DE102009029347A1 - Method for determining charging condition of secondary intercalation cell, involves soaking anode, cathode and separator in electrolyte phase, and incorporating diffusion mechanisms of moving ions in electrochemical simulation model - Google Patents

Abstract

The method involves soaking an anode (35), a cathode (36) and a separator in an electrolyte phase. The diffusion mechanisms (43,44) of moving ions in the active material of the anode and cathode modifying with the charging condition (SOC) are incorporated separately in an electrochemical simulation model (21).

Description

State of the art

The invention relates to a method for determining the state of charge of a secondary dual intercalation cell of a rechargeable battery, in particular for a motor vehicle, according to the preamble of claim 1.

Secondary electrochemical cells, commonly referred to as accumulators, differ from primary electrochemical cells in their rechargeability.

In many technical applications it is desirable and even necessary to obtain information about the charge or discharge state, in particular of a secondary cell, from variables measurable outside the cell.

For charge state determination and prediction of secondary cells, simulation models or model-based approaches are generally used. These include so-called equivalent circuit models, which are intended to approximate the electrical behavior of a cell or battery with linear-passive elements, such as R, L, C members. In general, however, the state of charge (SOC) is not directly measurable.

In the prior art, the SOC is typically used as a function of the quiescent voltage, i. e. the battery or battery return voltage and / or from a current integration and / or from a combination, which different state variables, such as the last determined SOC, the cell or battery temperature, the cell or Batteryieresespannung, the strength of the cell or battery currents and the like.

By the DE 198 31 723 A1 For example, a method for determining the state of charge of a rechargeable battery provided as a vehicle starter battery in a vehicle with a starter is known. It is provided to detect the voltage drop of the battery voltage during operation of the starter and subsequently assign a state of charge value.

In the DE 199 13 627 A1 a method for determining the state of charge of an accumulator is described, which provides for an accumulator which is charged by means of a variable energy source by the energy generated by the variable energy source is converted into defined current pulses and pulse pauses and fed in this form to the accumulator, the State of charge to determine that the voltage profile in the accumulator is measured and evaluated in response to the current pulses.

bestimmt, wobei U_R,min und U_R,max die minimale bzw. maximale Ruhespannung bei den vom Batteriehersteller angegebenen Werten der Säuredichte für eine leere bzw. vollgeladene Batterie bezeichnen.Also by the DE 198 31 723 A1 a method for determining the state of charge of a designated as a vehicle starter battery accumulator is known, which vehicle starter battery is used in a vehicle operation without rest periods. In this case, in the case of a work area which preferably concerns the discharge operating range of the battery, the state of charge is calculated on the basis of a model calculation in which a measured and a calculated battery voltage are adjusted via a feedback. The underlying model calculation assumes a nearly linear relationship between the charge Q of the battery and the rest voltage U _R of the battery, given by the capacity C of the battery. The dynamics of gravity balance between the plate pores, and the free acid volume of the vehicle starter battery is designed as a classical lead-acid battery is used in the model calculation using a concentration overvoltage U _K via a arranged in series to the capacitance C of the battery capacity C _K and a plane parallel to the capacitance C _K resistor R _K reproduced. Furthermore, the model calculation includes an internal resistance R _I of the battery arranged in series with the capacity C of the battery. First, a battery voltage U _Batt and a battery current I _{Batt are} measured. The battery current I _Batt is entered directly in the model calculation. The measured battery voltage U _Batt is compared with an estimated battery voltage U _Batt 'and also entered into the model calculation to calculate a quiescent voltage value U _R. To estimate the rest voltage U _R , the concentration overvoltage U _K and the internal resistance R _I is an observer z. B. used in the form of a Kalman filter. The model calculation is balanced in the discharge work area by feedback of the error between measured battery voltage U _Batt and estimated battery voltage U _Batt '. In the remaining workspaces, the feedback of the model calculation error is interrupted and the quiescent voltage is calculated from the current integral and the quiescent voltage last estimated during the last discharge workspace. The SOC is then according to an equation of the form

where U _{R, min} and U _{R, max} denote the minimum and maximum open circuit voltages, respectively, at the acid density values indicated by the battery manufacturer for an empty or fully charged battery.

By the DE 101 39 049 A1 Another method for determining the state of charge of a vehicle battery is known. For this purpose, a state of charge determining operation is first activated, then set by controlling at least one electric machine of the vehicle, a defined load current and derived a voltage characteristic of a measured vehicle electrical system voltage. In addition, information about the battery temperature of the vehicle is provided and finally determines the state of charge of the vehicle battery using the voltage characteristic, the battery temperature and a stored map.

From the DE 103 01 823 A1 Also, a method for determining the state of charge of a rechargeable battery is known. In order to determine the charge which can be taken from a lead-acid battery up to a predetermined discharge deadline, a model calculation is used which mathematically represents the electrical properties of the lead-acid battery. With the help of the model calculation, the charge which can be taken from a given discharge current is calculated, wherein state variables and / or parameters for the model calculation are determined from current operating variables battery voltage, battery current and battery temperature of the lead-acid battery.

A disadvantage of the above-mentioned methods is that their simple structure for determining the SOC with only a few parameters is paid for by complex dependencies of the parameters of SOC, cell temperature and current intensity. Consequently, the model calculations apply only in a narrow operating range. Accordingly, to cover all possible operating states, a number of model calculations or model-variant model calculations would have to be applied. This can lead to instability of the algorithm underlying the model calculations if the parameters change greatly.

Furthermore, a metrological realization of the current integration is generally very faulty, which can lead to strong deviations in the SOC prediction or determination. Furthermore, the dependency of the battery capacity on the extracted power is not considered.

In addition, the accumulators, in which the above-mentioned methods are provided for the prediction of the respective SOC and are also largely suitable to z. B. used as vehicle starter batteries lead acid batteries. Although they meet requirements, such as those required for use in particular for short-term applications in motor vehicles, for. B. high discharge currents, simple construction and cost-effective production; However, they have significant disadvantages in terms of their energy density.

Much higher energy densities have so-called intercalation, in which the electromotive force is not such. B. in lead-acid batteries by a chemical transformation of the material of the electrodes, but is generated by a shift of ions.

In general, molecules, ions or atoms are intercalated into compounds without the compounds significantly changing their structure during the intercalation process. Especially in inorganic chemistry, intercalation refers to the incorporation of atoms, ions or small molecules between the crystal lattice planes of layered crystals.

In an intercalation cell, during the charging process, positively charged ions migrate from the cathode through an electrolyte between the crystal lattice planes, preferably made of a porous material, e.g. B. from a porous layer crystal material, existing anode, while the charging current supplies the electrons via the external circuit. The ions form so-called intercalation complexes with the material of the anode. During discharge, the ions migrate back through the electrolyte into the metal oxide of the cathode and the electrons can flow to the cathode via the external circuit. Dual secondary intercalation cells have porous intercalation electrodes of a porous material both on the anode side and on the cathode side.

A well-known example of an intercalation cell is a lithium-ion battery and its advancements such. As a lithium polymer battery, a lithium titanate battery, a super charge Ion Battery (SCiB), a lithium-manganese battery or a lithium-iron-phosphate battery.

In an intercalation cell, the determination of the state of charge or of the SOC is much more difficult than z. As in a conventional lead-acid battery, since the intercalation forms a spatial distribution that significantly influences an underlying simulation model.

An alternative approach for determining the SOC which can also be used for intercalation cells is the modeling by means of the underlying physical and / or chemical effects in the cell. In this context, we speak of an electrochemical simulation model.

By M. DOYLE, T. FULLER, J. NEWMAN "Modeling of galvanostatic charge and discharge of the lithium / polymer / insertion cell ", Journal of the Electrochemical Society 140 (1993), pp. 1526-1533 , and through T. FULLER, M. DOYLE, J. NEWMAN, "Simulation and Optimization of the Dual Lithium Ion Insertion Cell," Journal of the Electrochemical Society 141 (1994), p. 1-10 For example, electrochemical simulation models are known which show the physical and chemical effects in a schematic way 1 in their construction, dual secondary lithium-ion intercalation cell 01 replicate. That also simplifies as a cell 01 designated lithium-ion intercalation cell 01 consists essentially of one by active particles 02 formed porous cathode 11 or positive electrode 11 one by active particles 04 formed porous anode 12 or negative electrode 12 and one between the electrodes 11 . 12 arranged separator 13 , Between the particles 02 . 04 The electrodes contain binders and fillers 14 , Remaining voids between the active particles 02 . 04 the electrodes 11 . 12 are with one as well as electrolyte phase 10 designated electrolyte 10 flooded.

• – Diffusion von Lithium-Ionen Li+ innerhalb der Partikel 02, 04 zur Grenzfläche der aktiven Partikel 02, 04 zum Elektrolyt 10,
• – Diffusion von Lithium-Ionen Li+ in der Elektrolytphase 10 zwischen den Elektroden 11, 12,
• – Ohm'sches Gesetz für das Potenzial in der Elektrolytphase 10,
• – Ohm'sches Gesetz für das Potenzial im aktiven Elektrodenmaterial 02, 04 der Elektroden 11, 12,
• – Strombilanz in der Elektrolytphase 10, sowie
• – Butler-Volmer-Reaktionskinetik für den Ladungsdurchtritt durch die Grenzschicht zwischen den aktiven Partikeln und dem Elektrolyt.

These electrochemical simulation models allow the calculation or consideration of the physical and chemical effects:

• - Diffusion of lithium-ion Li + within the particles 02 . 04 to the interface of the active particles 02 . 04 to the electrolyte 10 .
• - Diffusion of lithium ions Li + in the electrolyte phase 10 between the electrodes 11 . 12 .
• - Ohm's law for the potential in the electrolyte phase 10 .
• - Ohm's law for the potential in the active electrode material 02 . 04 the electrodes 11 . 12 .
• - Current balance in the electrolyte phase 10 , such as
• - Butler-Volmer reaction kinetics for the passage of charge through the boundary layer between the active particles and the electrolyte.

These simulation models belong to the class of the so-called distributed systems, since they provide a local variation of state variables over the in 1 by a linear scale 09 consider schematically illustrated cell cross-section or because the local variation of state variables over the cell cross-section are also calculated. Every subdivision of the scale 09 symbolizes a discretization point for the partial differential equations in the distributed system. This leads to a high model order, combined with a corresponding computational effort.

From a control point of view, in the case of the simulation models, the diagram is shown schematically by the arrows 06 respectively. 07 in 1 The introduced or demanded current represents the input quantity and the cell voltage shown schematically by a voltmeter 08 the observable output. The cell voltage 08 results from the potential of the active electrode material 02 on the right side 03 the cathode of the cell 01 minus the potential of the active electrode material 04 on the left edge 05 the cathode of the cell 01 , The SOC results physically from the diffusion-based concentration of lithium ions Li + in the active particles of the electrodes 02 . 04 or in the active electrode material 02 . 04 and becomes from the also called clamping voltage cell voltage 08 recalculated.

Advantages of these distributed systems forming electrochemical simulation models are an accurate reproduction of the cell behavior, a consideration of a power-dependent capacity as well as a physical calculation of the SOC from the lithium-ion concentration in the active electrode material.

Disadvantages of these distributed systems forming electrochemical simulation models are a large number of parameters (over 50 parameters), a huge amount of computational complexity and a disadvantageous numerical conditioning. Moreover, the processes underlying the distributed electrochemical simulation models are not observable in practical applications where only current, voltage and temperature are measurable.

By S. SANTHANAGOPALAN, RE WHITE "Online estimation of the state of charge of a lithium ion cell", Journal of Power Sources 161 (2006), pp 1346-1355 , a system also known as a single particle model is known, which, in contrast to the distributed systems described above, averages the physicochemical properties across the electrodes and neglects the effects of the processes in the electrolyte phase and in the separator. Averaging over the electrodes is accomplished by averaging the physicochemical properties considered in the distributed system over a variety of spatial discretization points across each of the anode and cathode. The effects of the processes in the electrolyte phase and in the separator are thereby neglected by neglecting the influence of the lithium ions in the electrolyte phase.

More specifically, in the single-particle model, each porous electrode is simplified as a single spherical particle immersed in the electrolyte phase, the surface of which is extrapolated to the entire electrode by taking into account the porosity by means of a shape factor and the electrode volume. For the accurate description of the material transport or diffusion of the lithium ions, the representative spherical particle has the same radius as that of the distributed model. In addition, in the single-particle model, concentration and potential changes in the electrolyte phase is ignored. In addition, all parameters are kept constant and thermal influences neglected. The lithium concentration in the anode and in the cathode is determined by the lithium concentration at the surface of each spherical particle and the average concentration within the spherical particle. Butler-Volmer reaction kinetics are used for the surfaces of the spherical particles forming the anode and the cathode, respectively.

• – Butler-Volmer-Reaktionskinetik für den Ladungsdurchtritt durch die Grenzschicht zwischen den beiden die Elektroden bildenden kugelförmigen Partikeln und der sie umgebenden Elektrolytphase sowie
• – Diffusion von Lithium-Ionen in den durch jeweils ein kugelförmiges Partikel gebildeten bzw. als solche angenommenen Elektroden.

Starting from a distributed system, a simulation model formed thereby essentially reduces to the electrochemical effects:

• Butler-Volmer reaction kinetics for the passage of charge through the boundary layer between the two spherical particles forming the electrodes and the electrolyte phase surrounding them, and
• - Diffusion of lithium ions in each formed by a spherical particle or assumed as such electrodes.

The SOC results physically from the concentration of the lithium ions in the two electrodes, which are regarded as homogeneous and can also be labeled as electrode particles.

The single-particle model is a so-called lumped parameter system whose core feature is to average localized system states. The resulting benefits are that it eliminates spatial discretization and leaves only five to six dynamic equations per time step to solve, making the single-particle model real-time capable; H. is in principle suitable for predicting the SOC of an intercalation cell in operation or use.

A disadvantage of the single-particle model is that the output voltage only up to a charge or discharge current of up to ± 3 C with the distributed systems forming simulation models match. At higher currents, the single-particle model deviates significantly more than 10 mV. This is associated with a significant SOC error of over 5%.

Disclosure of the invention

The invention is based on an initially described method for determining the state of charge or SOC and thus preferably for example with regard to a termination voltage of the available power of a secondary intercalation cell of a rechargeable battery with an anode, a cathode, a separator and the anode, the cathode and the electrolyte phase impregnating the separator, wherein the SOC is recalculated by means of an electrochemical simulation model on the basis of measured variables measured at the intercalation cell. According to the invention, it is provided that in the simulation model for refinement of its quality, the diffusion mechanisms of mobile ions in the active material of the anode and cathode, which change the SOC, are taken into account separately.

• – die Erholungskurve besitzt zwei Zeitkonstanten, die sich um etwa eine Größenordnung unterscheiden, und die auf eine unterschiedliche Dynamik in den beiden Elektroden Anode und Kathode zurückzuführen sind.
• – Die beiden Zeitkonstanten ändern sich sprungartig ab bestimmten Ladezuständen.

If the voltage recovery of, for example, a lithium-ion cell is analyzed after switching off the load current, two effects can be observed:

• - The recovery curve has two time constants, which differ by about one order of magnitude, and which are due to a different dynamics in the two electrodes anode and cathode.
• - The two time constants change abruptly from certain states of charge.

The invention takes these two observations into account in the calculation of the SOC by means of an electrochemical simulation model. The two time constants characterize the material or ion transport in the active material of the electrodes. To H. MORE "Diffusion in Solids", Springer Series in Solid-State Sciences, Springer Verlag Berlin Heidelberg, Germany, 2007 the sudden changes are due to a change in the underlying diffusion mechanism.

The order of magnitude by which the two time constants differ approximately corresponds to that in the introductory state of the art as well as FIG J. NEWMAN, K. THOMAS-ALYEA "Electrochemical Systems", Electrochemical Society Series, John Wiley & Sons, Inc., 2004 and from V. SUBRAMANIAN, V. DIWAKAR, D. TAPRIYAL "Efficient Macro-Microscale Coupled Modeling of Batteries", Journal of the Electrochemical Society, 152 (2005), A2002-A2008 removable ratio of the diffusion coefficients of the active material of the anode and cathode to each other. The method according to the invention makes it possible to take account of this detectable, abrupt change in the underlying diffusion mechanisms in a simulation model for calculating the SOC.

The transition region of the diffusion mechanisms which change with the SOC can preferably be described in each case with a charge-state-dependent diffusivity or a charge-state-dependent diffusion coefficient D = D (SOC) for the anode and the cathode or the respective electrodes.

Particular preference is given to the charge-state-dependent diffusivity or the Charge state dependent diffusion coefficient D = D (SOC) depending on the anode and the cathode according to D (SOC) = D _ref * ½ (1 + tanh {-γ * (SOC-δ)}) calculated. D _ref here denotes a standard value for a specific active material of the respective electrode in the case of interstitial diffusion. Preferably, γ and δ are parameters to be determined. The used hyperbolic tangent function or hyperbolic tangent (tanh) ensures numerical stability in the mapping of the jump of the diffusion coefficient between the states of charge. It is important to emphasize that for the transition between two or more diffusion mechanisms or for their description any functional and / or sectionally defined relationships D = D (SOC) are conceivable, which are adapted to the respective cell chemistry or are adaptable. Instead of a functional relationship, a map is also conceivable, which is based on no clear functional relationship of D = D (SOC).

In the electrochemical simulation model, before and / or during and / or after switching on an electrical load, eg. B. a discharge current, obtained measured variables at least included. The electrical load causes a current drain through which the cell voltage changes. The removable electrical energy is limited for safety reasons by a lower termination voltage of the cell. This lower termination voltage is reached sooner or later depending on the extracted power corresponding to the electric load. The same is true in reverse for the charging process, wherein the charging current of a cell is typically much smaller than their discharge current.

Preferably, in the electrochemical simulation model, a voltage recovery of the intercalation cell after removal of the electrical load, such as a discharge current, at least with a.

Advantages of the invention over the prior art are, inter alia, by providing a modeling of the transition between two diffusion mechanisms in the active material of the electrodes during the change of the SOC of the intercalation cell, such as that in, for example, US Pat H. MORE "Diffusion in Solids", Springer Series in Solid-State Sciences, Springer Verlag Berlin Heidelberg, Germany, 2007 described transition z. From interstitial to vacancy diffusion. Each of the two mechanisms has approximately constant diffusivity. According to the invention, the transition region is preferably described with a charge-state-dependent diffusivity D (SOC).

Further advantages resulting from the invention include an improved quality of the simulation model in the area of the upper and lower break-off voltage, the possibility of mapping the strong voltage recovery when the load current at the lower break-off voltage is removed, and high numerical stability by using the proposed tanh Equation.

Particularly preferred in the simulation model physicochemical properties in the anode and the cathode, such. As a concentration of intercalated atoms and / or molecules and / or ions, simplified as each considered homogeneous and volume-average over the local areas anode and cathode. This is in contrast to a distributed model, which takes into account a local resolution of state variables at specific locations.

A particularly advantageous embodiment of the invention provides that in the simulation model each have a Butler-Volmer kinetics is calculated for the anode and for the cathode, the Butler-Volmer kinetics, at least the anode side (to a potential portion according to a particularly advantageous embodiment, Φ ₂ ) is extended in the electrolyte phase of the anode.

The resulting advantages of the invention over the prior art result, inter alia, from the fact that a high accuracy, as in a distributed system with a simple and thus real-time algorithm with only a few, typically five to six, state differential equations as in a lumped Parameter system is reached.

• – Strom I(t);
• – mittlere Leitfähigkeit k der Elektrolytphase;
• – mindestens einen Korrekturfaktor bzw. eine Gewichtung w.

For the anode-side extension of the Butler-Volmer reaction kinetics by a potential component in the electrolyte phase of the anode, the potential component in the electrolyte phase of the anode is preferably estimated by

• - current I (t);
• - average conductivity k of the electrolyte phase;
• At least one correction factor or weight w.

According to an alternative embodiment of the invention, for the anode-side extension of the Butler-Volmer reaction kinetics, the potential component in the electrolyte phase of the anode is preferably based on the charge or discharge current of the cell, the average conductivity of the electrolyte phase and the thickness of a through the layers of the anode Separators and the cathode formed anode-separator-cathode sandwich estimated.

The invention thus enables a model-based prediction of the state of charge of a Secondary intercalation cell for all operating points within the specification of cell temperature, cell voltage and charge or discharge current of the cell by measuring the charging current.

The overpotential η _{s, a,} which is also referred to as overvoltage, is the Butler-Volmer reaction kinetics of the anode, which is extended by the potential component in the electrolyte phase of the anode η _{s, a} = Φ _{s, a} - U _a (c _{s, a} ) - Φ ₂ (k, I, L) - Φ _SEI calculated, with the voltage drop Φ _{s, a} in the solid phase at a charge or discharge current I of the cell, the rest voltage U _a (c _{s, a} ) of the anode as a function of the concentration c _{s, a} of in the active particles the anode at the intercalation embedded atoms and / or molecules and / or ions, the potential drop Φ _SEI by the film resistance at the surface of the anode and the voltage drop corresponding potential portion Φ ₂ (k, I, L) in the electrolyte phase of the anode in dependence of the average conductivity k of the electrolyte phase, the charge or discharge current I of the cell and the thickness L of the anode-separator-cathode sandwich.

An advantageous embodiment of the method according to the invention provides that the potential component Φ ₂ (k, I, L) in the electrolyte phase of the anode according to Φ ₂ = k ^-1 · L · I (t) is calculated with the mean conductivity k of the electrolyte phase, the thickness L of the anode-separator-cathode sandwich and the charge or discharge current of the cell I (t) as a function of the time t, wherein the average conductivity k of the electrolyte phase based the charging or discharging current of the cell I (t) and preferably the resulting terminal voltage and the temperature development of the cell is estimated.

Preferably, the average conductivity k of the electrolyte phase is weighted with an empirical weight w. The mean conductivity of the electrolyte phase together with the empirical weighting w thus results in a lumping parameter.

The state of charge is preferably recalculated by means of the simulation model on the basis of the measured variables cell temperature and / or cell voltage and / or charging or discharging current of the cell.

A particularly advantageous embodiment of the invention provides that when calculating the Butler-Volmer reaction kinetics for the anode and for the cathode, the anode and the cathode are considered as being in each case a spherical particle within which the physicochemical properties are distributed in a spherically symmetric manner , and whose surfaces are preferably extrapolated to the entire electrode in each case by means of a shape factor and the electrode volume taking into account the porosity.

The physico-chemical properties in the anode and in the cathode are preferably calculated on the basis of the respectively last-calculated physico-chemical properties in the anode and in the cathode and on the basis of the physicochemical properties on the surface of the anode and the cathode.

Another particularly advantageous embodiment of the invention provides that the respectively in the anode and in the cathode considered to be homogeneously distributed physicochemical properties at least the concentration of intercalated atoms and / or molecules and / or ions respectively in the anode and in the cathode.

Most preferably, the secondary intercalation cell is a lithium-ion intercalation cell.

Embodiments of the invention will be explained with reference to the drawings. Show it:

1 : a schematic structure of a secondary or dual intercalation cell.

2 : a schematic representation of an application of the method according to the invention.

3 : A schematic representation of a method according to the invention underlying electrochemical simulation model.

4 : A schematic representation of the course of the voltage recovery of a lithium-ion cell after switching off the load current or discharge current of the cell.

Embodiments of the invention

A method for determining the state of charge or SOC of a secondary dual intercalation cell, which is preferably designed as a lithium-ion accumulator 20 is preferably, as in 2 shown schematically, inserted by the SOC of the intercalation cell 20 based on at the intercalation cell 20 measured at the time t measured cell temperature T (t), cell voltage U (t) and Charging or discharging current of the cell I (t), by means of an electrochemical simulation model 21 is recalculated. Preferably, the measured charge or discharge current of the cell I (t) serves as the input variable of the simulation model 21 , being a comparison 24 the output quantities cell temperature T _m (t) and cell voltage U _m (t) of the simulation model with the measured values cell temperature T (t) and cell voltage U (t) of the intercalation cell 20 is carried out.

A feedback gain 22 one out of the comparison 24 resulting observation error e (t) can be determined according to Luenberger or Kalman, preferably in such a way that the observation error e (t) abates asymptotically, ie goes to zero. The SOC is thereby reconstructed from the measured variables and charging or discharging current of the cell I (t), cell temperature T (t) and cell voltage U (t). A start SOC can be done by a state observer 23 , such as As a Kalman filter can be determined.

To be in an in 2 shown application, preferably at the same time or promptly at time t to obtain a prediction of the SOC, the simulation model 21 an algorithm is based, which manages without computation-intensive and potentially numerically unstable models with time-variant parameters or maps.

For example, for a vehicle application, e.g. B. in a vehicle equipped with a secondary Interkalationszelle motor vehicle, for. As an electric or hybrid vehicle, a provided for a method for determining the SOC of the secondary intercalation cell and formed by such an algorithm simulation model must map the power and temperature-dependent capacity of the intercalation cell, one with a distributed system, for example with a M. DOYLE, T. FULLER, J. NEWMAN "Modeling of galvanostatic charge and discharge of the lithium / polymer / insertion cell", Journal of the Electrochemical Society 140 (1993), pp. 1526-1533 , and from T. FULLER, M. DOYLE, J. NEWMAN, "Simulation and Optimization of the Dual Lithium Ion Insertion Cell," Journal of the Electrochemical Society 141 (1994), p. 1-10 known, have a distributed system-forming simulation model comparable quality, be observable in the regulatory sense, and it may comprise at most about each ten system states to z. B. real-time capability according to the prior art in terms of computing power and processor technology of current control devices for automotive applications.

This is ensured by a method for determining the SOC of a secondary intercalation cell having an anode, a cathode, a separator and an electrolyte phase soaking the anode, the cathode and the separator, wherein the state of charge is determined by means of an electrochemical simulation model based on measured variables at the intercalation cell 21 is recalculated in which simulation model 21 physico-chemical properties, such. For example, a diffusion-based concentration of intercalated atoms and / or molecules and / or ions in the anode and in the cathode can be considered as being homogeneously distributed in the anode and in the cathode, and in which simulation model 21 in each case a Butler-Volmer reaction kinetics for the anode and for the cathode is calculated. The measure of a homogeneously distributed consideration ensures that the simulation model 21 only a few system states, so that the underlying algorithm is real-time capable. In order to maintain the accuracy of a distributed system without its disadvantages such. B. lack of real-time ability to accept, is also provided to expand the Butler-Volmer reaction kinetics on the anode side by a potential share in the electrolyte phase of the anode.

According to the invention, in the simulation model 21 to refine its quality with the state of charge (SOC) changing diffusion mechanisms 43 . 44 mobile ions in the active material of anode 11 and cathode 12 each considered separately.

The transition region of the diffusion state (SOC) changing diffusion mechanisms 43 . 44 can in this case each with a state of charge-dependent diffusivity or a charge state-dependent diffusion coefficient D = D (SOC) for the anode 11 and the cathode 12 or the respective electrodes 11 . 12 to be discribed.

For example, the charge-state-dependent diffusivity or the charge-state-dependent diffusion coefficient D = D (SOC) depending for the anode and the cathode according to FIG D (SOC) = D _ref * ½ (1 + tanh {-γ * (SOC-δ)}) be calculated. Here D _ref denotes a standard value for a specific active material of the respective electrode 11 . 12 with interstitial diffusion. γ and δ can be parameters to be determined. The used hyperbolic tangent function or hyperbolic tangent (tanh) ensures numerical stability in the mapping of the jump of the diffusion coefficient between the states of charge.

It is important to emphasize that for the transition between two or more diffusion mechanisms or for their description any functional and / or sectionally defined relationships D = D (SOC) are conceivable, which are adapted to the respective cell chemistry or are adaptable. Instead of a functional relationship, a map is conceivable that no clear functional relationship of D = D (SOC) is the basis.

In the electrochemical simulation model, measured quantities obtained before and / or during and / or after switching on an electrical load can at least be incorporated. The electrical load causes a current drop through which the cell voltage changes.

In addition, a voltage recovery of the intercalation cell after removal of the electrical load can at least be included in the electrochemical simulation model.

• – die Erholungskurve 40 besitzt zwei Zeitkonstanten τ_anode, τ_cathode, die sich um etwa eine Größenordnung unterscheiden, wobei τ_cathode ≈ 10·τ_anode ist. Diese unterschiedlichen Zeitkonstanten τ_anode, τ_cathode lassen sich auf eine unterschiedliche Dynamik in den beiden Elektroden 11, 12, der Anode 11 und der Kathode 12, zurückführen.
• – Die beiden Zeitkonstanten τ_anode, τ_cathode ändern sich sprungartig ab bestimmten SOC.

Becomes a course 40 one in 4 Analyzing the voltage recovery of, for example, a lithium-ion cell after switching off the load current, two effects can be observed:

• - the recovery curve 40 has two time constants τ _anode , τ _cathode , which differ by about one order of magnitude, where τ _cathode ≈ 10 · τ _anode . These different time constants τ _anode , τ _cathode can be attributed to a different dynamics in the two electrodes 11 . 12 , the anode 11 and the cathode 12 to lead back.
• - The two time constants τ _anode , τ _cathode change abruptly from certain SOC.

The invention takes these two observations into account in the calculation of the SOC by means of an electrochemical simulation model. The two time constants τ, here τ _anode , τ _cathode , characterize the material or ion transport in the active material of the electrodes, where D ~ 1 / τ. To H. MORE "Diffusion in Solids", Springer Series in Solid-State Sciences, Springer Verlag Berlin Heidelberg, Germany, 2007 the sudden changes are due to a change in the underlying diffusion mechanism. The order of magnitude by which the two time constants τ _anode , τ _cathode differ approximately corresponds to the ratio of the diffusion coefficients of the active material of the anode 11 and cathode 12 to each other. The inventive method allows this detectable, abrupt change in the underlying diffusion mechanisms in the simulation model 21 to take into account.

The simulation model on which the method according to the invention is based is preferably based 21 on the off S. SANTHANAGOPALAN, RE WHITE "Online estimation of the state of charge of a lithium ion cell", Journal of Power Sources 161 (2006), pp 1346-1355 known, real-time capable single-particle model in which the Butler-Volmer reaction kinetics according to the invention is extended on the anode side by a potential component in the electrolyte phase of the anode.

This expansion can preferably take place by an estimate of the potential component Φ ₂ in the electrolyte phase of the anode based on the charge or discharge current of the cell I, the average conductivity k of the electrolyte phase and the thickness L of the anode-separator-cathode sandwich.

This is deviating too S. SANTHANAGOPALAN, RE WHITE "Online estimation of the state of charge of a lithium ion cell", Journal of Power Sources 161 (2006), pp 1346-1355 both with charging and discharge currents> 3 C accuracy z. B. from M. DOYLE, T. FULLER, J. NEWMAN "Modeling of galvanostatic charge and discharge of the lithium / polymer / insertion cell", Journal of the Electrochemical Society 140 (1993), pp. 1526-1533 , and from T. FULLER, M. DOYLE, J. NEWMAN, "Simulation and Optimization of the Dual Lithium Ion Insertion Cell," Journal of the Electrochemical Society 141 (1994), p. 1-10 achieved known distributed systems. Computing time and number of system states, however, remain at the level of a lumped parameter system, such. B. the single-particle model.

An electrochemical simulation model 21 is in 3 shown in its essential components. It includes Butler-Volmer reaction kinetics 31 for the anode 35 , a Butler-Volmer reaction kinetics 32 for the cathode 36 , a simplified, about the volume of the anode 35 averaged calculation 33 the concentration of the intercalated atoms and / or molecules and / or ions in the anode 35 and a simplified, about the volume of the cathode 36 averaged calculation 34 the concentration of the atoms intercalated during the intercalation and / or molecules and / or ions in the cathode 36 , Furthermore, as indicated by the arrow 38 indicated by convection and / or radiation delivered to the environment heat flow 30 be taken from the ohmic performance. Butler-Volmer reaction kinetics 31 is on the anode side an estimate 37 the potential component in the electrolyte phase of the anode 35 extended. The charge or discharge current I forms the input variable, the cell voltage U and the cell temperature T and the SOC form the output variables of the simulation model 21 ,

The inventive consideration of the different diffusion mechanisms 43 . 44 in the simulation model 21 preferably takes place within the calculations 33 . 34 instead of.

The anode-side extension of the Butler-Volmer reaction kinetics by a potential fraction Φ ₂ in the electrolyte phase of the anode is preferably such that the overpotential η _{s, a} in the Butler-Volmer reaction kinetics of the anode or the negative electrode to η _{s, a} = Φ _{s, a} - U _a (c _{s, a} ) - Φ ₂ (k, I, L) - Φ _SEI gives, with the voltage drop Φ _{s, a} in the solid phase, ie in the active particles of the anode at a charge or discharge current I of the cell, the rest voltage U _a (c _{s, a} ) of the anode as a function of the concentration c _{s, a} of atoms and / or ions embedded in the active particles of the anode during the intercalation, the potential drop Φ _SEI through the film resistance at the surface of the anode and the potential component Φ ₂ corresponding to a voltage drop (k, I, L ) in the electrolyte phase of the anode as a function of the average conductivity k of the electrolyte phase, the charge or discharge current I of the cell, and the thickness L of the anode-separator-cathode sandwich.

In this case, the almost stationary value at the left edge of the anode is estimated after a current jump by the invention. This is possible because the potential share Φ ₂ at the right edge of the cathode is zero.

The potential component Φ ₂ (k, I, L) in the electrolyte phase of the anode can according to Φ ₂ = w · k ^-1 · L · I (t) are calculated, with the average conductivity k of the electrolyte phase, the thickness L of the anode-separator-cathode sandwich and the charge or discharge current of the cell I (t) as a function of time t, wherein the average conductivity k of the electrolyte phase based the charging or discharging current of the cell I (t) and preferably the clamping voltage and cell temperature is estimated and is preferably weighted with an empirical weight w. The mean conductivity of the electrolyte phase together with the empirical weighting w thus results in a lumping parameter.

Particularly preferably, the weighting w is selected with w = 0.7, so that the potential portion Φ ₂ (k, I, L) in the electrolyte phase of the anode to Φ ₂ = 0.7 · k ^-1 · L · I (t) results.

The mean conductivity k of the electrolyte phase can be determined from a comparison of the measured and the simulated temperature development of the cell.

Alternatively, the mean conductivity k of the electrolyte phase can be taken from the parameter set of a distributed model. The concentration c _{s, a} of embedded in the active particles of the anode during the intercalation atoms and / or molecules and / or ions may, for. B. over one V. SUBRAMANIAN, V. DIWAKAR, D. TAPRIYAL "Efficient macro-micro scale coupled modeling of batteries", Journal of Electrochemical Society 152 (2005), A2002-A2008 known fourth-order polynomial.

The said polynomial serves for the approximate calculation of the concentration c _{s, a} of atoms embedded in the active particles of the anode during the intercalation and / or molecules and / or ions and the concentration c _{s, k} of in the active particles of the cathode during the intercalation embedded atoms and / or molecules and / or ions and replaces the calculation of each of a partial differential equation in anode and cathode for the diffusion of the intercalated in the anode or cathode embedded atoms and / or molecules and / or ions

The calculation of the potential component Φ ₂ (k, I, L) in the electrolyte phase of the anode according to Φ ₂ = w · k ^-1 · L · I (t) replaces the calculation of a partial differential equation for the potential component in the electrolyte as a whole.

Φ ₂ and the rest potentials or rest voltages U _a (c _{s, a} ) of the anode and U _k (c _{s, k} ) of the cathode as a function of the concentration c _{s, a} of embedded in the active particles of the anode during the intercalation atoms and / or molecules and / or ions or in dependence on the concentration c _{s, k} of atoms embedded in the active particles of the cathode during the intercalation and / or molecules and / or ions serve to determine the overvoltages of anode and cathode, _see above that the terminal voltage U _{kl of} the cell can be calculated as U _kl = Φ _{s, k} - Φ _{s, a} via the Butler-Volmer reaction kinetics. This establishes a direct mathematical relationship between clamping voltage U _kl and SOC.

It should be emphasized that the Butler-Volmer reaction kinetics can also be extended on the cathode side by a potential component in the electrolyte phase of the cathode. However, the influence of the potential component in the anode's electrolyte phase on the prediction of the SOC is much higher than the influence of the potential component in the cathode's electrolyte phase, which is why the latter is preferably disregarded to simplify the algorithm.

It is equally important to emphasize that the idea underlying the invention can also be extended to other cell chemistries of comparable internal structure.

QUOTES INCLUDE IN THE DESCRIPTION

This list of the documents listed by the applicant has been generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Cited patent literature

• DE 19831723 A1 [0006, 0008]
• DE 19913627 A1 [0007]
• DE 10139049 A1 [0009]
• DE 10301823 A1 [0010]

Cited non-patent literature

• M. DOYLE, T. FULLER, J. NEWMAN "Modeling of galvanostatic charge and discharge of the lithium / polymer / insertion cell", Journal of the Electrochemical Society 140 (1993), pp. 1526-1533 [0020]
• T. FULLER, M. DOYLE, J. NEWMAN, "Simulation and Optimization of the Dual Lithium Ion Insertion Cell," Journal of the Electrochemical Society 141 (1994), p. 1-10 [0020]
• S. SANTHANAGOPALAN, RE WHITE "Online estimation of the state of charge of a lithium ion cell", Journal of Power Sources 161 (2006), pp 1346-1355 [0026]
• H. MORE "Diffusion in Solids", Springer Series in Solid-State Sciences, Springer Verlag Berlin Heidelberg, Germany, 2007 [0034]
• J. NEWMAN, K. THOMAS-ALYEA "Electrochemical Systems", Electrochemical Society Series, John Wiley & Sons, Inc., 2004 [0035]
• V. SUBRAMANIAN, V. DIWAKAR, D. TAPRIYAL "Efficient Macro-Microscale Coupled Modeling of Batteries", Journal of the Electrochemical Society, 152 (2005), A2002-A2008 [0035]
• H. MORE "Diffusion in Solids", Springer Series in Solid-State Sciences, Springer Verlag Berlin Heidelberg, Germany, 2007 [0040]
• M. DOYLE, T. FULLER, J. NEWMAN "Modeling of galvanostatic charge and discharge of the lithium / polymer / insertion cell", Journal of the Electrochemical Society 140 (1993), pp. 1526-1533 [0064]
• T. FULLER, M. DOYLE, J. NEWMAN, "Simulation and Optimization of the Dual Lithium Ion Insertion Cell," Journal of the Electrochemical Society 141 (1994), p. 1-10 [0064]
• H. MULTIPLE "Diffusion in Solids", Springer Series in Solid-State Sciences, Springer Verlag Berlin Heidelberg, Germany, 2007 [0073]
• S. SANTHANAGOPALAN, RE WHITE "Online estimation of the state of charge of a lithium ion cell", Journal of Power Sources 161 (2006), pp 1346-1355 [0074]
• S. SANTHANAGOPALAN, RE WHITE "Online estimation of the state of charge of a lithium ion cell", Journal of Power Sources 161 (2006), pp 1346-1355 [0076]
• M. DOYLE, T. FULLER, J. NEWMAN "Modeling of galvanostatic charge and discharge of the lithium / polymer / insertion cell", Journal of the Electrochemical Society 140 (1993), pp. 1526-1533 [0076]
• T. FULLER, M. DOYLE, J. NEWMAN, "Simulation and Optimization of the Dual Lithium Ion Insertion Cell," Journal of the Electrochemical Society 141 (1994), p. 1-10 [0076]
• V. SUBRAMANIAN, V. DIWAKAR, D. TAPRIYAL "Efficient macro-micro scale coupled modeling of batteries", Journal of The Electrochemical Society 152 (2005), A2002-A2008 [0084]

Claims (17)

Method for determining the state of charge (SOC) of a secondary intercalation cell ( 01 ) with an anode ( 11 ), a cathode ( 12 ), a separator and an anode ( 11 ), the cathode ( 12 ) and the separator impregnating electrolyte phase ( 10 ), wherein the state of charge (SOC) is determined on the basis of the intercalation cell (SOC) 01 ) measured quantities ( 06 . 07 . 08 ) by means of an electrochemical simulation model ( 21 ) is recalculated, characterized in that with the state of charge (SOC) changing diffusion mechanisms ( 43 . 44 ) mobile ions in the active material of anode ( 11 ) and cathode ( 12 ) each separately in the simulation model ( 21 ). Method according to Claim 1, characterized in that the transition region of the diffusion mechanisms (SOC) which change with the state of charge (SOC) 43 . 44 ) each having a charge-state-dependent diffusion coefficient D = D (SOC) for the anode ( 11 ) and the cathode ( 12 ) is described. Method according to Claim 2, characterized in that the charge-state-dependent diffusion coefficient D = D (SOC) per respective anode ( 11 ) and the cathode ( 12 ) according to D (SOC) = D _ref * ½ (1 + tanh {-γ * (SOC-δ)}) calculated with a default D _ref for a given active material of the respective electrode ( 11 . 12 ) with interstitial diffusion. Method according to one of the preceding claims, characterized in that in the electrochemical simulation model ( 21 ) measured quantities obtained before and / or during and / or after switching on an electrical load ( 06 . 07 . 08 ) at least include. Method according to claim 4, characterized in that in the electrochemical simulation model ( 21 ) a voltage recovery of the intercalation cell ( 01 ) at least with the removal of the electrical load. Method according to one of the preceding claims, characterized in that in the simulation model ( 21 ) physico-chemical properties in the anode ( 11 ) and the cathode ( 12 ) than in each case via the anode ( 11 ) and the cathode ( 12 ) are averaged. Method according to one of the preceding claims, characterized in that in the simulation model ( 21 ) in each case a Butler-Volmer reaction kinetics for the anode ( 11 ) and for the cathode ( 12 ), wherein the Butler-Volmer reaction kinetics on the anode side by a potential component (Φ2) in the electrolyte phase ( 10 ) of the anode ( 11 ) is extended. A method according to claim 7, characterized in that for the anode-side extension of the Butler-Volmer reaction kinetics by a potential component (Φ ₂ ) in the electrolyte phase ( 10 ) of the anode ( 11 ) the potential component (Φ ₂ ) in the electrolyte phase ( 10 ) of the anode ( 11 ) is estimated by - current I (t); - average conductivity k of the electrolyte phase; At least one correction factor or weight w. A method according to claim 7, characterized in that for the anode-side extension of the Butler-Volmer reaction kinetics of the potential component (Φ ₂ ) in the electrolyte phase ( 10 ) of the anode ( 11 ) based on the charge or discharge current (I (t)) of the cell, the average conductivity (k) of the electrolyte phase ( 10 ) and the thickness (L) of an anode-separator-cathode sandwich is estimated. A method according to claim 9, characterized in that the overpotential η _{s, a} of the potential component (Φ ₂ ) in the electrolyte phase ( 10 ) of the anode ( 11 ) extended Butler-Volmer reaction kinetics of the anode according to η _{s, a} = Φ _{s, a} - U _a (c _{s, a} ) - Φ ₂ (k, I, L) - Φ _SEI is calculated, with the voltage drop Φ _{s, a} in the solid phase at a charge or discharge current I of the cell, the rest voltage U _a (c _{s, a} ) of the anode as a function of the concentration c _{s, a} of in the anode ( 11 ) embedded in the intercalation atoms and / or molecules and / or ions, the potential drop Φ _SEI by the film resistance at the surface of the anode ( 11 ) and the potential component Φ ₂ (k, I, L) in the electrolyte phase ( 10 ) of the anode ( 11 ) as a function of the average conductivity k of the electrolyte phase ( 10 ), the charging or discharging current I of the cell, as well as the thickness L of the anode-separator-cathode sandwich. A method according to claim 10, characterized in that the potential component Φ ₂ (k, I, L) in the electrolyte phase ( 10 ) of the anode ( 11 ) according to Φ ₂ = k ^-1 · L · I (t) is calculated with the mean conductivity k of the electrolyte phase ( 10 ), the thickness L of the anode-separator-cathode sandwich and the charge or discharge current of the cell I (t) as a function of time t, wherein the average conductivity k of the electrolyte phase ( 10 ) is estimated on the basis of the charge or discharge current of the cell I (t). Method according to claim 10 or 11, characterized in that the mean conductivity k of the electrolyte phase ( 10 ) is weighted with a weight w. Method according to one of the preceding claims, characterized in that the state of charge based on the measured quantities cell temperature and / or cell voltage ( 08 ) and / or charging or discharging current ( 06 . 07 ) of the cell ( 01 ) is recalculated. Method according to one of the preceding claims, characterized in that the anode ( 11 ) and the cathode ( 12 ) in the calculation of Butler-Volmer reaction kinetics in each case simplified as a spherical particle are considered, within which the physico-chemical properties are distributed spherically, and their surfaces preferably by means of a shape factor and the electrode volume, taking into account the porosity on the entire respective Electrode ( 11 . 12 ) are extrapolated. Process according to claim 14, characterized in that the physico-chemical properties in the anode ( 11 ) and in the cathode ( 12 ) based on the respectively last calculated physico-chemical properties in the anode ( 11 ) and in the cathode ( 12 ) and the physical-chemical properties at the surface of the anode ( 11 ) and the cathode ( 12 ) be calculated. Method according to one of the preceding claims, characterized in that each in the anode ( 11 ) and in the cathode ( 12 ) considered as homogeneously distributed physicochemical properties, at least the concentration of the intercalation stored atoms and / or molecules and / or ions in each case in the anode ( 11 ) and in the cathode ( 12 ). Method according to one of the preceding claims, characterized in that it is in the secondary intercalation cell ( 01 ) around a lithium-ion intercalation cell ( 01 ).

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