Method, program, device, and system for estimating parameter of target system

Abstract

A method according to the present disclosure is for estimating at least one parameter of a target system and is executed by at least one processor. A state space model of the target system is expressed by using an augmented system having a state variable including a partial differentiation, to an N-th-order (N is a natural number), obtained by using at least one parameter. The method includes: a step (S1061) for calculating a reference state vector with respect to a reference value of at least one parameter on the basis of a first measurement value of an input to the target system and a state equation of the augmented system; a step (S1071) for acquiring reduction time-series data in which the number of time-series data points is reduced from each of the first measurement value, a second measurement value of an output from the target system, and the reference state vector; and a step (S1091) for estimating at least one parameter on the basis of the state space model and the reduction time-series data.

Description

Method, program, device, and system for estimating parameters of a target system

[0001] The present disclosure relates to a method, a program, an apparatus, and a system for estimating parameters of a target system.

[0002] Conventionally, configurations for estimating parameters of a target system are known. For example, Japanese Patent Application Laid-Open No. 2014-86313 (Patent Document 1) discloses a configuration for identifying parameters of a continuous-time system. In this configuration, a nonlinear optimization method is applied to time-series data of current and voltage during charging and discharging of a storage battery based on an output error method, thereby estimating parameters of a storage battery model so that the output voltage of the storage battery model constructed as a continuous-time system matches the measured voltage. With this configuration, by appropriately selecting initial values ​​of the estimated parameters, it is possible to estimate the parameters with high accuracy while taking into account the nonlinearity of the open circuit voltage (OCV) characteristics.

[0003] JP 2014-86313 A

[0004] However, the parameter estimation technology used for system modeling, such as that disclosed in Patent Document 1, is based on offline batch processing of input / output data of the target system, and therefore requires the storage of all measurement data. Furthermore, the parameter estimation calculation requires calculations using a matrix with a size including the same dimensions as the number of data points. As such, configurations that estimate system parameters based on offline batch processing often have the problem that both the data storage cost (data volume) and the calculation cost (calculation time) during estimation are relatively high.

[0005] In particular, data storage costs can be a problem when implementing parameter estimation technology on a microcomputer with limited memory capacity. Even when data is stored on a server or the like and retrieved as needed for parameter estimation calculations, server usage costs can be incurred. Furthermore, if past data sets are cumulatively stored, data storage costs will increase even further. However, Patent Document 1 does not consider reducing the number of stored data points while maintaining the accuracy of system parameter estimation.

[0006] The present disclosure has been made to solve the above-mentioned problems, and its purpose is to estimate parameters of a target system using a smaller amount of data while maintaining the estimation accuracy of the parameters of the target system.

[0007] According to one aspect of the present disclosure, there is provided a method for estimating at least one parameter of a target system, the method being executed by at least one processing circuit. A state-space model of the target system is represented using an augmented system having state variables including partial derivatives up to Nth order (N is a natural number) with respect to at least one parameter. The method includes the steps of: calculating a reference state vector for a reference value of the at least one parameter based on first measurement values ​​of an input to the target system and a state equation of the augmented system; acquiring reduced time-series data in which the number of points of time-series data for each of the first measurement values, second measurement values ​​of an output of the target system, and the reference state vector are reduced; and estimating the at least one parameter based on the state-space model and the reduced time-series data.

[0008] Another aspect of the present disclosure provides a system for estimating at least one parameter of a target system, the system being executed by at least one processing circuit. A state-space model of the target system is expressed using an augmented system having state variables including partial derivatives up to Nth order (N is a natural number) with respect to at least one parameter. The system includes an augmented system vector calculation unit, a reduced time-series data acquisition unit, and a parameter estimation unit. The augmented system vector calculation unit calculates a reference state vector for a reference value of at least one parameter based on a first measurement value of an input to the target system and a state equation of the augmented system. The reduced time-series data acquisition unit acquires reduced time-series data in which the number of time-series data points for the first measurement value, the second measurement value of the output of the target system, and the reference state vector are reduced. The parameter estimation unit estimates at least one parameter based on the state-space model and the reduced time-series data.

[0009] According to the method and system disclosed herein, by estimating at least one parameter of a target system based on a state space model and reduced time-series data, it is possible to estimate the parameter of the target system with a smaller amount of data while maintaining the estimation accuracy of the parameter of the target system, thereby reducing the amount of stored data and the amount of calculation required to estimate the parameter of the target system.

[0010] 1 is a block diagram showing an example of a functional configuration of a parameter estimation device according to a first embodiment. FIG. 2 is a block diagram showing an example of a hardware configuration of the parameter estimation device of FIG. 1. FIG. 3 is a diagram showing an equivalent circuit model which is an example of a model of a storage battery. FIG. 4 is a time chart showing time series data of current and voltage during charging and discharging of a storage battery cell. FIG. 5 is a diagram showing the relationship between the Taylor approximation order and the ratio of the parameter estimation accuracy when the sampling period is 200 s to the parameter estimation accuracy when the sampling period is 1 s (normal). FIG. 6 is a diagram showing the relationship between the sampling ratio and the ratio of the parameter estimation accuracy when the Taylor approximation order is 5 to the parameter estimation accuracy when the sampling period is 1 s (normal). FIG. 7 is a flowchart showing an example of the flow of processing performed by a processing circuit that executes the parameter estimation program of FIG. 2.

[0011] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the drawings. In the drawings, the same or corresponding parts are designated by the same reference numerals, and their description will not be repeated in principle.

[0012] Recently, stationary energy storage systems that utilize renewable energy have become widespread in order to reduce environmental impact. Furthermore, electric vehicles such as electric vehicles (EVs), hybrid electric vehicles (HEVs), and plug-in hybrid vehicles (PHVs) have been put to practical use. Furthermore, the development of electric ships, electric aircraft, and the like is also progressing.

[0013] These systems use storage batteries such as lithium-ion batteries. It is known that storage batteries deteriorate with use, resulting in a decline in performance. Therefore, there is a demand for parameter estimation techniques for modeling a system with high accuracy from its operational data, in order to estimate the state of charge (SOC), diagnose deterioration, predict the battery's lifespan, or achieve highly efficient control. The following describes such parameter estimation techniques.

[0014] 1 is a block diagram showing an example of a functional configuration of a parameter estimation device 4 according to embodiment 1. In order to estimate parameters of a target system 1, the parameter estimation device 4 is provided in a storage battery system 100 having the target system 1.

[0015] 1 , the parameter estimation device 4 is connected to each of the input detection device 2 and the output detection device 3. The input detection device 2 detects an input to the target system 1 and outputs the input to the parameter estimation device 4. The output detection device 3 detects an output of the target system 1 and outputs the output to the parameter estimation device 4.

[0016] When the target system 1 is a storage battery, the input to the target system 1 is the current I (first measurement value) of the storage battery, and the output from the target system 1 is the terminal voltage V (second measurement value) of the storage battery. In this case, the storage battery is typically a lithium-ion storage battery, but it may be other types of storage batteries such as a lithium polymer storage battery, a lithium-ion capacitor, a lead-acid battery, a nickel-metal hydride storage battery, a nickel-cadmium storage battery, or an all-solid-state storage battery. Furthermore, the storage battery may be a single cell or a storage battery module in which multiple cells are connected in any combination of series and parallel connections. Furthermore, the storage battery module may be a pack or the like in which the storage battery module is connected in any combination of series and parallel connections, and the unit used to define a group of storage batteries is arbitrary.

[0017] The target system 1 is not limited to a storage battery, but may be various objects other than a storage battery. For example, the target system 1 may be various objects such as a power converter, a motor, or a robot. The technology of the present disclosure is applicable to any object that can be mathematically described by a state space representation such as that described below.

[0018] The parameter estimation device 4 includes a model acquisition unit 5, an augmented system vector calculation unit 6, a reduced time series data acquisition unit 7, an approximate expression acquisition unit 8, and a parameter estimation unit 9. Note that the parameter estimation device 4 may be configured as a parameter estimation system in which the model acquisition unit 5, the augmented system vector calculation unit 6, the reduced time series data acquisition unit 7, the approximate expression acquisition unit 8, and the parameter estimation unit 9 are realized by a plurality of devices.

[0019] The model acquisition unit 5 acquires a reference model. The reference model is a model based on a state space representation of the target system 1 using certain reference parameters. The reference parameters may be parameters estimated by a parameter estimation unit 9 (described later) or other predetermined values.

[0020] The augmented system vector calculation unit 6 sequentially calculates and outputs an augmented system reference state vector online based on the input detected by the input detection device 2, the state equation of the reference model acquired from the model acquisition unit 5, and the state equation of the augmented system of the reference model. The augmented system reference state vector is a state vector in the augmented system of the reference model. However, the augmented system and the augmented system reference state vector are configured so that the state variables include higher-order partial derivatives of the state variables of the reference model with respect to the reference parameters.

[0021] The reduced time series data acquisition unit 7 acquires and outputs reduced time series data based on the time series values ​​of the input detected by the input detection device 2, the time series values ​​of the output detected by the output detection device 3, and the time series values ​​of the augmented system reference state vector acquired from the augmented system vector calculation unit 6. The reduced time series data is time series data in which the number of data points of the time series values ​​of the input, the output, and the augmented system reference state vector has been reduced. The reduction of the number of data points performed by the reduced time series data acquisition unit 7 is typically performed by downsampling, but other methods may also be used, and the method of reducing the number of data points is not limited to downsampling. Note that the reduction of the number of data points may be performed after acquiring each time series value for all time periods, but is preferably performed sequentially each time a new time value is acquired, or each time multiple time series values ​​are acquired within a certain period of time. Reducing the time series data in this manner can conserve memory for storing data. For example, when downsampling, each time series value may be acquired sequentially at a sampling period coarser than the sampling period of the original time series values. The acquired reduced time series data may be stored inside the reduced time series data acquisition unit 7, or may be transmitted to and stored in a PC (Personal Computer), a server, or a cloud outside the parameter estimation device 4, and may be acquired from there as needed.

[0022] The approximation equation acquisition unit 8 acquires and outputs a state variable approximation equation (approximate state variable) based on the input acquired from the reduced time series data acquisition unit 7 and the reduced time series data relating to the augmented system reference state vector. The state variable approximation equation is an approximation equation for the state variables corresponding to the reduced time series and for the state variables of the original reference model, not the augmented system. To acquire the state variable approximation equation, a known approximation method using higher-order partial derivatives can be used based on higher-order partial derivatives of the reference state variables of the original reference model included in the augmented system reference state vector. A known approximation method is typically Taylor approximation, but other methods such as Padé approximation or Hermite interpolation can also be used, and the approximation method is not limited to one.

[0023] The parameter estimation unit 9 estimates and outputs parameters that minimize the error between the estimated value of the output of the target system 1 based on the output equation using the approximate state variables and the measured value of the output of the target system 1, based on the reference model output by the model acquisition unit 5, the reduced time series data regarding the input and output of the target system 1 output by the reduced time series data acquisition unit 7, and the approximate state variables corresponding to the reduced time series data output by the approximate equation acquisition unit 8. Here, the error can typically be the sum of squares of the error. Furthermore, a known nonlinear optimization method or system identification method can be used to estimate the parameters.

[0024] Fig. 2 is a block diagram showing an example of the hardware configuration of the parameter estimation device 4 of Fig. 1. As shown in Fig. 2, the parameter estimation device 4 includes a processing circuit 20a, a storage device 20b, and an input / output unit 20c. The storage device 20b includes a main storage device 21b and an auxiliary storage device 22b.

[0025] The main storage device 21b is a volatile storage device, and may include, for example, a dynamic random access memory (DRAM) and / or a static random access memory (SRAM). The auxiliary storage device 22b is a non-volatile storage device, and may include, for example, a flash memory (solid state drive (SSD)), a hard disk drive (HDD), a read-only memory (ROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM)), a magnetic disk, a flexible disk, an optical disk, a compact disk, a mini disk, and / or a digital versatile disk (DVD).

[0026] The processing circuit 20a includes a CPU (Central Processing Unit) that executes a program stored in the main memory device 21b. The processing circuit 20a may also include a GPU (Graphics Processing Unit). The functions of the parameter estimation device 4 are realized by software, firmware, or a combination of software and firmware. The software or firmware is written as a program and stored in the auxiliary memory device 22b. The processing circuit 20a loads the program stored in the auxiliary memory device 22b into the main memory device 21b and executes the program. The CPU is also called a central processing unit, processing device, arithmetic unit, microprocessor, microcomputer, processor, or DSP (Digital Signal Processor).

[0027] The auxiliary storage device 22b stores a parameter estimation program Pg1. The parameter estimation program Pg1 is a program for estimating parameters used in modeling the target system 1. The processing circuit 20a that executes the parameter estimation program Pg1 functions as the model acquisition unit 5, the augmented system vector calculation unit 6, the reduced time-series data acquisition unit 7, the approximate expression acquisition unit 8, and the parameter estimation unit 9 shown in FIG.

[0028] The input / output unit 20c receives operations from a user and outputs processing results to the user. The input / output unit 20c includes, for example, a mouse, a keyboard, a touch panel, a display, and a speaker.

[0029] <General Description of the Technology of the Present Disclosure> In the following, the technical content of the parameter estimation device 4 and the parameter estimation method according to the present disclosure will be described in a general problem setting, without limiting the target system 1 to a storage battery.

[0030] First, it is assumed that the state space representation of the target system 1 is expressed as the following equations (1) and (2).

[0031]

[0032] Equation (1) is called the state equation, and equation (2) is called the output equation. x represents the state. θ represents the parameter vector included in the state equation. t represents time. a ｐ , b ｑ , c ｒ represents parameters or coefficients parameterized by p, q, and r, respectively. y represents the output. φ represents the parameter vector included in the output equation. Note that in equations (1) and (2), the state space representation of the target system 1 is assumed to be a one-input, one-output system to simplify the problem, but the state space representation of the target system 1 may also be assumed to be a one-input, multiple-output system, multiple-input, one-output system, or multiple-input, multiple-output system.

[0033] Here, the problem we want to solve is typically the measurement time series data {(u(t ｋ ), y(t ｋ)) |k=0, 1, 2, ... N} is given, the objective is to find θ and φ that minimize the evaluation function J(θ, φ) expressed by the sum of the squared error between the measured value y of the output and the estimated value y^, as shown in the following equation (3). ｋ is the sampling time at which input and output data is measured, and N is an integer equal to or greater than 0.

[0034]

[0035] To solve this problem based on the output error method as described in Patent Document 1, it is necessary to store all time-series data of input and output. In addition, every time the parameter θ is updated, it is necessary to recalculate the state equation or its augmented system and calculate the state variable vector at each time.

[0036] On the other hand, the problem to be solved by the present disclosure is to reduce the number of data points to be stored in advance, such as measurement time series data, while maintaining accuracy as much as possible when solving the above problem, and to eliminate the need to re-calculate the state equation numerically every time a parameter is updated. To achieve this, an augmented system of state equations using higher-order partial derivatives of x from 1st to dth order (d is a natural number) using the parameter θ is first obtained. Note that, for the sake of simplicity, the higher-order partial differential coefficients can be expressed as in the following equations (4) to (7).

[0037]

[0038] By partially differentiating both sides of the equation of state (1) from the first to dth orders using only the parameter q and combining it with the original equation of state, the following equation (8) is obtained.

[0039]

[0040] When both sides of the state equation of Equation (1) are partially differentiated from the first order to the d−j order (0≦j≦d−1) with respect to the parameter p and then partially differentiated j-th order with respect to q, the following Equation (9) is obtained.

[0041]

[0042] In order to partially differentiate both sides of the state equation of Equation (1) with respect to the parameter r, a general solution of the state equation of Equation (1) is derived, and the following Equation (10) is obtained as the general solution.

[0043]

[0044] Since the first and second terms on the right side of equation (10) are independent of r, when the state x is partially differentiated by the parameters p, q, and r by the i-th, j-th, and k (k≧1)-th orders, the following equation (11) is obtained.

[0045]

[0046] Since the right-hand side of equation (11) does not depend on x, the left-hand side of equation (11) can be calculated directly.

[0047] From the above, by using equations (8), (9), and (11), x for any {(i, j, k)|i≧0, j≧0, k≧0, 0≦i+j+k≦d} can be calculated. （ｉ，ｊ，ｋ） (t, θ) can be calculated sequentially. Specifically, first, x （ｉ，ｊ，ｋ） A state vector z of the extended system is previously constructed by vertically arranging (t, θ) and a reference state vector z(t, θ) is ｔｙｐ ) is acquired prior to parameter estimation by sequential calculation in response to acquisition of the detection input.

[0048] Next, a reference value θ of the parameter obtained in advance is ｔｙｐ :=[p ｔｙｐ , q ｔｙｐ , r ｔｙｐ ] Ｔ x for （ｉ，ｊ，ｋ） (t, θ ｔｙｐ ) is used to approximate x(t, θ) for any parameter θ. As a method of approximation, for example, Taylor approximation can be used. According to Taylor's theorem, θ = θ ｔｙｐ The multivariate Taylor approximation for +δθ is expressed as the following equation (12).

[0049]

[0050] R in formula (12) ｄ＋１ is a remainder term, and is expressed as the following equation (13) using λ in the range of 0<λ<1.

[0051]

[0052] Therefore, the previously obtained θ = θ ｔｙｐ x for （ｉ，ｊ，ｋ） (t, θ ｔｙｐ ) (or x （ｉ，ｊ，ｋ） (t, θ ｔｙｐ ) are arranged vertically, the remainder term R is obtained from equation (12). ｄ＋１ By calculating the Taylor approximation polynomial excluding x(t, θ), an approximate value of x(t, θ) for any θ can be obtained.

[0053] Other known approximation techniques besides multivariate Taylor approximation, such as Pade approximation and Hermite interpolation, can also be used. However, because the partial differential coefficients required for calculations may differ depending on the approximation technique, it is necessary to prepare appropriate partial differential coefficients for each approximation technique. For example, Hermite interpolation, multipoint Taylor approximation, and multipoint Pade approximation are multipoint interpolation techniques. Therefore, interpolation-based approximation calculations require partial differential coefficients for each of two or more different parameter reference values. Note that increasing the number of values ​​that must be prepared in advance may improve parameter estimation accuracy, but may also increase data storage costs and calculation costs. Therefore, it is desirable to determine the approximation technique and the partial differential coefficients to be stored by considering the trade-off between accuracy and cost.

[0054] The approximate value x of the state variable vector x calculated by the known method described above ａ is expressed as the following equation (14).

[0055]

[0056] Using equation (14), the estimated value y^ of the output y is expressed as in equation (15) below.

[0057]

[0058] As shown in equation (15), z(t, θ ｔｙｐ) is acquired in advance, the state space expression of the target system 1 can be approximately expressed by only the output equation without the state equation. As a result, by substituting Equation (15) into Equation (2), the problem re-formulated as the given {u(τ ｋ ), y(τ ｋ ), x(τ ｋ , θ ｔｙｐ ) |k=0, 1, . . . M} (M is an integer equal to or greater than 0), an evaluation function J expressed as the following formula (16) is ２ The goal is to find θ and φ that minimize (θ, φ). ｋ is the sampling time t = t in the original problem ｋ (k=0, 1, . . . , N), where M<N, and are typically downsampled sampling times.

[0059]

[0060] Evaluation function J ２ The problem of minimizing (θ, φ) is simply a least-squares problem for a static nonlinear function, since the state space expression of the target system 1 is approximately expressed only by the output equation as described above. ２ To solve the problem of minimizing (θ, φ), known methods for nonlinear optimization such as the gradient method, Gauss-Newton method, Levenberg-Marquardt method, or Nelder-Mead method can be used. ２ Metaheuristics can also be used to solve the problem of minimizing (θ, φ). ２ The optimization method for solving the problem of minimizing (θ, φ) is not limited to one method. ２ The reason why it is possible to reduce the sampling data of the original problem in the problem of minimizing (θ, φ) is because the evaluation function J ２This is because the problem of minimizing (θ, φ) is a least-squares problem for a static nonlinear function, and there is no need to recalculate the state variables for variations in the parameter θ. Note that the amount of reduction in the original sampling data is preferably determined by considering the trade-off between the accuracy of parameter estimation and the cost of storing the data and the computational cost of solving the problem.

[0061] <Example of Case Where Target System 1 is a Storage Battery> In the following, a case where the target system 1 is a storage battery will be described.

[0062] FIG. 3 is a diagram showing an equivalent circuit model 1A, which is an example of a model of the storage battery 1. In FIG. 3, OCV represents open circuit voltage, and SOC represents state of charge. ＯＣＶ represents an OCV function that represents a one-to-one correspondence between SOC and OCV.

[0063] As shown in FIG. 3, the equivalent circuit model 1A includes terminals P1 and P2 and a resistor R ０ , R ｄ and capacitor C ｄ and an OCV. Terminal P1 is connected to the negative electrode of the OCV. Resistor R ｄ and capacitor C ｄ is the resistance R ０ and terminal P2. ０ The other end of the resistor R is connected to the positive electrode of the OCV. ０ represents the DC resistance that simulates the DC component of the overvoltage. ｄ and capacitor C ｄ and represent the resistance and capacitance simulating the overvoltage mitigation component resulting from the ion diffusion phenomenon inside the electrode, etc. The model of the storage battery 1 is not limited to the equivalent circuit model 1A, and may be, for example, a so-called electrochemical model.

[0064] The state space expression (state space model) of the equivalent circuit model 1A in FIG. 3 is expressed, for example, as in the following equations (17) and (18).

[0065]

[0066] In equations (17) and (18), FCC represents the full charge capacity, and I represents the measured current. ｏｆｆ represents the offset error of the current sensor. ｄ is the capacitor C ｄ represents the amount of electricity stored in τ ｄ (C ｄ and R ｄ The product of τ and τ represents the time constant of diffusion. V is the voltage between terminals P1 and P2 of the storage battery 1 (terminal voltage). That is, equation (17) is expressed as follows: ｄ The quantity of electricity q ｄ It includes differential equations for

[0067] The initial value of SOC is SOC ｉｎｉ When the differential equation for SOC in equation (17) is solved, the SOC is expressed as in the following equation (19): In equation (19), Q represents the electrical quantity obtained by integrating the measured current.

[0068]

[0069] By substituting equation (19) into equations (17) and (18), the following equations (20) and (21) are obtained, respectively.

[0070]

[0071] According to the formulas (20) and (21), it is not necessary to approximately express the SOC, and therefore the number of data points to be stored for the approximate expression can be reduced.

[0072] The OCV function f ＯＣＶ If is unknown, it becomes impossible to estimate the SOC including the initial SOC. In this case, the OCV function g ＯＣＶ In the equation (22) for the terminal voltage V expressed using ＯＣＶ The parameters of may be estimated.

[0073]

[0074] Specifically, the OCV function g ＯＣＶAs the function form of the above, a polynomial function or a piecewise linear function with the integrated amount of electricity as an argument can be assumed, and the coefficients included in the function form can be used as the parameters to be estimated.

[0075] Furthermore, −1 / τ ｄ is parameterized by p, and I ｏｆｆ By parameterizing with r, the state equation (20) is expressed as the following equation (23). In equation (23), θ is [p, r] Ｔ Represents.

[0076]

[0077] There are various methods for parameterization, for example, τ ｄ For example, the reference value τ ｄ，ｔｙｐ For τ ｄ = τ ｄ，ｔｙｐ (1+p) or by using α such that α>0 and α≠1, ｄ = τ ｄ，ｔｙｐ ・α －ｐ The specific method of parameterization is not limited. When the latter parameterization method using exponents is used, the property that physical parameters such as resistance, capacitance, or time constant are non-negative can be naturally satisfied. Furthermore, since the convergence radius of Taylor series expansion in this method is infinite, this method has the advantage that the series does not diverge when Taylor approximation is performed.

[0078] Capacitor C ｄ The amount of electricity stored in ｄ With respect to the quantity of electricity q ｄ The partial differential coefficient of is expressed as the following equation (24).

[0079]

[0080] By partially differentiating both sides of equation (24) with respect to p from the first to dth orders, the following equation (25) is obtained.

[0081]

[0082] a ｐ = -1 / (τ ｄ ・e －ｐ) and (a ｐ ) （ｉ） =a ｐ Therefore, from the lower triangular matrix on the right side, a ｐ As a result, a ｐ and a lower triangular matrix according to Pascal's triangle, the calculation is simplified, and Equation (25) is expressed as Equation (26) below.

[0083]

[0084] On the other hand, in {(i, j)|i≧0, j≧1, 1≦i+j≦d}, when both sides of equation (26) are partially differentiated by the i-th order with respect to p and by the j-th order with respect to r, the following equation (27) is obtained.

[0085]

[0086] Equation (27) does not depend on the state and can be calculated directly. ｒ = r, the following equation (28) is obtained.

[0087]

[0088] By substituting equation (28) into equation (27), the following equation (29) is obtained, which simplifies the calculation of equation (27).

[0089]

[0090] From the above, the expanded system of state equations expressed by equation (26) can be expressed as θ ｔｙｐ = [p ｔｙｐ , r ｔｙｐ ] Ｔ = [0, 0] Ｔ If you calculate it online in advance, you can use it with θ=θ ｔｙｐ By calculating equation (24) for ｄ can be approximately calculated.

[0091] For example, when using the Taylor polynomial, the state q ｄ can be approximately calculated.

[0092]

[0093] In this way, the state quantity q ｄApproximate formula f for (t, θ) ａ (z(t,θ ｔｙｐ ), θ-θ ｔｙｐ ) can be obtained. By using this approximation formula, the state space representation of the storage battery can be expressed in the form of only an output equation. For example, when the OCV function is known, the following formula (31) can be obtained. In formula (31), θ=[q ｄ , I ｏｆｆ ] Ｔ and φ=[R ０ , C ｄ , FCC, SOC ｉｎｉ ] Ｔ is.

[0094]

[0095] On the other hand, when the OCV function is unknown, if the OCV function is assumed to be, for example, an s-th degree polynomial function, the following equation (32) is obtained. In equation (32), θ=[q ｄ , I ｏｆｆ ] Ｔ and φ=[R ０ , C ｄ , c ０ , c １ , ..., c ｓ ] Ｔ is.

[0096]

[0097] In this way, the state space expression of the storage battery can be reduced to a state space expression of only the output equation. As a result, the parameters of the target system 1 can be estimated using the evaluation function J as expressed by equation (16). ２ This is realized by estimating parameters that minimize the above. Specifically, the above-mentioned well-known nonlinear optimization method may be used.

[0098] An example of a parameter estimation method for the output equation of Equation (32) will be described below. ０ , τ １ , …, τ Ｍ By vertically arranging the output equations for the time series data corresponding to

[0099]

[0100] From equation (33), φ is expressed as equation (34) below, which represents the linear least squares solution, depending on θ.

[0101]

[0102] As a result, by applying a nonlinear optimization method to the vector θ using the right-hand side of equation (34) with the vector θ as an argument instead of the vector φ itself, the vector φ can be automatically obtained as a linear least-squares solution even if the dimension of the vector φ is large. Therefore, parameter estimation can be performed efficiently by estimating only the vector θ. This parameter estimation method can also be used when x is not expressed as an approximation, as in equation (14). In that case, if the parameter θ included in x fluctuates, it is necessary to recalculate the value of x at each time based on the state equation.

[0103] As described above, by utilizing the parameter estimation device, parameter estimation program, and parameter estimation method according to the present disclosure, which are based on approximate calculation of state quantities, it is possible to reduce the data storage costs and calculation costs required for parameter estimation while maintaining the accuracy of parameter estimation.

[0104] Below, the results of a simulation for confirming the effectiveness of the technology of the present disclosure will be described with reference to FIGS. 4, 5, and 6. Note that, for the sake of simplicity of the simulation, the target of parameterization is τ ｄ It is limited to.

[0105] 4 is a time chart showing time-series data of current and voltage during charging and discharging of a storage battery cell. In FIG. 4, the sampling period of data indicated by solid lines is 1 s (seconds). The sampling period of data indicated by circles is 200 s.

[0106] 5 is a diagram showing the relationship between the ratio of the parameter estimation accuracy when the sampling period is 200 s to the parameter estimation accuracy when the sampling period is 1 s (normal) and the Taylor approximation order. When the sampling period is 1 s, the state variables are calculated precisely using the state equation. In FIG. 5, the resistance R ０ , R ｄ , capacitor C ｄ , root mean square error of voltage V ｒｍｓｅ The ratio of estimation accuracy for each of the above is shown. Also, the closer the value of the ratio of estimation accuracy is to 1, the closer the parameter estimates obtained by 200-second sampling are to the parameter estimates obtained by 1-second sampling, which indicates a better result. The same applies to FIG. 6 , which will be described later. In the case of a sampling period of 200 seconds, the state variables are approximated using the technology of the present disclosure. Taylor approximation is used to approximate the state variables.

[0107] As shown in FIG. 5, in the range of Taylor approximation orders from 0 to around 4, the ratio of the estimation accuracy for each parameter approaches 1, and the estimation accuracy for each parameter is improved. Note that in the range of Taylor approximation orders of 5 or more, the resistance R ｄ The reason why the estimation accuracy of is saturated is that the voltage error V ｒｍｓｅ It can be noted that the value converges to the normal value.

[0108] 6 is a diagram showing the relationship between the ratio of the parameter estimation accuracy when the Taylor approximation order is 5 to the parameter estimation accuracy when the sampling period is 1 s (normal operation), and the sampling ratio. The sampling ratio is the ratio of the sampling period when the Taylor approximation order is 5 to the sampling period of 1 s. When the Taylor approximation order is 5, the state variables are approximated using the technology disclosed herein. As shown in FIG. 6 , when the sampling ratio is in the range of 0 to 200, the estimation accuracy when the Taylor approximation order is 5 is approximately the same as the estimation accuracy under normal conditions.

[0109] As described above, FIGS. 5 and 6 show that the number of stored data points can be significantly reduced while maintaining estimation accuracy by using a lower-order approximation.

[0110] <Processing Procedure of Parameter Estimation Device> A parameter estimation method performed by the parameter estimation device 4 according to the embodiment will be described with reference to FIG. 7. FIG. 7 is a flowchart showing an example of the flow of processing performed by the processing circuit 20a that executes the parameter estimation program Pg1 of FIG. 2. Hereinafter, steps will be simply referred to as S. Note that the content and order of processing described in FIG. 7 are merely examples, and the parameter estimation method according to the embodiment is not limited to the content and order of processing shown in FIG. 7. Furthermore, it is not necessary for all of the multiple steps shown in FIG. 7 to be performed by a single processing circuit, and the multiple steps may be performed cooperatively by multiple processing circuits.

[0111] As shown in FIG. 7, in step S1051, the processing circuit 20a (model acquisition unit 5) acquires a reference model of the target system 1 expressed in state space based on the reference parameters, and proceeds to S1061.

[0112] In S1061, the processing circuit 20a (augmented system vector calculation unit 6) sequentially calculates an augmented system reference state vector including higher-order partial derivatives based on the parameters of the reference state variable based on the current I of the target system 1 and the reference model, and proceeds to S1071.

[0113] In S1071, the processing circuit 20a (reduced time-series data acquisition unit 7) acquires reduced time-series data in which the amount of time-series data of the current I, voltage V, and augmented system reference state vector has been reduced, and the process proceeds to S1081.

[0114] In S1081, the processing circuit 20a (approximate equation acquisition unit 8) calculates the time series values ​​of the approximate state variables (state variable approximate equation) based on the time series values ​​of the reduced augmented system reference state vector, and proceeds to S1091.

[0115] In S1091, the processing circuit 20a (parameter estimation unit 9) estimates parameters based on the reduced time series data of the current I and the voltage V and the state variable approximation equation so as to minimize the error between the reduced time series data of the voltage V and the estimated voltage, and then proceeds to S1052.

[0116] The processing circuitry 20a (model acquisition unit 5) acquires the estimated parameters, updates the model, and ends the processing in S1052. In S1052, the processing circuitry 20a may update the reference parameters based on the latest parameters.

[0117] As described above, the method, program, and device according to the embodiments can estimate the parameters of the target system with a smaller amount of data while maintaining the estimation accuracy of the parameters of the target system. As a result, the amount of stored data and the amount of calculation required to estimate the parameters of the target system can be reduced.

[0118] The embodiments disclosed herein should be considered to be illustrative in all respects and not restrictive. The scope of the present disclosure is defined by the claims, not the above description, and is intended to include all modifications within the meaning and scope of the claims.

[0119] 1 Target system (storage battery), 1A Equivalent circuit model, 2 Input detection device, 3 Output detection device, 4 Parameter estimation device, 5 Model acquisition unit, 6 Augmented system vector calculation unit, 7 Reduced time series data acquisition unit, 8 Approximation equation acquisition unit, 9 Parameter estimation unit, 20a Processing circuit, 20b Storage device, 20c Input / output unit, 21b Main storage device, 22b Auxiliary storage device, 100 Storage battery system, C ｄ Capacitor, I current, P1, P2 terminal, Pg1 parameter estimation program, R ０ , R ｄ Resistance, V: voltage between terminals.

Claims

1. A method for estimating at least one parameter of a target system, which is executed by at least one processing circuit, wherein the state space model of the target system is expressed using an extended system having state variables including partial derivatives up to the Nth order (N is a natural number) with respect to the at least one parameter, and the method includes: calculating a reference state vector with respect to a reference value of the at least one parameter based on a first measurement value of an input to the target system and a state equation of the extended system; obtaining reduced time series data in which the number of data points of each of the first measurement value, a second measurement value of an output of the target system, and the reference state vector is reduced; and estimating the at least one parameter based on the state space model and the reduced time series data.

2. The method according to claim 1, further including obtaining an approximation formula of a state variable having the at least one parameter as an argument based on the reduced time series data of each of the first measurement value and the reference state vector, wherein the step of estimating the at least one parameter estimates the at least one parameter so as to minimize an error between an estimated value of the output calculated from the output equation to which the approximation formula is applied and the reduced time series data of the second measurement value, based on the reduced time series data of the first measurement value, the output equation of the state space model, and the approximation formula.

3. The method according to claim 2, wherein the step of obtaining the approximation formula uses an Mth-order Taylor polynomial (M is a natural number) as the approximation formula.

4. The method according to claim 2, wherein the step of obtaining the approximation formula uses a Padé approximation as the approximation formula.

5. The at least one parameter is a parameter mediated by an exponent p as a product of the reference value and α ｐ ｐ (α > 0 and α ≠ 1) in the partial derivative, according to any one of claims 1 to 4.

6. The method according to claim 5, wherein the target system includes a storage battery, the input includes a current of the storage battery, and the output includes a voltage between terminals of the storage battery.

7. The state space model of the storage battery is represented by an equivalent circuit model, the equivalent circuit model includes a first resistor, a second resistor, a capacitor, and an open circuit voltage, the second resistor and the capacitor are connected in parallel, the state variable includes the electric quantity of the capacitor, the at least one parameter includes a time constant which is the product of the second resistor and the capacitance of the capacitor, and the state equation includes a differential equation regarding the electric quantity using the time constant. The method according to claim 6.

8. The method according to claim 7, wherein the at least one parameter further includes an offset error of a current sensor that measures the current.

9. A program which, when executed by a processing circuit, causes the processing circuit to execute the method according to any one of claims 1 to 8.

10. An apparatus comprising a storage device that stores the program according to claim 9, and a processing circuit configured to execute the program.

11. A system for estimating at least one parameter of a target system, which is executed by at least one processing circuit, wherein the state space model of the target system is represented by an extended system having a state variable including partial derivatives up to N-th order (N is a natural number) with respect to the at least one parameter, and the system includes: an extended system vector calculation unit that calculates a reference state vector with respect to a reference value of the at least one parameter based on a first measurement value of an input to the target system and a state equation of the extended system; a reduced time series data acquisition unit that acquires reduced time series data in which the number of points of each of the time series data of the first measurement value, a second measurement value of an output of the target system, and the reference state vector is reduced; and a parameter estimation unit that estimates the at least one parameter based on the state space model and the reduced time series data.

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