Method and apparatus for determining state of charge and state of health of a rechargeable battery

Abstract

The invention relates to a method and a device for determining the state of charge (SOC) of a rechargeable battery (106) of a specified battery type or a parameter physically related thereto, in particular the residual charge Q contained in the battery, wherein the method operates with the aid of a voltage-controlled battery model (102) which is parameterized for the battery (106) in question or for the corresponding battery type. mess The present invention also relates to a method and apparatus for determining the state of health (SOH) of a battery (102), wherein the battery model (102) also used to determine the SOC provides a modeled battery current I mod From this the modelled charge during the charging and discharging phases of the battery (106) can be determined and compared to the measured battery current I mess Since the battery model (102) does not age, the battery's SOH can be determined from it.

Description

[0001] The present invention relates to a method for determining the state of charge of a rechargeable battery of a predetermined battery type or a parameter physically related thereto, in particular the remaining charge contained in the battery, and a method for determining the state of health of a rechargeable battery of a predetermined battery type or a parameter physically related thereto, in particular the actual capacity of the battery. The invention also relates to a device for carrying out the method.

[0002] The state of charge (SOC) of a rechargeable battery is defined as:

[0003]

[0004] The state of health (SOH) of a rechargeable battery is defined as:

[0005]

[0006] In these equations, Q represents the remaining charge in the battery, C represents the capacity, or the amount of charge that can be drawn from a fully charged battery, and C represents the N It represents the nominal capacity, i.e. the capacity of a new battery. SOC and SOH are defined here as dimensionless values ​​between 0 and 1. In practice, SOC and SOH are usually given as percentages.

[0007] In many current battery systems, SOC determination is performed by a so-called battery management system (BMS), which provides this information to the user, for example, via a display. Many different methods are known for approximate SOC determination, including, in particular, model-based methods. These operate solely based on a current-controlled battery model and therefore require a measured value of the battery current as an input signal. However, current measurement cannot be achieved with the desired accuracy, so the accuracy of known methods for determining SOC is often insufficient.

[0008] Methods for determining SOH are typically based on measuring the battery current during cycling between fully discharged and fully charged states of the battery. This cannot be done during normal battery use.

[0009] Starting from this prior art, the object of the present invention is to provide a method for approximately determining the state of charge of a rechargeable battery of a predetermined battery type or a parameter physically related thereto, in particular the remaining charge of the battery, which has a higher degree of accuracy and is also easy to implement in a battery management system. Another object of the present invention is to provide a method for determining the state of health of a rechargeable battery of a predetermined battery type or a parameter physically related thereto, in particular the actual battery capacity, which allows for an approximate determination of the battery's state of health during normal use of the battery. Finally, the object of the present invention is to provide a device that allows for carrying out one or both of the above-mentioned methods.

[0010] The present invention is based on the recognition that the use of a voltage-controlled dynamic mathematical battery model described by an implicit system of equations allows for a simple determination of an approximate value for the SOC. For this purpose, only the battery voltage (over a period of time) needs to be measured. Furthermore, depending on the battery model selected, the battery temperature or the ambient temperature can be used as an input parameter for the battery model. The model can also incorporate certain temporal relationships, such as battery hysteresis characteristics or the temporal dependence of the double layer.

[0011] At the same time, the voltage-controlled battery model provides the (model) battery current as output parameter, which is used according to the invention to determine the SOH of the battery.

[0012] The method according to the invention uses a dynamic mathematical battery model for a battery or a predetermined battery type (ie a large number of similar batteries) which converts the state of charge SOC of the battery into mod Or parameters related to physics, especially the remaining battery capacity Q and battery current I mod Related and defined with the battery open circuit voltage U 0 The voltage U measured between the two terminals (poles) of the battery is related to the sum of the overvoltages η mess , where the open circuit voltage U 0 At least related to the remaining capacity Q or a parameter physically related to it, while the overvoltage η is at least related to the battery current I mod Related.

[0013] The dynamic mathematical battery model can then be parameterized for a specific battery or a specific battery type, ie the parameters for the battery model are selected such that the parameterized model describes the specific battery or the specific battery type with sufficiently high accuracy.

[0014] The method according to the invention thus allows the battery voltage U to be measured by mess And use the parameterized dynamic mathematical battery model to calculate the approximate SOC mod To determine the actual state of charge (SOC) of the battery or an approximate value of a parameter physically related to it mod .

[0015] Therefore, a device for carrying out the method only needs to be designed to measure the battery voltage U mess , for example by means of a device for measuring the battery voltage U mess unit, and from the measured battery voltage U mess Calculate the approximate value of battery SOC mod For this purpose, the device may comprise a calculation unit for calculating the SOC. For this purpose, a parameterized battery model may also be stored in the calculation unit or may be provided to it by a higher-level unit.

[0016] The battery model also allows calculation of the (model) battery current Imod According to the invention, this can also be used in a further step to determine an approximate value SOH for the actual SOH of the battery. mod (See below). It is not necessary to also determine the SOC of the battery when using the method according to the invention for determining an approximate value for the SOH of a battery. This is because the use of a voltage-controlled dynamic mathematical battery model obviously allows only the (model) battery current I to be calculated. mod , without having to output or use the SOC of the battery first or simultaneously.

[0017] However, in its complete design, the method of the invention provides an algorithm (mathematical rule) which allows to calculate the battery voltage U mess and current intensity I mess The measured value and optionally the battery temperature T mess The state of charge (SOC) and state of health (SOH) are determined by measuring the value of the ambient temperature or the ambient temperature. Figure 1 It consists of an overall algorithm 100 comprising two components, namely a first component 102 with a battery model and an algorithm for SOC determination and a second component 104 with an SOH algorithm for SOH determination. mess As the necessary input parameters required, the first component 102 is inputted, optionally also the measured battery temperature T mess If the battery model includes a thermal sub-model, the ambient temperature T can also be provided to the battery model. umg Instead of measuring the temperature T mess In a complete embodiment of the method according to the invention, the first algorithm component 102 with the dynamic mathematical battery model provides the value SOC as an output parameter mod , which is used as an approximation for the actual SOC of the battery 106. As input parameters, the second algorithm component 104 receives, on the one hand, the calculated value for the model battery current I mod On the other hand, the measured battery current I mess As output parameter, the second algorithm component provides the value SOH mod , which is used as an approximation for the actual SOH of the battery 106 .

[0018] According to one design solution of the present invention, the dynamic mathematical battery model can be composed of or derived from an implicit equation system, which includes the following equations:

[0019]

[0020] U mess =U 0 (SOCmod , T mess ,t)+η(I mod , SOC mod , T mess , t)

[0021] Among them, C N Indicates the predetermined nominal capacity of the battery, expressed as T mess represents the measured temperature of the battery, and t represents the time, wherein the open circuit voltage U 0 Indicates the state of charge SOC mod The necessary relationship with the measured temperature T mess The relationship between the overvoltage η and the time t is optional, and wherein the overvoltage η indicates the relationship between the overvoltage η and the battery current I mod The inevitable relationship between the state of charge SOC mod , measure temperature T mess The relationship to time t is optional.

[0022] These two still commonly stated relations implicitly describe the two unknowns SOC mod and I mod The first equation simply describes the variation of the remaining charge contained in the battery as a function of the battery current and can be applied in this way to all other specific designs or formulas of mathematical battery models, while the second equation can be adapted to the specific selected battery model and, if necessary, can be replaced by a complex system of equations that describes the selected battery model in mathematical and physical terms.

[0023] For example, according to one design of the present invention, the open circuit voltage U 0 Can depend only on the state of charge SOC mod , and the constant internal resistance R of the battery can be assumed i It is also possible to assume that the battery model is independent of temperature. In this case, the general battery model equation above can be replaced by the following equation:

[0024]

[0025] U mess =U 0 (SOC mod )-R i I mod ,

[0026] Among them, the open circuit voltage U 0 State of charge SOC mod The relationship is determined in particular by measurements, in particular as discrete values ​​of the measurements or analytical functions. In this case, there is a very easy-to-solve system of equations that can be implemented in the battery management system without much effort.

[0027] In this battery model, the above two equations can be solved by analytical inversion, where the state of charge SOC mod It can be calculated from the following equation:

[0028]

[0029] Correlation U 0 (SOC mod ) can be given in table form (ie in the form of measured values) or in the form of analytical functions. It should be noted here that when SOH is to be determined in addition to SOC, the model current I can obviously also be calculated from this equation. mod Depending on the method chosen to solve the two equations above, the first equation alone may be sufficient to calculate the SOC. mod , then the latter equation should also be considered in any case.

[0030] In practice, people will use numerical methods to solve the above-mentioned problem for calculating SOC mod The equation pair, as provided for determining SOH mod The input parameters of the algorithm are also detected as discrete measured values, preferably at equidistant time intervals Δt (sampling intervals). In particular, the voltage U mess Here, the voltage is measured discretely at predetermined time intervals Δt. The form is measured. The predetermined time interval can also be varied. The measured value can also be determined at a predetermined time.

[0031] In order to numerically solve the above equations for the assumed very simple battery model, an explicit forward Euler discretization method can be used. This discretization method leads to the following relationship:

[0032]

[0033] Each parameter has an index i, which represents the time step Δt. The initial value of .

[0034] Instead of the explicit forward Euler method, other explicit or implicit methods can also be used to discretize the above equations. However, with the implicit backward Euler method, a complete solution is no longer possible. In this case, other numerical methods, such as Newton's method, should be used.

[0035] However, according to one design of the present invention, a special case occurs when a linear relationship between the open circuit voltage and the SOC of the battery is assumed. Therefore, the equation for the above simple battery model is further simplified to:

[0036] and

[0037]

[0038] Among them, U L Indicates the end-of-charge voltage, with U E Indicates the discharge end voltage.

[0039] From the equations, it is possible to calculate an approximate value for the state of charge SOC, ie the value SOC, using mathematical discretization methods and possibly other numerical methods. mod If the implicit backward Euler method is used, this leads to the following equation:

[0040] and

[0041]

[0042] From this, the SOC can be easily calculated mod As mentioned above, it is not necessary to calculate the battery current I mod The value of SOH mod , but in this special case it exists automatically because of the combination of the two equations.

[0043] According to another embodiment of the present invention, the method for determining the SOC or SOH of a battery can also be performed with the aid of a relatively complex equivalent circuit model for the battery according to FIG3 . The battery model can be expressed by the following formula:

[0044]

[0045] U mess =U 0 (SOC mess , T mod )+ΔU hys (I mod )-U RC，an -U RC，ca -I mod ·R s (T mod )

[0046]

[0047] Among them, U RC Represents the voltage drop across an RC element, using R CT Represents the charge transfer resistance, C DL Indicates the double-layer capacity, C th Indicates heat capacity, using R th Indicates the thermal resistance at the battery surface, expressed as dU 0 (SOC mod) / dT represents the temperature dependence of the open circuit voltage, and T 0 Indicates the relevant reference temperature, using represents the measured battery ambient temperature, where the indices "an" and "ca" refer to the anode and cathode of the battery, and here, the open circuit voltage U 0 The asymmetry of ΔU hys Describe the asymmetry of the cathode resistance through the current dependence R CT，ca Description. From this system of equations, the SOC mod The value of , ie, the approximation for the actual state of charge SOC, is preferably determined with the aid of one or more numerical arithmetic methods.

[0048] The method according to the invention for determining the state of health of a rechargeable battery of a predetermined battery type or a parameter physically related thereto, in particular the actual capacity C of the battery, comprises the following steps:

[0049] By the battery current I output or received by the battery mess Measurements are taken and integrated to determine the amount of charge Q accepted by the battery during the first observation period. in,mess and / or the charge Q output by the battery during the second observation period out,mess , wherein the second observation period is preferably selected to be the same as the first observation period or at least partially overlap with the first observation period;

[0050] Calculating the charge Q received by the battery during the first observation period using a voltage-controlled dynamic mathematical battery model parameterized for the battery or predetermined battery type, in particular the dynamic mathematical battery model of the present invention in,mod and the charge Q output by the battery during the second observation period out,mod ;

[0051] · By calculating the charge Q in,mess and charge Q in,mod Zhishang's charging health status SOH in and / or as the charge Q out,mess and charge Q out,mod The discharge health status SOH of the quotient out And use the charging health status SOH in or discharge state of health SOH out Or the average value calculated from this is used as an approximation for the actual health status SOH mod To determine the approximate value SOH for the actual state of health SOH mod .

[0052] It should be noted here that when using the voltage control battery model to calculate the charge Q in,mod or Q out,modIn the step of , it is obvious that the battery voltage measurement data can also be used.

[0053] According to one embodiment, the first and second time periods may be selected such that the charge amount Q charged during the relevant time period is in,mess and / or the amount of charge discharged Q out,mess and / or their values ​​and are greater than respective predetermined values, wherein the predetermined value is preferably greater than the nominal capacity C of the battery N This ensures that the determined value SOH mod Accurate enough.

[0054] According to another embodiment, the end times of the first and second time periods can be selected such that the same state of charge SOC is present at the end time as at the start time. ref , and / or at the end time there is a measured battery current I mess The current flows in the same direction. This reduces the influence of hysteresis effects or model deviations.

[0055] The battery model variant explained above and the method for solving the system of equations shown therefor allow the calculation of the battery current I in a simple manner. mod According to the present invention, the charge Q in,mod and Q out,mod The battery current I can be simply calculated from the dynamic mathematical battery model mod Therefore, it is also easy to determine the approximate value of the actual health state of the battery SOH mod .

[0056] The present invention will be explained in detail below with reference to the embodiments shown in the drawings, which show:

[0057] Figure 1 A schematic diagram showing the method according to the present invention is shown,

[0058] Figure 2 A schematic block diagram shows a battery in load operation together with a device according to the invention for carrying out the method;

[0059] Figure 3 shows a special and complex equivalent circuit model for lithium iron phosphate based lithium ion batteries, which consists of an electrical sub-model ( Figure 3a ) and a thermal model ( Figure 3b )composition;

[0060] Figure 4 The U diagram of a lithium-ion battery with nickel manganese cobalt oxide / graphite compound (NMC graphite) of the manufacturer Kokam, model SLPB533459H4 is shown. 0(SOC) curve, the battery has a nominal capacity of 0.74Ah and a nominal voltage of 3.7V;

[0061] FIG. 5 shows the temperature of the battery according to FIG. 3 at three temperatures ( Figure 5a At 5°C; Figure 5b At 20℃; Figure 5c Simulated discharge-charge characteristics (battery voltage variation with respect to charge quantity) at 35°C and three current intensities (0.06C, 0.28C, 0.93C), wherein for the simulation, model B is parameterized according to this battery;

[0062] FIG6 shows a method for Figure 4 Part of 100 consecutive Birkl charging cycles of the battery, where Figure 6a The measured voltage U is shown as an input parameter of the battery model mess and Figure 6b The measured current intensity (curve (a)) and the current intensity calculated using the battery model (model A) (curve (b)) are shown;

[0063] FIG. 7 shows a method for Figure 4 The results of the new method of battery (according to Model A), in which, Figure 7a shows the state of charge SOC during the first hours of the cycle according to Birkl, Figure 7b The state of charge SOC in the last few hours is shown; the result of this method (curve (b)) is compared with the result determined by the conventional method (curve (a));

[0064] Figure 8 The results of the new method for state-of-health SOH over the entire test period using Model A are shown (curve (b)); this result is compared with the SOH curve obtained by charge counting (curve (v));

[0065] FIG9 shows test results when the new method is applied to a lithium-ion battery for stationary storage, which has an LFP graphite compound and a nominal capacity of 158 Ah for a large number of discharge and charge cycles; Figure 9a shows the measured voltage, Figure 9b Measured current intensity (curve (a)) and simulated current intensity (curve (b)) (using battery model B) are shown;

[0066] FIG10 shows the results of this method for SOC ( Figure 10a ; curve (b)) and the results for SOH ( Figure 10b ); the results of this method are compared with the exact control measurement (curve (v)).

[0067] Figure 1 and Figure 2 The method for determining the load R according to the present invention is shown. L Schematic diagram of an apparatus or method for measuring the SOH and SOC of a battery 106 in operation. Figure 1 As can be seen in FIG, the method can be implemented with the aid of an overall algorithm 100, for example by integration into an existing battery management system. The overall algorithm 100 comprises a first component 102 for SOC determination, which also comprises a dynamic mathematical battery model selected for a specific battery or battery type. The measured battery voltage U mess and the measured battery temperature T mess As an input parameter is input to the first component. Instead of measuring the battery temperature, the measured ambient temperature It can also be input to the first component of the overall algorithm 100. The first component of the overall algorithm can be obtained from the measured battery voltage U mess (Input parameters) Calculate the battery's state of charge (SOC) mod and current intensity I mod (output parameter). The type of battery model itself is not important for this method, as long as these requirements are met. Empirical models, equivalent circuit models, multi-physics models or other models can be envisioned. For SOC determination, only the output parameter SOC mod .

[0068] To determine the SOH, the overall algorithm 100 has a second component 104 , which uses the current I calculated by the first component 102 to determine the SOH. mod and the measured current I mess is supplied as an input parameter to the second component.

[0069] The main feature of the present invention is that the dynamic model works in a voltage-controlled manner, that is, by measuring the voltage U mess The state of charge to be communicated to the user is directly derived from the model as an input parameter. This can be communicated, for example, via a display unit.

[0070] The accuracy of this method depends largely on how accurately the model represents the actual SOC and current intensity I of the actual battery from a given voltage. mess , that is, SOC mod and SOC or I mess and I mod To improve the accuracy, the battery temperature T mess or ambient temperature or other measured parameters are transmitted to the model.

[0071] like Figure 2As shown, the overall algorithm 100 can be easily integrated into an existing battery management system. To this end, the battery management system (not shown) only needs to include a device 108 for executing the method. The device 108 includes a device for measuring the battery voltage U mess The device 108 further comprises a unit 110 for measuring the battery current I mess The unit 112 can be designed in any manner. For example, the unit 112 may include any load R located at the battery pole and also indicated by reference numeral 114. L The unit 112 can be designed to measure the voltage across the shunt resistor and to calculate the current from the measured voltage drop and the resistance value of the shunt resistor.

[0072] The device 108 may also include a display unit 116 on which the determined value for the SOC or SOH is displayed. The device 108 includes a calculation unit 118 for performing the calculations required to implement the method, which may be designed as a microprocessor unit, for example. The microprocessor unit may also have an analog-to-digital converter, which regularly scans the analog parameter U input to the microprocessor unit. mess and I mess And converted into digital values.

[0073] Hereinafter, the basic principles and specific variations of the method of the present invention will now be explained in detail.

[0074] A battery model has two minimum requirements. First, it should be dynamic, that is, it should have at least one state variable that is time-dependent. This is usually the remaining charge Q or the state of charge. It changes with time due to the current intensity applied. Secondly, the voltage change process should be described as a function of the state of charge and the current intensity.

[0075] So in general representation the model consists of two equations,

[0076]

[0077] U mess =U 0 (SOC mod , T mess ,t)+η(I mod , SOC mod , T mess ,t) (2)

[0078] These two equations implicitly describe the N 、U 0 , η) as the measurement input parameter U messThe two unknowns of the related function (SOC mod , I mod )’s time characteristics.

[0079] The two terms on the right side of the second equation represent the open circuit voltage U 0 and the overvoltage η, i.e. the voltage drop caused by slow internal processes such as reactions and transport. Open circuit voltage U 0 Mainly depends on the SOC, and may also depend on the temperature and the charge / discharge history over time (for example in the case of battery materials with hysteresis, such as lithium iron phosphate). The overvoltage depends on the SOC, the current intensity I mod and temperature T mess And also because of the electrochemical double layer and has a significant dynamic (time) curve. Depending on the complexity of the model, other model equations can be used to describe U 0 Here and in the following, the sign of the (measured and calculated) battery current is chosen to be positive in the case of battery discharge, i.e. I>0, and negative in the case of battery charging, i.e. I<0.

[0080] According to SOC mod and I mod Solving the implicit equations (1) and (2) requires an inversion. Depending on the model or implementation, this can be done analytically or numerically. This solution is illustrated in the following example, but other methods are also conceivable.

[0081] One possible implementation of this method uses the open circuit voltage U 0 The real (e.g., measured) relationship between U and SOC 0 =U 0 (SOC), assuming that the overvoltage η = -R i I mod The constant internal resistance R i , and it is assumed to be independent of temperature. Therefore, equations (1) and (2) are simplified to:

[0082]

[0083] U mess =U 0 (SOC mod )-R i I mod (4)

[0084] Relationship U 0 (SOC mod ) can be given in tabular form (e.g., measured values) or in the form of analytical functions. This model is hereinafter referred to as "Model A" or "Simple Model". The system of equations (3) and (4) is simple enough to be analytically inverted. For this purpose,mod Solve equation (4) and use the obtained relationship in equation (3). This yields:

[0085]

[0086] Here, U mess As a (given) independent variable, SOC mod and I mod As the dependent variable, U 0 (SOC), R i and C N as model parameters.

[0087] In a real system, voltage measurements are usually taken as discrete values ​​at regular time intervals Δt. Here, i is the index representing the time step. Therefore, time discretization is necessary to solve the equations (5) and (6). The discretization according to the explicit forward Euler method gives the following solution:

[0088]

[0089] Equation (7) forms the specific calculation rules of the new SOC determination method. The only input parameter is the current voltage measurement value Only the values ​​calculated in the previous step are required As the stored value. The calculated new value The current SOC of the battery is transmitted to the user. Therefore, the determination of the SOC according to equation (7) is very simple and can be performed in a short time with little computing power. It can be easily implemented on a microcontroller because only simple calculation steps are required. The measurement workload is also very low, only time-discrete voltage values ​​need to be measured. Voltage in the form of U mess Unlike conventional methods for determining SOC, there is no need to measure the current intensity.

[0090] Equation (8) provides the related current intensity in parallel This is not required for SOC determination, but is necessary for SOH determination (see below).

[0091] Equations (7) and (8) are derived from Equations (5) and (6) by explicit forward Euler discretization. There are also alternative discretization methods. Although due to the nonlinear relationship U 0 (SOC mod ) and cannot perform implicit inverse Euler discretization, but other numerical methods (such as Newton's method) are needed here. But a special case is based on the relationship U 0 =(U L -U E)·SOC+U E Assume that there is a linear relationship between voltage and SOC, where U L Indicates the end-of-charge voltage, with U E represents the discharge end voltage. Equations (5) and (6) can be further simplified as:

[0092]

[0093] The inverse Euler discretization gives the following result:

[0094]

[0095] In this case, the calculation rules are also simple. This form is also more numerically stable. However, the result will be an oversimplification and unrealistic linear U 0 (SOC mod However, for sufficiently small time steps Δt ≤ 10 s, the calculations do not show any significant difference between the explicit and implicit discretizations.

[0096] Obviously, other analytically specified Us are also conceivable. 0 (SOC) relationship. Depending on the analytical form, the equations (5) and (6) can be solved analytically or using appropriate numerical methods.

[0097] The following example explains a complex battery model, also referred to as Model B, and its use in determining SOC or SOH. Real batteries have complex dynamic current-voltage-temperature characteristics that cannot be fully described by the simple models of Equations (5) and (6). Therefore, a more complex model can be used to improve the reliability of this method.

[0098] The following focuses on the equivalent circuit model shown in Figure 3. It is an electrical / thermal model. The electrical model consists of an open circuit voltage source U 0 (SOC), series resistance R S and two resistor-capacitor (RC) components (R CT and C DL , one for each of the two electrodes, namely the anode and cathode). The asymmetry describing the open circuit voltage (ΔU hys ) and the cathode resistance. Therefore, this model is suitable for describing lithium iron phosphate (LFP) / graphite lithium-ion batteries (see H. Kim, "Parameterized Modeling of Commercial LFP / Graphite Lithium-Ion Batteries Considering Charge and Discharge Characteristics," Master's Thesis, Offenburg University College, 2018), which accounts for these asymmetries. The thermal model consists of heat sources and heat transfer to the environment. It also assumes that all parameters are temperature-dependent.

[0099] The equivalent circuit model can be described by the following differential algebraic equations:

[0100]

[0101] U mess =U 0 (SOC mod , T mod )+ΔU hys (I mod )-U RC，an -U RC，ca -I mod ·R s (T mod ) (14)

[0102]

[0103] Here, U RC is the voltage drop across the RC element, R CT is the charge transfer resistance, C DL is the double-layer capacity, C th is the heat capacity, R th is the heat transfer resistance on the battery surface, dU 0 (SOC Modell ) / dT is the temperature dependence of the open circuit voltage, T 0 is the relevant reference temperature, and the indices an and ca denote the "anode" and "cathode", i.e. the two electrodes. The asymmetry of the open circuit voltage is given by ΔU hys The asymmetry of the cathode resistance is described by the current dependence R CT,ca Description. By comparing equations (13) and (14) with equations (1) and (2), it can be seen that this is another form of the basic model. The description requires the additional equations (15) to (17). As mentioned above, equations (13) to (17) implicitly describe the measured input parameters (i.e. voltage U mess and ambient temperature ) of the function to find the two unknowns (SOC mod , I mod )’s time characteristics.

[0104] Due to the coupling of the equations, an analytical solution cannot be achieved. The implicit numerical solver available in the MATLAB software package was used for the simulation results explained below. However, other methods can also be used to achieve the solution.

[0105] It is important to point out once again that the two proposed models A and B are only used to demonstrate the new method, but the new method is by no means limited to these two specific models. On the contrary, any simpler or more complex model is conceivable.

[0106] The above models (A: Simple Model and B: Equivalent Circuit Model) can be configured to describe different batteries or battery types based on parameter settings. The following describes parameter settings for the two models based on specific lithium-ion battery cells.

[0107] Lithium-ion batteries with nickel-manganese-cobalt oxide / graphite (NMC graphite), specifically the type SLPB533459H4 from the manufacturer Kokam with a nominal capacity of 0.74 Ah and a nominal voltage of 3.7 V, are considered to be an exemplary representative of batteries for use in the electric vehicle sector. Birkl and Howey have made a detailed data set from these batteries freely available (Christoph Birkl, David Howey, “Oxford Battery Degradation Dataset 1”, Oxford University Press, DOI: 10.5287 / bodleian:KO2kdmYGg, website: https: / / ora.ox.ac.uk / objects / uuid:03ba4b01-cfed-46d3-9b1a-7d4a7bdf6fac (2017)), which are very suitable for demonstrating the present method.

[0108] The model A (“simple model”) is parameterized for the battery as follows: the open circuit voltage curve U 0 The state of charge (SOC) is determined by averaging the charge and discharge characteristic curves, both acquired at 40 mA (quasi-open circuit voltage). The capacity is normalized to the maximum value. Figure 4 The U obtained in this way is shown 0 (SOC) relationship. Nominal capacity C N = 0.74Ah taken directly from the manufacturer's information. The internal resistance was determined by reading the battery charge voltage from the test at 50% SOC for discharge at 40mA and 740mA, respectively. It is assumed that this parameter is independent of temperature. Therefore, a complete parameter setting only requires two experimental charge / discharge characteristics (40mA and 740mA).

[0109] A lithium-ion battery with lithium iron phosphate / graphite compound (LFP graphite), in particular the type SP-LFP180AHA from the manufacturer Sinopoly with a nominal capacity of 180 Ah and a nominal voltage of 3.2 V, is considered below as an exemplary representative of a battery chemistry for use in the field of stationary electrical storage (home storage, commercial storage, storage for network applications, uninterruptible power supplies). This battery has been characterized by the University of Offenburg (see H. Kim, ibid.).

[0110] For this example, the parameters of model B (equivalent circuit model) are set for this specific battery cell. Figure 5 shows the simulated discharge-charge characteristic curves (battery voltage as a function of charge) after the parameters are successfully set at three temperatures (5°C, 20°C and 35°C) and three currents, where the current intensity is given in units of charge rate (C-rate) (i.e., 1C=180A in the present case). The arrows here indicate the direction of the curve, such as the discharge direction (right arrow) and the charging direction (left arrow). Here, the upper curves in the composite curve are respectively the charging curves, and the lower curves are respectively the discharge curves. The darkest curves (upper and lower) are the charge and discharge curves for a current of 0.93C, and the upper and lower curves in the innermost curve (the brightest drawing) are the charge and discharge curves for a current of 0.06C. The curve located between these curves is the charge and discharge curve for a current of 0.28C. The points of the curve represent the measured values, and the solid line represents the simulated values. As can be seen from FIG. 5 , the asymmetry and hysteresis including the measured values ​​as well as the experiments can be predicted very well by the model over the entire range.

[0111] The SOH determination using the SOH algorithm will be explained in more detail below. Its specific application also presupposes the parameter setting of the dynamic mathematical battery model used as described above.

[0112] In addition to the state of charge SOC mod In addition, the battery model shown above can also provide the current intensity I mod As output parameter. In addition to the current intensity according to the model, it is also necessary to measure the current intensity I mess To determine SOH. The SOH algorithm can be used from I mod and I mess Calculate the state of health (SOH).

[0113] The basis of this algorithm is that the battery model, which is a "digital twin", performs the same cycles as the real battery because it (as mentioned above) operates at the same voltage as the real battery. However, unlike the real battery, the battery model does not age. Therefore, the SOH can be calculated from the I mod (no capacity loss) and I mess (with capacity loss) is determined. For this purpose, a charge counter is used, that is, a charge counter is used to measure the current I mess and the current I determined by the model mod The calculation is shown below.

[0114] As mentioned above, the voltage-controlled battery model is a prerequisite for the algorithm, because only in this way can I mod Only I can mess The output parameters for comparison. Therefore, the new SOH determination method is closely related to the new SOC determination method.

[0115] For a value starting from time t0 and ending at time t l Complete battery discharge (from full to empty), SOH out It can be defined by the following relationship:

[0116]

[0117] Among them, I bat,n Indicates the battery current of a new battery (not aged battery), using I bat,akt Indicates the battery current of an aging battery.

[0118] Hypothesis I bat,akt corresponds to the measured current of a real battery (with capacity loss), while I bat,n Corresponding to the simulated current from the battery model (no capacity loss), the SOH out It can be expressed as:

[0119]

[0120] Similarly, if we assume that the battery is empty, we can also define the SOH during the battery full charge period as in :

[0121]

[0122] Here, it is assumed that the charging process starts at time t0 and ends at time t V Finish.

[0123] In practice, complete charging and discharging processes are rare (for example, an electric car battery is never completely drained because it would no longer work). Therefore, it should be feasible for the algorithm to be able to determine the SOH based on partial charging and discharging. For this purpose, we define an arbitrary period [t1; t2] without knowing in advance whether charging, discharging, or both are performed during this period (for example, one or more complete cycles or partial cycles). This period [t1; t2] usually lasts for several hours; more precise requirements are given below. During this period, we can calculate the SOH as:

[0124]

[0125] Where the indices "out" and "in" in the current represent the discharge (out) and charge (in) of the battery. In these equations:

[0126]

[0127]

[0128] Therefore, in equation (21) only the integration is done during discharge, and in equation (22) only the integration is done during charge. In principle, each of these SOH values, i.e., SOH out or SOH in can be used as an approximation for the actual SOH. However, the accuracy can be improved by averaging according to the following relationship:

[0129]

[0130] The time period [t1; t2] is arbitrary; however, the choice of the time period affects the accuracy of the method. In a specific implementation of the method, the time period is preferably selected taking into account the following conditions:

[0131] The amount of charge discharged and charged during this period should be greater than the predetermined threshold Q s (For example, C N or C N multiples of ).

[0132] Same state of charge (SOC) ref (e.g. 50%) at the beginning and end of the period respectively.

[0133] • The same current direction exists at the beginning and end of the period (e.g. a battery is charging).

[0134] It is also possible to use different partial overlap periods for the two parameters SOH out and SOH In This is used, for example, in the method implementation shown below.

[0135] The advantage of this method is that, unlike conventional methods, no full cycle needs to be carried out experimentally, and no cycle counting algorithm is required.

[0136] In one specific implementation as program code that can be run on a microcontroller, the algorithm can be designed so that it determines the four charge counters (Q out,mess , Q out,mod , Q in,mod , Q in,mod ) and two SOH values ​​(SOH out 、SOH in ) and are stored separately. The algorithm is called periodically according to a period Δt; ideally, this period is the same as that used in the SOC calculation. mod The values ​​of are obtained from the SOC algorithm.

[0137] Then proceed with the following logic:

[0138] 1. Charge counter

[0139] (a)Imod <0(discharge)?

[0140] Yes: Q out，mod =Q out，mod -I mod ·Δt

[0141] (b)I mod >0(Charging)?

[0142] Yes: Q in，mod =Q in，mod +I mod ·Δt

[0143] (c)I mess <0(discharge)?

[0144] Yes: Q out，mess =Q out，mess -I mess ·Δt

[0145] (d)I mess >0(Charging)?

[0146] Yes: Q in，mess =Q in，mess +I mess ·Δt

[0147] 2. SOH calculation

[0148] (a)Q out，mod >Q s And Q out，mess >Q s And SOC mod =SOC ref And is the battery discharging?

[0149] yes:

[0150] Reset Q out，mess and Q out，mod is zero.

[0151] (b)Q in，mod >Q s And Q in，mess >Q s And SOC mod =SOC ref And is the battery charging?

[0152] yes:

[0153] Reset Q in，mess and Q in，mod To zero.

[0154] (c)

[0155] For example, the last calculated value SOH is returned by the algorithm and can be displayed to the user. Parameter Q S and SOC ref Affects the performance of SOH fault diagnosis. In the example shown below, Q S =C N and SOC ref =50%.

[0156] The method is demonstrated below with reference to lithium-ion battery cells containing NMC graphite compounds (representative of the application area of ​​electric vehicles). For this purpose, freely available experimental data from Birkl (ibid.) are used. Model A ("simple model") will be used.

[0157] The Birkl experiment (supra) was carried out as follows: the test battery was subjected to a large number of continuous cycles until the battery life was exhausted, wherein the battery was charged in each cycle using the CCCV (constant current constant voltage) method and discharged using a dynamic load profile that simulates the urban driving cycle. After every 100 cycles, a measurement cycle was carried out to characterize the battery characteristics, wherein the battery or battery cell was discharged with a constant current intensity of 0.74 A to a final voltage of 2.7 V and then charged to a final voltage of 4.2 V. This characterization process was repeated about 80 times. However, only the complete discharge / charge cycles of the characterization cycle are published. They have been combined for the purpose of demonstration here and therefore represent accelerated aging behavior. At the same time, another advantage of the new method is demonstrated, namely the ability to switch to battery operation at any time and to cope with incomplete data.

[0158] FIG6 shows the measured and calculated parameters of this method using a simple model (Model A), namely, Figure 6a shows the measured voltage of the battery, Figure 6b Shows the measured current intensity I of the battery mess (curve (a)) or calculate the current intensity I mod (Model output parameters, SOH algorithm input parameters, curve (b)). The significant discrepancy between the model and the measurements stems from imperfections in the model used. However, convincing results can still be obtained, as shown below.

[0159] FIG7 shows the state of charge (SOC) of a battery determined according to the new method (in a specific design according to equation (7)) (curve (b)). Also shown is the SOC value determined according to the conventional method based on charge counting (normalized to a fully discharged battery) (curve (a)). Figure 7a The first few hours of the cycle are shown. The new method can determine the SOC very accurately (compared to conventional methods). Figure 7bThe last few hours of the cycle are shown. Here, the cell has clearly aged, meaning it has lost capacity. The new method reliably depicts the entire cycle. However, a disadvantage of conventional methods is cell aging: despite charging to the end-of-charge voltage, the SOC in conventional methods only reaches an (abnormal) value of approximately 75%. This comparison demonstrates the robustness of the new SOC determination method with respect to capacity loss caused by battery aging.

[0160] The results of SOH determination are Figure 8 is shown in (curve (b)). In addition, a comparison with the value from simple charge counting according to equation (19) is shown (curve (v)). The agreement is very good. From these results, it can be concluded that the SOH can be reliably determined with the new method.

[0161] The method is demonstrated below using a lithium-ion battery cell with an LFP graphite compound (representative of the field of stationary storage applications), with model B (“equivalent circuit model”) being used for this purpose.

[0162] For the experiment, more than 670 consecutive charge / discharge cycles were performed, with discharge at a constant current of 150 A and charging using the CCCV charging method. The discharge end voltage was 2.85 V, and the charge end voltage was 3.8 V. The test time was approximately 1500 hours. The capacity of the new battery was C N The battery life is 158 Ah. Using this data set, not only the SOC determination (during any individual cycle) but also the SOH determination (during the entire test period) can be demonstrated. Furthermore, highly accurate SOC and SOH values ​​were determined using suitable measurement techniques based on the common charge counting method, which were used for comparison with the new method.

[0163] FIG9 shows the input parameters of the method, namely the measured voltage U of the battery mess ( Figure 9a ) and measuring current intensity I mess ( Figure 9b , curve (a)). Figure 9b Also shown is the simulated current intensity I mod (Output parameters of the model and input parameters of the SOH algorithm, curve (b)) The significant discrepancy between the model and the measurements stems from the imperfections still present in the model used.

[0164] 10 shows the results of this method (curve (b)), namely the state of charge SOC and state of health SOH of the battery. For comparison, the values ​​from an accurate comparative measurement are also shown (curve (v)). Figure 10a The new method can reliably reflect the battery cycling between 0% and 100% SOC, although there is a small error compared to the exact measurement. Figure 10bThe SOH is shown. The new method reliably reflects the battery capacity loss during the approximately 1500 hours of testing. Compared to the precise measurement, only increased noise is shown.

[0165] These results demonstrate the ability of the above method to determine battery state of charge and state of health.

[0166] List of main names of variables and parameters

[0167] Reference Signs List

[0168] 100 Overall Algorithm

[0169] 102 The first part of the overall algorithm 100

[0170] 104 The second part of the overall algorithm 100

[0171] 106 batteries

[0172] 108 Apparatus for performing the method

[0173] 110 Voltage measurement unit

[0174] 112 Current measurement unit

[0175] 114 load

[0176] 116 display units

[0177] 118 computing units

Claims

1. A method for determining the state of charge of a rechargeable battery or a parameter physically related thereto, wherein: The method comprises the following steps: (a) creating a voltage-controlled dynamic mathematical battery model for the battery (106) or the battery (106) with a specified battery type, (i) The dynamic mathematical battery model calculates the state of charge (SOC) of the battery (106) mod or the parameters physically related thereto and the battery current I mod associated, and (ii) The dynamic mathematical battery model defines the open circuit voltage U of the battery (106) measured between the two electrodes of the battery (106) 0 Voltage U related to the sum of the overvoltage η mess , (iii) Wherein, the open circuit voltage U 0 At least depends on the remaining capacity Q or the parameters physically related thereto, and the overvoltage η at least depends on the battery current I mod ;and (iv) wherein the voltage-controlled dynamic mathematical battery model is composed of or derived from an implicit set of equations, the set of equations comprising the following equations: (1) (2)U mess =U 0 (SOC mod ,T mess ,t)+η(I mod ,SOC mod ,T mess ,t) Among them, C N The specified nominal capacity of the battery (106) is represented by T mess represents the measured temperature of the battery (106), and t represents the time, wherein the open circuit voltage U 0 With the state of charge SOC mod The relationship is required, and with the measurement temperature T mess The relationship between the overvoltage η and the battery current I is optional, and mod The relationship is required, and the state of charge SOC mod The relationship to this time t is optional; (b) parameterizing a dynamic mathematical battery model for said voltage control of the battery (106) or the specified battery type; and (c) By measuring the battery voltage U mess And calculate the approximate SOC using the voltage controlled dynamic mathematical battery model with parameter settings mod To determine an approximate value for the actual state of charge (SOC) of the battery (106) or to determine an approximate value for a parameter physically related thereto.

2. The method according to claim 1, characterized in that Assume that the open circuit voltage U 0 Only with the state of charge SOC mod It is assumed that the battery (106) has a constant internal resistance R i And assuming that the battery model is independent of temperature, the battery model is defined by the following equation: (a) (b)U mess =U 0 (SOC mod )-R i ·I mod , Among them, the open circuit voltage U 0 With the state of charge SOC mod The relationship is determined.

3. The method according to claim 2, characterized in that Both equations in claim 2 are solved by analytical inversion, where the state of charge SOC mod Calculated by the following equation:

4. The method according to claim 3, characterized in that Discrete voltage measurements at predetermined time intervals Δt or at specified times The voltage U is detected in the form of mess , and the approximate value for the state of charge SOC mod The calculation is performed by discretizing the equation according to claim 3 using a mathematical discretization method.

5. The method according to claim 4, characterized in that The approximate value for the state of charge SOC mod The equation according to claim 3 is discretized and calculated using a mathematical discretization method, that is, the explicit forward Euler method is used to calculate the equation as follows: Here, i is the index representing the time step.

6. The method according to claim 3, characterized in that It is also assumed that the open circuit voltage U 0 and the state of charge SOC mod There is a linear relationship between them, and the state of charge is calculated by the following relationship: and Among them, U L Indicates the end-of-charge voltage, with U E Indicates the discharge end voltage.

7. The method according to claim 6, characterized in that The discrete voltage measurement value is measured at a predetermined time interval Δt The voltage U is detected in the form mess , and calculating the approximate value SOC for the state of charge by discretizing the equation according to claim 6 using a mathematical discretization method mod .

8. The method according to claim 7, characterized in that The approximate value SOC for the state of charge is calculated by discretizing the equation according to claim 6 using a mathematical discretization method. mod , that is, using the implicit inverse Euler method, it is calculated by the following equation: and Here, i represents the index used for the time step.

9. The method according to claim 1, characterized in that (a) An equivalent circuit model is used as a mathematical battery model, the equivalent circuit model being described by the equations according to features (a)(iv)(1) and (a)(iv)(2) of claim 1, wherein the equations according to feature (a)(iv)(2) of claim 1 are replaced by the following system of equations: (i)U mess =U 0 (SOC mod ,T mod )+ΔU hys (I mod )-U RC，an -U RC，ca -I mod ·R s (T mod ) (ii) (iii) (iv) Among them, U RC Represents the voltage drop across an RC element, using R CT Represents the charge transfer resistance, C DL Denotes the double layer capacitance, C th Indicates heat capacity, using R th Indicates the thermal resistance at the battery surface, expressed as dU 0 (SOC mod ) / dT represents the temperature dependence of the open circuit voltage, and T 0 Indicates the relevant reference temperature, using The measured ambient temperature of the battery (106) is represented by T mod Indicates the model battery temperature, using R s represents the series resistance, wherein the indices "an" and "ca" refer to the anode and cathode of the battery (106), and wherein the open circuit voltage U 0 The asymmetry of ΔU hys The asymmetry of the cathode resistance is described by the current dependence R CT，ca Description, and (b) The state of charge (SOC) mod The value of is calculated by this system of equations.

10. A method for determining the state of health of a rechargeable battery of a specified battery type or a parameter physically related thereto, comprising the steps of: (a) creating a voltage-controlled dynamic mathematical battery model for the battery (106) or the battery with a specified battery type, (i) The voltage-controlled dynamic mathematical battery model converts the battery's state of charge (SOC) mod or the parameters physically related thereto and the battery current I mod associated, and (ii) The voltage-controlled dynamic mathematical battery model defines the open circuit voltage U of the battery (106) measured between the two electrodes. 0 Voltage U related to the sum of the overvoltage η mess , (iii) Wherein, the open circuit voltage U 0 At least depends on the remaining capacity Q or the parameters physically related thereto, and the overvoltage η at least depends on the battery current I mod ; (iv) wherein the voltage-controlled dynamic mathematical battery model is composed of or derived from an implicit set of equations, the set of equations comprising the following equations: (1) (2)U mess =U 0 (SOC mod ,T mess ,t)+η(I mod ,SOC mod ,T mess ,t) Among them, C N The specified nominal capacity of the battery (106) is represented by T mess represents the measured temperature of the battery (106), and t represents the time, wherein the open circuit voltage U 0 With the state of charge SOC mod The relationship is required, and with the measurement temperature T mess The relationship between the overvoltage η and the battery current I is optional, and mod The relationship is required to parameterize a dynamic mathematical battery model for said voltage control of the battery (106) or the specified battery type; (b) by controlling the battery current I outputted or received by the battery (106) mess Measurements are taken and integrated to determine the amount of charge Q received by the battery (106) during the first observation period. in,mess and / or the charge Q outputted by the battery (106) during the second observation period out,mess ; (c) calculating the charge Q received by the battery (106) during the first observation period using the voltage-controlled dynamic mathematical battery model parameterized for the battery (106) or the specified battery type in,mod and the charge Q output by the battery (106) during the second observation period out,mod ;and (d) By calculating the charge Q in,mess And the charge Q in,mod Zhishang's charging health status SOH in and / or as the charge Q out,mess And the charge Q out,mod The discharge health status SOH of the quotient out And use the charge health status SOH in or the discharge state of health SOH out Or the average value calculated from this is used as an approximation for the actual state of health SOH mod To determine the approximate value SOH for the actual state of health SOH mod .

11. The method according to claim 10, characterized in that The first observation period and the second observation period are selected in such a way that the amount of charge Q charged during the relevant period is in,mess and / or the amount of charge Q out,mess and / or the sum of their values ​​is greater than a respectively predetermined value.

12. The method according to claim 10 or 11, characterized in that The end times of the first observation period and the second observation period are selected such that at the end times the same state of charge SOC exists as at the start times. ref and / or the measured operating current I at the end time is the same as the measured operating current I at the start time. mess Same current direction.

13. The method according to claim 10, characterized in that The charge Q in,mod and Q out,mod By calculating the battery current I mod Calculate by integration.

14. The method according to claim 10, characterized in that Assume that the open circuit voltage U 0 Depends only on the state of charge SOC mod , assuming a constant internal resistance R of the battery (106) i , assuming that the battery model is temperature independent and the battery current I mod Calculated from the equations obtained by analytical inversion: Among them, the open circuit voltage U 0 With the state of charge SOC mod The relationship is determined through measurement.

15. The method according to claim 14, characterized in that The voltage U mess The discrete voltage measurement value is measured at a predetermined time interval Δt form is detected, and the battery current I mess The calculation is performed by discretizing the equation according to claim 14 using a mathematical discretization method.

16. The method according to claim 15, characterized in that The battery current I mess The calculation is performed by discretizing the equation according to claim 14 using a mathematical discretization method, that is, using an explicit positive Euler method from the following equation: Here, i represents the index used for the time step.

17. The method according to claim 14, characterized in that It is also assumed that the open circuit voltage U 0 With the state of charge SOC mod There is a linear relationship between them, and the battery current is calculated from the following relationship: and Among them, U L Indicates the end-of-charge voltage, with U E Indicates the discharge end voltage.

18. The method according to claim 17, characterized in that At predetermined time intervals Δt or at specified times, discrete voltage measurements are taken The voltage U is detected in the form mess , and the approximate value for the state of charge SOC mod The calculation is performed by discretizing the equation according to claim 17 using a mathematical discretization method.

19. The method according to claim 18, characterized in that The approximate value for the state of charge SOC mod The calculation is performed by discretizing the equation according to claim 17 using a mathematical discretization method, that is, using the implicit inverse Euler method from the following equation: and Here, i represents the index used for the time step.

20. The method according to claim 10, wherein (a) An equivalent circuit model is used as a mathematical battery model, the equivalent circuit model being described by equations according to features (a)(iv)(1) and (a)(iv)(2) of claim 10, wherein the equations according to feature (a)(iv)(2) of claim 10 are replaced by the following set of equations: (i)U mess =U 0 (SOC mod ,T mod )+ΔU hys (I mod )-U RC，an -U RC，ca -I mod ·R s (T mod ) (ii) (iii) (iv) Among them, U RC Represents the voltage drop across an RC element, using R CT Represents the charge transfer resistance, C DL Denotes the double layer capacitance, C th Indicates heat capacity, using R th Indicates the heat transfer resistance on the battery surface, expressed as dU 0 (SOC mod ) / dT represents the temperature relationship of the open circuit voltage, and T 0 Indicates the relevant reference temperature, using Indicates the measured battery ambient temperature, T mod Indicates the model battery temperature, using R s represents the series resistance, wherein the indices "an" and "ca" refer to the anode and cathode of the battery (106), and wherein the open circuit voltage U 0 The asymmetry of ΔU hys The asymmetry of the cathode resistance is described by the current dependence R CT,ca describe, (b) Calculate the battery current I from the equations mod ,and (c) The charge Q in,mod and Q out,mod By calculating the battery current I from the dynamic mathematical battery model mod Calculate by integration.

21. A device for carrying out the method according to any one of claims 1 to 9, comprising a device for measuring the battery voltage U mess A unit (110) and an approximate value SOC for calculating the actual state of charge SOC for the battery (106) mod unit.

22. A device for carrying out the method according to any one of claims 10 to 20, comprising a device for measuring the battery voltage U mess The unit (110) is used to measure the battery current I mess The unit (112) and the approximate value SOH for calculating the actual state of health SOH of the battery mod unit.

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