JP6363426B2 - Battery system - Google Patents

Description

  The present invention relates to a battery system capable of grasping an uneven salt concentration in an electrolytic solution.

  As described in Patent Document 1, it is known that the internal resistance value of the secondary battery increases when the salt concentration in the electrolytic solution is biased. In Patent Document 1, when the difference between the estimated current density estimated from the battery model and the measured current density measured by the current measurement unit (current sensor) increases, the salt concentration bias increases, and the secondary battery Recognizes that the internal resistance value of s. Under this recognition, the ratio of the estimated current density and the measured current density is calculated as the battery resistance increase rate.

JP 2010-060406 A (paragraphs [0127] to [0132])

  Patent Document 1 only recognizes the condition (difference between the estimated current density and the measured current density) when the salt concentration bias increases, and does not recognize the cause of the salt concentration bias. Moreover, in patent document 1, based on the difference of an estimated current density and a measured current density, only the bias | inclination of salt concentration is grasped | ascertained indirectly. According to the inventor of the present application, it has been found that the salt concentration is biased by the volume change (expansion and contraction) of the electrolytic solution. According to this knowledge, it is possible to directly grasp the deviation of the salt concentration in the electrolytic solution.

  The battery system of the present invention includes a secondary battery, a restraining member, and a controller. In a secondary battery, a power generation element and an electrolytic solution are accommodated in a battery case, and the power generation element has an electrode plate containing an active material, and performs charge and discharge. The restraining member has a protrusion that contacts the outer surface of the battery case, and applies a restraining load in a predetermined direction to the secondary battery via the protrusion. The controller calculates the distribution of the salt concentration in the electrolytic solution impregnated in the power generation element.

  The controller uses a liquid flow equation that defines the flow of the electrolyte, and the flow rate when the electrolyte flows from the inside of the power generation element to the outside of the power generation element, and from the outside of the power generation element to the inside of the power generation element. The flow rate at which the electrolyte flows is calculated for each position in the power generation element in the direction in which the electrolyte flows. And a controller calculates distribution of the salt concentration in an electric power generation element based on the flow velocity for every position in an electric power generation element. When calculating the flow rate, a liquid flow equation is used that includes as parameters the pressure of the electrolyte, the density of the electrolyte that changes according to the temperature of the secondary battery, and the volume fraction of the electrolyte in the power generation element.

  The bias in the salt concentration is generated by the flow of the electrolyte solution from the inside of the power generation element to the outside of the power generation element and the flow of the electrolyte solution from the outside of the power generation element to the inside of the power generation element. It has been found that such a flow of the electrolytic solution is generated by a volume change (expansion and contraction) of the electrolytic solution and a volume change (expansion and contraction) of the active material. The volume change of the electrolytic solution depends on the temperature of the secondary battery, and is defined by the density of the electrolytic solution that changes according to the temperature of the secondary battery. Further, when the volume change of the active material occurs, the volume fraction of the electrolytic solution in the power generation element changes. For this reason, if the flow rate of the electrolytic solution is calculated using the liquid flow equation including the density and volume fraction of the electrolytic solution as parameters, the concentration of the salt generated due to the volume change of the electrolytic solution or active material (that is, the salt concentration) Distribution).

  Here, the volume fraction of the electrolytic solution is calculated based on the amount of change in the volume fraction. Further, the amount of change in the volume fraction is calculated from the amount of volume change in the space where the electrolytic solution exists in the power generation element. The volume change amount of the space where the electrolyte solution exists is calculated based on the volume change amount of the power generation element excluding the electrolyte solution and the volume change amount of the power generation element including the electrolyte solution. The volume change amount of the power generation element excluding the electrolyte is calculated from the volume expansion coefficient of the power generation element excluding the electrolyte. The volume change amount of the power generation element including the electrolytic solution is the volume change amount in the first region in the power generation element facing the protrusion in the predetermined direction and the second region in the power generation element not facing the protrusion in the predetermined direction. It is the amount added. The volume change amount in the first region and the second region is calculated based on the pressure of the electrolytic solution.

  The power generation element receives a restraining load from the restraining member, but the restraining loads received by the first region and the second region are different from each other. Accordingly, the volume change amount of the first region and the volume change amount of the second region are different from each other. Therefore, in the present invention, the volume change amount of the power generation element including the electrolytic solution is calculated after calculating the volume change amounts in the first region and the second region, respectively. Accordingly, the volume change amount of the power generation element including the electrolytic solution can be calculated in consideration of the difference in volume change between the first region and the second region.

It is a figure which shows the structure of a battery system. It is a figure which shows the structure of a secondary battery. It is an expanded view of an electric power generation element. It is an external view of a power generation element. It is a top view which shows a secondary battery and a partition member. It is a figure explaining the bias | inclination of the salt concentration in the direction where a negative electrode plate and a positive electrode plate oppose. It is a figure explaining the bias | inclination of the salt concentration on each surface of a negative electrode plate and a positive electrode plate. It is a figure explaining the direction through which electrolyte solution flows by expansion and contraction of electrolyte solution. It is a figure which shows the relationship between the variation | change_quantity of the volume of an electric power generation element, and the pressure of electrolyte solution. It is a figure which shows the relationship between resistance increase amount and salt concentration difference. It is a flowchart explaining the process which calculates salt concentration distribution. It is a flowchart explaining the process which controls charging / discharging of a secondary battery.

  Examples of the present invention will be described below.

  The battery system of the present invention will be described with reference to FIG. The assembled battery 1 is connected to the load 2 via the positive electrode line PL and the negative electrode line NL. The assembled battery 1 has a plurality of secondary batteries (unit cells) 10 connected in series. The assembled battery 1 may include a plurality of secondary batteries 10 connected in parallel. The load 2 operates by receiving power output from the assembled battery 1. The load 2 can also generate power, and the electric power generated by the load 2 is supplied to the assembled battery 1. Thereby, the assembled battery 1 is charged.

  The battery system shown in FIG. 1 can be mounted on a vehicle, for example. A motor / generator can be used as the load 2. The motor / generator receives the electric power output from the assembled battery 1 and generates power for running the vehicle. The power generated by the motor / generator is transmitted to the wheels. The motor / generator can convert kinetic energy generated during braking of the vehicle into electric power and supply the electric power to the assembled battery 1.

  The monitoring unit 31 detects the voltage value Vb of each secondary battery 10 and outputs the detection result to the controller 40. The current sensor 32 detects the current value Ib of the secondary battery 10 and outputs the detection result to the controller 40. In the present embodiment, the current value Ib when the secondary battery 10 is discharged is a positive value, and the current value Ib when the secondary battery 10 is charged is a negative value.

  The controller 40 can control charging / discharging of the secondary battery 10 based on the voltage value Vb and the current value Ib. Further, the controller 40 can calculate the SOC (State of Charge) of the secondary battery 10 based on the voltage value Vb and the current value Ib. The SOC is the ratio of the current charge capacity to the full charge capacity. As a method for calculating the SOC, a known method can be adopted as appropriate, and a detailed description regarding the method for calculating the SOC is omitted.

  The temperature sensor 33 detects the temperature (battery temperature) Tb of the assembled battery 1 (secondary battery 10), and outputs the detection result to the controller 40. Here, a plurality of temperature sensors 33 may be arranged. By using the plurality of temperature sensors 33, it is possible to detect the temperatures Tb of the plurality of secondary batteries 10 arranged at different positions. The controller 40 has a memory 41. The memory 41 stores information used when the controller 40 performs predetermined processing (particularly processing described in the present embodiment). Note that the memory 41 can also be provided outside the controller 40.

  Next, the structure of the secondary battery 10 will be described with reference to FIG. In FIG. 2, the X axis and the Z axis are axes orthogonal to each other. In this embodiment, the axis corresponding to the vertical direction is the Z axis. Note that an axis orthogonal to the X axis and the Z axis is defined as a Y axis.

  The secondary battery 10 includes a battery case 110 and a power generation element 120. The battery case 110 houses the power generation element 120. The battery case 110 is hermetically sealed, and an electrolytic solution is injected into the battery case 110. A negative electrode terminal 111 and a positive electrode terminal 112 are fixed to the battery case 110. The negative electrode terminal 111 and the positive electrode terminal 112 are electrically connected to the power generation element 120.

  The power generation element 120 is an element that performs charging and discharging, and as shown in FIG. 3, a negative electrode plate (corresponding to the electrode plate of the present invention) 121, a positive electrode plate (corresponding to the electrode plate of the present invention) 122, And a separator 123. FIG. 3 is a developed view of a part of the power generation element 120. The negative electrode plate 121 includes a current collector foil 121a and a negative electrode active material layer 121b formed on the surface of the current collector foil 121a. The negative electrode active material layer 121b includes a negative electrode active material, a conductive agent, a binder, and the like. The negative electrode active material layer 121b is formed in a part of the current collector foil 121a, and the negative electrode active material layer 121b is not formed in the remaining region of the current collector foil 121a.

  The positive electrode plate 122 includes a current collector foil 122a and a positive electrode active material layer 122b formed on the surface of the current collector foil 122a. The positive electrode active material layer 122b includes a positive electrode active material, a conductive agent, a binder, and the like. The positive electrode active material layer 122b is formed in a part of the current collector foil 122a, and the positive electrode active material layer 122b is not formed in the remaining region of the current collector foil 122a.

  The negative electrode active material layer 121b, the positive electrode active material layer 122b, and the separator 123 are impregnated with an electrolytic solution. This electrolytic solution exists inside the power generation element 120. On the other hand, an electrolyte as an excess liquid is also present outside the power generation element 120, in other words, in a space formed between the power generation element 120 and the battery case 110.

  The power generation element 120 is configured by laminating the negative electrode plate 121, the positive electrode plate 122, and the separator 123 in the order shown in FIG. 3 and winding the laminate around the X axis in the direction of the arrow D shown in FIG. . Here, a separator 123 is disposed between the negative electrode plate 121 and the positive electrode plate 122.

  At one end of the power generation element 120 in the direction in which the X axis extends (referred to as the X direction), only the current collector foil 121a of the negative electrode plate 121 is wound. The portion where only the current collector foil 121a is wound is electrically connected to the negative electrode terminal 111 shown in FIG. Further, only the current collector foil 122a of the positive electrode plate 122 is wound at the other end of the power generation element 120 in the X direction. The portion where only the current collector foil 122a is wound is electrically connected to the positive terminal 112 shown in FIG.

  In the present embodiment, as described above, the power generation element 120 is configured by winding the laminate, but the present invention is not limited thereto. Specifically, the power generation element 120 can also be configured by simply stacking the negative electrode plate 121, the positive electrode plate 122, and the separator 123 without winding a laminate.

  A region A illustrated in FIG. 4 is a region in which the negative electrode active material layer 121b and the positive electrode active material layer 122b face each other with the separator 123 interposed therebetween. In region A, a chemical reaction is performed in accordance with charge / discharge of secondary battery 10 (power generation element 120).

  The plurality of secondary batteries 10 constituting the assembled battery 1 are arranged side by side in the direction in which the Y axis extends (referred to as the Y direction), and between two secondary batteries 10 that are adjacent in the Y direction, FIG. A partition member 20 (corresponding to the restraining member of the present invention) 20 is disposed. A plurality of protrusions 21 are provided on one end surface of the partition member 20 in the Y direction. Each protrusion 21 protrudes in the Y direction, and the tip of the protrusion 21 is in contact with the outer surface of the battery case 110. The other end surface of the partition member 20 in the Y direction is a flat surface and is in contact with the battery case 110 as shown in FIG.

  By bringing the protrusion 21 into contact with the battery case 110, a space is formed between the partition member 20 and the battery case 110, and this space is a heat exchange medium (air) for adjusting the temperature of the secondary battery 10. Etc.) becomes a moving path. It is sufficient if a space can be formed between the partition member 20 and the battery case 110, and the shape of the protrusion 21 can be designed as appropriate.

  A pair of end plates (not shown) are disposed at both ends of the assembled battery 1 in the Y direction, and both ends of a connecting member extending in the Y direction are fixed to the pair of end plates. The secondary battery 10 receives a restraining load from the partition member 20 by displacing the pair of end plates in a direction approaching each other (Y direction). This restraining load is a load that restrains the secondary battery 10 in the Y direction (corresponding to a predetermined direction of the present invention).

  As illustrated in FIG. 5, the region A of the power generation element 120 includes a first region A11 that faces the protruding portion 21 in the Y direction and a second region A12 that does not face the protruding portion 21 in the Y direction. The first region A11 is susceptible to a load from the protrusion 21 and the second region A12 is less likely to receive a load from the protrusion 21. For this reason, the load which 1st area | region A11 receives becomes higher than the load which 2nd area | region A12 receives.

  In the secondary battery 10, the internal resistance value of the secondary battery 10 increases due to the occurrence of a bias in the salt concentration in the electrolytic solution. Such an increase amount of the internal resistance value is defined as a resistance increase amount Rh. The resistance increase amount Rh is different from the increase amount of the internal resistance value accompanying the deterioration of the secondary battery 10. The amount of increase in the internal resistance value due to the deterioration only increases and does not decrease. On the other hand, since the resistance increase amount Rh depends on the bias of the salt concentration, the resistance increase amount Rh increases as the salt concentration is biased, and the resistance increase amount Rh decreases as the salt concentration bias is relaxed.

  As a state of uneven concentration of salt, there are states shown in FIGS. FIG. 6 shows a state in which an uneven salt concentration occurs in the direction (Y direction) in which the negative electrode plate 121 and the positive electrode plate 122 face each other. In FIG. 6, a schematic diagram showing the positional relationship between the negative electrode plate 121, the positive electrode plate 122, and the separator 123 (the upper diagram in FIG. 6), and a diagram showing an example of the salt concentration distribution (the lower diagram in FIG. 6). Represents.

  In the diagram showing the salt concentration distribution, the vertical axis is the salt concentration, and the horizontal axis is the position in the Y direction. In FIG. 6 (upper view), the negative electrode plate 121 and the positive electrode plate 122 are separated from the separator 123, but actually, the negative electrode plate 121 and the positive electrode plate 122 are in contact with the separator 123. As shown in FIG. 6 (lower diagram), when the secondary battery 10 is charged, a salt concentration distribution indicated by a solid line may occur as a deviation in salt concentration. Further, when the secondary battery 10 is discharged, a salt concentration distribution indicated by an alternate long and short dash line may occur as a deviation in salt concentration.

  In addition, although FIG. 6 shows the deviation of the salt concentration in the Y direction, it is not limited to this. As described above, in the power generation element 120 of the present embodiment, since the negative electrode plate 121 and the positive electrode plate 122 are wound around the X axis, the negative electrode plate 121 (negative electrode active material layer 121b) and the positive electrode plate 122 (positive electrode active) are wound. In the direction in which the material layer 122b opposes, the same salt concentration deviation as in FIG. 6 occurs.

  When the secondary battery 10 is charged / discharged, the salt moves between the negative electrode plate 121 and the positive electrode plate 122 in the direction in which the negative electrode plate 121 and the positive electrode plate 122 face each other (for example, the Y direction shown in FIG. 6). When the secondary battery 10 is a lithium ion secondary battery, this salt becomes a lithium salt. When the salt moves in the direction in which the negative electrode plate 121 and the positive electrode plate 122 face each other, the salt concentration is uneven in the direction in which the negative electrode plate 121 and the positive electrode plate 122 face each other.

  FIG. 7 shows a state in which an uneven salt concentration occurs on the surface of each of the negative electrode plate 121 and the positive electrode plate 122 (in the region A). In response to the occurrence of the salt concentration bias shown in FIG. 6, the salt concentration bias shown in FIG. 7 occurs. In FIG. 7, a part of the negative electrode plate 121 including the region A and a part of the positive electrode plate 122 including the region A are illustrated separately. Here, a part of the negative electrode plate 121 and a part of the positive electrode plate 122 are opposed to each other with the separator 123 interposed therebetween.

  As shown by the arrows in FIG. 7, the salt concentration bias tends to occur in the X direction in the region A. FIG. 7 also shows a salt concentration distribution (one example) in the region A in each of the negative electrode plate 121 and the positive electrode plate 122. In the diagram showing the salt concentration distribution, the vertical axis is the salt concentration, and the horizontal axis is the position in the X direction. Here, when the secondary battery 10 is charged, a salt concentration distribution indicated by a solid line may occur as a deviation in salt concentration. Further, when the secondary battery 10 is discharged, a salt concentration distribution indicated by an alternate long and short dash line may occur as a deviation in salt concentration.

  As described above, the negative electrode plate 121 (current collector foil 121a) and the positive electrode plate 122 (current collector foil 122a) are only wound around the X axis at both ends of the power generation element 120 in the X direction. For this reason, electrolyte solution tends to pass in the both ends of the electric power generation element 120 in a X direction. In other words, the electrolytic solution easily moves from the inside of the power generation element 120 toward the outside of the power generation element 120, or the electrolytic solution easily moves from the outside of the power generation element 120 toward the inside of the power generation element 120.

  As a result, as shown in FIG. 7, the salt concentration tends to be biased in the X direction in the region A. As described above, even when the negative electrode plate 121, the positive electrode plate 122, and the separator 123 are simply stacked, the electrolytic solution moves from the inside of the power generation element 120 toward the outside of the power generation element 120, It is easy for the electrolyte to move from the outside to the inside of the power generation element 120.

  It was found that the salt concentration deviation shown in FIG. 7 is generated by the flow of the electrolyte. Further, it was found that the flow of the electrolytic solution is generated by the volume change (expansion and contraction) of the electrolytic solution. Specifically, when the electrolytic solution expands, a flow of the electrolytic solution from the inside of the power generation element 120 toward the outside of the power generation element 120 is generated in the X direction. That is, in FIG. 8, the electrolyte flows in the direction indicated by the arrow X1 with the center C of the region A in the X direction as a reference. On the other hand, when the electrolytic solution contracts, a flow of the electrolytic solution from the outside of the power generation element 120 toward the inside of the power generation element 120 is generated in the X direction. That is, in FIG. 8, the electrolyte flows in the direction toward the center C of the region A (the direction indicated by the arrow X2). When the electrolyte flows in the directions indicated by the arrows X1 and X2, the salt concentration unevenness shown in FIG. 7 occurs.

  Therefore, in this embodiment, the flow (flow velocity) of the electrolytic solution generated by the expansion and contraction of the electrolytic solution is calculated, thereby grasping the salt concentration bias (salt concentration distribution) shown in FIG. If the deviation of the salt concentration shown in FIG. 7 is grasped, for example, the resistance increase amount Rh generated by the deviation of the salt concentration can be grasped. The distribution of salt concentration in the present invention is the salt concentration distribution shown in FIG.

  Hereinafter, a method for calculating the flow (flow velocity) of the electrolyte will be described.

  Equation (1) below is an equation that defines the flow of the electrolyte, and is known as the Brinkman-Navier-Stokes equation. The following formula (2) is a continuous formula regarding the flow of the electrolyte, and is a formula derived from the law of conservation of mass. The following formulas (1) and (2) correspond to the liquid flow equation of the present invention.

In the above formulas (1) and (2), u _j is the flow rate of the electrolytic solution, ρ is the density of the electrolytic solution, ε _{e, j} is the volume fraction of the electrolytic solution, and t is the time. In the above formula (1), μ is the viscosity of the electrolytic solution, K _j is the transmission coefficient, and p is the pressure of the electrolytic solution.

  Here, the subscript j is used to distinguish the negative electrode plate 121, the positive electrode plate 122, and the separator 123, and the subscript j includes “n”, “p”, and “s”. When the subscript j is “n”, a value related to the negative electrode plate 121 is shown. When the subscript j is “p”, a value related to the positive electrode plate 122 is shown. When the subscript j is “s”, a value related to the separator 123 is shown. Indicates.

As described above, the negative electrode plate 121 (negative electrode active material layer 121b), the positive electrode plate 122 (positive electrode active material layer 122b), and the separator 123 are impregnated with the electrolytic solution. For this reason, parameters relating to the electrolyte (flow velocity u _j , volume fraction ε _{e, j} , transmission coefficient K _j ) are defined for each of negative electrode plate 121, positive electrode plate 122, and separator 123. In this specification, the subscript j may be used in addition to the parameters shown in the above formulas (1) and (2).

  As the viscosity μ, a predetermined fixed value can be used, or the viscosity μ can be changed according to the temperature of the electrolytic solution. As the temperature of the electrolytic solution, the battery temperature Tb detected by the temperature sensor 33 is used. If information (map or arithmetic expression) indicating the correspondence relationship between the viscosity μ and the battery temperature Tb is prepared in advance by an experiment or the like, the viscosity μ can be specified by detecting the battery temperature Tb. Information indicating the correspondence between the viscosity μ and the battery temperature Tb is stored in the memory 41.

The density ρ is a parameter that defines expansion and contraction of the electrolytic solution, and indicates a value corresponding to the expansion and contraction of the electrolytic solution. The expansion and contraction of the electrolytic solution depend on the temperature of the electrolytic solution (that is, the battery temperature Tb), and the density ρ also depends on the temperature of the electrolytic solution (battery temperature Tb). Therefore, if information (map or arithmetic expression) indicating the correspondence relationship between the density ρ and the battery temperature Tb is prepared in advance by experiments or the like, the density ρ can be specified by detecting the battery temperature Tb. By specifying the density ρ, the expansion and contraction of the electrolytic solution can be grasped. Information indicating the correspondence relationship between the density ρ and the battery temperature Tb is stored in the memory 41. A predetermined fixed value can be used as the transmission coefficient K _j . A method for calculating the volume fraction ε _{e, j} will be described later.

In the above equation (1), since the flow velocity u _j and the pressure p are unknown, the continuous equation shown in the above equation (2) is defined and the simultaneous equations of the above equations (1) and (2) are solved to obtain the flow velocity. u _j and pressure p can be calculated. Since the above equations (1) and (2) include the density ρ that defines the expansion and contraction of the electrolytic solution, by solving the simultaneous equations of the above equations (1) and (2), A flow rate u _j corresponding to the expansion and contraction can be calculated. The flow velocity u _j includes the flow velocity in the direction indicated by the arrow X1 in FIG. 8 and the flow velocity in the direction indicated by the arrow X2 in FIG. When calculating the flow velocity u _j , for example, the convergence calculation can be performed using the above formulas (1) and (2). In addition, the calculations using the above formulas (1) and (2) are performed in a predetermined cycle, but the flow velocity u _j can be calculated by using the value calculated in the previous calculation cycle in the current calculation cycle.

In the negative electrode plate 121, the electrolytic solution moves inside the negative electrode active material layer 121b. For this reason, the flow velocity u _j (that is, the flow velocity u _n ) is calculated for each position in the negative electrode active material layer 121b. When gripping the bias of salt concentration shown in FIG. 7, at different positions in the X direction, the flow velocity u _n is calculated.

In the positive electrode plate 122, the electrolytic solution moves inside the positive electrode active material layer 122b. For this reason, the flow velocity u _j (that is, the flow velocity u _p ) is calculated for each position in the positive electrode active material layer 122b. When gripping the bias of salt concentration shown in FIG. 7, at different positions in the X direction, the flow velocity u _p is computed. In the separator 123, the electrolyte moves inside. For this reason, the flow velocity u _j (that is, the flow velocity u _s ) is calculated for each position in the separator 123. When gripping the bias of salt concentration shown in FIG. 7, at different positions in the X direction, the flow velocity u _s is calculated.

  On the other hand, in the above equations (1) and (2), the above equation (1) can be simplified after assuming various conditions. Hereinafter, a method (an example) for simplifying the above equation (1) will be described.

Assuming that the density ρ of the electrolyte is constant regardless of the position (including the position in the X direction) where the flow velocity u _j is calculated, the above expression (2) is expressed by the following expression (3).

The following formula (4) can be derived from the above formula (3). V _p , v _n , and v _s shown in the following formula (4) are kinematic viscosity coefficients (v = μ / ρ) of the electrolytic solution in each of the positive electrode plate 122, the negative electrode plate 121, and the separator 123. X and y shown in the following formula (4) indicate positions in the X direction and the Y direction, respectively. Here, the Y direction is a direction in which the negative electrode plate 121 and the positive electrode plate 122 face each other with the separator 123 interposed therebetween (up and down direction in FIG. 8).

  Considering the continuity of the electrolytic solution, the above formula (4) is represented by the following formula (5).

  On the other hand, in the above formula (1), the following formula (7) is obtained by assuming the following formula (6).

  Assuming that the pressure distribution in the negative electrode plate 121, the positive electrode plate 122, and the separator 123 is equal to each other with respect to the pressure distribution of the electrolytic solution in the X direction, the following formula (8) is obtained.

According to the above formulas (5) and (8), the following formula (9) can be derived. Formula (9), in the negative electrode plate 121, it shows a flow velocity _{u n} in accordance with the position in the X direction. X shown in the following formula (9) indicates a position in the X direction.

The above expression (9) is integrated in the x, when the flow velocity u _n when x is 0 assuming 0, the following equation (10) is obtained. Here, the position when x is 0 indicates one end of the region A in the X direction. Further, if the length of the region A in the X direction is L, x is L at the other end of the region A in the X direction.

Similar to the flow velocity _{u n,} the flow velocity _u p, _{u s} formula (11), represented by (12).

The formula (10) to (12) become expressions simplify the above equation (1), the negative electrode plate 121, in each of the positive electrode plate 122 and the separator 123, the flow velocity _u n in accordance with the position in the X _{direction, u} p, It can be calculated u _s. The above formulas (10) to (12) correspond to the liquid flow equation in the present invention. The equation for calculating the flow rate u _{j of the} electrolytic solution is not limited to the above (1), (2), and (10) to (12). Since the flow of the electrolytic solution is generated by the volume change of the electrolytic solution, the present invention can be used as long as the equation includes the density of the electrolytic solution that defines the volume change of the electrolytic solution as a parameter (variable) and can define the flow of the electrolytic solution. Applicable.

If the flow velocity u _j is calculated, the salt concentration c _{e, j} in the electrolytic solution can be calculated based on the following equation (13). Here, when calculating the salt concentration _{c e, j,} the flow rate _{u n,} u p, may be taking into account all _{u s,} a part of the flow velocity _{u n,} u p, _{u s} (e.g., velocity u Only _n ) may be considered.

In the above formula (13), D _{e, j} ^eff is the effective diffusion coefficient of the electrolytic solution, and t ₊ ⁰ is the transport number of the salt in the electrolytic solution. F is a Faraday constant, and j _j is the amount of salt produced in the electrolytic solution in a unit volume and unit time.

The first term on the left side of the above equation (13) defines the change in salt concentration over a predetermined time Δt. The second term on the left side of the equation (13) defines a change in salt concentration depending on the flow of the electrolyte (flow velocity u _j ). The first term on the right side of the above formula (13) defines the diffusion state of the salt in the electrolytic solution. The second term on the right side of the formula (13) defines the amount of salt produced. Here, when the secondary battery 10 is discharged, salt is generated on the surface of the negative electrode plate 121 (negative electrode active material layer 121b), and when the secondary battery 10 is charged, the surface of the positive electrode plate 122 (positive electrode active material layer 122b). ) To form a salt.

Next, a method for calculating the volume fraction ε _{e, j} will be described. The flow of the electrolytic solution is generated by the expansion and contraction of the active material (positive electrode active material or negative electrode active material) in addition to the expansion and contraction of the electrolytic solution. The volume of each active material layer 121b, 122b changes due to the expansion and contraction of the active material. When the volume of each active material layer 121b, 122b changes, the volume fraction ε _{e, j} changes in accordance with the change in the volume of the space in which the electrolyte exists in each active material layer 121b, 122b.

In each of the positive electrode active material layer 122b, the negative electrode active material layer 121b, and the separator 123 _, the change amount ΔV _{e, j} of the volume V _{e, j} of the space where the electrolytic solution exists is calculated based on the following formula (14). .

In the above formula (14), V _{s, j} represents the volume (V _{s, n} , V _{s, p} ) of the active material contained in each active material layer 121b, 122b in each active material layer 121b, 122b, In the separator 123, the volume (V _{s, s} ) of the separator 123 itself is shown. Here, the volume V _{s, j} is the volume of the power generation element 120 excluding the electrolyte. Then, the change amount of the volume V _{s, j} becomes ΔV _{s, j} . V _{all, j} is the sum of volume V _{s, j} and volume V _{e, j} . Here, the volume V _{all, j} is the volume of the power generation element 120 including the electrolytic solution. Then, the change amount of the volume V _{all, j} is ΔV _{all, j} .

The change amount ΔV _{all, j} and the change amount ΔV _{s, j} are expressed by the following equations (15) and (16).

The volume V _{all, j} is the sum of the volumes V _{s, j} , V _{e, j} in the first region A11 and the second region A12. Therefore, as shown in the equation (15), the amount of change [Delta] V _{all, j} is the variation [Delta] V ₁₁ volume (total volume _{V s, j, V e,} j) in the first region A11 shown in FIG. 5 _{, J} and the change amount ΔV _{12, j} of the volume (total of volumes V _{s, j} , V _{e, j} ) in the second region A12 shown in FIG. Here, as shown in FIG. 5, since a plurality of first regions A11 are provided, the amount of change ΔV11 _{, j} is the sum of the amount of change in volume in all the first regions A11. Similarly, the change amount ΔV _{12, j} is the sum of the change amounts of the volumes in all the second regions A12.

Each change amount ΔV _{11, j} , ΔV _{12, j} depends on the pressure p of the electrolytic solution. For this reason, the correspondence (map or arithmetic expression) between each change amount ΔV _{11, j} , ΔV _{12, j} and the pressure p can be obtained in advance based on experiments or the like. FIG. 9 shows a correspondence relationship (an example) between each change amount ΔV _{11, j} , ΔV _{12, j} and the pressure p. As shown in FIG. 9, according to the change of the pressure p, each variation | change_quantity (DELTA) V11 _{, j} , (DELTA) V12 _{, j} changes. However, as the pressure p is higher, the change amounts ΔV _{11, j} and ΔV _{12, j} are less likely to change.

Here, when the pressures p are equal, the change amount ΔV _{12, j} is larger than the change amount ΔV _{11, j} . Since the load received by the second region A12 is lower than the load received by the first region A11, the change amount ΔV12 _{, j} is larger than the change amount ΔV11 _{, j} . When calculating each change amount ΔV _{11, j} , ΔV _{12, j} based on the correspondence relationship between each change amount ΔV _{11, j} , ΔV _{12, j} and the pressure p, the pressure p is calculated in the previous calculation cycle. The value of the pressure p can be used.

As described above, the loads received by the first region A11 and the second region A12 are different from each other. For this reason, the amount of change in volume in the first region A11 is different from the amount of change in volume in the second region A12. Therefore, as described above, the difference in volume change between the first region A11 and the second region A12 is calculated by calculating the change amounts ΔV11 _{, j} , ΔV12 _{, j} in the first region A11 and the second region A12. The amount of change ΔV _{all, j} can be calculated in consideration of

In the above formula (16), β _j (specifically β _n or β _p ) is a volume expansion coefficient of the active material (negative electrode active material or positive electrode active material). As the volume fraction ε _{e, j} and volume V _{all, j} shown in the above equation (16), values calculated in the previous calculation cycle are used.

Here, when the amount of change Δε _{e, j} is first calculated, a value corresponding to the battery temperature Tb or the SOC of the secondary battery 10 can be used as the previous volume fraction ε _{e, j} . If information indicating a correspondence relationship between at least one of the battery temperature Tb and the SOC and the volume fraction ε _{e, j} is obtained in advance by an experiment or the like, the volume fraction ε _e is specified by specifying the battery temperature Tb or the SOC. _{, J} can be specified.

The volume expansion coefficient β _j can be calculated from the linear expansion coefficient α _j . That is, a value that is three times the linear expansion coefficient α _j is the volume expansion coefficient β _j . Here, since the linear expansion coefficient α _j depends on the battery temperature Tb and the SOC of the secondary battery 10, the linear expansion coefficient α _j can be specified from at least one of the battery temperature Tb and the SOC. For example, if information (map or arithmetic expression) indicating a correspondence relationship between the linear expansion coefficient α _j and the battery temperature Tb is prepared in advance by an experiment or the like, the linear expansion coefficient α _j can be specified by detecting or estimating the battery temperature Tb. . Further, if information (map or arithmetic expression) indicating the correspondence relationship between the linear expansion coefficient α _j and the SOC is prepared in advance by experiments or the like, the linear expansion coefficient α _j can be specified by estimating the SOC. Information indicating the correspondence relationship described above can be stored in the memory 41. Note that the volume expansion coefficient β _j can also be directly calculated from at least one of the battery temperature Tb and the SOC without calculating the linear expansion coefficient α _j .

In the above description, the transmission coefficient K _j is a fixed value, but the transmission coefficient K _j can be changed based on the volume expansion coefficient β _j . Specifically, if information (map or arithmetic expression) indicating a correspondence relationship between the transmission coefficient K _j and the volume expansion coefficient β _j is prepared in advance by an experiment or the like, the transmission coefficient K _j corresponding to the volume expansion coefficient β _j is prepared. Can be identified. The transmission coefficient K _j specified in this way can be used in the above formula (1) or the above formulas (10) to (12).

If the change amounts ΔV _{all, j} , ΔV _{s, j} are calculated based on the equations (15) and (16), the change amount ΔV _{e, j} can be calculated based on the equation (14). Here, since the above-mentioned formula (14) contains a volume expansion factor beta _j, can be calculated change amount [Delta] V _e, a _j based on the volumetric expansion rate beta _j.

In the equations for calculating the flow rate u _{j of the} electrolyte (the above equations (1), (10) to (12)), the change amount ΔV _{e, j} is not included as a parameter. However, when the volume of the space in which the electrolytic solution exists changes, the volume fraction ε _{e, j} of the electrolytic solution changes, so that the change amount ΔV _{e, j} can be converted into the change amount Δε _{e, j} . Specifically, when it is assumed that the volume V _{all, j} is a predetermined constant volume V _{all_model, j} , the volume V _{all_model, j} and the change amount ΔV _{e, j are expressed} as shown in the following equation (17). From this, the change amount Δε _{e, j} can be calculated.

If the change amount Δε _{e, j} is calculated, the current volume fraction ε _{e, j} is calculated by adding the change amount Δε _{e, j} to the volume fraction ε _{e, j} calculated in the previous calculation cycle. it can. Using the volume fraction ε _{e, j} calculated this time, the flow velocity u _j can be calculated based on the above formulas (1) and (2) or based on the above formulas (10) to (12). Also, the volume fraction ε _{e, j} calculated this time can be used when calculating the salt concentration c _{e, j} based on the above equation (13).

In addition to the change amounts Δε _{e, n} , Δε _{e, p} related to the active material layers 121b, 122b _{, the} change amount Δε _{e, s} related to the separator 123 may be calculated. When calculating the change amount Δε _{e, s} , the volume expansion coefficient β _j (that is, β _s ) shown in the above equation (16) is the volume expansion coefficient of the material constituting the separator 123. The volume expansion rate β _s depends on the battery temperature Tb. For this reason, if information (map or arithmetic expression) indicating a correspondence relationship between the volume expansion rate β _s and the battery temperature Tb is prepared in advance by an experiment or the like, the volume expansion rate β _s is specified by detecting or estimating the battery temperature Tb. it can.

According to the above formula (13), it is possible to grasp the uneven salt concentration shown in FIGS. The salt concentration c _{e, j} can be calculated by solving the above equation (13). Here, since the flow velocity u _j corresponding to the position in the X direction is used as the flow velocity u _j , the salt concentration c _{e, j} corresponding to the position in the X direction can be calculated by solving the above equation (13). . Thereby, the distribution (see FIG. 7) of the salt concentration c _{e, j} in the X direction can be calculated.

Note that the method for calculating the salt concentration c _{e, j} is not limited to the method using the above equation (13). If the salt concentration c _{e, j} varies in the X direction _, the distribution of the salt concentration c _{e, j} in the X direction can be calculated based on the flow velocity u _j . In the above equation (13), in order to grasp the variation in the salt concentration c _{e, j} , the diffusion state of the salt and the amount of salt produced are defined. For example, if the variation of the salt concentration c _{e, j} is set in advance _, the distribution of the salt concentration c _{e, j} can be calculated based on the flow velocity u _j without considering the salt diffusion state and the generation amount.

Further, according to the above formula (13), the diffusion state of the salt in the electrolytic solution is defined, but the diffusion state of the salt may not be considered. Since the time constant related to salt diffusion is larger than the time constant related to salt formation, salt diffusion may not occur. Therefore, the salt diffusion state may not be considered when calculating the distribution of the salt concentration c _{e, j} .

If the distribution of the salt concentration c _{e, j} is calculated as described above _, the maximum difference (salt concentration difference) Δc _e, j_max of the salt concentration c _{e, j} can be calculated. The salt concentration difference Δc _{e, j —} max is a difference between the salt concentration (maximum value) c _e and the salt concentration (minimum value) c _e .

As shown in FIG. 10, if the correspondence between the resistance increase amount Rh and the salt concentration difference Δc _{e —} max is obtained in advance by experiments or the like, the salt concentration difference Δc _{e —} max is calculated by calculating the salt concentration difference Δc _{e —} max. The resistance increase amount Rh corresponding to can be calculated. As shown in FIG. 10, the resistance increase amount Rh increases as the salt concentration difference Δc _{e —} max increases. In other words, the resistance increase amount Rh decreases as the salt concentration difference Δc _{e —} max decreases. According to the equation (13), the salt concentration _{c e} is calculated in each of the negative electrode plate 121 and cathode plate 122. Here, when the salt concentration difference Δc _{e —} max shown in FIG. 10 is calculated, first, the distributions of the salt concentrations c _e in the negative electrode plate 121 and the positive electrode plate 122 are added together. Specifically, in the negative electrode plate 121 and the positive electrode plate 122, the salt concentrations c _e at the positions facing each other are added together. Then, in the distribution of the combined salt concentration _{c e,} it calculates the difference in salt concentration (maximum value) _{c e} and salt concentration (minimum) _{c e} as salt concentration difference .DELTA.c _e _max.

The correspondence relationship between the resistance increase amount Rh and the salt concentration difference Δc _{e —} max can be expressed as a map or an arithmetic expression. Information for specifying the correspondence relationship can be stored in the memory 41. According to the above equation (13), the salt concentration c _{e, j} is calculated every time the predetermined time (calculation cycle) Δt elapses _{, and} the distribution of the salt concentration c _{e, j} can be grasped. Therefore, the predetermined time Δt elapses. The resistance increase amount Rh is calculated each time. Along with this, it is possible to grasp the change in the resistance increase amount Rh.

On the other hand, the resistance increase amount Rh may depend on the average salt concentration c _e _ave. Therefore, the resistance increase amount Rh can also be calculated based on the average salt concentration c _e _ave. The average salt concentration c _e _ave is a salt concentration (average value) obtained by averaging the distribution of the salt concentration (total value described above) c _{e in} the negative electrode plate 121 and the positive electrode plate 122. Similarly to the salt concentration difference Δc _e _max, the average salt concentration c _e _ave is calculated if the correspondence (map or arithmetic expression) between the resistance increase amount Rh and the average salt concentration c _e _ave is obtained in advance by experiment or the like. Thus, the resistance increase amount Rh corresponding to the average salt concentration c _e _ave can be calculated.

The resistance increase amount Rh can also be calculated based on the salt concentration difference Δc _{e —} max and the average salt concentration c _{e —} ave. In this case, a correspondence relationship (map or arithmetic expression) between the salt concentration difference Δc _{e —} max, the average salt concentration c _{e —} ave and the resistance increase amount Rh may be obtained in advance. By calculating the salt concentration difference .DELTA.c _e _max and average salt concentration _c e _ave, can calculate the corresponding resistance increase amount Rh to the calculated salt concentration difference .DELTA.c _e _max and average salt concentration _c e _ave.

  FIG. 11 is a flowchart showing a process for calculating the salt concentration distribution. The process shown in FIG. 11 is executed by the controller 40.

In step S <b> 101, the controller 40 detects the battery temperature Tb using the temperature sensor 33. In step S102, the controller 40 calculates the flow rate u _{j of the} electrolytic solution. Specifically, as described above, the controller 40 calculates the flow velocity u _j according to the position in the X direction. When calculating the flow velocity u _j , the battery temperature Tb detected in the process of step S101 is used.

In step S103, the controller 40 calculates the distribution of the salt concentration c _{e, j} based on the flow velocity u _j calculated in the process of step S102. The method for calculating the distribution of the salt concentration c _{e, j} is as described above.

  In the present embodiment, the battery temperature Tb is detected using the temperature sensor 33 in the process of step S101, but the present invention is not limited to this. Specifically, in the process of step S101, the amount of heat generated when the secondary battery 10 is charged / discharged (the amount of increase in the battery temperature Tb) and the amount of heat released from the secondary battery 10 (the amount of decrease in the battery temperature Tb) are calculated. By taking into consideration, the battery temperature Tb can be estimated.

  The calorific value of the secondary battery 10 can be calculated from the current value Ib and the internal resistance value of the secondary battery 10. The internal resistance value of the secondary battery 10 can be calculated from the current value Ib and the voltage value Vb. The heat dissipation amount of the secondary battery 10 can be calculated based on the battery temperature Tb and the temperature in the atmosphere (environment temperature) existing around the secondary battery 10. Here, when the battery temperature Tb is higher than the environmental temperature, the amount of heat radiation tends to increase as the difference between the battery temperature Tb and the environmental temperature increases.

  If the secondary battery 10 is not charged / discharged, the battery temperature Tb becomes equal to the environmental temperature. Therefore, the ambient temperature is detected using a temperature sensor different from the temperature sensor 33, and based on the calorific value calculated each time the secondary battery 10 is charged and discharged, and the heat dissipation amount of the secondary battery 10, The current battery temperature Tb can be calculated (estimated). As a method for estimating the battery temperature Tb based on the heat generation amount and the heat dissipation amount, a known method can be appropriately employed. When the secondary battery 10 is mounted on a vehicle, the vehicle is provided with a temperature sensor that detects the temperature outside the vehicle. Using this temperature sensor, the environmental temperature can be detected.

  When the salt concentration distribution is calculated by the processing shown in FIG. 11, the resistance increase amount Rh is calculated based on the salt concentration distribution, and charging / discharging of the secondary battery 10 can be controlled based on the resistance increase amount Rh. Here, a process (one example) when controlling charging / discharging of the secondary battery 10 will be described with reference to a flowchart shown in FIG. The process shown in FIG. 12 is executed by the controller 40.

In step S201, the controller 40 calculates the resistance increase amount Rh based on the distribution of the salt concentration _{ce, j} calculated in the process shown in FIG. The method of calculating the resistance increase amount Rh is as described above. In step S202, the controller 40 determines whether or not the resistance increase amount Rh is greater than or equal to a threshold value Rh_th. The threshold value Rh_th is the upper limit value of the resistance increase amount Rh, and can be set as appropriate based on the viewpoint of suppressing the deterioration of the secondary battery 10. Information specifying the threshold value Rh_th can be stored in the memory 41.

  When the resistance increase amount Rh is equal to or greater than the threshold value Rh_th, the controller 40 decreases the allowable charge power value Win and the allowable discharge power value Wout in step S203. The allowable charge power value Win is an upper limit power value that allows charging of the secondary battery 10, and the allowable discharge power value Wout is an upper limit power value that allows discharge of the secondary battery 10.

  As described above, since the current value Ib when the secondary battery 10 is charged is a negative value, the charging power value is also a negative value. On the other hand, since the current value Ib when the secondary battery 10 is discharged becomes a positive value, the discharge power value becomes a positive value. When the secondary battery 10 is charged, charging is controlled so that the charging power value (absolute value) does not become higher than the allowable charging power value (absolute value) Win. Further, when the secondary battery 10 is discharged, the discharge is controlled so that the discharge power value does not become higher than the discharge power allowable value Wout.

  Based on the battery temperature Tb and the SOC of the secondary battery 10, the allowable charge power value Win_ref and the allowable discharge power value Wout_ref are set as reference values. In the process of step S203, the allowable charge power value (absolute value) Win is decreased below the allowable charge power value (absolute value) Win_ref, or the allowable discharge power value Wout is decreased below the allowable discharge power value Wout_ref. By reducing the allowable charge power value Win and the allowable discharge power value Wout, an increase in the resistance increase amount Rh can be suppressed.

  When the resistance increase amount Rh is smaller than the threshold value Rh_th, the controller 40 ends the process shown in FIG. At this time, the allowable charge power value Win_ref described above is set as the allowable charge power value Win, and the allowable discharge power value Wout_ref described above is set as the allowable discharge power value Wout.

  In the process shown in FIG. 12, when the resistance increase amount Rh is equal to or greater than the threshold value Rh_th, the allowable charge power value (absolute value) Win and the allowable discharge power value Wout are reduced, but the present invention is not limited to this. Specifically, only one of the allowable charge power value (absolute value) Win and the allowable discharge power value Wout can be reduced.

The resistance increase amount Rh includes a resistance increase amount Rh resulting from charging of the secondary battery 10 and a resistance increase amount Rh resulting from discharging of the secondary battery 10. As shown in FIG. 7, the distribution of the salt concentration c _{e, j} is different during charging and discharging. Therefore, if the distribution of the salt concentration c _{e, j} is grasped, the resistance increase amount Rh resulting from charging of the secondary battery 10 and the resistance increase amount Rh resulting from discharging of the secondary battery 10 can be distinguished.

Here, when the salt concentration difference Δc _{e —} max is generated by charging the secondary battery 10 and the resistance increase amount Rh calculated from the salt concentration difference Δc _{e —} max is equal to or greater than the threshold value Rh_th, the charge power allowable value (absolute value) ) Only Win can be reduced. Thereby, with respect to the resistance increase amount Rh resulting from charging, an increase in the resistance increase amount Rh can be suppressed or the resistance increase amount Rh can be decreased.

On the other hand, when the secondary battery 10 discharges, a salt concentration difference Δc _{e —} max occurs, and when the resistance increase amount Rh calculated from the salt concentration difference Δc _{e —} max is equal to or greater than the threshold value Rh_th, only the discharge power allowable value Wout is decreased. Can be made. As a result, with respect to the resistance increase amount Rh resulting from the discharge, an increase in the resistance increase amount Rh can be suppressed or the resistance increase amount Rh can be decreased.

In this embodiment, it calculates the resistance increase amount Rh based on the distribution of the salt concentration c _e, not limited to this. That is, by calculating the distribution of the salt concentration c _e as in this embodiment, the distribution of the salt concentration c _e, can be applied to various techniques for grasping the internal state of the rechargeable battery 10. The internal state of the secondary battery 10 includes, for example, SOC and current value distribution as described below.

  For example, according to the technique described in Japanese Patent Application Laid-Open No. 2013-083525, SOC (estimated value) is calculated from the OCV (Open Circuit Voltage) of the secondary battery 10, and the SOC (estimated value) is calculated using the SOC (correction amount). ) Is corrected. The SOC (correction amount) is calculated by multiplying a basic value specified from the SOC (estimated value) and the battery temperature Tb by a gain. The gain is set according to the salt concentration bias.

In JP2013-083525A, the gain is calculated based on the current integrated value obtained by integrating the current values of the secondary battery 10 and the battery temperature Tb. That is, the gain is calculated after indirectly grasping the distribution of the salt concentration using the current integrated value and the battery temperature Tb. Here, as in the present embodiment, by calculating the distribution of the salt concentration c _e, it is possible to calculate the gain based on the distribution of the salt concentration c _e.

On the other hand, if grasp the distribution of the salt concentration c _e, it can grasp the distribution of the current value corresponding to the X direction position shown in FIG. If you change the salt concentration c _e, easy to run through the current (i.e., current value) changes. For this reason, the current values are different from each other at positions where the salt concentrations c _e are different (positions in the X direction shown in FIG. 7). It is known that when the secondary battery 10 is a lithium ion secondary battery, lithium is more likely to be deposited as current flows more easily. Therefore, using the current distribution value grasped from the distribution of the salt concentration c _e, considered possible to grasp the precipitation state of the lithium.

1: assembled battery, 10: secondary battery, 2: load, 31: monitoring unit, 32: current sensor, 33: temperature sensor, 40: controller, 41: memory, 110: battery case,
111: negative electrode terminal, 112: positive electrode terminal, 120: power generation element, 121: negative electrode plate,
121a: current collector foil, 121b: negative electrode active material layer, 122: positive electrode plate, 122a: current collector foil,
122b: positive electrode active material layer, 123: separator

Claims (1)

A power generation element that has an electrode plate containing an active material and performs charging and discharging, and a secondary battery housed in a battery case together with an electrolyte,
A constraining member having a projecting portion that contacts the outer surface of the battery case, and applying a restraining load in a predetermined direction to the secondary battery via the projecting portion;
A controller for calculating a distribution of salt concentration in the electrolytic solution impregnated in the power generation element,
The controller is
Using the liquid flow equation defining the flow of the electrolyte, the flow rate when the electrolyte flows from the inside of the power generation element toward the outside of the power generation element, and the inside of the power generation element from the outside of the power generation element Calculating the flow rate when the electrolyte flows toward the position for each position in the power generation element in the direction in which the electrolyte flows,
Based on the flow velocity at each position, calculate the distribution of the salt concentration in the power generation element,
When calculating the flow rate, the pressure includes the pressure of the electrolyte, the density of the electrolyte that changes according to the temperature of the secondary battery, and the volume fraction of the electrolyte in the power generation element as parameters. Using the liquid flow equation,
Based on the change in the volume fraction calculated from the volume change in the space where the electrolyte is present in the power generation element, the volume fraction is calculated,
Calculated from the volume expansion coefficient of the power generation element excluding the electrolyte, and based on the volume change of the power generation element excluding the electrolyte and the volume change of the power generation element including the electrolyte Calculate the volume change of the space where
The volume change amount in the first region in the power generation element facing the projection in the predetermined direction and the second region in the power generation element not facing the projection in the predetermined direction is set to the pressure of the electrolyte. Calculated based on each of these, and adding these volume changes to calculate the volume change of the power generation element including the electrolyte,
A battery system characterized by that.