MODEL PARAMETER ESTIMATOR AND MODEL PARAMETER ESTIMATION METHOD

Abstract

This model parameter estimation device comprises a state quantity calculation unit (332) for calculating state quantities indicative of a state of a storage battery (1) with respect to a measured value of a current based on a state equation obtained by assigning values to nonlinear parameters (ϕ) for a model representing the storage battery (1) using the nonlinear parameters (ϕ) and linear parameters (ψ), and time series data of the current and terminal voltage of the storage battery (1), a linear parameter estimation unit (333) for estimating the linear parameters (ψ) that minimize an error between the measured value of the terminal voltage and an estimated value of the terminal voltage calculated based on the model, the state quantities, and the measured value of the current,and a nonlinear parameter updating unit (331) for repeatedly updating the values of the nonlinear parameters (ϕ) to make the minimized error small until a convergence condition is met.,

Description

Technical area

[0001] The present application relates to a model parameter estimation apparatus and a model parameter estimation method. State of the art

[0002] To reduce environmental impacts, electric power storage systems for utilizing renewable energy have become widespread. In addition, electric vehicles such as electric vehicles (EVs), hybrid electric vehicles (HEVs), and plug-in hybrid vehicles (PHVs) have been put into practice, and electric aircraft and the like have been developed.

[0003] On the other hand, these devices use a storage battery such as a lithium-ion battery, but it is known that the storage battery degrades with use and its performance decreases. Therefore, there is a demand for a model parameter estimation technique for modeling a storage battery with high accuracy to estimate a state of charge (SOC) with high accuracy, diagnose degradation, predict a service life, and the like for the storage battery.

[0004] Therefore, a model parameter estimation method using a continuous-time system identification method based on an output error method has been proposed (see, for example, Patent Document 1). Specifically, by applying a nonlinear optimization method to time series data of currents and voltages during charging and discharging of a storage battery, model parameters are estimated such that an output voltage of a storage battery model constructed as a continuous-time system matches a measured voltage. According to this method, by appropriately selecting initial estimation values, it is possible to estimate model parameters with high accuracy while considering the nonlinearity of an open-circuit voltage (OCV) characteristic. Prior art documents Patent document

[0005] Patent Document 1: Japanese Patent Application No. 2014-86313 (paragraphs 0017 to 0018, Fig. 1, paragraphs 0044 to 0045, Fig. 5) Summary of the inventionProblems to be solved by the invention

[0006] However, the method proposed in Patent Document 1 requires setting the initial values of all parameters before estimation. However, depending on the initial values, the estimated values may deviate from the actual values or converge to a local solution that is different from the actual values. Therefore, it is important to set the initial values based on prior information about a target system, making it difficult to apply the method to a system with little prior information.

[0007] The present application discloses a technique for solving the above-described problem, and an object thereof is to obtain a model parameter estimation apparatus and a model parameter estimation method capable of estimating parameters with little information. Means to solve the problems

[0008] A model parameter estimation device disclosed in the present application includes a state quantity calculation unit for calculating state quantities indicating a state of a storage battery with respect to a measured value of a current based on a state equation obtained by assigning values to nonlinear parameters for a state-space model representing the storage battery using the nonlinear parameters and linear parameters, and time series data of each of the measured values of the current and a terminal voltage of the storage battery; a linear parameter estimation unit for estimating the linear parameters that minimize an error between the measured value of the terminal voltage and an estimated value of the terminal voltage calculated based on the state-space model, the state quantities, and the measured value of the current;and a nonlinear parameter updating unit for repeatedly updating the values of the nonlinear parameters to make the minimized error small until a predetermined convergence condition is met.

[0009] A model parameter estimation method disclosed in the present application includes a step of setting initial values of nonlinear parameters of a state-space model representing a storage battery using the nonlinear parameters and linear parameters, a state-quantity calculation step including calculating state quantities representing a state of the storage battery with respect to a measured value of a current based on a state equation obtained by assigning values to the nonlinear parameters for the state-space model and time series data of each of the measured values of the current and a terminal voltage of the storage battery, a linear parameter estimation step estimating the linear parameters minimizing an error between the measured value of the terminal voltage and an estimated value of the terminal voltage obtained based on the state-space model,the state variables and the measured value of the current, and a nonlinear parameter updating step of updating the nonlinear parameters by repeatedly updating the values of the nonlinear parameters to make the minimized error small until a predetermined convergence condition is met. Advantageous effect of the invention

[0010] According to the model parameter estimation apparatus or method disclosed in the present application, it is possible to estimate the parameters with little information because the model parameters can be estimated by setting the initial values of only nonlinear parameters. Short description of the drawings Fig. 1 is a block diagram for describing a configuration of a model parameter estimation apparatus according to Embodiment 1. Fig. 2 is a block diagram showing a hardware configuration example of a part that executes the arithmetic processing of the model parameter estimation device according to Embodiment 1. Fig. Figure 3 is a diagram showing an equivalent circuit of a storage battery for which model parameters are to be estimated. Fig. Figure 4 is a diagram showing a Foster-type circuit as another model of a storage battery for which model parameters are to be estimated. Fig. 5 is a flowchart showing an operation of the model parameter estimation apparatus or a model parameter estimation method according to Embodiment 1. Fig. 6 is a diagram in the form of a graph showing temporal changes of measured values of currents, measured values of voltages, and estimated values of currents by a model when the model parameter estimation device or the model parameter estimation method according to Embodiment 1 is applied to a specific storage battery system. Fig. 7 is a diagram in the form of a graph showing a relationship between an electrical quantity and an open-circuit voltage as an OCV function estimated when the model parameter estimation apparatus or method according to Embodiment 1 is applied to a specific storage battery system. Mode for carrying out the inventionEmbodiment 1

[0011] Fig. 1 to Fig. 7 are diagrams for describing a configuration and an operation of a model parameter estimation apparatus and a model parameter estimation method according to Embodiment 1, wherein Fig. 1 is a block diagram of a storage battery system including a storage battery as an estimation target and the model parameter estimation device for describing the configuration of the model parameter estimation device, and Fig. 2 is a block diagram showing a hardware configuration example of a part that executes the arithmetic processing of the model parameter estimation device.

[0012] Furthermore, Fig. 3 is a diagram showing an equivalent circuit in which a storage battery, for which model parameters are to be estimated, is represented by a DC component and a relaxation component of an overvoltage, and Fig. Figure 4 is a diagram showing an equivalent Foster-type circuit in which multiple CR parallel elements are connected in series to represent a diffusion impedance as another model of a storage battery. Fig. 5 is a flowchart showing an operation for estimating model parameters in the model parameter estimator, that is, a model parameter estimation method.

[0013] Furthermore, Fig. 6 is a diagram in which three graphs showing respective changes over time in measured values of voltages of a storage battery, in measured values of currents of the storage battery, and in estimated values of currents by a model when the device for estimating model parameters or the method for estimating model parameters is applied to a specific storage battery system are arranged vertically, with a horizontal axis indicating a common (synchronized) time, and a vertical axis indicating a measurement result of voltages, a measurement result of currents, and estimated values of currents, respectively. Furthermore, Fig. 7 is a diagram in the form of a graph showing an OCV function estimated at that time, where the horizontal axis represents an electrical quantity standardized by a certain standard capacitance and the vertical axis represents an open-circuit voltage.

[0014] The model parameter estimation device and the model parameter estimation method according to an embodiment of the present application will be described in detail below with reference to the drawings. Note that the same reference numerals denote the same or corresponding parts in the drawings.

[0015] As in Fig. As shown in FIG. 1, a model parameter estimation device 3 according to Embodiment 1 is provided in a storage battery system 100 including a storage battery 1 to diagnose the storage battery 1. Then, the model parameter estimation device is connected to a detection unit 2 including a current detection device 21 for detecting a current and a voltage detection device 22 for detecting a voltage, which are an output characteristic of the storage battery 1, and is configured to estimate model parameters of the storage battery 1.

[0016] The storage battery 1 is typically assumed to be a lithium-ion storage battery, but is not limited to the lithium-ion storage battery and may be another type of storage battery, such as a lead-acid storage battery, a nickel-metal hydride storage battery, a nickel-cadmium storage battery, or a solid-state storage battery. In addition, the storage battery 1 to be diagnosed may be a battery module in which a plurality of cells are connected in any combination of series connection and parallel connection, in addition to a single-cell storage battery. In addition, the storage battery 1 may be a pack in which modules are further connected in any combination of series connection and parallel connection, or the like, and it is arbitrary which unit is regarded as a single storage battery 1.

[0017] The model parameter estimation device 3 includes a time series data acquisition unit 31 that acquires time series data of measured values of a current value I and a voltage value V detected by the acquisition unit 2, and a model acquisition unit 32 that acquires a storage battery model and sets initial values of nonlinear parameters ϕ, which will be described later. Furthermore, the model parameter estimation device includes a parameter estimation unit 33 that estimates model parameters from the data acquired by the time series data acquisition unit 31, the storage battery model set by the model acquisition unit 32, and the initial values of the nonlinear parameters ϕ. Note that an example in which the model acquisition unit 32 sets the initial values has been described here, but an initial setting unit may be provided separately or in the parameter estimation unit 33 to set (or read) the initial values.

[0018] The parameter estimation unit 33 includes a nonlinear parameter update unit 331 that updates the nonlinear parameters ϕ, and a state quantity calculation unit 332 that calculates the state quantities (or state quantities) of the storage battery model based on a state equation of the storage battery model when the nonlinear parameters ϕ are set. Furthermore, a linear parameter estimation unit 333 that estimates linear parameters ψ based on the storage battery model and the state quantities, and a determination unit 334 that determines whether the parameter estimation has converged based on a convergence determination condition, are provided.

[0019] As in Fig. As shown in Figure 2, the model parameter estimation device 3 may be configured with hardware 30 including a processor 30a and a storage device 30b. Although not shown, the storage device 30b includes a volatile storage device such as a random access memory and a non-volatile auxiliary storage device such as a flash memory. Further, an auxiliary storage device such as a hard disk may be provided instead of the flash memory. The processor 30a executes program input from the storage device 30b. In this case, the program is input from the auxiliary storage device to the processor 30a via the volatile storage device. In addition, the processor 30a may output data such as a calculation result to the volatile storage device of the storage device 30b or store the data in the auxiliary storage device via the volatile storage device.

[0020] That is, each of the functions of the units constituting the model parameter estimator 3, for example, the functions of the model acquisition unit 32, the state variable calculation unit 332, the linear parameter estimation unit 333, and the nonlinear parameter update unit 331, is implemented by software, firmware, or a combination thereof. The software and firmware are written as programs and stored in the memory 30b. The processor 30a reads a program stored in the memory 30b and executes the program, thereby implementing the function of each unit of the model parameter estimator 3. <Allgemeine Beschreibung der Technologie der vorliegenden Anmeldung>

[0021] Technical details of the model parameter estimation device 3 and the model parameter estimation method of the present application will first be described using a general problem in which the target is not limited to the storage battery. First, assume that a state-space model of a target system is expressed as Equation (1). {y=gT(x,u;ϕy)ψx˙=f(x,u;ϕx)

[0022] Here, x is a vector representing state variables, u is an input, y is an output, and both f and g are certain nonlinear vector-valued functions. Furthermore, ϕx and ϕy are nonlinear parameters in the state equation and the corresponding output equation, and ψ is a linear parameter.

[0023] What is to be solved here is to determine a parameter θ that minimizes an evaluation function J(θ) based on the sum of the squares of an error ε between an output ŷ (estimated value) and a measured value y in the model shown in equation (2) when measured values of time series data for input / output {u(t k ) | k = 0, ..., N} and {y(t k ) | k = 0,..., N} at times {t k | k = 0,..., N} are measured, which are arbitrarily sampled at equal or unequal intervals. J(θ)=1N+1∑k=0Nϵ2(tk)=1N+1∑k=0N(y^(tk,θ)−y(tk))2

[0024] Here, θ is a vector in which the linear parameters ψ and the nonlinear parameters ϕ are arranged, and is defined as θ: = [ϕ T , ψ T ] T in relation to ψ:=[ψxT,ψyT]T.

[0025] Since this is a nonlinear optimization problem, it is possible to obtain a locally optimal solution by a well-known nonlinear optimization method. For example, it is possible to use a Gauss-Newton method, a Levenberg-Marquardt method, or the like based on a gradient with respect to a parameter of the evaluation function or a gradient with respect to a parameter of the output ŷ(t k , θ) of the estimation. Furthermore, it is also possible to use a gradient-free method, that is, a method such as a Nelder-Mead method that does not rely on information about the gradient, and there is no restriction on the specific method of nonlinear optimization.

[0026] To determine the gradient with respect to a parameter, a method based on calculating a sensitivity equation as described in Patent Literature 1 may be used. Further, a gradient approximation method using a one-sided difference, a two-sided difference, or the like may be used, or an adjoint method by introducing an adjoint variable may be used.

[0027] Although Equation (1) describes a continuous-time state-space model, the target system can be considered in discrete time. At this point, the state-space model is described as Equation (3). {yk=gdT(xk,uk;ϕy)ψxk+1=fd(xk,uk;ϕx)

[0028] Here is x k a vector representing the state variables at time k, u k and y k are the input and output corresponding to time k, and f d and gd are each a specific nonlinear vector-valued function. To convert a continuous-time system into a discrete-time system, a well-known method such as the zero-holding method or the first-place stopping method can be used.

[0029] On the other hand, when dealing with a continuous-time system, it is possible to calculate quantities of a state at any time from series data of the input by applying a numerical solution of a known differential equation to an original equation of state. The Euler method or the Runge-Kutta method can typically be used as numerical solutions of the differential equation.

[0030] However, a general problem in an output-error method addressing a nonlinear optimization problem is that an estimation parameter value depends on an initial value. As described in the background, therefore, a global optimal solution can only be achieved if the initial values of the estimation parameters are set appropriately. Therefore, the focus is on the structure of the state-space model of Equation (1) and consideration is given to reducing the dependence on the initial value. First, Equation (4) is obtained by arranging the model outputs vertically according to the time series. [y^(t0,θ)⋮y^(tN,θ)]=[gT(x(t0,ϕx),u(t0);ϕy)⋮gT(x(tN,ϕx),u(tN);ϕy)]ψ↔Y^(ϕ,ψ)=G(ϕ)ψ

[0031] That is, the linear parameters ψ and the nonlinear parameters ϕ can be expressed separately. At this time, a relationship of equation (5) holds for a vector of output Y: = [y (t0), ..., y(t N )] T and a vector of the error E:=[ε(t0),…,ε(tN)]T. Y=G(ϕ)ψ+E

[0032] Therefore, if the nonlinear parameters ϕ are fixed in equation (5), a linear least squares solution (or least squares solution) of the linear parameters ψ as in equation (6) is obtained by the linear least squares method (or least squares method). Ψ=(ϕ)=(GT(ϕ)G(ϕ))−1GT(ϕ)Y

[0033] Using the linear least squares solution of equation (6), the problem to be solved is converted into a problem P2 of equation (8), while the original optimization problem is a problem P1 of equation (7). P1:minϕ,ψ‖Y−G(ϕ)ψ‖2 P2:minϕ‖Y−G(ϕ)(GT(ϕ)G(ϕ))−1GT(ϕ)Y‖

[0034] That is, problem P1, which originally requires estimating all linear parameters ψ and the nonlinear parameters ϕ, is converted into an estimation problem (problem P2) for only the nonlinear parameters ϕ. If the solution for the nonlinear parameters ϕ of problem P2 is obtained (can be specified), the solution for the linear parameters ψ is also immediately obtained by substituting the solution into equation (6).

[0035] Note that since problem P2 is also a nonlinear optimization problem, various well-known nonlinear optimization methods can be used, as described above, as in the case of solving problem P1. When problem P1 is converted to problem P2, the parameters for estimation are only the nonlinear parameters ϕ, and thus the following advantage is achieved.

[0036] First, the dependence on the initial value can be reduced. If the original problem P1 is to be solved, the initial values of all linear parameters ψ and the nonlinear parameters ϕ must be set, whereas in problem P2, the linear parameters ψ are determined as a linear least-squares solution without initial values. For this purpose, the problem can be solved by setting only the initial values of the nonlinear parameters ϕ. This simplifies the problem of estimating the true values of the parameters.

[0037] Second, when applying many nonlinear optimization methods, the amount of computation is reduced. For example, if a technique is used that utilizes gradient information related to the model output parameters, the sizes of the gradient vector, Jacobian matrix, or the like are reduced to the extent that the gradient information of the linear parameters ψ is unnecessary. Additionally, from another perspective, it is expected that the number of repeated calculations until the parameters converge can be reduced by reducing the number of estimation parameters.

[0038] Third, numerical stability is improved. Generally, a problem such as truncation of significant figures occurs when the magnitude of a value differs significantly between estimation parameters. However, such a problem is expected to be less likely to occur when the number of estimation parameters is reduced.

[0039] Next, a specific method for obtaining a solution is described separately for a case where the linear parameters ψ include a linear equality condition and for a case where the linear parameters ψ include a linear equality condition and a linear inequality condition. <1: When linear parameters include a linear equality condition>

[0040] If the linear parameters ψ include a linear equality constraint, a least squares problem (or least squares problem) with restricted equality constraints of the linear parameters ψ is formulated as problem P3 in equation (9). P3:minϕ,ψ‖Y−G(ϕ)ψ‖2 subject to Ceqψ=deq

[0041] Here are C eq and d eq a matrix and a vector describing a linear condition for the linear parameters ψ. To solve problem P3 based on the same idea as described above, if a subproblem SP3 of problem P3 is considered with respect to G = G (ϕ), in which the nonlinear parameters ϕ are fixed to certain values, equation (10) is obtained. SP3:minψ‖Y−Gψ‖2subject to Ceqψ=deq

[0042] Since subproblem SP3 is a restricted linear least squares problem, it can be solved using the Lagrange multiplier method. More specifically, subproblem SP3 consists in finding ψ that minimizes an evaluation function L, represented by Equation (11), using the Lagrange multiplier vector λ. L(ψ)=12‖Y−Gψ‖2+λT(Ceqψ−deq)

[0043] Then, if we consider a case where the gradients of the evaluation function L with respect to ψ and λ become 0, we obtain equation (12). ∂L∂ψ=GTGψ−GTy+CeqTλ=0∂L∂λ=Ceqψ−deq=0

[0044] In summary, equation (13) is obtained, and a solution can be obtained immediately. [GTGCeqTCeq0][ψλ]=[GTydeq]↔[ψλ]=[GTGCeqTCeq0]−1[GTydeq]

[0045] To solve problem P3, the updating of the nonlinear parameters by the nonlinear optimization method and the calculation of the linear parameters by the Lagrange multiplier method can be repeated alternately. <2: Case where the linear parameter includes a linear equality constraint and a linear inequality constraint>

[0046] When the linear parameters include the linear equality constraint and the linear inequality constraint, the least squares problem with restricted inequalities for the linear parameters is formulated as problem P4 in equation (14). P4:minϕ,ψ‖Y−G(ϕ)ψ‖2subject to Ceqψ=deq Cineqψ≤dineq

[0047] Here are C ineq and d ineqa matrix and a vector describing the linear inequality condition for the linear parameters ψ. If a subproblem SP4 of problem P4 is considered in the same way as in the case of problem P3, equation (15) is obtained. SP4:minψ‖Y−Gψ‖2subject to Ceqψ=deq Cineqψ≤dineq

[0048] As a method for solving subproblem SP4, an interior point method, a sequential quadratic programming method, or similar methods can be used. In this case, iterative calculation is required, but since subproblem SP4 is a convex optimization problem, a global optimal solution is obtained. Since subproblem SP3 includes subproblem SP4, it is of course possible to apply such a solution method to subproblem SP3 through iterative calculation. To do this, the updating of the nonlinear parameters by the nonlinear optimization method and the calculation of the linear parameters by the solution method of the convex optimization problem should be repeated to solve problem P4.

[0049] Now, a specific procedure for applying the nonlinear optimization method to problem P1, problem P3, and problem P4 will be described, with problem P4 as the objective. Note that it is sufficient to describe problem P4 as the objective, since problem P1 and problem P3 are encompassed within problem P4. In fact, problem P1 is a special case where there are no inequality and equality constraints in problem P4. Furthermore, problem P3 is also a special case where there is no inequality constraint in problem P4.

[0050] If an optimal solution of the linear parameters ψ with respect to certain nonlinear parameters ϕ in subproblem SP4 is ψ = ψ* (ϕ), an evaluation function that needs to be minimized in problem P4 is equation (16). L(ϕ)=∑k=0N(y(tk)−y^(tk,ϕ,ψ*(ϕ)))2=∑k=0N(y(tk)−gT(x(tk,ϕx),u(tk);ϕy)ψ*(ϕ))2=‖Y−G(ϕ)ψ*(ϕ)‖2

[0051] Since ψ* (ϕ) can be obtained by solving subproblem SP4 using the method described above, only the nonlinear parameters ϕ that minimize L(ϕ) need to be found to solve problem P4. Below, a steepest descent method, which is a type of gradient method, a Gauss-Newton method, and a Nelder-Mead method, which is one of the gradient-free methods, are described as the nonlinear optimization methods. <Verfahren des steilsten Abstiegs>

[0052] When the steepest descent method is used, an update equation of the nonlinear parameters ϕ is equation (17). ϕl+1=ϕl−α[∂L(ϕl)∂ϕ1⋮∂L(ϕl)∂ϕnϕ]

[0053] Here, α is a predetermined positive value and can be determined by a line search or the like for each update.

[0054] If it is difficult to obtain the gradient directly, a value such as a one-sided difference or a two-sided difference can be used as an approximate value for the gradient. For example, in the one-sided difference, the partial difference can be approximately calculated as in equation (18) by j by a sufficiently small Δ j is disturbed. ∂L(ϕ)∂ϕj≈L(ϕ+Δjej)−L(ϕ)Δj

[0055] Here, e j a unit vector that has the same length as the nonlinear parameters ϕ and where only the j-th element is equal to 1. That is, ϕ + Δ j e j is a perturbation value obtained by perturbing only the j-th element of the nonlinear parameters ϕ. At this time, an update equation of the nonlinear parameters ϕ is Equation (19). ϕl+1=ϕl−α[L(ϕl+Δ1e1)−L(ϕl)Δ1⋮L(ϕl+Δnϕenϕ)−L(ϕl)Δnϕ]

[0056] Note that when calculating the evaluation function L, it is necessary to calculate the sets of states for each value of the nonlinear parameters ϕ, estimate the linear parameters ψ, and calculate an estimate of the output. <Gauß-Newton-Verfahren>

[0057] An update equation of the Gauss-Newton method is equation (20), where Λ(ψ) is expressed by equation (21) and ∂ŷ(t k , ϕ, ψ* (ϕ)) / ∂ϕ j is a sensitivity function, i.e. a partial derivative of the estimate of the output with respect to a certain nonlinear parameter ϕ j . ϕl+1=ϕl−[ΛT(ϕl)Λ(ϕl)]−1ΛT(ϕl){Y−Y^(ϕl,ψ*(ϕl))} Λ(ϕ)=[∂y^(t0,ϕ,ψ*(ϕ))∂ϕ1…∂y^(t0,ϕ,ψ*(ϕ))∂ϕn ϕ⋮…⋮∂y^(tN,ϕ,ψ*(ϕ))∂ϕ1…∂y^(tN,ϕ,ψ*(ϕ))∂ϕnϕ]

[0058] When it is difficult to obtain the sensitivity function directly, an approximate value of the sensitivity function is used instead of the sensitivity function. That is, an approximate value of the gradient is used instead of the gradient itself. In this case, too, the calculation formula for using the one-sided difference is Equation (22). ∂y^(tk,ϕ,ψ*(ϕ))∂ϕj≈y^(tk,ϕ+Δjej,ψ*(ϕ+Δjej))−y^(tk,ϕ,ψ*(ϕ))Δj <nelder-mead-verfahren>

[0059] For example, when the Nelder-Mead method is used, the values of the evaluation function L(ϕ 1,1 ), L (ϕ 1,2 ), ..., L (φ 1,nϕ+1 ) using n ϕ + 1 variables ϕ 1,1ϕ1,2 , ..., ϕ1,nϕ+1 in terms of the number of iterations 1 and the number of nonlinear parameters n ϕ within a parameter update. Furthermore, values of the evaluation function are also calculated for parameter values that are subject to four types of operations: mirroring, expansion, contraction, and reduction. Then, the parameter of ϕ 1 to ϕ 1 + 1 updated according to a known algorithm, while using the values of the evaluation function calculated in this way.

[0060] As described above, depending on the nonlinear optimization method, it is necessary to obtain the evaluation functions or the estimated output values for a variety of different nonlinear parameter estimates in order to update the nonlinear parameter estimates.

[0061] Note that, although a description has been omitted due to the deviation from the gist of the present application, even in a case where the original problem P1 includes at least one of the equality constraint and the inequality constraint for the nonlinear parameters ϕ, a known constrained nonlinear optimization method can be applied when updating the nonlinear parameters ϕ. For example, a local solution can be obtained by applying the interior point method, the sequential quadratic programming method, or similar methods described above.

[0062] Above, the details of the technique for estimating the parameters of the present application were described, with a general problem as the objective. Given the above details, a case is described in which the existing technology is applied to Memory 1. <Anwendung auf Speicherbatterie>

[0063] As with regard to Fig. 1, the current detection device 21 detects the current of the storage battery 1 and outputs a detected current value I. The voltage detection device 22 detects a terminal voltage (or terminal voltage) of the storage battery 1 and outputs a detected voltage value V. Note: When the storage battery 1 is configured by a serial parallel connection of a plurality of cells, the detection current and the detection voltage may be those of a single cell or the plurality of cells constituting a part of the storage battery 1. In the following description, it is assumed that the sampling period of the time series data t s seconds. Note: The sampling period t s does not have to be fixed and can be variable.

[0064] The time series data acquisition unit 31 acquires time series data {I(t k ) | k = 0, 1, ..., N} of the detected currents and time series data {V(t k ) | k = 0, 1, ..., N} of the detected voltages for a time series {t k | k = 0, 1, ..., N} of certain times. For simplification, consider a case where the sampling period t s is fixed, a relationship of t k = t0 + kt s with respect to the initial time t0. Note that the series data may be stored within the time series data acquisition unit 31 or acquired via an external PC, a server, a cloud, or the like.

[0065] The model acquisition unit 32 contains a storage battery model for the storage battery 1 to be estimated, and the storage battery model is used in the parameter estimation unit 33. Then, parameters of the storage battery model, including initial values, are appropriately updated based on the parameters estimated by the parameter estimation unit 33. Note that the storage battery model held by the model acquisition unit 32 may be originally held within the model parameter estimation device 3 or may be acquired from an external PC, a server, a cloud, or the like.

[0066] As a storage battery model, for example, an equivalent circuit model as in Fig. 3 shown. In Fig. 3, a resistor R0 serves to represent a DC component of an overvoltage derived from an electrolyte solution resistance, a collector metal resistance, a contact resistance, a charge transfer resistance, and the like of the storage battery 1. In addition, a resistance element R d and a capacitor element C d to represent a relaxation component of an overvoltage derived from a diffusion component of the storage battery 1.

[0067] At this time, a state space model of the storage battery 1 is described, for example, by equation (23) to equation (25). q˙=I−Ioff q˙d=−1τdqd+I−Ioff V=R0(I−Ioff)+qdCd+fOCV(q)

[0068] Here q is an electrical quantity, I is a detected current value (detected current), I off is an offset error of the current included in the detected current, q d is a capacitor element C d stored charge and f OCV is a function (OCV function f OCV ), which represents an OCV characteristic that depends on the electrical quantity q of the storage battery 1. It should be noted that the electrical quantity q can be a normalized value, and in this case the OCV function f OCV also a function for the normalized electrical quantity q.

[0069] For example, when a discrete-time state-space model is used, equations (23) to (25) are converted to equations (26) to (28) by keeping zero-order. qk+1=qk+Ik−Ioff qd,k+1=e−1τdtsqd,k+τd(1−e−1τdts)(Ik−Ioff) Vk=R0(Ik−Ioff)+qd,kCd+fOCV(qk)

[0070] Another model for a storage battery can be a Foster equivalent circuit model in which several CR parallel elements are connected in series, as in Fig. 4. The Fig. The equivalent circuit model shown in Figure 4 is a more detailed storage battery model than the one shown in Fig. 3, since the three CR parallel elements are connected in series. Of course, the number of CR parallel elements connected in series can be arbitrary.

[0071] In addition, if a diffusion impedance is approximated by the Foster-type circuit, each CR parallel element can be expressed using only a diffusion resistance Rd and a diffusion capacitance Cd as follows (see, for example, Kuhn, Estelle, et al. "Modelling Ni-mH battery using Cauer and Foster structures." Journal of power sources 158.2 (2006): 1490-1497.). Ri=8Rd(2i−1)2π2,Ci=Cd2 for i=1,2,…,nd

[0072] Here is n d an approximate order. For example, if the approximate order n d = 3, the diffusion impedance is approximated by three states of the CR parallel element, as in the equivalent circuit model in Fig. 4.

[0073] At this time, equation (27) and equation (28) become equation (30) and equation (31). q˙d,i=−1kiτdqd,i+I−Ioff for i=1,2,…,nd V=R0(I−Ioff)+2Cd∑i=1ndqd,i+fOCV(q)

[0074] Here is k i as described in equation (32) ki=4 / ((2i−1)2π2)

[0075] It should be noted that other battery models may be used, for example, a Cauer-type circuit may be used. Alternatively, a so-called electrochemical model may be used, which attempts to directly describe an internal phenomenon of the storage battery 1 without using an equivalent circuit. Various known models can be used as the model of the storage battery 1, and the model is not limited as long as the model can be expressed within the framework of equation (1) or equation (3). It should be noted that for the sake of simplicity, the following description adopts the equivalent circuit model, which is related to Fig. 3 is described.

[0076] As OCV function f OCV , which represents the OCV characteristic, typically uses a linear or piecewise linear function with respect to the electrical quantity q. For example, if a polynomial is used, it is expressed as in Equation (33), and a linear expression of the parameter is possible. fOCV(q)=∑i=0mpciqi=[qmp,qmp−1,…,q0][CmpCmp−1⋮C0]

[0077] Here m represents p the degree of the polynomial and c i is a coefficient of q i .

[0078] Alternatively, the piecewise linear function (first-order spline curve) shown in equation (34) is used. fOCV(q)={a1q+b1for p1≤q≤p2⋮⋮ams−1q+bms−1for pms−1≤q≤pms

[0079] Here is m s (≥ 2) is the number of nodes, and in equation (34) the function is divided into ms-1 sections by m s Points of q = p1, p2, ..., p ms divided, and if m s ≥ 3, equation (35) is satisfied as a condition for equality. aipi+1+bi=ai+p1i+1+bi+1 for i=1,…,ms−2

[0080] Alternatively, a cubic spline curve of equation (36) is used. fOCV(q)={a1q+b1q2+c1q+d1for p1≤q≤p2⋮⋮ams−1q+bms−1q2+cms−1q+dms−1for pms−1≤q≤pms

[0081] It should be noted that if m s ≥3, equation (37) is satisfied as a condition for equality. aipi+13+bipi+13+cipi+1+di=aipi+13+bipi+12+ci+1pi+1+di+13aipi+12+2bipi+1+ci=3ai+1pi+12+2bi+1pi+1+ci+16aipi+1+2bi=6ai+1pi+1+2bi+1 for i=1,…,ms−2

[0082] Alternatively, a spline curve of any other order can be used.

[0083] An expression with linear parameters is also possible in a piecewise polynomial such as a spline curve. For example, in the case of a piecewise linear function, it can be expressed as in equation (38). Here, δ i,k as shown in equation (39). fOCV(q(tk))=[δ1,kq(tk),…,δms,kq(tk),δ1,k,…,δms,k][a1⋮ams−1b1⋮bms−1] δi,k={1,ifpi≤q(tk)≤pi+10,otherwise

[0084] Similarly, an expression with linear parameters is also possible in other cases, such as a cubic spline curve. Furthermore, it is also possible to use f as another OCV function. OCV to consider a case that includes both the linear parameters ψ and the nonlinear parameters ϕ. In this case, the function is formed as in equation (40). fOCV(x)=gOCVT(q,ϕOCV)ψOCV

[0085] Here, g OCV a vector-valued function and ϕ OCV and ψ OCV are vectors of the nonlinear parameters ϕ and the linear parameters ψ contained in the OCV function f OCV are included accordingly.

[0086] As an additional OCV function f OCV it is also possible to consider the case where only the nonlinear parameters ϕ are included. That is, the functional form of the OCV function f OCV is not necessarily restricted to the form that includes the linear parameters ψ. However, the advantage of the approach of converting problem P1 into problem P2 is greatly exploited in the present application, especially when a large number of linear parameters ψ are involved. Note that the following describes a case in which equation (34) is defined as the OCV function f OCV is used.

[0087] The nonlinear parameter updating unit 331 updates the nonlinear parameters ϕ of the storage battery model based on the time series data {I(t k ) | k = 0, 1, ..., N} of the detected currents, the time series data {V(t k ) | k = 0, 1, ..., N} of the detected voltages and the storage battery model. Note that the nonlinear parameters ϕ are represented here as in equation (41). ϕ=[τd Ioff ϕOCVT]T

[0088] That is, in the state-space model of storage battery 1, this refers to parameters included in the state equation and to nonlinear parameters (parameters that cannot be expressed as a linear expression) included in the output equation. Note that it is not necessary to include all nonlinear parameters ϕ in the estimation parameters, for example, if a specific nonlinear parameter value is known.

[0089] Depending on how the state-space model of storage battery 1 is created, the elements of the nonlinear parameters ϕ can vary. For example, if the nonlinear parameters ϕ OCV not in the OCV function f OCV are included, the nonlinear parameters ϕ do not necessarily include ϕ OCV . Furthermore, the parameters included in the equation of state of equation (24) and equation (30) include only one time constant τ d and the current offset error I off , but depending on the procedure, other parameters may also be included in the equation of state.

[0090] For example, in a case where multiple states of the CR parallel element are expressed by a diffusion impedance approximation as in equation (29), the time constant is a parameter of only τ d , but in a case where the multiple states of the CR parallel element are not expressed by the approximation, the parameters of the time constant exist independently of the number of CR parallel elements. In addition, C includes d the nonlinear parameters ϕ, not the linear parameters ψ, if, for example, the CR overvoltage equation of state from equation (42) is used instead of the CR overvoltage equation of state from equation (24) and the output equation is set to equation (43) instead of equation (25). V˙d=−1τdVd+1Cd(I−Ioff) V=R0(I−Ioff)+Vd+fOCV(q)

[0091] However, in this case, considering that both τ d as well as C d included in the nonlinear parameters ϕ, it is better to use equation (24) to make the most of the advantage of the technical idea of the existing application.

[0092] As a specific method for updating the nonlinear parameters ϕ, it is possible to use a nonlinear optimization method based on a known iterative calculation as described above.

[0093] Predetermined values are used as initial values of the nonlinear parameters ϕ. The predetermined values use prior knowledge of the true values of the nonlinear parameters ϕ, if possible. For example, since it is known that the diffusion time constant τ d in a lithium-ion storage battery is usually about several tens of seconds to several hundred seconds, the diffusion time constant τ d For example, it is set to 100 seconds as the initial value. Furthermore, since the current offset error I off is a very small value, an initial value is set to 0 A, for example.

[0094] These settings are very suitable values for a typical lithium-ion storage battery and a current sensor and do not depend on the parallel connection configuration of the storage battery 1. Therefore, an advantage in terms of application to the product is that an operation to tune the initial value is not necessary in many cases. Additionally, data from a datasheet or the like may be available if an evaluation result of the characteristics of the storage battery 1 of a brand-new product is available. Furthermore, the result of a past estimation of the parameters may be used if such an estimation has been performed in the past.

[0095] Note that the initial values can be set in the model acquisition unit 32, in the nonlinear parameter update unit 331, or in a separately provided initial setting unit (not shown). At this time, the initial values can be set automatically based on the prior knowledge described above, or based on an input by requesting input after presenting prior information, candidate initial values, and the like through an input interface (not shown).

[0096] Note that for updating the nonlinear parameters ϕ, the operations of the state variable calculation unit 332 and the linear parameter estimation unit 333, which will be described later, can be included within the unit. For example, when using the information about the gradient of the evaluation function with respect to the nonlinear parameters ϕ to update the nonlinear parameters ϕ, the same calculations as in the state variable calculation unit 332 and the linear parameter estimation unit 333 are required.

[0097] The state quantity calculation unit 332 calculates time series values of the state quantities in the storage battery model (ie, state space model of the storage battery 1) based on the series data {I(t k ) | k = 0, 1, ..., N} of the detected currents and the storage battery model. For example, the state variables in the state-space model from equation (23) to equation (25) refer to the electric quantity q and the electric charge q d .

[0098] For the calculation of the time series values of the state variables based on the state-space model, as described above, either a continuous-time or a discrete-time state-space model can be used. In the former case, a well-known numerical method such as a fourth-order Runge-Kutta method can be used, and in the latter case, the calculation can be performed sequentially according to the model. Alternatively, it can be calculated based on the solution to the equation of state.

[0099] The linear parameter estimation unit 333 estimates the linear parameters ψ based on the time series data {I(t k ) | k = 0, 1, ..., N} of the detected currents, the time series data {V(t k ) | k = 0, 1, ..., N} of the detected voltages, the storage battery model, and the state variables, and calculates a model voltage output. Specifically, the linear parameters ψ can be expressed separately in the output equation, as in Equation (44), thereby being expressed as in Equation (45). V=R0(I−Ioff)+qdCd+gOCVT(q,ϕOCV)ψOCV=[I−Ioff, qd, gOCVT(q,ϕOCV)][R0Cd−1ψOCV] [V(t0) ⋮V(tN)]=[I(t0)−Ioff qd(t0)gOCVT(q(t0),ϕOCV)⋮⋮⋮I(tN)−Ioffqd(tN)gOCVT(q(tN),ϕOCV)][R0Cd−1ψOCV]↔V=G(ϕ)ψ

[0100] Thus, the linear least squares solution of the linear parameter ψ with respect to the estimated values of some nonlinear parameters ϕ can be estimated according to equation (46). ψ(ϕ)=(GT(ϕ)G(ϕ))−1GT(ϕ)ν

[0101] Accordingly, problem P1, which is a voltage error minimization problem based on the output deviation method in storage battery 1, can be converted into problem P2 by Equation (46). Furthermore, the model voltage output can also be calculated using the estimated values of the linear parameters ψ.

[0102] If an equality condition is included, problem P3 can be considered in light of the equality condition. For example, if the OCV function f OCV is a linear spline curve (a function that is linear in parts), equation (35) must be satisfied, and for this, if ψ OCV,i = [a i b i ] T , the equation of the condition of equality becomes equation (48) in terms of equation (47). Xi=[pi+1 1]T [00−χ1Tχ1T⋮⋮⋱⋱00−χms−2Tχms−2T][R0Cd−1ψOCV,1ψOCV,2⋮ψOCV,ms−1]=[0000⋮0]

[0103] Additionally, if the OCV function f OCV is a cubic spline curve, equation (37) must be satisfied if ψ OCV,i = [a i b i c i d i ] T , and the equality condition becomes equation (50) corresponding to equation (49). χi=[pi+13 pi+12 pi+1 1]Tχi(1)=[3pi+12 2pi+1 pi+1 1 0]Tχi(2)=[6pi+1 2 0 0]T [00−χ1Tχ1T00−χ1(1)T−χ1(1)T⋱00−χ1(2)T−χ1(2)T⋱⋱⋮⋮⋱⋱⋱00⋱⋱−χms−2Tχms−2T00⋱−χms −2(1)χms−2(1)T00−χms−2(2)Tχms−2(2)T][R0Cd−1ψOCV,1ψOCV,2⋮ψOCV,ms−1]=[0000⋮0]

[0104] Using this formulation, the problem to be solved can be treated as problem P3 and subproblem SP3. The solution procedure at this time is as described above. Note that the equality constraint equation is not limited to those described in the above example and can be a single equation or multiple equations expressed by a linear equality constraint equation.

[0105] Furthermore, it is also possible to consider the case where the inequality condition includes the linear parameters ψ. For example, if it is desired to have prior knowledge regarding the upper and lower boundary conditions of R 0,min ≤ R0 ≤ R 0,max and C d,min ≤ C d ≤ C d,max with respect to R0 and C d , the inequality condition can be expressed as in equation (51). [−100…0100…0010…00−10…0][R0Cd−1ψOCV]≤[−R0,minR0,maxCd,min−1−Cd,max−1]

[0106] This allows the problem to be solved to be treated as problem P4 and subproblem SP4. The solution procedure at this time is as described above. Note that the inequality condition is not limited to the example described above and can be a single inequality or multiple inequalities expressed by a linear inequality condition.

[0107] Although a polynomial approximation method and a spline approximation method of the OCV function f OCV described, the dependence of the circuit parameters such as R0, R d , C d and τ d of the electrical quantity can be modeled using a similar method. Furthermore, the temperature dependence of the circuit parameters can be modeled using a similar method. Note that when modeling the temperature dependence, it is necessary to separately measure the temperature of the storage battery 1, and in this case, the model parameter estimator 3 must acquire an output signal from a temperature detector. A well-known Arrhenius equation or the like can be used as the temperature model.

[0108] The determination unit 334 determines the convergence of the parameter estimates and the voltage estimates based on the time series data {V(t k ) | k = 0, 1, ..., N} of the detected stresses, the stress model output, the linear parameter estimates, and the nonlinear parameter estimates. If a predetermined determination criterion is met, the estimation is terminated and the model parameters are output externally. If the determination criterion is not met, the process returns to the nonlinear parameter update unit 331, and the update of the nonlinear parameters ϕ is repeated.

[0109] In particular, if the j-th element of the 1-th estimated value of the parameter θ j 1 is determined whether or not Equation (52) is satisfied as in Patent Document 1. maxj=1,..,nθ|θjl+1−θjlθjl|<εθ where n θ is the number of elements of θ and ε θ a predetermined, sufficiently small value.

[0110] Alternatively, it is determined whether equation (53) is satisfied only for the nonlinear parameters ϕ or not. maxj=1,..,nθ|ϕjl+1−θjlθjl|<εϕ where n ϕ is the number of elements of ϕ and ε ϕ a predetermined, sufficiently small value.

[0111] Alternatively, whether equation (54) is satisfied or not is determined based on the root mean square error (RMSE) with respect to the voltage. RMSE(ϕl+1)=1N+1‖V−G(ϕl)ψl‖2<ϵV

[0112] Here, Ev a predetermined, sufficiently small value.

[0113] Alternatively, the determination may be based on the mean absolute error (MAE) with respect to stress, or it may be determined whether the number of iterations of estimating the nonlinear parameters ϕ has a predetermined upper limit as a convergence condition. Alternatively, a composite determination may be performed using the above-described multiple methods, or any other arbitrary convergence determination method may be used. Since various methods are known as determination methods for convergence of estimated parameters in nonlinear optimization, the convergence determination method is not limited.

[0114] Note that the final values of the estimated parameters of the parameter estimation unit 33 may be stored in the model acquisition unit 32 and used as initial values for the next estimation of the parameters of the model, or may be stored in an external PC, a server, a cloud, or the like. <Verarbeitungsverfahren der Modellparameterschätzvorrichtung>

[0115] Next, a processing procedure of the model parameter estimation device 3 according to Embodiment 1, that is, the model parameter estimation method, will be described with reference to a flowchart of Fig. 5. Note that the most typical case, that is, the case of using the nonlinear optimization method using a gradient approximation value, is described here.

[0116] First, the time series data acquisition unit 31 acquires the current values I of the storage battery 1 output from the current detection device 21 and the voltage values V of the storage battery 1 output from the voltage detection device 22 as time series values of measured values (step S1310). Next, the model acquisition unit 32 acquires an externally or internally held storage battery model and sets or reads initial values of the nonlinear parameters φ (step S1320). As the storage battery model, for example, the state space model represented by Equations (23) to (25) or (26) to (28) corresponding to Equation (3) is acquired.

[0117] The acquired series data, the storage battery model, and the initial values are the output to the parameter estimation unit 33, and the following repeated calculation (step S2331 to step S2400) is executed in each unit in the parameter estimation unit 33.

[0118] In step S2331, the nonlinear parameter updating unit 331 updates the nonlinear parameters φ according to a nonlinear optimization method, such as a type of gradient method based on iterative calculations, so that errors minimized for the linear parameters ψ are reduced. In calculating the gradient, for example, when an approximate value of the gradient by the one-sided difference is used, the approximate value of the gradient is calculated based on an estimated value of the output with respect to a disturbance value for each element of a previous value of the nonlinear parameter update (previous value), which will be described later. Note that when calculating the approximate value of the gradient by the one-sided difference or the like, the estimated value of the output for the previous value is also used.It should be noted that the first time, predetermined values are set as initial values of the nonlinear parameters (for example, τ. d = 100, I off = 0 or similar).

[0119] In step S2332, the state quantity calculation unit 332 calculates the state quantities of the storage battery model based on the state equation of the storage battery model through the updated nonlinear parameters ϕ. In step S2333, the linear parameter estimation unit 333 estimates the linear parameters ψ and the output values of the storage battery model based on the state quantities output by the state quantity calculation unit 332.

[0120] Then, in step S2334, the determination unit 334 determines the convergence of the parameter estimation in the parameter estimation unit 33 according to a predetermined convergence determination condition. If it is determined that the convergence determination condition is satisfied ("Yes" in step S2400), the parameter estimation is terminated, and the parameters of the estimation result are output externally. At this time, the parameters of the estimation result may be retained by the model acquisition unit 32.

[0121] On the other hand, if it is determined that the convergence determination condition is not satisfied ("No" in step S2400), the process proceeds to step S3331, and the execution of each step after step S3331 continues.

[0122] In step S3331, the nonlinear parameter updating unit 331 sets a disturbance value for each of the nonlinear parameter elements. In step S3332, the state quantity calculating unit 332 calculates the state quantities of the storage battery model with respect to each of the disturbance values for each of the nonlinear parameter elements based on the state equation of the storage battery model according to each of the disturbance values for each of the nonlinear parameter elements set by the nonlinear parameter updating unit 331.

[0123] In step S3333, the linear parameter estimation unit 333 estimates the linear parameters ψ with respect to each of the disturbance values for each of the elements of the nonlinear parameters and the output value of the storage battery model based on the state quantities with respect to each of the disturbance values for each of the elements of the nonlinear parameters output from the state quantity calculation unit 332. Then, the execution of each step continues after the above-described step S2331.

[0124] The above is the processing method of the model parameter estimation device 3 according to Embodiment 1, that is, an example of the operation in the model parameter estimation method. The details and the order of processing described with reference to Fig. 5 are merely an example, and the details and order are not limited thereto.

[0125] Next, a result of applying the model parameter estimation device 3 or the method for estimating model parameters according to Embodiment 1 to data of current and voltage series during the operation of a certain storage battery system 100 will be described with reference to Fig. 6. In this application, the current and voltage in the storage battery system 100 with a configuration of series and parallel connections are converted into a cell as storage battery 1.

[0126] Here, the model of storage battery 1 is replaced by the Fig. 4, and R1, R2, R3, C1, C2, and C3 correspond to equation (29) for the finite approximation of the diffusion impedance. Furthermore, the OCV function f OCV a cubic spline curve is used, which is divided by equal intervals of ms = 10. For simplicity, it is assumed that the nonlinear parameters ϕ are only τ d and the linear parameters ψ R0, C d and all parameters of the spline curve are third order.

[0127] In the series data of the current value I in the upper part of Fig. 6, the first half is free charging and discharging, and the second half is constant power charging. In each case, it can be seen that the actual data (measured values: solid line) in the middle row and the model output (estimated values: dashed line) in the bottom row exactly match.

[0128] In addition, the OCV function f estimated at this time is OCV in Fig. 7. Note that the horizontal axis represents the electrical quantity q / q typ which is determined by a certain standard capacity q typ As a result of the estimation, the nonlinear variation of the OCV with respect to the electrical quantity of q / q typ which is not completely linear, while each of the points is smoothly connected. Due to the above-mentioned effect, the voltages, which comprise a subtle uneven shape during the charging process, can be Fig. 6 (middle row: actual data, bottom row: model output) can be accurately estimated. Embodiment 2

[0129] In Embodiment 1, the processing for the case where the OCV function is unknown was described. In Embodiment 2, a case where the OCV function is known is described. Note that the configuration of the model parameter estimation apparatus and the basic operation of the model parameter estimation method are the same as in Embodiment 1, and therefore, the description of the same parts is omitted and reference is made to the drawings used in Embodiment 1.

[0130] If the OCV function f OCV is known, in the state space model of the storage battery 1 expressed by equation (23) to equation (25), equation (25) can be calculated using a full charge capacity q max be expressed as equation (55). V=R0(I−Ioff)+qdCd+fOCV(qqmax)

[0131] At this time, since the OCV function f OCV is known, the nonlinear parameters ϕ are expressed by equation (56). ϕ=[τdIoffqmax]T

[0132] Furthermore, when the output is converted as shown in equation (57), and since the linear expression of the parameter is possible as in embodiment 1, the linear parameters ψ are as shown in equation (58). V−fOCV(qqmax)=R0(I−Ioff)+qdCd=[I−Ioffqd]τ[R0Cd−1] ψ=[R0Cd−1]τ

[0133] In this case, in contrast to embodiment 1, there is the advantage that the full charge capacity q max may be included in the estimate.

[0134] It is further assumed that if more detailed information about the OCV function f OCV present, a function of the potential of the positive electrode f p and a function of the potential of the negative electrode f n are known and the OCV function f OCV can be expressed as equation (59) using the parameters of the electrodes. fOCV(S)fp(q+qp,0qp,max)−fn(q+qn,0qn,max)

[0135] Here, among the parameters of the electrodes q p,0 and q n,0 the amounts of the initial charge of the positive electrode and the negative electrode, respectively, and d p,max and q n,max the full charge capacities of the positive electrode and the negative electrode, respectively. When expressed in this expression, the nonlinear parameters ϕ are as shown in equation (60). ϕ=[τdIoffqp,0qp,maxqn,oqn,max]T

[0136] The linear parameters ψ are the same as in equation (58).

[0137] In this case, the OCV function f OCV can be modeled in more detail, and the deterioration of the storage battery 1 can be diagnosed in more detail. In particular, it is possible to distinguish and detect a decrease in the positive electrode capacity, a decrease in the negative electrode capacity, and a deviation in the electrical quantity between the positive electrode and the negative electrode due to the deterioration of the storage battery 1. It should be noted that the deviation in the electrical quantity between the positive electrode and the negative electrode is caused by a phenomenon mainly resulting from the growth of a film (SEI: Solid Electrolyte Interface) on the surface of the negative electrode and the precipitation of lithium, which leads to a decrease in the full charge capacity of the storage battery 1.

[0138] As described above, in the model parameter estimation device 3 or the model parameter estimation method of the present application, the update of the nonlinear parameters ϕ and the estimation of the linear parameters ψ are separated. Alternatively, the nonlinear parameters ϕ are updated considering a problem in which the linear least squares solution of the linear parameters is embedded, as in problem P2. As described above, there are roughly three advantages in the optimization calculation.

[0139] First, there is a reduction in dependence on the initial value due to the fact that setting the initial value only requires the nonlinear parameter ϕ. Second, there is a reduction in the amount of computation. Third, numerical stability is improved.

[0140] By estimating the linear parameters ψ, it is possible to obtain an optimal solution in any of the following problems: an unconstrained linear least squares problem, a linear least squares problem with constrained equality, and a problem with constrained linear inequality. In particular, for the unconstrained linear least squares problem, a linear least squares solution is obtained without iterative computation. For the linear least squares problem constrained by a linear equation, a global optimal solution can also be obtained using the Lagrange multiplier method without repeated computation.

[0141] These advantages become even more pronounced as the battery model becomes more complex and the number of parameters to be estimated increases. Therefore, it is also useful to separately record the positive electrode potential characteristics and the negative electrode potential characteristics as the OCV characteristic in advance and estimate part or all of the electrode parameters if more detailed modeling and degradation diagnosis are performed.

[0142] Here, the continuous-time system identification method based on the output method described in Patent Document 1 is re-examined. Although the OCV characteristic data is not essential, a model parameter estimation method is not clearly described when the OCV characteristic data is not stored. In practice, a model parameter estimation technique that does not rely on OCV characteristic data is also important. For example, since it is known that the OCV characteristic varies due to wear or the like, it is important to estimate model parameters that include the OCV characteristic to improve the estimation accuracy and apply the estimation to wear diagnosis.

[0143] Furthermore, when reusing the storage battery, modeling may be required when there is little or no information about the true values of the model parameters, including the OCV characteristic. If the OCV characteristic is expressed by a specific function using parameters and is collectively estimated by incorporating the parameters into the model parameters, the method described in Patent Document 1 suffers from the above-described problems of initial value setting and convergence, and therefore, it is more difficult to approximate the OCV characteristic to the optimal value.

[0144] In contrast, in the present application, the OCV characteristic, which is the relationship between the electric quantity (which can be the SOC or the normalized electric quantity) and the OCV, is expressed by a function including parameters, and then the parameters are estimated. This makes it possible to estimate the OCV characteristic even if the OCV characteristic is unknown.

[0145] In particular, when it is expressed by a function that includes a large number of linear parameters ψ, such as a polynomial or a polynomial in parts, the feature of the existing application is utilized in which the process of updating the nonlinear parameters ϕ and the process of estimating the linear parameters ψ are separated. This allows for easy estimation of all parameters without having to precisely set the initial values of the large number of linear parameters ψ. In addition, as described above, in the estimation of the linear parameters ψ, it is possible to easily perform parameter estimation if the OCV function f OCV is treated as a piecewise polynomial that includes the linear equality constraint, since a global solution is obtained even when the linear equality constraint is included. Note that using a piecewise polynomial instead of a polynomial makes it easier to accurately express a curve that includes local variations.

[0146] Although various exemplary embodiments and examples are described in this application, various features, aspects, and functions described in one or more embodiments are not included in an application of the contents disclosed in a particular embodiment and may be applicable to any embodiment alone or in various combinations. Accordingly, countless variations are contemplated within the scope of the art disclosed in the description of this application, which are not illustrated. For example, the case where at least one component is modified, added, or omitted, and the case where at least one component is taken and combined with a component disclosed in another embodiment are included.

[0147] As described above, the model parameter estimation device 3 according to the present application includes the state quantity calculation unit 332 for calculating the state quantities representing the state of the storage battery 1 (for example, the electric quantity q, the electric charge q d ) corresponding to the measured value of the current I based on the state equation obtained by assigning values (for example, initial values) to nonlinear parameters ϕ for the state-space model representing the storage battery 1 using the nonlinear parameters ϕ and the linear parameters ψ, and the time series data of each of the measured values of the current (current value I) and the terminal voltage (voltage value V) of the storage battery 1, the linear parameter estimation unit 333 for estimating the linear parameters ψ representing an error between the measured value of the voltage value V and the estimated value of the voltage V calculated based on the state-space model, the state variables and the measured value of the current I, the determination unit 334 for determining whether the estimated linear parameters ψ have converged or not, and the nonlinear parameter update unit 331,to repeatedly update the values of the nonlinear parameters ϕ to minimize the minimized error until the predetermined convergence condition is met and the determination unit 334 determines convergence. Because the setting of the initial values is limited only to the nonlinear parameters ϕ, the parameters can be estimated with a small amount of information.

[0148] Furthermore, the dependence on initial values can be reduced, the amount of computation is reduced, and numerical stability is improved. In this case, it is possible to use values that are generally known and have high validity for the memory battery as initial values, thus making it possible to perform the estimation without additional information, even when the system is updated.

[0149] In particular, when the nonlinear parameter updating unit 331 updates the values of the nonlinear parameters ϕ using a gradient or an approximate value of the gradient of the estimated value of the voltage V corresponding to the nonlinear parameters ϕ or using a gradient-free nonlinear optimization method, the convergence can be easily realized.

[0150] Alternatively, when the nonlinear parameter updating unit 331, when updating the values of the nonlinear parameters ϕ, generates a perturbation value for each of the nonlinear parameters ϕ obtained by perturbing previous values that are values before the update, the state quantity calculating unit 332 calculates state quantities for each perturbation value, the linear parameter estimating unit 333 estimates the linear parameters ψ with respect to the quantities for the state for each perturbation value, and the nonlinear parameter updating unit 331 calculates a gradient approximation value of the estimated value of the terminal voltage (voltage value V) with respect to the nonlinear parameters ϕ based on at least the estimated values of the linear parameters ψ with respect to the state quantities for each perturbation value and updates the previous values based on the calculated gradient approximation value,convergence can be achieved with higher reliability.

[0151] In these cases, if the nonlinear parameters ϕ include at least one of the following parameters: the state of charge, the full charge capacity q max and the diffusion time constant τ d of the storage battery 1 and the offset current (current offset error I off ) of the sensor used to measure the current (current value I), and the linear parameters ψ include at least one of the following parameters: a DC resistance, the diffusion resistance R d and a capacitance of the capacitor of the storage battery 1, the state of the storage battery 1 can be reliably evaluated.

[0152] In these cases, the amount of calculation is reduced when the linear parameter estimation unit 333 estimates the linear parameters ψ using the linear least squares solution of the linear least squares problem.

[0153] In this case, if the state space model uses the OCV function f OCV which represents a relationship between the electrical quantity q and the open-circuit voltage and includes the linear parameters ψ, the storage battery 1 can be accurately modeled.

[0154] Furthermore, the nonlinear deviation of the OCV with respect to the electrical quantity q can be modeled if the OCV function f OCV is a polynomial of the electrical quantity q and the linear parameters ψ comprise coefficients of the polynomial.

[0155] When the state space model includes the linear equality condition for the linear parameters ψ and the linear parameter estimation unit 333 estimates the linear parameters ψ by solving the linear least squares problem including the linear equality condition by the Lagrange multiplier method, the convergence can be made reliable by alternately repeating the updating of the nonlinear parameters ϕ and the calculation of the linear parameters ψ by the Lagrange multiplier method.

[0156] If the state space model uses the OCV function f OCV a piecewise polynomial representing a relationship between the electrical quantity q and the open-circuit voltage and comprising the linear parameters ψ, the linear parameters ψ comprise linear parameters of the piecewise polynomial, and the linear condition for equality comprises a linear condition for equality at nodes of the piecewise polynomial, the feature of the present application in which the process of updating the nonlinear parameters ϕ and the process of estimating the linear parameters ψ are separated from each other can be sufficiently utilized.

[0157] Alternatively, the optimal solution can be obtained when the state space model includes the linear inequality condition for the linear parameters ψ and the linear parameter estimation unit 333 estimates the linear parameters ψ by solving the linear least squares problem including the linear inequality condition.

[0158] In addition, the degradation of the storage battery 1 can be diagnosed in detail if the state-space model includes the OCV characteristic information, which represents a relationship between the state of charge and the open-circuit voltage of the storage battery 1, and the nonlinear parameters ϕ, the full charge capacity q max include.

[0159] In this case, if the state space model includes positive electrode potential characteristic information representing a relationship between a positive electrode electrical quantity and a positive electrode potential of the storage battery, and negative electrode potential characteristic information representing a relationship between a negative electrode electrical quantity and a negative electrode potential of the storage battery, and the nonlinear parameters ϕ include at least one of the following quantities: positive electrode capacitance, negative electrode capacitance, positive electrode electrical quantity and negative electrode electrical quantity instead of the full charge capacity q max , the degradation of the storage battery 1 can be diagnosed in more detail.

[0160] Furthermore, the model parameter estimation method of the present application includes the step (S1320) of setting initial values of the nonlinear parameters ϕ of the state space model representing the storage battery 1 using the nonlinear parameters ϕ and the linear parameters ψ, the state quantity calculation step (S2332) of calculating the state quantities representing the state of the storage battery (for example, the electrical quantity q, the electrical charge q d ) corresponding to a measured value of a current I based on the state equation obtained by assigning values to the nonlinear parameters ϕ for the state-space model, and series data of each of the measured values of the current (current value I) and the terminal voltage (voltage value V) of the storage battery 1, the linear parameter estimation step (S2333) of estimating the linear parameters ψ which represent an error between the measured value of the terminal voltage V and an estimated value of the terminal voltage V calculated based on the state-space model, the state variables, and the measured value of the current I, the determination step (S2334) of determining whether the estimated linear parameters ψ have converged or not, and the nonlinear parameter updating step (S2331) of updating the nonlinear parameters by repeatedly updating the values of the nonlinear parameters ϕ to make the minimized error small,until a predetermined convergence condition is met and the linear parameters ψ are determined to be converged. Because the initial setting is limited to the nonlinear parameters ϕ, the parameters can be estimated with a small amount of information.

[0161] Furthermore, the dependence on initial values can be reduced, the amount of computation is reduced, and numerical stability is improved. In this case, it is possible to use values that are generally known and have high validity for the memory battery as initial values, thus making it possible to perform the estimation without additional information, even when the system is updated.

[0162] In the nonlinear parameter update step (S2331), convergence can be easily realized if the values of the nonlinear parameters are updated using a gradient or a gradient approximation of the estimated value of the voltage V with respect to the nonlinear parameters ϕ or using a gradient-free nonlinear optimization method.

[0163] Alternatively, if the method is further configured to include a disturbance value setting step (S3331) consisting of generating a disturbance value of each of the nonlinear parameters ϕ (their elements) obtained by perturbing previous values that are values before the update when the values of the nonlinear parameters ϕ are updated, a per-disturbance state quantity calculation step (S3332) for calculating the state quantities per disturbance, in which state quantities are calculated for each disturbance value, and a per-disturbance linear parameter estimation step (S3333) in which linear parameters ψ corresponding to the state quantities are estimated for each disturbance value.In the nonlinear parameter updating step (S2331), a gradient approximation of the estimated value of the terminal voltage (voltage value V) with respect to the nonlinear parameters ϕ is calculated based on at least the estimated values of the linear parameters with respect to the quantities of the state for each disturbance value, and the previous values are updated based on the calculated gradient approximation, whereby convergence with higher reliability is possible.

[0164] In these cases, if the nonlinear parameters ϕ include at least one of the following parameters: the state of charge, the full charge capacity q max , the diffusion time constant of the storage battery 1 and the offset current (current offset error I off ) of the sensor used to measure the current (current value I), and the linear parameters ψ include at least one of the following parameters: the DC resistance, the diffusion resistance R d and the capacitance of the capacitor of the storage battery 1, the condition of the storage battery 1 can be reliably evaluated.

[0165] In the linear parameter estimation step (S2333), when the linear parameters ψ are estimated using the linear least squares solution of the linear least squares problem, the amount of calculation is reduced.

[0166] If the state space model contains the OCV function f OCV which represents a relationship between the electrical quantity q and the open-circuit voltage, and includes the linear parameters ψ, the storage battery 1 can be accurately modeled.

[0167] Furthermore, the nonlinear deviation of the OCV with respect to the electrical quantity q can be modeled if the OCV function f OCV is a polynomial of the electrical quantity q and the linear parameters ψ comprise coefficients of the polynomial.

[0168] When the configuration is such that the state space model includes a linear equality condition for the linear parameters ψ, and in the linear parameter estimation step (S2333), the linear parameters ψ are estimated by solving a linear least squares problem including the linear equality condition by a Lagrange multiplier method, the convergence can be made reliable by alternately repeating the updating of the nonlinear parameters ϕ and the calculation of the linear parameters ψ by the Lagrange multiplier method.

[0169] If the state space model uses the OCV function f OCV a piecewise polynomial representing a relationship between the electrical quantity q and the open-circuit voltage and including the linear parameters ψ, the linear parameters ψ include linear parameters of the piecewise polynomial, and the linear equality condition includes a linear equality condition at nodes of the piecewise polynomial, the feature of the existing application in which the process of updating the nonlinear parameters ϕ and the process of estimating the linear parameters ψ are separated from each other is sufficiently utilized.

[0170] Alternatively, the optimal solution can be obtained if the state-space model includes a linear inequality condition for the linear parameters ψ and the linear parameters ψ are estimated in the linear parameter estimation step (S2333) by solving a linear least squares problem including the linear inequality condition.

[0171] Furthermore, the degradation of the storage battery 1 can be diagnosed in detail if the state-space model includes OCV characteristic information representing a relationship between the state of charge and the open-circuit voltage of the storage battery 1, and the nonlinear parameters ϕ the full charge capacity q max include.

[0172] At this time, if the configuration is such that the state space model includes positive electrode potential characteristic information representing a relationship between a positive electrode electrical quantity and a positive electrode potential of the storage battery 1, and negative electrode potential characteristic information representing a relationship between a negative electrode electrical quantity and a negative electrode potential of the storage battery 1, and the nonlinear parameters ϕ include at least one of the following quantities: a positive electrode capacitance, a negative electrode capacitance, the positive electrode electrical quantity, and the negative electrode electrical quantity instead of the full charge capacity q max the degradation of the storage battery 1 can be diagnosed in more detail. Description of reference numbers and symbols

[0173] 1: Storage battery, 21: Current detection device, 22: Voltage detection device, 3: Model parameter estimation device, 31: Time series data acquisition unit, 32: Model acquisition unit, 33: Parameter estimation unit, 331: Nonlinear parameter update unit, 332: State variable calculation unit, 333: Linear parameter estimation unit, 334: Determination unit, I: Current value, I off : current offset error, q: electrical quantity, q max : Full charge capacity, R d : diffusion resistance, V: voltage value, τ d : diffusion time constant QUOTES CONTAINED IN THE DESCRIPTION

[0000] This list of documents submitted by the applicant was generated automatically and is included solely for the convenience of the reader. This list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions. Cited patent literature

[0000] JP 2014-86313

[0005] Cited non-patent literature

[0000] Kuhn, Estelle, et al. "Modeling Ni-mH battery using Cauer and Foster structures." Journal of power sources 158.2 (2006): 1490-1497

[0071]

Claims

[1] Model parameter estimation device comprising: a state quantity calculation unit for calculating state quantities indicative of a state of a storage battery with respect to a measured value of a current based on a state equation obtained by assigning values to nonlinear parameters for a state space model representing the storage battery using the nonlinear parameters and linear parameters, and time series data of each of the measured values of the current and a terminal voltage of the storage battery; a linear parameter estimation unit for estimating the linear parameters that minimize an error between the measured value of the terminal voltage and an estimated value of the terminal voltage calculated based on the state space model, the state variables, and the measured value of the current; and a nonlinear parameter updating unit for repeatedly updating the values of the nonlinear parameters to make the minimized error small until a predetermined convergence condition is satisfied. [2] The model parameter estimation device according to claim 1, wherein the nonlinear parameter updating unit updates the values of the nonlinear parameters using a gradient or an approximate value of the gradient of the estimated value of the terminal voltage with respect to the nonlinear parameters or using a gradient-free nonlinear optimization method. [3] Model parameter estimation device according to claim 1, wherein the nonlinear parameter updating unit, when updating the values of the nonlinear parameters, generates a perturbation value for each of the nonlinear parameters obtained by perturbing previous values that are values before the update; the state variable calculation unit calculates state variables for each disturbance value; the linear parameter estimation unit estimates the linear parameters with respect to the state variables for each disturbance value; and the nonlinear parameter updating unit calculates an approximate gradient value of the estimated value of the terminal voltage corresponding to the nonlinear parameters based on at least the estimated values of the linear parameters corresponding to the amounts of the state for each disturbance value, and updates the previous values based on the calculated approximate gradient value. [4] The model parameter estimation device according to any one of claims 1 to 3, wherein the non-linear parameters include at least one of a state of charge, a full charge capacity, and a diffusion time constant of the storage battery, and an offset current of a sensor used to measure the current, and the linear parameters include at least one of a DC resistance, a diffusion resistance, and a capacitor capacitance of the storage battery. [5] The model parameter estimation device according to any one of claims 1 to 4, wherein the linear parameter estimation unit estimates the linear parameters using a linear least squares solution of a linear least squares problem. [6] The model parameter estimation device according to claim 5, wherein the state space model includes an OCV function representing a relationship between an electric quantity and an open circuit voltage and including the linear parameters. [7] The model parameter estimator of claim 6, wherein the OCV function is a polynomial of the electrical quantity and the linear parameters comprise coefficients of the polynomial. [8] The model parameter estimation device according to any one of claims 1 to 4, wherein the state space model includes a linear equality condition for the linear parameters, and the linear parameter estimation unit estimates the linear parameters by solving a linear least squares problem including the linear equality condition by a Lagrange multiplier method. [9] The model parameter estimation device according to claim 8, wherein the state space model comprises an OCV function of a piecewise polynomial representing a relationship between an electrical quantity and an open circuit voltage and comprising the linear parameters, wherein the linear parameters comprise linear parameters of the piecewise polynomial, and the linear equality condition comprises a linear equality condition at nodes of the piecewise polynomial. [10] The model parameter estimation device according to any one of claims 1 to 4, wherein the state space model includes a linear inequality condition for the linear parameters, and the linear parameter estimation unit estimates the linear parameters by solving a linear least squares problem including the linear inequality condition. [11] The model parameter estimation device according to any one of claims 1 to 5, 8 and 10, wherein the state space model includes OCV characteristic information representing a relationship between a state of charge and an open circuit voltage of the storage battery, and the nonlinear parameters include a full charge capacity. [12] The model parameter estimation device according to claim 11, wherein the state space model includes: positive electrode potential characteristic information representing a relationship between a positive electrode electrical quantity and a positive electrode potential of the storage battery, and negative electrode potential characteristic information representing a relationship between a negative electrode electrical quantity and a negative electrode potential of the storage battery, and the nonlinear parameters include at least one of the following: positive electrode capacitance, negative electrode capacitance, positive electrode electrical quantity, and negative electrode electrical quantity instead of the full charge capacity. [13] Model parameter estimation methods, including: a step of setting initial values of nonlinear parameters of a state space model representing a storage battery using the nonlinear parameters and linear parameters; a state quantity calculation step of calculating state quantities indicative of a state of the storage battery with respect to a measured value of a current based on a state equation obtained by assigning values to the nonlinear parameters for the state space model and time series data of each of the measured values of the current and a terminal voltage of the storage battery; a linear parameter estimation step of estimating the linear parameters that minimize an error between the measured value of the terminal voltage and an estimated value of the terminal voltage calculated based on the state space model, the state variables, and the measured value of the current; and a nonlinear parameter updating step of updating the nonlinear parameters by repeatedly updating the values of the nonlinear parameters to make the minimized error small until a predetermined convergence condition is satisfied. [14] The model parameter estimation method according to claim 13, wherein in the nonlinear parameter updating step, values of the nonlinear parameters are updated using a gradient or an approximate value of the gradient of the estimated value of the terminal voltage with respect to the nonlinear parameters or using a gradient-free nonlinear optimization method. [15] The model parameter estimation method of claim 13, further comprising: a disturbance value setting step of generating a disturbance value of each of the nonlinear parameters obtained by disturbing previous values that are values before the update when the values of the nonlinear parameters are updated; a per-fault state quantity calculation step of calculating state quantities for each disturbance value; and a per-disturbance linear parameter estimation step of estimating linear parameters with respect to the amounts of the state for each disturbance value, wherein in the non-linear parameter updating step, a gradient approximation of the estimated value of the terminal voltage with respect to the non-linear parameters is calculated based on at least the estimated values of the linear parameters with respect to the amounts of the state for each disturbance value, and the previous values are updated based on the calculated gradient approximation. [16] The model parameter estimation method according to any one of claims 13 to 15, wherein the non-linear parameters include at least one of the following parameters: a state of charge, a full charge capacity, a diffusion time constant of the storage battery, and an offset current of a sensor used to measure the current, and the linear parameters include at least one of the following parameters: a DC resistance, a diffusion resistance, and a capacitor capacitance of the storage battery. [17] A model parameter estimation method according to any one of claims 13 to 16, wherein in the linear parameter estimation step, the linear parameters are estimated using a linear least squares solution of a linear least squares problem. [18] The model parameter estimation method according to claim 17, wherein the state space model comprises an OCV function representing a relationship between an electrical quantity and an open circuit voltage and comprising the linear parameters. [19] The model parameter estimation method of claim 18, wherein the OCV function is a polynomial of the electrical quantity and the linear parameters comprise coefficients of the polynomial. [20] The model parameter estimation method according to any one of claims 13 to 16, wherein the state space model includes a linear equality condition for the linear parameters, and the linear parameters are estimated in the linear parameter estimation step by solving a linear least squares problem including the linear equality condition by a Lagrange multiplier method. [21] The model parameter estimation method according to claim 20, wherein the state space model comprises an OCV function of a piecewise polynomial representing a relationship between an electrical quantity and an open circuit voltage and comprising the linear parameters, wherein the linear parameters comprise linear parameters of the piecewise polynomial, and the linear equality condition comprises a linear equality condition at nodes of the piecewise polynomial. [22] The model parameter estimation method according to any one of claims 13 to 16, wherein the state space model includes a linear inequality condition for the linear parameters, and the linear parameters are estimated in the linear parameter estimation step by solving a linear least squares problem including the linear inequality condition. [23] The model parameter estimation method according to any one of claims 13 to 17, 20 and 22, wherein the state space model includes OCV characteristic information representing a relationship between a state of charge and an open circuit voltage of the storage battery, and the nonlinear parameters include a full charge capacity. [24] The model parameter estimation method according to claim 23, wherein the state space model comprises: positive electrode potential characteristic information representing a relationship between a positive electrode electrical quantity and a positive electrode potential of the storage battery, and negative electrode potential characteristic information representing a relationship between a negative electrode electrical quantity and a negative electrode potential of the storage battery, and the nonlinear parameters include at least one of the following: positive electrode capacitance, negative electrode capacitance, positive electrode electrical quantity, and negative electrode electrical quantity instead of the full charge capacity.

Images