Method for estimating fuel utilization rate and oxygen-to-carbon ratio

Abstract

The invention relates to a method for estimating a fuel utilization rate (FUStk) and an oxygen-to-carbon ratio (ϕOC) of a fuel cell stack (12) in a fuel cell device (10). It is proposed that in at least one method step (14) the fuel utilization rate (FUStk) and an oxygen-to-carbon ratio (ϕOC) are estimated using a state-space model (16) of a fuel cell path (18) of the fuel cell device (10), wherein the state-space model (16) is fitted using a Kalman filter algorithm (20).

Description

Prior ArtA method for estimating a fuel utilization rate and an oxygen-to-carbon ratio of a fuel cell stack in a fuel cell device has already been proposed.Disclosure of the InventionThe invention is based on a method for estimating a fuel utilization rate and an oxygen-to-carbon ratio of a fuel cell stack in a fuel cell device.It is proposed that in at least one method step, the fuel utilization factor and an oxygen-to-carbon ratio is estimated by means of a state space model of a fuel cell path of the fuel cell device, wherein the state space model is adapted by means of a Kalman filter algorithm.The configuration according to the invention enables continuous estimation of all relevant mole fractures and thus the calculation of the important system variables, namely the fuel utilization factor FU Stk and the oxygen-to-carbon ratio φ OC, in a fuel cell device with anode exhaust gas recirculation with the aid of a Kalman filter algorithm. The state space model of the fuel path and the Kalman filter algorithm enable short computing times with high accuracy and thus use on a computing unit and / or a control device with low computing power. By means of a detailed and additionally validated dynamic system model, the Kalman filter algorithm can be executed in such a way that the mole fractures and thus the gas composition can be estimated without the use of further gas measurement sensors. This soft sensor enables the control of the two system sizes with comparatively little financial expenditure. Moreover, the adaptive execution enables a correct calculation of the fuel utilization factor FU Stk and the oxygen-to-carbon ratio φ OC even in the case of fluctuating natural gas composition.A "fuel cell device" is to be understood to mean, in particular, at least a part, in particular a subassembly, of a fuel cell, preferably of a fuel cell system, in particular of a solid oxide fuel cell system. In particular, the fuel cell device can also comprise the entire fuel cell, in particular the entire fuel cell system. The fuel cell device is preferably designed at least as part of a high-temperature fuel cell, in particular as a high-temperature solid oxide fuel cell, or HT-SOFC for short, in particular as a high-temperature solid oxide fuel cell system. The at least one fuel cell device preferably comprises at least one fuel cell stack which is designed to react a fuel gas and oxygen to generate electrical energy. The at least one fuel cell device may have a plurality of fuel cell stacks, such as two, three, four or the like. Each fuel cell stack preferably comprises at least one fuel cell, preferably at least two fuel cells, which is / are provided in particular for electrochemical conversion of fuel, in particular fuel gas, for generating electrical energy. Preferably, all fuel cells, in particular of a fuel cell stack, are of identical shape, in particular of identical dimensions. Preferably, each fuel cell comprises at least one anode. Preferably, each fuel cell comprises at least one cathode. Preferably, each fuel cell comprises at least one electrolyte which is arranged between the at least one anode and the at least one cathode. Preferably, the at least one electrolyte is connected to the at least one anode and the at least one cathode. The fuel cell device preferably comprises a computing unit which is provided for controlling and / or regulating components of the fuel cell device. The fuel cell device preferably comprises an air flow unit which is designed for supplying air to the at least one fuel cell stack and for supplying fuel, in particular fuel gas, to the at least one fuel cell stack. The fact that an object is "formed" into a specific function is preferably intended to mean that the object fulfills and / or carries out this specific function in at least one application state and / or operating state. Preferably, the fuel cell device comprises a reformer unit. The fuel is preferably reformed in at least one process step, in particular in all process steps. Fuel is to be understood as meaning, in particular, the fuel gas. The fuel, in particular the combustion gas, can be referred to as anode gas. A fuel utilization level is to be understood as meaning a fuel utilization level.The Kalman filter algorithm comprises a stochastic method with the aid of which state variables of a dynamic system that are derived from a direct measurement can be estimated. The central element of the Kalman filter algorithm is, in particular, a dynamic route model, in particular the state space model, with the aid of which the output vector ŷis estimated and compared with the measurement vector y of the real system. The difference is used for correcting the predicted state quantities with the Kalman gain K. The accuracy of the reduced model is significantly improved with this algorithm. The Kalman filter algorithm requires no gas sensors in particular. Preferably, only a few temperature sensors are required. In addition, in particular the measurement of a cell voltage and a current intensity of the fuel cell stack is necessary.It is furthermore proposed that the state space model is formed by an, in particular linear, time-discrete, state model. The linear, discrete-time state space model of the fuel cell path is described in particular by the definition of its states and of its inputs and outputs. In principle, however, non-linear as well as continuous-time models would also be applicable. By forming the state model as a linear model, the Kalman filter algorithm can be used in particular advantageously. The state space model of the fuel path and the Kalman filter algorithm enable short computing times with high accuracy and thus use on a computing unit and / or a control device with low computing power. By configuring the state model as a linear, time-discrete state model, an advantageously simple and despite all accurate state model can be provided in particular. The underlying physical process is basically nonlinear. In order to be able to use the linear Kalman filter algorithm, the state model was linearized around the operating point. Instead of the linear Kalman filter algorithm, a nonlinear approach such as an extended Kalman filter algorithm or an unscented Kalman filter algorithm could be used to improve accuracy throughout the operating range of the plant.Furthermore, it is proposed that the state model be described via at least one equation, in particular at least two equations, which comprises a plurality of matrices which result from a physical model of a fuel path of the fuel cell stack, and at least two vectors, in particular state and / or input vectors. The state model is described in particular with equations (1) and (2):In the equations, F, G, H, C, and D are specifically matrices resulting from the physical model. The matrices are formed in particular by time-invariant system matrices. However, the matrices could also be designed as time-variant matrices. Some inputs would then be found as time variant parameters in the matrices. The state model further comprises, in particular, a state vector x, an input vector u and an output vector y. Preferably, the equations of the state space model in the context of the Kalman filter theory also contain the statistical variables:In particular, an advantageously detailed state model can thereby be provided.It is further proposed that at least one of the vectors, in particular the state vector x, comprises molar fractions y of the relevant components of the gas mixture in a reformer unit, in particular a pre-reformer, of the fuel cell device and in an anode of the fuel cell stack of the fuel cell device, and also a recirculation volume flow Vegr AgbBlwr. Accordingly, the following applies in particular:In particular, an advantageously detailed state model can thereby be provided.In addition to the volume flow of the recirculation blower, the gas composition is selected as system states on the background that the Nernst voltage has a direct functionality of the gas composition at the stack inlet, in particular of hydrogen and water vapor partial pressure at the stack inlet. Alternatively, the electron-mole current could be used as a state and thus the number of states could be significantly reduced if a functional relationship between Nernst voltage and electron-mole current and / or between cell voltage and electron-mole current can be detected. This functionality could be determined either by a validated system model or by an experimental study.It is further proposed that in at least one acquisition step, in particular for an input vector, a natural gas volume flow Vegr Ng, an arrangement outlet temperature T AnOut, a reformer outlet temperature T Refout, a cathode outlet temperature T caOut and a stack flow I are determined. The state model is understood here to mean the natural gas valve in particular as a delay-free actuator. The setpoint value of the natural gas volume flow Vegr Ng accordingly corresponds to the actual value in particular in each time step. Differentiated consideration and the measurement of the natural gas volume flow Vegr Ng are thus not necessary. The stack current I can in particular already be made available by the inverter. Preferably, for the input vector in the acquisition step, in particular, a setpoint recirculation volume flow and an equilibrium temperature at the reformer outlet T EquiRef are also acquired. The input vector resulting therefrom is preferably in particular:In the case of an adiabatic reformer unit, in particular an adiabatic pre-reformer, in particular T EquiRef ≈T RefOut could be assumed. Therefore, in particular, the equilibrium temperature at the reformer outlet T EquiRef could be set equal to the reformer outlet temperature T RefOut so that an inlet could be dispensed with. In this way, in particular an advantageously accurate input vector can be determined and provided. In this way, an advantageously detailed state model can be provided in turn.It is furthermore proposed that an average cell voltage is measured in at least one, in particular a further, detection step and a cell voltage of an output vector, in particular of the state model, is picked out in at least one comparison step, in particular following the detection step, and is compared with the average cell voltage. The average cell voltage can in particular already be made available by the inverter. The starting vector is preferably defined as follows:Preferably, the cell voltage U cell is extracted from the output vector of the state model and compared with the mean cell voltage measured in the acquisition step.It is furthermore proposed that in at least one calculation step, corrected state variables of the state model are calculated by means of the Kalman filter algorithm on the basis of the comparison between the cell voltage of the output vector and the detected mean cell voltage, said state variables in turn representing the basis for the corrected values for the fuel utilization factor FU Stk and the oxygen-to-carbon ratio φ OC. This approach allows inaccuracies resulting from the simplified modeling of the fuel path to be partially compensated by the comparison to the measured voltage. In addition, in a further variant of the present invention, the covariance matrix Q k is designed adaptively. By means of this adaptation, the filter should be able to recognize changes in the natural gas quality on the basis of the voltage change, to estimate the system variables accordingly and thus to provide a control difference which can be compensated by an adaptation of the natural gas and the recirculation volume flow.It is furthermore proposed that the state space model has at least one time-variant component which is provided for mapping temporal influences, such as, in particular, aging. The modeling of the mean cell voltage contains, in particular, time-variant components in order to be able to depict temporal influences such as aging.Furthermore, a fuel cell device is proposed having at least one arithmetic unit for carrying out a method according to the invention. The computing unit is preferably connected to the individual components of the fuel cell device, such as a recirculation blower unit, the reformer unit and / or the at least one fuel cell stack, in particular for controlling and / or regulating the components. The fuel cell device preferably comprises a sensor unit, which comprises in particular temperature sensors and / or air flow sensors. A system can be achieved in which the fuel cell stack and the computing unit are advantageously compatible with one another. The computing unit comprises in particular a processor and / or a processor unit, a memory unit and an operating, control and / or calculation program stored in the memory unit. A computing unit which can be advantageously connected to different fuel cell stacks can be achieved.It is furthermore proposed that the fuel cell device has at least one fuel cell stack, at least one reformer unit, in particular a pre-reformer, and an anode off-gas recirculation unit, wherein the fuel cell stack, the reformer unit and the anode off-gas recirculation unit form part of a fuel cell path. The anode off-gas recirculation unit preferably comprises a recirculation fan. The anode exhaust gas recirculation unit is provided in particular for at least partial recirculation of an anode exhaust gas. Preferably, the recirculated anode off-gas is provided in particular for being supplied to the reformer unit together with a fuel. The mixture of fuel and anode off-gas is preferably introduced into the reformer and converted to a hydrogen-rich fuel gas, which is electrochemically electrified in the fuel cell stack. The reformer is used in particular for reforming the fuel. Preferably, the fuel cell device further comprises a plurality of heat exchangers. The fuel cell device with the anode off-gas recirculation unit has, in particular, a complex fuel path.Furthermore, it is proposed that the fuel cell path is free of gas sensors. The Kalman filter does not require gas sensors. Only a few temperature sensors are needed. In addition, the measurement of the cell voltage and the current intensity is necessary.The method according to the invention and / or the fuel cell device according to the invention should / should not be limited to the application and embodiment described above. In particular, the method according to the invention and / or the fuel cell device according to the invention can / can have a number which differs from a number of individual elements, components and units and method steps mentioned herein in order to fulfil a mode of operation described herein. In addition, in the value ranges specified in this disclosure, values lying within the stated limits should also be considered as disclosed and usable as desired.DRAWINGFurther advantages are evident from the following description of the drawings. The drawing shows an embodiment of the invention. The drawings, specification and claims contain numerous features in combination. The skilled person will expediently also consider the features individually and summarize them to form meaningful further combinations.The following are shown: FIG. 1 shows a fuel cell device according to the invention, which has a computing unit according to the invention, in a schematic illustration, FIG. 2 shows the fuel cell device according to the invention in a schematic illustration, and FIG. 3 shows the method according to the invention in a schematic illustration.DESCRIPTION OF THE EMBODIMENTFIG. 1 shows a fuel cell device 10.The fuel cell device 10 comprises, for example, a fuel cell stack 12. The fuel cell stack 12 is designed to allow a fuel 40, in particular a fuel gas, and oxygen to react to generate electrical energy, in particular power. The fuel cell stack 12 comprises, for example, only one fuel cell 42 here. the fuel cell 42 is provided for electrochemical conversion of fuel 40, in particular fuel gas, for generating electrical power.The fuel cell 42 shown as an example includes an anode 24. the fuel cell 42 includes a cathode 44. the fuel cell 42 includes an electrolyte 46. the electrolyte 46 is disposed between the anode 24 and the cathode 44. The electrolyte 46 is connected to the anode 24 and the cathode 44.The fuel cell device 10 comprises an air flow unit 48, The air flow unit 48 is configured to supply air 50 to the fuel cell stack 12. For example, the airflow unit 48 includes a pump, a blower, a fan, valves, or the like for moving gases.The fuel cell device 10 comprises a reformer unit 22, The reformer unit 22 is designed for reforming the fuel 40, in particular the fuel gas. The reformer unit 22 is formed by a pre-reformer. The fuel cell device 10 comprises a sensor unit 52, which in particular comprises temperature sensors and / or air flow sensors, in particular for measuring temperatures and / or volume flows. The sensor unit 52 comprises a temperature sensor for detecting an anode outlet temperature T AnOut, a temperature sensor for detecting a reformer outlet temperature T RefOut and a temperature sensor for detecting a cathode outlet temperature T caOut. The sensor unit 52 can also be provided for detecting a natural gas volume flow Vegr Ng. A state space model 16 is understood to mean the natural gas valve in particular as a delay-free actuator. The setpoint value of the natural gas volume flow Vegr Ng accordingly corresponds to the actual value in particular in each time step. Differentiated consideration and the measurement of the natural gas volume flow Vegr Ng are thus not necessary. A stack current I can be provided in particular by the inverter 62.The fuel cell device 10 comprises a heat exchanger unit 54 for tempering air 50 which is supplied to the fuel cell stack 12 and for tempering the fuel 40 which is supplied to the fuel cell stack 12.The fuel cell device 10 comprises an afterburner unit 56 for burning fuel gas residues. The fuel cell device 10 includes an anode off-gas recirculation unit 36. the anode off-gas recirculation unit 36 includes a recirculation line 58 for recirculating fuel gas residues into a fuel gas line. The anode off-gas recirculation unit 36 has a recirculation blower 60. The anode off-gas recirculation unit 36 is provided for a partial recirculation of an anode off-gas. The recirculated anode off-gas is provided to be supplied to the reformer unit 22 together with a fuel 40. The mixture of fuel 40 and anode off-gas is preferably introduced into the reformer unit 22 and converted to a hydrogen-rich fuel gas, which is electrochemically electrified in the fuel cell stack 12.The fuel cell stack 12, the reformer unit 22 and the anode off-gas recirculation unit 36 form part of a fuel cell path 18. the fuel cell path 18 further comprises the heat exchanger unit 54. the fuel cell path 18 is free of gas sensors.Furthermore, the fuel cell device 10 comprises an inverter 62 electrically coupled to the fuel cell stack 12.The fuel cell device 10 comprises a computing unit 32. The computing unit 32 is provided for controlling and / or regulating components of the fuel cell device 10. The arithmetic unit 32 is provided for carrying out a method 34 to be described below.The computing unit 32 is connected to the individual components of the fuel cell device 10, such as the air flow unit 48, the reformer unit 22, the sensor unit 52, the inverter 62 and / or the fuel cell stack 12, in particular for controlling and / or regulating the components.The computing unit 32 comprises in particular a processor and / or a processor unit, a memory unit and an operating, control and / or calculation program stored in the memory unit.FIG. 2 schematically shows the fuel cell device 10, a state space model 16 and a Kalman filter algorithm 20 as a diagram of the various vectors and their alignment.FIG. 3 schematically shows a method 34 for estimating a fuel utilization factor FU stk and an oxygen-to-carbon ratio φ OC of the fuel cell stack 12 in the fuel cell device 10.The method 34 is designed as a continuous method in which the method steps of the method 34 run repeatedly and / or in parallel. FIG. 3 shows only one of many possible sequences of individual method steps or method sections of method 34 as an example.Method 34 is for continuous estimation of all relevant mole fractures and thus the calculation of the important system variables, namely the fuel utilization factor FU Stk and the oxygen-to-carbon ratio φ OC, in fuel cell device 10 with anode exhaust gas recirculation unit 36 with the aid of Kalman filter algorithm 20. Method 34 is carried out during operation of fuel cell device 10, in particular for controlling or regulating operation of fuel cell device 10.Method 34 includes at least one method step 14, in which fuel utilization factor FU Stk and an oxygen-to-carbon ratio φ OC are estimated by means of a state space model 16 of a fuel cell path 18 of fuel cell device 10. The state space model 16 is formed by a linear, time-discrete state space model 16. The linear, discrete-time state space model 16 of the fuel cell path 18 is described by the definition of its states and of its inputs and outputs. The state space model 16 is described using two equations. The equations comprise a plurality of matrices F, G, H, C, D, which result from a physical model of a fuel cell path 18 of the fuel cell stack 12, and at least two, in particular three, vectors x, u, y. The state space model 16 is described using equations (1) and (2):In the equations, F, G, H, C, and D are specifically matrices resulting from the physical model of the fuel cell path 18. The state space model further comprises a state vector x, an input vector u and an output vector y. The state vector x comprises the molar fractions y of the relevant components of the gas mixture in the reformer unit 22 of the fuel cell device 10 and in the anode 24 of the fuel cell stack 12 of the fuel cell device 10 and a recirculation volume flow Vegr AgbBlwr. Accordingly, the situation applies to the state vector x:Before method step 14, a detection step 26 takes place. In detection step 26, for input vector u, natural gas volume flow Vegr Ng, arrangement outlet temperature T AnOut, reformer outlet temperature T RefOut, cathode outlet temperature T CaOut and stack flow I are determined. The state space model 16 is understood to mean a natural gas valve as a delay-free actuator. The setpoint value of the natural gas volume flow Vegr Ng accordingly corresponds to the actual value in particular in each time step. Differentiated consideration and the measurement of the natural gas volume flow Vegr Ng are thus not necessary. The stack current I can already be made available by the inverter 62. The anode outlet temperature T AnOut, the reformer outlet temperature T Refout and the cathode outlet temperature T CaOut are detected and provided by the sensor unit 52. Furthermore, for the input vector u in the detection step 26, a setpoint value of the recirculation volume flow and an equilibrium temperature at the reformer outlet T EquiRef are detected and provided. The following applies accordingly to the input vector u:In method step 14, an estimated output vector ŷ is furthermore calculated by means of the state space model 16. The output vector is defined as follows:A further detection step 28 is then carried out. In the further detection step 28, an average cell voltage U cell is measured. Furthermore, in a comparison step 29 following in particular the acquisition step 28, a cell voltage U cell of the output vector ŷ, which is estimated in particular by means of the state space model 16, is picked out and compared with the measured mean cell voltage U cell. The average cell voltage U cell is provided by the inverter 62. In the comparison step 29, the cell voltage U cell is extracted from the output vector ŷ of the state space model 16 and compared with the mean cell voltage U cell measured in the acquisition step 28.The comparison step 29 is followed by a calculation step 30, and in the calculation step 30, corrected state variables of the state space model 16 are calculated by means of the Kalman filter algorithm 20 on the basis of the comparison between the cell voltage U cell the output vector ŷ of the state space model 16 and the acquired, real mean cell voltage U cell which in turn represent the basis for the corrected values for the fuel utilization factor FU Stk and the oxygen-to-carbon ratio φ OC. In particular, after the calculation step 30, the fuel utilization factor FU Stk and the oxygen-to-carbon ratio φ OC are ascertained, in particular estimated, again in the method step 14 by means of the corrected state space model 16. The state space model 16 is adjusted by means of the Kalman filter algorithm 20, in particular continuously. The equations of the state space model 16 additionally contain the statistical variables in the context of the Kalman filter theory:

Claims

Method for estimating a fuel utilization factor (FU Stk) and an oxygen-to-carbon ratio (φ OC) of a fuel cell stack (12) in a fuel cell device (10), characterized in that, in at least one method step (14), the fuel utilization factor (FU Stk) and an oxygen-to-carbon ratio (φ OC) are estimated by means of a state space model (16) of a fuel cell path (18) of the fuel cell device (10), wherein the state space model (16) is adjusted by means of a Kalman filter algorithm (20).Method according to Claim 1, characterized in that the state space model (16) is formed by an, in particular linear, time-discrete, state model.Method according to Claim 1 or 2, characterized in that the state space model (16) is described via at least one equation, in particular at least two equations, which comprises a plurality of matrices (F, G, H, C, D) which result from a physical model of a fuel cell path (18) of the fuel cell stack (12), and at least two vectors (x, u, y), in particular state and / or input vectors.Method according to Claim 3, characterized in that at least one of the vectors (x), in particular a state vector, comprises the molar fractions (y) of the relevant components of the gas mixture in a reformer unit (22) of the fuel cell device (10) and in an anode (24) of the fuel cell stack (12) of the fuel cell device (10) and also a recirculation volume flow (Vegr AgbBlwr).Method according to one of the preceding claims, characterized in that in at least one acquisition step (26), in particular for an input vector (u), a natural gas volume flow (Vshift Ng), an anode outlet temperature (T AnOut), a reformer outlet temperature (T RefOut), a cathode outlet temperature (T CaOut) and a stack flow (I) are determined.Method according to one of the preceding claims, characterized in that in at least one detection step (28), an average cell voltage is measured and in at least one comparison step (29), in particular following the detection step (28), a cell voltage (U cell) of an output vector (y), in particular of the state space model (16), is picked up and compared with the average cell voltage.Method according to Claim 6, characterized in that, in at least one calculation step (30), corrected state variables of the state space model (16) are calculated by means of the Kalman filter algorithm (20) on the basis of the comparison between the cell voltage (U cell) of the output vector (ŷ) of the state space model (16) and the detected mean cell voltage, said state variables in turn representing the basis for the corrected values for the degree of fuel utilization (FU Stk) and the oxygen-to-carbon ratio (φ OC).Method according to one of the preceding claims, characterized in that the state space model (16) has at least one time-variant component which is provided for mapping temporal influences, such as in particular aging.Fuel cell device having at least one arithmetic unit (32) for carrying out a method (34) according to one of Claims 1 to 8.Fuel cell device according to Claim 9, characterized byat least one fuel cell stack (12), at least one reformer unit (22), in particular a prereformer, and an anode off-gas recirculation unit (36), wherein the fuel cell stack (12), the reformer unit (22) and the anode off-gas recirculation unit (36) form part of a fuel cell path (18).Fuel cell device according to Claim 9, characterized in that the fuel cell path (18) is free of gas sensors.

Images