JP6945485B2 - Hysteresis voltage estimator of storage battery, remaining amount estimation device of storage battery using this, management system of storage battery - Google Patents

Description

The present application relates to a storage battery hysteresis voltage estimation device used for estimating the remaining amount of a storage battery, a storage battery remaining amount estimating device using the same, and a storage battery management system.

In order to use the storage battery efficiently, it is important to accurately grasp the remaining amount (SoC: State of Charge) of the storage battery. However, since SoC is not a physical quantity that can be directly measured, it is necessary to estimate SoC from the current flowing through the storage battery, the voltage between terminals of the storage battery, and the like.

As a method for obtaining SoC, the open circuit voltage (OCV: Open Circuit Voltage) is obtained from the measured values of the current and voltage of the storage battery, and the OCV is added to the lookup table showing the relationship between OCV and SoC obtained in advance in the experiment. A technique for converting OCV to SoC by inputting is disclosed (see, for example, Patent Document 1).

Since an actual storage battery may have a hysteresis characteristic in which the relationship between OCV and SoC differs between after charging and after discharging, it is not possible to accurately and uniquely obtain SoC from a look-up table. Therefore, a method for obtaining a SoC with improved accuracy by supplying a predetermined current to a storage battery and identifying the parameters of the hysteresis model is disclosed (see, for example, Patent Document 2).

International Publication No. 2013/11231 JP-A-2017-198542

In Patent Document 1, the SoC can be estimated after obtaining the OCV from the measured values of the current and the voltage. However, since it may have the above-mentioned hysteresis characteristic, there is a problem that the estimated SoC has a large error depending on the type of the storage battery.

In Patent Document 2, the hysteresis model is parameterized by the maximum width of the hysteresis voltage and the rate of change of the hysteresis voltage, and the rate of change of the hysteresis voltage is proportional to the absolute value of the current. Therefore, the hysteresis voltage can be calculated based on the hysteresis parameter obtained by the method of Patent Document 2, and the SoC with improved accuracy can be estimated by combining with the method of Patent Document 1. However, since the hysteresis voltage of the storage battery does not always follow the hysteresis model described in Patent Document 2, there is a problem that the hysteresis voltage cannot be estimated accurately.

The present application has been made to solve the above-mentioned problems, and an object of the present application is to obtain a hysteresis voltage estimation device for a storage battery capable of accurately estimating a hysteresis voltage.

The storage battery hysteresis voltage estimation device disclosed in the present application includes a current measuring unit that measures the current flowing through the storage battery in which a plurality of stage structures are formed in the process of charging and discharging, and a voltage measuring unit that measures the inter-terminal voltage of the storage battery. The SoC estimation unit that estimates the SoC of the storage battery from the current value measured by the current measurement unit or the voltage value measured by the voltage measurement unit, and the first molar fraction of the electrode material at each stage when the storage battery is charged. And the molar fraction storage unit that stores the second variable coefficient which is the molar fraction of the electrode material at each stage when the storage battery is discharged, the current value, the first variable group, and the second variable. From the group, when charging, the first coefficient group of proportional coefficients representing the individual charging transition probabilities between the first variable group and the second variable group is calculated, and when discharging, the first variable group and the second variable group are calculated. A transition probability calculation unit that calculates a second coefficient group of proportional coefficients representing individual discharge transition probabilities between the variable groups of, and a first coefficient group in addition to the first variable group and the second variable group. Alternatively, the new first variable group and the new second variable group at the current time are calculated from the second coefficient group, and the new first variable group and the new second variable group are stored in the molar fraction storage unit. It is provided with a molar fraction calculation unit for calculating the hysteresis voltage and a hysteresis voltage calculation unit for calculating the hysteresis voltage from the ratio of the sum of the new first variable group and the sum of the new second variable group and the voltage determined by using the SoC. It is a coefficient.

According to the storage battery hysteresis voltage estimation device disclosed in the present application, the hysteresis voltage of the storage battery can be estimated accurately.

It is explanatory drawing of the stage structure at the time of charge / discharge of a graphite negative electrode. It is a state transition diagram between three stages when hysteresis is not considered. It is a flow diagram which calculates the transition probability. It is a state transition diagram between three stages when hysteresis is taken into consideration. It is a block diagram of the hysteresis voltage estimation apparatus of the storage battery in Embodiment 1. FIG. It is a flowchart which shows a part of the process of the hysteresis voltage estimation apparatus of the storage battery in Embodiment 1. FIG. It is a block diagram which shows an example of the hardware of the hysteresis voltage estimation apparatus of a storage battery. It is a state transition diagram between n stages when hysteresis is taken into consideration. It is a block diagram of the hysteresis voltage estimation apparatus of the storage battery in Embodiment 2. FIG.

Hereinafter, the hysteresis voltage estimation device of the storage battery of the embodiment will be described with reference to the drawings, but the same or corresponding members and parts will be described with the same reference numerals in each figure.

Embodiment 1.
In explaining the hysteresis voltage estimation device 101 of the storage battery, a case of a lithium ion storage battery using a graphite negative electrode as the storage battery 109 will be described. However, the hysteresis voltage estimation device 101 of the storage battery can be applied to a lithium ion storage battery using a graphite negative electrode. It is not limited, and can be applied to, for example, a lithium titanate electrode.

The present application is based on the fact that the transition between stages, that is, the rate of change in the mole fraction p of the negative electrode material in each stage is proportional to the transition probability (indicated by k during charging and l during discharging), which is a proportional coefficient. The hysteresis voltage is estimated by obtaining the transition probability as a variable and the mole fraction as a variable. The process of estimating the hysteresis voltage of this storage battery will first be described using a mathematical formula. The explanation will be given step by step using a basic model. Prior to the introduction of the model, the stage structure of the graphite negative electrode, which has a plurality of stage structures due to the insertion and desorption of lithium ions, will be described.

FIG. 1 is an explanatory diagram of a stage structure during charging and discharging of a general graphite negative electrode. Lithium ion 2 is inserted into each layer of hexagonal graphite 1. The stage when the storage battery is completely discharged and the lithium ion is absent is shown by the stage ∞ at the right end of FIG. In graphite without lithium ions inserted, the hexagonal lattices are offset by half a cycle and overlap, so each layer is shifted and displayed. As the storage battery is charged, the stage of the graphite negative electrode changes to stage 4, stage 3, and stage 2, and when fully charged, it becomes stage 1. If lithium ions are inserted between the layers of graphite, the misaligned grids will be aligned. Here, the number representing the stage indicates how many layers of graphite the lithium ion of one layer is inserted. For example, in stage 2, one layer of lithium ions is inserted into two layers of graphite. When the storage battery is discharged, the stage transitions from stage 1 to stage ∞, which is the opposite of charging. Specifically, when the storage battery is charged, the graphite negative electrode is initially in a mixed state of stage ∞ and stage 4. The proportion of the stage 4 increases with charging, and after the whole becomes almost the stage 4, the graphite negative electrode transitions to the mixed state of the stage 4 and the stage 3. The same applies to the subsequent transition from stage 3 to stage 2 and the transition from stage 2 to stage 1.

となる。ステージ２からステージ１への遷移について充電時遷移確率をｋ_１とすると、ｐ_１、ｐ_２の変化率も同様に、

となる。放電時の遷移については比例係数、すなわち放電時遷移確率をｌ_１、ｌ_２とすると、ｐ_１、ｐ_２、ｐ_∞の変化率は、

となる。 First, consider a first model composed of only three simplified stages, and explain the calculation of transition probability and mole fraction. FIG. 2 is a state transition diagram between three stages when hysteresis is not taken into consideration. The three stages are stage 1, stage 2, and stage ∞. Here, the mole fractions of the negative electrode material in each stage are set to p ₁ , p ₂ , and p _∞ . The transition from stage ∞ to stage 2 during charging is considered to be proportional to _{p ∞.} Therefore, if the proportional coefficient, that is, the transition probability during charging is k ₂ , the rate of change of _{p ∞ is}

Will be. Regarding the transition from stage 2 to stage 1, assuming that the transition probability during charging is k ₁ , the _{rate of change of p 1} and p ₂ is also the same.

Will be. Regarding the transition at the time of discharge, the proportional coefficient, that is, assuming that the transition probability at the time of discharge is l ₁ , l ₂ , the rate of change of _{p 1} , p ₂ , and p _{∞ is}

Will be.

が成立し、グラファイト負極容量とモル分率ｐの変化率の関係式となる。またステージの切り替わり時といった特異な場合を除くと、ステージ１とステージ∞が同時に存在することはないため、ｐ_∞が０に近い値を取るとｐ１は０に近い値から離れることになる。このことを微小な定数μを用いて、

と表す。式（５）の両辺を微分すると、

となり、満充放電時におけるモル分率ｐの関係式となる。式（１）と式（２）は充電時の遷移確率ｋとモル分率ｐの変化率の関係式であり、式（２）を式（４）に代入した式と、式（１）と式（２）を式（６）に代入した式とは２元連立方程式となるため、後述するモル分率記憶部１０６に記憶された前回時刻のモル分率を利用してこれを解くことで、第１の係数群としての充電時の遷移確率ｋ_１、ｋ_２を求めることができる。図３に遷移確率を計算するフロー図を示す。遷移確率ｋ_１、ｋ_２を式（１）と式（２）に代入すると３元連立常微分方程式となり、これを解くことで変数群としてのモル分率ｐ_１、ｐ_２、ｐ_∞を時間の関数として求めることができ、後述するモル分率記憶部１０６に記憶された前回時刻のモル分率を利用して各ステージの現在時刻における最新のモル分率を計算することができる。また式（１）、式（２）に代えて、放電時の遷移確率ｌとモル分率ｐの変化率の関係式である式（３）を式（４）と式（６）に代入することで第２の係数群としての放電時の遷移確率ｌ_１、ｌ_２を求めることができ、同様に変数群としてのモル分率ｐ_１、ｐ_２、ｐ_∞を時間の関数として求めることができる。なお遷移確率の計算は後述する遷移確率計算部１０５で、モル分率の計算は後述するモル分率計算部１０７で行われる。 The amount of lithium ions contained in stage 2 because half the amount of lithium ions contained in stage 1, increase or decrease of the amount of lithium entire graphite anode is represented by dp 1 ₊ dp _2/2. Since this is equal to the SoC change of the graphite negative electrode, assuming that the negative electrode capacity is Q [C] and the battery current is I [A],

Is established, and the relational expression between the graphite negative electrode capacity and the rate of change of the mole fraction p is obtained. Further, except for a peculiar case such as when the stage is switched, stage 1 and stage ∞ do not exist at the same time. Therefore, when p _∞ takes a value close to 0, p1 departs from a value close to 0. This is done using a minute constant μ.

It is expressed as. Differentiating both sides of equation (5)

Therefore, it becomes a relational expression of the mole fraction p at the time of full charge / discharge. Equations (1) and (2) are relational equations between the transition probability k at the time of charging and the rate of change of the mole fraction p, and the equation (2) is substituted into the equation (4), and the equation (1) Since the equation in which equation (2) is substituted into equation (6) is a binary simultaneous equation, it can be solved by using the mole fraction of the previous time stored in the mole fraction storage unit 106, which will be described later. _{, The transition probabilities k 1} and k ₂ at the time of charging as the first coefficient group can be obtained. FIG. 3 shows a flow chart for calculating the transition probability. Substituting the transition probabilities k ₁ and k ₂ into equations (1) and (2) yields a ternary simultaneous normal differential equation, and by solving this, the mole fractions p ₁ , p ₂ , and p _∞ as a variable group are timed. It can be obtained as a function of, and the latest mole fraction at the current time of each stage can be calculated by using the mole fraction of the previous time stored in the mole fraction storage unit 106 described later. Further, instead of the equations (1) and (2), the equation (3), which is the relational expression between the transition probability l at the time of discharge and the rate of change of the mole fraction p, is substituted into the equations (4) and (6). _{Therefore, the transition probabilities l 1} and l ₂ at the time of discharge as the second coefficient group can be obtained, and similarly, the mole fractions p ₁ , p ₂ , and p _∞ as the variable group can be obtained as a function of time. can. The transition probability is calculated by the transition probability calculation unit 105, which will be described later, and the mole fraction is calculated by the mole fraction calculation unit 107, which will be described later.

となる。ただし、Ｅ_２は所定の定数、Ｒは気体定数［Ｊ／Ｋｍｏｌ］、Ｔは温度［Ｋ］、Ｆはファラデー定数［Ｃ／ｍｏｌ］である。同様にステージ２とステージ∞が共存しているときの電位は、

となる。ただし、Ｅ_∞は所定の定数である。求めたｐ_１、ｐ_２、ｐ_∞と、式（７）と式（８）からグラファイト負極の電位を求めることができる。第１のモデルではヒステリシスを考慮しないため、グラファイト負極の電位計算で第１モデルを用いた説明を終了する。 The calculation of the potential of the graphite negative electrode using the mole fraction will be described. When stage 1 and stage 2 coexist in the graphite negative electrode, the potential E of the graphite negative electrode is determined from the Nernst equation.

Will be. However, E ₂ is a predetermined constant, R is a gas constant [J / Kmol], T is a temperature [K], and F is a Faraday constant [C / mol]. Similarly, the potential when stage 2 and stage ∞ coexist is

Will be. However, E _∞ is a predetermined constant. The potential of the graphite negative electrode can be obtained from the obtained p ₁ , p ₂ , p _∞, and the equations (7) and (8). Since hysteresis is not considered in the first model, the description using the first model in the potential calculation of the graphite negative electrode ends.

Next, consider a second model with a stage containing defects that cause hysteresis, and calculate the hysteresis voltage. FIG. 4 is a state transition diagram between four stages when hysteresis is taken into consideration. The four stages are stage 1, stage 2 without defects, stage 2L with defects, and stage ∞.

In reality, the stage structure of the graphite negative electrode is not completely achieved globally, and includes defects. That is, even if it is the graphite negative electrode of the stage 4, lithium ions can be partially inserted into one layer in three layers or one layer in five layers. It is known from observation facts that this defect occurs mainly during charging. Further, since the potential of the stage containing defects is slightly lower than the potential of the stage not containing defects, this difference in potential causes hysteresis.

と変形され、式（３）は、

と変形される。ただしβは放電時にステージ１からステージ２とステージ２Ｌへ、どの割合で遷移するかを表す０から１の値を取る定数である。ここでｋ_１、ｋ_２が第１の係数群としての充電時の遷移確率、ｌ_１、ｌ_２が第２の係数群としての充電時の遷移確率、ｐ_１、ｐ_２Ｌが第１の変数群としてのモル分率、ｐ_２、ｐ_∞が第２の変数群としてのモル分率となる。また式（４）は、

となり、式（７）は、

となる。ただしＥ_２Ｌは所定の定数である。ヒステリシス電圧は、式（１２）によって計算された電位と式（７）のｐ_２をｐ_２＋ｐ_２Ｌで置き換えた式によって計算された電位との差として計算される。すなわち、

となる。式（８）についても同様である。式（１３）は、ＳｏＣの関数として、任意の充放電に対してＥ_ｈｙｓｔの取り得る最大値をＥ_Ｌ（ＳＯＣ）、最小値をＥ_Ｂ（ＳＯＣ）とおくことで、

を得る。この式（１４）の形式とすることで、ステージ１とステージ２の共存領域とステージ２とステージ∞の共存領域における式を共通化することができる。なおＳｏＣについては、例えば電流積算法のような公知の手法を用いて推定してもよいし、

によって求めても構わない。 At the time of charging, the stage ∞ transitions to the stage 2L including defects. Even if the stage 2L contains a defect, the defect is eliminated according to the transition to the stage 1, so the transition destination from the stage 2L is the stage 1. At the same time, the stage 2 generated by the discharge also transitions to the stage 1. Since there are fewer defects during discharging than during charging, the transition destination from stage 1 is both stage 2 without defects and stage 2L with defects. When discharging from stage 2, the transition destination is stage ∞, but at the same time, stage 2L generated by charging also transitions to stage ∞. As a result, equations (1) and (2) are

And the equation (3) is

Is transformed. However, β is a constant that takes a value of 0 to 1 indicating the ratio of transition from stage 1 to stage 2 and stage 2L at the time of discharge. Here, k ₁ and k ₂ are the transition probabilities during charging as the first coefficient group, l ₁ and l ₂ are the transition probabilities during charging as the second coefficient group, and p ₁ and p 2 _L are the first variables. the mole fraction of the group, p _2, p _∞ is the mole fraction of the second variable group. Equation (4) is

And the formula (7) is

Will be. However, E _2L is a predetermined constant. Hysteresis voltage is calculated as the difference between the potential of the p ₂ was calculated by the equation is replaced by p _{2 +} p _2L of formula (12) calculated potential and the formula by (7). That is,

Will be. The same applies to equation (8). Equation (13), by placing as a function of SoC, and _E the maximum possible value of _{E hyst} for any discharge L (SOC), the minimum value _E B (SOC),

To get. By adopting the form of this equation (14), it is possible to standardize the equations in the coexistence region of stage 1 and stage 2 and the coexistence region of stage 2 and stage ∞. Note that the SoC may be estimated using a known method such as a current integration method.

You may ask for it.

Next, a schematic configuration of the hysteresis voltage estimation device 101 of the storage battery according to the first embodiment will be described. FIG. 5 is a configuration diagram of the hysteresis voltage estimation device 101 of the storage battery according to the first embodiment, and FIG. 6 is a flowchart showing a part of the processing of the hysteresis voltage estimation device 101 of the storage battery. Note that FIG. 5 also shows the storage battery 109 in which a plurality of stage structures are formed in the process of charging and discharging, the SoC estimation unit 110 using the hysteresis voltage, and the storage battery control device 111 together with the hysteresis voltage estimation device 101 of the storage battery. .. The storage battery residual amount estimation device 101 and the SoC estimation unit 110 using the hysteresis voltage constitute the storage battery remaining amount estimation device 100, and the storage battery remaining amount estimation device 100, the storage battery control device 111, and the storage battery 109 manage the storage battery. System 112 is configured.

The storage battery hysteresis voltage estimation device 101 includes a current measurement unit 102, a voltage measurement unit 103, a SoC estimation unit 104, a transition probability calculation unit 105, a mole fraction storage unit 106, a mole fraction calculation unit 107, and a hysteresis voltage calculation unit 108. Be prepared. As shown in FIG. 7, the hysteresis voltage estimation device 101 of the storage battery includes a processor 113 and a storage device 114 as an example of hardware. Although the storage device is not shown, it includes a volatile storage device such as a random access memory and a non-volatile auxiliary storage device such as a flash memory. Further, an auxiliary storage device of a hard disk may be provided instead of the flash memory. The processor 113 executes the program input from the storage device 114. In this case, a program is input from the auxiliary storage device to the processor 113 via the volatile storage device. Further, the processor 113 may output data such as a calculation result to the volatile storage device of the storage device 114, or may store the data in the auxiliary storage device via the volatile storage device.

The hysteresis voltage estimation device 101 of the storage battery can be realized, for example, as software of a microcontroller mounted on the storage battery management system 112. In FIG. 6, the uppermost row indicates the start of the flowchart, and the lowermost row indicates the loop end. The mole fraction calculation process required to estimate the hysteresis voltage of the storage battery is looped, and the latest mole fraction at the calculated current time is used to estimate the hysteresis voltage. The calculation processing loop is repeated at a predetermined time. Although it is implemented as software, it is not limited to the flowchart of FIG. 6, and if the information required for each process of the flowchart can be obtained before the process, the processing can be replaced.

In FIG. 6, the current measuring unit 102 measures the current flowing through the storage battery 109 and outputs the measured current value to the SoC estimation unit 104 and the transition probability calculation unit 105 (step S101). The voltage measuring unit 103 measures the voltage between the terminals of the storage battery 109 and outputs the measured voltage value to the SoC estimation unit 104 (step S102). The SoC estimation unit 104 estimates the SoC of the storage battery 109 based on at least one of the measured current value and the measured voltage value using, for example, the current integration method, and the estimated SoC is calculated by the hysteresis voltage calculation unit 108. Is output to (step S103).

The mole fraction storage unit 106 is a first variable group which is a mole fraction of the electrode material in each stage when the storage battery 109 is charged, and a second variable group which is a mole fraction of the electrode material in each stage when the storage battery 109 is discharged. The variable group of the above is stored, and the stored first variable group and the second variable group are output to the transition probability calculation unit 105 and the mole fraction calculation unit 107 (step S104). The transition probability calculation unit 105 uses the input current value, the first variable group, and the second variable group to determine the individual charging transition probabilities between the first variable group and the second variable group during charging. The first coefficient group representing the above, and the second coefficient group representing the individual discharge transition probabilities between the first variable group and the second variable group at the time of discharge are calculated, and the calculated first coefficient group is calculated. And the second coefficient group are output to the molar fraction calculation unit 107 (step S105).

The molar fraction calculation unit 107 is the latest first variable group and the first coefficient group at the current time from the input first variable group and the second variable group, as well as the first coefficient group or the second coefficient group. Two variable groups (hereinafter referred to as new first variable group and new second variable group) are calculated, and the obtained new first variable group and new second variable group are stored in the molar fraction storage unit 106. And output to the hysteresis voltage calculation unit 108 (step S106). The hysteresis voltage calculation unit 108 calculates the hysteresis voltage from the ratio of the sum of the new first variable group to the sum of the new second variable group and the voltage determined by SoC, which will be described later using a mathematical formula. The estimated hysteresis voltage of the storage battery is output to the SoC estimation unit 110 using the hysteresis voltage. Here, the SoC is estimated accurately using the estimated hysteresis voltage of the storage battery. The estimated SoC is input to the storage battery control device 111 and used for controlling the storage battery 109. The new first variable group and the new second variable group stored in the mole fraction storage unit 106 are used as the first variable group and the second variable group in the calculation of the next time, and are used as the transition probability calculation unit. It is output to 105 and the mole fraction calculation unit 107.

Finally, the hysteresis voltage is calculated by considering a generalized third model in which the number of stages used in the hysteresis voltage estimation device 101 of the storage battery is not limited to four. FIG. 8 is a state transition diagram between n stages when hysteresis is taken into consideration. It is considered that each stage from stage ∞ to stage 1 has a stage containing defects, and the stage including defects and the stage not containing defects also transition to each other.

となる。ただし、αは放電時にステージｊ＋１からステージｊとステージｊＬへ、どの割合で遷移するかを表す０から１の値を取る定数である。ただし、ｊ＝１のときとｊ＝∞のときは、

となる。放電時については、

となり、ｊ＝１のときとｊ＝∞のときは、

となる。グラファイト負極全体のリチウムイオンの増減を考慮すると、式（１１）は、

となる。同時に存在できないステージについての制約を考えると、第１の変数群ｐ_１、ｐ_２Ｌ、・・・、ｐ_ｎＬおよび第２の変数群ｐ_２、・・・、ｐ_ｎ、ｐ_∞に含まれる変数を、満充電されたときの変数を含む充電側の第１の分類と完全に放電された時の変数を含む放電側の第２の分類との２つに分類したとき、ｊ＝２、・・・、ｎに対して、

となる。式（２１）の第１項が第１の分類、第２項が第２の分類に関する。ただしμは、式（５）と同様に微小な定数である。式（２１）の両辺を微分すると、

となる。 Similar to the model shown above, the transition probabilities and mole fractions are calculated first. The transition of stage j during charging is

Will be. However, α is a constant that takes a value of 0 to 1 indicating the ratio of transition from stage j + 1 to stage j and stage jL at the time of discharge. However, when j = 1 and when j = ∞,

Will be. For discharge,

And when j = 1 and j = ∞,

Will be. Considering the increase / decrease of lithium ions in the entire graphite negative electrode, equation (11) is

Will be. Considering the constraints on the stages that cannot exist at the same time, the variables included in the first variable group p ₁ , p _2L , ..., P _nL and the second variable group p ₂ , ..., p _n , p _∞ When is classified into two categories, the first classification on the charging side including the variable when fully charged and the second classification on the discharging side including the variable when fully discharged, j = 2, ...・ ・ For n

Will be. The first term of the formula (21) relates to the first classification, and the second term relates to the second classification. However, μ is a minute constant as in Eq. (5). Differentiating both sides of equation (21)

Will be.

The transition probability calculation unit 105 solves the simultaneous equations of equations (20) and (22) at each time in the same manner as the method shown in the first model, so that n first coefficient groups k ₁ and The k ₂ , ..., K _n and the second coefficient groups l ₁ , l ₂ , ..., L _n are determined. The molar fraction calculation unit 107 uses equations (16) and (17), or equations (18) and equations (18) and equations (16) and equations (17) using the first coefficient group or the second coefficient group calculated by the transition probability calculation unit 105. _{The new first variable group p 1} , p _2L , ..., P _nL and the new second variable group p ₂ , ..., p at the current time by integrating the simultaneous differential equations consisting of 19) for a unit time. _{Find n} and p _∞ .

によって計算する。ヒステリシス電圧は、新第１の変数群の総和と新第２の変数群の総和との比率およびＳｏＣを用いて決定される電圧から計算される。ただし、Ｅ_ＢとＥ_Ｌは上述したように所定のＳｏＣの関数である。 The hysteresis voltage calculation unit 108 calculates the hysteresis voltage from the new first variable group and the new second variable group of the current time calculated by the mole fraction calculation unit 107.

Calculated by. The hysteresis voltage is calculated from the ratio of the sum of the new first variable group to the sum of the new second variable group and the voltage determined using SoC. However, _{E B} and _{E L} is a function of predetermined SoC as described above.

When the hysteresis voltage estimation device 101 of the storage battery is first operated, the variable group of the previous time is not stored in the mole fraction storage unit 106. At that time, since the first operation starts from the state where the storage battery is fully charged, p ₁ is almost 1, and the sum of the mole fractions of the others is 1, so it is sufficient to start from a small value.

As described above, the hysteresis voltage estimation device 101 of this storage battery observes the property of remarkably relaxing at the point where the pair of the stage structure in which the hysteresis voltage coexists is switched, and models it as a phenomenon closely related to the stage transition. Therefore, the hysteresis voltage of the storage battery can be estimated more accurately. Further, when SoC is 0 or 1, the mole fraction of the stage is concentrated in stage 1 or stage ∞, and the hysteresis voltage at that time is naturally given the characteristic of being 0 in calculation. Therefore, the conventional hysteresis voltage calculation method is used. If this characteristic is not given carefully, numerical calculation problems may occur, but in principle, numerical calculation problems can be eliminated.

In the present embodiment, the restrictions on the stages that cannot exist at the same time are expressed as in Eq. (21), but are not limited to this, and are expressed using a function such as ^{srel (θ) or log (1 + e θ).} It doesn't matter.

Embodiment 2.
The schematic configuration of the hysteresis voltage estimation device 101 of the storage battery according to the second embodiment will be described. FIG. 9 is a configuration diagram of the hysteresis voltage estimation device 101 of the storage battery according to the second embodiment. In the first embodiment, the first coefficient group and the second coefficient group are regarded as constants between the previous time and the current time, but in the second embodiment, the operation cycle of the hysteresis voltage estimation device 101 of the storage battery is relatively long. In consideration of a long case, the first coefficient group and the second coefficient group are made non-constant. Since the other configurations are the same as those described in the first embodiment, the same reference numerals are given and the description thereof will be omitted.

As shown in FIG. 9, the hysteresis voltage estimation device 101 of the storage battery is configured to include a DAE calculation unit 201 (DAE: Differential Algebraic Equations) in place of the transition probability calculation unit 105 and the mole fraction calculation unit 107 of FIG. NS. The molar fraction storage unit 106 stores the first variable group, the second variable group, the first coefficient group, and the second coefficient group, and stores the stored first variable group, second variable group, and second variable group. The coefficient group of 1 and the second coefficient group are output to the DAE calculation unit 201. The DAE calculation unit 201 solves the differential algebra equation (DAE) described later from the input current value, the first variable group, the second variable group, and the first coefficient group or the second coefficient group. Therefore, the new first variable group and the new second variable group at the current time, and the new first coefficient group or the new second coefficient group are calculated, and the calculated result is stored in the molar fraction storage unit 106. And output to the hysteresis voltage calculation unit 108.

となる。ただしｅ_１とは第１要素が１であり第２要素以降が０であるようなベクトルである。また式（１８）および式（１９）と、式（２０）と式（２２）はまとめて、

となる。ここでＨ_ＣとＨ_Ｄは全域で正則であるため、式（２４）と式（２５）の第３式は、

となり、両式を微分することで、

となる。ここで、Ｈ_ＣおよびＨ_Ｄはｐ_Ｌおよびｐ_Ｂの線形行列式であるため、

となる。ただしＦ_Ｃｊ、Ｇ_Ｃｊ、Ｆ_Ｄｊ、Ｇ_Ｄｊは定数行列であり、ｐ_Ｌｊ、ｐ_Ｂｊはそれぞれｐ_Ｌ、ｐ_Ｂの第ｊ要素である。式（２７）中のｄＨ_ＣおよびｄＨ_Ｄは、

と計算できる。ただしｆ_Ｌｊ、ｆ_Ｂｊ、ｇ_Ｌｊ、ｇ_Ｂｊはそれぞれｆ_Ｌ、ｆ_Ｂ、ｇ_Ｌ、ｇ_Ｂの第ｊ要素である。式（２７）と式（２４）または式（２５）の第１式、第２式を連立させたものは通常の常微分方程式であり、公知の手法で計算することができる。当然ながら、微分代数方程式を取り扱う他の公知手法を用いて計算してもよい。計算の結果、現在時刻における新第１の変数群と新第２の変数群、および新第１の係数群または新第２の係数群を得ることができる。 If the first coefficient group and the second coefficient group are regarded as constants between the previous time and the current time, there is a problem that the calculation error becomes large when the operation cycle of the hysteresis voltage estimation device 101 of the storage battery is relatively long. , Eqs. (16) and (17), or Eqs. (18) and (19), and all of Eqs. (20) and (22) are combined to obtain a differential algebraic equation. Here, the first coefficient group is collectively represented by the symbol k, and the second coefficient group is collectively represented by the symbol l. Further, the first variable group is _{represented by the symbol p L} , and the second variable group is represented _{by the symbol p B.} At this time, since equation (20) is a homogeneous line form with respect to the coefficient k and equation (22) is a linear form with respect to k, equations (16) and (17), equations (20) and equations (22) Collectively,

Will be. However, e ₁ is a vector in which the first element is 1 and the second and subsequent elements are 0. Further, the equations (18) and (19), and the equations (20) and (22) are collectively combined.

Will be. Here, since _{H C} and _{H D} is regular across, third equation formula (24) wherein the (25),

By differentiating both equations,

Will be. Since _{H C} and _{H D} is the linear matrix equation of _{p L} and _{p B,}

Will be. However, _FCj , G _Cj , F _Dj , and G _Dj are constant matrices, and p _Lj and p _Bj are the j elements of _{p L} and p _{B, respectively.} DH _C and dH _D in formula (27),

Can be calculated. However, f _Lj , f _Bj , g _Lj , and g _Bj are the jth elements of _{f L} , f _B , g _L , and g _{B, respectively.} The combination of the first equation and the second equation of the equation (27) and the equation (24) or the equation (25) is an ordinary ordinary differential equation, and can be calculated by a known method. Of course, it may be calculated using other known methods dealing with differential algebraic equations. As a result of the calculation, the new first variable group and the new second variable group at the current time, and the new first coefficient group or the new second coefficient group can be obtained.

As described above, the hysteresis voltage estimation device 101 of this storage battery explicitly handles the non-linear differential equation and obtains the first coefficient group and the second coefficient group as non-constants, so that an error that increases when the operation cycle is long Therefore, the hysteresis voltage of the storage battery can be estimated accurately even when the operation cycle of the entire device is relatively long.

The configuration shown in the above embodiments 1 and 2 is an example of the configuration of the present application, and the configuration may be modified by omitting a combination or a part of the embodiments without departing from the gist of the present application. Needless to say, it is also possible.

100 Rechargeable battery remaining amount estimation device, 101 Storage battery hysteresis voltage estimation device, 102 Current measurement unit, 103 Voltage measurement unit, 104 SoC estimation unit, 105 Transition probability calculation unit, 106 molar fraction storage unit, 107 molar fraction calculation unit , 108 Hysteresis voltage calculation unit, 109 storage battery, SoC estimation unit using 110 hysteresis voltage, 111 storage battery control device, 112 storage battery management system, 201 DAE calculation unit

Claims (7)

A current measuring unit that measures the current flowing through a storage battery in which multiple stage structures are formed in the process of charging and discharging,
A voltage measuring unit that measures the voltage between the terminals of the storage battery,
A SoC estimation unit that estimates the SoC of the storage battery from the current value measured by the current measurement unit or the voltage value measured by the voltage measurement unit.
The mole fraction that stores the first variable group that is the mole fraction of the electrode material in each stage when the storage battery is charged and the second variable group that is the mole fraction of the electrode material in each stage when the storage battery is discharged. Rate memory and
The first of the proportional coefficients representing the individual charging transition probabilities between the current value, the first variable group and the second variable group when charging, between the first variable group and the second variable group. With a transition probability calculation unit that calculates the coefficient group of the above and calculates the second coefficient group of the proportional coefficient representing the individual discharge transition probability between the first variable group and the second variable group at the time of discharge. ,
In addition to the first variable group and the second variable group, a new first variable group and a new second variable group at the current time are calculated from the first coefficient group or the second coefficient group. In addition, the molar fraction calculation unit that stores the new first variable group and the new second variable group in the molar fraction storage unit, and
A hysteresis voltage calculation unit that calculates the hysteresis voltage from the ratio of the sum of the new first variable group to the sum of the new second variable group and the voltage determined by using the SoC.
Hysteresis voltage estimation device for storage batteries. A current measuring unit that measures the current flowing through a storage battery in which multiple stage structures are formed in the process of charging and discharging,
A voltage measuring unit that measures the voltage between the terminals of the storage battery,
A SoC estimation unit that estimates the SoC of the storage battery from the current value measured by the current measurement unit or the voltage value measured by the voltage measurement unit.
The first variable group which is the molar fraction of the electrode material in each stage when the storage battery is charged, the second variable group which is the molar fraction of the electrode material in each stage when the storage battery is discharged, and the first variable group. The first coefficient group representing the individual charging transition probability between the variable group and the second variable group and the individual discharging transition probability representing the individual discharging transition probability between the first variable group and the second variable group. A molar fraction storage unit that stores the second coefficient group,
In addition to the current value, the first variable group, and the second variable group, a new first variable group and a new second variable group at the current time are obtained from the first coefficient group or the second coefficient group. In addition to the group, the new first coefficient group or the new second coefficient group is calculated, and in addition to the new first variable group and the new second variable group, the new first coefficient group or the new A DAE calculation unit that stores the second coefficient group in the molar fraction storage unit,
It is provided with a hysteresis voltage calculation unit that calculates a hysteresis voltage from the ratio of the sum of the new first variable group to the sum of the new second variable group and the voltage determined by using the SoC.
In the DAE calculation unit
It depends on the relational expression between the first variable group and the second variable group, the first coefficient group or the second coefficient group, and the first coefficient group or the second coefficient group. By solving the differential algebra equation satisfied by the first variable group and the second variable group, in addition to the new first variable group and the new second variable group, the new first coefficient group or the new A storage battery hysteresis voltage estimation device, characterized in that the second coefficient group is calculated. The variables included in the first variable group and the second variable group are classified into the first classification on the charging side including the variables when fully charged and the first on the discharging side including the variables when completely discharged. Classify into two categories, two categories,
The product of the sum of the increase / decrease of the variables included in the first classification, the sum of the variables included in the second classification, the sum of the variables included in the first classification, and the variables included in the second classification. The proportional coefficient included in the first coefficient group and the second coefficient group is calculated by solving the equation indicating that the sum of the products of the sums of increases and decreases of is 0 by the transition probability calculation unit. The hysteresis voltage estimation device for a storage battery according to claim 1. The variables included in the first variable group and the second variable group are classified into the first classification on the charging side including the variables when fully charged and the first on the discharging side including the variables when completely discharged. Classify into two categories, two categories,
The product of the sum of the increase / decrease of the variables included in the first classification, the sum of the variables included in the second classification, the sum of the variables included in the first classification, and the variables included in the second classification. The proportional coefficient included in the first coefficient group and the second coefficient group is calculated by solving the equation representing that the sum of the products of the sums of increase and decrease of is 0 by the DAE calculation unit. 2. The hysteresis voltage estimation device for a storage battery according to claim 2. The hysteresis voltage estimation device for a storage battery according to any one of claims 1 to 4, wherein the device is connected to a lithium ion storage battery provided with a graphite negative electrode. A storage battery remaining amount estimation device comprising the hysteresis voltage estimation device for the storage battery according to any one of claims 1 to 5 and a SoC estimation unit using the hysteresis voltage. A storage battery management system comprising the storage battery remaining amount estimation device according to claim 6 and a storage battery control device.

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