High-temperature solid oxide electrolytic hydrogen production system regulation and control optimization method considering oxygen electrode degradation

Abstract

The invention relates to a regulation and control optimization method for a high-temperature solid oxide (SOEC) electrolytic hydrogen production system considering oxygen electrode degradation. An optimization module and a neural network predictive control (NNPC) module are included. The optimization module calculates and generates an optimal operation curve of the high-temperature electrolytic hydrogen production system in a preset operation range, namely a minimum oxygen partial pressure and maximum hydrogen production efficiency curve; the NNPC control module obtains a value of a current input variable according to the optimal operation curve, obtains a predicted value of a system output variable, and reduces an error with an expected value through rolling optimization to determine a control sequence; and the high-temperature electrolytic hydrogen production system module describing the oxygen partial pressure characteristics receives the control sequence as a system operation condition, feeds back key parameters in the system to the NNPC control module, and continuously updates the parameters of the model and the controller. According to the method, the optimal operation curve serves as feedforward control, SOEC electrolysis voltage, inlet and outlet temperature difference and system outlet stream variables in the system serve as feedback control, and therefore the system can achieve rapid and safe thermoelectric response when dealing with external disturbance, and the working conditions that the oxygen electrode degradation risk is lowest and the system efficiency is highest are kept all the time.

Description

Technical Field

[0001] The present invention relates to the field of control optimization of high-temperature solid oxide electrolysis hydrogen production, and in particular to a control optimization method of a high-temperature solid oxide electrolysis hydrogen production system taking oxygen electrode degradation into consideration. Background Art

[0002] The high-temperature solid oxide electrolysis hydrogen production system operates at high temperature for a long time, and the SOEC oxygen electrode is prone to degradation, especially when responding to external disturbances. Simply reducing the probability of oxygen electrode degradation will increase the system's unnecessary BOP power consumption, resulting in a waste of input power in the hydrogen production system. Therefore, it is necessary to add relevant indicators to describe the oxygen electrode degradation, and to weigh the oxygen electrode degradation and system hydrogen production efficiency in long-term operation. In addition, in order to cope with external disturbances such as changes in operating variables such as electrolysis current, hydrogen and air feed, it is necessary to use a fast, low overshoot control method to perform thermoelectric coordinated regulation of the high-temperature solid oxide electrolysis hydrogen production system.

[0003] Therefore, the present invention describes the degradation of the SOEC oxygen electrode by the oxygen partial pressure at the oxygen electrode-electrolyte interface, takes the optimal operating curve under the lowest oxygen partial pressure and the highest hydrogen production efficiency as the feedforward signal, takes the SOEC electrolysis voltage, the inlet and outlet temperature difference and the system outlet stream variable as the feedback signal, and utilizes the neural network predictive control algorithm to realize fast and safe thermoelectric coordinated control of the system. Summary of the invention

[0004] In view of the fact that the existing high-temperature solid oxide electrolysis hydrogen production system control optimization method is difficult to solve the problems of SOEC oxygen electrode degradation and system inefficiency in long-term operation, the present invention provides a high-temperature solid oxide electrolysis hydrogen production system control optimization method considering oxygen electrode degradation. First, the optimizer calculates the optimal operating curve of the high-temperature electrolysis hydrogen production system under the current electrolysis current, and then the error between the predicted value and the expected value is optimized by the NNPC controller to obtain the optimal control sequence as the operating condition of the hydrogen production system, and finally the key output variables in the system are fed back to the NNPC controller for model correction and update.

[0005] The present invention provides a control and optimization method for a high-temperature solid oxide electrolysis hydrogen production system taking into account oxygen electrode degradation, comprising:

[0006] optimizers and neural network predictive controllers;

[0007] Among them, the optimizer uses a multi-objective optimization algorithm to calculate and generate the operating curve of the optimal oxygen partial pressure at the oxygen electrode-electrolyte interface and system efficiency within the preset operating range of the high-temperature electrolytic hydrogen production system. The oxygen partial pressure will affect the degree of oxygen electrode stratification; the neural network predictive controller uses a neural network predictive control algorithm to predict and optimize the error between the predicted value and the expected value of the SOEC stack voltage, temperature and system outlet stream variables, and determine the control sequence. The high-temperature electrolytic hydrogen production system receives the control sequence and feeds back the key output variables of the system to the neural network predictive controller to correct the deviation of the model prediction results.

[0008] Optionally, the optimizer calculates and generates the optimal operating curve, i.e., the curve with the lowest oxygen partial pressure and the highest hydrogen production efficiency, as a feedforward control input variable based on the upper and lower limits of the SOEC stack current, steam conversion rate, inlet temperature and air-to-gas ratio under normal operating conditions, with oxygen partial pressure and system hydrogen production efficiency as optimization targets.

[0009] Optionally, the neural network predictive controller collects the input and output variables of the high-temperature electrolysis hydrogen production system to train the neural network model, and then predicts the system output variables based on the input variables under the current operating conditions, and minimizes the error between the expected output and the predicted output of the voltage composition and temperature of the SOEC stack in the system and the system outlet stream variables through rolling optimization, and obtains the control sequence of the current, steam conversion rate, inlet temperature and air-gas ratio of the SOEC stack. The high-temperature electrolysis hydrogen production system receives the control sequence as the current operating condition of the system, and feeds back the SOEC stack voltage, inlet and outlet temperature difference and system outlet stream variables in the system to the NNPC controller, and continuously updates the parameters of the model and controller.

[0010] Among them, the optimization model of oxygen partial pressure and hydrogen production efficiency of the optimizer is as follows:

[0011]

[0012]

[0013] in, represents the oxygen partial pressure at the SOEC oxygen electrode-electrolyte interface, represents the hydrogen production efficiency of the hydrogen production system; I represents the electrolysis current of the system, α steam represents the steam conversion rate, T in Indicates the SOEC stack inlet temperature, k AF Indicates the air-gas ratio, ΔT out-in Indicates the temperature difference between the inlet and outlet of the SOEC stack.

[0014] Optionally, the neural network predictive controller includes a multi-layer neural network predictive model, whose input includes system feed water flow, pressure and temperature, feed air flow, pressure and temperature, SOEC stack inlet temperature and electrolysis current; its output includes performance indicators such as oxygen partial pressure and hydrogen production efficiency at the oxygen electrode-electrolyte interface, as well as product hydrogen flow and temperature, air flow and temperature in the anode tail gas, PEN (anode-electrolyte-cathode structure) temperature inside the stack, outlet temperature, voltage and power.

[0015] Optionally, the neural network predictive controller has a rolling optimization function to determine the control sequence by minimizing the cost function, and the expression is as follows:

[0016]

[0017] Among them, O is the number of output variables, P is the optimization time domain, q m,i is the output weighting coefficient, y p,m (k+i) and y r,m (k+i) are the predicted output and expected output of the mth variable respectively; L is the number of input variables, M is the control time domain, r n,j is the input weighting coefficient, u n (k+j-1) is the input variable.

[0018] The method for optimizing the control of a high-temperature solid oxide electrolysis hydrogen production system considering oxygen electrolysis degradation comprises the following steps:

[0019] Collect system performance data of the high-temperature solid oxide electrolysis hydrogen production system within the working range of electrolysis current, steam conversion rate, inlet temperature and air-gas ratio, including the oxygen partial pressure of the SOEC stack, the inlet and outlet temperature difference, and the system hydrogen production efficiency;

[0020] Based on the multi-objective optimization algorithm, the collected data is optimized with the lowest oxygen partial pressure and the highest hydrogen production efficiency as the optimization goals to obtain the optimal operation curve;

[0021] The operating parameters in the optimal operating curve are used as the feedforward input of the neural network predictive controller, and the optimal control sequence is obtained by rolling optimization of the cost function, including the current, steam conversion rate, inlet temperature and air-gas ratio of the SOEC stack;

[0022] The high-temperature solid oxide electrolysis hydrogen production system receives the control sequence as the operating variable, and feeds back the SOEC electrolysis voltage, inlet and outlet temperature difference, product hydrogen flow and temperature, and air flow and temperature in the anode tail gas to the NNPC controller, continuously updating the parameters of the model and controller.

[0023] Among them, the SOEC stack voltage model in the high-temperature solid oxide electrolysis hydrogen production system is as follows:

[0024] V=E+η act +η conc +η ohm

[0025] Where V is the electrolysis voltage, E is the equilibrium potential, η act is the activation overpotential, η conc is the concentration overpotential, η ohm is the Ohmic overpotential.

[0026] The thermal dynamic model of the SOEC stack is as follows:

[0027]

[0028] Among them, ρ i is the density of each part of the stack, c p,i is the specific heat capacity, V i is the component volume, T i is the temperature of each component, k i is the convective heat transfer coefficient, A i is the surface area, Φ i,in and Φ i,out are the heat fluxes at the inlet and outlet of the stream, respectively; F is the Faraday constant, 96485 C mol -1 , ΔH is the reaction heat, J is the current density, and U is the stack voltage. (i=a,c,s,l)

[0029] Optionally, the calculation formula reflecting the oxygen partial pressure at the oxygen electrode-electrolyte interface in the high-temperature solid oxide electrolysis hydrogen production system is as follows:

[0030]

[0031] in, is the anode gas flow pressure, η act,a is the anode activation overpotential, and R is the universal gas constant, which is 8.3145 J mol -1 K -1 , T s is the PEN temperature inside the stack.

[0032] Optionally, the calculation formula for the hydrogen production efficiency of the high-temperature solid oxide electrolysis hydrogen production system is as follows:

[0033]

[0034] in, is the lower calorific value of hydrogen, P SOEC is the SOEC stack power, P BOP Power for auxiliary equipment.

[0035] The present invention generates an optimal operating curve with the lowest oxygen partial pressure at the oxygen electrode-electrolyte interface and the highest hydrogen production efficiency through an optimizer, and regulates the high-temperature solid oxide electrolysis hydrogen production system near the optimal operating curve through an NNPC controller. In the long-term operation, the system can maintain high hydrogen production efficiency and low oxygen partial pressure, avoid problems such as excessive temperature difference between the inlet and outlet of the SOEC stack and degradation of the oxygen electrode, and realize long-term safe and stable operation of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0037] Figure 1 This is a diagram of the control optimization structure of the high-temperature solid oxide electrolysis hydrogen production system considering the degradation of the oxygen electrode of the present invention.

[0038] Figure 2 Flow chart of the high-temperature solid oxide electrolysis hydrogen production system considering oxygen electrode degradation of the present invention

[0039] The equipment marks in the figure are:

[0040] 1. Water purifier; 2. Water pump; 3. Air cooler; 4. Steam generator; 5. Mixer; 6. Cathode side heat exchanger; 7. Cathode side electric heater; 8. SOEC stack; 9. Air compressor; 10. Anode side heat exchanger; 11. Anode side electric heater; 12. Hydrogen cooler; 13. Steam-water separator; 14. Hydrogen compressor; 15. Dryer. DETAILED DESCRIPTION

[0041] In order to enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without making creative work are within the scope of protection of the present application.

[0042] Reference to "embodiments" in this application means that a particular feature, structure, or characteristic described in conjunction with the embodiments may be included in at least one embodiment of the present application. The appearance of the phrase in various locations in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment that is mutually exclusive with other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described in this application may be combined with other embodiments.

[0043] See also Figure 1 This embodiment provides a control optimization method for a high-temperature solid oxide electrolysis hydrogen production system taking into account oxygen electrode degradation, including:

[0044] optimizers and neural network predictive controllers;

[0045] Among them, the optimizer uses a multi-objective optimization algorithm to calculate and generate the operating curve of the optimal oxygen partial pressure at the oxygen electrode-electrolyte interface and system efficiency within the preset operating range of the high-temperature electrolytic hydrogen production system. The oxygen partial pressure will affect the degree of oxygen electrode stratification; the neural network predictive controller uses a neural network predictive control algorithm to predict and optimize the error between the predicted value and the expected value of the SOEC stack voltage, temperature and system outlet stream variables, and determine the control sequence. The high-temperature electrolytic hydrogen production system receives the control sequence and feeds back the key output variables of the system to the neural network predictive controller to correct the deviation of the model prediction results.

[0046] The method for optimizing the control of a high-temperature solid oxide electrolysis hydrogen production system considering oxygen electrolysis degradation comprises the following steps:

[0047] S1: Collect system performance data of the high-temperature solid oxide electrolysis hydrogen production system within the working range of electrolysis current, steam conversion rate, inlet temperature and air-gas ratio, including the oxygen partial pressure of the SOEC stack, the inlet and outlet temperature difference, and the system hydrogen production efficiency;

[0048] S2: Based on the multi-objective optimization algorithm, the collected data is optimized with the lowest oxygen partial pressure and the highest hydrogen production efficiency as the optimization goals to obtain the optimal operation curve;

[0049] S3: Using the operating parameters in the optimal operating curve as the feedforward input of the neural network predictive controller, the optimal control sequence is obtained by rolling optimization of the cost function, including the current, steam conversion rate, inlet temperature and air-gas ratio of the SOEC stack;

[0050] S4: The high-temperature solid oxide electrolysis hydrogen production system receives the control sequence as the operating variable, and feeds back the SOEC electrolysis voltage, inlet and outlet temperature difference, product hydrogen flow and temperature, and air flow and temperature in the anode tail gas to the NNPC controller, continuously updating the parameters of the model and controller.

[0051] Optionally, the optimizer calculates and generates the optimal operating curve, i.e., the curve with the lowest oxygen partial pressure and the highest hydrogen production efficiency, as a feedforward control input variable based on the upper and lower limits of the SOEC stack current, steam conversion rate, inlet temperature and air-to-gas ratio under normal operating conditions, with oxygen partial pressure and system hydrogen production efficiency as optimization targets.

[0052] Optionally, the neural network predictive controller collects the input and output variables of the high-temperature electrolysis hydrogen production system to train the neural network model, and then predicts the system output variables based on the input variables under the current operating conditions, and minimizes the error between the expected output and the predicted output of the voltage composition and temperature of the SOEC stack in the system and the system outlet stream variables through rolling optimization, and obtains the control sequence of the current, steam conversion rate, inlet temperature and air-gas ratio of the SOEC stack. The high-temperature electrolysis hydrogen production system receives the control sequence as the current operating condition of the system, and feeds back the SOEC stack voltage, inlet and outlet temperature difference and system outlet stream variables in the system to the NNPC controller, and continuously updates the parameters of the model and controller.

[0053] Among them, the optimization model of oxygen partial pressure and hydrogen production efficiency of the optimizer is as follows:

[0054]

[0055]

[0056] in, represents the oxygen partial pressure at the SOEC oxygen electrode-electrolyte interface, represents the hydrogen production efficiency of the hydrogen production system; I represents the electrolysis current of the system, α steam represents the steam conversion rate, T in Indicates the SOEC stack inlet temperature, k AF Indicates the air-gas ratio, ΔT out-in Indicates the temperature difference between the inlet and outlet of the SOEC stack.

[0057] Optionally, the neural network predictive controller includes a multi-layer neural network predictive model, whose input includes system feed water flow, pressure and temperature, feed air flow, pressure and temperature, SOEC stack inlet temperature and electrolysis current; its output includes performance indicators such as oxygen partial pressure and hydrogen production efficiency at the oxygen electrode-electrolyte interface, as well as product hydrogen flow and temperature, air flow and temperature in the anode tail gas, PEN (anode-electrolyte-cathode structure) temperature inside the stack, outlet temperature, voltage and power.

[0058] Optionally, the neural network predictive controller has a rolling optimization function to determine the control sequence by minimizing the cost function, and the expression is as follows:

[0059]

[0060] Among them, O is the number of output variables, P is the optimization time domain, q m,i is the output weighting coefficient, y p,m (k+i) and y r,m (k+i) are the predicted output and expected output of the mth variable respectively; L is the number of input variables, M is the control time domain, rn,j is the input weighting coefficient, u n (k+j-1) is the input variable.

[0061] Among them, the SOEC stack voltage model in the high-temperature solid oxide electrolysis hydrogen production system is as follows:

[0062] V=E+η act +η conc +η ohm

[0063] Where V is the electrolysis voltage, E is the equilibrium potential, η act is the activation overpotential, η conc is the concentration overpotential, η ohm is the Ohmic overpotential.

[0064] The thermal dynamic model of the SOEC stack is as follows:

[0065]

[0066] Among them, ρ i is the density of each part of the stack, c p,i is the specific heat capacity, V i is the component volume, T i is the temperature of each component, k i is the convective heat transfer coefficient, A i is the surface area, Φ i,in and Φ i,out are the heat fluxes at the inlet and outlet of the stream, respectively; F is the Faraday constant, 96485 C mol -1 , ΔH is the reaction heat, J is the current density, and U is the stack voltage. (i=a,c,s,l)

[0067] Optionally, the calculation formula reflecting the oxygen partial pressure at the oxygen electrode-electrolyte interface in the high-temperature solid oxide electrolysis hydrogen production system is as follows:

[0068]

[0069] in, is the anode gas flow pressure, η act,a is the anode activation overpotential, and R is the universal gas constant, which is 8.3145 J mol -1 K -1 , T s is the PEN temperature inside the stack.

[0070] See also Figure 2The power consumption of the high-temperature solid oxide electrolysis hydrogen production system comes from the SOEC stack, as well as auxiliary equipment such as a pure water machine, a water pump, a steam generator, an anode-cathode electric heater, an air compressor, a hydrogen cooler, and a hydrogen compressor. The calculation formula for hydrogen production efficiency is as follows:

[0071]

[0072] in, is the lower calorific value of hydrogen, P SOEC is the SOEC stack power, P BOP Power for auxiliary equipment.

[0073] The above description is only a preferred embodiment of the present invention and is not intended to limit the scope of the substantial technical content of the present invention. The substantial technical content of the present invention is broadly defined in the scope of the claims of the application. Any technical entity or method completed by others, if it is exactly the same as that defined in the scope of the claims of the application or an equivalent variation, will be deemed to be included in the scope of the claims.

Claims

1. A method for optimizing the control of a high-temperature solid oxide electrolysis hydrogen production system taking into account oxygen electrode degradation, comprising: optimizers and neural network predictive controllers; The optimizer adopts a multi-objective optimization algorithm to calculate and generate an operating curve of the optimal oxygen partial pressure at the oxygen electrode-electrolyte interface and system efficiency of the high-temperature electrolytic hydrogen production system within a preset operating range. The oxygen partial pressure will affect the degree of oxygen electrode stratification. The neural network predictive controller adopts a neural network predictive control algorithm to predict and optimize the error between the predicted value and the expected value of the SOEC stack voltage, temperature and system outlet stream variables, and determine the control sequence. The high-temperature electrolysis hydrogen production system receives the control sequence and feeds back the key output variables of the system to the neural network predictive controller to correct the deviation of the model prediction result.

2. The method for optimizing the control of a high-temperature solid oxide electrolysis hydrogen production system considering oxygen electrode degradation according to claim 1, characterized in that: The optimizer calculates and generates the optimal operating curve, i.e., the curve with the lowest oxygen partial pressure and the highest hydrogen production efficiency, as the feedforward control input variable based on the upper and lower limits of the current, steam conversion rate, inlet temperature and air-to-gas ratio of the SOEC stack under normal operating conditions, and takes the oxygen partial pressure and system hydrogen production efficiency as the optimization targets. The neural network predictive controller collects input and output variables of the high-temperature electrolysis hydrogen production system to train the neural network model, and then predicts the system output variables based on the input variables under the current operating conditions. Through rolling optimization, the error between the expected output and the predicted output of the voltage composition and temperature of the SOEC stack in the system and the system outlet stream variables is minimized, and the control sequence of the current, steam conversion rate, inlet temperature and air-gas ratio of the SOEC stack is obtained. The high-temperature electrolysis hydrogen production system receives the control sequence as the current operating condition of the system, and feeds back the SOEC stack voltage, inlet and outlet temperature difference and system outlet stream variables in the system to the NNPC controller, continuously updating the parameters of the model and controller.

3. The control and optimization method for a high-temperature solid oxide electrolysis hydrogen production system considering oxygen electrode degradation according to claim 1 or 2, characterized in that: The optimization model of oxygen partial pressure and hydrogen production efficiency of the optimizer is as follows: in, represents the oxygen partial pressure at the SOEC oxygen electrode-electrolyte interface, represents the hydrogen production efficiency of the hydrogen production system; I represents the electrolysis current of the system, α steam represents the steam conversion rate, T in Indicates the SOEC stack inlet temperature, k AF Indicates the air-gas ratio, ΔT out-in Indicates the temperature difference between the inlet and outlet of the SOEC stack.

4. The neural network predictive controller according to claim 1 or 2, characterized in that: The neural network predictive controller includes a multi-layer neural network predictive model, whose input includes system feed water flow, pressure and temperature, feed air flow, pressure and temperature, SOEC stack inlet temperature and electrolysis current; Its output includes performance indicators such as oxygen partial pressure at the oxygen electrode-electrolyte interface and hydrogen production efficiency, as well as product hydrogen flow and temperature, air flow and temperature in the anode tail gas, PEN (anode-electrolyte-cathode structure) temperature inside the stack, outlet temperature, voltage and power.

5. The neural network predictive controller according to claim 1 or 2, characterized in that: The neural network predictive controller has a rolling optimization function, which determines the control sequence by minimizing the cost function. The expression is as follows: Among them, O is the number of output variables, P is the optimization time domain, q m,i is the output weighting coefficient, y p,m (k+i) and y r,m (k+i) are the predicted output and expected output of the mth variable respectively; L is the number of input variables, M is the control time domain, r n,j is the input weighting coefficient, u n (k+j-1) is the input variable.

6. A method for optimizing the control of a high-temperature solid oxide electrolysis hydrogen production system taking into account oxygen electrolysis degradation, characterized in that: The method comprises the following steps: S1: Collect system performance data of the high-temperature solid oxide electrolysis hydrogen production system within the working range of electrolysis current, steam conversion rate, inlet temperature and air-gas ratio, including the oxygen partial pressure of the SOEC stack, the inlet and outlet temperature difference, and the system hydrogen production efficiency; S2: Based on the multi-objective optimization algorithm, the collected data is optimized with the lowest oxygen partial pressure and the highest hydrogen production efficiency as the optimization goals to obtain the optimal operation curve; S3: Using the operating parameters in the optimal operating curve as the feedforward input of the neural network predictive controller, the optimal control sequence is obtained by rolling optimization of the cost function, including the current, steam conversion rate, inlet temperature and air-gas ratio of the SOEC stack; S4: The high-temperature solid oxide electrolysis hydrogen production system receives the control sequence as the operating variable, and feeds back the SOEC electrolysis voltage, inlet and outlet temperature difference, product hydrogen flow and temperature, and air flow and temperature in the anode tail gas to the NNPC controller, continuously updating the parameters of the model and controller.

7. The method according to claim 6, characterized in that The SOEC stack voltage model in the high-temperature solid oxide electrolysis hydrogen production system in step S1 is as follows: V=E+η act +n conc +n ohm Where V is the electrolysis voltage, E is the equilibrium potential, η act is the activation overpotential, η conc is the concentration overpotential, η ohm is the Ohmic overpotential. The thermal dynamic model of the SOEC stack is as follows: Among them, ρ i is the density of each part of the stack, c p,i is the specific heat capacity, V i is the component volume, T i is the temperature of each component, k i is the convective heat transfer coefficient, A i is the surface area, Φ i,in and Φ i,out are the heat fluxes at the inlet and outlet of the stream, respectively; F is the Faraday constant, 96485 Cmol -1 , ΔH is the reaction heat, J is the current density, and U is the stack voltage. (i=a,c,s,l).

8. The method according to claim 6, characterized in that The calculation formula reflecting the oxygen partial pressure at the oxygen electrode-electrolyte interface in the high-temperature solid oxide electrolysis hydrogen production system is as follows: in, is the anode gas flow pressure, η act,a is the anode activation overpotential, and R is the universal gas constant, which is 8.3145 J mol -1 K -1 , T s is the PEN temperature inside the stack. The calculation formula for the hydrogen production efficiency of the high-temperature solid oxide electrolysis hydrogen production system is as follows: in, is the lower calorific value of hydrogen, P SOEC is the SOEC stack power, P BOP Power for auxiliary equipment.

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