Patent Grant
10209319
This application is a National Stage of International Application No. PCT/JP2013/000581 filed Feb. 1, 2013, the contents of all of which is incorporated herein by reference in its entirety.
The present invention relates to a battery system in which the deterioration state and the charge state of a secondary battery are estimated.
Patent Document 1 has described that an evaluation value is calculated in accordance with a change of imbalance in concentration of lithium ions in an electrolytic solution, and the output from the secondary battery is controlled on the basis of the evaluation value. The evaluation value is a value for evaluating the deterioration of the secondary battery.
When the secondary battery is discharged, the lithium ions in the electrolytic solution move from a negative electrode toward a positive electrode to produce the imbalance in the concentration of the lithium ions in the electrolytic solution. Assuming that the imbalance in the lithium ion concentration is a factor in deterioration of the secondary battery, the evaluation value is calculated in accordance with the imbalance in the lithium ion concentration between electrodes in Patent Document 1.
[Patent Document 1] Japanese Patent Laid-Open No. 2009-123435
When the secondary battery is charged and discharged, the imbalance in the lithium ion concentration is not produced only between the electrodes. Specifically, an imbalance in lithium ion concentration may occur in a plane in which the positive electrode and the negative electrode are opposite to each other, and the concentration of lithium ions present between the positive electrode and the negative electrode may be changed. The imbalance in the lithium ion concentration in the plane of the electrodes and the change in the lithium ion concentration between the electrodes also affect the deterioration of the secondary battery.
A battery system according to an aspect of the present invention includes a chargeable and dischargeable secondary battery, and a controller configured to estimate the deterioration state or the charge state of the secondary battery. When the controller estimates the deterioration state or the charge state, the controller uses an average ion concentration between a positive electrode and a negative electrode. The average ion concentration is changed in accordance with an electric current flowing through the secondary battery.
The average ion concentration between the positive electrode and the negative electrode, that is, the amount of ions present between the positive electrode and the negative electrode, is changed depending on the electric current flowing through the secondary battery. For example, an electrolytic solution leaks from between the positive electrode and the negative electrode depending on the discharge state of the secondary battery, resulting in a reduction in the average ion concentration between the electrodes.
Such a change in the average ion concentration between the electrodes influences the deterioration state and the charge state of the secondary battery. In view of this, in the present invention, the average ion concentration between the electrodes is taken into account in estimating the deterioration state and the charge state of the secondary battery. This can provide a knowledge of the deterioration state and the charge state in which the average ion concentration is incorporated.
The average ion concentration between the electrodes can be calculated with a computing expression including a surface pressure of the secondary battery as a variable. Since the average ion concentration between the electrodes depends on the surface pressure of the secondary battery, the average ion concentration between the electrodes can be calculated once the surface pressure of the secondary battery can be obtained.
For example, variations in the surface pressure cause the electrolytic solution to leak from between the positive electrode and the negative electrode to reduce the average ion concentration. The average ion concentration between the electrodes can be calculated once the surface pressure of the secondary battery is obtained. The surface pressure of the secondary battery can be detected by a pressure sensor. Since the surface pressure of the secondary battery depends on an electric current flowing through the secondary battery, the surface pressure can also be estimated from the electric current through the secondary battery. The electric current through the secondary battery can be detected by a current sensor.
The deterioration state or the charge state of the secondary battery depends not only on the average ion concentration but also on an ion concentration imbalance between the positive electrode and the negative electrode. The accuracy in estimating the deterioration state and the charge state can be improved by finding not only the average ion concentration between the electrodes but also the ion concentration imbalance between the electrodes.
The ion concentration imbalance between the electrodes is changed in accordance with the electric current flowing through the secondary battery. When a current sensor is used to detect the electric current flowing through the secondary battery, the ion concentration imbalance between the electrodes can be calculated. Specifically, the ion concentration imbalance between the electrodes can be calculated by substituting a value detected by the current sensor into a computing expression including the current value as a variable.
The deterioration state of the secondary battery depends not only on the average ion concentration but also on an ion concentration imbalance in a plane (in an electrode plane) in which the positive electrode and the negative electrode are opposite to each other. The accuracy in estimating the deterioration state can be improved by finding not only the average ion concentration between the electrodes but also the ion concentration imbalance in the electrode plane.
The ion concentration imbalance in the electrode plane depends on the surface pressure of the secondary battery. Specifically, variations in the surface pressure tend to cause the ion concentration imbalance in the electrode plane. Once the surface pressure of the secondary battery is obtained, the ion concentration imbalance in the electrode plane can be calculated. Specifically, the ion concentration imbalance can be calculated by using a computing expression including the surface pressure as a variable.
When the average ion concentration between the electrodes, the ion concentration imbalance between the electrodes, and the ion concentration imbalance in the electrode plane are obtained, the accuracy in estimating the deterioration state can be further improved. The controller can limit an output from or an input to the secondary battery when the deterioration state is estimated and a parameter specifying the estimated deterioration state is larger than a threshold value.
This can prevent an increase in the parameter specifying the deterioration state to extend the life of the secondary battery. When the accuracy in estimating the deterioration state can be improved as described above, excessive limitation of the input to and output from the secondary battery can be avoided to improve the input/output characteristics of the secondary battery. In addition, excessive relaxation of the input to and output from the secondary battery can also be prevented to avoid extremely advanced deterioration of the secondary battery. As a result, the life of the secondary battery can be extended.
The charge state of the secondary battery can be estimated by calculating an average ion concentration in an active material. When the correspondence between the average ion concentration in the active material and the charge state is previously determined, the charge state of the secondary battery can be specified by calculating the average ion concentration in the active material. The average ion concentration in the active material can be calculated from the ion concentration distribution in the active material.
The ion concentration distribution in the active material can be calculated with a diffusion equation after a boundary condition at an interface of the active material is set. Since the boundary condition depends on a current density, the boundary condition can be specified by calculating the current density. The current density can be calculated from the voltage and the concentration overvoltage of the secondary battery by using a battery model expression.
The voltage of the secondary battery can be detected with a voltage sensor. The concentration overvoltage depends on the average ion concentration between the electrodes and the ion concentration imbalance between the electrodes. The concentration overvoltage can be obtained by calculating the average ion concentration between the electrodes and the ion concentration imbalance between the electrodes as described above.
Embodiments of the present invention will hereinafter be described.
The HV includes not only an assembled battery, later described, but also another power source such as an internal-combustion engine or a fuel cell, as the power source for running of the vehicle. The PHV is a variant of the HV in which the assembled battery can be charged with electric power from an external power source. The EV includes only the assembled battery as the power source of the vehicle and allows charge of the assembled battery by receiving electric power from the external power source. The external power source is a power source (for example, a commercial power source) provided outside and independently of the vehicle.
The assembled battery 100 includes a plurality of secondary batteries 1 electrically connected in series. Examples of the secondary battery 1 serving as a cell include a nickel metal hydride battery and a lithium-ion battery. The number of the secondary batteries 1 can be set as appropriate based on the output required of the assembled battery 100 or the like.
Although all the secondary batteries 1 are connected electrically in series in the assembled battery 100 of the present embodiment, the present invention is not limited thereto. Specifically, the assembled battery 100 may include a plurality of secondary batteries 1 connected electrically in parallel. A monitor unit 201 detects a voltage between terminals of the assembled battery 100 or detects a voltage Vb of each secondary battery 1 and outputs the detection result to a controller 300.
When the plurality of secondary batteries 1 constituting the assembled battery 100 is grouped into a plurality of battery blocks, the monitor unit 201 can also detect the voltage of each battery block. The battery block is formed of a plurality of secondary batteries 1 connected electrically in series, and a plurality of such battery blocks are connected electrically in series to constitute the assembled battery 100.
A current sensor 202 detects a current Ib flowing through the assembled battery 100 and outputs the detection result to the controller 300. In the present embodiment, it is assumed that a discharge current Ib has a positive value (Ib>0) and a charge current Ib has a negative value (Ib<0). Although the current sensor 202 is provided on a positive electrode line PL connected to a positive electrode terminal of the assembled battery 100 in the present embodiment, the present invention is not limited thereto. The current sensor 202 is only required to detect the current Ib. For example, the current sensor 202 can be provided on a negative electrode line NL connected to a negative electrode terminal of the assembled battery 100. A plurality of current sensors 202 may be provided.
A temperature sensor 203 detects a temperature Tb of the assembled battery 100 (secondary battery 1) and outputs the detection result to the controller 300. The number of the temperature sensors 203 can be set as appropriate. When a plurality of temperature sensors 203 are used, temperatures Tb of a plurality of secondary batteries 1 disposed at different positions can be detected.
The controller 300 includes a memory 300a. The memory 300a stores various types of information for allowing the controller 300 to perform predetermined processing (for example, processing described in the present embodiment). Although the memory 300a is contained in the controller 300 in the present embodiment, the memory 300a may be provided outside the controller 300.
The positive electrode line PL is provided with a system main relay SMR-B. The system main relay SMR-B is switched between ON and OFF in response to a control signal from the controller 300. The negative electrode line NL is provided with a system main relay SMR-G. The system main relay SMR-G is switched between ON and OFF in response to a control signal from the controller 300.
The system main SMR-G is connected electrically in parallel to a system main relay SMR-P and a current limiting resistor 204. The system main relay SMR-P and the current limiting resistor 204 are connected electrically in series. The system main relay SMR-P is switched between ON and OFF in response to a control signal from the controller 300. The current limiting resistor 204 is used to prevent a flow of inrush current when the assembled battery 100 is connected to a load (specifically, an inverter 205).
For connecting the assembled battery 100 to the inverter 205, the controller 300 first switches the system main relay SMR-B from OFF to ON and the system main relay SMR-P from OFF to ON. This causes an electric current to pass through the current limiting resistor 204.
Next, the controller 300 switches the system main relay SMR-G from OFF to ON and switches the system main relay SMR-P from ON to OFF. This completes the connection between the assembled battery 100 and the inverter 205, and the battery system shown in
On the other hand, when the ignition switch is switched from ON to OFF, the controller 300 switches the system main relays SMR-B and SMR-G from ON to OFF. This breaks the connection between the assembled battery 100 and the inverter 205, and the battery system shown in
The inverter 205 converts a DC power from the assembled battery 100 into an AC power and outputs the AC power to a motor generator 206. For example, a three-phase AC motor can be used as the motor generator 206. The motor generator 206 receives the AC power from the inverter 205 to generate a kinetic energy for running of the vehicle. The kinetic energy generated by the motor generator 206 is transferred to wheels to enable the running of the vehicle.
For decelerating or stopping the vehicle, the motor generator 206 converts a kinetic energy generated in braking of the vehicle into an electric energy (AC power). The inverter 205 converts the AC power generated by the motor generator 206 into a DC power and outputs the DC power to the assembled battery 100. Thus, the assembled battery 100 can accumulate the regenerative electric power.
Although the assembled battery 100 is connected to the inverter 205 in the present embodiment, the present invention is not limited thereto. Specifically, a step-up circuit can be provided on the current path connecting the assembled battery 100 with the inverter 205. The step-up circuit can increase the voltage output from the assembled battery 100 and output the electric power at the increased voltage to the inverter 205. The step-up circuit can also reduce the voltage output from the inverter 205 and output the electric power at the reduced voltage to the assemble battery 100.
Next, the configuration of the secondary battery 1 is described with reference to
The secondary battery 1 has a positive electrode 141, a negative electrode 142, and a separator 143. The separator 143 is located between the positive electrode 141 and the negative electrode 142 and contains an electrolytic solution. A solid electrolyte may be used instead of the electrolytic solution. In this case, a layer of the solid electrolyte can be disposed between the positive electrode 141 and the negative electrode 142.
The positive electrode 141 has a collector plate 141a made of aluminum or the like. The collector plate 141a is electrically connected to a positive electrode terminal 11 of the secondary battery 1. The negative electrode 142 has a collector plate 142a made of copper or the like. The collector plate 142a is electrically connected to a negative electrode terminal 12 of the secondary battery 1.
The negative electrode 142 and the positive electrode 141 have groups of spherical active materials 142b and 141b, respectively. As shown in
When the secondary battery 1 is charged, a chemical reaction occurs at the interface of the active material 142b in the negative electrode 142 to absorb a lithium ion Li+ and an electron e−. In addition, a chemical reaction occurs at the interface of the active material 141b in the positive electrode 141 to release a lithium ion Li+ and an electron e−. The lithium ions Li+ are passed between the negative electrode 142 and the positive electrode 141 in this manner to perform charge and discharge of the secondary battery 1 to produce the charge current Ib (Ib<0) or the discharge current Ib (Ib>0).
Three states occur in the concentration of lithium ions in the electrolytic solution. The three states described below influence the performance (in other words, the deterioration state) of the secondary battery 1. It is thus preferable to consider the three states described below in order to keep track of the performance of the secondary battery 1.
A first state relates to a lithium ion concentration imbalance between the positive electrode 141 and the negative electrode 142. As described above, when the secondary battery 1 is charged or discharged, the lithium ions move in the electrolytic solution from one electrode toward the other electrode. As a result, the lithium ions are located predominantly in the positive electrode 141 or the negative electrode 142 depending on the charge or discharge of the secondary battery 1. Specifically, when the secondary battery 1 is discharged, the lithium ions are located predominantly in the positive electrode 141. When the secondary battery 1 is charged, the lithium ions are located predominantly in the negative electrode 142.
Specifically, the lithium ion concentration close to the negative electrode 142 is higher than the lithium ion concentration close to the positive electrode 141. The lithium ion concentration may be increased close to the positive electrode 141. In this case, the lithium ion concentration close to the positive electrode 141 is higher than the lithium ion concentration close to the negative electrode 142.
A second state relates to a lithium ion concentration imbalance in a plane of the electrode. When the secondary battery 1 is charged or discharged, the lithium ion concentration imbalance may be found not only between the positive electrode 141 and the negative electrode 142 but also in the plane of the electrode. The plane of the electrode means a plane (referred to as an electrode plane) in which the positive electrode 141 and the negative electrode 142 are opposite to each other.
The example shown in
When the secondary battery 1 is charged, the lithium ion concentration imbalance behaves oppositely to that shown in
A third state relates to a change in lithium ion concentration within the electrolytic solution. When the pressure in the electrode plane varies, the electrolytic solution may be pushed out from between the positive electrode 141 and the negative electrode 142. Specifically, when the secondary battery 1 is discharged, the electrolytic solution may be pushed out from between the positive electrode 141 and the negative electrode 142.
The pushing out of the electrolytic solution reduces the lithium ions present between the positive electrode 141 and the negative electrode 142. In other words, the lithium ions contributing to the charge and discharge of the secondary battery 1 are reduced. The reduction in the lithium ions lowers the average value of the concentration of the lithium ions located between the positive electrode 141 and the negative electrode 142. As described above, the lithium ion concentration imbalance may occur between the positive electrode 141 and the negative electrode 142. To allow for such an imbalance, the average value of the lithium ion concentration is used. The average value of the lithium ion concentration is referred to as an average ion concentration.
As the secondary battery 1 is charged or discharged at a higher rate (current value), more pressure variations occur in the electrode plane.
When the secondary battery 1 is charged, the behavior opposite to that shown in
With respect to the first state described above, the lithium ion concentration imbalance between the positive electrode and the negative electrode is referred to as an inter-electrode ion concentration imbalance. The inter-electrode ion concentration imbalance can be calculated on the basis of the following expression (1):
dCe(t+Δt)=dCe(t)−dCerelaxation+dCegeneration (1)
In the above expression (1), dCe represents the inter-electrode ion concentration imbalance, t represents time, and Δt represents a cycle (cycle time) for calculating the ion concentration imbalance. As shown in the expression (1), the ion concentration imbalance dCe(t+Δt) after the elapse of the cycle time Δt is calculated on the basis of the ion concentration imbalance dCe(t) at a time t (previous time).
The cycle time Δt can be set as appropriate. As the cycle time Δt is shorter, the ion concentration imbalance dCe can be determined more accurately. However, as the cycle time Δt is shorter, the computing load is increased. Thus, the value of the cycle time Δt can be set as appropriate by considering the accuracy of the ion concentration imbalance dCe and the computing load.
In the above expression (1), dCerelaxation represents a term (relaxation term) for relaxing the ion concentration imbalance during the cycle time Δt. The relaxation term dCerelaxation is subtracted from the ion concentration imbalance dCe (t) at the time t (the previous time). As the relaxation term dCerelaxation is increased, the ion concentration imbalance dCe(t+Δt) is reduced, that is, the inter-electrode ion concentration imbalance dCe is reduced.
In the above expression (1), dCegeneration represents a term (generation term) for generating the ion concentration imbalance during the cycle time Δt. The generation term dCegeneration is added to the ion concentration imbalance dCe (t) at the time t (the previous time). As the generation term dCegeneration is increased, the ion concentration imbalance dCe (t+Δt) is increased, that is, the lithium ion concentration imbalance between the electrodes tends to be increased.
As described above, the inter-electrode ion concentration imbalance includes the state in which the lithium ion concentration is increased close to the positive electrode 141 and the state in which the lithium ion concentration is increased close to the negative electrode 142. The ion concentration imbalance dCe can be calculated for each of the state in which the lithium ion concentration is increased close to the positive electrode 141 and the state in which the lithium ion concentration is increased close to the negative electrode 142. This can determine the ion concentration imbalance dCe when the secondary battery 1 is preferentially discharged or determine the ion concentration imbalance dCe when the secondary battery 1 is preferentially charged.
The relaxation term dCerelaxation can be calculated, for example, based on the following expression (2). It should be noted that the expression for calculating the relaxation term dCerelaxation is not limited to the following expression (2), and any expression may be used as long as the relaxation of the inter-electrode ion concentration imbalance can be specified:
dCerelaxation=α×dCe(t)×Δt (2)
In the expression (2), dCe(t) represents the ion concentration imbalance at the time t (previous time) and Δt represents the cycle time described above. According to the above expression (2), the relaxation term dCerelaxation depends on the ion concentration imbalance dCe(t) and the cycle time Δt.
α represents a relaxation coefficient. The relaxation coefficient α depends on the State Of Charge (SOC), the temperature Tb of the secondary battery 1 and the like. Once the correspondence (map) between the relaxation coefficient α and the SOC is determined by experiment or the like, the SOC is estimated and then the relaxation coefficient α corresponding to the estimated SOC can be specified. The SOC refers to the proportion of the present charge capacity to the full charge capacity.
Once the correspondence (map) between the relaxation coefficient α and the battery temperature Tb is determined by experiment or the like, the battery temperature Tb is detected and then the relaxation coefficient α corresponding to the detected temperature Tb can be specified. The correspondence (map) between the SOC and the battery temperature Tb and the relaxation coefficient α may be previously determined by experiment or the like. In this case, the SOC is estimated and the battery temperature Tb is detected, and then the relaxation coefficient α corresponding to that SOC and that battery temperature Tb can be specified. The map for specifying the relaxation coefficient α can be stored in the memory 300a.
The generation term dCegeneration can be calculated, for example, based on the following expression (3). It should be noted that the expression for calculating the generation term dCegeneration is not limited to the following expression (3), and any expression may be used as long as the generation of the inter-electrode ion concentration imbalance can be specified:
dCegeneration=β×Ib(t)×Δt (3)
In the expression (3), Ib(t) represents the value of current flowing through the secondary battery 1 at time the t and Δt represents the cycle time described above. The value (absolute value) detected by the current sensor 202 is used as the current value Ib. According to the above expression (3), the generation term dCegeneration depends on the current value Ib(t) and the cycle time Δt.
β represents a generation coefficient. The generation coefficient β depends on the SOC, the temperature Tb of the secondary battery 1 and the like. The correspondence (map) between at least one of the SOC and the battery temperature Tb and the generation coefficient β can be previously determined by experiment or the like. Through the use of the map, the SOC is estimated or the battery temperature Tb is detected, and then the generation coefficient β corresponding to at least one of that SOC and that battery temperature Tb can be specified. The map for specifying the generation coefficient β can be stored in the memory 300a.
With respect to the second state described above, the lithium ion concentration imbalance in the electrode plane can be calculated on the basis of the following expression (4):
ΔCe(t+Δt)=ΔCe(t)−ΔCerelaxationΔCegeneration (4)
In the above expression (4), ΔCe represents the ion concentration imbalance in the electrode plane, t represents time, and Δt represents the cycle (cycle time) for calculating the ion concentration imbalance ΔCe and is the same as the cycle time described in the above expression (1). As shown in the expression (4), the ion concentration imbalance ΔCe(t+Δt) after the elapse of the cycle time Δt is calculated on the basis of the ion concentration imbalance ΔCe(t) at the time t (the previous time).
In the above expression (4), ΔCerelaxation represents a term (relaxation term) for relaxing the ion concentration imbalance during the cycle time Δt. The relaxation term ΔCerelaxation is subtracted from the ion concentration imbalance ΔCe(t) at the time t (the previous time). As the relaxation term ΔCerelaxation is increased, the ion concentration imbalance ΔCe(t+Δt) is reduced, that is, the lithium ion concentration imbalance in the electrode plane is reduced.
In the above expression (4), ΔCegeneration represents a term (generation term) for generating the ion concentration imbalance during the cycle time Δt. The generation term ΔCegeneration is added to the ion concentration imbalance ΔCe(t) at the time t (the previous time). As the generation term ΔCegeneration is increased, the ion concentration imbalance ΔCe(t+Δt) is increased, that is, the lithium ion concentration imbalance in the electrode plane tends to be increased.
As described above, the ion concentration imbalance in the electrode plane includes the state in which the lithium ion concentration is increased close to both ends of the positive electrode 141 and the negative electrode 142 (see
The relaxation term ΔCerelaxation can be calculated, for example, based on the following expression (5). It should be noted that the expression for calculating the relaxation term is not limited to the following expression (5), and any expression may be used as long as the relaxation of the ion concentration imbalance in the electrode plane can be specified:
ΔCerelaxation=α′×ΔCe(t)×Δt (5)
In the expression (5), ΔCe(t) represents the ion concentration imbalance at the time t (previous time) and Δt represents the cycle time described above. According to the above expression (5), the relaxation term ΔCerelaxation depends on the ion concentration imbalance ΔCe(t) and the cycle time Δt.
α′ represents a relaxation coefficient. The relaxation coefficient α′ depends on the SOC, the temperature Tb of the secondary battery 1 and the like. The correspondence (map) between the relaxation coefficient α′ and at least one of the SOC and the battery temperature Tb can be previously determined by experiment or the like. The SOC is estimated or the battery temperature Tb is detected, and then the relaxation coefficient α′ corresponding to at least one of that SOC and that battery temperature Tb can be specified. The map for specifying the relaxation coefficient α′ can be stored in the memory 300a.
The generation term ΔCegeneration can be calculated, for example, based on the following expression (6). It should be noted that the expression for calculating the generation term ΔCegeneration is not limited to the following expression (6), and any expression may be used as long as the generation of the ion concentration imbalance in the electrode plane can be specified:
ΔCegeneration=β′×P×ΔCe(t)×Δt (6)
In the expression (6), ΔCe represents the ion concentration imbalance at the time t (previous time), P represents a surface pressure of the secondary battery 1, and Δt represents the cycle time. According to the expression (6), the generation term ΔCegeneration depends on the ion concentration imbalance ΔCe, the cycle time Δt, and the surface pressure P.
The surface pressure P can be actually measured or can be estimated with a map previously obtained by experiment or the like. For actually measuring the surface pressure P, a pressure sensor may be placed outside or inside a battery case constituting the exterior of the secondary battery 1. The controller 300 can detect the surface pressure P based on the output from the pressure sensor.
The surface pressure P depends on the value of current Ib flowing through the secondary battery 1, the SOC and the temperature Tb of the secondary battery 1 and the like. Thus, a map representing the correspondence between at least one of the current value Ib, the SOC, and the battery temperature Tb, and the surface pressure P can be previously created. The current value Ib is detected, the SOC is estimated, or the battery temperature Tb is detected, and then the surface pressure P corresponding to at least one of those current value Ib, SOC, and battery temperature Tb can be specified. The map for specifying the surface pressure P can be stored in the memory 300a.
β′ represents a generation coefficient. The generation coefficient β′ depends on the SOC, the temperature Tb of the secondary battery 1 and the like. Thus, a map representing the correspondence between at least one of the SOC and the battery temperature Tb and the generation coefficient β′ can be previously determined. The SOC is estimated or the battery temperature Tb is detected, and then the generation coefficient β′ corresponding to at least one of that SOC and that battery temperature Tb can be specified.
With respect to the third state described above, the inter-electrode average ion concentration can be calculated on the basis of the following expression (7):
Ceave(t+Δt)=Ceave(t)−Ceaverelaxation+Ceavegeneration (7)
In the expression (7), Ceave represents the average ion concentration, t represents time, and Δt represents the cycle (cycle time) for calculating the average ion concentration Ceave and is the same as the cycle time Δt described in the above expression (1). As shown in the expression (7), the average ion concentration Ceave(t+Δt) after the elapse of the cycle time Δt is calculated on the basis of the average ion concentration Ceave(t) at the time t (the previous time).
In the above expression (7), Ceaverelaxation represents a term (reduction term) for reducing the average ion concentration Ceave during the cycle time Δt. The reduction term Ceaverelaxation is subtracted from the average ion concentration Ceave(t) at the time t (the previous time). As the reduction term Ceaverelaxation is increased, the average ion concentration Ceave(t+Δt) is reduced.
In the above expression (7), Ceavegeneration presents a term (increase term) for increasing the average ion concentration Ceave during the cycle time Δt. The increase term Ceavegeneration is added to the average ion concentration Ceave(t) at the time t (the previous time). As the increase term Ceavegeneration is increased, the average ion concentration Ceave(t+Δt) is increased.
The reduction term Ceaverelaxation can be calculated, for example, based on the following expression (8). It should be noted that the expression for calculating the reduction term Ceaverelaxation is not limited to the following expression (8), and any expression may be used as long as the reduction of the inter-electrode average ion concentration Ceave can be specified:
Ceaverelaxation=α″×Ceave(t)×Δt (8)
In the expression (8), Ceave (t) represents the average ion concentration at the time t (previous time) and Δt represents the cycle time. According to the above expression (8), the reduction term Ceaverelaxation depends on the average ion concentration Ceave(t) and the cycle time Δt.
α″ represents a reduction coefficient. The reduction coefficient α″ depends on the SOC, the temperature Tb of the secondary battery 1 and the like. The correspondence (map) between at least one of the SOC and the battery temperature Tb and the reduction coefficient α″ can be previously determined by experiment or the like. The SOC is estimated or the battery temperature Tb is detected, and then the reduction coefficient α″ corresponding to at least one of that SOC and that battery temperature Tb can be specified. The map for specifying the reduction coefficient α″ can be stored in the memory 300a.
The increase term Ceavegeneration can be calculated, for example, based on the following expression (9). It should be noted that the expression for calculating the increase term Ceavegeneration is not limited to the following expression (9), and any expression may be used as long as the increase of the inter-electrode average ion concentration Ceave can be specified:
Ceavegenerationβ″×P×Ceave(t)×Δt (9)
In the expression (9), Ceave represents the average ion concentration at the time t (previous time), Δt represents the cycle time, and P represents the surface pressure of the secondary battery 1. As described in the expression (6), the surface pressure P can be actually measured or can be estimated with the map previously obtained by experiment or the like. According to the expression (9), the increase term Ceavegeneration depends on the average ion concentration Ceave, the cycle time Δt, and the surface pressure P.
β″ represents an increase coefficient. The increase coefficient β″ depends on the SOC, the temperature Tb of the secondary battery 1 and the like. A map representing the correspondence between at least one of the SOC and the battery temperature Tb and the increase coefficient β″ can be previously determined. The SOC is estimated or the battery temperature Tb is detected, and then the increase coefficient β″ corresponding to at least one of that SOC and that battery temperature Tb can be specified. The map used for specifying the increase coefficient β″ can be stored in the memory 300a.
When the ion concentration imbalances dCe, ΔCe and the average ion concentration Ceave are calculated as described above, a deterioration value D of the secondary battery 1 can be calculated on the basis of these calculated values. The deterioration value D is a parameter which specifies the deterioration state of the secondary battery 1. As the deterioration of the secondary battery 1 proceeds, the deterioration value D increases.
The deterioration value D can be calculated by using at least one of the ion concentration imbalances dCe, ΔCe and the average ion concentration Ceave. For example, the deterioration value D can be calculated with one of the following expressions (10) to (15):
D(t)=Ceave(t)×k1 (10)
D(t)=ΔCe×k2 (11)
D(t)=dCe×k3 (12)
D(t)=Ceave(t)×k1+ΔCe×k2 (13)
D(t)=Ceave(t)×k1+dCe×k3 (14)
D(t)=k1×Ceave(t)+k2×ΔCe(t)+k3×dCe(t) (15)
In each of the expressions (10) to (15), D(t) represents the deterioration value D at the time t. The expression (10) is an expression for calculating the deterioration value D from the average ion concentration Ceave. A conversion coefficient k1 shown in the expression (10) represents a value used for converting the average ion concentration Ceave into the deterioration value D.
The expression (11) is an expression for calculating the deterioration value D from the ion concentration imbalance ΔCe in the electrode plane. A conversion coefficient k2 shown in the expression (11) represents a value used for converting the ion concentration imbalance ΔCe in the electrode plane into the deterioration value D. The expression (12) is an expression for calculating the deterioration value D from the inter-electrode ion concentration imbalance dCe. A conversion coefficient k3 shown in the expression (12) represents a value used for converting the inter-electrode ion concentration imbalance dCe into the deterioration value D.
The expression (13) is an expression for calculating the deterioration value D from the average ion concentration Ceave and the ion concentration imbalance ΔCe. Conversion coefficients k1 and k2 shown in the expression (13) correspond to the conversion coefficients described in the expressions (10) and (11), respectively. The expression (14) is an expression for calculating the deterioration value D from the average ion concentration Ceave and the ion concentration imbalance dCe. Conversion coefficients k1 and k3 shown in the expression (14) correspond to the conversion coefficients described in the expressions (10) and (12), respectively.
The expression (15) is an expression for calculating the deterioration value D from the average ion concentration Ceave and the ion concentration imbalances ΔCe and dCe. Conversion coefficients k1, k2, and k3 shown in the expression (15) correspond to the conversion coefficients described in the expressions (10) to (12), respectively.
In general, the average ion concentration Ceave and the ion concentration imbalance ΔCe change over a longer term than the ion concentration imbalance dCe does. For predicting long-term performance (deterioration) of the secondary battery 1, at least one of the average ion concentration Ceave and the ion concentration imbalance ΔCe can be used to calculate the deterioration value D.
For predicting short-term performance (deterioration) of the secondary battery 1, only the ion concentration imbalance dCe can be used to calculate the deterioration value D. In this manner, the average ion concentration Ceave, the ion concentration imbalance ΔCe or dCe can be selected as appropriate for the term in the prediction of the performance (deterioration) of the secondary battery 1 to calculate the deterioration value D.
Next, description is made of the processing of calculating the inter-electrode ion concentration imbalance dCe with reference to a flowchart shown in
At step S101, the controller 300 detects the current value Ib of the secondary battery 1 based on the output from the current sensor 202. At step S202, the controller 300 calculates the SOC of the secondary battery 1. The calculation of the SOC can be performed with a known method as appropriate.
For example, the SOC of the secondary battery 1 can be calculated by summing the current values Ib when the secondary battery 1 is charged and discharged. Alternatively, the SOC of the secondary battery 1 can be specified by measuring the Open Circuit Voltage (OCV) of the secondary battery 1. The OCV and the SOC have a correspondence, and the correspondence can be previously determined. Once the OCV is measured, the SOC corresponding to that OCV can be specified.
At step S103, the controller 300 detects the temperature Tb of the secondary battery 1 based on the output from the temperature sensor 203. At step S104, the controller 300 specifies the relaxation coefficient α based on the SOC and the battery temperature Tb. The controller 300 can use the map stored in the memory 300a to specify the relaxation coefficient α corresponding to the SOC and the battery temperature Tb. The value calculated in the processing at step S102 is used as the SOC, and the value detected in the processing at step S103 is used as the battery temperature Tb.
At step S105, the controller 300 specifies the ion concentration imbalance dCe(t) at the time t (previous time). In the present embodiment, each time the cycle time Δt elapses, the ion concentration imbalance dCe is calculated and is stored in the memory 300a. This allows the controller 300 to read the ion concentration imbalance dCe (t) at the time t (previous time) from the memory 300a.
At step S106, the controller 300 calculates the relaxation term dCerelaxation. Specifically, the controller 300 can calculate the relaxation term dCerelaxation based on the above expression (2). The value specified in the processing at step S104 is used as the relaxation coefficient α used in the expression (2). The value specified in the processing at step S105 is used as the ion concentration imbalance dCe(t) used in the expression (2).
At step S107, the controller 300 specifies the generation coefficient β. Specifically, the controller 300 uses the map stored in the memory 300a to specify the generation coefficient β corresponding to the SOC and the battery temperature Tb. The value calculated in the processing at step S102 is used as the SOC, and the value detected in the processing at step S103 is used as the battery temperature Tb.
At step S108, the controller 300 calculates the generation term dCegeneration. Specifically, the controller 300 calculates the generation term dCegeneration based on the above expression (3). The value detected in the processing at step S101 is used as the current value Ib used in the expression (3). The value specified in the processing at step S107 is used as the generation term β used in the expression (3).
At step S109, the controller 300 calculates the ion concentration imbalance dCe(t+Δt) at the present time. Specifically, the controller 300 can calculate the ion concentration imbalance dCe(t+Δt) based on the above expression (1). The value specified in the processing at step S105 is used as the ion concentration imbalance dCe(t) used in the expression (1). The value calculated in the processing at step S106 is used as the relaxation term dCerelaxation. The value calculated in the processing at step S108 is used as the generation term dCegeneration.
At step S110, the controller 300 stores the ion concentration imbalance dCe(t+Δt) calculated in the processing at step S109 into the memory 300a. The ion concentration imbalance dCe(t+Δt) stored in the memory 300a is used for calculating the ion concentration imbalance dCe in the next processing. In other words, the ion concentration imbalance dCe(t+Δt) stored in the memory 300a is used next time the processing at step S105 is performed.
Next, description is made of the processing of calculating the ion concentration imbalance ΔCe in the electrode plane with reference to a flow chart shown in
The processing from step S201 to step S203 is identical to the processing from step S101 to step S103 shown in
In the present embodiment, the calculation of the surface pressure P is performed by using the values detected in the processing at steps S201 and S203 (current value Ib and battery temperature Tb) and the SOC calculated in the processing at step S202. Alternatively, the pressure sensor can be used to measure the surface pressure P. In this case, the processing at step S201 can be omitted.
At step S205, the controller 300 specifies the relaxation coefficient α′ based on the SOC and the battery temperature Tb. The controller 300 can use the map stored in the memory 300a to specify the relaxation coefficient α′ corresponding to the SOC and the battery temperature Tb. The value calculated in the processing at step S202 is used as the SOC, and the value detected in the processing at step S203 is used as the battery temperature Tb.
At step S206, the controller 300 specifies the ion concentration imbalance ΔCe(t) at the time t (previous time). In the present embodiment, each time the cycle time Δt elapses, the ion concentration imbalance ΔCe is calculated and is stored in the memory 300a. This allows the controller 300 to read the ion concentration imbalance ΔCe (t) at the time t (previous time) from the memory 300a.
At step S207, the controller 300 calculates the relaxation term ΔCerelaxation. Specifically, the controller 300 can calculate the relaxation term ΔCerelaxation based on the above expression (5). The value specified in the processing at step S205 is used as the relaxation coefficient α′ used in the expression (5). The value specified in the processing at step S206 is used as the ion concentration imbalance ΔCe(t) used in the expression (5).
At step S208, the controller 300 specifies the generation coefficient β′. Specifically, the controller 300 uses the map stored in the memory 300a to specify the generation coefficient β′ corresponding to the SOC and the battery temperature Tb. The value calculated in the processing at step S202 is used as the SOC, and the value detected in the processing at step S203 is used as the battery temperature Tb.
At step S209, the controller 300 calculates the generation term ΔCegeneration. Specifically, the controller 300 calculates the generation term ΔCegeneration based on the above expression (6). The value calculated in the processing at step S204 is used as the surface pressure P used in the expression (6). The value specified in the processing at step S206 is used as the ion concentration imbalance ΔCe(t) used in the expression (6). The value specified in the processing at step S208 is used as the generation coefficient β′ used in the expression (6).
At step S210, the controller 300 calculates the ion concentration imbalance ΔCe(t+Δt) at the present time. Specifically, the controller 300 can calculate the ion concentration imbalance ΔCe(t+Δt) based on the above expression (4). The value specified in the processing at step S206 is used as the ion concentration imbalance ΔCe(t) used in the expression (4). The value calculated in the processing at step S207 is used as the relaxation term ΔCerelaxation. The value calculated in the processing at step S209 is used as the generation term ΔCegeneration.
At step S211, the controller 300 stores the ion concentration imbalance ΔCe(t+Δt) calculated in the processing at step S210 into the memory 300a. The ion concentration imbalance ΔCe(t+Δt) stored in the memory 300a is used for calculating the ion concentration imbalance ΔCe in the next processing. In other words, the ion concentration imbalance ΔCe(t+Δt) stored in the memory 300a is used next time the processing at step S206 is performed.
Next, description is made of the processing of calculating the inter-electrode average ion concentration Ceave with reference to a flow chart shown in
The processing from step S301 to step S304 is identical to the processing from step S201 to step S204 shown in
The controller 300 can use the map stored in the memory 300a to specify the reduction coefficient α″ corresponding to the SOC and the battery temperature Tb. The value calculated in the processing at step S302 is used as the SOC, and the value detected in the processing at step S303 is used as the battery temperature Tb.
At step S306, the controller 300 specifies the average ion concentration Ceave(t) at the time t (previous time). In the present embodiment, each time the cycle time Δt elapses, the average ion concentration Ceave is calculated and is stored in the memory 300a. This allows the controller 300 to read the average ion concentration Ceave(t) at the time t (previous time) from the memory 300a.
At step S307, the controller 300 calculates the reduction term Ceaverelaxation. Specifically, the controller 300 can calculate the reduction term Ceaverelaxation based on the above expression (8). The value specified in the processing at step S305 is used as the reduction coefficient α″ used in the expression (8). The value specified in the processing at step S306 is used as the average ion concentration Ceave(t) used in the expression (8).
At step S308, the controller 300 specifies the increase coefficient β″. Specifically, the controller 300 uses the map stored in the memory 300a to specify the increase coefficient β″ corresponding to the SOC and the battery temperature Tb. The value calculated in the processing at step S302 is used as the SOC, and the value detected in the processing at step S303 is used as the battery temperature Tb.
At step S309, the controller 300 calculates the increase term Ceavegeneration. Specifically, the controller 300 calculates the increase term Ceavegeneration based on the above expression (9). The value calculated in the processing at step S304 is used as the surface pressure P used in the expression (9). The value specified in the processing at step S306 is used as the average ion concentration Ceave(t) used in the expression (9). The value specified in the processing at step S308 is used as the increase coefficient β″ used in the expression (9).
At step S310, the controller 300 calculates the average ion concentration Ceave(t+Δt) at the present time. Specifically, the controller 300 can calculate the average ion concentration Ceave(t+Δt) based on the above expression (7). The value specified in the processing at step S306 is used as the average ion concentration Ceave(t) used in the expression (7). The value calculated in the processing at step S307 is used as the reduction term Ceaverelaxation. The value calculated in the processing at step S309 is used as the increase term Ceavegeneration.
At step S311, the controller 300 stores the average ion concentration Ceave(t+Δt) calculated in the processing at step S310 into the memory 300a. The average ion concentration Ce(t+Δt) stored in the memory 300a is used for calculating the average ion concentration Ceave in the next processing. In other words, the average ion concentration Ceave(t+Δt) stored in the memory 300a is used next time the processing at step S306 is performed.
Next, description is made of the processing of calculating the deterioration value D with reference to a flow chart shown in
At step S401, the controller 300 calculates the inter-electrode ion concentration imbalance dCe(t). The processing at step S401 corresponds to the processing shown in
At step S403, the controller 300 calculates the inter-electrode average ion concentration Ce(t). The processing at step S403 corresponds to the processing shown in
After the calculation of the deterioration value D(t), the controller 300 can control the input to and output from the secondary battery 1 based on the deterioration value D(t). Next, the processing of controlling the output from the secondary battery 1 is described with reference to a flow chart shown in
At step S501, the controller 300 calculates the deterioration value D(t) in the secondary battery 1 at the present time. The processing at step S501 corresponds to the processing shown in
The threshold value Glim(t) is now described with reference to
The charge and discharge of the secondary battery 1 can be controlled such that the deterioration value D reaches the deterioration value GMAX when the secondary battery 1 reaches the end of its life. The life of the secondary battery 1 can be defined as a time tMAX. The time t represents the elapsed time since the first use of the secondary battery 1. The secondary battery 1 reaches the end of its life when the elapsed time reaches the time tMAX.
A maximum value G(t) is the maximum allowable value of the deterioration value D at a time t. The maximum value G(t) is determined on the basis of the deterioration value GMAX and the time tMAX. In
Although the maximum value G(t) is determined from the chain line (straight line) shown in
The threshold value Glim(t) is a value smaller than the maximum value G(t) by a predetermined amount ΔG. The output from the secondary battery 1 may be controlled with respect to the maximum value G(t), but in this case, the deterioration value D(t) may be larger than the maximum value G(t) due to delayed control or the like. To address this, in the present embodiment, the output from the secondary battery 1 is controlled with respect to the threshold value Glim(t) smaller than the maximum value G(t). This can prevent the deterioration value D(t) from reaching the maximum value G(t) even when the deterioration value D(t) is larger than the threshold value Glim(t).
The difference ΔG between the maximum value G(t) and the threshold value Glim(t) can be set as appropriate. Alternatively, the output from the secondary battery 1 may be controlled with respect to the maximum value G(t).
As described above, the threshold value Glim(t) is preset on the basis of the maximum value G(t). The information about the threshold value Glim(t) can be stored in the memory 300a in advance. The controller 300 can measure the present time t and specify the threshold value Glim(t) corresponding to the measured time t. The present time t is the elapsed time since the first use of the secondary battery 1 and can be measured with a timer. In the processing at step S502, the threshold value Glim(t) is specified as described above.
At step S503, the controller 300 determines whether or not the deterioration value D(t) calculated in the processing at step S501 is larger than the threshold value Glim(t) specified in the processing at step S502. When the deterioration value D(t) is larger than the threshold value Glim(t), the controller 300 performs processing at step S504. When the deterioration value D(t) is smaller than the threshold value Glim(t), the controller 300 performs processing at step S509.
When the deterioration value D(t) is larger than the threshold value Glim(t), the controller 300 determines that the output from the secondary battery 1 needs to be limited, and performs the processing at step S504 and the subsequent steps. The limitation of the output from the secondary battery 1 can cause the deterioration value D(t) to fall below the threshold value Glim(t).
The limitation of the output from the secondary battery 1 can reduce the deterioration value D(t). As described above, the deterioration value D(t) is calculated on the basis of the average ion concentration Ce and the ion concentration imbalances dCe and ΔCe. The limitation of the output from the secondary battery 1 can reduce a lowering of the average ion concentration Ceave and can reduce the ion concentration imbalances dCe and ΔCe. As a result, the deterioration value D(t) can be reduced.
At step S504, the controller 300 specifies the maximum value G(t) at the present time t. As described above, the maximum value G(t) is preset on the basis of the deterioration value GMAX and the time tMAX. The information about the maximum value G(t) can be stored in the memory 300a in advance. In other words, the correspondence between the elapsed time t since the first use of the secondary battery 1 and the maximum value G(t) can be stored in the memory 300a. The controller 300 can measure the time t up to the present and specify the maximum value G(t) corresponding to the present time t.
At step S505, the controller 300 calculates a maximum output electric power Wout,max(t) allowable at the time t. The output electric power Wout,max(t) is calculated on the basis of the following expression (16):
Wout,max(t)=Wout,MAX−Wlimit
D(t)>Glimit(t) (16)
In the above expression (16), Wout,MAX represents a maximum electric power value obtained when the secondary battery 1 is discharged. The output electric power Wout,MAX is preset on the basis of the output characteristics of the secondary battery 1. The information about the output electric power Wout,MAX can be stored in the memory 300a in advance. Wlimit represents an electric power amount used when the output from the secondary battery 1 is limited. As obvious from the expression (16), when the output from the secondary battery 1 is limited, the output electric power w out,max (t) is lower than the output electric power Wout,MAX by the limiting electric power amount Wlimit.
The limiting electric power amount Wlimit can be calculated, for example, based on the following expression (17):
Wlimit(t)=k×(D(t)−Glimit(t))
D(t)>Glimit(t) (17)
In the expression (17), D(t) represents the deterioration value at the time t, Glimit(t) represents the threshold value (deterioration value) at the time t, k represents a weighting coefficient and can be set as appropriate. The weighting coefficient k can be stored in the memory 300a in advance.
According to the expression (17), the limiting electric power amount Wlimit is determined in accordance with the difference between the threshold value Glimit(t) and the deterioration value D(t). This determination of the limiting electric power amount Wlimit can incorporate the difference between the threshold value Glimit (t) and the deterioration value D(t) into the processing of limiting the output from the secondary battery 1. Specifically, as the difference between the deterioration value D(t) and the threshold value Glimit(t) is increased, the limiting electric power amount Wlimit is increased to limit the output from the secondary battery 1 to a larger extent. In other words, as the difference between the deterioration value D(t) and the threshold value Glimit (t) is reduced, the limiting electric power amount Wlimit is reduced to limit the output from the secondary battery 1 to a lesser extent.
At step S506, the controller 300 specifies an output electric power Wout(t) required of the secondary battery 1. For example, the required output electric power Wout(t) is increased as an accelerator pedal of the vehicle is pressed more. At step S507, the controller 300 determines whether or not the output electric power Wout (t) specified in the processing at step S506 is higher than the output electric power Wout,max(t) calculated in the processing at step S505.
When the output electric power Wout (t) is higher than the output electric power Wout,max(t), the controller 300 performs processing at step S508. When the output electric power Wout(t) is lower than the output electric power Wout,max(t), the controller 300 performs processing at step S509. At step S508, the controller 300 sets an actual output electric power Wout(t) of the secondary battery 1 at the output electric power Wout,max(t).
When the controller 300 proceeds from the processing at step S507 to the processing at step S508, the required output electric power Wout(t) is higher than the output electric power Wout,max(t). In the processing at step S508, the actual output electric power Wout(t) of the secondary battery 1 is set at the output electric power Wout,max(t) to cause the actual output electric power Wout(t) to be lower than the required output electric power Wout(t). In other words, the output from the secondary battery 1 is limited.
At step S509, the controller 300 sets the required output electric power Wout(t) as the actual output electric power Wout(t) of the secondary battery 1. When the controller 300 proceeds from the processing at step S507 to the processing at step S509, the required output electric power Wout(t) is lower than the output electric power Wout,max(t). The output electric power Wout,max(t) is the maximum output electric power determined by factoring in the deterioration value D(t).
Thus, when the required output electric power Wout(t) is lower than the output electric power Wout,max(t), the required output electric power Wout(t) can be set as the actual output electric power Wout(t) of the secondary battery 1. In this manner, the output from the secondary battery 1 is not limited in the processing at step S509.
The output from the secondary battery 1 is not limited either when the controller 300 proceeds from the processing at step S503 to the processing at step S509. When the controller 300 proceeds from the processing at step S503 to the processing at step S509, the deterioration value D(t) does not reach the threshold value Glimit(t). In this case, a certain increase in the deterioration value D(t) can be allowed, and the limitation of the output from the secondary battery 1 is not required.
As described above, the limitation of the output from the secondary battery 1 can reduce the deterioration value D(t). When the deterioration value D(t) is reduced below the threshold value Glimit(t) the limitation of the output from the secondary battery 1 is canceled, that is, the output electric power Wout,max(t) is set at the output electric power Wout,MAX. This can achieve the control of the output from the secondary battery 1 while the deterioration of the secondary battery 1 is monitored.
According to the present embodiment, the deterioration value D(t) can be specified on the basis of the average ion concentration Ceave(t). When the average ion concentration Ceave(t) is changed, the amount of lithium ions contributing to the charge and discharge of the secondary battery 1 is also changed to easily influence the input/output performance (in other words, the deterioration) of the secondary battery 1. Thus, specifying the deterioration value D(t) on the basis of the average ion concentration Ceave(t) can provide a clear knowledge of the deterioration state of the secondary battery 1.
When the ion concentration imbalance dCe or the ion concentration imbalance ΔCe is factored in to specify the deterioration value D(t) in addition to the average ion concentration Ceave(t), a clearer knowledge of the deterioration state of the secondary battery 1 can be provided. In other words, the accuracy in estimating the deterioration state of the secondary battery 1 can be enhanced.
When both the ion concentration imbalance dCe and the ion concentration imbalance ΔCe are factored in to specify the deterioration value D(t) in addition to the average ion concentration Ceave(t), a still clearer knowledge of the deterioration state of the secondary battery 1 can be provided. In other words, the accuracy in estimating the deterioration state of the secondary battery 1 can be enhanced further.
Since the accuracy in estimating the deterioration state of the secondary battery 1 can be enhanced, the output control can be performed in accordance with that deterioration state. Specifically, it is possible to prevent excessive limitation of the output from the secondary battery 1 or excessive relaxation of the output from the secondary battery 1. When the excessive output limitation is prevented, the output performance of the secondary battery 1 can be improved. When the excessive output relaxation is prevented, extremely advanced deterioration of the secondary battery 1 can be prevented to extend the life of the secondary battery 1.
According to the present embodiment, the deterioration value D(t) can be changed along the threshold value Glimit(t). This allows the secondary battery 1 to be used continuously until the time tMAX when the secondary battery 1 reaches the end of its life.
Although the processing shown in
The processing from step S601 to step S604 is identical to the processing from step S501 to step S504 shown in
At step S605, the controller 300 calculates a maximum input electric power Win,max(t) allowable at the time t. The input electric power Win,max(t) is calculated on the basis of the following expression (18):
Win,max(t)=Win,MAX−Wlimit
D(t)>Glimit(t) (18)
In the above expression (18), Win,MAX represents a maximum electric power value obtained when the secondary battery 1 is charged. Wlimit represents an electric power amount when the input to the secondary battery 1 is limited. As obvious from the expression (18), when the input to the secondary battery 1 is limited, the input electric power Win,max(t) is lower than the input electric power Wout,MAX by the limiting electric power amount Wlimit. The limiting electric power amount Wlimit can be determined in accordance with the difference between the threshold value Glimit(t) and the deterioration value D(t), similarly to the expression (17).
This determination of the limiting electric power amount Wlimit can incorporate the difference between the threshold value Glimit(t) and the deterioration value D(t) into the processing of limiting the input to the secondary battery 1. Specifically, as the difference between the deterioration value D(t) and the threshold value Glimit(t) is increased, the limiting electric power amount Wlimit is increased to limit the input to the secondary battery 1 to a larger extent. As the difference between the deterioration value D(t) and the threshold value Glimit(t) is increased, the limiting electric power amount Wlimit is reduced to limit the input to the secondary battery 1 to a lesser extent.
At step S606, the controller 300 specifies an electric power Win(t) to be input to the secondary battery 1. At step S607, the controller 300 determines whether or not the input electric power Win(t) specified in the processing at step S606 is higher than the input electric power Win,max(t) calculated in the processing at step S605.
When the input electric power Win(t) is higher than the input electric power Win,max(t), the controller 300 performs processing at step S608. When the input electric power Win(t) is lower than the input electric power Win,max(t), the controller 300 performs processing at step S609. At step S608, the controller 300 sets an actual input electric power Win(t) of the secondary battery 1 at the input electric power Win,max(t).
When the controller 300 proceeds from the processing at step S607 to the processing at step S608, the input electric power Win(t) is higher than the maximum allowable in put Win,max(t). In the processing at step S608, the actual input electric power Win(t) of the secondary battery 1 is set at the input electric power Win,max(t) to cause the actual input electric power Win(t) to be lower than the electric power Win(t) to be input. In other words, the input to the secondary battery 1 is limited.
At step S609, the controller 300 sets the electric power Win(t) to be input as the actual input electric power Win(t) of the secondary battery 1. When the controller 300 proceeds from the processing at step S607 to the processing at step S609, the electric power Win(t) to be input is lower than the input electric power Wout,max(t). The input electric power Wout,max(t) is the maximum input electric power determined by factoring in the deterioration value D(t).
Thus, when the electric power Win(t) to be input is lower than the input electric power Win,max(t), the electric power Wout(t) to be input can be set as the actual input electric power Wout(t) of the secondary battery 1. In this manner, the input to the secondary battery 1 is not limited in the processing at step S609.
The input to the secondary battery 1 is not limited either when the controller 300 proceeds from the processing at step S603 to the processing at step S609. When the controller 300 proceeds from the processing at step S603 to the processing at step S609, the deterioration value D(t) does not reach the threshold value Glimit(t). In this case, a certain increase in the deterioration value D(t) can be allowed, and the limitation of the input to the secondary battery 1 is not required.
The limitation of the input to the secondary battery 1 can reduce the deterioration value D(t). As described above, the deterioration value D(t) is calculated on the basis of the average ion concentration Ce and the ion concentration imbalances dCe and ΔCe. The limitation of the input to the secondary battery 1 can reduce a change in the average ion concentration Ce and can reduce the ion concentration imbalances dCe and ΔCe. As a result, the deterioration value D(t) can be reduced.
When the deterioration value D(t) is reduced below the threshold value Glimit(t), the limitation of the input to the secondary battery 1 is canceled, that is, the input electric power Win,max(t) is set at the input electric power Win,MAX. This can achieve the control of the input to the secondary battery 1 while the deterioration of the secondary battery 1 is monitored.
The processing shown in
Embodiment 2 of the present invention will hereinafter be described. In the present embodiment, a battery model, later described, is used to estimate the internal state and the SOC of a secondary battery 1. In the present embodiment, components identical to those described in Embodiment 1 are designated with the same reference numerals, and detailed description thereof is omitted.
First, the battery model used in the present embodiment is described. A basic battery model expression is represented by basic equations including the following expressions (19) to (29).
In the variables and constants in the model expression described below, a subscript e means a value in an electrolytic solution and a subscript s means a value in an active material. A subscript j makes a distinction between a positive electrode and a negative electrode, wherein j equal to 1 means a value in the positive electrode and j equal to 2 means a value in the negative electrode. When the variables or the constants in the positive electrode and the negative electrode are collectively represented, the subscript j is omitted. The denotation of (t) representing a function of time, the denotation of (T) representing battery temperature dependence, the denotation of (θ) representing local SOCθ dependence and the like may be omitted in the present specification. A symbol # attached to the variables or the constants represents an average value.
The above expressions (19) and (20) represent an electrochemical reaction in the electrode (active material) and are called the Butler-Volmer equation.
The following expression (21) holds as an expression relating to the conservation law of lithium ion concentration within the electrolytic solution. A diffusion equation (22) and boundary condition expressions shown in expressions (23) and (24) are used as expressions relating to the conservation law of lithium ion concentration within the active material. The expression (23) represents a boundary condition at the center of the active material. The expression (24) represents a boundary condition at the interface between the active material and the electrolytic solution (hereinafter also referred to simply as an interface).
A local SOCθj corresponding to local lithium concentration distribution (concentration distribution) at the active material interface is defined by the following expression (25). In the expression (25), csei represents the lithium concentration at the active material interface in the positive electrode and the negative electrode as shown in the following expression (26), and csj,max represents the maximum lithium concentration within the active material.
The following expression (27) holds as an expression relating to the conservation law of charge within the electrolytic solution, and the following expression (28) holds as an expression relating to the conservation law of charge within the active material. The following expression (29) representing the relationship between a current density I(t) and a reaction current density JjLi holds as an electrochemical reaction expression at the active material interface.
∇·└kjeff(x,t)∇ϕej(x,t)┘+∇·└kDjeff(x,t)∇ ln cej(x,t)┘+jjLi(x,θj,t)=0 (27)
∇·[σjeff(x,t)∇ϕsj(x,t)]−jjLi(x,θj,t)=0 (28)
I(t)=∫0L
The battery model expression represented by the basic equations including the expressions (19) to (29) can be simplified as described below. The simplification of the battery model expression can reduce computing load or shorten a computing time.
It is assumed that a uniform electrochemical reaction is seen in each of a negative electrode 142 and a positive electrode 141. Specifically, it is assumed that the reaction in the x direction uniformly occurs in each of the electrodes 142 and 141. In addition, since it is assumed that uniform reactions occur in a plurality of active materials 142b and 141b included in each of the electrodes 142 and 141, the active materials 142b and 141b in each of the electrodes 142 and 141 are handled as single active material models. Thus, the structure of the secondary battery 1 shown in
In a battery model shown in
As shown in
According to the battery model shown in
In the expression (21′), it is assumed that cej(t) takes a constant value by assuming that the electrolytic solution has a lithium concentration constant over time. For the active material models 141b and 142b, the diffusion equations (22) to (24) are transformed into the diffusion equations (22′) to (24′) in view of only the distribution in the polar coordinate direction. In the expression (26′), the lithium concentration csej at the active material interface corresponds to the lithium concentration csi(t) in the outermost area of the N divided areas shown in
The expression (27) relating to the conservation law of charge within the electrolytic solution is simplified into the following expression (30) by using the expression (21′). Thus, a potential φej of the electrolytic solution is approximated as a quadric function of x. An average potential φej# within the electrolytic solution used for calculation of an overvoltage ηj# is determined from the following expression (31) provided by integrating the expression (30) with an electrode thickness Lj.
For the negative electrode 142, the following expression (32) holds on the basis of the expression (30). Thus, a difference (a potential difference) between an electrolytic solution average potential φe2# and an electrolytic solution potential at the boundary between the negative electrode 142 and the separator 143 is represented by the following expression (33). For the positive electrode 141, a difference (a potential difference) between an electrolytic solution average potential φe1# and an electrolytic solution potential at the boundary between the positive electrode 141 and the separator 143 is represented by the following expression (34):
The expression (28) relating to the conservation law of charge within the active material can be simplified into the following expression (35). Thus, a potential φsj of the active material is also approximated as a quadratic function of x. An average potential φsj# within the active material used for calculation of the overvoltage ηj# is determined from the following expression (36) provided by integrating the expression (35) with the electrode thickness Lj. For the positive electrode 141, a difference (a potential difference) between an active material average potential φs1# and an active material potential at the boundary between the active material model 141b and a collector plate 141a is represented by the following expression (37). Similarly, for the negative electrode 142, the expression (38) holds:
Since the electrochemical reaction in each electrode is assumed to be uniform, the following expression (39) holds between the current density I(t) per unit area of the electrode plate and the reaction current density (lithium production amount) JjLi:
I(t)=−j1Li(θ1,t)L1=j2Li(θ2,t)L2 (39)
The following expression (40) holds for a battery voltage V(t) based on the potential relationship shown in
Next, an average overvoltage η#(t) is calculated. When jjLi is set to be constant, and αaj and αej are set to 0.5 with the same charge and discharge efficiency in the Butler-Volmer equation, then the following expression (42) holds. The following expression (42) is inversely transformed to determine the average overvoltage η#(t) from the following expression (43):
Average potentials φs1 and φs2 are determined with
An active material diffusion model expression (M2a) for the active material models 141b and 142b is calculated from the above expression (22′) corresponding to the conservation law of lithium concentration (diffusion equation) and the boundary condition expressions (23′) and (24′):
The first term of the right side of the model expression (M1a) represents an Open Circuit Voltage (OCV) determined by the concentration of the reaction material (lithium) at the active material surface. The second term of the right side represents the overvoltage (η1#-η2#). The third term of the right side represents the voltage drop when the current passes through secondary battery 1. Thus, the DC pure resistance of the secondary battery 1 is represented by Rd(T) in the above expression (M2a).
In the expression (M2a), diffusion coefficients Ds1 and Ds2 used as parameters for specifying the diffusion speed of the lithium corresponding to the reaction material have temperature dependence. Thus, the diffusion coefficients Ds1 and Ds2 can be set, for example by using a map shown in
For the diffusion coefficients Ds1 and Ds2, dependence on the local SOCθ may be considered in addition to the dependence on the battery temperature Tb. In this case, preferably, a map representing the correspondence between the battery temperature Tb, the local SOCθ, and the diffusion coefficients Ds1 and Ds2 is previously prepared.
As shown in
Exchange current densities i01 and i02 included in the above expression (M1a) have dependence on the local SOCθ and the battery temperature Tb. When a map representing the correspondence between the exchange current densities i01 and i02, the local SOCθ, and the battery temperature Tb is previously prepared, the exchange current densities i01 and i02 can be specified from the local SOCθ and the battery temperature Tb.
A DC pure resistance Rd has dependence on temperature Tb. When a map representing the correspondence between the DC pure resistance Rd and the battery temperature Tb is previously prepared, the DC pure resistance Rd can be specified from the battery temperature Tb. The abovementioned maps can be formed on the basis of the results of experiments such as well-known AC impedance measurements for the secondary battery 1.
The battery model shown in
The model expressions (M1a) and (M2a) can be represented by the following expressions (M1b) and (M2b), respectively. For the battery model using the single active material model, the following expression (39′) is used instead of the above expression (39) as a relationship expression of the current density I(t) and the reaction current density j1Li:
An arcsinh term in the above expression (M1a) can be linearly approximated to provide the following expression (M1c). The linear approximation can reduce the computing load and shorten the computing time.
In the above expression (M1c), the second term of the right side is represented by the product of the current density I(t) and a reaction resistance Rr as a result of the linear approximation. As shown in the above expression (45), the reaction resistance Rr is calculated from the exchange current densities i01 and i02 dependent on the local SOCθ and the battery temperature Tb. Thus, when the above expression (M1c) is used, a map representing the correspondence between the local SOCθ, the battery temperature Tb, and the exchange current densities i01 and i02 may be previously prepared. According to the above expression (M1c) and the above expression (45), the above expression (46) is obtained.
An arcsinh term corresponding to the second term of the right side in the above expression (M1b) can be linearly approximated to provide the following expression (M1d):
Next, description is made of the configuration for estimating the state of the secondary battery 1 by using the above battery model expression.
Although the current density I(t) is calculated by using the above expression (M1d) in the present embodiment, the present invention is not limited thereto. Specifically, the current density I(t) can be calculated on the basis of an arbitrary combination of any of the above expressions (M1a) to (M1d) with the above expression (M2a) or (M2b).
The diffusion estimating section 311 uses the above expression (M2b) to calculate the lithium concentration distribution within the active material based on the boundary condition set in the boundary condition setting section 315. The boundary condition is set on the basis of the above expression (23′) or the above expression (24′). The diffusion estimating section 311 uses the above expression (25) to calculate the local SOCθ based on the calculated lithium concentration distribution. The diffusion estimating section 311 outputs information about the local SOCθ to the open circuit voltage estimating section 312.
The open circuit voltage estimating section 312 specifies the open circuit voltages U1 and U2 of the electrodes 141 and 142, respectively, based on the local SOCθ calculated by the diffusion estimating section 311. Specifically, the open circuit voltage estimating section 312 can use the maps shown in
The parameter setting section 314 sets parameters used in the battery model expression in accordance with the battery temperature Tb and the local SOCθ. The temperature Tb detected by the temperature sensor 203 is used as the battery temperature Tb. The local SOCθ is obtained from the diffusion estimating section 311. The parameters set by the parameter setting section 314 include a diffusion constant Ds in the above expression (M2b), and the current density i0 and the DC resistance Rd in the above expression (M1f).
The current estimating section 313 uses the following expression (M3a) to calculate (estimate) the current density I(t). The following expression (M3a) is provided by transforming the above expression (M1d). In the following expression (M3a), an open circuit voltage U(θ, t) corresponds to an open circuit voltage U(θ) estimated in the open circuit voltage estimating section 312. A voltage V(t) corresponds to the battery voltage Vb obtained by a monitor unit 201. Rd(t) and i0(θ, T, t) are values set in the parameter setting section 314.
When any of the above expressions (M1a) to (M1d) is used, the current density I(t) can also be calculated in the same manner as that for the expression (M3a) described above.
The boundary condition setting section 315 uses the above expression (39) or the above expression (39′) to calculate the reaction current density (lithium production amount) jjLi from the current density I(t) calculated by the current estimating section 313. The boundary condition setting section 315 uses the above expression (24′) to update the boundary condition in the above expression (M2b). Once the boundary condition is updated, the lithium concentration distribution in the active material model can be calculated on the basis of the expressions (M2a) and (M2b).
Once the lithium concentration distribution in the active material model is calculated, the lithium average concentration csave can be calculated on the basis of the following expression (47):
The lithium concentration csj,k(t) (k=1 to N) shown in the expression (47) represents the lithium concentration in each area provided by dividing the active material models 141b and 142b into N in the diameter direction as shown in
Linear interpolation can be performed to specify the relationship between the lithium average concentration csave and the SOCe as shown in
The secondary battery 1 experiences a voltage drop due to a concentration overvoltage. The concentration overvoltage is caused by nonuniform concentration distribution (concentration gradient) in the electrolytic solution located between the positive electrode 141 and the negative electrode 142. When the voltage drop due to the concentration overvoltage is factored in, the expressions (M1a) to (M1d) can be replaced with the following expressions (M1a′) to (M1d′):
The expression (M3a) can be replaced with the following expression (M3a′):
The concentration overvoltage Δφe mentioned above can be represented by the following expression (49):
The expression (49) can be transformed into the following expression (50). From the expression (50), the following expression (51) can be derived:
From the expression (51), the following expression (52) can be derived:
The expression (52) can be transformed as shown in the following expression (53):
The expression (53) can be transformed as shown in the following expression (54) by linear approximation:
ΔCe shown in the expressions (53) and (54) correspond to the ion concentration imbalance dCe(t) described in Embodiment 1. The ion concentration imbalance dCe(t) is calculated as described in Embodiment 1, and then the value of the ion concentration imbalance dCe(t) can be substituted into ΔCe shown in the expressions (53) and (54).
Ce shown in the expressions (53) and (54) correspond to the average ion concentration Ceave (t) described in Embodiment 1. The average ion concentration Ceave(t) is calculated as described in Embodiment 1, and then the value of the average ion concentration Ceave(t) can be substituted into Ce shown in the expressions (53) and (54). In this manner, the concentration overvoltage Δφe can be calculated on the basis of the expressions (53) and (54).
As described in Embodiment 1, the ion concentration imbalance dCe(t) and the average ion concentration Ceave(t) are updated once in the cycle time Δt. When the concentration overvoltage Δφe is calculated on the basis of the ion concentration imbalance dCe(t) and the average ion concentration Ceave(t), the concentration overvoltage Δφe can be estimated accurately in the secondary battery 1 at the present time.
Since the concentration overvoltage Δφe can be estimated accurately, the expressions (M1a′) to (M1d′) and (M3a′) can be used to calculate the current density I(t) with the concentration overvoltage Δφe factored in. As described above, the boundary condition in the expression (M2b) is updated to calculate the lithium concentration distribution in the active material model to allow the calculation of the lithium average concentration csave. Then, the SOC of the secondary battery 1 can be calculated from the lithium average concentration csave Since the SOC of the secondary battery 1 is calculated in this manner, the accurate estimation of the concentration overvoltage Δφe can also improve the estimation accuracy of the SOC.
Next, the processing of calculating the SOC of the secondary battery 1 is described with reference to a flow chart shown in
At step S701, the controller 300 (battery state estimating section 310) detects the voltage (battery voltage) Vb of the secondary battery 1 based on the output from the monitor unit 201. At step S702, the controller 300 (battery state estimating section 310) detects the temperature (battery temperature) Tb of the secondary battery 1 based on the output from the temperature sensor 203.
At step S703, the controller 300 (diffusion estimating section 311) calculates the local SOCθ based on the lithium concentration distribution in the previous computing with the above expression (M2b). At step S704, the controller 300 (open circuit voltage estimating section 312) calculates the open circuit voltage U(θ) from the local SOCθ calculated in the processing at step S703.
At step S705, the controller 300 calculates the concentration overvoltage Δφe based on the expression (53) or the expression (54). For calculating the concentration overvoltage Δφe, the ion concentration imbalance dCe(t) and the average ion concentration Ceave(t) are calculated as described in Embodiment 1 in advance. The ion concentration imbalance dCe(t) is calculated with the processing described in
At step S706, the controller 300 (current estimating section 313) calculates (estimates) a current density Im(t) with the above expressions (M1a′) to (M1d′) and (M3a′). The current density Im(t) is calculated, for example, by substituting the battery voltage Vb, the open circuit voltage U(θ) calculated in the processing at step S704, the concentration overvoltage Δφe calculated in the processing at step S705, and the parameter values set in the parameter setting section 314 into the above expression (M3a′).
At step S707, the controller 300 (boundary condition setting section 315) calculates the reaction current density (lithium production amount) jjLi from the current density I(t) calculated in the processing at step S706. The controller 300 (boundary condition setting section 315) also uses the calculated reaction current density to set the boundary condition (active material interface) at the active material interface in the above expression (M2b).
At step S708, the controller 300 (diffusion estimating section 311) uses the above expression (M2b) to calculate the lithium concentration distribution within the active material model and updates the estimated value of the lithium concentration in each area. The lithium concentration (updated value) in the outermost divided area is used for calculating the local SOCθ in the processing at step S703 next time the processing shown in
At step S709, the controller 300 calculates the lithium average concentration csave within the positive electrode active material. As described above, the lithium average concentration csave is calculated from the lithium concentration distribution calculated in the processing at step S708. At step S710, the controller 300 calculates the SOC of the secondary battery 1. Specifically, the controller 300 uses the correspondence shown in
Although the processing shown in
In this case, the average ion concentration Ceave(t) can be a fixed value in a predetermined time period longer than the cycle time Δt. Specifically, the average ion concentration Ceave(t) used in the predetermined time period can be provided by using the average ion concentration Ceave(t) calculated immediately before the measurement of the predetermined time period is started. The predetermined time period may be a time period from the start of the running to the end of the running of the vehicle, for example.
| Filing Document | Filing Date | Country | Kind |
|---|---|---|---|
| PCT/JP2013/000581 | 2/1/2013 | WO | 00 |
| Publishing Document | Publishing Date | Country | Kind |
|---|---|---|---|
| WO2014/118824 | 8/7/2014 | WO | A |
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| 20150338468 A1 | Nov 2015 | US |
