block 705, all of the equations of the prediction component are computed. Matrix A is computed by taking the one-way function of function f with respect to x, and predicting the next iteration,

and

Is computed. At block 706 the time indicator k is incremented and the operation begins again at the next time step at block 701.

Kalman Filter Behavior

는 배터리의 내적 상태를 나타내는 예측된 벡터를 지금 나타내는 반면,

은 상기 예측된 상태-오차 공분산(state-error covariance)(불확정성)을 지금 나타낸다. 보정 컴퍼넌트(802)의 수식 862에서 실제 측정 항목은 지금 m_k로 표현된다고 이해되어야 한다. 8A and 8B show an embodiment for a Kalman filter. Equations 14 and 15 from a temperature-independent model are used as the basis for the Kalman filter. In another embodiment, Equations 16 and 17 from the temperature-dependent model are used. In both figures, the equations in both the predictive component and the correction component retain the general form of the Extended Kalman Filter, as shown in FIG. However, there are some variations in the variable names in this embodiment. In one embodiment, the difference reflects the use of variables, Equations 14 and 15, used in the battery SOC measurement. In another embodiment, the difference reflects the use of variables, [Equation 16] and [Equation 17], used to measure battery SOC.

Now represents a predicted vector representing the internal state of the battery,

Now represents the predicted state-error covariance (uncertainty). It is to be understood that the actual measurement item in Equation 862 of the correction component 802 is now expressed in m _k .

과

의 이전 추정값(prior estimates)으로 초기화된다. 하나의 실시예에서,

는 [수학식 14]의 함수 f에서 오는 반면,

은 [수학식 15]의 함수 h에서 온다. 이 실시예는 온도-독립적이다. 다른 실시예에서,

는 [수학식 16]의 함수 f에서 오는 반면,

은 [수학식 17]의 함수 h에서 온다. 이 실시예는 온도-종속적이다. 블록 900의 완료 후,

과

의 추정값으로 상기 알고리즘은 확장 칼만 필터의 보정 컴퍼넌트를 개시한다.

과

의 추정값은 보정 컴퍼넌트에 의하여 요구된 예측 컴퍼넌트로부터의 출력으로 역할한다. 블록 901에서, 칼만 게인 L_k이 매트릭스 C,

과

을 이용하여 연산된다. 이것은 도 8B에서 보정 컴퍼넌트(802)의 첫번째 수식(수식 861)에 대응한다. 그 다음, 블록 902에서, 예측된 내적 상태 벡터

, 칼만 게인 L_k 및 단자전압의 측정값 m_k가 보정된 상태 벡터

를 계산하는데 사용된다. 이것은 확장 칼만 필터에서 보정 컴퍼넌트의 두번째 수식에 대응한다. 블록 903에서는, 상기 예측된 상태-오차 공분산

이 보정된 상태-오차 공분산

을 연산하기 위하여 이용된다. 이것은 보정 컴퍼넌트의 세번째 수식에 대응한다. 블록 904에서, 상기 예측 컴퍼넌트의 양 수식들이 연산된다. 다음 반복에 대한 예측값 즉,즉,

과

이 연산된다. 블록 905에서 시간 지표 k는 증대되고 동작과정은 블록 901에서 다시 다음 시간 단계로 시작된다.9 illustrates an operation of a Kalman filter according to an embodiment of the present invention. In block 900 the algorithm is

and

It is initialized with prior estimates of. In one embodiment,

Comes from the function f in equation (14),

Comes from the function h in (15). This embodiment is temperature-independent. In another embodiment,

Comes from the function f in equation (16),

Comes from the function h in [Equation 17]. This embodiment is temperature dependent. After completion of block 900,

and

With an estimate of, the algorithm initiates a correction component of the Extended Kalman Filter.

and

The estimated value of 으로 serves as the output from the predictive component required by the correction component. In block 901, Kalman gain L _k is matrix C,

and

It is calculated using This corresponds to the first equation (Equation 861) of the correction component 802 in FIG. 8B. Then, at block 902, the predicted internal state vector

, Kalman Gain L _k State vector with measured value m _k of terminal voltage

Used to calculate This corresponds to the second equation of the correction component in the Extended Kalman Filter. In block 903, the predicted state-error covariance

2 corrected state-error covariance

Is used to compute. This corresponds to the third equation of the correction component. At block 904, both equations of the predictive component are computed. The prediction for the next iteration, i.e.

and

Is computed. In block 905 the time indicator k is incremented and the operation begins again in block 901 with the next time step.

Specific formulas

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

And the governing equation for each state is

Battery SOC is the first element of the state vector. The variables are defined as follows. I _k is the instantaneous current, Δt is the interval between the instants of time, C _p (temp ...) is the "peukert" capacity of the battery adjusted to be temperature-dependent, n Is the fuguert exponent relative to fugue. Capacity and η (I _k ) are the battery coulombic efficiency as a function of current. State variables FILT and IF are filter states that obtain most of the flat, slow battery dynamic state.

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

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

In another embodiment, the following form of function f is used. The inner 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.), and y _{k -1} is the previous battery voltage estimate. α, β, and γ are positive constants that are chosen to create an acceptable model with parsimonious numbers of state variables. The governing equation for the SOC state is

In this embodiment, the specific form of function h is used.

y _k = h (x _k , T _k )

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

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

Changing parameters

10 illustrates the operation of one embodiment of the present invention to dynamically change modeling equations for battery SOC. In this embodiment, the computing circuit can adapt the changing behaviors of the battery using different parameters for different time periods. At block 1000, a change in battery current level is detected. For example, in a heterogeneous electric vehicle (HEV), a sudden drain of battery power is caused by the vehicle going uphill. This abrupt change in condition triggers the computational circuit to use another set of modeling equations to more accurately estimate the SOC under new conditions. In block 1010 a new set of modeling equations is used. At block 1020, the new equation is used to determine the SOC. This adaptive modeling behavior is useful in highly dynamic applications such as hybrid electric vehicles (HEVs) and electric vehicles (EVs).

Moreover, various embodiments of methods, systems, and apparatus for parameter estimation of electrochemical cells using filtering are disclosed herein. Referring to Figures 11 and 12, the following figures, numerous specific details, are set forth in order to provide a more complete understanding of the present invention. Example embodiments are described with reference to battery cells, but various electrochemical cells, referred to below as cells, include batteries, battery packs, ultracapacitors, capacitor banks, fuel cells, and electricity. It should be understood and understood to include, without limitation, combinations including at least one of the foregoing as well as electrolysis cells and the like. Moreover, it is to be understood that a battery or battery pack may comprise a plurality of cells, and the example embodiments disclosed herein may be applied to the plurality of one or more cells.

One or more exemplary embodiments of the present invention estimate the cell parameter value using a filtering method. One or more exemplary embodiments of the present invention estimate the cell parameter value using Kalman filtering. Some embodiments of the present invention estimate extended cell parameter values using extended Kalman filtering. Some embodiments estimate cell total capacity. Some embodiments estimate other time-varying parameter values. The term filtering is employed for illustration and illustration of example embodiments, but the term method is used for recursive prediction and correction generally expressed by filtering including, without limitation, Kalman filtering and / or Extended Kalman filtering. It should also be understood that it is intended to include the methodology.

Battery good condition ( SOH , State Of Health Implementation of estimation

11 illustrates components of a parameter estimator system 10 according to an embodiment of the present invention. An electrochemical cell pack 20 (eg a battery) comprising a plurality of cells 22 is connected to a load circuit 30. For example, the load circuit 30 may be a motor of an electric vehicle (EV) or a heterogeneous vehicle (HEV). Apparatus for measuring the characteristics and properties of the various cells is provided at 40. The measuring device 40 may include, without limitation, a device for measuring a cell terminal voltage, such as a voltage sensor 42 (eg, a voltmeter, etc.). On the other hand, the measurement of the cell current is made by the current sensing device 44 (for example, ammeter, etc.). Optionally, the temperature of the cell is measured by a temperature sensor 46 (eg a thermometer, etc.). Additional cell characteristics such as internal pressure or impedance may be measured with (eg) pressure sensors and / or impedance sensors 48 and may be employed for the type of cell selected. Various sensors necessary for evaluating the characteristics and properties of the cell may be employed. Voltage, current, and optionally temperature and cell-property measurements are performed by an arithmetic circuit 50 (e.g., processor, computer), which estimates the state and parameters of the cell. The system may also include a storage medium 52 that includes a computer usable storage medium known to those of ordinary skill in the art. The storage medium is in a state capable of communicating with the arithmetic circuit 50 by employing various means including, without limitation, a radio wave signal 54. It should be understood that no means for measuring from the intrinsic chemical composition of the cell 12 is required, although it may be used in the present invention. In addition, all measurements can be non-invasive. That is, it should be understood that no signal is injected into the system that may interfere with the normal operation of the load circuit 30.

As a result of performing the above-described functions and desirable processing and operations, the calculation circuit 50 includes a processor (s), a gate array (s), custom logic, and a computer (computer). s)), memory, storage, register (s), timing, interrupt (s), communication interfaces, and input / output signal interfaces (input / output signal interfaces) and combinations of at least one or more of the above descriptions, and the like. The computing circuit 50 may also include input and input signal filtering, etc. to perform signal acquisition or conversion and accurate sampling from the communication interface and input d. Additional features and processors of the computing circuit 50 are discussed in detail later.

One or more embodiments of the present invention may be implemented by newly updated firmware and software that is executed in the computing circuit 50 and / or other processing control means. Software functions include, without limitation, firmware, and may be implemented in hardware, software or a combination thereof. Thus, a distinct advantage of the present invention is that it can be realized through the use of current and / or new processing systems for charging and controlling electrochemical cells.

In an exemplary embodiment, the computation circuit 50 uses a mathematical model of the cell 22 that includes an indicia of the dynamic system state. In one embodiment of the invention, a discrete-time model is used. An example model (possibly nonlinear) in discrete-time state-space has the form

In the above equation, x _k is a system state, θ _k is a set of time-varying model parameters, u _k is an input from the outside, y _k is a system output, and w _k and v _k are “noise” inputs. All quantities can be scalar or vector. f (·, ·, ·) and g (·, ·, ·) are functions defined by the model being used. The non-time-varying numerical values required by the model can be embedded within f (·, ·, ·) and g (·, ···) and not included in θ _k .

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

There are many existing methods of estimating the cell state to include without being limited to the state of charge of the cell 22. SOC is typically a percentage value, which refers to the portion of cell capacity that is currently operating. Many approaches have been taken to measure SOC. Discharge test, amp-hour counting (coulomb counting), electrolyte measurement, open circuit voltage measurement, linear / nonlinear circuit modeling, impedance spectrometer, measurement of internal registor, coup de fouet and some forms of Kalman filtering This is the case. Each of these methods exhibits advantages as well as limitations.

Filters, preferably Kalman filters, are used by employing known mathematical models of cell dynamics and cell voltage, current and temperature measurements in accordance with this embodiment of the present invention for the implementation of a battery state (SOC). Preferably, the method directly estimates the state value for the cell when the SOC is at least one of the states. However, it should be understood that there are a variety of well known methodologies for the operation of SOC.

Following FIG. 12, a mathematical model of parameter dynamics is also utilized. An exemplary model has the following form.

The first equation indicates that the parameter is essentially constant, but may change slowly over time in the example modeled by the fictitious noise process denoted by 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 a function of the system state x _k , the external input u _k and a series of time-varying parameters θ _k . .

으로 표시되는 파라미터 추정값(parameter estimate)을 사실(true) 파라미터의 최상의 추측값(the best guess)(예를 들어,

)으로 정함(setting)으로써 초기화된다. 상태 추정이 요구되거나 정의되지는 않지만

로 표시되는 상기 상태 추정값은 셀 상태의 최상의 추정값(best estimate)(예를 들어,

으로 정해질 수 있다. 추정-오차 공분산(estimation-error covariance) 매트릭스

또한 초기화된다. 예를 들어, 상태의 초기화, 그리고 특히 SOC는 룩업 테이블에서의 셀 전압 또는 배터리 팩/셀이 마지막으로 전력 다운(powerdown)된 때에 이전에 저장되었던 정보에 기초되거나/추정될 수 있다. 다른 예들은 전력다운 등으로부터 배터리 시스템이 휴지된(rested) 시간의 길이를 통합할 수 있다.In one embodiment, the procedure for filtering with a cell system, a requirement for dynamic state and a model of defined dynamic parameters is applied. Once again, alternatively a double Kalman filter or a double expansion Kalman filter can be employed. Table 1 shows an example implementation of a system and method utilizing the Extended Kalman Filter 1100. While the cell model and the parameter estimation model employ state x _k of cell 22, it should be understood once again that the state is not necessarily predicted as part of the parameter estimation process. For example, in one example embodiment, the state x _k of cell 22 is computed by another process with the resulting state information supplied to the parameter model. Following the example implementation of Table 1, the procedure

The parameter estimate, denoted by the true, is the best guess of the parameter (e.g.,

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

The state estimate denoted by denotes the best estimate of the cell state (e.g.,

Can be determined. Estimation-error covariance matrix

It is also initialized. For example, the initialization of the state, and in particular the SOC, may be based on / estimated based on the cell voltage in the lookup table or the information previously stored when the battery pack / cell was last powered down. Other examples may incorporate the length of time the battery system has been rested from power down or the like.

Table 1: Extended Kalman Filters for Parameter Updates

=

, 파라미터 오차 불확정성은 시간의 흐름(구동 노이즈 r_k에 의해 모델에서 적응된) 때문에 더 크다. 파라미터 불확정성 추정의 업데이터에 대한 많은 가능성이 존재하며, 상기 테이블은 설명적인 예를 제공한다. 셀 출력의 측정이 이루어지고, 상태 추정값

(추정되거나 제공되더라도)과 파라미터 추정값

에 기초하여 상기 예측된 출력값과 비교된다. 이 차이는

의 값을 업데이트하는 데 이용된다. 또한, 상태 추정값

은 파라미터 추정값에 의해 앞으로 진전될 수 있거나 앞서 확인된 바와 같이 외부 수단을 경유하여 공급될 수도 있다.

는 다음의 순환 관계를 이용하여 연산될 수 있다.In this example, various steps are performed at each measurement interval. First, previous parameter estimates advance in time. The new parameter estimate is the same as the previous parameter estimate

=

However, the parameter error uncertainty is greater because of the passage of time (adapted in the model by the driving noise r _k ). There are many possibilities for the updater of the parameter uncertainty estimation, and the table provides an illustrative example. Measurement of cell output is made and state estimates

(Even if estimated or provided) and parameter estimates

Based on the predicted output value. This difference is

It is used to update the value of. Also, state estimate

May be advanced by parameter estimates or may be supplied via external means as previously identified.

Can be computed using the following recursive relationship.

The differential calculation is essentially recursive and develops over time as the state x _k develops. If the side information does not yield a better estimate of the value, then the dx ₀ / dθ term is initialized to zero. It should be clearly understood that the steps shown in the above table can be executed in various orders. Although the table lists example sequences for purposes of illustration, those skilled in the art will recognize many equivalent sequences of equations.

을 적합하게 한다. 상기 필터는 시간 업데이트 또는 예측(1100) 측면과 측정 업데이트 또는 보정(1104) 측면을 가진다. 파라미터 시간 업데이터/예측 블록(1103)은 입력으로서 이전 외부 입력 u_{k -1}, 이전 시변 파라미트 예측값(previous time varying parameters estimate)

및 보정된 파라미터 불확정성 추정값

을 수신한다. 파라미터 시간 업데이터/예측 블록(1103)은 예측된 파라미터

와 예측된 파라미터 불확정성

을 파라미터 측정 업데이트/보정 블록(1104)에 출력한다. Turning back to FIG. 12, an example implementation of an example embodiment of the present invention is shown. Recursive filter 1100 is the parameter estimate

To fit. The filter has a time update or prediction 1100 aspect and a measurement update or correction 1104 aspect. The parameter time updater / prediction block 1103 is a previous external input u _{k -1} as an input, a previous time varying parameter estimate.

And corrected parameter uncertainty estimates

Receive The parameter time updater / prediction block 1103 is a predicted parameter

And predicted parameter uncertainty

To the parameter measurement update / calibration block 1104.

과 파라미터 불확정성 추정값

을 제공하는 파라미터 측정 업데이트/보정 블록(1104)은 상기 예측된 파라미터

과 예측된 파라미터 불확정성

뿐만 아니라 외부 입력 u_k 와 모델된 시스템 출력 y_k를 수신한다. 마이너스 표기는 벡터가 상기 필터(1100)의 상기 예측 컴퍼넌트(1103)의 결과임을 의미하는 반면, 플러스 표기는 벡터가 상기 필터(1100)의 상기 보정 컴퍼넌트(1104)의 결과임을 의미하는 것으로 이해되어야 한다.Current parameter estimate

And parameter uncertainty estimates

The parameter measurement update / calibration block 1104 which provides the predicted parameter

And predicted parameter uncertainty

As well as external input u _k And receive the modeled system output y _k . Minus notation means that a vector is the result of the predictive component 1103 of the filter 1100, while plus notation should be understood to mean that the vector is the result of the correction component 1104 of the filter 1100. .

Embodiments of this invention require mathematical models of cell state and dynamic output for specific applications. In this embodiment, this can be achieved by defining specific functions for f (,,) and g (,,) to facilitate the reception or estimation of the various states and estimates of the various parameters of interest. One embodiment uses a cell model that includes the effects of one or more of the cell's open circuit voltage (OCV), intrinsic resistance, voltage polarization time constant, and hysteresis level. Although the structure and the methods presented herein are generic and can also be applied to other electrochemistries, for illustrative purposes the parameter values are tailored to this model structure for modeling the dynamics of a high power Lithium-ion Polymer Battery (LiPB) cell . For example, in one embodiment, the state and parameters of interest are embedded in f (,,) and g (,,). An example follows.

Where η _{i, k} is an efficiency factor such as coulomb efficiency,

C _k is the cell capacity (s),

,...

는 분극 전압 시정수(들),

, ...

Is the polarization voltage time constant (s),

,...

는 분극 전압 조화 요소(들),

, ...

Is the polarization voltage harmonic element (s),

R _k is the cell resistance (s),

M _k is the hysteresis harmonic element (s) and

r _k is the hysteresis rate constant (s).

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

Where Δt represents the intersample period (in seconds), C _k represents the cell capacity (in amperes-seconds), Z _k is the cell SOC at time indicator k, i _k is the cell current and η _{i , k} is a coulomb efficiency of the cell at the current level i _k.

In this example, the polarization voltage levels are obtained by various filter states. Assuming that n _f polarization voltage time constant,

는 실값(real-valued) 분극 전압 시정수

...

를 가진 단위 행렬일 수 있다. 그러하다면, 모든 엔트리들이 1 보다 작은 값을 가지면 시스템은 안정적이다. 상기 벡터

는 단순히 n_f "1"로 정해질 수 있다. B_f의 엔트리들은 그것들이 0이 아닌 한 임계적이지 않다. A_f 매트릭스에서 n_f엔트리 값은 모델 파라미터를 측정된 셀 데이터에 가장 잘 맞도록 하는 시스템 확인 절차의 일부로 선택될 수 있다. 상기 Af와 Bf 매트릭스는 시간과 현재 배터리 팩 구동 조건과 관련된 다른 팩터들에 따라 변할 수 있다. The matrix

Is the real-valued polarization voltage time constant

...

It can be an identity matrix with If so, the system is stable if all entries have a value less than one. Vector

Can simply be set to n _f "1". The entries of B _f are not critical unless they are zero. The n _f entry value in the A _f matrix may be selected as part of the system identification procedure to best fit the model parameter to the measured cell data. The Af and Bf 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.

R _k is the hysteresis rate constant found again by system identification.

In another embodiment the overall model state is a combination of the above examples as follows.

Other orders of states in the above equations are possible.

In this example, the output formula combining the state values for predicting the cell voltage is as follows.

는 출력에서 상기 분극 전압 상태를 함께 조화시키는 분극 전압 조화 팩터

,...

의 벡터이며, R_k는 셀 저항이다(다른 값들은 방전/충전에 사용될 수 있다). 그리고, M_k는 히스테리시스 조화 팩터이다. G_k는 i_k에서 G_kf_k까지의 dc게인이 0이 되도록 강제될 수 있고, 이것은 R_k의 추정값이 정확해지도록 한다.In the above formula

Is a polarization voltage harmonic factor that harmonizes the polarization voltage states together at the output

, ...

Is the vector of R _k is the cell resistance (other values can be used for discharge / charge). And 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 becomes zero, which allows the estimate of R _k to be accurate.

는 실값 분극 전압 시정수

...

를 가진 단위 행렬이다)에서 분극 전압 시정수에 대한 항을 포함할 수 있다. 이러한 시정수들은 a_{i ,k}=tanh(α_i,k)로써 연산될 수 있고, 상기 수식에서, 상기 모델의 파라미터 벡터는 α_i,k를 포함하나 직접적으로 a_{i ,k}를 포함하지는 않는다. 상기 tanh( )함수는 a_{i ,k}가 α_i,k의 값에 관계없이 항상 ±1 이내(즉, 안정적)가 되도록 확실하게 보장한다.Some embodiments of the invention may include a method of forcing a parameter of the model to be a stable system. In one embodiment, the state formula is of the form f _{k + 1} = A _f f _k + B _f i _k , where the matrix

Is the real-time polarization voltage time constant

...

It can be a unit matrix with the polarization voltage time constant. These time constants can be computed as a _{i , k} = tanh (α _{i, k} ) _{, where} the parameter vector of the model includes α _{i, k} but does not directly include a _{i , k} . The tanh () function reliably ensures that a _{i , k} is always within ± 1 (ie stable), regardless of the value of α _{i, k} .

를 이용하여 G_k의 마지막 요소가 연산되도록 강제함으로써 이루어진다. 이것은 또한 Gk:

.에 관계되는

의 요소를 연산하는 경우, 더욱 세심한 주의가 필요하다. 만약 a_{i ,k}값이 항상 ±1 이내(예를 들어, 이전 단락에 기술된 방법을 사용하여)라면, 미분 연산에 서 0으로 나누어지는(divide-by-zero) 문제가 절대 없다.Some 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 makes the estimate of R _k accurate. This is due to the different elements of G _k and the polarization voltage time constant

By forcing the last element of G _k to be computed. This is also Gk:

Relative to

When calculating the element of, you need to be more careful. If a _{i , k} is always within ± 1 (for example, using the method described in the previous paragraph), there is never a problem of divide-by-zero in the derivative operation.

Another embodiment includes methods for estimating important aspects of SOH without employing a full filter 1100. The pull filter 1100 method is computationally intensive. If exact values for a full set of cell model parameters are not needed, other methods that are potentially less complex or computationally less intensive may be used. The example method uses a filtering method to determine cell capacity and resistance. The difference in capacity and resistance from nominal “new cell” values provides capacity decay and power decay, which is the most commonly employed indicator of cell SOH.

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

In the above formula, R _k is a cell resistance and is modeled as a constant with a fictitious noise process r _k that allows modification. y _k is an estimate of the cell's voltage, i _k is the cell current and e _k models the estimation error. If an externally generated and supplied estimate of z _k is employed, filter 1100 may be applied to this model to estimate cell resistance. In the standard filter 110, the model prediction of y _k is compared with the actual measured cell voltage. Any difference resulting from the comparison is used to fit R _k .

It should be noted that the above mentioned model 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 consists of a vector containing all the resistance values to be modified, and an appropriate element from the vector can be used for each time step of the filter during the calculation.

In this example, to estimate the cell capacity using filter 1100, the cell modes are formulated as follows.

In addition, a filter is formulated using this model to yield capacity estimates. As the filter 1100 is implemented, the operation of the second equation is compared to zero, and this difference is used to update the capacity estimate. It should be noted that a good estimate of the current and previous SOC is required from the filter estimating the SOC if possible. The estimated dose can, if desired, be again a function of temperature or the like by employing a dose vector, from which the appropriate element is used at each time step during the calculation.

Thus, the method for estimating cell parameters has been described in conjunction with many specific embodiments. One or more embodiments use Kalman filters. Some embodiments use extended Kalman filter 1100. Moreover, some implementations include a mechanism that enforces the convergence of one or more parameters. One or more embodiments include a simplified parameter filter to estimate the resistance, while some implementations include a simplified parameter filter to estimate the total capacitance. The present invention can be applied to a wide range of applications and cell electrochemistry.

The disclosed method can be embodied in the form of a procedure performed on a computer or an apparatus for executing the procedure. The method may also be realized in the form of computer program code comprising instructions embodied / shaped on a tangible medium 52, such as a floppy disk, CD-ROM, hard disk or any computer-readable storage medium. Wherein the computer program code is loaded into a computer and executed by a computer, the computer becoming an instrument capable of carrying out the method. The method may be in the form of a computer program, for example stored in a storage medium, executed by a computer and / or loaded into a computer, in the form of a modulated carrier wave, any transmission medium, electrical wiring or cabling, optical fiber, electromagnetic waves. It may also be realized in the form of a data signal 54 or the like transmitted in the form of via a bowel or the like. Wherein the computer program code is loaded into a computer and executed by the computer. When implemented in a general purpose microprocessor, the computer program code segments are configured to cause the microprocessor to make specific logic circuits.

The use of the first, second, or other similar names to indicate similar constructions should not be considered to imply or imply any particular order unless stated otherwise.

Although the present invention has been described with reference to one embodiment, it will be understood by those skilled in the art that various changes and equivalent components may be made in the scope without departing from the scope of the present invention. In addition, many modifications may be made to adapt a particular situation and context to the teachings of the present invention without departing from the essential scope thereof. Therefore, the invention is not limited to the specific embodiments disclosed as the best mode contemplated for carrying out the invention, and the invention includes all embodiments falling within the scope of the appended claims.

Claims (40)

Estimating the SOC in the battery where the SOC constitutes one of the internal states; And Estimating the SOH in the battery, wherein the SOH constitutes one of the internal parameters. The method of claim 1, wherein estimating the SOC in the battery comprises: Performing internal state prediction of the battery, the SOC being one of the internal states; Performing uncertainty prediction of the internal state prediction; Correcting the internal state prediction and the uncertainty prediction; And Applying an algorithm that repeats performing the internal state prediction, performing the uncertainty prediction, and correcting to estimate the ongoing estimate for the SOC and the ongoing uncertainty for the SOC estimate. And estimating a value representing a current operating condition of the battery. The method of claim 2, wherein performing the internal state prediction comprises: Determining a current measurement; Determining a voltage measurement; And Using the current measurement and the voltage measurement in a mathematical model for performing the internal state prediction. The method of claim 3, wherein performing the uncertainty prediction comprises: Using the current measurement and the voltage measurement in a mathematical model for performing the uncertainty prediction. The method of claim 4, wherein the correcting step, Calculating a gain factor; Calculating a corrected internal state prediction using the gain factor, the voltage measurement, and the internal state prediction; And Computing a corrected uncertainty prediction using the gain factor and the uncertainty prediction. The method of claim 5, wherein the applying step, Using the corrected internal state prediction and the corrected uncertainty prediction to obtain a prediction for a next time step in which the algorithm is repeated again. . The method of claim 6, wherein the algorithm is A method for estimating a value representing a current operating condition of a battery, characterized in that it is a Kalman filter. The method of claim 6, wherein the algorithm is And an extended Kalman filter. The method of claim 8, wherein performing the internal state prediction comprises: Using another mathematical model for prediction based on changing battery conditions. The method of claim 8, wherein performing the uncertainty prediction comprises: Using another mathematical model for prediction based on changing battery conditions. The method of claim 3, wherein performing the internal state prediction comprises: Determining a temperature; And Using the temperature measurement, the current measurement and the voltage measurement in a mathematical model for performing the internal state prediction. The method of claim 11, wherein performing the uncertainty prediction comprises: Using the temperature measurement, the current measurement, and the voltage measurement in a mathematical model for performing the uncertainty prediction. A component configured to estimate the SOC in the battery where the SOC constitutes one of the internal states; 12. An apparatus for estimating a value indicative of a current operating condition of a battery comprising a component configured to estimate SOH in a battery in which the SOH constitutes one of the internal parameters. The component of claim 13, wherein the component configured to estimate SOC in the battery comprises: A component configured to perform internal state prediction of the battery, wherein the SOC is one of the internal states; A component configured to perform an uncertainty prediction of the internal state prediction; A component configured to correct the internal state prediction and the uncertainty prediction; And Apply a component configured to perform the internal state prediction, a component configured to perform the uncertainty prediction, and an algorithm that repeats the correction step to calculate an ongoing estimate for the SOC and an ongoing uncertainty for the SOC estimate An apparatus for estimating a value representing a current operating condition of a battery, comprising a component configured. 15. The component of claim 14, wherein the component configured to perform the internal state prediction comprises: A component configured to determine a current measurement; A component configured to determine a voltage measurement; And And a component configured to use the current measurement and the voltage measurement in a mathematical model for performing the internal state prediction. The component of claim 15, wherein the component configured to correct is: A component configured to calculate a gain factor; A component configured to calculate a corrected internal state prediction using the gain factor, the voltage measurement, and the internal state prediction; And And a component configured to calculate a corrected uncertainty prediction using the gain factor and the uncertainty prediction. The component of claim 15, wherein the component configured to perform the internal state prediction comprises: A component configured to determine a temperature measurement; And And using the temperature measurement, the current measurement, and the voltage measurement in a mathematical model for performing the internal state prediction. Performing internal parameter prediction of the cell; Performing uncertainty prediction of the internal parameter prediction; Correcting the internal parameter prediction and the uncertainty prediction; And Applying an algorithm that repeats the internal parameter prediction, the performing the uncertainty prediction, and the correcting step to calculate the ongoing estimation for the parameter and the ongoing uncertainty for the parameter prediction. And estimating a current parameter of the electrochemical cell system. 19. The method of claim 18, wherein performing the internal parameter prediction comprises: Receiving a status estimate; Determining a current measurement; Determining a voltage measurement; And Using the state estimate, the current measurement, and the voltage measurement in a mathematical model for performing the internal parameter prediction. 20. The method of claim 19, wherein performing the uncertainty prediction comprises: Using the state estimate, the current measurement, and the voltage measurement in a mathematical model for performing the uncertainty prediction. The method of claim 20, wherein the correcting step, Calculating a gain factor; Calculating a corrected internal parameter prediction using the gain factor, the voltage measurement and the internal parameter prediction; And Computing a corrected uncertainty prediction using the gain factor and the uncertainty prediction. The method of claim 21, wherein said applying step, Using the corrected internal parameter prediction and the corrected uncertainty prediction to obtain predictions for the next time step in which the algorithm is repeated. The method of claim 22, wherein the algorithm is At least one of a Kalman filter and an Extended Kalman filter. The method of claim 23, wherein the internal parameter is At least one of resistance, capacitance, polarization voltage time constant, polarization voltage harmonic constant, hysteresis harmonic factor, hysteresis rate constant, and efficiency factor. 19. The method of claim 18, wherein performing the uncertainty prediction comprises: Receiving a status estimate; Determining a current measurement; Determining a voltage measurement; And Using the state estimate, the current measurement, and the voltage measurement in a mathematical model for performing the uncertainty prediction. The method of claim 25, wherein performing the uncertainty prediction, Determining the temperature measurement, The performing of the uncertainty prediction may include: Using said state prediction value, said current measurement value, said voltage measurement value and said temperature measurement value in a mathematical model. 20. The method of claim 19, wherein performing the internal parameter prediction comprises: Determining a temperature measurement; And Estimating a current parameter of the electrochemical cell system further comprising using the state measurement, the temperature measurement, the current measurement and the voltage measurement in a mathematical model for performing the internal parameter prediction. How to. The method of claim 18, The method of estimating a current parameter of an electrochemical cell system, further comprising ensuring convergence of one or more parameters for each physical value. 29. The method of claim 28, wherein assuring Forcing the dc gain of the voltage polarization filter to zero. The method of claim 18, Ensuring the stability of the cell model dynamics; the method of estimating current parameters of an electrochemical cell system. 31. The method of claim 30, wherein assuring Forcing the filter poles to have a value less than one. The method of claim 30, wherein the filter pole, A method for estimating current parameters of an electrochemical cell system, characterized in that it is computed using the tanh function to ensure that the size of the filter pole is less than one. The method of claim 18, Receiving an initial state value and an initial parameter value associated with the electrochemical cell. The component of claim 13, wherein the component configured to estimate a current parameter of the battery comprises: A component configured to perform internal parameter prediction of the cell; A component configured to perform an uncertainty prediction of the internal parameter prediction; A component configured to correct the internal parameter prediction and the uncertainty prediction; Taken by a component configured to perform the internal parameter prediction, a component configured to perform the uncertainty prediction, and a component configured to calibrate to calculate an ongoing estimate for the parameter and an ongoing uncertainty for the parameter estimate And a component configured to repeat the true step. 35. The component of claim 34, wherein the component configured to perform the internal parameter prediction comprises: A component configured to receive a state estimate; A component configured to determine a current measurement; A component configured to determine a voltage measurement; And And a component configured to use the state estimate, the current measure, and the voltage measure in a mathematical model for performing the internal parameter prediction. 36. The component of claim 35, wherein the component configured to correct is: A component configured to calculate a gain factor; A component configured to calculate a corrected internal parameter prediction using the gain factor, the voltage measurement, and the internal parameter prediction; And And a component configured to calculate a corrected uncertainty prediction using the gain factor and the uncertainty prediction. 35. The component of claim 34, wherein the component configured to perform the uncertainty prediction comprises: 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 And a component configured to use the state estimate, the temperature measurement, the current measurement, and the voltage measurement in a mathematical model for performing the uncertainty prediction. Estimating device. 36. The component of claim 35, wherein the component configured to perform the internal parameter prediction comprises: A component configured to determine a temperature; And And a component configured to use the state estimate, the temperature measurement, the current measurement, and the voltage measurement in a mathematical model for performing the internal parameter prediction. Device for estimating a value. Means for performing internal parameter prediction of the cell; Means for performing an uncertainty prediction of the internal parameter prediction; Means for correcting the internal parameter prediction and the uncertainty prediction; And Means for applying an algorithm that repeats the internal parameter prediction, the uncertainty prediction, and the correction to calculate an ongoing estimate for the parameter and an ongoing uncertainty for the parameter prediction. System for estimating parameters. Performing internal parameter prediction of the cell; Performing uncertainty prediction of the internal parameter prediction; Correcting the internal parameter prediction and the uncertainty prediction; And Applying an algorithm that repeats performing the internal parameter prediction, performing the uncertainty prediction, and correcting to calculate the ongoing estimation for the parameter and the ongoing uncertainty for the parameter prediction. A storage medium encoded with machine-readable computer program code comprising instructions for causing a computer to perform a method for estimating a current parameter of an electrochemical cell that includes.

Images