This application claims priority to Japanese Patent Application No. 2014-223124 filed on Oct. 31, 2014, the entire disclosure of which is incorporated herein by reference.
The disclosure relates to a parameter estimation device for a battery capable of sequentially estimating parameters of an equivalent circuit model of the battery by Kalman filtering.
A conventional battery internal state/parameter estimation device described in Patent Literature (PTL) 1 is known as an example. This conventional battery parameter estimation device detects the charge and discharge current and terminal voltage of a battery and, with these values as input, estimates (calculates) the parameters of the battery and the internal state quantity and open circuit voltage value of the battery by Kalman filtering using an equivalent circuit model of the battery including a resistance.
However, in the aforementioned equivalent circuit model of the battery, the temperature of the battery, which is a factor significantly affecting the internal resistance of the battery, is not taken into account. This causes a large estimation error of the internal resistance of the battery. In detail, in the case where the last estimation result in the previous estimation is used as an initial value in the present estimation upon starting battery state estimation, there is a possibility that the temperature of the battery has changed from when the battery state was estimated last in the previous estimation. In this case, estimation is started with such an initial value that is far from a value to be estimated in the present estimation, and it takes time for the estimation result to correspond to the present temperature (i.e. converge). Thus, not using information of the temperature of the battery leads to poor SOC estimation accuracy.
It could be helpful to provide a parameter estimation device for a battery capable of reducing an error in estimate of an internal resistance of the battery caused by a temperature difference and estimating parameters more quickly and accurately.
A parameter estimation device for a battery according to a first aspect is a parameter estimation device for a battery for sequentially estimating parameters including a resistance in an equivalent circuit model of the battery based on a temperature of the battery and at least one of a voltage of the battery and a current of the battery, wherein as a resistance value of the resistance in the equivalent circuit model of the battery, a resistance value RT0 at a predetermined temperature T0 is estimated, and a resistance value at a present temperature is calculated based on the resistance value at the predetermined temperature and the present temperature.
A parameter estimation device for a battery according to a second aspect is the parameter estimation device for a battery wherein the resistance value at the present temperature is calculated using the following expression that includes the resistance value at the predetermined temperature and a temperature-dependent coefficient:
where T is the present temperature, R(T) is the resistance value at the present temperature T, T0 is the predetermined temperature, RT0 is the resistance value at the predetermined temperature T0, and aR is the temperature-dependent coefficient.
A parameter estimation device for a battery according to a third aspect is the parameter estimation device for a battery wherein the temperature-dependent coefficient aR is a constant obtained beforehand.
A parameter estimation device for a battery according to a fourth aspect is the parameter estimation device for a battery wherein the temperature-dependent coefficient aR is determined based on a table obtained beforehand and indicating a relationship between the temperature-dependent coefficient aR and the temperature T.
A parameter estimation device for a battery according to a fifth aspect is the parameter estimation device for a battery wherein the temperature-dependent coefficient aR and the resistance value RT0 at the predetermined temperature T0 are obtained by simultaneous estimation.
The parameter estimation device for a battery according to the first aspect can reduce an error in estimate of an internal resistance caused by a temperature difference, and estimate parameters more quickly and accurately.
The parameter estimation device for a battery according to the second aspect can reduce an error in estimate of an internal resistance caused by a temperature difference, and estimate parameters more quickly and accurately.
The parameter estimation device for a battery according to the third aspect can improve estimation accuracy using temperature information, while limiting the number of parameters to be estimated to that of a conventional model.
The parameter estimation device for a battery according to the fourth aspect can estimate parameters more quickly and accurately using the temperature-dependent coefficient aR corresponding to the temperature, in the case where the rate-determining process changes at some temperature.
The parameter estimation device for a battery according to the fifth aspect can estimate parameters more quickly and accurately even in the case where the temperature-dependent coefficient changes due to battery degradation or the like.
In the accompanying drawings:
The following describes one of the disclosed embodiments in detail, with reference to drawings.
A parameter estimation device for a battery according to this embodiment is used in a vehicle such as an electric vehicle or a hybrid electric vehicle. The vehicle includes an electric motor for driving the vehicle, a battery, controllers for these components, etc., and the power supply (discharge) to the electric motor, the regeneration of braking energy from the electric motor during braking, and the power recovery (charge) from a ground charging facility to the battery are performed. Such charge and discharge current entering and leaving the battery changes the internal state of the battery. By monitoring the internal state while estimating the internal state using the parameter estimation device for a battery, necessary information such as remaining battery level is collected.
As illustrated in
The battery 1 is, for example, a rechargeable battery (secondary battery). Although this embodiment describes the case where the battery 1 is a lithium ion battery, other types of battery may be used.
The terminal voltage detection unit 2 is, for example, a voltage sensor, and detects the terminal voltage value v of the battery 1. The terminal voltage detection unit 2 supplies the detected terminal voltage value v to the estimation unit 4.
The charge and discharge current detection unit 3 is, for example, a current sensor, and detects the charge and discharge current value i of the battery 1. The charge and discharge current detection unit 3 supplies the detected charge and discharge current value i to the estimation unit 4.
The battery temperature detection unit 8 is, for example, a temperature sensor, and detects the temperature T of the battery 1. The battery temperature detection unit 8 supplies the detected temperature T to the estimation unit 4.
The estimation unit 4 includes a battery equivalent circuit model 41 of the battery 1, and a Kalman filter 42. The estimation unit 4 is capable of estimating (calculating) the parameter values of the battery equivalent circuit model 41, the open circuit voltage OCV of the battery 1, and the internal state quantity of the battery 1 using the Kalman filter 42. In this embodiment, the estimation unit 4 simultaneously estimates the parameter values and the internal state quantity based on the terminal voltage v from the terminal voltage detection unit 2 and the charge and discharge current i from the charge and discharge current detection unit 3, and calculates the open circuit voltage OCV based on the estimated parameter values. The estimation and calculation process performed by the estimation unit 4 will be described in detail later. The estimation unit 4 supplies the calculated open circuit voltage OCV to the state of charge calculation unit 6 and the state of health calculation unit 7.
The battery equivalent circuit model 41 is realized by, for example, a Foster-type RC ladder circuit in which parallel circuits of a resistor and a capacitor are connected and that is represented by approximation by an infinite series sum, or a Cowell-type RC ladder circuit in which series-connected resistors are grounded with a capacitor and that is represented by approximation by a continued fraction expansion. Such resistor and capacitor are included in the parameters of the battery equivalent circuit model 41.
The Kalman filter 42 designs a model (the battery equivalent circuit model 41 in this embodiment) of a target system, supplies the same input signal to the model and the actual system, and compares their respective outputs. If there is an error between the outputs, the Kalman filter 42 multiplies the error by the Kalman gain and feeds it back to the model, thus correcting the model so as to minimize the error. The Kalman filter 42 repeatedly performs this process to estimate the parameters of the model.
The charge quantity calculation unit 5 receives the charge and discharge current value i of the battery 1 detected by the charge and discharge current detection unit 3, and sequentially integrates the received value to calculate the quantity of charge entering and leaving the battery 1. The charge quantity calculation unit 5 subtracts the entering and leaving charge quantity from the remaining charge quantity stored before the sequentially integration, to calculate the present charge quantity Q of the battery 1. The charge quantity Q is output to the state of health calculation unit 7.
The state of charge calculation unit 6 stores, for example as a characteristic table, relational data obtained by determining the relationship between the open circuit voltage value and the state of charge by experiment or the like beforehand, given that their relationship is unlikely to be affected by temperature, degradation of the battery 1, etc. Based on this characteristic table, the state of charge calculation unit 6 estimates the present state of charge SOC from the open circuit voltage estimate obtained by the estimation unit 4. The state of charge SOC is used for battery management of the battery 1.
The state of health calculation unit 7 has a characteristic table indicating the relationship between the charge quantity Q and the open circuit voltage OCV for each range of state of health SOH divided by a predetermined width. This characteristic table is, for example, disclosed in JP 2012-57956 A by the applicant of this application. The state of health calculation unit 7 receives the open circuit voltage OCV estimated by the estimation unit 4 and the charge quantity Q calculated by the charge quantity calculation unit 5, calculates which range of state of health SOH in the characteristic table the received values belong to, and outputs the state of health SOH that applies.
The equivalent circuit model 41 of the battery 1 is described below. Typically, the electrode reaction of a battery involves a charge transfer process in the interface between an electrolytic solution and an active material and an ion diffusion process in the electrolytic solution or the active material. In a physical process (non-Faradaic process) battery such as a lithium ion battery, that is, a battery in which the diffusion phenomenon is dominant, the effect of Warburg impedance which is the impedance resulting from the diffusion process is dominant.
First, suppose the model of the battery is an open circuit that has the open circuit voltage OCV and in which internal resistance R0 and Warburg impedance Zw are connected in series, as illustrated in
The open circuit voltage OCV is the nonlinear function of the state of charge SOC, as illustrated in
The transfer function of the Warburg impedance Zw is represented by Expression (2).
where s is a Laplace operator, and the diffusion resistance Rd is a low-frequency limit (ω→0) of Zw(s). The diffusion time constant τd denotes the rate of the diffusion reaction. Using the diffusion resistance Rd and the diffusion time constant τd, diffusion capacitance Cd is defined by Expression (3).
Due to the presence of the square root of the Laplace operator s in Expression (2), it is difficult to directly convert the Warburg impedance Zw into the time domain. Hence, consider approximating the Warburg impedance Zw. For example, the Warburg impedance Zw can be approximated by an infinite series sum or a continued fraction expansion.
Approximation by an infinite series sum is described below. The Warburg impedance Zw can be represented as an infinite series sum as shown by Expression (4).
where
The aforementioned approximate expression is represented by a circuit diagram of an nth-order Foster-type circuit in which n parallel circuits of a resistor and a capacitor are connected in series (see
The battery equivalent circuit model 41 in the case of approximation by a tertiary Foster-type circuit is described below (see
[Math. 7]
x=[SOC v
3
v
2
v
1]T (7)
u=i (8)
y=v (9)
where v1 to v3 are each a voltage drop in the capacitor corresponding to the subscript, i is a current flowing through the whole circuit, and v is a voltage drop of the whole circuit. The superscript T of the matrix denotes its transposed matrix.
Then, the state space is
Here, Expression (10) is a state equation, and Expression (11) is an output equation.
There is a case where the resistance components (direct resistance R0 and diffusion resistance Rd) in the model are constant regardless of temperature. In this embodiment, the resistance components (direct resistance R0 and diffusion resistance Rd) in the model are treated as being temperature-dependent based on Arrhenius' equation (a formula for predicting the rate of a chemical reaction at a temperature).
An expression indicating the temperature dependence of a resistance based on Arrhenius' equation is derived here. Battery characteristics are typically known to change depending on battery temperature.
In Expression (15), A is a frequency factor, Ea is activation energy, and T is the absolute temperature of the battery.
By substituting the frequency factor A by a resistance value R∞ at infinite temperature and substituting the ratio of the activation energy and the gas constant by a temperature-dependent coefficient aR, Expression (15) is rewritten as Expression (16).
Here, the resistance value R∞ at infinite temperature is an ideological reference value. As a reference value that can be easily obtained by experiment, a resistance value RT0 at a practical temperature T0[K] is defined, to substitute for R∞. Suppose T=T0 in Expression (16). Then, Expression (17) is derived.
Modifying Expression (17) yields Expression (18).
Substituting Expression (18) into Expression (16) yields Expression (19).
Using Expression (19), the direct resistance R0 and the diffusion resistance Rd are respectively represented by Expressions (20) and (21).
where R0T0 and RdT0 are respectively the resistance values of the resistors R0 and Rd at the temperature T0 [K], and aR0 and aR0 are respectively the temperature-dependent coefficients of the resistors R0 and Rd. In this model, R0To and RdT0 are estimated. Since the temperature T of the battery is measured by the temperature measurement unit 8, R0 and Rd can be calculated respectively from the estimates of R0T0 and RdT0. In this embodiment, aR0 and aR0 are constants.
As described above, the parameter estimation device for a battery according to this embodiment is a parameter estimation device for a battery for sequentially estimating parameters including a resistance in an equivalent circuit model of the battery based on a temperature of the battery and at least one of a voltage of the battery and a current of the battery, wherein as a resistance value of the resistance in the equivalent circuit model of the battery, a resistance value RT0 at a predetermined temperature T0 is estimated, and a resistance value R(T) at a present temperature T is calculated using Expression (19) that includes the resistance value RT0 at the predetermined temperature T0 and a temperature-dependent coefficient aR. With the model in this embodiment, temperature information can be used in battery parameter estimation, and an error in estimate of an internal resistance caused by a temperature difference can be reduced. In detail, estimating a resistance value at a predetermined temperature contributes to better followability for a temperature difference when estimation is performed, because the resistance value at the predetermined temperature hardly changes. The parameters can thus be estimated more quickly and accurately.
The following describes examples in the case of estimating the parameters of a battery using a model having the temperature dependence represented by Expression (19). In the case of taking the temperature dependence into account, the influence of the error in measured temperature needs to be considered. The influence of which part of the battery is subjected to temperature measurement, the influence of how much measurement error the temperature sensor has, etc. need to be considered, too.
In Example 1, the temperature-dependent coefficient aR is obtained beforehand using continuous-time system identification or the like, and only the resistance value RT0 corresponding to T0=300 K is calculated by simultaneous estimation during actual driving.
Thus, the parameter estimation device for a battery according to Example 1 has a feature that the temperature-dependent coefficient aR is a constant obtained beforehand. With the model of Example 1, estimation accuracy can be improved using temperature information, while limiting the number of parameters to be estimated to that of a conventional model.
There are cases where the temperature-dependent coefficient aR is not always a constant value but differs depending on temperature. In Example 2, a table indicating the relationship between the temperature-dependent coefficient aR and the temperature T is obtained beforehand, and the resistance value RT0 corresponding to T0=300 K is calculated by simultaneous estimation while changing the temperature-dependent coefficient aR to be applied to the model with a change in temperature. The reason that the temperature-dependent coefficient aR differs depending on temperature is because the battery characteristics are affected by the rate-determining process. The rate-determining process is a process with the lowest reaction rate in a chemical reaction system made up of a plurality of processes. This is the state where the rate-determining process is a bottleneck and determines the rate of the overall reaction.
Thus, the parameter estimation device for a battery according to Example 2 has a feature that the temperature-dependent coefficient aR is determined based on the table obtained beforehand and indicating the relationship between the temperature-dependent coefficient aR and the temperature T. With the model of Example 2, the parameters can be estimated more quickly and accurately using the temperature-dependent coefficient aR corresponding to the temperature, in the case where the rate-determining process changes at a temperature.
There are cases where the temperature-dependent coefficient aR not only differs depending on temperature, but changes even at the same temperature due to a temporal change of the battery. In Example 3, the temperature-dependent coefficient aR is not a constant and its relationship with the temperature is not obtained beforehand, and both the temperature-dependent coefficient aR and the resistance value RT0 corresponding to T0=300 K are calculated by simultaneous estimation. It should be noted that, in this example, the temperature-dependent coefficient is also subjected to estimation, and so the number of parameters to be estimated increases and the estimation tends to be more difficult.
Thus, the parameter estimation device for a battery according to Example 3 has a feature that the temperature-dependent coefficient aR and the resistance value RT0 at the predetermined temperature T0 are calculated by simultaneous estimation. With the model of Example 3, the parameters can be estimated more quickly and accurately even in the case where the temperature-dependent coefficient changes due to battery degradation or the like.
Although the disclosed device has been described by way of the drawings and examples, various changes or modifications may be easily made by those of ordinary skill in the art based on this disclosure. Such various changes or modifications are therefore included in the scope of this disclosure. For example, the functions included in the structural units, steps, etc. may be rearranged without logical inconsistency, and a plurality of structural units, steps, etc. may be combined into one structural unit, step, etc. and a structural unit, step, etc. may be divided into a plurality of structural units, steps, etc.
For example, although the foregoing embodiment describes the case where the Warburg impedance Zw is approximated by an infinite series expansion or a continued fraction expansion, the Warburg impedance Zw may be approximated by any method. The Warburg impedance Zw may be approximated, for example, using an infinite product expansion.
Number | Date | Country | Kind |
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2014-223124 | Oct 2014 | JP | national |
Filing Document | Filing Date | Country | Kind |
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PCT/JP2015/005365 | 10/26/2015 | WO | 00 |