Methods for simulating battery packs

Abstract

A method for simulating a battery pack includes the following steps: selecting an equivalent circuit model (ECM) and connection relationships for each battery cell; receiving a pack current value; determining a pack voltage value based on the pack current value and initial values ​​of the G-parameters and H-parameters of the battery pack; determining a cell voltage value, a cell current value, and a state parameter value for each battery cell based on the pack current value, the pack voltage value, and initial parameter values ​​for each battery cell; determining an ECM parameter value for each battery cell based on the state parameter value for each battery cell; determining G-parameters and H-parameters for each battery cell based on the ECM parameter values ​​for each battery cell; and determining the G-parameters and H-parameters of the battery pack based on the G-parameters and H-parameters for each battery cell.

Description

Technical Field

[0001] The disclosure relates to a method for simulating a battery pack. Background Technology

[0002] Compared to other energy storage devices, batteries are highly applicable and possess relatively high energy and power density, thus they are widely used not only in portable devices but also in electric vehicles (EVs) and hybrid electric vehicles (HEVs) powered by electric drive sources. In particular, when high output is required, battery packs containing multiple batteries connected in series or parallel can be used.

[0003] Battery management is crucial for the energy-efficient and safe use of electrical devices powered by batteries or battery packs. To this end, in a battery system, a device acting as a battery management system (BMS) assesses the state of the battery and manages the battery or battery pack based on that assessment.

[0004] The primary function of a Battery Management System (BMS) is to measure measurable physical quantities (such as voltage, current, and temperature) of a battery or battery pack, and to assess the internal state of the battery or battery pack based on pre-programmed correlations between the measured values ​​and the internal state of the battery or battery pack. The main state variables measured here include the battery's state of charge (SOC), state of health (SoH), and state of power (SoP).

[0005] Other functions of the BMS include managing batteries or battery packs by using the assessed state of charge. Representative functions include temperature management, cell balancing, and abnormal cell detection. Temperature management activates cooling fans or guides a reduction in the battery pack's output to lower its temperature. Cell balancing matches the state of charge of multiple batteries connected in series or parallel to ensure optimal performance in the battery pack. Abnormal cell detection preemptively detects abnormal cells within a battery pack connected in series or parallel. The BMS can stably manage the battery pack's state by preventing abnormal cells from deteriorating further internally or by notifying the outside of cells where an abnormality has occurred.

[0006] To assess the internal state of a battery or battery pack and perform various management functions to maintain optimal condition, a Battery Management System (BMS) includes state assessment algorithms and control algorithms. A BMS may include software programs for performing the state assessment and management functions described above, sensors for measuring measurable physical quantities, actuators for performing actual operations, and control hardware for controlling the actuators.

[0007] To determine whether a Battery Management System (BMS) is properly performing its state assessment and management functions, a method is used to verify the BMS by directly connecting it to an actual battery or battery pack. This method is relatively straightforward when the battery consists of individual cells; however, verifying a BMS connected to a battery pack in which multiple battery cells are connected in series or parallel may increase time and cost. Furthermore, when verifying the BMS by including multiple sensors not actually included in the battery pack for accurate state measurements, the measurements may be based on state values ​​not measured within the actual battery pack, thus potentially compromising the BMS's functionality within the actual battery pack.

[0008] Furthermore, to test the abnormal cell detection function, the operability of the BMS must be tested by actually manufacturing and measuring batteries or battery packs containing cells that exhibit abnormalities. However, artificially manufacturing cells with predetermined abnormalities is extremely difficult. Even if abnormal cells are artificially manufactured and tested, there are risks of fire / explosion, making it difficult to fully verify the BMS's functionality.

[0009] To address these issues, hardware-in-the-loop simulation (HILS) and model-based design (MBD) methods have been developed and widely applied. Initially, they were extensively used in the aerospace field, where practical testing was difficult, and later in the automotive field, where measurement and verification were costly. Furthermore, recently, methods for verifying the functionality of controllers using these approaches have been widely adopted across various other fields.

[0010] When implementing the HILS / MBD method, by using a system model capable of performing real-time simulations, it is possible to virtually implement a controller in a real system that is difficult to test in practice due to high cost or danger. Then, the various functions and algorithms of the controller can be effectively verified by simulating the output signals of various sensors.

[0011] However, with HILS / MBD-based verification methods, the computational speed of the central processing unit (CPU) must increase proportionally to the computational load to handle large amounts of computation in real time. Furthermore, the verification of the controller's functionality and the algorithm's operability is limited by the accuracy and complexity of the model used. In other words, when the complexity of the system model is increased to improve accuracy, it becomes difficult to simulate the system's real-time response due to the increased computational load. Summary of the Invention

[0012] Technical issues

[0013] To overcome the shortcomings of previous models, a battery pack model capable of real-time response processing in low-specification devices is disclosed, which can reduce computational load while maintaining the same accuracy as previous models, and a method for simulating a battery pack using the battery pack model.

[0014] The purpose of this disclosure is to provide a high-speed computational model that can simultaneously and in real time calculate the internal state of a battery pack in which individual battery cells are connected in series or parallel.

[0015] Technical solution

[0016] According to one aspect of the disclosure, a method for simulating a battery pack, executed by a computing device including a processor and a memory, is provided. The method includes the following steps: selecting the connection relationships of battery cells included in the battery pack and an equivalent circuit model (ECM) of the battery cells; determining initial values ​​of parameters for each battery cell and initial values ​​of G-parameters and H-parameters of the battery pack; receiving one of a pack current value and a pack voltage value of the battery pack; determining another of the pack current value and pack voltage value of the battery pack based on said one of the pack current value and pack voltage value and the initial values ​​of G-parameters and H-parameters; determining values ​​of a cell voltage value, a cell current value, and a state parameter for each battery cell based on the pack current value and pack voltage value of the battery pack and the initial values ​​of parameters for each battery cell; determining values ​​of ECM parameters for each battery cell based on the values ​​of state parameters for each battery cell; determining values ​​of G-parameters and H-parameters for each battery cell based on the values ​​of ECM parameters for each battery cell; and determining values ​​of G-parameters and H-parameters for the battery pack based on the values ​​of G-parameters and H-parameters for each battery cell.

[0017] According to another aspect of the disclosure, a computer program stored in a medium is provided for performing a method of simulating a battery pack by using a computing device including a processor and a memory.

[0018] Beneficial effects

[0019] Compared to previous methods, the method for simulating battery packs according to the various disclosed embodiments offers significant improvements in cost, scalability, and adaptability.

[0020] In the case of Matlab / Simulink-based battery or battery pack models, which were mainly used for the development of previous BMS algorithms, the model must be reconfigured according to the changed connection relationship when the series / parallel connection relationship between battery cells changes. Moreover, the computational load increases exponentially with the number of battery cells.

[0021] However, in the case of publicly available battery pack models, even if the series / parallel connection relationship between battery cells changes, a single line of instructions can be easily modified, so the scalability is excellent, and even if the number of battery cells increases, the computational load only increases proportionally to the increase in the number of cells, so the processing speed does not decrease exponentially.

[0022] Furthermore, the publicly available battery pack model does not have highly complex code, thus it can be loaded onto hardware with an 8-bit core, and hardware with input / output (I / O) functionality for outputting voltage / current signals can operate alongside the virtual battery pack. Previously commonly used Matlab / Simulink-based code is large in size and has low computational speed, therefore it cannot be applied to hardware with low specifications (such as 8-bit cores). The publicly available battery pack model can be loaded onto an embedded board and can implement a "virtual battery." Attached Figure Description

[0023] Figure 1 This is a schematic structural diagram of a computing device for performing a method for simulating a battery pack according to an embodiment.

[0024] Figure 2 A battery pack model is shown according to an embodiment of a method for performing a simulated battery pack.

[0025] Figure 3 This is a flowchart of a method for simulating a battery pack according to an embodiment.

[0026] Figure 4 A battery pack is shown, comprising individual cells (1,1) to (m,n) connected to each other in a combination of parallel and series configurations.

[0027] Figure 5 It shows Figure 4 The equivalent circuit of the battery pack.

[0028] Figure 6 The second-order Thevenin's model is shown based on the published equivalent circuit model (ECM) chosen as the battery cell. Detailed Implementation

[0029] References and Appendix Figure 1The advantages and features of the disclosed embodiments, as well as methods of implementing them, will become clear from the detailed description of the embodiments provided below. However, the disclosure is not limited to the embodiments provided below. Rather, the disclosure may be implemented in a variety of different forms and should be understood to include all variations, equivalents, or substitutions contained within the concept and scope of the disclosure. The embodiments described below are provided to fully disclose the scope of the disclosure so that those skilled in the art can thoroughly understand it. In describing the disclosure, well-known techniques in the art will not be described in detail where it is determined that a detailed description of these techniques might unnecessarily obscure the concept of the disclosure.

[0030] The terminology used in this specification is for describing specific embodiments of the disclosure only and is not intended to limit the disclosure. As used herein, unless the context clearly indicates otherwise, the singular terms “a” and “an” are also intended to include the plural forms. The terms “comprising,” “having,” etc., as used herein should be understood to indicate the presence of the features, quantities, steps, operations, components, parts (components), or combinations thereof described herein, and should not be construed as preemptively excluding the possibility of the presence or addition of one or more other features, quantities, steps, operations, components, parts (components), or combinations thereof. Although the terms first, second, etc., may be used herein to describe various components, these terms do not limit the components. These terms are used only to distinguish one component from another.

[0031] The disclosed embodiments are described in detail below with reference to the accompanying drawings. In the description with reference to the drawings, the same reference numerals denote the same elements, and the same descriptions are not repeated.

[0032] Figure 1 This is a schematic structural diagram of a computing device for performing a method for simulating a battery pack according to an embodiment.

[0033] Reference Figure 1 The computing device 100 includes a processor 110, a memory 120, and an input and output device 130.

[0034] Processor 110 can perform basic arithmetic operations, logical operations, and input and output operations. For example, processor 110 can execute program code stored in memory 120, or read data stored in memory 120 and use that data for operations. Processor 110 can perform a method for simulating a battery pack according to an embodiment.

[0035] The processor 110 can be configured to: select the connection relationships between battery cells in the battery pack and the equivalent circuit model (ECM) of the battery cells; determine the initial values ​​of parameters for each battery cell and the initial values ​​of G-parameters and H-parameters of the battery pack; receive one of the pack current value and pack voltage value of the battery pack; determine the other of the pack current value and pack voltage value of the battery pack based on the one of the pack current value and pack voltage value of the battery pack and the initial values ​​of G-parameters and H-parameters; determine the cell voltage value, cell current value, and state parameter value of each battery cell based on the pack current value and pack voltage value of the battery pack and the initial values ​​of state parameters for each battery cell; determine the ECM parameter value of each battery cell based on the state parameter value of each battery cell; determine the G-parameter value and H-parameter value of each battery cell based on the ECM parameter value of each battery cell; and determine the G-parameter value and H-parameter value of the battery pack based on the G-parameter value and H-parameter value of each battery cell.

[0036] The processor 110 can be configured to: receive one of a new pack current value and a new pack voltage value of the battery pack; determine another of the new pack current value and new pack voltage value of the battery pack based on the one of the new pack current value and new pack voltage value of the battery pack and previously determined G parameter values ​​and previously determined H parameter values; determine a new cell voltage value, a new cell current value, and a new state parameter value for each of the battery cells based on the new pack current value and new pack voltage value of the battery pack and previously determined state parameter values ​​for each of the battery cells; determine a new ECM parameter value for each of the battery cells based on the new ECM parameter value for each of the battery cells; and determine a new G parameter value and a new H parameter value for the battery pack based on the new G parameter value and new H parameter value for each of the battery cells.

[0037] The processor 110 can perform the simulation of the battery pack by repeating the following process: receiving one of a new pack current value and a new pack voltage value; determining a new cell voltage value, a new cell current value, and a new state parameter value for each of the battery cells based on the received value; and determining a new G parameter value and a new H parameter value for each of the battery cells.

[0038] Refer to the following Figure 3 The method for simulating a battery pack is described in more detail.

[0039] Memory 120 is a recording medium readable by the processor 110 of computing device 100, and may include random access memory (RAM), read-only memory (ROM), and permanent mass storage devices (such as disk drives). An operating system and at least one program or at least a piece of application code may be stored in memory 120. Program code for performing a method for simulating a battery pack according to an embodiment may be stored in memory 120. Furthermore, a lookup table may be stored in memory 120, which defines ECM parameter values ​​used in the ECM of the battery cell based on at least one state parameter value of the battery cell.

[0040] The input and output device 130 can receive input from the user, send the input to the processor 110, and output information received from the processor 110 to the user. The computing device 100 may include a communication module, which can receive input from the user, send the input to the processor 110, and send information received from the processor 110 to the user.

[0041] Figure 2 A battery pack model is shown according to an embodiment of a method for performing a simulated battery pack.

[0042] Reference Figure 2 The battery pack model 115 is executed by the processor 110. When the processor 110 executes the program code stored in the memory 120 for performing a method to simulate a battery pack, the processor 110 can operate as the battery pack model 115.

[0043] When initial value data and input data are input to the battery pack model 115, the battery pack model 115 outputs output data based on the input data. For example, the input data can be the battery pack current value, and the output data can be the battery pack voltage value, as well as the voltage and current values ​​of the individual battery cells included in the battery pack. As another example, the input data can be the battery pack voltage value, and the output data can be the battery pack current value, as well as the voltage and current values ​​of the individual battery cells included in the battery pack.

[0044] Figure 3 This is a flowchart of a method for simulating a battery pack according to an embodiment.

[0045] Reference Figure 3 In operation S10, the connection relationship of the battery cells in the battery pack and the ECM of the battery cells are selected.

[0046] A battery pack may include battery cells connected in parallel, battery cells connected in series, or battery cells connected in both parallel and series. A battery pack may include, for example... Figure 4 The battery cells are connected as shown in the diagram.

[0047] A battery pack includes at least one battery cell as a component for storing electrical energy. The battery cell may include a rechargeable secondary battery. For example, the battery cell may include nickel-cadmium batteries, lead-acid batteries, nickel-metal hydride (NiMH) batteries, lithium-ion batteries, lithium polymer batteries, etc. The number of battery cells included in the battery pack can be determined based on the required output voltage and charging capacity.

[0048] Figure 4 A battery pack is shown, comprising individual cells (1,1) to (m,n) connected in a combination of parallel and series configurations.

[0049] Reference Figure 4 The battery pack consists of m battery groups bank(1) to bank(m). The battery group bank(i) represents the i-th battery group among the m battery groups bank(1) to bank(m), where i is a natural number greater than or equal to 1 and less than or equal to m.

[0050] Each of the m battery banks bank(1) to bank(m) comprises n individual battery cells cell(1,1) to cell(1,n), ..., or cell(m,1) to cell(m,n). A single battery cell cell(i,j) represents the j-th individual cell among the n individual cells cell(i,1) to cell(i,n) of the i-th battery bank bank(i), where j is a natural number greater than or equal to 1 and less than or equal to n. A battery pack comprises a total of m×n individual battery cells cell(1,1) to cell(1,n), ..., and cell(m,1) to cell(m,n).

[0051] In this specification, the battery pack includes, for example, Figure 4 An embodiment of battery cells connected to each other as shown is described. However, Figure 4 The battery pack shown is merely an example, and the disclosed simulation method can be applied in the same way to battery packs that include battery cells connected in parallel with each other or battery packs that include battery cells connected in series with each other.

[0052] In the following text, individual battery cells (1,1) to cell (m,n) are collectively referred to as individual battery cells, and battery banks (1) to bank (m) are collectively referred to as battery banks.

[0053] Figure 5 It shows Figure 4 The equivalent circuit of the battery pack.

[0054] Reference Figure 5The equivalent circuit of the battery pack includes m-1 sets of resistors R_b(1) to R_b(m-1) connected in series between m battery banks (1) to bank (m). The m-1 sets of resistors R_b(1) to R_b(m-1) can be contact resistors between m battery banks (1) to bank (m).

[0055] The equivalent circuit of the battery pack includes contact resistors R_cnt(1,1) to R_cnt(1,n), ..., and R_cnt(m,1) to R_cnt(m,n) respectively included in m×n individual battery cells cell(1,1) to cell(1,n), ..., and cell(m,1) to cell(m,n).

[0056] Each of the battery cells cell(1,1) to cell(1,n), ..., or cell(m,1) to cell(m,n) has G parameters G_cell(1,1) to G_cell(1,n), ..., or G_cell(m,1) to G_cell(m,n) as internal state parameters and H parameters H_cell(1,1) to H_cell(1,n), ..., or H_cell(m,1) to H_cell(m,n).

[0057] Each of the battery banks (1) to (m) has G parameters G_bank(1) to G_bank(m) and H parameters H_bank(1) to H_bank(m) as internal state parameters. Based on the G-parameters G_cell(1,1) to G_cell(1,n), ..., and G_cell(m,1) to G_cell(m,n) of the individual cells cell(1,1) to cell(1,n), ..., and cell(m,1) to cell(m,n), the H-parameters H_cell(1,1) to H_cell(1,n), ..., and H_cell(m,1) to H_cell(m,n), and the contact resistance values ​​R_cnt(1,1) to R_cnt(1,n), ..., and R_cnt(m,1) to R_cnt(m,n), the G-parameters G_bank(1) to G_bank(m) and the H-parameters H_bank(1) to H_bank(m) included in the battery packs bank(1) to bank(m) can be calculated respectively.

[0058] The battery pack has G-parameter G_pack and H-parameter H_pack as internal state parameters. Based on the G-parameter G_bank(1) to G_bank(m) and H-parameter H_bank(1) to H_bank(m) included in the battery banks (1) to bank (m) respectively, and the m-1 group resistance values ​​R_b(1) to R_b(m-1), the G-parameter G_pack and H-parameter H_pack of the battery pack can be calculated.

[0059] The G parameter G is a state quantity representing the sensitivity of a battery's voltage to changes in current and is expressed in units of resistance. The H parameter H is the effective potential determined by the local equilibrium potential distribution and resistance distribution within the battery and is expressed in units of voltage. A battery can refer to a single cell, a battery bank, or a battery pack.

[0060] The G-parameters G and H-parameters H of a battery can be quantified using theoretical models via explicit correlation formulas relating battery material properties and design variables. The G-parameters G and H-parameters H of a battery are described below.

[0061] Regarding the battery, we can assume that the voltage V and the current i have a relationship such as V = f(i; x, p). Here, x is a physical quantity representing the internal state of the battery, and p is a parameter.

[0062] The function f is a nonlinear implicit function, and when the function f can be divided into a rapidly changing quantity g and a slowly changing quantity h, the above correlation formula can be expressed as V = g(i; x, p) + h(i; x, p).

[0063] When assuming the existence of a function G(i;x,p) = dg / di that changes slowly with respect to current i, the above correlation formula can be expressed as V = G(i;x,p)i + H(i;x,p).

[0064] In the above correlation formula, dG / di and dH / di have very small values. In other words, when the described assumptions are met, G and H are functions that change slowly with respect to current i. Therefore, the function f representing the nonlinear relationship between voltage V and current i can be represented by the quasi-linear relationship in the above correlation formula.

[0065] Here, G is called the G parameter, and H is called the H parameter. When the current i is the charging and discharging current, and Ueq is the battery's equilibrium potential, the discharge overvoltage can be represented by Ueq-V = -G·i + (Ueq-H) using the G parameter G and the H parameter H.

[0066] Here, -G·i is the overvoltage caused by current leakage through the battery terminals, and includes the dynamic polarization of the reaction and the electronic and ionic resistivity polarization. (Ueq-H) is the overvoltage caused by the deviation of the battery's local thermodynamic equilibrium from the equilibrium state of the entire system. That is, (Ueq-H) represents the low efficiency caused by thermodynamic non-uniformity in the battery, and when the internal system of the battery reaches thermodynamic equilibrium, the H parameter H is equal to the equilibrium potential Ueq.

[0067] According to the method for simulating a battery pack, and based on the disclosed embodiments, the state of the battery pack can be simulated relatively more simply by calculating and using the G parameter G and H parameter H of each of the individual battery cells, the battery bank, and the battery pack.

[0068] Refer again Figure 3 You can choose the ECM of a single battery cell. For example, as the ECM, you can choose the internal resistance battery model, the first-order Thevenin model, the second-order Thevenin model, the nth-order Thevenin model (n is a natural number greater than or equal to 3), etc.

[0069] According to the internal resistance battery model, a single battery cell can be modeled using a voltage source with an open-circuit voltage and a series resistor. According to the first-order Thevenin model, a single battery cell can be modeled using a voltage source with an open-circuit voltage, a series resistor, and a first parallel resistor and a first parallel capacitor connected in parallel.

[0070] According to the second-order Thevenin model, a battery cell can be modeled by a voltage source with an open-circuit voltage value, a series resistor, a first parallel resistor and a first parallel capacitor connected in parallel, and a second parallel resistor and a second parallel capacitor connected in parallel.

[0071] Figure 6 The second-order Thevenin model is shown based on the published ECM selected as the battery cell.

[0072] Reference Figure 6 A single battery cell (i,j) can be modeled using a voltage source with an open-circuit voltage value OCV (i,j), a series resistor Rs (i,j), a first parallel resistor Rp1 (i,j) and a first parallel capacitor Cp1 (i,j) connected in parallel, and a second parallel resistor Rp2 (i,j) and a second parallel capacitor Cp2 (i,j) connected in parallel.

[0073] The single-cell voltage of a battery cell (cell(i,j)) is V_cell(i,j), and the single-cell current of a battery cell (cell(i,j)) is I_cell(i,j). The voltage between the first parallel resistor Rp1(i,j) and the first parallel capacitor Cp1(i,j) is denoted as the first voltage V1(i,j), and the voltage between the second parallel resistor Rp2(i,j) and the second parallel capacitor Cp2(i,j) is denoted as the second voltage V2(i,j). V_cell(i,j) equals OCV(i,j) + V1(i,j) + V2(i,j). The single-cell current I_cell(i,j) can be defined as having a positive (+) value during charging and a negative (-) value during discharging.

[0074] This specification describes an embodiment in which a second-order Thevenin model is selected as the ECM for a single battery cell. However, the disclosed methods for simulating battery packs can also be applied to cases where other ECMs besides the second-order Thevenin model are selected.

[0075] Refer again Figure 3 Determine the initial values ​​of the parameters of each individual battery cell and the initial values ​​of the G parameter G_pack[0] and H parameter H_pack[0] of the battery pack.

[0076] According to an embodiment, the initial parameter values ​​for each battery cell may include the initial state parameter values ​​for each battery cell and the initial ECM parameter values ​​for each battery cell.

[0077] According to an embodiment, the initial values ​​of the state parameters for each battery cell may include the initial value of the cell's state of charge (SOC). Furthermore, the initial values ​​of the state parameters for each battery cell may also include the initial value of the cell's temperature.

[0078] In this specification, embodiments in which the state parameters of each battery cell include the cell's state of charge (SOC) and cell temperature are described. However, the disclosure is not limited thereto, and the state parameters may include only the cell's SOC, or may include other parameters in addition to the cell's SOC and cell temperature.

[0079] According to the embodiment, the initial values ​​of the state parameters of each battery cell can be received. For example, in operation S20, the initial value of the cell SOC, SOC_cell[0], and the initial value of the cell temperature, T_cell[0], of each battery cell can be received. For example, for all battery cells in the battery cell, the initial value of the cell SOC, SOC_cell(i,j)[0], and the initial value of the cell temperature, T_cell(i,j)[0], of the cell cell (i,j) can be received.

[0080] In this specification, the initial value is represented as "[0]". Input data is a set of input values ​​with a predetermined time interval. Output data is also a set of output values ​​with a predetermined time interval. The input or output value at the first moment is represented as "[1]", and the input or output value at the second moment is represented as "[2]". For example, the predetermined time interval can be the same as the sampling period used to measure the package voltage or package current. The predetermined time interval can be represented as "Δt". When the first moment is t0, the second moment can be t0+Δt.

[0081] According to the embodiments, other parameter values ​​used in the disclosed simulation method can be received. For example, the group resistance value R_b(i) of each in the battery pack and the contact resistance value R_cnt(i,j) of each in the battery cell can be received. Furthermore, the total capacity Qtotal_cell(i,j) of each battery cell can be received. Additionally, information related to the cell mass (design mass (DM)), cell specific heat Cpk, and surface area (design area (DA)) of the battery cell can be received. Furthermore, information regarding the convective heat transfer coefficient h with external air and the external air temperature T_amb can be received. Furthermore, information related to the time interval Δt of the input values ​​of the input data can be received or predetermined.

[0082] The initial value of the ECM parameter of each battery cell can be determined based on the initial value of the state parameter of each battery cell. According to the embodiment, in operation S30, the initial value of the ECM parameter of each battery cell can be estimated based on the initial value of the cell SOC_cell[0] and the initial value of the cell temperature T_cell[0].

[0083] In this specification, a second-order Thevenin model is used as the ECM. Therefore, the ECM parameters may include the open-circuit voltage value OCV, the series resistance value Rs, the first parallel resistance value Rp1, the first parallel capacitance value Cp1, the second parallel resistance value Rp2, and the second parallel capacitance value Cp2.

[0084] To estimate the initial values ​​of the ECM parameters for each battery cell, a lookup table defining the ECM parameter values ​​based on the state parameter values ​​of each battery cell can be stored in memory 120. According to an embodiment, the lookup table can store the ECM parameter values ​​(i.e., open-circuit voltage value OCV, series resistance value Rs, first parallel resistance value Rp1, first parallel capacitance value Cp1, second parallel resistance value Rp2, and second parallel capacitance value Cp2) based on the cell's SOC value SOC_cell and cell temperature value T_cell.

[0085] According to the embodiment, by referring to a lookup table stored in the memory 120, the initial values ​​of the open-circuit voltage OCV[0], series resistance Rs[0], first parallel resistance Rp1[0], first parallel capacitance Cp1[0], second parallel resistance Rp2[0], and second parallel capacitance Cp2[0] of each battery cell can be estimated based on the initial values ​​of the cell SOC_cell[0] and cell temperature T_cell[0]. Therefore, for all battery cells in the battery cell, the initial values ​​of the open-circuit voltage OCV(i,j)[0], series resistance Rs(i,j)[0], first parallel resistance Rp1(i,j)[0], first parallel capacitance Cp1(i,j)[0], second parallel resistance Rp2(i,j)[0], and second parallel capacitance Cp2(i,j)[0] of each battery cell cell(i,j) can be determined.

[0086] In operation S40, based on the initial value of the ECM parameter of each battery cell, the initial value of the G parameter G_cell[0] and the initial value of the H parameter H_cell[0] of each battery cell can be determined.

[0087] For all battery cells, the initial value of the G parameter G_cell(i,j)[0] of the battery cell cell(i,j) can be determined as the initial value of the series resistance Rs(i,j)[0] of the battery cell cell(i,j), and the initial value of the H parameter H_cell(i,j)[0] of the battery cell cell(i,j) can be determined as the initial value of the open circuit voltage OCV(i,j)[0].

[0088] In operation S50, based on the initial values ​​of the G parameter G_cell[0] and H parameter H_cell[0] of each battery cell, the initial values ​​of the G parameter G_pack[0] and H parameter H_pack[0] of the battery pack can be determined.

[0089] According to the embodiment, based on the initial G parameter value G_cell[0], the initial H parameter value H_cell[0], and the contact resistance value R_cnt of each battery cell, the initial G parameter value G_bank[0] and the initial H parameter value H_bank[0] of each battery pack can be determined.

[0090] For example, the initial value of the G parameter G_bank[0] of each battery pack can be calculated using the following equation based on the initial value of the G parameter G_cell[0] and the contact resistance value R_cnt of each individual battery cell.

[0091]

[0092] For example, the initial value of the H parameter H_bank[0] of each battery pack can be calculated using the following equation based on the initial value of the G parameter G_cell[0], the initial value of the H parameter H_cell[0], and the contact resistance value R_cnt of each individual battery cell.

[0093]

[0094] The above equation can be derived using the following relationships: the group current I_bank(i) flowing in the i-th battery bank (i) is the same as the sum of the individual cell currents I_cell(i,1) to I_cell(i,n) flowing in the n individual cells cell(i,1) to cell(i,n) included in the i-th battery bank (i); the group voltage V_bank(i) of the i-th battery bank (i) is the same as the value obtained by adding the individual cell voltages V_cell(i,1) to V_cell(i,n) corresponding to the n individual cells cell(i,1) to cell(i,n) respectively, obtained by multiplying the corresponding contact resistance R_cnt(i,j) by the corresponding individual cell current I_cell(i,1) to I_cell(i,n); and V_bank(i) = H_bank(i) + G_bank(i) × I_bank(i).

[0095] According to the embodiment, based on the initial values ​​of the G parameters G_bank[0] and H parameters H_bank[0] of each battery pack and the resistance values ​​R_b of m-1 groups, the initial values ​​of the G parameters G_pack[0] and H parameters H_pack[0] of the battery pack can be determined.

[0096] For example, the initial value of the G parameter of the battery pack, G_pack[0], can be calculated based on the initial value of the G parameter of each battery pack, G_bank[0], and the resistance values ​​of m-1 groups, R_b, using the following equation.

[0097]

[0098] For example, the initial H parameter value H_pack[0] of the battery pack can be calculated based on the initial H parameter value H_bank[0] of each battery pack using the following equation.

[0099]

[0100] The above equations can be derived using the following relationships: the pack current I_pack flowing in the battery pack is the same as the group current I_bank(i) flowing in the series-connected battery bank(i); the pack voltage V_pack of the battery pack is the same as the value obtained by adding the sum of the group voltages V_bank of the battery banks to the value obtained by multiplying the group resistance R_b by the pack current I_pack; and V_pack = H_pack + G_pack × I_pack.

[0101] Through operations S10 to S50 described above, the initial configuration of the battery pack model 115 can be completed. Afterwards, the simulation operation of the battery pack model 115 based on the input data is described.

[0102] First, in order to represent the order of input values ​​with a predetermined time interval, in operation S60, 1 can be input as the time variable t. The value corresponding to t=1 can be represented as "[1]".

[0103] As input data, one of the pack current value I_pack[1] and pack voltage value V_pack[1] of the battery pack can be received.

[0104] Based on one of the battery pack current value I_pack[1] and the battery pack voltage value V_pack[1], as well as the initial values ​​of the battery pack's G parameter G_pack[0] and H parameter H_pack[0], the other of the battery pack current value I_pack[1] and the battery pack voltage value V_pack[1] can be determined. For example, by using the correlation formula V_pack[1]=H_pack[0]+G_pack[0]×I_pack[1], when the battery pack current value I_pack[1] is received, the battery pack voltage value V_pack[1] can be calculated, and when the battery pack voltage value V_pack[1] is received, the battery pack current value I_pack[1] can be calculated.

[0105] In this specification, an embodiment in which the pack current value I_pack[1] of the battery pack is received is described. However, the disclosure is not limited thereto, and can be applied in the same way to the case in which the pack voltage value V_pack[1] of the battery pack is received.

[0106] According to the embodiment, in operation S70, the pack current value I_pack[1] of the battery pack can be received. In operation S80, based on the pack current value I_pack[1] of the battery pack and the initial values ​​received or determined in operations S20 to S50, the pack voltage value V_pack[1] of the battery pack, the cell voltage value V_cell[1] of each battery cell, the cell current value I_cell[1], the cell SOC value SOC_cell[1], and the cell temperature value T_cell[1] can be calculated.

[0107] The pack voltage value V_pack[1] can be calculated using the correlation formula V_pack[1]=H_pack[0]+G_pack[0]×I_pack[1] based on the pack current value I_pack[1] of the battery pack and the initial values ​​of the G parameters G_pack[0] and H parameters H_pack[0] of the battery pack.

[0108] According to the embodiment, based on the pack current value I_pack[1] of the battery pack and the initial values ​​of the G parameters G_bank[0] and H parameters H_bank[0] of each battery group, the group voltage value V_bank[1] and the group current value I_bank[1] of each battery group can be calculated. For example, for all battery groups in the battery pack, the group current value I_bank(i)[1] of the battery group bank(i) can be the same as the pack current value I_pack[1]. For all battery groups, the group voltage value V_bank(i)[1] of the battery group bank(i) can be calculated by using the correlation formula V_bank(i)[1]=H_bank(i)[0]+G_bank(i)[0]×I_bank(i)[1].

[0109] According to another embodiment, the group voltage value V_bank(i) of the battery pack bank(i) can be calculated by repeated calculations [1]. For example, for V_bank(i)[0+(k)] = H_bank(i)[0+(k-1)] + G_bank(i)[0+(k-1)] × I_bank(i)[0+(k)], V_bank(i)[0+(k)] can be calculated by incrementing k by 1 starting from 1. Here, when the difference between V_bank(i)[0+(k)] and V_bank(i)[0+(k-1)] is less than or equal to a predetermined reference value, the group voltage value V_bank(i)[1] can be determined as V_bank(i)[0+(k)]. H_bank(i)[0+(k)] and G_bank(i)[0+(k)] can also be calculated by repeated calculations, and the calculation process can be easily understood through the following description.

[0110] According to the embodiment, based on the group voltage value V_bank[1] of each battery pack and the initial values ​​of the G parameters G_cell[0], H parameters H_cell[0] and contact resistance value R_cnt of each battery cell, the cell current value I_cell[1] of each battery cell can be calculated. For example, for all battery cells, the cell current value I_cell(i,j)[1] of the battery cell cell(i,j) can be calculated by using the correlation formula I_cell(i,j)[1]={V_bank(i)[1]-H_cell(i,j)[0]} / {G_cell(i,j)[0]+R_cnt(i,j)}.

[0111] According to another embodiment, the cell current value I_cell(i,j)[1] of a battery cell cell(i,j) can be calculated by repeated calculations. For example, for I_cell(i,j)[0+(k)]={V_bank(i)[0+(k)]-H_cell(i,j)[0+(k-1)]} / {G_cell(i,j)[0+(k-1)]+R_cnt(i,j)}, I_cell(i,j)[0+(k)] can be calculated by incrementing k by 1 from 1. Here, when the difference between I_cell(i,j)[0+(k)] and I_cell(i,j)[0+(k-1)] is less than or equal to a predetermined reference value, the cell current value I_cell(i,j)[1] can be determined as I_cell(i,j)[0+(k)]. H_cell(i,j)[0+(k)] and G_cell(i,j)[0+(k)] can also be calculated by repeated calculations, and the calculation process can be easily understood through the following description.

[0112] According to the embodiment, the cell voltage value V_cell[1] of each battery cell can be calculated based on the group voltage value V_bank[1] of each battery pack and the cell current I_cell[1] and contact resistance value R_cnt of each battery cell. For example, for all battery cells, the cell voltage value V_cell(i,j)[1] of the battery cell cell(i,j) can be calculated by using the correlation formula V_cell(i,j)[1]=V_bank(i)[1]+R_cnt(i,j)×I_cell(i,j)[1].

[0113] According to another embodiment, the cell voltage value V_cell(i,j)[1] of a battery cell cell(i,j) can be calculated by repeated calculations. For example, for V_cell(i,j)[0+(k)] = V_bank(i)[0+(k)] + R_cnt(i,j) × I_cell(i,j)[0+(k)], V_cell(i,j)[0+(k)] can be calculated by incrementing k by 1 from 1. Here, when the difference between V_cell(i,j)[0+(k)] and V_cell(i,j)[0+(k-1)] is less than or equal to a predetermined reference value, the cell voltage value V_cell(i,j)[1] can be determined as V_cell(i,j)[0+(k)].

[0114] According to the embodiment, the SOC value of each battery cell, SOC_cell[1], can be calculated based on the initial SOC value of each battery cell, SOC_cell[0], the current value of each battery cell, I_cell[1], the total capacity, Qtotal_cell, and the time interval Δt. For example, for all battery cells, the SOC value of battery cell cell(i,j) can be calculated by using the correlation formula SOC_cell(i,j)[1]=SOC_cell(i,j)[0]+I_cell(i,j)[1]×Δt / Qtotal_cell(i,j).

[0115] According to the embodiment, the cell temperature value T_cell[1] of each battery cell can be calculated based on the initial cell temperature T_cell[0], cell current value I_cell[1], initial series resistance value Rs[0], initial first parallel resistance value Rp1[0], initial second parallel resistance value Rp2[0], and time interval Δt. For example, for all battery cells, the correlation formula T_cell(i,j)[1]=T_cell(i,j)[0]+Δt×{I_cell(i,j)[1] can be used. 2 The cell temperature value T_cell(i,j)[1] of the battery cell is calculated using the formula: ×(Rs(i,j)[0]+Rp1(i,j)[0]+Rp2(i,j)[0])-h×DA×(T_cell(i,j)[0]-T_amb)} / (DM×Cpk). Here, DM represents the mass of the battery cell, Cpk represents the specific heat of the battery cell, DA represents the surface area of ​​the battery cell, h represents the convective heat transfer coefficient with the external air, and T_amb represents the temperature of the external air (e.g., room temperature).

[0116] The ECM parameter value of each battery cell can be determined based on the state parameter value of each individual battery cell.

[0117] According to the embodiment, in operation S90, the ECM parameter value of each battery cell can be estimated based on the cell SOC value SOC_cell[1] and cell temperature value T_cell[1] of each battery cell. As described above, the memory 120 can store a lookup table in which the ECM parameter values ​​(i.e., open-circuit voltage value OCV, series resistance value Rs, first parallel resistance value Rp1, first parallel capacitance value Cp1, second parallel resistance value Rp2 and second parallel capacitance value Cp2) are defined based on the cell SOC value SOC_cell and cell temperature value T_cell of each battery cell.

[0118] According to the embodiment, by referring to the lookup table stored in the memory 120, the open circuit voltage value OCV[1], series resistance value Rs[1], first parallel resistance value Rp1[1], first parallel capacitance value Cp1[1], second parallel resistance value Rp2[1] and second parallel capacitance value Cp2[1] of each battery cell can be estimated based on the cell SOC value SOC_cell[1] and cell temperature value T_cell[1] of each battery cell. Therefore, for all battery cells, by referring to the lookup table stored in memory 120, the open-circuit voltage value OCV(i,j)[1], series resistance value Rs(i,j)[1], first parallel resistance value Rp1(i,j)[1], first parallel capacitance value Cp1(i,j)[1], second parallel resistance value Rp2(i,j)[1] and second parallel capacitance value Cp2(i,j)[1] of the battery cell cell(i,j) can be determined based on the cell SOC value SOC_cell(i,j)[1] and the cell temperature value T_cell(i,j)[1].

[0119] According to the embodiment, in operation S100, based on the ECM parameter value of each battery cell, the G parameter value G_cell[1] and H parameter value H_cell[1] of each battery cell can be determined.

[0120] According to the embodiment, based on the open-circuit voltage value OCV[1], series resistance value Rs[1], first parallel resistance value Rp1[1], first parallel capacitance value Cp1[1], second parallel resistance value Rp2[1] and second parallel capacitance value Cp2[1] of each battery cell, the G parameter value G_cell[1] and H parameter value H_cell[1] of each battery cell can be calculated.

[0121] For all battery cells, the G-parameter value G_cell(i,j)[1] of battery cell cell(i,j) can be determined as the series resistance value Rs(i,j)[1] of battery cell cell(i,j). That is to say, the G-parameter value G_cell(i,j)[1] of battery cell cell(i,j) can be calculated according to G_cell(i,j)[1]=Rs(i,j)[1].

[0122] According to another embodiment, the G-parameter value G_cell(i,j)[1] of a battery cell cell(i,j) can be calculated by repeated calculations. For example, for G_cell(i,j)[0+(k)] = Rs(i,j)[0+(k)], G_cell(i,j)[0+(k)] can be calculated by incrementing k by 1 from 1. Here, when the difference between G_cell(i,j)[0+(k)] and G_cell(i,j)[0+(k-1)] is less than or equal to a predetermined reference value, the G-parameter value G_cell(i,j)[1] can be determined as G_cell(i,j)[0+(k)].

[0123] For all battery cells, the H parameter value H_cell(i,j)[1] of the battery cell cell(i,j) can be determined based on the open-circuit voltage value OCV(i,j)[1], the first voltage value V1(i,j)[1], and the second voltage value V2(i,j)[1] of the battery cell cell(i,j). For example Figure 6 As shown, the first voltage value V1(i,j)[1] can be the voltage value of the first parallel resistor Rp1(i,j)[1] and the first parallel capacitor Cp1(i,j)[1] connected in parallel with each other, and the second voltage value V2(i,j)[1] can be the voltage value of the second parallel resistor Rp2(i,j)[1] and the second parallel capacitor Cp2(i,j)[1] connected in parallel with each other.

[0124] For example, for all battery cells, the H parameter value H_cell(i,j)[1] of battery cell cell(i,j) can be determined as the value obtained by adding the first voltage value V1(i,j)[1] and the second voltage value V2(i,j)[1] to the open-circuit voltage value OCV(i,j)[1] of battery cell cell(i,j). That is, the H parameter value H_cell(i,j)[1] of battery cell cell(i,j) can be calculated according to H_cell(i,j)[1]=OCV(i,j)[1]+V1(i,j)[1]+V2(i,j)[1].

[0125] The first voltage value V1(i,j)[1] of the battery cell cell(i,j) can be calculated as V1(i,j)[1]=(V1(i,j)[0]×exp(-Δt / τ1(i,j)[1])+Rp1(i,j)[1]×(1-exp(-Δt / τ1(i,j)[1]))×I_cell(i,j)[1]). Here, τ1(i,j)[1] is defined as Rp1(i,j)[1]×Cp1(i,j)[1].

[0126] The second voltage value V2(i,j)[1] of the battery cell cell(i,j) can be calculated as V2(i,j)[1]=(V2(i,j)[0]×exp(-Δt / τ2(i,j)[1])+Rp2(i,j)[1]×(1-exp(-Δt / τ2(i,j)[1]))×I_cell(i,j)[1]). Here, τ2(i,j)[1] is defined as Rp2(i,j)[1]×Cp2(i,j)[1].

[0127] According to another embodiment, the H parameter value H_cell(i,j) of a battery cell cell(i,j) can be calculated by repeated calculations[1]. For example, for H_cell(i,j)[0+(k)]=OCV(i,j)[0+(k)]+V1(i,j)[0+(k)]+V2(i,j)[0+(k)]=OCV(i,j)[0+(k)]+{(V1(i,j)[0+(k-1)]×exp(-Δt / τ1(i,j)[0+(k)])+Rp1(i ,j)[0+(k)]×(1-exp(-Δt / τ1(i,j)[0+(k)]))×I_cell(i,j)[0+(k)]}+{(V2(i,j )[0+(k-1)]×exp(-Δt / τ2(i,j)[0+(k)])+Rp2(i,j)[0+(k)]×(1-exp(-Δt / τ2(i, (where τ1(i,j)[0+(k)]=Rp1(i,j)[0+(k)]×Cp1(i,j)[0+(k)],τ2(i,j)[0+(k)]=Rp2(i,j)[0+(k)]×Cp2(i,j)[0+(k)]) can be calculated by incrementing k by 1 from 1. Here, when the difference between H_cell(i,j)[0+(k)] and H_cell(i,j)[0+(k-1)] is less than or equal to a predetermined reference value, the H parameter value H_cell(i,j)[1] can be determined as H_cell(i,j)[0+(k)].

[0128] In operation S110, based on the G parameter value G_cell[1] and H parameter value H_cell[1] of each battery cell, the G parameter value G_pack[1] and H parameter value H_pack[1] of the battery pack can be determined.

[0129] According to the embodiment, based on the G parameter value G_cell[1], H parameter value H_cell[1] and contact resistance value R_cnt of each battery cell, the G parameter value G_bank[1] and H parameter value H_bank[1] of each battery pack can be determined.

[0130] For example, the G parameter value G_bank(i) of the i-th battery bank(i) can be calculated by the following equation based on the G parameter values ​​G_cell(i,1)[1] to G_cell(i,n)[1] and the contact resistance values ​​R_cnt(i,1) to R_cnt(i,n) included in the n battery cells cell(i,1) to cell(i,n) included in the i-th battery bank(i).

[0131]

[0132] For example, the H parameter value H_bank(i) of the i-th battery bank(i) can be calculated by the following equation based on the G parameter values ​​G_cell(i,1)[1] to G_cell(i,n)[1], H parameter values ​​H_cell(i,1)[1] to H_cell(i,n)[1] and contact resistance values ​​R_cnt(i,1) to R_cnt(i,n) included in the n battery cells cell(i,1) to cell(i,n) included in the i-th battery bank(i).

[0133]

[0134] The above equations can be derived using the following relationships: the group current I_bank(i) flowing in the i-th battery bank(i) is the same as the sum of the individual cell currents I_cell(i,1) to I_cell(i,n) flowing in the n individual cells cell(i,1) to cell(i,n) included in the i-th battery bank(i); the group voltage V_bank(i) of the i-th battery bank(i) is the same as the value obtained by adding the individual cell voltages V_cell(i,1) to V_cell(i,n) corresponding to the n individual cells cell(i,1) to cell(i,n) respectively, obtained by multiplying the corresponding contact resistance R_cnt(i,j) by the corresponding individual cell current I_cell(i,1) to I_cell(i,n); and V_bank(i) = H_bank(i) + G_bank(i) × I_bank(i).

[0135] According to the embodiment, the G parameter value G_pack[1] and H parameter value H_pack[1] of the battery pack can be determined based on the G parameter value G_bank[1] and H parameter value H_bank[1] of each battery pack and the resistance values ​​R_b of m-1 groups.

[0136] For example, the G parameter value G_pack[1] of the battery pack can be calculated based on the G parameter values ​​G_bank(1)[1] to G_bank(m)[1]) and the m-1 group resistance values ​​R_b(1) to R_b(m-1) respectively included in the battery pack by the following equation.

[0137]

[0138] For example, the H parameter value H_pack[1] of the battery pack can be calculated by the following equation based on the H parameter values ​​H_bank(1)[1] to H_bank(m)[1] respectively included in the battery pack.

[0139]

[0140] The above equations can be derived using the following relationships: the pack current I_pack flowing in the battery pack is the same as the group current I_bank(i) flowing in the series-connected battery bank(i); the pack voltage V_pack of the battery pack is the same as the value obtained by adding the sum of the group voltages V_bank of the battery banks to the value obtained by multiplying the group resistance R_b by the pack current I_pack; and V_pack = H_pack + G_pack × I_pack.

[0141] As described above, based on the pack current value I_pack[1] received in operation S70, the pack voltage value V_pack[1], as well as the cell voltage value V_cell[1], cell current value I_cell[1], cell SOC value SOC_cell[1], and cell temperature value T_cell[1] of each battery cell can be calculated in operation S80. Furthermore, the G parameter value G_cell[1] and H parameter value H_cell[1] of each battery cell, as well as the G parameter value G_pack[1] and H parameter value H_pack[1] of the battery pack, can be updated in operations S90 to S110. Afterward, the calculation can proceed to operation S120, and t can be incremented by 1.

[0142] In operation S70, the pack current value I_pack[2] can be received. Based on the pack current value I_pack[2], the pack voltage value V_pack[2], the cell voltage value V_cell[2], the cell current value I_cell[2], the cell SOC value SOC_cell[2], and the cell temperature value T_cell[2] of each battery cell can be calculated in operation S80. In operations S90 to S110, the G parameter value G_cell[2] and H parameter value H_cell[2] of each battery cell, as well as the G parameter value G_pack[2] and H parameter value H_pack[2] of the battery pack can be updated. After that, the calculation can proceed to operation S120, and t can be incremented by 1.

[0143] Through this process, based on input data including pack current values, the battery pack model 115 can accurately and quickly simulate the state changes of each individual battery cell and the state changes of the battery pack.

[0144] According to the disclosed simulation method, calculations can be performed very quickly. As a result of simulating a battery pack in which ten individual cells are connected in series, based on the disclosed method and a prior art Simulink-based method, the disclosed method completes the calculation in an average of five seconds, while the prior art Simulink-based method takes forty minutes or more. In this experiment, the time interval Δt was 0.01 seconds, and the simulation was performed based on a scenario where the battery was discharged and charged once, with a total execution time of 60 minutes. The disclosed method demonstrates a 520-fold improvement in calculation speed compared to the previous method.

[0145] Furthermore, in the disclosed method, the operating time increases proportionally with the number of battery cells. However, in the previous method, the operating time increases exponentially with respect to the number of battery cells. Therefore, the disclosed method achieves a greater speed improvement compared to the previous method as the number of battery cells increases.

[0146] The disclosed concepts should not be limited to the embodiments described above. Furthermore, all scopes equivalent to or modified from the claims, other than those appended, should be considered as disclosed concepts.

Claims

1. A method of simulating a battery pack, the method performed by a computing device including a processor and a memory, the method comprising the steps of: selecting connection relationships of battery cells included in the battery pack and equivalent circuit models of the battery cells; determining initial values of parameters of each of the battery cells and initial values of G parameters and initial values of H parameters of the battery pack, wherein a G parameter is a state quantity representing a sensitivity of a voltage of a battery with respect to a change in a current and has a unit of resistance, a H parameter is an effective potential determined by a local equilibrium potential distribution and a resistance distribution in a battery and has a unit of voltage, and a battery refers to a battery cell, a battery pack, or a battery pack; receiving one of a pack current value and a pack voltage value of the battery pack; determining the other of the pack current value and the pack voltage value of the battery pack based on the one of the pack current value and the pack voltage value of the battery pack and the initial values of G parameters and the initial values of H parameters; determining a cell voltage value, a cell current value, and a value of a state parameter of each battery cell based on the pack current value and the pack voltage value of the battery pack and the initial values of parameters of each battery cell; determining a value of an equivalent circuit model parameter of each battery cell based on the value of the state parameter of each battery cell; determining a value of a G parameter and a value of a H parameter of each battery cell based on the value of the equivalent circuit model parameter of each battery cell; and determining a value of a G parameter and a value of a H parameter of the battery pack based on the value of the G parameter and the value of the H parameter of each battery cell.

2. The method of simulating a battery pack of claim 1, wherein, the G parameter is a parameter representing a sensitivity of a voltage of the battery pack or the battery cell with respect to a change in a current, and the H parameter is a parameter representing an effective potential determined by a local equilibrium potential distribution and a resistance distribution in the battery pack or the battery cell.

3. The method of simulating a battery pack of claim 1, wherein, The step of determining the initial values of parameters of each of the battery cells and the initial values of G parameters and the initial values of H parameters of the battery pack includes: receiving initial values of state parameters of each battery cell; determining initial values of equivalent circuit model parameters of each battery cell based on the initial values of state parameters of each battery cell; determining initial values of G parameters and initial values of H parameters of each battery cell based on the initial values of equivalent circuit model parameters of each battery cell; and determining initial values of G parameters and initial values of H parameters of the battery pack based on the initial values of G parameters and the initial values of H parameters of each battery cell.

4. The method of simulating a battery pack of claim 1, wherein, The state parameter of each battery cell includes a state of charge of each battery cell.

5. The method of simulating a battery pack of claim 1, wherein, The state parameter of each battery cell includes a temperature of each battery cell.

6. The method of simulating a battery pack of claim 1, wherein, The equivalent circuit model of the battery cell is a second-order Thevenin model including a series resistor, first and second parallel resistors, and first and second parallel capacitors.

7. The method of simulating a battery pack of claim 1, wherein, The battery pack includes m battery packs connected in series to each other, each of the m battery packs includes n battery cells connected in parallel to each other, wherein m and n are natural numbers greater than or equal to 1. 8.The method of simulating a battery pack according to claim 7, the method further comprising: receiving m-1 pack resistance values between the m battery banks and a contact resistance value of each battery cell.

9. The method of simulating a battery pack of claim 8, wherein, The step of determining the initial values of the parameters of each of the battery cells and the initial values of the G parameters and the initial values of the H parameters of the battery pack comprises: receiving initial values of state parameters of each battery cell; determining initial values of equivalent circuit model parameters of each battery cell based on the initial values of state parameters of each battery cell; determining initial values of the G parameters and the H parameters of each battery cell based on the initial values of equivalent circuit model parameters of each battery cell; determining initial values of the G parameters and the H parameters of each of the battery banks based on the initial values of the G parameters and the initial values of the H parameters of each battery cell and the contact resistance value; and determining the initial values of the G parameters and the initial values of the H parameters of the battery pack based on the initial values of the G parameters and the initial values of the H parameters of each battery bank and the m-1 pack resistance values.

10. The method of simulating a battery pack of claim 8, wherein, The memory stores a lookup table in which a plurality of values of equivalent circuit model parameters based on values of state parameters of each battery cell are defined, and The values of equivalent circuit model parameters of each battery cell are determined based on the lookup table and the values of state parameters of each battery cell.

11. The method of simulating a battery pack of claim 8, wherein, The values of equivalent circuit model parameters of each battery cell include an open circuit voltage value, a series resistance value, a first parallel resistance value and a second parallel resistance value, and a first parallel capacitance value and a second parallel capacitance value, The value of the G parameter of each battery cell is determined as the series resistance value of each battery cell, The value of the H parameter of each battery cell is determined based on the open circuit voltage value, a first voltage value and a second voltage value of each battery cell, wherein the first voltage value is a voltage value of a first parallel resistor and a first parallel capacitor connected in parallel to each other, and the second voltage value is a voltage value of a second parallel resistor and a second parallel capacitor connected in parallel to each other.

12. The method of simulating a battery pack of claim 8, wherein, The step of determining the values of the G parameters and the values of the H parameters of the battery pack based on the values of the G parameters and the values of the H parameters of each battery cell comprises: determining the values of the G parameters and the values of the H parameters of each battery bank based on the values of the G parameters, the values of the H parameters of each battery cell and the contact resistance value; and determining the values of the G parameters and the values of the H parameters of the battery pack based on the values of the G parameters and the values of the H parameters of each battery bank and the m-1 pack resistance values.

13. The method of simulating a battery pack of claim 12, wherein, The values of the G parameters and the values of the H parameters of each battery bank are determined by the following equations: wherein i is a natural number greater than or equal to 1 and less than or equal to m, j is a natural number greater than or equal to 1 and less than or equal to n, G_bank(i) is the value of the G parameter of the i-th battery bank among the m battery banks, H_bank(i) is the value of the H parameter of the i-th battery bank among the m battery banks, G_cell(i,j) is the value of the G parameter of the j-th battery cell among the n battery cells included in the i-th battery bank, H cell(i,j) is a value of an H parameter of the jth battery cell among the n battery cells included in the ith battery pack, and R cnt(i,j) is a value of a contact resistance of the jth battery cell of the ith battery pack.

14. The method of simulating a battery pack of claim 13, wherein, The value of the G parameter and the value of the H parameter of the battery pack are determined by the following equations: where G pack is the value of the G parameter of the battery pack, H pack is the value of the H parameter of the battery pack, and R b(i) is a value of a pack resistance between the ith battery pack and the ith+1 battery pack.

15. The method of simulating a battery pack of claim 1, further comprising: receiving one of a new pack current value and a new pack voltage value of the battery pack; determining the other of the new pack current value and the new pack voltage value of the battery pack based on the one of the new pack current value and the new pack voltage value of the battery pack and previously determined values of the G parameter and the H parameter of the battery pack; determining a new cell voltage value, a new cell current value, and a new value of a state parameter of each battery cell based on the new pack current value, the new pack voltage value, and the previously determined values of the G parameter and the H parameter of each battery cell; determining new values of equivalent circuit model parameters of each battery cell based on the new value of the state parameter of each battery cell; determining new values of the G parameter and the H parameter of each battery cell based on the new values of the equivalent circuit model parameters of each battery cell; and determining new values of the G parameter and the H parameter of the battery pack based on the new values of the G parameter and the H parameter of each battery cell.

16. A computer-readable storage medium having stored thereon a computer program for executing a method of simulating a battery pack according to any one of claims 1 to 15, the computer program for executing the method by using the computing device comprising the processor and the memory.

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