Method for operating a fuel cell system

Abstract

The presented invention relates to a method (100) for operating a fuel cell system (200), wherein the method (100) comprises: - calculating (101) a predictive maximum permissible electrical power output (ML) for at least one fuel cell stack (201, 203) of the fuel cell system (200), - adjusting (103) an electrical power output of the at least one fuel cell stack (201, 203) taking into account the calculated ML, wherein the ML of the at least one fuel cell stack (201, 203) is calculated as a function of heat capacities of predetermined components (201, 203, 209, 213) of a cooling circuit for cooling the at least one fuel cell stack (201, 203) and a temperature currently present in the predetermined components (209, 213) and / or at least a predetermined temperature change rate and / or at least a predetermined temperature.

Description

The present invention relates to a method for operating a fuel cell system, a fuel cell system and a computer program product according to the appended claims.Prior ArtFor calculating a currently maximally permissible electrical power output of a fuel cell stack that is predictive due to thermal conditions, methods are known that only take into account variables, i.e., calculated and / or measured signals, that relate to the system fuel cell stack, so that the system boundary around the fuel cell stack is drawn in itself.The variables which are generally taken into account in known methods for calculating an currently maximum permissible electrical power output of a fuel cell stack that is predictive on the basis of thermal conditions are a coolant mass flow through the fuel cell stack, the temperature of the fuel cell stack or its coolant outlet temperature and / or coolant inlet temperature. Accordingly, the cooling circuit i in which the fuel cell stack is arranged is not considered as a whole, but rather only the system fuel cell stack is focused on the fuel cell stack in the calculation of a currently maximum permissible electrical power output of a fuel cell stack that is predictive on account of thermal conditions.Focusing only on the fuel cell stack system, however, excludes heat capacities and temperatures in respective coolant lines and heat capacities and temperatures of other components located in the cooling circuit i, such as a radiator, for example, in the calculation of a currently maximally permissible electrical power output of a fuel cell stack that is predictive due to thermal conditions.Furthermore, focusing only on the system fuel cell stack does not take into account a current or maximum possible heat flow emitted to the ambient air via a radiator.Accordingly, known methods for calculating a currently maximally permissible electrical power output of a fuel cell stack that is predictive due to thermal conditions are inaccurate.Disclosure of the InventionWithin the scope of the present invention, a method for operating a fuel cell system, a fuel cell system, and a computer program product are presented. Further features and details of the invention are evident from the respective dependent claims, the description and the drawings. Features and details which are described in connection with the method according to the invention naturally also apply in connection with the fuel cell system according to the invention or the computer program product according to the invention and vice versa, so that with regard to the disclosure reference is or can always be made to the individual aspects of the invention in a mutually alternating manner.The present invention is used in particular to enable an accurate calculation of a currently maximally permissible electrical power output of a fuel cell stack that is predictive due to thermal conditions.According to a first aspect of the present invention, a method for operating a fuel cell system is thus provided.The presented method comprises calculating a predictive maximum permissible electrical power output (ML) for at least one fuel cell stack of the fuel cell system and setting an electrical power output of the at least one fuel cell stack taking into account the calculated ML, wherein the ML of the at least one fuel cell stack depends on the heat capacities of the predefined components (for example. The heat capacities of the coolant in the coolant line (and possibly also the heat capacities of the coolant lines themselves) of the coolant circuit i (in which the fuel cell stack is i), the heat capacities of the coolant in the coolant line (and possibly also the heat capacities of the coolant lines themselves) of the coolant circuit i and the known (i.e. measured and / or calculated) temperatures and / or at least one predefined temperature change rate and / or at least one predefined temperature assigned to these heat capacities are calculated.With regard to the thermal system, not the electrical power output, but rather the power loss is relevant here. However, knowing the power dissipation, the electrical power output can be determined, and vice versa. The relationship between the electrical power output and the thermal power loss is given by the so-called polarization curve of the fuel cell stack.In the context of the present invention, a predictive maximum permissible electrical power output (ML) is understood to mean a variable (specifically a signal) which is used for controlling or regulating an electrical power provided by a fuel cell stack, such that this provided power does not become greater than the ML. By the calculation according to the invention and the setting according to the invention of the electrical power output of the at least one fuel cell stack taking into account the ML, a thermal load which the fuel cell stack introduces into a cooling circuit is limited.The components specified according to the invention can be, for example, a fuel cell stack, a radiator, a coolant line and coolant flowing in the coolant line.The coolant inlet temperature into a predefined component (for example. Fuel cell stack, radiator, coolant line, branch point, mix point, etc.) may be either measured or calculated. A calculation of a coolant inlet temperature, in particular into a coolant line, can be modeled here, for example, using a thermal model of a mixing point and the coolant lines (i.e. upstream) opening into this mixing point, wherein these coolant lines are each modeled by a "model of the coolant line" assigned to the coolant line, which model in turn receives its coolant inlet temperature (either measured or calculated).The amount of heat currently stored in the predefined components can be calculated, for example, via a temperature measured by at least one temperature sensor and / or by at least one mathematical model.As a result, in the calculation of the ML, which can be provided or is permitted by a fuel cell stack arranged in the cooling circuit, the enthalpy or heat currently present or stored in the cooling circuit, and the heat absorption capacity of the cooling circuit, are taken into account.Since, according to the invention, the ML of a respective fuel cell stack is calculated as a function of heat capacities of predefined components of a cooling circuit for cooling the at least one fuel cell stack and a temperature currently present in the predefined components and / or at least one predefined temperature change rate and / or at least one predefined temperature, as a result of which the stored quantity of heat is thus taken into account, overloading of the cooling circuit by an introduction of thermal energy from the fuel cell stack can be reliably prevented.Furthermore, the calculation of the ML of a respective fuel cell stack as a function of heat capacities of predefined components of a cooling circuit for cooling the at least one fuel cell stack and a temperature currently present in the predefined components and / or at least one predefined temperature change rate and / or at least one predefined temperature brings about an expansion of the system limit under consideration, such that not only the fuel cell stack or a coolant flow flowing through the fuel cell stack, but rather the entire cooling circuit of a fuel cell system is under consideration.It may be arranged that the fuel cell system includes a plurality of fuel cell stacks, and an ML is calculated for each fuel cell stack of the plurality of fuel cell stacks, and the electric power output of a specific fuel cell stack is set in consideration of its ML as compared to the ML of the other fuel cell stacks. This comparison of the ML of a fuel cell stack with the predictive maximum permissible electrical power outputs of the other fuel cell stacks can be carried out, for example, by dividing the ML of the fuel cell stack under consideration by the sum of the ML of all fuel cell stacks of the fuel cell system.In a multi-box system in which multiple fuel cell stacks are used to provide a required (i.e. required) total electrical power for the fuel cell vehicle, the so-called "power split" (i.e. the power split), i.e. the proportion of the required (i.e. required) total electrical power that a fuel cell stack is to provide, can be calculated based on this comparison (i.e. the above-described comparison of the predictive maximum permissible electrical power outputs of the fuel cell stacks) of the thermal system.In particular in so-called "multibox systems" which comprise a plurality of fuel cell stacks in order to provide a required total electrical power for the fuel cell vehicle, the presented method can be used for calculating a currently maximum permissible electrical power output of a specific fuel cell stack which is predictive on the basis of thermal conditions in order to calculate the proportion of the total power which each specific fuel cell stack is intended to provide. In other words, a so-called "power split" or the power split, i.e. the proportion of a total power of a fuel cell system which is intended to be supplied by a specific fuel cell stack, can be calculated. In this case, it may be provided to request, i.e. demand, a fuel cell stack in which the method calculates a higher predictive currently maximally permissible electrical power output than in the case of another fuel cell stack a higher proportion of the currently necessary total power. However, other aspects, such as the state of aging of the respective stack, can also be included in this "power split". It can furthermore be provided that the predefined components of the cooling circuit are selected from the following list of components: fuel cell stack, radiator, coolant in respective coolant lines, coolant line.The following formula signs are used below: k time step i index for cooling circuit j index for coolant line of the cooling circuit i t index for partial volumes of the "model of coolant line" (for t=1,..., N) N number of partial volumes into which a coolant line is divided into the "model of coolant line", T denotes a temperature; i.e. the formula sign T always denotes a temperature. The script specifies which temperature is exactly involved. Ṫ time derivative of a temperature; i.e., the formula symbol Ṫ always denotes a time derivative of a temperature (i.e., a temperature change rate). The subscript specifies what temperature change rate is concerned. c pCoolt( T) specific heat capacity of the coolant as a function of the temperature ρ Coolt( T) coolant density as a function of the temperature V j volume of the coolant line with the index j V T,j size of the partial volume (i.e, (T j,t the temperature C that can be assigned to the subvolume with index t of the coolant line j j,t the heat capacity (of the coolant) of the subvolume with index t of the coolant line j " the weighted temperature change rate of the coolant circuit" of coolant circuit i (see equation (8)) T i" the weighted temperature of the coolant circuit" of coolant circuit i (see equation (14)) " the maximum permissible temperature change rate of the coolant circuit" (of coolant circuit i) Q̇ LossMax,i( predictive) the currently maximum permissible power loss of the fuel cell stack in the coolant circuit i i StckMax,i( predictive) current maximum permissible stack flow of the fuel cell stack in the cooling circuit i Qegr Radr2Air( k) current heat flow which the radiator discharges to the ambient air Q Radr2AirMax( k) current maximum possible heat flow which the radiator could discharge to the ambient airIt can furthermore be provided that the amount of heat currently stored in the predefined components is calculated and / or measured.If the variables a) volume of coolant lines (as measured or taken from design drawings), b) the actual coolant mass flow of a coolant pump (measured directly or indirectly or via an actuator model which models the dynamic response behavior of the coolant mass flow required by the coolant pump to the coolant flow provided by the coolant pump), c) the actual mass flow ratio between coolant mass flows which prevails after branch points, d) the coolant inlet temperature into a coolant line (either measured or calculated), the instantaneous distribution of the coolant temperature in a coolant line can be calculated approximately by the so-called "model of the coolant line". In other words, the "model of the coolant line" can be used to calculate how the coolant temperature is carried along with the coolant mass flow present in a coolant line. The continuous temperature distribution in the direction of flow is in this case discretized with sufficient accuracy by the "model of the coolant line". The temperature distribution transversely to the direction of flow is assumed to be constant, which can be justified by the turbulent flow present in the coolant line.For example, a method for approximating a momentary distribution of the coolant temperature in a coolant line can proceed as follows:the volume V of a coolant line is divided into a plurality of individual partial volumes of specific size. For example, the volume V can be divided into N equal parts V T which will be assumed below.a ring memory of size N storing coolant temperatures is applied and the following steps are carried out in each time step:the coolant volume flow is calculated by dividing the actual coolant mass flow with the coolant densitythe coolant volume flow is numerically integrated over time (i.e. a volume V integral( k) covered by the coolant in the coolant line is thus obtained)calculating the coolant temperature at the coolant outlet of the coolant line T pipe,out( k) by linear interpolation between the oldest and second oldest coolant temperatures (which are stored in the ring memory of the size N). If T oldest( k) denotes the oldest coolant temperature (which is currently stored in the annular store of the size N) and Tsecondoldest(k) denotes the second oldest coolant temperature (which is currently stored in the annular store of the size N), the coolant temperature at the coolant outlet of the coolant line T pipe,out( k) is calculated according to equation (1):• In each time step, in which the integrated coolant volume flow is greater than the partial volume V T, the following steps are carried out:The storage element of the ring store of size N, which has stored the oldest coolant temperature, is overwritten with the coolant temperature at the coolant inlet of the coolant line.the partial volume V T is once subtracted from the integrated coolant volume flow (i.e. V integral( k+1)=V integral( k) -1·V T)By means of the above calculations, the dead time of the coolant temperature, which is dependent on the coolant mass flow and which prevails between the coolant temperature at the inlet and the coolant temperature at the outlet of a coolant line, can thus be modeled / calculated. The model that performs the above-described computations (i.e., the method) is referred to herein as "refrigerant line model". As a "by-product" of the "model of the coolant line", the instantaneous distribution of the coolant temperature in a coolant line is thus approximately known on the basis of the coolant temperatures stored in the annular store and can thus be used for the method presented in this invention message.Depending on the requirement for the accuracy of the calculation, it can also be taken into account in the "model of the coolant line" that a heat exchange takes place via the tube wall of the coolant line.It applies here that if the coolant volume flow is so large that in the current time step the integrated coolant volume flow, i.e. the volume covered by the coolant in the coolant line, exceeds an integer multiple n integer greater than one of the sub-volume V T i.e. V integral( k) > n integer · V T wherein n integer >1 is an integer, thus, the integer multiple n integer of the subvolume V T is subtracted from V integral( k) (i.e. V integral( k+1) = V integral( k) - n integer · V T).Since the instantaneous distribution of the coolant temperature in a coolant line j, i.e. that present in the time step k, can be calculated approximately via the "model of the coolant line" and is therefore known, and furthermore the coolant density as a function of the coolant temperature ρ Coolt( T), the specific heat capacity as a function of the coolant temperature c pCoolt( T) and, of course, the partial volumes V T,j used in the "model of the coolant line" are known, the temperature-dependent heat capacity of the coolant can be calculated for each partial volume V T,j.If the requirement for accuracy does not require that the temperature dependence of the coolant density and the specific heat capacity be taken into account in the calculation of the heat capacity of the partial volume V T,j the following equation (2) can be replaced by equation (3).The heat capacity of the piping including the partial volume V T,j may be added to either the equation (2) or the equation (3), or a separate model is prepared for the heat exchange between the refrigerant and the piping.The heat capacity of the fuel cell stack is determinable by equation (4).In equation (4), m Stck denotes the effective mass of the fuel cell stack or its thermodynamically effective mass, c pStck denotes the specific heat capacity of the effective mass of the fuel cell stack, m CooltStck denotes the coolant mass in the fuel cell stack, and c pCooltStck denotes the specific heat capacity of the coolant in the fuel cell stack.It can furthermore be provided that, when calculating the ML of the at least one fuel cell stack, a current heat flow through which a radiator comprised by the cooling circuit discharges to ambient air or a maximum possible heat flow through which the radiator could potentially discharge to ambient air if a maximum possible air mass flow and / or a maximum possible coolant flow flowed through the radiator and / or the radiator inlet air temperature were lowered as much as possible by means of water injection is also taken into account.The heat capacity of a radiator may be modeled by equation (5).In equation (5), m Radr denotes the effective mass of the radiator, i.e., its thermodynamic effective mass, c pRadr denotes the specific heat capacity of the effective mass of the radiator, m CooltRadr denotes the coolant mass in the radiator, and C pCooltRadr denotes the specific heat capacity of the coolant in the radiator.It may further be provided that when calculating the ML of the at least one fuel cell stack, a mathematical dynamic thermal model of the at least one fuel cell stack is further used that includes a correction term that corrects a requested heat flow error of the at least one fuel cell stack in the dynamic thermal model.It may further be provided that when calculating the ML of the at least one fuel cell stack, a mathematical dynamic thermal model of a radiator of the cooling circuit is further used, comprising a correction term that corrects a requested heat flow error of the radiator in the dynamic thermal model.For the coolant lines and components (i.e. fuel cell stack, radiator) belonging to the cooling circuit i, the following dynamic thermal model, referred to hereafter as the "overall dynamic thermal model of the cooling circuit", may be created.In equation (6), C i,j,t corresponds to the variable C j,t from equation (2) or (3), wherein only the index i which denotes the cooling circuit under consideration has been added, C ṫ i,j,t denotes the first time derivative of the temperature T i,j,t, wherein only the index i which denotes the cooling circuit under consideration has been added to T j,t C pStck,i corresponds to C pStck from equation (4), wherein only the index i which denotes the cooling circuit under consideration in which this fuel cell stack is located has been added, ṫ Stck,i denotes the first time derivative of the fuel cell stacks temperature Ṫ Stck,i of this fuel cell stack, C pRadr,i corresponds to C pRadr from equation (5), wherein only the index i which denotes the cooling circuit under consideration in which this radiator is located has been added, Ṫ Radr,i denotes the first time derivative of the radiator temperature Ṫ Radr,i of this radiator, Q̇ Radr2Air,i denotes the heat flow which the radiator of this cooling circuit i discharges to the ambient air, Q̇ Loss,i denotes the thermal power loss of the fuel cell stack of this cooling circuit i, Q 12 ErrorStck,req,i denotes the requested heat flow error of the dynamic thermal model of the fuel cell stack, which may also be referred to as a requested compensation term d req( k), and Q 12 ErrorRadr,req,i denotes the requested heat flow error of the dynamic thermal model of the radiator, which may also be referred to as a requested compensation term d req( k).Equations (7) and (8) allow the so-called "weighted temperature change rate of the cooling circuit" to be defined by weighting the time derivatives of the individual temperatures, i.e. the individual temperature change rates Ṫ i,j,t, Ṫ Stck,i and Ṫ Radr,i with their associated heat capacities, i.e. with C i,j,t, C pStck,i and C pRadr,i.The first time derivative of a temperature can, if necessary, be calculated, for example, by numerical differentiation of the temperature or by filtering the temperature by means of DT1 filters.If certain coolant lines (or any additional components) are no longer flowed through by the coolant, or if they are no longer flowed through by the coolant (for example due to a certain position of a valve, e.g.: the bypass valve is set such that it no longer allows a coolant mass flow through the bypass path), their associated heat capacities (in the case of the coolant line j of the cooling circuit i, these would be the C i,j,t) set equal to zero in order to take into account that these coolant lines (or any additional components) can therefore no longer absorb heat.If equation (7) is used in equation (6) and the resulting equation is transformed into Q Loss,i equation (9) resultsEquation (10) can be used to calculate the stack current I Stck,i of the fuel cell stack in the cooling circuit i, if necessary.In equation (10), U Stck,i denotes the output voltage of the fuel cell stack in the cooling circuit i, and U OC,i denotes the open circuit voltage of the fuel cell stack in the cooling circuit i. The above-mentioned power split in a multi-box fuel cell system can thus be carried out either on the basis of Q Loss,i or on the basis of I Stck,i.There are now several possibilities as to how one can determine the predictive currently maximum permissible power loss Qshift LossMax,i or the predictive currently maximum permissible stack current I StckMax,i by presetting it from equation (9).The variable is referred to below as "maximum permissible temperature change rate of the cooling circuit".Furthermore, there are several possibilities which can be used for Q Radr2Air,i in equation (9) or (11). These possibilities are presented below.The heat flow which the radiator of this cooling circuit i discharges to the ambient air can be modeled by the following equation (12):In equation (12), K Radr,i denotes the heat transfer coefficient of the radiator of the cooling circuit i as a function of the air mass flow ≅ Air,Radr,i and the coolant mass flow ≅ Coolt,Radr,i which flows through this radiator, T Env denotes the ambient temperature, and T x denotes a temperature for which there are several possibilities for selecting them. For example, the following is selected for T x• T x( k)=T i( k)• T x( k)=T d,i( k)• T x( k)=T CooltRadrOut,i( k), where T CooltRadrOut,i( k) denotes the current radiator coolant outlet temperature of the radiator in the cooling circuit i• T x( k)=T CooltRadrOut,max,i( k), where T CooltRadrOut,max,i( k) denotes the (currently) maximum permissible radiator coolant outlet temperature of the radiator in the cooling circuit i• T x( k)=T CooltStckIn,max,i( k), wherein T CooltStckIn,max,i( k) is the (currently) maximum permissible coolant inlet temperature into the fuel cell stack of the cooling circuit i• etc.There are also several possibilities for selecting Coolt,Radr,i in equation (12):• ṁ Coolt,Radr,i( k)= ṁ CooltAct,Radr,i( k), where m CooltAct,Radr,i( k) denotes the current coolant mass flow through the radiator of the cooling circuit i• ≅ Coolt,Radr,i( k)= ≅ CooltMax,Radr,i( k), where ≅ CooltMax,Radr,i( k) denotes the (currently) maximum possible coolant mass flow through the radiator of the cooling circuit i• etc.There are also several possibilities for selecting Air,Radr,i in equation (12):• ṁ Air,Radr,i( k)= ṁ AirAct,Radr,i( k), where ṁ AirAct,Radr,i( k) denotes the current air mass flow through the radiator of the cooling circuit i• ≅ Air,Radr,i( k)= ≅ AirMax,Radr,i( k), where ≅ Airmax,Radr,i( k) denotes the (currently) maximum possible air mass flow (i.e. the radiator fans rotate as quickly as possible) through the radiator of the cooling circuit i• etc.Another possibility is to use a calculated requested heat flow error of the dynamic thermal model of the fuel cell stack Qlm ErrorStck,req,i, which may also be referred to as requested compensation term d req( k) and / or a requested heat flow error of the dynamic thermal model of the radiator Qlm ErrorRadr,req,i, which may also be referred to as requested compensation term d req( k), in equation (9) or equation (11), or to choose Qlm ErrorStck,req,i= 0 and / or Qlm ErrorRadr,req,i= 0 respectively. This depends on whether Q is ErrorStck,req,i or Q is Q. Qshift ErrorRadr,req,i and which of the options for the specification of Qis selected.A so-called requested compensation term or correction term can be determined, for example, by means of a model-based control method, in particular an internal model controller (IMC). In this case, it is possible, for example, to determine by measuring or observing a controlled variable y(k) and time derivatives ẏ(k), ÿ(k),..., y (n)( k) of the controlled variable y(k) up to a system order n of a route model Σ m( ·) or an augmented route model Σ m,aug( ·) of the controlled route Σ p( ·), and to determine by, for example. Measuring or modelling and / or estimating an actual manipulated variable u act( k) of an actuator Σ a( ·) of the controlled system Σ p( ·) can be carried out.Accordingly, exactly where the uncertainties / inaccuracies of the route model Σ m( ·) and / or the unknown interference variables z u( k) are the greatest, the controller intervention can be provided by a requested compensation term / correction term d req( k), so that the controller attacks and compensates these uncertainties / inaccuracies of the route model Σ m( ·) and / or the unknown interference variables z u( k). In this way, the achieved (implicit / intrinsic) operating point-dependent linearization can match at the operating point of the nonlinear controlled system and at the operating point of the nonlinear system model, which leads to a considerable increase in robustness in a corresponding control method.The augmented (optionally dynamic nonlinear) route model Σ m,aug( ·) can be obtained by augmentation of the (optionally dynamic nonlinear) route model Σ m( ·) by introducing an additional deviation term or error term d(k), for example in the form of an additive term, a multiplicative term, etc., into one of the equations of the route model Σ m( ·).If an actuator Σ a( ·) or an actuator can deliver information about its actual manipulated variable, then this information can be taken into account in an advantageous manner in the model-based control concept. Further, an intrinsic additional model Σ a,m( ·) modeling the dynamic response of the actuator Σ a( ·) may be used to determine an actual manipulated variable u act( k).It can furthermore be provided that when calculating the ML of the at least one fuel cell stack, a calculated maximum permissible temperature change rate of the cooling circuit is taken into account, wherein the maximum permissible temperature change rate is calculated as a function of a temperature weighted by means of respective heat capacities of the predefined components of the cooling circuit.The "maximum allowable temperature change rate of the refrigerant circuit" is set as a function f i( ·) of the temperature T i weighted by the heat capacities for the refrigerant circuit i. This means that equation (13) holds:In this case, the temperature T i weighted by means of the heat capacities can be determined, for example, by means of equation (14).The function f i( ·) can be realized, for example, as a parameterizable characteristic curve and, of course, can also be selected identically for all cooling circuits i (for i=1,2,... ) (i.e., f(·)=f 1( ·)=f 2( ·)=... ).Alternatively, in equation (13), instead of T i it is also possible to use a different temperature, for example the fuel cell stack coolant outlet temperature or the radiator coolant outlet temperature.It can furthermore be provided that when calculating the ML of the at least one fuel cell stack, a calculated maximum permissible temperature change rate of the cooling circuit is taken into account, wherein the maximum permissible temperature change rate is calculated as a function of a temperature of the at least one fuel cell stack, a temperature of at least one coolant line and a temperature of a radiator of the cooling circuit.The "maximum allowable temperature change rate of the cooling cycle" can be calculated according to Equation (15).The relationships according to equations (16), (17) and (18) apply here.In equation (16), g Pipe,i,j,t( ·) is a function which is realized, for example, as a parameterizable characteristic curve, and T i,j,t is the temperature which supplies the "model of the coolant line" which models the coolant line j of the cooling circuit i, for the corresponding partial volume (index t).In equation (17), g Stck,i( ·) is a function which is realized, for example, as a parameterizable characteristic curve, and T St,k,i is the temperature of the fuel cell stack of the cooling circuit i, which is possibly set equal to the coolant temperature at the outlet of the fuel cell stack.In equation (18), g Radr,i( ·) is a function which is realized, for example, as a parameterizable characteristic curve, and Ṫ Radr,i is the temperature of the radiator of the cooling circuit i, which is possibly set equal to the coolant temperature at the outlet of the radiator.It can furthermore be provided that when calculating the ML of the at least one fuel cell stack, a calculated maximum permissible temperature change rate of the cooling circuit and a calculated maximum permissible temperature of the cooling circuit are taken into account, wherein the maximum permissible temperature change rate of the cooling circuit and the maximum permissible temperature of the cooling circuit are determined via a trajectory generator.For example, a flat output T i of the "dynamic thermal overall model of the cooling circuit" can be used for what is known as flatness-based trajectory planning.Since equation (9) or (11) is a first-order model, a trajectory generator Σ des( ·), for example a PT1 filter, can be used to preset T i and its first time derivative T i.Generally speaking, where n denotes the model order, the trajectory generator Σ des( ·) must specify the temperature T i and its time derivatives up to the nth order (i.e. ).In the following, the variables calculated by the trajectory generator ∑ des( ·), for example a PT1 filter, denote, i.e., signals. In other words, equation (9) or equation (11) is used.In the case where a PT1 filter is used as the trajectory generator Σ des( ·) to calculate the desired quantities, the equations of the trajectory generator Σ des( ·) are as follows:In Equation (20), the assist quantity Q 1 is calculated based on the sampling time ΔT and the filter time constant of the PT1 filter T PT1( T PT1 is the tuning parameter of the trajectory generator ∑ des( ·)). This auxiliary variable Q 1 is then used in the equation of the time-discrete PT1 filter ( 20).Equation (21) gives the continuous-time formulation of the PT1 filter.In equations (20) and (21), k denotes the current time step, u denotes the input to the PT1 filter, y denotes the output of the PT1 filter, and y denotes the first time derivative of the output of the PT1 filter.In equations (20) to (21), u(k) corresponds to the setpoint temperature T set,i( k) for the temperature T i( k), y(k) corresponds to the desired temperature T d,i( k) and ẏ(k) corresponds to the desired first time derivativeThe quantities are thus calculated via equations (19) to (21) based on the set point temperature T set,i( k). If one employs in equation (9) or (11), the predictive currently maximally permissible thermal power loss (from the perspective of the thermal system) of the fuel cell stack of the cooling circuit i under consideration can be calculated according to equation (22):Here, for Q̈ Radr2Air,i( k) in (Equation 22), Equation (23) can be used.This means that T d,i( k) is selected for T x( k) in equation (12).It may further be provided that an estimated heat flow error of the entire cooling circuit is taken into account in calculating the ML of the at least one fuel cell stack.The dynamic non-linear route model ∑ m( ·), i.e. the "overall dynamic thermal model of the cooling circuit" according to equation (6), can be augmented to the so-called "augmented overall dynamic thermal model of the cooling circuit" ∑ m,aug( ·) by introducing an additional deviation term / error term d(k), such as an additive term, a multiplicative term, etc., into one of its equations.For example, this augmentation can be performed according to equation (24).The term Q̈ErrorCircuit,i referred to below as estimated heat flow error of the overall model of the cooling circuit i, thus corresponds to the additional deviation term / error term d(k). This additional deviation term / error term d(k) is estimated and is therefore referred to as estimated deviation term d(k). In this case, this estimated deviation term or error term d(k) is filtered by the filter ∑ IMC( ·). The output of the filter Σ IMC( ·) is then the so-called requested compensation term or correction term d req( k) (i.e., d req( k) = ∑ IMC( d(k))). In the present invention message, the requested compensation term or correction term d req( k) corresponds to the requested heat flow error of the overall model of the cooling circuit QErrorCircuit,req,i The currently maximally permissible thermal power loss of the fuel cell stack (of the cooling circuit i under consideration) that is predictive from the perspective of the thermal system is then calculated according to equation (25):As already mentioned above, Q̈ ErrorStck,req,i( k)=0 and Q̈ ErrorRadr,req,i( k)=0 can also be chosen in equation (25).According to a second aspect, the present invention relates to a computer program product, including instructions which, when the computer program product is executed by a computer, cause the computer to carry out a possible embodiment of the present method.According to a third aspect, the present invention relates to a fuel cell system, the fuel cell system including a computing unit that is configured to execute a possible configuration of the present method.It can be provided that the fuel cell system comprises a plurality of fuel cell stacks which can be temperature-controlled by a plurality of partially coupled cooling circuits, and the computing unit is configured to determine an ML for each fuel cell stack by dividing, in particular dynamically dividing, the thermal capacities of the predefined components into the respective cooling circuits.The heat capacities of the predefined components can be divided among the respective cooling circuits, for example, as a function of a mass flow through the respective components, in particular a mass flow through the respective components over time or in a current time range.Further advantages, features and details of the invention will become apparent from the following description, in which exemplary embodiments of the invention are described in detail with reference to the drawings. The features mentioned in the claims and in the description can be essential to the invention individually or in any combination.The following are shown: FIG. 1 shows a possible embodiment of the presented method, FIG. 2 shows a possible embodiment of the fuel cell system presented, FIG. 3 shows a possible form of functions f i( T i) which is used in equation (13) according to a possible embodiment of the presented method, FIG. 4 shows a possible form of functions g Pipe,i,j,t( T i,j,t), g Stck,i( T Stck,i) and g Radr,i( T Radr,i) which are used in equations (16), (17) and (18) according to a possible embodiment of the presented method.FIG. 1 illustrates a method 100 for operating a fuel cell system.The method 100 comprises a calculation step 101 in which a predictive maximum permissible electrical power output (ML) for at least one fuel cell stack of the fuel cell system is calculated, and a setting step 103 in which an electrical power output of the at least one fuel cell stack is set taking into account the calculated ML.In this case, the ML of the at least one fuel cell stack is calculated as a function of heat capacities of predefined components of a cooling circuit for cooling the at least one fuel cell stack and of a temperature currently present in the predefined components and / or of at least one predefined temperature change rate and / or of at least one predefined temperature, for example by means of a trajectory generator.FIG. 2 illustrates a fuel cell system 200. The fuel cell system 200 includes a first fuel cell stack 201 and a second fuel cell stack 203, and a computation unit 205. The first fuel cell stack 201 is arranged in a first cooling circuit 207 having a first radiator 209.The second fuel cell stack 203 is arranged in a second cooling circuit 211 with a second radiator 213.In the present case, the first cooling circuit 207 and the second cooling circuit 211 are thermally decoupled by way of example, wherein naturally a thermal coupling of the first cooling circuit 207 to the second cooling circuit 211 in regions can also be provided.In order to determine a predictive maximum permissible electrical power output (ML) for the first fuel cell stack 201, the arithmetic unit 205 calculates heat capacities of the first fuel cell stack 201, the first radiator 209, and lines of the first cooling circuit and coolant flowing in the lines of the first cooling circuit.Furthermore, the arithmetic unit 205 calculates and / or acquires (i.e. measures) a temperature and / or stored heat quantity currently present in the first fuel cell stack 201, in the first radiator 209 and in the lines of the first cooling circuit 207 and in the coolant flowing in the lines of the first cooling circuit 207. For this purpose, for example, a temperature of the first fuel cell stack 201, of the first radiator 209 and of the lines of the first cooling circuit 207 and of the coolant flowing in the lines of the first cooling circuit 207 can be measured by means of a number of temperature sensors and / or modeled by means of a mathematical model.In FIG. 3, a curve 301 according to an exemplary function for f i( T i), which is used in equation (13), is shown. To ensure that the reduction of the ML occurs smoothly with increasing temperature T i could be defined as having a curve similar to that shown in FIG. 3. In the case that the temperature T i is already very hot, f i( is T i) < 0 and thus the ML is calculated in such a way that this must lead to a decreasing temperature T i in the cooling circuit.In FIG. 4, exemplary functions for g Pipe,i,j,t( T i,j,t), g Stck,i( T Stck,i) and g Radr,i( T Radr,i), which are used in equations (16), (17) and (18), are shown.In order to ensure that the reduction of the ML takes place uniformly with increasing temperature T i,j,t, T Stck,i, or T Radr,i ẗ Max,i,j,t, ẗ SteckMax,i or T . In the examples of the present invention, the term "RadrMax,i is used to denote as ẗ Max,i,j,t= g Pipe,i,j,t( T i,j,t), ẗ StckMax,i= g Stck,i( T Stck,i), or ẗ RadrMax,i= g Radr,i( T Radr,i) having a curve similar to or according to curves 401, 403 and 405 shown in FIG. 4. In the case that the temperature T i,j,t is already very hot, g Pipe,i,j,t( is T i,j,t), < 0 and thus the ML is calculated in such a way that this must lead to a decreasing temperature.In the case that the temperature Ṫ Stck,i is already very hot, g is Stck,i( T Stck,i) < 0 and thus the ML is calculated in such a way that this must lead to a decreasing temperature.In the case that the temperature Ṫ Radr,i is already very hot, g is Radr,i( T Radr,i) < 0 and thus the ML is calculated in such a way that this must lead to a decreasing temperature.

Claims

Method (100) for operating a fuel cell system (200), wherein the method (100) comprises: - calculating (101) a predictive maximum permissible electrical power output (ML) for at least one fuel cell stack (201, 203) of the fuel cell system (200), - setting (103) an electrical power output of the at least one fuel cell stack (201, 203) taking into account the calculated ML, wherein the ML of the at least one fuel cell stack (201, 203) is calculated as a function of heat capacities of predefined components (201, 203, 209, 213) of a cooling circuit for cooling the at least one fuel cell stack (201, 203) and a temperature currently present in the predefined components (209, 213) and / or at least one predefined temperature change rate and / or at least one predefined temperature.The method (100) according to claim 1, characterized in that the fuel cell system (200) comprises a plurality of fuel cell stacks (201, 203), and an ML is calculated for each fuel cell stack (201, 203) of the plurality of fuel cell stacks (201, 203), and the electric power output of a specific fuel cell stack (201, 203) is adjusted in consideration of its ML as compared to the ML of the other fuel cell stacks.Method (100) according to Claim 1 or 2, characterized in that the predefined components of the cooling circuit (201, 203, 209, 213) are selected from the following list of components: fuel cell stack (201, 203), radiator (209, 213), coolant in respective coolant lines, coolant line.Method (100) according to one of the preceding claims, characterized in that the temperature currently present in the predetermined components (201, 203, 209, 213) and / or the stored quantity of heat is calculated and / or measured.Method (100) according to one of the preceding claims, characterized in that, when calculating the ML of the at least one fuel cell stack (201, 203), a current heat flow which a radiator (209, 213) comprised by the cooling circuit (207, 211) discharges to ambient air or a maximum possible heat flow which the radiator (209, 213) could potentially discharge to ambient air if a maximum possible air mass flow and / or a maximum possible coolant flow flowed through the radiator (209, 213) and / or the radiator inlet air temperature was lowered by means of water injection to a maximum possible extent is also taken into account.Method (100) according to any one of the preceding claims, characterized in that in calculating the ML of the at least one fuel cell stack (201, 203), a mathematical dynamic thermal model of the at least one fuel cell stack (201, 203) is further used, comprising a correction term that corrects a requested heat flow error of the at least one fuel cell stack (201, 203) in the dynamic thermal model.Method (100) according to any of the preceding claims, characterized in that in calculating the ML of the at least one fuel cell stack (201, 203), a mathematical dynamic thermal model of a radiator (209, 213) of the cooling circuit (207, 211) is further used, comprising a correction term that corrects a requested heat flow error of the radiator (209, 213) in the dynamic thermal model.Method (100) according to one of the preceding claims, characterized in that a calculated maximum permissible temperature change rate of the cooling circuit (207, 211) is taken into account in the calculation of the ML of the at least one fuel cell stack (201, 203), wherein the maximum permissible temperature change rate is calculated as a function of a temperature weighted by means of respective heat capacities of the predetermined components (201, 203, 209, 213) of the cooling circuit (207, 211).Method (100) according to one of Claims 1 to 7, characterized in that a calculated maximum permissible temperature change rate of the cooling circuit (207, 211) is taken into account in the calculation of the ML of the at least one fuel cell stack (201, 203), wherein the maximum permissible temperature change rate is calculated as a function of a temperature of the at least one fuel cell stack (201, 203) and / or a temperature of at least one coolant line and / or a temperature of a radiator (209, 213) of the cooling circuit (207, 211).Method (100) according to one of Claims 1 to 7, characterized in that, when calculating the ML of the at least one fuel cell stack (201, 203), a calculated maximum permissible temperature change rate of the cooling circuit (207, 211) and a calculated maximum permissible temperature of the cooling circuit (207, 211) are taken into account, wherein the maximum permissible temperature change rate of the cooling circuit (207, 211) and the maximum permissible temperature of the cooling circuit (207, 211) are determined via a trajectory generator.Method (100) according to claim 10, characterized in that an estimated heat flow error of the entire cooling circuit (207, 211) is taken into account in calculating the ML of the at least one fuel cell stack (201, 203).A computer program product comprising instructions which, when the computer program product is executed by a computer, cause the computer to perform the method (100) of any one of claims 1 to 11.A fuel cell system (200), wherein the fuel cell system (200) comprises a computing unit (205) configured to perform a method (100) according to any one of claims 1 to 11.Fuel cell system (200) according to claim 13, wherein the fuel cell system (200) comprises a plurality of fuel cell stacks (201, 203) that are temperature controllable by a plurality of partially coupled cooling circuits (207, 211), and the computing unit (205) is configured to determine an ML for each fuel cell stack (201, 203) by dividing, in particular dynamically dividing, the heat capacities of the predetermined components (201, 203, 209, 213) among the respective cooling circuits (207, 211).

Images