WO2018011993A1

WO2018011993A1 - Simulation method and simulation device

Info

Publication number: WO2018011993A1
Application number: PCT/JP2016/071079
Authority: WO
Inventors: 哲也松本; 前田　謙一; 近藤　隆文; 孟光大沼
Original assignee: 日立化成株式会社
Priority date: 2016-07-15
Filing date: 2016-07-15
Publication date: 2018-01-18
Also published as: JP2018009963A; JP6988132B2

Abstract

Provided is a simulation method such that the characteristics of a power storage device after deterioration can be estimated accurately. In this simulation method, a simulation is performed using an equivalent circuit model for the power storage device. The simulation method comprises the step of calculating a terminal voltage V(t) in the equivalent circuit model on the basis of a current I(t) flowing through the equivalent circuit model. The equivalent circuit model comprises a plurality of characteristic parameters. At least one of the characteristic parameters includes a time function representing an effect of deterioration on the power storage device. The time function has terms including a time integral of a value representing the operating state of the power storage device, and a coefficient representing a deterioration rate multiplied by the time integral.

Description

Simulation method and simulation apparatus

The present invention relates to a simulation method and a simulation apparatus.

Patent Document 1 describes a battery model identification method. In this method, the current waveform input to the battery is measured using a current sensor, and the voltage waveform of the battery terminal voltage is measured using a voltage sensor. And a system identification calculating part performs system identification of a battery model based on these current waveforms and voltage waveforms.

JP 2016-3963 A

Currently, various power storage devices such as lead storage batteries, lithium ion batteries, and lithium ion capacitors are used as in-vehicle power storage devices. Various types of hybrid systems have been put into practical use by combining these batteries. For example, in recent years, a so-called μHEV (Hybrid Electric 設ける Vehicle) method, in which a sub power storage device for energy regeneration during deceleration and power supply to an auxiliary device is provided separately from the main power storage device, has been particularly useful.

On the other hand, for example, in a fuel consumption simulation of a vehicle, various power sources such as an engine and a power storage device and a load are modeled, and a fuel consumption is calculated by inputting a predetermined traveling pattern into the model. In the simulation of power storage devices included in such fuel consumption simulations, it is extremely important to accurately model the complicated power storage device configuration in the hybrid system in order to perform simulation accurately. However, in the conventional simulation, the power storage device is modeled without considering the deterioration due to the use of the power storage device. Therefore, in order to accurately estimate the characteristics of the power storage device at the time of deterioration, the characteristic parameter of the model is set. When identifying, there is a problem that it is necessary to prepare an actually deteriorated power storage device.

An object of the present invention is to provide a simulation method and a simulation apparatus that can accurately estimate the characteristics of an electricity storage device when it has deteriorated without using an actually deteriorated electricity storage device.

A simulation method according to an embodiment of the present invention is a method of performing a simulation using an equivalent circuit model of an electricity storage device, and includes a step of calculating a terminal voltage of the equivalent circuit model based on a current flowing through the equivalent circuit model, The equivalent circuit model includes a plurality of characteristic parameters, and at least one characteristic parameter includes a time function indicating the influence of deterioration of the storage device, and the time function is a time integration of a numerical value indicating the operating state of the storage device. And a coefficient representing the deterioration rate multiplied by the time integration.

The simulation device according to an embodiment of the present invention is a device that performs a simulation using an equivalent circuit model of a power storage device, and calculates a terminal voltage of the equivalent circuit model based on a current flowing through the equivalent circuit model. The equivalent circuit model includes a plurality of characteristic parameters, at least one characteristic parameter includes a time function representing an influence of deterioration of the power storage device, and the time function represents an operation state of the power storage device. A term including a numerical time integration and a coefficient representing a deterioration rate multiplied by the time integration.

In these simulation methods and simulation apparatuses, at least one characteristic parameter includes a time function representing the influence of deterioration of the electricity storage device. By inputting an appropriate time within the usage period (total cycle time) of the electricity storage device (for example, an operation time related to a numerical value representing an operation state) to such a time function, the degree of deterioration of the electricity storage device when the usage time has elapsed Can be reflected in the characteristic parameter. According to the knowledge of the present inventor, the time function includes a term obtained by multiplying the coefficient representing the deterioration rate by the time integral of the numerical value representing the operating state of the power storage device (that is, the usage history of the power storage device). Thus, it is possible to accurately represent the degree of deterioration of the electricity storage device. Therefore, according to the above method and apparatus, it is possible to accurately estimate the input / output characteristics of the electricity storage device when it is deteriorated without using the actually deteriorated electricity storage device. Simulation and the like can be performed with high accuracy. In addition, this electrical storage device is a lead acid battery, for example.

In the above simulation method, the numerical value indicating the operating state of the power storage device may be the current. Accordingly, the input / output characteristics of the deteriorated power storage device can be estimated with higher accuracy in consideration of the influence of deterioration (energization deterioration) based on the total amount of current flowing through the power storage device during the usage period. In this case, the term may further include depth of discharge (DOD) multiplied by time integration. Accordingly, the input / output characteristics of the deteriorated power storage device can be estimated with higher accuracy in consideration of the influence of the deterioration based on the DOD of the power storage device during the usage period.

In the above simulation method, the numerical value representing the operation state of the power storage device may be one or both of a charging rate (State Of Charge; SOC) during dark current discharge and a SOC during rest. Accordingly, the input / output characteristics of the deteriorated power storage device can be estimated with higher accuracy in consideration of the influence of deterioration during dark current discharge or rest during the use period.

In the above simulation method, the coefficient may change according to the temperature of the electricity storage device. Thereby, the deterioration degree which changes according to the temperature of an electrical storage device can be represented accurately.

According to the simulation method and the simulation apparatus of the present invention, it is possible to accurately estimate the characteristics of the electricity storage device when it is deteriorated without using the actually deteriorated electricity storage device.

FIG. 1 is a diagram illustrating a schematic configuration of an apparatus that performs a fuel consumption simulation. FIG. 2 is a diagram illustrating an example of an equivalent circuit model. FIG. 3 is a diagram illustrating a schematic configuration of a simulation apparatus according to an embodiment. FIG. 4 is a diagram illustrating an example of a hardware configuration of the simulation apparatus of FIG. FIG. 5 is a diagram illustrating terminal voltage calculation processing executed by the simulation apparatus. FIG. 6A to FIG. 6C are graphs conceptually showing examples of the waveform of the current flowing through the power storage device. FIG. 7 is a graph showing changes in DC resistance when the current waveforms of FIGS. 6 (a) to 6 (c) are input using a lithium ion battery as an example. FIG. 8 is a graph plotting calculated values of the time integral of the energization deterioration term corresponding to the current waveforms of FIGS. 6 (a) to 6 (c). FIG. 9 is a graph plotting calculated values of the time integration of the self-heating deterioration term corresponding to the current waveforms of FIGS. 6 (a) to 6 (c). FIG. 10 is a graph plotting calculated values of the time integration of the pause degradation term corresponding to the current waveforms of FIGS. 6 (a) to 6 (c). FIG. 11A to FIG. 11C are graphs conceptually showing the state of curve fitting. FIG. 12 is a chart showing numerical examples of coefficients of each characteristic parameter. FIG. 13 compares the maximum value of the fuel consumption error between the case where the characteristic parameter of the embodiment is used for the equivalent circuit model of the power storage device and the case where the characteristic parameter not considering the influence of deterioration is used in the vehicle fuel consumption simulation. It is a graph which shows the result. FIG. 14 is a diagram illustrating a current waveform used for identification of each characteristic parameter. FIG. 15 is a graph illustrating an example of a fuel consumption simulation result according to an embodiment.

Hereinafter, embodiments of a simulation method and a simulation apparatus according to the present invention will be described in detail with reference to the accompanying drawings. In the description of the drawings, the same elements are denoted by the same reference numerals, and redundant description is omitted. In the following description, the current flowing through the power storage device refers to both the charging current input to the power storage device and the discharge current output from the power storage device. When the sign of the current is positive, it represents charging. When the sign is negative, it represents discharge.

The simulation method and simulation apparatus according to an embodiment are used, for example, in a fuel consumption simulation of a vehicle equipped with an electricity storage device. This power storage device is, for example, a main power storage device mounted on a vehicle adopting the μHEV method, or a sub power storage device provided separately from the main power storage device. When the power storage device is a sub power storage device, the power storage device is used to cover the current consumption of a 12V auxiliary device mounted on the vehicle.

[Outline of fuel consumption simulation device]
FIG. 1 is a diagram illustrating a schematic configuration of an apparatus that performs a fuel consumption simulation. As shown in FIG. 1, the fuel consumption simulation device 90 includes an input unit 91, a control unit 92, and an output unit 93 as functional blocks.

The input unit 91 inputs data necessary for fuel consumption simulation. An example of input data is a running pattern of a vehicle. In addition, parameters that determine characteristics of various devices such as an engine mounted on the vehicle, types of charge / discharge control methods for the power storage device, configuration of the power storage device, power consumption of auxiliary devices mounted on the vehicle, and vehicle Data such as the weight of the can be entered.

The control unit 92 performs a fuel consumption simulation using the data input by the input unit 91. Although the specific method of a fuel consumption simulation is not specifically limited, For example, it performs in the following procedures.

First, the control unit 92 determines, for example, the power required for the vehicle to travel for each section from the traveling pattern input by the input unit 91 (hereinafter simply referred to as “required power”) and the consumption current of the auxiliary machine. Is calculated. The sections include a stop section, an acceleration section, a constant speed traveling section, and a deceleration section. The required power is relatively large in the acceleration section and relatively small in the constant speed traveling section. The required power may be 0 in the stop section and the deceleration section. The current consumption of the auxiliary machine varies depending on the type of the auxiliary machine. For example, the consumption current of an auxiliary machine that is continuously used, such as an audio device, is almost constant regardless of the section. On the other hand, the current consumption of auxiliary equipment that is temporarily used, such as an engine ignition device, increases only during use.

Next, the control unit 92 calculates the engine output for each section. The engine output is, for example, 0 when the engine is stopped in a stop section, and a predetermined output in other sections. Of the engine output, the output exceeding the required power is converted into electric power by the alternator and supplied from the alternator toward the auxiliary device and the power storage device. When the power supplied from the alternator exceeds the power consumption of the auxiliary machine, a current flows from the alternator to the power storage device, and the power storage device is charged. When the power supplied from the alternator falls below the power consumption of the auxiliary machine, a current flows from the power storage device to the auxiliary machine, and the power storage device is discharged. Here, the terminal voltage of the electricity storage device depends on the SOC of the electricity storage device, the magnitude of the charge / discharge current, and the like. The terminal voltage of the electricity storage device is estimated using, for example, an equivalent circuit model for calculating the terminal voltage of the electricity storage device. Details of terminal voltage estimation will be described later. From the charge / discharge current of the power storage device and the terminal voltage of the power storage device, the control unit 92 also calculates charge / discharge power of the power storage device for each section.

Thereafter, the control unit 92 calculates an integrated value of the engine output and the charge / discharge power of the power storage device in all sections. The integrated value of the engine output in all sections indicates the amount of energy that the engine will consume when the vehicle travels in the travel pattern input by the input unit 91. The integrated value of the charge / discharge power of the power storage device in all sections indicates the amount of energy that will increase or decrease in the power storage device when the vehicle travels in the travel pattern input by the input unit 91. The total energy amount of the energy amount that the engine will consume and the energy amount that will decrease in the power storage device is the energy amount required for traveling of the vehicle of the traveling pattern input by the input unit 91. Since the travel distance of the vehicle is also known from the travel pattern, the control unit 92 calculates a travelable distance per predetermined energy amount as fuel consumption based on the travel distance and the energy amount required for the travel distance.

The output unit 93 outputs the fuel consumption calculated by the control unit 92. Thereby, the result of the fuel consumption simulation based on the running pattern inputted by the input unit 91 is obtained.

As described above, the terminal voltage of the electricity storage device is estimated in the fuel consumption simulation. Since the accuracy of the fuel consumption simulation is improved by improving the estimation accuracy of the terminal voltage of the electricity storage device, for example, the simulation apparatus (an electricity storage device simulator) according to the embodiment is used for the purpose of improving the accuracy of calculation of the fuel consumption. Also good. In the following description, a single lead storage battery is used as the power storage device. The power storage device is not limited to a lead storage battery, and may be another power storage device or a composite power storage device in which a plurality of power storage devices are combined.

In the present embodiment, the simulation apparatus estimates the terminal voltage of the power storage device using the power storage device model for calculating the terminal voltage of the power storage device. In the present embodiment, an equivalent circuit model of an electricity storage device is used as the electricity storage device model. First, an example of an equivalent circuit model will be described with reference to FIG.

[Equivalent circuit model of electricity storage device]
In the example shown in FIG. 2, the equivalent circuit model 40 includes a circuit 10, a circuit 20, and a constant voltage source 30 that are connected in series between nodes N ₁ and N _{2 having} opposite polarities.

The node N ₁ and the node N ₂ are portions that are electrically connected to an external element of the power storage device, and provide a voltage generated in the equivalent circuit model 40. The voltage generated in the equivalent circuit model 40 is the terminal voltage V (t) of the electricity storage device. Node N ₁ is an anode, providing a current flowing in the electricity storage device I (t). In addition, (t) etc. may be attached | subjected to the code | symbol which shows the physical quantity which changes with time, such as a voltage and an electric current, but the physical quantity shown in this way shall mean the value of the said physical quantity at the time t. The time t is an integer equal to or greater than 0, and indicates the elapsed time from the start time of the estimation of the terminal voltage V (t). Time t = 0 is the estimation start time of the terminal voltage V (t).

The circuit 10 is a DC resistance unit that simulates the DC impedance (DC resistance component) of the power storage device. The circuit 10 includes a resistor 11. The resistor 11 simulates a linear DC resistance component of the electricity storage device. Examples of the linear DC resistance component include electrode resistance. The resistance value of the resistor 11 is a constant. The impedance of the circuit 10 is determined by the resistance value of the resistor 11 of the circuit 10. If the impedance of the circuit 10 is determined, when the current I (t) flows in the equivalent circuit model 40, the current I (t) also flows in the circuit 10, so that the current I (t) and the impedance of the circuit 10 From this, the voltage generated in the circuit 10 can be calculated. A voltage generated in the circuit 10 is referred to as a DC resistance voltage Vdc (t).

The circuit 20 is a polarization model unit that simulates the polarization impedance component of the electricity storage device. The circuit 20 includes a resistor and a capacitor (RC parallel circuit) connected in parallel. In the example shown in FIG. 2, two RC parallel circuits are connected in series. Specifically, a resistor 21 and a capacitor 22 (first RC parallel circuit) connected in parallel and a resistor 23 and a capacitor 24 (second RC parallel circuit) connected in parallel are connected in series. Yes. The resistance value of the resistor 21 and the capacitance value of the capacitor 22 constituting the first RC parallel circuit are constants. The resistor 21 simulates the first polarization resistance component of the electricity storage device, and the capacitor 22 simulates the first polarization capacitance component of the electricity storage device. The resistance value of the resistor 23 and the capacitance value of the capacitor 24 constituting the second RC parallel circuit are constants. The resistor 23 simulates the second polarization resistance component of the electricity storage device, and the capacitor 24 simulates the second polarization capacitance component of the electricity storage device.

In the example shown in FIG. 2, the circuit 20 includes first and second RC parallel circuits, but the circuit 20 includes at least a first RC parallel circuit (resistor 21 and capacitor 22). It only has to be. The circuit 20 may include three or more RC parallel circuits.

The impedance of the circuit 20 is determined by the resistance value of each resistor of the circuit 20 and the capacitance value of each capacitor. If the impedance of the circuit 20 is determined, when the current I (t) flows in the equivalent circuit model 40, the current I (t) also flows in the circuit 20, so that the current I (t) and the impedance of the circuit 20 From this, the voltage generated in the circuit 20 can be calculated. A voltage generated in the circuit 20 is referred to as a polarization voltage Vpol (t).

The polarization voltage Vpol is a total voltage of the voltage generated in the resistor 21 and the capacitor 22 and the voltage generated in the resistor 23 and the capacitor 24. A voltage generated in the resistor 21 and the capacitor 22 is referred to as a first polarization voltage Vp1 (t) and illustrated. A voltage generated in the resistor 23 and the capacitor 24 is referred to as a second polarization voltage Vp2 (t) and illustrated. That is, in the circuit 20, the following relational expression (1) is established.

Here, when the time constant of the first RC parallel circuit composed of the resistor 21 and the capacitor 22 is a time constant τ1, the time constant τ1 is obtained by multiplying the resistance value of the resistor 21 and the capacitance value of the capacitor 22. It is determined as a value. The time constant τ1 is reflected in the time change of the first polarization voltage Vp1 (t) generated in the resistor 21 and the capacitor 22. For example, the time change of the first polarization voltage Vp1 (t) becomes slower as the time constant τ1 is larger. Similarly, when the time constant of the second RC parallel circuit composed of the resistor 23 and the capacitor 24 is a time constant τ2, the time constant τ2 is obtained by multiplying the resistance value of the resistor 23 and the capacitance value of the capacitor 24. It is determined as a value. The time constant τ2 is reflected in the time change of the second polarization voltage Vp2 (t) generated in the resistor 23 and the capacitor 24. The time constants τ1 and τ2 may be set to different values. Since the circuit 20 includes RC parallel circuits having a plurality of different time constants, the time change of the voltage of the polarization voltage Vpol (t) can be expressed more accurately. Each time constant may be set such that time constant τ1 <time constant τ2, for example.

The constant voltage source 30 has a constant direct current (DC) voltage. The voltage of the constant voltage source 30 is an open circuit voltage (OCV: Open Circuit Voltage) of the electricity storage device. The impedance of the constant voltage source 30 is zero. The open circuit voltage of the electricity storage device is referred to as open circuit voltage Vocv (t). The open circuit voltage Vocv (t) is obtained from the SOC of the power storage device, for example. In that case, the open circuit voltage Vocv (t) is a function with the SOC as an argument. The temperature of the electricity storage device may be included in the argument.

The DC resistance voltage Vdc (t) generated in the circuit 10 described above, the polarization voltage Vpol (t) generated in the circuit 20, the open-circuit voltage Vocv (t) of the constant voltage source 30, and the terminal voltage V (t) In the meantime, the following relational expression (2) holds.

Using the above-described equivalent circuit model 40 of the electricity storage device, the simulation apparatus according to the embodiment estimates the terminal voltage V (t) of the electricity storage device.

FIG. 3 is a diagram illustrating a schematic configuration of a simulation apparatus according to an embodiment. The simulation apparatus 1 includes an input unit 2, an SOC calculation unit 3, a parameter setting unit 4, a DC resistance calculation unit 5, a polarization calculation unit 6, an OCV calculation unit 7, and a terminal voltage calculation unit as functional blocks. 8 and so on.

FIG. 4 is a diagram illustrating an example of a hardware configuration of the simulation apparatus 1 of FIG. As shown in FIG. 4, the simulation apparatus 1 physically includes one or more CPUs (Central Processing Units) 101, a RAM (Random Access Memory) 102 as a main storage device, and a ROM (Read Only Memory). 103, a communication module 104 that is a data transmission / reception device, an auxiliary storage device 105 such as a hard disk and a flash memory, an input device 106 that accepts user input such as a keyboard, and an output device 107 such as a display. It is configured. Each function of the simulation apparatus 1 shown in FIG. 3 is obtained by reading one or a plurality of predetermined computer software on hardware such as the CPU 101 and the RAM 102, thereby controlling the communication module 104 and the input device 106 under the control of the CPU 101. And the output device 107 are operated, and data is read and written in the RAM 102 and the auxiliary storage device 105. Although the above description has been given as the hardware configuration of the simulation apparatus 1, the fuel consumption simulation apparatus 90 is a main storage device such as the CPU 101, the RAM 102 and the ROM 103, the communication module 104, the auxiliary storage device 105, the input device 106, and the output device. 107 may be configured as a normal computer system.

Referring to FIG. 3 again, details of each function of the simulation apparatus 1 will be described. The input unit 2 is a part for inputting a specified value (bat_demand) to the power storage device. The specified value includes, for example, the magnitude of charge / discharge current and the magnitude of charge / discharge power required for the power storage device in the fuel consumption calculation by the fuel consumption simulation apparatus 90 described above. The input unit 2 outputs the input specified value to the DC resistance calculation unit 5.

The SOC calculation unit 3 is a part that calculates the SOC of the power storage device. For example, the SOC (t) of the power storage device is calculated from the initial SOC (0) of the power storage device and the subsequent charge / discharge electricity amount of the power storage device. The initial SOC (0) value of the electricity storage device is not particularly limited, and may be set as appropriate. The amount of charge / discharge electricity of the electricity storage device is obtained by integrating the charge / discharge current of the electricity storage device by the charge / discharge time. The SOC (t) of the power storage device is obtained based on the charge / discharge electricity amount of the power storage device and the full charge capacity of the power storage device at time t. In the calculation of the SOC (t) at time t, the current I that has flowed through the equivalent circuit model 40 from time 0 to time t−1 can be used as the current flowing through the power storage device. In this case, the SOC calculation unit 3 calculates SOC (t) by the following equation (3), for example. The SOC calculation unit 3 outputs the calculated SOC (t) to the parameter setting unit 4, the polarization calculation unit 6, and the OCV calculation unit 7, respectively.

The parameter setting unit 4 is a part for setting various characteristic parameter values necessary for estimating the terminal voltage of the power storage device. The characteristic parameters include, for example, the resistance value (DC resistance) of the resistor 11, the resistance value of the resistor 21 (first polarization resistance), the time constant τ1 (first polarization time constant), and the resistance value of the resistor 23 ( Second polarization resistance) and time constant τ2 (second polarization time constant). In addition, the value of each characteristic parameter may be changed according to the SOC of the power storage device.

The parameter setting unit 4 sets the value of each parameter by referring to, for example, a lookup table that describes the value of each parameter. A lookup table is provided for each parameter. The lookup table is a table in which, for example, the SOC is associated with the value of each parameter. In this case, the parameter setting unit 4 acquires the value of each parameter associated with the SOC (t) received from the SOC calculation unit 3 by referring to each lookup table, and uses the acquired value for each parameter. Set to value. Each lookup table may be prepared for each temperature of the power storage device. In that case, the value of each parameter is set in consideration of the temperature of the power storage device. The value of each parameter may be determined in advance. The parameter setting unit 4 outputs the set parameter values to the DC resistance calculation unit 5 and the polarization calculation unit 6.

The DC resistance calculation unit 5 is a part that calculates the DC resistance voltage Vdc (t) generated in the circuit 10 in the equivalent circuit model 40. The direct current resistance calculation unit 5 is also a part that calculates the current I (t) flowing through the equivalent circuit model 40 from the specified value (bat_demand) input by the input unit 2. The polarization calculator 6 is a part that calculates a polarization voltage Vpol (t) generated in the circuit 20 in the equivalent circuit model 40. The OCV calculation unit 7 is a part that calculates the open circuit voltage Vocv (t) of the power storage device. As described above, the open circuit voltage Vocv (t) is obtained from the SOC of the power storage device. For example, a table in which each SOC value is associated with the open circuit voltage Vocv is prepared in advance. The OCV calculation unit 7 calculates the open circuit voltage Vocv (t) from the SOC (t) received from the SOC calculation unit 3 by referring to the table. Note that the above-described table may be prepared for each temperature. In that case, the open-circuit voltage Vocv (t) is calculated in consideration of the temperature of the power storage device.

The terminal voltage calculation part 8 is a part which calculates the terminal voltage V (t) of an electrical storage device. As described above, the DC resistance voltage Vdc (t) calculated by the DC resistance calculator 5, the polarization voltage Vpol (t) calculated by the polarization calculator 6, and the open circuit voltage calculated by the OCV calculator 7. Vocv (t) is sent to the terminal voltage calculator 8. The terminal voltage calculation unit 8 calculates the terminal voltage V (t) based on the DC resistance voltage Vdc (t), the polarization voltage Vpol (t), and the open circuit voltage Vocv (t). Specifically, the terminal voltage calculator 8 adds the DC resistance voltage Vdc (t), the polarization voltage Vpol (t), and the open circuit voltage Vocv (t) as shown in the above equation (2), The total voltage is calculated as the terminal voltage V (t). The terminal voltage calculation unit 8 outputs the calculated terminal voltage V (t) to the outside of the simulation apparatus 1 and the DC resistance calculation unit 5.

Next, a calculation process (simulation method) of the terminal voltage V (t) executed by the simulation apparatus 1 will be described with reference to FIG. FIG. 5 is a flowchart illustrating an example of calculation processing of the terminal voltage V (t) executed by the simulation apparatus 1. The process of the flowchart shown in FIG. 5 is executed, for example, when estimating the terminal voltage of the electricity storage device at a certain time t in the fuel consumption calculation of the fuel consumption simulation device 90.

First, the input unit 2 inputs a specified value (bat_demand) (step S01). For example, the input unit 2 receives a specified value from an external device of the simulation apparatus 1 and inputs the specified value. Then, the input unit 2 outputs the input designated value to the DC resistance calculation unit 5. Then, the SOC calculation unit 3 calculates the SOC of the power storage device (step S02). The SOC calculation unit 3 calculates SOC (t) using, for example, the above-described equation (3). Then, the SOC calculation unit 3 outputs the calculated SOC (t) to the parameter setting unit 4, the polarization calculation unit 6, and the OCV calculation unit 7.

Subsequently, the parameter setting unit 4 sets each characteristic parameter of the equivalent circuit model 40 (step S03). The characteristic parameters set in step S03 are, for example, the resistance value of the resistor 11, the resistance value of the resistor 21, the time constant τ1, the resistance value of the resistor 23, and the time constant τ2. The parameter setting unit 4 acquires, for example, the value of each parameter associated with the SOC (t) received from the SOC calculation unit 3 by referring to a lookup table that describes the value of each characteristic parameter. Set the value to the value of each parameter. Then, the parameter setting unit 4 outputs the set parameters to the DC resistance calculation unit 5 and the polarization calculation unit 6.

Subsequently, the DC resistance calculation unit 5 calculates the current I (t) and the DC resistance voltage Vdc (t) using the resistance value of the resistor 11 provided from the parameter setting unit 4 (step S04). When the charge / discharge mode is a constant current discharge mode (a mode in which a constant current flows regardless of the terminal voltage V (t)), the DC resistance calculation unit 5 is included in the specified value input by the input unit 2 The designated current is set to the current I (t). Then, the DC resistance calculation unit 5 calculates the DC resistance voltage Vdc (t) based on the current I (t). Further, in the DC resistance calculation unit 5, the charge / discharge mode is a constant voltage charge mode (a mode in which the power storage device is charged with a constant output voltage of a voltage source (eg, an alternator) for charging the power storage device). First, the DC resistance voltage Vdc (t) is calculated. Based on the DC resistance voltage Vdc (t), a current I (t) flowing through the equivalent circuit model 40 is calculated.

Subsequently, the polarization calculator 6 calculates the polarization voltage Vpol (t) (step S05). Specifically, the polarization calculation unit 6 uses the resistance value of the resistor 21, the time constant τ 1, the resistance value of the resistor 23, and the time constant τ 2 provided from the parameter setting unit 4 to use the first polarization voltage Vp 1. (T) and the second polarization voltage Vp2 (t) are calculated. Then, the polarization calculator 6 calculates the total value of the first polarization voltage Vp1 (t) and the second polarization voltage Vp2 (t) as the polarization voltage Vpol (t).

Subsequently, the OCV calculation unit 7 calculates the open circuit voltage Vocv (t) (step S06). For example, the OCV calculation unit 7 calculates the open-circuit voltage Vocv (t) from the SOC (t) received from the SOC calculation unit 3 by referring to a table in which each SOC value is associated with the open-circuit voltage Vocv value. To do. Then, the OCV calculation unit 7 outputs the calculated open circuit voltage Vocv (t) to the terminal voltage calculation unit 8.

Subsequently, the terminal voltage calculation unit 8 calculates the terminal voltage V (t) (step S07). Specifically, the terminal voltage calculation unit 8 includes a DC resistance voltage Vdc (t) calculated by the DC resistance calculation unit 5, a polarization voltage Vpol (t) calculated by the polarization calculation unit 6, and an OCV calculation unit 7. Based on the calculated open circuit voltage Vocv (t), the terminal voltage V (t) is calculated. More specifically, the terminal voltage calculator 8 adds the DC resistance voltage Vdc (t), the polarization voltage Vpol (t), and the open circuit voltage Vocv (t) as shown in the above equation (2), The total voltage is calculated as the terminal voltage V (t). Then, the terminal voltage calculation unit 8 outputs the calculated terminal voltage V (t) to the outside of the simulation apparatus 1 and the DC resistance calculation unit 5. As described above, the calculation process of the terminal voltage V (t) at time t is completed.

In addition, the process of step S05 and the process of step S06 may be performed in parallel, and the order of implementation may be reversed.

Here, the characteristic parameters constituting the equivalent circuit model 40 will be described in detail. As described above, the equivalent circuit model 40 includes, for example, the resistance value (DC resistance) of the resistor 11, the resistance value of the resistor 21 (first polarization resistance), the time constant τ1 (first polarization time constant), and resistance. It has a plurality of characteristic parameters such as a resistance value (second polarization resistance) of the capacitor 23 and a time constant τ2 (second polarization time constant). Normally, these characteristic parameters are calculated without taking into account deterioration due to the use of the electricity storage device. In that case, there is a problem that the input / output characteristics of the electricity storage device when it deteriorates cannot be estimated with high accuracy.

Therefore, in the present embodiment, at least one characteristic parameter among the plurality of characteristic parameters is set as in the following formula (4). That is, an arbitrary characteristic parameter A is

As a model. The first term A _{0 on} the right side is an initial value of the characteristic parameter corresponding to when the power storage device is not used, and the second term A _{1 on} the right side is a change in the characteristic parameter after the power storage device has been used for a certain period of time. This change is a time function representing the influence of the deterioration of the electricity storage device, and by inputting an appropriate time within the use period, a corresponding deteriorated characteristic parameter can be obtained after the use time has elapsed. This time is, for example, several hundred hours to thousands of hours.

By expressing the characteristic parameter A as shown in Formula (4), for example, the characteristic parameter A after an arbitrary period of time is obtained by calculation only by identifying the initial characteristic parameter A ₀ using an unused power storage device. be able to.

The second term A ₁ described above may be different depending on the type of the electric storage device. When the electricity storage device is a lead storage battery, the second term A ₁ is defined as, for example, the following formula (5). The coefficients a ₁ , a ₂ , and a ₃ are constants, SOC ₁ (t) is the SOC during dark current discharge, and SOC ₂ (t) is the SOC at rest. These SOCs are a function of time t.

A ₁ shown in Equation (5) includes three terms. The first term is

It is. This term includes a time integral of the absolute value of the current I (t) and a coefficient a ₁ multiplied by the time integral. In this case, the current I (t) is a numerical value representing the operating state of the electricity storage device, and the time integral of the absolute value of the current I (t) represents the total amount of current flowing through the electricity storage device during the usage period, and the coefficient a ₁ represents the rate of deterioration of the electricity storage device relative to the total amount of current. Therefore, the term represented by Equation (6) represents deterioration based on the total amount of current flowing through the power storage device (hereinafter referred to as energization deterioration). In addition, t1 is charging / discharging time. In addition, there are a plurality of characteristic parameters of the electricity storage device, and the values of these characteristic parameters change as the deterioration progresses. However, the change due to energization deterioration may be increased or decreased depending on the characteristic parameters. . Therefore, the sign of the coefficient a ₁ is determined for each characteristic parameter.

The second term is

It is. This term includes the time integral of the absolute value of the current I (t), the coefficient a ₂ multiplied by the time integral, and the depth of discharge (DOD). DOD is a constant, for example. Alternatively, DOD may be a function of time t, in which case the product of the absolute value of I (t) and DOD (t) is time integrated. The coefficient a _2, which represents the rate of deterioration of the electric storage device for DOD. Therefore, the term represented by Formula (7) represents deterioration based on DOD (DOD deterioration) of the electricity storage device. Note that the amount of change in the characteristic parameter due to DOD deterioration may be increased or decreased depending on the characteristic parameter. Therefore, the sign of the coefficient a ₂ is determined for each characteristic parameter.

The third and fourth terms are

It is. The third term includes the time integral of SOC ₁ (t) and a coefficient a ₃ multiplied by this time integral. The fourth term includes a time integral of SOC ₂ (t) and a coefficient a ₃ common to the third term multiplied by the time integral. SOC ₁ (t) and SOC ₂ (t) are numerical values representing the operating state of the electricity storage device. The coefficient a ₃ represents the rate of deterioration of the electricity storage device with respect to each SOC during dark current discharge and rest. The third term and the fourth term represented by Expression (8) represent deterioration (dark current discharge deterioration and rest deterioration) based on each SOC during dark current discharge and rest of the electricity storage device, respectively. The change in the characteristic parameter due to the dark current discharge deterioration and the pause deterioration may be increased or decreased depending on the characteristic parameter. Therefore, the sign of the coefficient a ₃ is determined for each characteristic parameter. The dark current discharge is a weak current supplied to the car navigation system and the timepiece when the vehicle engine is stopped (ie, the alternator is not generating power, except when idling is stopped). The dark current discharge is a period during which such a weak current flows. The term “rest” refers to a state in which no dark current flows, and the term “rest” refers to a period in which the rest state is maintained. Note that t2 is dark current discharge time, and t3 is rest time. In Equation (8), _{one of the} time integral terms of SOC ₁ (t) and SOC ₂ (t) (that is, one of the third term and the fourth term) may be omitted as necessary.

Note that SOC ₁ (t) = 0 and SOC ₂ (t) = 0 during normal charging / discharging. At the time of dark current discharge, I (t) = 0 and SOC ₂ (t) = 0. At the time of rest, I (t) = 0 and SOC ₁ (t) = 0.

Further, when the power storage device is a lithium ion battery, the second term A ₁ of the formula (4) is defined as the following formula (9), for example.

A ₁ shown in Equation (9) includes three terms. The first term is an energization deterioration term. The second term is

It is. This term includes the time integral of the absolute value of the current I (t), the coefficient a ₂ multiplied by the time integral, and the self-heating multiplied by the time integral. That is, the function T of time τ represented by the following formula (11) represents self-heating of the electricity storage device.

The self-heating T is obtained by time integration of the square of the current I (τ) as shown in the equation (11). The coefficient a ₂ represents the speed of deterioration of the electricity storage device with respect to the self-heating T. Therefore, the term represented by Formula (10) represents deterioration based on self-heating of the electricity storage device (hereinafter referred to as self-heating deterioration).

The third term is

It is. This term includes the time integration of SOC ₂ (t) at rest and the coefficient a ₃ multiplied by the time integration. These meanings are the same as the fourth term in the case of the lead storage battery described above. That is, this term is a pause degradation term.

In the above example, the dark current discharge deterioration term exists in Equation (8), but the same dark current discharge deterioration term does not exist in Equation (12). The reason is as follows. For example, when a single electricity storage device is used, there is always a period during which dark current flows even when the vehicle engine is stopped. Examples of such a single electricity storage device include a lead storage battery. On the other hand, for example, when the main power storage device and the sub power storage device are used as in the μHEV system, a situation is considered in which dark current is supplied only from the main power storage device and no dark current is supplied from the sub power storage device. In such a situation, no dark current state occurs in the sub power storage device. Lithium ion batteries are often used as such sub power storage devices. Therefore, the dark current discharge deterioration term is omitted in Equation (12).

Further, the electric storage device be a nickel-zinc battery, the second term A ₁ Equation (4) is defined as for example, the following equation (13).

A ₁ shown in Equation (13) includes three terms. The first term is an energization deterioration term. The second term is a DOD degradation term. The third term is a pause deterioration term. The nickel zinc battery is also often used as a sub power storage device, similar to the lithium ion battery described above. Therefore, the dark current discharge deterioration term is omitted in Equation (13).

Here, a method of calculating the coefficients a _1, a _2, a ₃ described above. In order to calculate the _three coefficients a ₁ , a ₂ , and a ₃ , three different model expressions are required. Therefore, three currents I (t) having different time waveforms from each other are input to the characteristic parameter formulas, three model formulas are established, and the coefficients a ₁ , a ₂ , and a ₃ are obtained based on them. FIGS. 6A to 6C are graphs conceptually showing examples of such a waveform of the current I (t). In these figures, the vertical axis represents current I (t), and the horizontal axis represents time. These current waveforms include a constant voltage charging period Ta, a constant current discharging period Tb, and a rest period Tc. FIG. 6A shows a case where the current in the constant voltage charging period Ta is relatively large, and the constant current discharging period Tb is lengthened by the amount of the charging current being large. FIG. 6B shows a case where the current in the constant voltage charging period Ta is relatively small, and the constant current discharging period Tb is shortened by the amount of the charging current being small. FIG. 6C shows a case where the suspension period Tc is longer than those in FIGS. 6A and 6B.

FIG. 7 shows a direct current resistance (resistance value of the resistor 11 in FIG. 2) among a plurality of characteristic parameters when the current waveforms in FIGS. 6 (a) to 6 (c) are input using a lithium ion battery as an example. It is a graph which shows a change. The vertical axis represents DC resistance (unit: mΩ), and the horizontal axis represents total cycle time (usage time, unit: time). Further, in the figure, a rhombus plot P1 shows a case where the current waveform shown in FIG. 6A is inputted, and a square plot P2 shows a case where the current waveform shown in FIG. 6B is inputted. A triangular plot P3 shows a case where the current waveform shown in FIG. As shown in FIG. 7, it can be seen that when the waveform of the input current I (t) is different, the degradation of the DC resistance (A _{1 in} Formula (4)) changes accordingly.

FIG. 8 is a graph plotting calculated values of the time integral of the energization deterioration term corresponding to the current waveforms of FIGS. 6 (a) to 6 (c). FIG. 9 is a graph plotting calculated values of the time integration of the self-heating deterioration term corresponding to the current waveforms of FIGS. 6 (a) to 6 (c). FIG. 10 is a graph plotting calculated values of the time integration of the pause degradation term corresponding to the current waveforms of FIGS. 6 (a) to 6 (c). 8 to 10, the vertical axis represents the time integral value, and the horizontal axis represents the total cycle time (unit: time). In these figures, the rhombus plot P4 shows the values when the current waveform shown in FIG. 6A is input, and the square plot P5 inputs the current waveform shown in FIG. 6B. The triangular plot P6 shows the values when the current waveform shown in FIG. 6C is input.

As shown in FIGS. 8 to 10, the time integral values in the energization degradation term, the self-heating degradation term, and the pause degradation term are calculated based on the current waveforms in FIGS. 6 (a) to 6 (c). Is done. Therefore, _three independent functions including the coefficients a ₁ , a ₂ , and a ₃ as variables can be created, and the coefficients a ₁ , a ₂ , and a ₃ are obtained by performing optimization by curve fitting with experimental values. be able to. FIG. 11A to FIG. 11C are graphs conceptually showing the state of curve fitting. FIGS. 11 (a) to 11 (c) show how the functions of a ₁ , a ₂ , and a ₃ obtained from the current waveforms shown in FIGS. 6 (a) to 6 (c) are fitted with experimental values, respectively. Is shown. Plots P7 to P9 in the figure are experimental values, and curves R1 to R3 are estimated values from functions.

FIG. 12 is a chart showing numerical examples of the coefficients a ₁ , a ₂ , and a ₃ of each characteristic parameter obtained by the method described above. As shown in FIG. 12, the coefficients a ₁ , a ₂ , and a ₃ are suitably obtained by the method described above. FIG. 12 also shows the fitting error (%). The error between the first polarization resistance and the second polarization resistance is relatively large. This is considered to be caused by the fact that the test period is short and the progress of deterioration is small.

The effects obtained by the simulation method and the simulation apparatus 1 according to the present embodiment described above will be described. In the simulation method and the simulation apparatus 1 according to the present embodiment, as shown in Formula (4), at least one characteristic parameter A includes a time function A ₁ that represents the influence of deterioration of the power storage device. By inputting the usage time (total cycle time) of the electricity storage device to such a time function A ₁ , the deterioration degree of the electricity storage device when the usage time has elapsed can be reflected in the characteristic parameter A.

The present inventor has found that the time function A _{1 includes} a coefficient (for example, a ₁ , a ₂ , a _3, etc.) indicating the deterioration rate, and a numerical value (for example, current I (t), SOC indicating the operating state of the power storage device. ₁ (t), SOC ₂ (t), etc.) by including a term (for example, formulas (6) to (8), (10) to (12), etc.)) multiplied by the time integral of the storage device usage history. The present inventors have found that the deterioration degree of the electricity storage device can be expressed with high accuracy. Therefore, according to the present embodiment, it is possible to accurately estimate the input / output characteristics of the electricity storage device when it has deteriorated without using an actually deteriorated electricity storage device, such as a fuel consumption simulation using the deteriorated electricity storage device. Can be performed with high accuracy.

FIG. 13 shows the case where the characteristic parameter of the present embodiment is used for the equivalent circuit model of the lithium ion battery in the vehicle fuel consumption simulation (graph G11), and the characteristic parameter that does not consider the influence of deterioration (that is, the right side of Expression (4)). it is a graph showing a result of comparing the maximum value of the fuel consumption error in the case with (graph G12) using second term a ₁ that there is no). In FIG. 13, the vertical axis represents the maximum value (unit:%) of the fuel efficiency error, and the horizontal axis represents the test period (unit: day). Note that the current waveform shown in FIG. 14 was used as the current I (t) used to identify the initial value of the characteristic parameter (that is, the first term A ₀ on the right side of Equation (4)). This current waveform repeats the first to third periods TA to TC including the constant voltage charging period T1, the constant current discharging period T2 after the constant voltage charging period T1, and the cranking period T3 after the constant current discharging period T2. Contains. Note that the voltage value of the constant voltage charging period T1 in the first to third periods TA to TC is constant at 14 (V), and the time of the constant current discharging period T2 and the cranking period T3 is 59 seconds, 1 Constant in seconds. The current values in the first to third periods TA to TC are as follows.
<First period TA>
Constant voltage charging period T1: 100 (A)
Constant current discharge period T2: -20 (A)
Cranking period T3: -300 (A)
<Second period TB>
Constant voltage charging period T1: 200 (A)
Constant current discharge period T2: -45 (A)
Cranking period T3: -300 (A)
<Third period TC>
Constant voltage charging period T1: 50 (A)
Constant current discharge period T2: -10 (A)
Cranking period T3: -300 (A)

Also, the maximum value of the fuel efficiency error is the maximum value of the difference between the result of the fuel efficiency simulation using the equivalent circuit model including the characteristic parameter and the actually measured fuel efficiency. Here, there are innumerable combinations of characteristic parameter values in which the voltage error (difference between the measured value of the terminal voltage of the power storage device and the estimated value of the terminal voltage by the model) at the time of extracting the characteristic parameter of the power storage device is the same value Even with the same voltage error value, the fuel consumption calculation result varies depending on the combination of the characteristic parameter values. The above-mentioned “maximum value” refers to the value of the maximum fuel efficiency error among the calculated fuel efficiency errors by preparing a plurality of combinations of characteristic parameter values that have the same voltage error, calculating the fuel efficiency error for each combination.

As shown in FIG. 13, the fuel efficiency error increases as the test period becomes longer. However, when the influence of deterioration is not taken into consideration, the maximum value of the fuel efficiency error exceeds 0.3% after the test period exceeds 60 days. ing. On the other hand, in the present embodiment in which the influence due to deterioration is taken into consideration, the maximum value of the fuel consumption error is 0.05% or less even when the test period exceeds 60 days. Thus, according to the method and apparatus of this embodiment, the longer the test period, the more accurately the deterioration state of the electricity storage device can be reflected in the fuel consumption simulation result.

The fuel consumption simulation result according to the present embodiment can be applied to, for example, selection of the power storage device capacity employed in the vehicle. In general, the fuel efficiency of a vehicle becomes better as the capacity of an electricity storage device mounted increases. On the other hand, as the years from the start of use, the performance of the electricity storage device deteriorates, and the fuel consumption of the vehicle decreases. Conventionally, since it was unclear how much performance deteriorated due to deterioration of the electricity storage device in the simulation, an electricity storage device capacity having a sufficient margin than the electricity storage device capacity selected from the fuel consumption simulation result was selected. In such a selection method, the storage device capacity tends to increase more than necessary, which may hinder vehicle cost reduction.

In order to solve such a problem, the simulation method and the simulation apparatus 1 according to the present embodiment can perform a simulation according to the degree of deterioration of the power storage device, and therefore accurately perform a fuel consumption simulation in consideration of the years since the start of use. Can do. Therefore, based on the estimated fuel consumption after a predetermined number of years, it is possible to accurately select the power storage device capacity that can satisfy the predetermined fuel consumption condition.

FIG. 15 is a graph showing an example of a fuel consumption simulation result according to the present embodiment. In FIG. 15, the vertical axis represents fuel consumption (unit: km / l), and the horizontal axis represents the number of years of use (unit: year). In addition, a rhombus plot P10, a square plot P11, and a triangle plot P12 in the figure indicate cases where the initial storage device capacities are 3 Ah, 5 Ah, and 7 Ah, respectively. As shown in FIG. 15, the fuel consumption of the vehicle is better as the storage device capacity is larger. However, the fuel consumption of the vehicle is lower as the service life is longer. Therefore, for example, when it is desired to set the fuel consumption at the time of five years of use to 30 (km / l) or more, according to this graph, it is understood that the initial capacity of the power storage device mounted on the vehicle should be 5 Ah. As described above, according to the present embodiment, it is possible to accurately select the power storage device capacity that can satisfy the predetermined fuel consumption condition based on the estimated fuel consumption after a predetermined number of years.

Note that the selection of the storage device capacity is not limited to the case where the estimated fuel consumption is used as a reference. According to the present embodiment, it is possible to accurately select a power storage device capacity that can satisfy a predetermined condition based on the estimated characteristics of the power storage device after a predetermined number of years.

Further, as in the present embodiment, the numerical value representing the operating state of the power storage device and time-integrated may be the current I (t) flowing through the equivalent circuit model (for example, Formula (6), Formula (7), (See Equation (11)). Accordingly, the input / output characteristics of the deteriorated power storage device can be estimated with higher accuracy in consideration of the influence of deterioration (energization deterioration) based on the total amount of current flowing through the power storage device during the usage period. In this case, the term obtained by multiplying the coefficient and the time integral may further include a DOD multiplied by the time integral (see, for example, Equation (7)). Accordingly, the input / output characteristics of the deteriorated power storage device can be estimated with higher accuracy in consideration of the influence of the deterioration based on the DOD of the power storage device during the usage period.

Further, as in the present embodiment, the numerical values that represent the operating state of the power storage device and are integrated over time are the SOC during dark current discharge (that is, SOC ₁ (t) in Expression (8)) and the SOC during rest (that is, One or both of Formula (8) and SOC ₂ (t) in Formula (12) may be used (see Formula (8) and Formula (12), for example). Accordingly, the input / output characteristics of the deteriorated power storage device can be estimated with higher accuracy in consideration of the influence of deterioration during dark current discharge or rest.

(Modification)
In the above embodiment, it does not describe the relationship between the coefficient a _1, a _2, a ₃ and a temperature of the electric storage device. That is, the coefficients a ₁ , a ₂ , and a ₃ may be constant regardless of the temperature of the power storage device. However, in many cases, the preferable values of the coefficients a ₁ , a ₂ , and a ₃ depend on the temperature of the electricity storage device. Accordingly, the coefficients a ₁ , a ₂ , and a ₃ may change according to the temperature of the electricity storage device. Thereby, the deterioration degree which changes according to the temperature of an electrical storage device can be represented accurately.

Specifically, the coefficients a ₁ , a ₂ , and a ₃ may be functions a ₁ (TH), a ₂ (TH), and a ₃ (TH) of the temperature TH, or differ for each of a plurality of temperatures. The coefficients a ₁ , a ₂ , and a ₃ may be set. Therefore, when performing optimization by curve fitting with experimental values, it is preferable to acquire experimental values while changing the temperature of the power storage device.

The simulation method and the simulation apparatus according to the present invention are not limited to the above-described embodiments and modification examples, and various other modifications are possible. For example, in the above-described embodiment, the current I (t) flowing through the power storage device, the SOC ₁ (t) during dark current discharge, and the SOC ₂ (when resting) are represented as numerical values that represent the operating state of the power storage device and are integrated over time. Although t) has been illustrated, as the numerical value in the present invention, various numerical values other than these can be adopted as long as they represent the operating state of the electric storage device. For example, the terminal voltage of the electricity storage device may be used as a numerical value instead of SOC ₁ (t) and SOC ₂ (t).

The present invention can be used as a simulation method and a simulation apparatus that can accurately estimate the characteristics of a deteriorated power storage device.

DESCRIPTION OF SYMBOLS 1 ... Simulation apparatus, 2 ... Input part, 3 ... SOC calculation part, 4 ... Parameter setting part, 5 ... DC resistance calculation part, 6 ... Polarization calculation part, 7 ... OCV calculation part, 8 ... Terminal voltage calculation part, 10, DESCRIPTION OF SYMBOLS 20 ... Circuit, 11, 21, 23 ... Resistor, 22, 24 ... Capacitor, 30 ... Constant voltage source, 40 ... Equivalent circuit model, 90 ... Fuel consumption simulation apparatus, 91 ... Input part, 92 ... Control part, 93 ... Output Part, N ₁ , N ₂ ... Node.

Claims

A method of performing simulation using an equivalent circuit model of an electricity storage device,
Calculating a terminal voltage of the equivalent circuit model based on a current flowing through the equivalent circuit model;
The equivalent circuit model includes a plurality of characteristic parameters;
At least one of the characteristic parameters includes a time function representing an influence of deterioration of the electricity storage device;
The simulation method has a term in which the time function includes a time integration of a numerical value representing an operating state of the power storage device and a coefficient representing a deterioration rate multiplied by the time integration.
The simulation method according to claim 1, wherein a numerical value representing an operating state of the power storage device is the current.
3. The simulation method according to claim 2, wherein the term further includes a discharge depth multiplied by the time integration.
The simulation method according to claim 1, wherein the numerical value representing the operating state of the electricity storage device is one or both of a charging rate during dark current discharge and a charging rate during rest.
The simulation method according to any one of claims 1 to 4, wherein the coefficient changes according to a temperature of the power storage device.
6. The simulation method according to claim 1, wherein the power storage device is a lead storage battery.
An apparatus that performs a simulation using an equivalent circuit model of an electricity storage device,
A voltage calculator that calculates a terminal voltage of the equivalent circuit model based on a current flowing through the equivalent circuit model;
The equivalent circuit model includes a plurality of characteristic parameters;
At least one of the characteristic parameters includes a time function representing an influence of deterioration of the electricity storage device;
The simulation apparatus, wherein the time function includes a term including a time integral of a numerical value representing an operating state of the power storage device and a coefficient representing a deterioration rate multiplied by the time integral.