Method and device for determining degradation parameters of an electrochemical device, in particular a fuel cell or electrolyzer cell

Abstract

The invention relates to a method (500) and a device (100) for determining degradation variables of an electrochemical device (10, 20, 30), in particular of an electrochemical system, in particular a fuel cell or a fuel cell system, wherein degradation of the device (10, 20, 30) can be characterized using multiple degradation variables. Furthermore, the invention relates to a method (600) for monitoring an aging state of one or more electrochemical devices and to a method (700) for controlling multiple electrochemical devices (10, 20, 30).

Description

The present invention relates in particular to a method and a device for determining the state of aging, also called degradation state, and preferably to the determination of local internal state variables of electrochemical devices with a hybrid approach that connects a physical model to advanced data methods with the inclusion of measurement data. The disclosed approach is directed in particular to the determination of degradation states which are defined via more than one degradation variable.Prior ArtElectrochemical systems, such as polymer electrolyte membrane or solid oxide fuel cells, or lithium or sodium ion batteries, must meet demanding requirements throughout their life, ranging in part from several thousands to several tens of thousands of hours of operation. Preliminary testing to the end of the service life is practically hardly possible due to the speed of development cycles today. For this reason, even with short operating hours, it is necessary to make statements as precise as possible about the current state of aging and the aging rate in order to be able to estimate whether the degradation develops to an acceptable extent. In addition, reliable determination of the degradation state of electrochemical systems is also essential for further applications and business models, such as, for example, a demand-controlled maintenance operation (predictive maintenance) or ageing-optimized operating modes of individual or multiple systems in combination.However, the degradation state in typical electrochemical systems usually does not result without further processing of the measured data. This is because a direct comparison of variables relevant to the power, such as the voltage, between different times is usually not sufficiently meaningful, since the associated operating conditions are not identical. This is due, on the one hand, to the fact that different loads can be applied to an electrochemical system in a targeted manner at different times, for example in the form of differently high interrogated electrical currents. On the other hand, however, there are also boundary conditions which cannot be controlled or can be controlled only incompletely by the operator of the system. Examples here are completely freely varying variables such as, in the case of fuel cells in natural gas operation, the exact natural gas composition or else variables which themselves change as a result of the degradation of the system, such as specific temperatures or volume flows.The operation of an electrochemical system can be described via physical models, in particular in the stationary state. Such models are available as simulation models in commercial programs (for example. In COMSOL Multiphysics® 1 or AVL Fire™2) or in OpenSource projects (for example. OpenFCST3 or OpenFuelCell4).As an exemplary example of a physical model describing the effect of degradation on a solid oxide fuel cell system, the work by Zaccaria et al., 2016 is provided. A distributed real-time model of degradation in a solid oxide fuel cell, part I: model characterization. Journal of Power Sources 311, 175-181 doi:10.1016 / j.jpowsour.2016.02.040. Here, the effect of aging is described by providing the ohmic component of the internal voltage losses with an aging-dependent prefactor. As a consequence, the internal resistance of the fuel cell increases over the operation time, and the available power decreases.Disclosure of the InventionAdvantages of the InventionAgainst this background, the invention relates to a method for determining degradation variables of an electrochemical device, wherein degradation of the device can be characterized via a plurality of degradation variables.In a measurement step, values relating to operating conditions of the device and performance values of the device are provided in each case for a plurality of points in time. In particular, these values are detected and / or at least partially measured, i.e., for example, queried from a control to the device and / or, in particular, the power values are measured via sensors.In a selection step, a time window is selected in which a plurality of these points in time lie and wherein during the time window a predefined value profile, for example a linear profile, a constant value or another parameterizable profile, is assumed for all degradation variables except for a selected degradation variable. Taking into account the measured values of the operating conditions and the measured power values, the time window is selected in such a way that at least one of the operating conditions changes in its value during the time window. This at least one operating condition, for example a current density or current intensity demanded by the device, is an operating condition which, depending on the value of the selected degradation variable, has a varying effect on at least one of the power values, in particular on the voltage drawn at the output of the device.In a determination step, a value of the selected degradation variable is then determined taking into account a physical model, which can determine the performance values of the device for predefined operating conditions and predefined values of the degradation variables, and using the provided, in particular measured, values of the operating conditions and the provided, in particular measured, performance values at the times lying in the time window. As explained above, the values of the other degradation variables, i.e., the degradation variables with the exception of the selected degradation variable, are predefined, for example, in the form of constant values and / or a predefined parameterizable curve, for example, linear or exponential changes, during the time window.The electrochemical device can be, in particular, a fuel cell, an electrolyser cell or a fuel cell system or an electrolyser cell system comprising one or more fuel cells or electrolyser cells, in particular a high temperature system comprising, for example, one or more solid oxide electrolyte cell (SOEC) and / or solid oxide fuel cells (SOFC) or a low temperature system comprising, for example, one or more proton exchange membrane electrolyte cell (PEM-ELY), proton exchange membrane fuel cells (PEMFC), Anion exchange membrane electrolyte cell (AEM-ELY) or anion exchange membrane fuel cells (AEMFC). The electrochemical device can also have a plurality of parts which are spatially separated from one another, for example each comprising one or more cells, it preferably being possible for the parts to exchange data via a wired or wireless communication connection. Furthermore, the electrochemical device can be a battery, i.e. an electrochemical energy storage system, such as a lithium ion battery, a sodium ion battery or a solid state battery.The degradation variables characterize in particular effects of the physical aging of the device, which manifests itself in a change in internal variables of the system, for example an increase in internal resistances in the system, in particular in cells of the system, or a decrease in the electrochemically active surface (ECSA), in particular of a catalyst-coated membrane (CCM). The changing degradation of the system can thus be characterized by changing values of the degradation variables in the form of preferably location-dependent prefactors (aging prefactors) of the internal variables in the physical model of the device. The above-mentioned selected degradation variable is preferably a pre-factor of the electrochemically active surface (in particular. ECSA Prefactor).In the context of the invention, the power of the system can be understood to mean generally a measure of the performance (performance) of the system during its operation, for example an electrical voltage or electrical power provided by the system, in particular in the case of a fuel cell, or a hydrogen volume flow in the case of an electrolysis.The selected time window can be, in particular, a time period of preferably one or more minutes or also more hours. In addition to taking into account a change in at least one operating condition acting on the power to different extents depending on the degradation state as described above, the time window is selected such that the lead of the values of the other degradation variables is well defined during the time window, that is to say, as described above, can be predefined as being constant during the time window or following a predefined profile.The method according to the invention is thus advantageously suitable for electrochemical devices, the state of aging of which can be defined via more than one degradation variable. For this purpose, the method uses an advantageous hybrid approach that connects a physical model to measured data. The method according to the invention can thus advantageously be used as a virtual sensor for degradation, for example for a real-time application, for example as part of a digital process twin to such an electrochemical device. The method according to the invention is advantageously independent of the physical model specifically used, provided that the model provides an input of the operating conditions as boundary conditions and an output of the power that is established in the electrochemical device (in particular the voltage in the case of fuel cells, the hydrogen volume flow in the case of electrolyzers), and also contains a plurality of degradation variables for describing the aging-related power loss of the device.According to a particularly advantageous development, in an optimization step, the determination step is carried out iteratively a plurality of times, wherein the values of the other degradation variables are optimized with respect to a target variable. The target variable can be a fluctuation, in particular a variance, of the value of the selected degradation variable during the optimization step. The values of the other degradation variables are preferably optimized for an extreme value, in particular a minimum, of the target variable.In particular, the values of the other degradation variables during the respective inversion step follow the respective predefined value or predefined profile during the time window, wherein the respective predefined value or the respective predefined profile can change on the basis of the optimization via the inversion steps until the desired optimization with respect to the target variable is achieved. The optimization with respect to the target variable can be defined as being achieved in particular when a predefined termination criterion is reached, wherein the termination criterion can be selected as usual in the case of optimization methods.The consideration of the physical model in the determination step can comprise a use of the physical model or a surrogate model, wherein the surrogate model outputs values, in particular at least for a part of the space of the possible parameter values and / or at least for a part of the space of the possible input values of the physical model, at least for an output variable of the physical model, which values are within a tolerance range to the output values of this variable of the physical model. The surrogate model can preferably be a data-based surrogate model, i.e. a model in which one or more parameter values are defined on the basis of data outside the model. These parameter values are preferably defined via machine learning of the surrogate model, i.e. via training of the surrogate model.According to a preferred embodiment, the physical model is taken into account in the determination step by inverting the physical model or a surrogate model to the physical model, so that the inverted model determines the value of the selected degradation variable as a function of the measured values of the operating conditions, the measured performance values and the defined values of the other degradation variables.The inversion, in particular of the physical model, can basically be carried out analytically or numerically, if mathematically possible. According to an advantageous embodiment, the physical model or the surrogate model is taken into account in an optimization method for an optimized determination of the value of the selected degradation variable. The optimization method can comprise, for example, a Bayesian optimization, simulated annealing or gradient-descendant approaches.In particular, the consideration of the physical model in the determination step can comprise a use of a data-based surrogate model, in particular a regression model, wherein the surrogate model is trained in advance using data generated with the physical model. As in the case of inverting the model described above, the trained surrogate model directly outputs a value of the selected degradation variable upon input of respective values of the operational connections and respective performance value and preferably further an input of values of the other degradation parameters.If required, the method can comprise a processing step situated between the selection step and the determination step, in which the values of the operating conditions, which are measured in particular, and the performance values, which are measured in particular, are processed for input into the physical model at the times situated in the time window. In particular, these values can be combined and / or converted in the form and units of the physical model or of the surrogate model.According to a preferred embodiment, the method is preferably repeated for different time windows in each case in the selection step in order to determine the value of the selected degradation variable and preferably the values of the other degradation variables for these different time windows. An evolution of the degradation variable or degradation variables can thus advantageously be determined for all selected time windows. The different time windows can directly adjoin one another or also partially overlap at least for some time windows. Alternatively, the time windows can also be partially spaced apart from one another in time, in particular in order not to take into account non-relevant time segmentsAccording to a particularly advantageous development of the method, the physical model contains at least one internal physical variable of the electrochemical device, wherein at least one value of one of these internal physical variables is determined after the determination step has taken place and preferably after the optimization step has taken place, preferably using the physical model or the trained surrogate model. The internal physical quantities can be, in particular, internal local or averaged quantities, for example (local) temperatures or (local) current densities in the cell or in the stack, local hydrogen or oxygen concentration and gradients, local relative humidity, local partial pressures, local mechanical voltage values or a distribution of overpotentials. Typically, no direct sensor data is available for these internal variables. With the method according to the invention, however, such quantities can advantageously be estimated and made available for a further data analysis.The invention also relates to a method for monitoring an ageing state of one or more electrochemical devices, wherein the method described above is carried out for determining degradation variables of the one or more electrochemical devices, preferably for a plurality of time windows which are different in each case in the selection step, wherein an indication is output if the determined values of the degradation variables deviate from predetermined values more than a respectively predetermined tolerance.The invention further relates to a method for controlling a plurality of electrochemical devices, wherein values of at least one degradation variable, preferably a plurality of degradation variables, are determined for each device using a method described above for determining the degradation variables, wherein a load requested overall to the devices is distributed to the devices as a function of the determined values, preferably as a function of a prioritization of the devices as a function of the degradation of the devices derived via the determined values. This has the advantage that more heavily degraded devices must provide a lower proportion of the overall load requested and their further degradation is therefore slowed down.The methods according to the invention can be embodied in particular as computer-implemented methods. Accordingly, the invention also comprises a computer program for each of the methods, which comprises instructions which, when executed by a computer, cause the computer to execute the respective method according to the invention, and a computer-readable data carrier on which this computer program is stored. Finally, the invention also comprises a computer, a part of a cloud computing architecture or another programmable device having a processor which comprises such a computer-readable data carrier, and an evaluation and control unit which comprises such a computer-readable data carrier and furthermore comprises means for carrying out the respective method steps according to the invention. In particular, the methods according to the invention can also be used as part of a digital process twin and can be implemented as part, in particular as a virtual sensor, of such a process twin, in particular for process and / or quality monitoring of one or more electrochemical devices.Brief Description of the DrawingsExemplary embodiments of the invention are schematically illustrated in the drawings and explained in more detail in the following description. The same reference numerals are used for the elements shown in the different figures and acting in a similar manner, wherein a repeated description of the elements is omitted.They show FIG. 1 shows a flow diagram of an exemplary embodiment of the method according to the invention for determining degradation variables of an electrochemical device, FIG. 2 shows an exemplary embodiment of a device according to the invention, FIG. 3 shows a flow diagram of an exemplary embodiment of the method according to the invention for monitoring an ageing state of one or more electrochemical devices, and FIG. 4 shows a flow diagram of an exemplary embodiment of the method according to the invention for controlling a plurality of electrochemical devices.Embodiments of the InventionFIG. 1 shows a flow chart of an exemplary embodiment of method 500 according to the present invention described below. FIG. 2 schematically shows an exemplary embodiment of a device 100 according to the invention, on which the method according to the invention is implemented, for example a computer, a part of a cloud computing architecture or another programmable device having a processor, for example for use as a virtual sensor or as part of a digital twin for an electrochemical device 10. The determination device 100 is designed to receive this data and preferably also to transmit data to the electrochemical device 10, for example requests for transmission of the data or control commands for a change in the operating conditions of the electrochemical device 10.The electrochemical devices 10, 20, 30 can be, in particular, SOECs, SOFCs, PEM-ELYs or PEMFCs of the same type or can each be systems comprising a plurality of such cells, as described at the beginning.Without limiting generality, the following exemplary embodiment is explained on the basis of a PEMFC as electrochemical device 10, in which the reduction of the electrochemically active surface and the increase of electrical (contact) resistances can be taken into account as degradation mechanisms. For this purpose, on the one hand, the expression of the electrochemically active surface on which the relevant reactions take place can be multiplied by a prefactor which decreases with increasing aging. On the other hand, one or more electrical resistances which act on the charge transport in the electrochemical system can be multiplied by separate prefactors which increase as aging increases. The selection and number of aging factors selected in the form of these prefactors, which are referred to below as degradation variables, is preferably limited in the approach described here only in that their effects on the electrochemical system should in principle be able to be differentiated by measurements.In order to represent inhomogeneous degradation of the electrochemical system, the purely scalar degradation variables, which are initially assumed to be simplified and which have a location-independent effect on all relevant constituents of the electrochemical system, can be multiplied by location-dependent starting functions or alternatively themselves represent location-dependent functions. With an approach function, which has a value of 1 for example in the vicinity of the fuel gas inlet of a PEMFC fuel cell and the direction of the fuel gas outlet falls to the value 0, degradation can thus be described, which has a stronger effect at the fuel gas inlet and weaker at the fuel gas outlet. The location dependence of the approach functions can be physically motivated or derived by means of further experiments and investigations. Alternatively or additionally, a single aging effect and thus the degradation variable can be broken down into a plurality of prefactors and associated location-dependent approach functions (analogous to the basic idea of the approach functions in the finite element method). Inhomogeneous degradation distributions can then also be displayed and measured indirectly. The different proportions should also have a sufficiently different effect on the performance under given operating conditions. This then results in a higher number of aging factors which at least partially describe the same physical but locally differently weighted effect.The progressive state of aging, also referred to as degradation state, can thus be characterized via values of a plurality of fundamentally time-dependent degradation variables. For this purpose, a physical model f model is used, which determines the provided power, i.e. the power values, as a function of the values of the operating conditions and the degradation, i.e. the values of the degradation variables. The physical model f model is, for example, a simulation model in commercial programs (for example in COMSOL Multiphysics® www.comsol.de / model / download / 813751 / models.fce.sofc unit cell.pdf for an SOFC or AVL Fire™ https: / / www.avl.com / documents / 10138 / 3372595 / Solution+Sheet+for+PFC for a PEMFC), OpenSource projects (for example. OpenFCST3 or OpenFuelCell4) or implemented in self-written codes, in particular in the form of a finite element method. For example, in the case of a PEMFC, the physical model f model is based on an COMSOL® implemented model with the "Application ID: 103241" https: / / www.comsol.com / modelj pem-fuel-cell-stack-103241.In a first step 501 of the method (measuring step 501), values of the operating conditions x operation( t) and power values x performance( t) of the electrochemical device 10 are recorded for a plurality of points in time. A point in time with the data measured or acquired at this point in time, in particular the values of the operating conditions and / or the power values at this point in time, is also referred to below as a data point. Depending on the model and device used, values of set operating conditions can be interrogated by a processor for controlling the electrochemical device 10 or from a memory of the device 10, while values of set operating conditions and / or values of power provided by the device 10 can be measured in particular by sensors on the electrochemical device 10 or on devices in particular electrically connected to the device. For example, the operating conditions are a sensed load current, temperatures, volume flows, pressures, gas compositions, the presence of which, in particular depending on the control strategy, can be set at the inlet of the fuel gas side and air side of the device, for example, and / or can be measured at the outlet of the device. The detected power value can be, for example, the output voltage currently provided by the device, also referred to as stack voltage in the case of a combination ("stack") of a plurality of cells. Thus, for each time t, a state vector {x operation( t), x performance( t)}α(where α represents the electrochemical device under consideration) comprising the detected values of the operating conditions at this time and the detected power values at this time may be provided to the method 500. The set of these vectors thus forms a time series at the selected points in time.In a second step 502 (selection step 502), a degradation variable x SOH[ m] with m≤n is selected from the n degradation variables. Furthermore, a time window [t i,..., t i+k] comprising at least some of the above-mentioned points in time and thus of the above-mentioned state vectors is selected, for example comprising a few minutes. The time window and thus the points in time contained therein are preferably selected such that the states of the electrochemical device at these points in time can be described by the physical model f model i.e. preferably that the respective values of the operating conditions are each in a permissible parameter and function range of the model f model. If the model f model is applicable only to steady-state operating conditions, for example, only data from the field should also be used, for which an at least quasi-steady state can be assumed. For the detection of such stationary states, there are a multiplicity of approaches which range, inter alia, from the evaluation of the gradient of characteristic variables to statistical methods, described, for example, in Jeffrey D. Kelly, John D. Hedengren, 2013. "A steady-state detection (SSD) algorithm to detect nonstationary drifts in processes", Journal of Process Control 23 (3) 326-331. doi:10.1016 / j.jprocont.2012.12.001 S Narasimhan, Chen Shan Kao and RSH Mah. "Detecting changes of steady states using the mathematical theory of evidence", AlCHE journal 33.11 (1987), pp. 1930-1932, Mining Kim et al., "Design of a steady-state detector for fault detection and diagnosis of a residential air conditioner", International journal of correction 31.5 (2008), pp. 790-799 and Edwin L Crow et al., "Statistics manual: with examples taken taken from order development development", vol. 3369. Courier Corporation, 1960.The selection of the degradation variable and the selection of the time window are furthermore carried out in such a way that a profile can be predefined in each case for the other degradation variables, that is to say preferably for all degradation variables with the exception of the selected degradation variable (referred to below as the "other" or "n-1" degradation variables). The specification of a course is to be understood in particular here to mean that a value for these other degradation variables can be specified in each case for the points in time within the selected time window, in particular from an assumed, preferably continuous or even continuous, value curve of the respective degradation variable during the time window. In the simplest case, a constant value or at least one linear profile for one or more degradation variables can be assumed during the time window, in particular as an estimated approximation for an actual profile. It is recommended to use the aging factor with the shortest time scale, i.e., the aging factor whose value changes most rapidly compared with the other aging factors.Thirdly, the values of at least one of the operating conditions of the points in time encompassed by the time window should exhibit such a great variation that a different effect of the degradation variables on the electrochemical system can be separated from one another. For example, in electrochemical systems, there are aging effects whose effect on system performance is strongly dependent on how high the requested current density is, and others whose effect is independent thereof. In order that the associated degradation variables can be determined as unambiguously as possible in this example, data having at least two sufficiently different current densities are required accordingly in the selected time window. A selection of suitable time windows or a classification of the available time windows for sufficient variation of the operating conditions can be effected via suitable prefiltering. Possible approaches are, for example, a checking of the covered value range of specific operating conditions or also so-called clustering with respect to the operating conditions, in which it is counted how many data points in the selected time window fall into which class of values. Taking into account the points explained, generally the degradation variable can first be selected and then, depending on this, a time window can be selected in which at least some of the aforementioned points in time lie and in which the aforementioned conditions are satisfied or approximately satisfied. Alternatively, the time window with at least some of the times can first be selected according to the conditions and a degradation variable can be selected depending thereon.A desired time window can also be divided into two or more than two partial time windows, wherein, in the event of a change from one of the partial time windows to the subsequent partial time window, another of the degradation variables is defined as a selected degradation variable. In addition, the respective subsequent sub-time window can be selected such that it differs from the last sub-time window only by one data point. The calculated degradation variables can then be assigned to the first, last or middle data point, for example, so that a separately calculated set of degradation variables is also present for each data point.In an optional third step 503 (processing step 503) which is dependent in particular on the physical model f model used, the input and output variables of the physical model f model, that is to say the operating conditions and the power provided, {x operation([ t i,..., t i+k]), x performance([ t i,..., t i+k]) are processed in a different manner, in particular partially combined and converted, in such a way that they have a required shape and units for implementing the physical model as a simulation model. For example, in a fuel cell system having a plurality of stacks, averaging can first be carried out over the individual stacks or the total current measured in the field can be converted into a current density possibly required by the simulation model. An exemplary list of the form {x operation([ t i,..., t i+k]), x performance([ t i,..., t i+k])} could then appear, for example, as follows: {[Current i,..., Current i+k], [ Fuel Gas Utilization i,..., Fuel Gas Utilization i+k], [ Temperaturei,..., Temperaturei+k],...], [[Stack Voltagei,..., Stack Voltage i+k],...]}.In a fourth step 504 (determination step) and a preferably fifth step 505 (optimization step), the values of the selected degradation variable and preferably of the other degradation variables are determined.In the fourth step 504, the physical model f model: x SOH, x operation → x performance, ( x internal) is used (wherein x internal can be further internal parameters of the model and in particular of the electrochemical device) in order to determine the value of the selected degradation variable {x SOH[ m](t*)}αfür t* ∈ {t i,..., t i+k}, for the power measured by the model f model together with the operating conditions {x operation( t*)}α, {x performance( t*)}αvorhersagt. In this case, values or value characteristics are predefined for the other degradation variables, i.e. x SOH[ j](t*) with j ∈{1,..., n} \{m}, as described above, and are preferably each initialized with a physically consistent value. Different optimization methods can be used for the determination of the values {x SOH[ m](t*)}αzu at the respective points in time, depending on the structure of the model, in particular Bayesian optimization, simulated annealing or gradient-decentr approaches.If the physical model f model is analytically invertible, the values {x SOH[ m](t*)}αalternativ can also be calculated directly, i.e. without optimization or other numerical approximation methods. Alternatively, instead of the physical model f model it is also possible to use a surrogate model, in particular a data-based model based on machine learning, which has preferably been trained with the aid of the physical model, to determine the value of the selected degradation variable directly as a function of the operating conditions and the performance.In the fifth step 505, the values of the other degradation variables aging factors x SOH[ j](t*) for j ∈{1,..., n} 205{m} are determined. For this purpose, the fourth step 504 is repeated several times with differently selected value characteristics respectively predefined over the selected time window, in the simplest case constant values x SOH[ j] for j ∈ {1,..., n} ∂ {m}. Possible optimization methods can be, in particular, Bayesian optimization, simulated annealing or gradient-sent approaches. The selection of the x SOH[ j] is optimized with respect to a defined target variable, wherein the target variable is selected in accordance with the expected profile of the selected degradation variable x SOH[ m](t*) in the time window. For example, if an approximately constant value is expected for x SOH[ m](t*), the selection of the x SOH[ j](t*) for j ∈ {1,..., n} ∂ {m} is particularly good when the spread of x SOH[ m](t*) in the time window is small. The target variable can then be, in particular, a smallest possible standard deviation σ of x SOH[ m](t*) for t* ∈ {t i,..., t i+k}. The optimization then corresponds to a minimization of σ[x SOH[ m]({t i,..., t i+k})]. Alternative target variables can be, for example, an L1normal of x SOH[ m] that is as small as possible, a difference between the minimum value and the maximum value of x SOH[ m] that is as small as possible or a standard deviation of the logarithm of x SOH[ m] that is as small as possible.For the convergence of the iterative optimization in the fourth step 504 and in the fifth step 505, the exact form in which the x SOH( t*) enter the model should be designed such that the mapping is unambiguous and invertible in a practical sense. In a practical sense, this also includes the possibility that outputs which are not physically meaningful are filtered out if the mapping is not ambiguous, so that the mapping becomes unambiguous again by the filtering. For example, in a quadratic relationship, in which both negative and positive degradation factors would be possible, the negative values can be neglected.The values of the degradation variables {x SOH( t*)}αdetermined in this way or variables derived therefrom can then be used as a measure for the degradation, that is to say the state of health (State of Health) of the electrochemical device 10.Depending on the nature of the model f model it is optionally also possible in a sixth step 506 to read out internal physical variables {x internal( t*)}α, and local temperatures, current densities or the like after the fifth step 505 has been carried out. For this purpose, the determined degradation variables {x SOH( t*)}αcan be used together with the operating state considered for the readout of the internal variables, i.e. the values of the operating conditions x operation([ t i,..., t i+k]) present in this operating state, in the optimized simulation model or a corresponding surrogate model.In the following, further exemplary embodiments for developments and variants of the method according to the invention, for example of the described exemplary embodiment 500, are presented.The surrogate model that can be used in the fourth step 504 as an alternative to the physical model f model can be generated in particular on the basis of results simulated beforehand with the physical model. In particular, "Design of Experiment" methods (DoE) can be used for this purpose. For this purpose, a DoE is generated from parameter combinations using a suitable approach, for example via Latin Hypercube Sampling or adaptively via Active Learning, at which the physical model f model is then evaluated. The DoE can also be designed to contain only data points that are as close as possible to operating conditions actually present in the field. This can be realized by defining a corresponding distance standard and filtering the original DoE carried out in this respect. Possible advantages in this case are shorter training times and improved accuracy of the regression model in the relevant parameter range. The results are then used for training a regression model, in particular based on linear regression, random forest, Gaussian processes or neural networks. This is an advantageous approach above all when the calculation of a single simulation for the physical model f model takes a comparatively large amount of time or computing resources or when similar or identical operating points are calculated repeatedly when using the approach. The actual simulation step is then performed upstream and the evaluation of the surrogate model derived therefrom requires only a comparatively short time in the determination of the degradation variable. In addition, as already described above, the surrogate model can also be trained directly in such a way that the regression model predicts the selected degradation variable from operating conditions and performance at given other degradation variables, so that a model inversion is completely omitted.The method 500 according to the invention can advantageously take place at the system level, in the case of a plurality of stacks per system also at the stack level and also at the repeat unit level (in the presence of the required measurement variables), provided that the required data can be acquired in the measurement step 501 and can be prepared for the physical model f model or surrogate model used.The physical model f model can be part of a system model into which further aging effects (for example. This is also attributable to losses in power at the air blower, changes in heat exchangers, etc.).When the method 500 is applied to a plurality of electrochemical devices 10, 20, 30, the physical model f model can be used in the same way, in particular generically or in the same initial parameterization, for all devices 10, 20, 30 or systems α=1,..., N. Alternatively, the model f model can also be individually adapted to the respective device or system by adaptation to manufacturing parameters, for example layer thicknesses or differences in tightness, or so-called pass-off tests for ensuring performance criteria following production, for example in the form of slightly different open-circuit voltages, which device or system is to be determined for the degradation and optionally values of internal variables.The degradation variables determined and in particular their temporal profile {x SOH( t)}αmay then be used in different application cases. A first application may use one or more of the determined degradation variables as a characteristic number(s) for the conditioning maintenance (predictive maintenance) of the electrochemical devices, for example, in order to shift, at regular intervals, defined maintenance deadlines back or forward if the conditioning is better or worse than expected. In a second application, one or more of the determined degradation quantities may be used to control electrochemical devices or systems operating in a internetwork ('microgrid') such that their state of aging remains in a similar range. For example, in the case of low load demands, one could pause those devices 20 which currently have a higher state of aging than other devices 10, 30. This could accommodate production variations affecting the aging rate of the systems, such that all devices 10, 20, 30 have similar life and maintenance intervals.Further possible applications result from the use of the internal variables {x internal( t)}α. Here, the invention can be used to avoid an adaptation of the load profile, i.e. a change of a distribution of a total load over a plurality of electrochemical devices 10, 20, 30, non-safe system states, depending on the determined values of the internal variables. For example, a respective, optionally location-dependent, internal temperature of the electrochemical devices can be determined via the physical model optimized according to method 500. For this purpose, the physical model used for the method can be based on spatially resolved models implemented in COMSOL® for example, which also describes such internal variables. If predefined, optionally step-shaped limit values are exceeded by this internal temperature, the load applied to the respective device via the setting of the operating conditions can be reduced, in particular by displacing a part of the load to another electrochemical device which has a comparatively lower internal temperature. A load distribution over a plurality of electrochemical devices can thus preferably be correlated or anti-correlated with values of one or more internal variables. Furthermore, an analysis of the correlation between the internal variables {x internal( t)}αand the development of the degradation variables x SOH( t) can provide further information as to which operating states and operating strategies are particularly harmful with respect to aging. These can then in turn be avoided in an optimized operating mode. Particularly in a network of several electrochemical systems, this results in high optimization potentials for avoiding such non-safe or particularly aging-relevant states.FIG. 3 shows a flow diagram of an exemplary embodiment of the method 600 for monitoring an ageing state of one or more electrochemical devices, for example of the above-described devices 10, 20, 30 in FIG. 2 In a first step 601 of the method 600, the method 500 according to the invention for determining the degradation variables is carried out for at least one of the devices 10, 20, 30, preferably for a plurality of time slots which are different in each case in the selection step 502. In a second step 602 of the method, an indication is output if the specific values of the degradation variables deviate from predefined values by more than a respectively predefined tolerance. For example, the indication can be output as an acoustic, optical or digital alarm signal.FIG. 4 shows a flow diagram of an embodiment of the method 700 for controlling a plurality of electrochemical devices, for example the above-described devices 10, 20, 30 of FIG. 2, for example in a network as described above. In a first step 701 of the method, values of at least one, preferably of a plurality of degradation variables are determined for each device 10, 20, 30 using the method 500 according to the invention for determining the degradation variables. In a second step 702, a load which is requested overall to the devices 10, 20, 30 is distributed to the individual devices 10, 20, 30 as a function of the specific values, preferably as a function of a prioritization of the devices 10, 20, 30 as a function of the degradation of the devices derived via the specific values. For example, the load distribution can be inversely proportional to the specific degradation values or can be anticorrelated with the specific degradation values in another manner.References included in the specificationThis list of documents cited by the applicant has been produced in an automated manner and is only included for the better information of the reader. The list is not part of the German patent application or utility model application. The DPMA does not take any adhesion for any faults or omissions.Cited Non-Patent LiteratureZaccaria et al., 2016. A distributed real-time model of degradation in a solid oxide fuel cell, part I: model characterization. Journal of Power Sources 311, 175-181 doi:10.1016 / j.jpowsour.2016.02.040

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[0035]

Claims

Method (500) for determining degradation variables of an electrochemical device (10, 20, 30), in particular of an electrochemical system, in particular of a fuel cell or of a fuel cell system, wherein degradation of the device (10, 20, 30) can be characterized via a plurality of degradation variables, • wherein in a measurement step (501) values relating to operating conditions of the device and power values of the device are provided, in particular measured, in each case for a plurality of points in time, • wherein in a selection step (502) a time window comprising a plurality of the points in time is selected, wherein during the time window in each case a value or a predefined value profile is assumed for all degradation variables except for a selected degradation variable and wherein during the time window at least one of the operating conditions which has a different effect on at least one of the power values depending on the value of the selected degradation variable changes in its value, • wherein in a determination step (504), taking into account a physical model or a data-based surrogate model relating to the physical model, which model can determine the performance values of the device for predefined operating conditions and predefined values of the degradation variables, and using the provided values of the operating conditions and the provided performance values at the points in time lying in the time window, a value of the selected degradation variable is determined for the assumed values or value characteristics of the other degradation variables.Method (500) according to Claim 1, wherein, in an optimization step (505), the determination step (504) is carried out iteratively a plurality of times, the values of the other degradation variables being optimized with respect to a target variable.Method (500) according to claim 2, wherein the target variable is a variation, in particular a variance, of the value of the selected degradation variable during the optimization step (505), and wherein the values of the other degradation variables are optimized for a minimum of the target variable.Method (500) according to one of the preceding claims, wherein the consideration of the physical model in the determination step (504) comprises an inversion of the physical model or of a surrogate model for a determination of the value of the selected degradation variable as a function of the measured values of the operating conditions, the measured performance values and the defined values of the other degradation variables.Method (500) according to one of the preceding claims, wherein the consideration of the physical model in the determination step (504) involves the use of the physical model or a surrogate model in an optimization method for an optimized determination (504) of the value of the selected degradation variable.Method (500) according to one of the preceding claims, wherein the consideration of the physical model in the determination step (504) comprises a use of a data-based surrogate model, in particular a regression model, wherein the surrogate model has been trained using data generated with the physical model.Method (500) according to one of the preceding claims, wherein in a processing step (503) situated between the selection step (502) and the determination step (504), the values of the operating conditions and the power values at the times situated in the time window are processed for an input into the physical model.Method (500) according to one of the preceding claims, wherein the method is repeated for respectively different time windows preferably in the selection step (502) in order to determine the value of the selected degradation variable and preferably the values of the other degradation variables for these different time windows.The method (500) according to any one of the preceding claims, wherein the physical model includes at least one internal physical quantity of the electrochemical device and wherein at least one value of one of these internal physical quantities is determined after the determination step has taken place and preferably after the optimization step has taken place, preferably using the physical model or the trained surrogate model.Method (600) for monitoring an ageing state of one or more electrochemical devices (10, 20, 30), wherein a device can be in particular an electrochemical system, in particular a fuel cell or a fuel cell system, wherein a method (500) according to one of the preceding claims is carried out for determining degradation variables of the one or more devices, preferably for a plurality of time slots which are respectively different in the selection step (502), wherein an indication is output if the determined values of the degradation variables deviate from predetermined values more than a respectively predetermined tolerance.Method (700) for controlling a plurality of electrochemical devices (10, 20, 30), wherein the devices can be in particular electrochemical systems, in particular fuel cells or fuel cell systems, wherein values of at least one, preferably a plurality of degradation variables are determined for each device using a method (500) according to one of Claims 1 to 9, wherein a load requested overall to the devices is distributed to the devices as a function of the determined values, preferably as a function of a prioritization of the devices as a function of the degradation of the devices derived via the determined values.Device (100), in particular virtual sensor, for determining degradation variables of an electrochemical device (10, 20, 30), in particular of an electrochemical system, in particular of a fuel cell or of a fuel cell system, wherein the device (100) is configured to execute a method (500, 600, 700) according to one of the preceding claims.Digital process twin, in particular for process and / or quality monitoring of one or more electrochemical systems (10), wherein the twin is configured to execute a method (500, 600, 700) according to one of Claims 1 to 11.A computer program comprising instructions which, when executed by a computer, cause the computer to perform a method (500, 600, 700) according to any one of claims 1 to 11.Computer-readable data medium on which the computer program according to Claim 14 is stored.

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