CN114077806A

CN114077806A - Apparatus and computer-implemented method for operating a fuel cell system

Info

Publication number: CN114077806A
Application number: CN202110913491.9A
Authority: CN
Inventors: C·齐默; J·布劳恩; S·格尔温; S·斯里拉姆; V·伊姆霍夫
Original assignee: Robert Bosch GmbH
Current assignee: Robert Bosch GmbH
Priority date: 2020-08-10
Filing date: 2021-08-10
Publication date: 2022-02-22
Also published as: DE102020210081A1

Abstract

The invention relates to a device and a computer-implemented method for operating a fuel cell system, wherein at least one manipulated variable (u _ req) for manipulating the fuel cell system is predefined, wherein a prediction (y _ pred, dy _ pred) of a variable (y _ mes, dy) of the fuel cell system is determined using a model (102) from the at least one manipulated variable (u _ req) or from at least one manipulated variable (u _ act, u _ pred) provided for the at least one manipulated variable (u _ req (t)), and wherein at least one parameter (P) of the model (102) is determined from the variable (y _ mes, dy) and the prediction (y _ pred, dy _ pred) of the variable (y _ mes, dy), wherein an uncertainty of the prediction (y _ pred, dy) of the variable (y _ mes, dy) is determined by the model (102), the uncertainty measure (h (u _ req)) satisfies a condition for the predefined at least one manipulated variable.

Description

Apparatus and computer-implemented method for operating a fuel cell system

Technical Field

The invention relates to an apparatus and a computer-implemented method for operating a fuel cell system.

Background

A fuel cell system is an integrated system comprising a large number of subsystems. A fuel cell system includes one or more fuel cell stacks and a number of subsystems that must be present in order to supply the one or more fuel cell stacks.

The fuel cell stack is typically free of an actuator, i.e., the fuel cell stack itself is a passive component or assembly alone.

While the individual subsystems of the overall system can be well described in terms of physical models, it is difficult to model the dynamic interactions between the different subsystems and the fuel cell stack. For example, the fuel cell stack contains inertias such as thermal mass, water or moisture that can change the dynamics of the overall system and can lead to direction-dependent effects such as differences between positive and negative load jumps.

Disclosure of Invention

The computer-implemented method and device according to the independent claims make it possible to predict the operating variables of the fuel cell system at one point in time from at least one manipulated variable at a next point in time.

The computer-implemented method for operating a fuel cell system provides for specifying at least one manipulated variable for manipulating the fuel cell system, wherein a prediction of a variable of the fuel cell system is determined using a model on the basis of the at least one manipulated variable or on the basis of at least one manipulated variable provided for the at least one manipulated variable, and wherein at least one parameter of the model is determined on the basis of the variable and the prediction of the variable, wherein the specified at least one manipulated variable is determined by the model on the basis of a predicted uncertainty measure for the variable, which uncertainty measure satisfies a condition for the specified at least one manipulated variable.

In one aspect, measured values of the operating variables are determined, wherein a prediction of the operating variables of the fuel cell system is determined using the model as a function of the at least one manipulated variable or as a function of at least one manipulated variable provided for the at least one manipulated variable.

In a further aspect, it is advantageously provided that a prediction of an operating variable of the fuel cell system is determined using a first model as a function of the at least one manipulated variable or of at least one manipulated variable provided for the at least one manipulated variable, wherein the variable is a deviation between the prediction of the operating variable of the fuel cell system and a measured value of the operating variable, wherein the prediction of the deviation is determined using a second model as a function of the at least one manipulated variable or of the at least one manipulated variable provided for the at least one manipulated variable.

Thereby enabling the operation of the fuel cell system to be improved based on the prediction. Improvements to the overall system may be used, for example, to optimize consumption, minimize aging or degradation or extend service life, improve dynamics or performance, save costs, for example, through optimized operation. The improvement may also be used to further optimize many of the above objectives, for example as adaptive multi-objective optimization.

The condition in this example is to maximize the uncertainty metric. This may be done, for example, according to safety conditions. The parameter may be a hyper-parameter, such as a hyper-parameter for a gaussian process. The uncertainty measure is an estimated uncertainty, which is present by the deviation of the set manipulated variables. The uncertainty is determined, for example, by means of a probability model (e.g., gaussian process). The uncertainty measure is defined, for example, by the entropy of the probability distribution of the time series of the non-linear autoregressive exogenous gaussian process model GP-NARX. For example, at least one manipulated variable that maximizes the uncertainty metric is determined. The most informative manipulated variable is thus determined for the training. At least one manipulated variable that maximizes the uncertainty measure, in particular if a safety condition is met, may also be determined. This is an iterative step in iterative training using training data, wherein the operating variables are predicted from at least one set manipulated variable. In the iterative training, in particular in active learning, a plurality of iterations of improving the model may be used. The first model is a physical model, which is based on, for example, differential equations describing the behavior of the fuel cell system (i.e., the fuel cell stack or various parts of the fuel cell system). The second model is a data-based model, which, for example, should predict the deviation of the physical model from the actual measured behavior of the fuel cell system by means of a gaussian process. The second model trained in this way can be used after training to correct the physical model independently of the measured values of the operating variables measured only during training, which are predicted by the model after training. The operating variable may be a scalar value. The condition is satisfied by at least one parameter, for example, if the prediction uncertainty of the model that has been trained is maximized due to the at least one parameter. The at least one parameter is determined, for example, by a gradient descent method. The at least one set manipulated variable may be a scalar value or may be a vector having multiple values for different manipulated variables. The measured value of the operating variable is detected on the fuel cell system. The operating variables are generated on the fuel cell system by controlling the subsystems supplied to the fuel cell stack, the control being set using a strategy for controlling the fuel cell system according to the required values of the operating variables.

Preferably, a sequence of at least one manipulated variable set over a period of time is provided for predicting the operating variable. The sequence is defined by a time sequence of discrete values of the at least one set manipulated variable. The length of the time period, i.e., the length of the time series, may be arbitrary. To reduce the calculation time, the time series may preferably comprise only the values of the previous point in time or only the values of at most the first ten points in time.

Preferably, the at least one set manipulated variable is detected with a sensor during operation of the fuel cell system. The set manipulated variable can be accurately detected by the sensor.

Preferably, a prediction of at least one set manipulated variable of at least one part of the fuel cell system is determined from the predefined manipulated variables for the at least one part of the fuel cell system using at least one third model for the at least one part of the fuel cell system, wherein the at least one set manipulated variable is defined on the basis of the prediction. The manipulated variable specified at the first point in time is not necessarily set precisely or not immediately precisely in a real fuel cell system. And determining the actually set manipulated variable according to the preset manipulated variable by using the third model. This reduces the cost of the sensor that would otherwise generate and/or allow manipulated variables where no sensor is available to be considered as well.

Preferably, a cost function is defined as a function of at least one manipulated variable to be specified, wherein the manipulated variable to be specified is determined for which the cost function satisfies a condition. The cost function is a security cost metric. For example, the security cost metric is defined by a probability that the time series is within a secure range. For example, the condition is that the cost function of the manipulated variable to be specified is greater than a threshold value. This means that the manipulated variables to be predefined maximize the uncertainty measure and satisfy the secondary conditions. The secondary condition is, for example, that the uncertainty measure is greater than the threshold.

Preferably, the operating variable is electrical power, for example the terminal power of the fuel cell stack, the voltage, the efficiency or waste heat, in particular the thermal power, of the fuel cell system. Or a variable derived therefrom or a substitute variable.

Preferably, the manipulated variable set defines a pressure difference between the anode and the cathode of the fuel cell system, a temperature difference between a first temperature of the coolant on its entry and a second temperature of the coolant on its exit from the fuel cell system, a humidity of the air, in particular a humidity of the air on its exit from the fuel cell system, a pressure of the air, hydrogen and/or coolant, an operating temperature, an air mass flow, a hydrogen molecular mass flow, a cooling medium mass flow or an electrical characteristic parameter, in particular a current, a current density or a voltage on the fuel cell system. The fuel cell stack together with the supply system represents a fuel cell system as an overall system. The manipulated variable defines, for example, the pressure or the air mass flow in a part of the fuel cell system for the supply and/or discharge of air. The manipulated variables may define a hydrogen molecular mass flow in a portion of the fuel cell system used for hydrogen cycling in the fuel cell system. The manipulated variable may define a cooling medium mass flow of a part of the fuel cell system for cooling the fuel cell system. The manipulated variable may define an electrical characteristic parameter of an electrical part of the fuel cell system, for example a current or a voltage of one of the fuel cells or of the fuel cell system.

Preferably, the at least one predefined manipulated variable defines a setpoint value for the pressure difference between the anode and the cathode of the fuel cell system, a setpoint value for the temperature difference between a first temperature of the coolant on its entry and a second temperature of the coolant on its exit from the fuel cell system, a setpoint value for the humidity of the air, in particular the humidity of the air on its exit from the fuel cell system, a setpoint value for the pressure of the air, hydrogen and/or coolant, a setpoint value for the operating temperature, a setpoint value for the air mass flow, a setpoint value for the hydrogen molecular mass flow, a setpoint value for the coolant mass flow or a setpoint value for an electrical characteristic variable, in particular the current, the current density or the voltage over the fuel cell system. The manipulated variables define, for example, setpoint values for the pressure or the air mass flow in the part of the overall system for the supply and/or discharge of air. The manipulated variables may define a nominal value for the hydrogen molecular mass flow in the portion of the overall system used for hydrogen cycling in the fuel cell system. The manipulated variable may define a setpoint value for a cooling medium mass flow of the overall system for cooling a part of the fuel cell system. The manipulated variable may define a nominal value of an electrical characteristic parameter of an electrical part of the overall system, for example the current or the voltage of one of the fuel cells or of the fuel cell system.

Preferably, at least one operating variable of the fuel cell system is determined as a function of the prediction of the operating variable and/or as a function of the prediction of the deviation, in particular independently of the deviation after training. The deviation is an actual or measured deviation defined from the measured value. This means that the prediction of the deviation by the physical model is corrected by using the data-based model to correct the prediction of the operating variable.

An apparatus for operating a fuel cell stack is provided, which is designed to carry out the method. The apparatus comprises at least one computing device for computing the steps in the method and at least one memory for the model, and may comprise one or more sensors detecting the measured variables.

Drawings

Further advantageous embodiments emerge from the following description and the drawings. In the attached drawings

Figure 1 shows a schematic view of an apparatus for operating a fuel cell system,

figure 2 shows a schematic diagram of the interaction of a model for operating a fuel cell system,

figure 3 shows steps in a method for operating a fuel cell system,

figure 4 shows another schematic diagram of the interaction of the models for operating the fuel cell system,

fig. 5 shows steps in a further method for operating a fuel cell system.

Detailed Description

An apparatus 100 for operating a fuel cell system having a fuel cell stack is schematically illustrated in fig. 1. The apparatus 100 is configured to perform the method described below. The device 100 comprises a first model 101, a second model 102 and at least one third model 103. The fuel cell system includes a fuel cell stack and a supply system. The fuel cell system forms an overall system, which in this example is at least partly modeled by at least one third model 103. In this example, the at least one third model 103 is likewise a chemical or physical model, which is described in particular by differential equations.

In this example, the following four third models 103 are shown:

a mold 103-1 for a portion of the overall system that is used for air input and/or exhaust.

Model 103-2 for a portion of the overall system that is used to add hydrogen from the reservoir system, remove purge gas from the anode path, vent anode path moisture and circulate hydrogen in the fuel cell system.

Model 103-3 for a portion of the overall system that is used to cool the fuel cell system.

A model 103-4 for the electrical part of the overall system, which transmits the electrical power of the fuel cell stack to the onboard electrical network or to another electrical network, for example by means of DC/DC converters and other components, such as devices for short-circuiting, current measurement, voltage measurement of the fuel cell stack and/or the battery pack and/or the individual cells of the fuel cell stack.

The first model 101 is configured as a physical model describing physical relationships in the fuel cell system, for example, by means of differential equations.

The second model 102 is configured as a data-based model that models a difference model between a physical model and an actual behavior of the fuel cell system.

To date, there is no accurate dynamic model to describe the behavior of the entire fuel cell system. Although the individual parts of the overall system can be well described by the at least one third model 103, the dynamic interaction between the individual parts in the overall system is not or hardly known.

The aim of the modeling is therefore to predict the electrical power of the fuel cell system at the next point in time T +1, for example, at point in time T from the possible manipulated variables at point in time T and during the preceding brief period of time T.

The modeling is based on a mixture model having chemical and/or physical components and data-based components. The chemical and physical components are composed of known parts of the overall system for which a first model 101 and at least one third model 103 are defined in the form of differential equations. Examples of differential equations used that describe the dynamic behavior of various parts of the overall system, such as the ventilation system, the cooling system, the hydrogen system, and the electrical system, are known, for example, from the following documents:

[1] control Analysis of an injector-Based Fuel Cell Anode Recirculation System (injector-Based Control Analysis of Fuel Cell Anode Recirculation System), Amey Y. Karnik, Jingsun, and Julia H. Buckland;

[2] model-based control of cathode pressure and oxygen evolution ratio of a PEM fuel cell system (Model-based PEM fuel cell system cathode pressure and oxygen excess rate control), Michael A. Danzer, J-ribbon Wilhelm, Harald achemann, Eberhard P.Hofer;

[3] humidity and Pressure Regulation in a PEM Fuel Cell Using a Gain-Scheduled Static feed Controller (Humidity and Pressure Regulation in PEM Fuel cells Using Gain-Scheduled Static Feedback controllers), Amey Y, Karnik, lacing Sun, IEEE members, Anna G, Stefanopoulou, and Julia H, Buckland;

[4] MODELING AND CONTROL OF AN EJECTOR BASED ANODE RECIRCULATION SYSTEM FOR FUEL CELLS (MODELING AND CONTROL OF injector-BASED FUEL cell ANODE RECIRCULATION SYSTEMs), Amey Y. Karnik, sting Sun;

[5] flachheitsbasierter Entwurf von Mehrgr a subband bam enrestgelung am Beispiel eines Brennstoffzellensystems (multivariable regulation design based on flatness, taking a fuel cell system as an example), Daniel Zirkel;

[6] modellpr ä differential regaining PEM-brenstoff zellensystems (model predictive tuning of PEM fuel cell systems), Jens Niemeyer;

[7] regelung zum efficienten betriebs eines PEM-Brennstoffzellensystems (conditioning for efficient operation of PEM fuel cell systems), Christian H ä hnel.

All these parts of the overall system have individual regulating variables that affect their dynamics. The following description of the manipulated variables of the fuel cell system and their description, by means of which the dynamics can be influenced or by means of which the dynamics can be influenced, is described in the exemplary section of the overall system. Furthermore, these variables are also important for the degradation or ageing of the individual components, in particular of the fuel cell stack, and also for the energy consumption or power requirement of the system supplied to the fuel cell stack, in particular due to parasitic losses. For example, only the air compressor of the fuel cell system may consume 15% of the fuel cell stack power. The fuel cell stack must bear this power more in total so that it can output the desired net power as useful power.

1) Ventilation system

lambda _ cath: excess air compared to stoichiometry in the cathode path of the fuel cell system;

mAir _ cath: air mass flow in the fuel cell system cathode path;

p _ cath: pressure in the fuel cell system cathode path;

t _ cath: temperature in the cathode path of the fuel cell system;

fi _ cath: humidity in the cathode path of the fuel cell system.

This part of the fuel cell system is used for feeding and/or discharging air for the fuel cell stack.

In this example, the variables lambda _ cath and mAir _ cath may be used instead of each other. Humidity may be used if the fuel cell system can set the humidity of the input air.

2) Hydrogen system

lambda _ animal: excess hydrogen molecules compared to stoichiometry in the anode path of a fuel cell system, i.e., excess H2

mH2_ anode: hydrogen molecular mass flow in the anode path of a fuel cell system, i.e. H2 mass flow

p _ anode: pressure in anode path of fuel cell system

dp _ anode _ cath: pressure differential between cathode path and anode path in a fuel cell system

mN2_ anod: mass flow of nitrogen, concentration of nitrogen or molecular flow of nitrogen in anode

mH2_ addfromstank: h2 mass or H2 mass flow added to the anode path from the H2 can of the fuel cell system or from outside

Purge _ action: manipulation of anode gas venting or removal from anode path

Drain _ action: operation of draining or removing liquid water from anode path

Purge & Drain _ action: the valves for the Purge _ activation and the Drain _ activation, or the common valve, are controlled in combination.

This part of the fuel cell system is used for hydrogen recycling and other functions of the fuel cell system.

In this example, the variables lambda _ anode and mH2_ anode may be used instead of each other. For example, if a hydrogen recirculation fan is present in the fuel cell system, the recirculation rate of the hydrogen recirculation fan is related to mH2_ anod.

The variable mH2_ addfromstank may additionally include a temperature specification. The variable mH2_ addfromthak may be used in addition to or in combination with lambda _ anode or mH2_ anode.

The variable mN2_ anod can be derived from model calculations or determined by sensors. The variable mN2_ anod may be used to trigger the purge operation.

The variable Purge actuation may describe the duration of opening and/or the opening interval of the valve for discharging or removing anode gas in a discrete manner in time. Both of which may be variable.

The variable Drain actuation may describe the duration of opening and/or the opening interval of the valve for draining or removing liquid water, in a discrete manner in time. Both of which may be variable.

3) Cooling system

T _ Stack _ op: the operating temperature of the fuel cell system coolant, i.e. approximately the operating temperature of the fuel cell system

Fan _ action: fan control

dT _ Stack: temperature variation of coolant, e.g. heating by fuel cell system

m _ Cool: coolant mass flow through a cooling path of a fuel cell system

dp _ Cool: pressure drop across cooling path of fuel cell system

Pump _ action: pump actuation for generating a coolant mass flow

Valve _ action: valve actuation for generating a coolant mass flow

p _ Cool: pressure in the coolant path of the stack.

This part of the fuel cell system is used to circulate coolant in the fuel cell system.

The variable T Stack op can be used in an expanded manner or more precisely also for the membrane representing the temperature-critical component of the fuel cell Stack. For this purpose, the membrane temperature can be inferred, for example, by means of a model of the coolant temperature, the stack exhaust gas temperature, the stack voltage and the stack current. The operating temperature can be modeled based on load, ambient temperature, Fan handling (i.e., based on Fan actuation).

The variable dT _ Stack may be determined from the temperature difference between the output temperature and the input temperature of the coolant and set by means of the mass flow of the coolant, for example using a pump and a three-way valve for the cooling system of the fuel cell system.

As an alternative to the variable p _ Cool, a pressure difference with the cathode and/or with the anode can be used.

4) Electrical system

Voltage:

current:

current density:

electric power:

short-circuit relay, short-circuit device and possible other electrical actuators

The electrical variables of the fuel cell stack, voltage, current density and electrical power, interact strongly with the current network, whose architecture can be very different.

For example, the electrical power of the fuel cell stack can be transmitted from the fuel cell stack to the current grid by means of a direct current converter, such as a DC/DC converter, as a function of the voltage and/or the current. For example, the DC/DC converter may set the current drawn from the fuel cell stack by the voltage drop.

A shorting relay may be provided that shorts out the fuel cell stack (i.e., both terminals). This can be used, for example, for freeze starting, in which case no electrical power is temporarily transmitted to the current network, but electrical power is converted into heat.

Variables derived therefrom, such as resistance or efficiency, may also be modeled.

These variables are variable quantities. Not all possible variables are explicitly recited. There may be model-based values and measured values in these variables, respectively. In addition or as an alternative to absolute variables, differential variables or differences from reference values can also be used. It is also possible to use only a subset of the possible variables as parameters for the modeling.

The apparatus 100 comprises a control device 104, which control device 104 is designed to control the fuel cell system or the subsystems in order to operate the fuel cell stack with the respective manipulated variables. The apparatus 100 may comprise a measuring device 106, in particular a sensor for detecting a variable on the fuel cell system. In this example, the apparatus comprises at least one computing device 108 configured to perform the steps of the method described below and at least one memory 110 for a model. The at least one computing device 108 may be a local computing device in the vehicle, a computing device on a server or in the cloud, or a computing device distributed over multiple servers or over the vehicle and at least one server, among others.

The interaction of the models for operating the fuel cell system is described based on fig. 2.

In this example, for the fuel cell system, the operation variable y _ req to be supplied is defined as an input variable. Preferably, the operating variable is the electrical power, the voltage, the efficiency or the waste heat, in particular the thermal power, of the fuel cell system. The fuel cell system should be manipulated with at least one manipulated variable u _ req such that the fuel cell actually provides the operating variable. The at least one manipulated variable u _ req is a setpoint value for the manipulation of the fuel cell system by the manipulation device 104. In this example, the operating variable y _ req to be provided is mapped to at least one manipulated variable u _ req by the strategy for the manipulation. The strategy may be to map the operating variable y _ req to be provided to the at least one manipulated variable u _ req by a predefined linear or nonlinear function or by a predefined table.

Due to dead time, inertia, hysteresis, aging effects or deviations of the actuator from the setpoint value, manipulated variables deviating from the setpoint value may occur. On the one hand, this manipulated variable can be detected as an actually set manipulated variable u _ act, for example, by a sensor. On the other hand, the set at least one manipulated variable u _ pred may be determined using the at least one third model 103 as a prediction. In this example, for at least one part of the fuel cell system, in particular for the fuel cell stack or for at least one of the subsystems for supplying the fuel cell stack, a prediction x [ subsy ] _ pred of at least one manipulated variable u _ pred provided for at least one part of the fuel cell system is determined from a manipulated variable x [ subsy ] _ req predefined for the at least one part of the fuel cell system, and the at least one set manipulated variable u _ pred is defined from the prediction [ subsy ] _ pred. In this example, the variable x [ subsy ] _ req is combined in a vector that defines the manipulated variable u _ req. Each of the above-described regulating variables may be used as a variable x subsy req of a corresponding portion of the fuel cell system. If multiple tuning variables are set for a section, the variable x subsy req is a vector including these tuning variables. Only selected variables are described below by way of example.

In fig. 2, a variable of the model 103-1 (i.e., the ventilation system) is represented by [ subsy ] = a, a variable of the model 103-2 (i.e., the hydrogen system) is represented by [ subsy ] = H, a variable of the model 103-3 (i.e., the cooling system) is represented by [ subsy ] = C, and a variable of the model 103-4 (i.e., the electrical system) is represented by [ subsy ] = E.

All or only part of the actual manipulated variables can be determined or measured by means of the model from the respectively predefined manipulated variables.

Regardless of whether the manipulated variable set is measured (i.e. u _ act) or modeled (i.e. u _ pred), the manipulated variable can be the pressure difference between the anode and the cathode of the fuel cell system, the temperature difference between a first temperature of the coolant on its entry and a second temperature of the coolant on its exit from the fuel cell system, the humidity of the air, in particular the humidity when the air exits the fuel cell system, the pressure of the air, hydrogen and/or coolant, the operating temperature, the air mass flow, the hydrogen molecular mass flow, the cooling medium mass flow or an electrical characteristic parameter, in particular the current, the current density or the voltage over the fuel cell system. The fuel cell system is an integrated system.

The manipulated variables define, for example, the pressure difference between the anode and the cathode of the fuel cell system, the temperature difference between a first temperature of the coolant on its entry and a second temperature of the coolant on its exit from the fuel cell system, the humidity of the air, in particular the humidity of the air when it exits from the fuel cell system, the pressure of the air, hydrogen and/or coolant, the operating temperature or the air mass flow in the part of the fuel cell system for the input and/or exhaust of air. The manipulated variables set may define the hydrogen molecular mass flow in the part of the fuel cell system for circulating hydrogen in the fuel cell system. The manipulated variable may define a cooling medium mass flow of a part of the fuel cell system for cooling the fuel cell system. The manipulated variable set may be defined as an operating temperature that approximates the temperature of the coolant. The manipulated variable set can define an electrical characteristic parameter of an electrical part of the fuel cell system, for example the current, the current density or the voltage of one of the fuel cells or of the fuel cell system.

Preferably, the at least one predefined manipulated variable u _ req defines a setpoint value for the pressure, the operating temperature, the air mass flow, the hydrogen molecule mass flow, the coolant mass flow or an electrical characteristic variable, in particular the current or the voltage of the fuel cell system. In this example, the manipulated variable xA _ req defines a setpoint value for the pressure or the air mass flow in the part of the overall system for the supply and/or discharge of air at the time t. In this example, the manipulated variable xH _ req defines a setpoint value for the hydrogen molecule mass flow at the time t in the part of the overall system used for the hydrogen circulation in the fuel cell system. In this example, the manipulated variable xC _ req defines a setpoint value for the cooling medium mass flow of the part of the overall system for cooling the fuel cell system at the time t. The manipulated variable may also be defined as an operating temperature that approximates the temperature of the coolant. In this example, the manipulated variable xE _ req defines a setpoint value for an electrical characteristic variable of an electrical part of the overall system, for example the current or the voltage of the fuel cell or the fuel cell system, at the time t. In this example, the predefined manipulated variable u _ req is the vector u _ req = (xA _ req, xH _ req, xC _ req, xE _ req)^T. Accordingly, the manipulated variables that occur are defined in this example by vectors. In the case that all the occurring manipulated variables are measurable, the resulting manipulated variable is u _ act = (xA _ act, xH _ act, xC _ act, xE _ act)^T. In the case where all the occurring manipulated variables are modeled, the resulting manipulated variable is u _ pred = (xA _ pred, xH _ pred, xC _ pred, xE _ pred)^T. Preferably, a hybrid form is used, in which the resulting manipulated variable, which can be measured with sensors available anyway on the fuel cell system, is measured and the other manipulated variables are modeled.

The operating variable y _ act of the fuel cell system is determined by means of the first model 101 from the at least one derived manipulated variable. In this example, the resulting operating variable is a scalar, but a vector of multiple values with different operating variables may also be determined by the first model 101. In this example, for the first model 101, which is a static model, a fuel cell model according to Kulikovsky is used. The model according to Kulikovsky was derived analytically from the system of basic differential equations used to describe the electrodynamics of the cathode catalyst layer. The model uses the following input variables: cathode mass flow, cathode lambda, cathode input pressure, cathode output pressure, air humidity at the cathode inlet, air humidity at the cathode outlet, current or current density, coolant entry temperature, and coolant exit temperature.

A prediction of the deviation dy _ pred of the operating variable y _ act determined by the first model 101 from the actual value of the operating variable on the fuel cell system is determined by the second model 102 from the at least one derived manipulated variable. For training, the actual value, i.e. the measured operating variable y _ mes, is determined. During training in the vehicle, the measured operating variable y _ mes is measured, for example on a test bench or online, i.e. during operation of the vehicle. During the training, the actual deviation dy is determined at the comparison means 201 from the measured operating variable y _ mes and the operating variable y _ act determined by the first model 101.

In this example, the second model 102 is a data-based model that should predict the deviation dy _ pred between the first model 101 and the actual measured behavior of the fuel cell system by a gaussian process. During training, the second model 102 may first be randomly initialized and trained in iterations as described below.

The second model 102 may have been trained. In this case, the measurement of the measured operating variable y _ mes and the determination of the actual deviation dy may be omitted.

From the operating variable y _ act determined by the first model 101 and from the prediction of the deviation dy _ pred, an operating variable y _ pred is determined at the correction means 202. This means that the prediction of the deviation by the physical model is corrected by using the data-based model for the prediction of the deviation.

The computing device 108 determines at least one parameter P for the first model 101 and/or the second model 102 during training. In this example, the at least one parameter P is determined from the at least one manipulated variable u _ req, the at least one derived manipulated variable (i.e. the measured manipulated variable u _ act and/or the modeled manipulated variable u _ pred), the prediction of the deviation dy _ pred and the deviation dy. This is described below.

The computer-implemented method for operating the fuel cell system described below with reference to fig. 3 provides in step 301 that at least one manipulated variable u _ req for actuating the fuel cell system is predefined. During training, at least one manipulated variable u _ req is determined by the first model 101 from an uncertainty measure h (u _ req) for predicting an operating variable y _ pred of the fuel cell system, independently of the strategy, according to the following procedure. To this end, in this example either a time series of set manipulated variables u _ act (T) of the subsystem at the time point T =1.. T is used, or a time series of modeled set manipulated variables u _ pred (T) at the time point T =1.. T from the prediction x [ subsys ] _ pred (T) calculated for the subsystem is used.

For the uncertainty measure h (u _ req), at least one predefined manipulated variable u _ req is determined for which the uncertainty measure h (u _ req) satisfies a condition.

The uncertainty metric is an estimated uncertainty that exists through the manipulated variables that are actually set. The uncertainty is determined, for example, by means of a probability model (e.g., gaussian process). The uncertainty measure is defined, for example, by the entropy of the probability distribution of the time series of the non-linear autoregressive exogenous gaussian process model NARX.

In this example, at least one manipulated variable u _ req is determined at a time t as at least one manipulated variable u _ req (t) to be specified, which maximizes the uncertainty measure. The most informative manipulated variable is thus determined for the training. At least one manipulated variable that maximizes the uncertainty metric under secondary conditions may also be determined. The secondary condition may be a safety condition.

In one aspect, the cost function s (u _ req (t)) is defined as a function of at least one manipulated variable u _ req (t) to be specified. In this case, a manipulated variable u _ req (t) is determined, for which the cost function s (u _ req (t)) satisfies the condition c. The cost function is in this example a security cost metric. The safety cost measure is defined, for example, by the probability of the time series determined for the manipulated variable u _ req (t) to be specified being within a safe range for the operation of the fuel cell system, which probability is specified, for example, by a gaussian process model. The condition c is, for example, that the cost function s (u _ req (t)) of the manipulated variable u _ req (t) to be specified is greater than a threshold value c. This means that the manipulated variable u _ req (t) to be predefined maximizes the uncertainty measure h (u _ req (t)) and satisfies the secondary condition s (u _ req (t)) > c.

The secondary condition of security, i.e. the security cost, can be defined in the following way:

a) based on physical knowledge with a set of secondary conditions that must all be satisfied,

b) based on physical knowledge with unique secondary conditions summarizing all security-related aspects,

c) based on a data-based machine learning model, such as one for each safety-related aspect in a),

d) based on a data-based machine learning model, such as the one in b) summarizing all safety-related aspects,

e) based on a combination of summarized criteria and individual criteria, which criteria are based on physical knowledge or machine learning models, respectively.

For example, it can be provided that the state of the cell membrane in the fuel cell system is evaluated or diagnosed by an impedance measurement. The impedance measurement corresponds to a sensor which can evaluate the operation or the quality of the operation by means of an impedance spectrum. The impedance measurement can use a signal having a frequency that does not interfere with the operation of the fuel cell system and provides a quality metric resulting from the totality of all stack operating variables, but cannot be traced back to each conditioning variable individually. The machine learning model can be trained to use this signal as a measure of robust operation or also as a safety or quality measure of the battery membrane.

The machine learning model is a hybrid model. The one or more machine learning models may be regression models or classification models, respectively.

In order to determine the manipulated variable u _ req (t) to be specified, the following operations are performed in this example:

based on the time series u _ req (T) = u _ req (T-1),.. u _ req (T-T) and the known measured values of the operating variables y _ mes (T) for this purpose, the deviation dy (T) is first determined. To approximate the deviation dy (t) by the second model 102, a gaussian process GP is defined for the input x with a mean function μ (x) and a covariance function k (x _ i, x _ j), which assigns the output dy _ pred (t) = f (x _ i) = GP (μ (x _ i), k (x _ i, x _ j)) to the input x _ i = u _ req (t-1). For the time series u _ req (T) = u _ req (T-1) · u _ req (T-T) as input x _ i, a prediction of the deviation dy _ pred (T) is assigned as output dy _ pred (T) = f (x _ i).

In this example, a gaussian kernel is used as the covariance function k (x _ i, x _ j) for the gaussian process and an average value of, for example, zero is used.

For training, a manipulated variable u _ req (t +1) to be specified is to be determined, for which the prediction dy _ pred (t +1) of the deviation provides the maximum possible information gain with respect to the assignment of the input x to the output f (x) by the gaussian process. For this purpose, an uncertainty measure h (u _ req) and a cost function s (u _ req) are used, which must satisfy the secondary condition on which the condition c is based. In this example, the manipulated variable u _ req (t +1) to be specified is determined as

Max _ { u _ req } h (u _ req), where s (u _ req) > C.

Here, h (u _ req) = σ (u _ req), where σ (u _ req) is the predicted variance of the gaussian process trained with the data.

In particular, the safety condition may be defined by a further gaussian process GP _ { saf }, with a prediction mean value μ _ { saf } (u _ req (t)) and a prediction covariance σ _ { saf } (u _ req } (t)) at position u _ { req } (t). The cost function s (u _ req) is then defined as

s(u_{req}(t))=\int_{s1>0,…,sT>0}\mathcal{N}(s1,…,sT|\mu_{saf}(u_req(t)), \Sigma_{saf}(u_{req}(t)))。

Subsequently, in step 302, a prediction of an operating variable y _ act of the fuel cell system is determined using the first model 101 as a function of the at least one manipulated variable u _ req or as a function of at least one manipulated variable set for the at least one manipulated variable u _ req (t), i.e. in this example the measured manipulated variable u _ act and/or the modeled manipulated variable u _ pred.

Subsequently in step 303, the deviation dy between the prediction of the operating variable y _ act of the fuel cell system and the measured value y _ mes of the operating variable is determined.

Preferably, a sequence of at least one set manipulated variable, in this example a measured manipulated variable u _ act and/or a modeled manipulated variable u _ pred, is provided for the prediction of the operating variable y _ act over a time period T. The sequence is defined by a time sequence of discrete values of the at least one set manipulated variable, i.e. in this example the measured manipulated variable u _ act and/or the modeled manipulated variable u _ pred. The length of the time period, i.e., the length of the time series, may be arbitrary. To reduce the calculation time, the time series may preferably comprise only the values of the previous point in time or only the values of at most the first ten points in time. Preferably, the at least one set manipulated variable u _ act is detected with a sensor while the fuel cell system is operating.

Subsequently, in step 304, a prediction dy _ pred of the deviation dy is determined with the second model 102 from the at least one manipulated variable u _ req or from at least one manipulated variable set for the at least one manipulated variable u _ req (t), i.e. in this example the measured manipulated variable u _ act and/or the modeled manipulated variable u _ pred.

Subsequently, in step 305, at least one parameter P of the first model 101 and/or the second model 102 is determined from the deviation dy and the prediction dy _ pred of the deviation dy.

Step 301 is then performed.

These steps are iterations in an iterative training using training data, wherein the operating variables are predicted from at least one predefined or set manipulated variable. In the iterative training, in particular in active learning, a number of iterations of the improved first model 101 and/or second model 102 may be used. The second model trained in this way can be used to correct the physical model after the training, independently of the measured values of the operating variables.

In this case, after the training, at least one manipulated variable u _ req is determined in step 306 using a strategy as a function of the operating variable y _ req to be set. The policy is set in this example.

Subsequently, in step 307, a prediction of the operating variable y _ act of the fuel cell system is determined using the first model 101 on the basis of the at least one manipulated variable u _ req or on the basis of at least one manipulated variable set for the at least one manipulated variable u _ req (t), i.e. in this example the measured manipulated variable u _ act and/or the modeled manipulated variable u _ pred.

Subsequently, in step 308, a prediction dy _ pred of the deviation dy is determined with the second model 102 from the at least one manipulated variable u _ req or from at least one manipulated variable set for the at least one manipulated variable u _ req (t), i.e. in this example the measured manipulated variable u _ act and/or the modeled manipulated variable u _ pred.

Subsequently in step 309, a corrected operating variable y _ pred is determined from the prediction of the operating variable y _ act and the prediction dy _ pred of the deviation dy.

Step 306 is then performed.

The method is terminated, for example, after the training or when the fuel cell system is shut down.

In one aspect, it can be provided that the method is performed independently of the first model 101. This is described based on fig. 4 and 5.

As shown schematically in fig. 4, in contrast to the above-described procedure, the actual deviation dy is determined using the comparison device 201 on the basis of the measured value y _ mes of the corrected operating variable y _ pred and the prediction of the corrected operating variable y _ pred by the second model 102. The first model 101 and the prediction of the operating variables y _ act are not used. Otherwise, the models will work in concert as described above. In fig. 4, the same reference numerals denote elements having the same functions as described with respect to fig. 3.

The difference from the above method is as follows.

In step 501, at least one manipulated variable u _ req for the manipulation of the fuel cell system is predefined, as described above for step 301.

The aspects described in

steps

302 and 303 relating to the first model 101 are not performed in this aspect.

In a subsequent step 502, the procedure is as described for step 304, but in contrast, a corrected operating variable y _ pred is determined using the second model 102 as a function of the at least one manipulated variable u _ req or as a function of at least one manipulated variable u _ act, u _ pred provided for the at least one manipulated variable u _ req (t). The corrected operating variable y _ pred is a prediction of the measured value y _ mes of the fuel cell system.

Subsequently in step 503, the deviation dy between the corrected operating variable y _ pred of the fuel cell system and the measured value y _ mes of this operating variable is determined.

In a subsequent step 504, the procedure is as described for step 305, but in contrast at least one parameter P of the model 102 is determined from the measured values y _ mes and the prediction y _ pred.

This means that in step 501, as described for step 301, at least one predefined manipulated variable u _ req is determined, for which the uncertainty measure h (u _ req) satisfies the condition, based on the uncertainty measure h (u _ req) of the corrected operating variable y _ pred (i.e. the prediction of the measured variable y _ mes by the second model 102).

Steps 501 to 504 may be repeated for training.

Step 505 is then performed as described for step 306 using the second model 102 trained in this manner.

Step 506 is then performed as described for step 307.

Step 507 is then performed as described for step 308.

Step 508 is then performed as described for step 309.

Steps 505 through 508 may be repeated.

The method ends, for example, after training or when the fuel cell system is shut down.

Claims

1. Computer-implemented method for operating a fuel cell system, characterized in that at least one manipulated variable (u _ req) for manipulating the fuel cell system is specified (301, 501), wherein a prediction (y _ pred, dy _ pred) of a variable (y _ mes, dy) of the fuel cell system is determined (304, 502) using a model (102) from the at least one manipulated variable (u _ req) or from at least one manipulated variable (u _ act, u _ pred) set for the at least one manipulated variable (u _ req (t)), and wherein at least one parameter (P) of the model (102) is determined (305, 504) from the variable (y _ mes, dy) and the prediction (y _ pred, dy _ pred) of the variable (y _ mes, dy), wherein the prediction (y _ pred, dy _ pred), determining (301, 501) by means of the model (102) at least one predefined manipulated variable (u _ req) for which the uncertainty measure (h (u _ req)) satisfies a condition.

2. The method according to claim 1, characterized in that the variable (y _ mes) is a measured value (y _ mes) of the operating variable, wherein a prediction (y _ pred) of the operating variable of the fuel cell system is determined (502) with the model (102) from the at least one manipulated variable (u _ req) or from at least one manipulated variable (u _ act, u _ pred) set for the at least one manipulated variable (u _ req (t)).

3. Method according to claim 1, characterized in that a prediction (302) of an operating variable (y _ act) of the fuel cell system is determined (302) using a first model (101) from the at least one manipulated variable (u _ req) or from at least one manipulated variable (u _ act, u _ pred) set for the at least one manipulated variable (u _ req (t)), wherein the variable (dy) is (303) the deviation (dy) between the prediction of an operating variable (y act) of the fuel cell system and the measured value (y mes) of the operating variable, wherein a prediction (dy _ pred) of the deviation (dy) is determined (304) with the second model (102) as a function of the at least one manipulated variable (u _ req) or as a function of at least one manipulated variable (u _ act, u _ pred) provided for the at least one manipulated variable (u _ req (t)).

4. Method according to any of the preceding claims, characterized in that for predicting the operating variables (y _ act, y _ pred) a sequence of at least one set manipulated variable (u _ act, u _ pred) within a time period (T) is provided.

5. Method according to any of the preceding claims, characterized in that at least one set manipulated variable (u act) is detected with a sensor during operation of the fuel cell system.

6. Method according to any of the preceding claims, characterized in that a prediction (x [ subsy ] _ pred) of at least one set manipulated variable (u _ pred) of at least one part of the fuel cell system is determined from predefined manipulated variables (x [ subsy ] _ req) for the at least one part of the fuel cell system using at least one third model (103) for the at least one part of the fuel cell system, wherein the at least one set manipulated variable (u _ pred) is defined from the prediction (x [ subsy ] _ pred (t)).

7. The method according to one of the preceding claims, characterized in that a cost function is defined as a function of at least one manipulated variable (u _ req) to be predefined, wherein the manipulated variable (u _ req) to be predefined is determined for which the cost function satisfies (301, 501) a condition (c).

8. Method according to any of the preceding claims, characterized in that the operating variable is the electrical power, the voltage, the efficiency or the waste heat, in particular the thermal power, of the fuel cell system.

9. Method according to any of the preceding claims, characterized in that the manipulated variables (u _ act, u _ pred) set define the pressure difference between the anode and the cathode of the fuel cell system, the temperature difference between a first temperature of the coolant on its entry and a second temperature of the coolant on its exit from the fuel cell system, the humidity of the air, in particular the humidity of the air on its exit from the fuel cell system, the pressure of the air, hydrogen and/or coolant, the operating temperature, the air mass flow, the hydrogen molecular mass flow, the cooling medium mass flow or electrical characteristic parameters, in particular the current, the current density or the voltage over the fuel cell system.

10. Method according to any one of the preceding claims, characterized in that the at least one predefined manipulated variable (u _ req) defines a nominal value for the pressure difference between the anode and the cathode of the fuel cell system, a nominal value for the temperature difference between a first temperature of the coolant on its entry and a second temperature of the coolant on its exit from the fuel cell system, a nominal value for the humidity of the air, in particular the humidity of the air on its exit from the fuel cell system, a nominal value for the pressure of the air, hydrogen and/or coolant, a nominal value for the operating temperature, a nominal value for the mass flow of the air, a nominal value for the mass flow of hydrogen molecules, a nominal value for the mass flow of the cooling medium or a nominal value for an electrical characteristic parameter, in particular the current, the current density or the voltage over the fuel cell system.

11. Method according to any of the preceding claims, characterized in that at least one operating variable (y act) of the fuel cell system is determined from a prediction (y pred) of the operating variable and/or from a prediction (dy pred) of the deviation, in particular independently of the deviation (dy) after training.

12. Device for operating a fuel cell system, characterized in that the device is configured for carrying out the method according to any one of claims 1 to 11.

13. Computer program, characterized in that it comprises machine-readable instructions which, when executed by a, in particular distributed, computer, carry out the method according to any one of claims 1 to 11.