An IES scheduling method, system and medium

Abstract

The application provides an IES scheduling method, system and medium, the method comprising: modeling electrochemical processes and thermal processes of cell units and SOFC auxiliary equipment in the SOFC respectively, and simultaneously obtaining a SOFC nonlinear output characteristic model to represent the relationship between the output electric power, thermal power and working state of the SOFC; based on the degradation effect of the SOFC under different working states, establishing a SOFC nonlinear degradation cost model to count the asset loss caused by the degradation process into the cost; constructing an ETC model according to the SOFC nonlinear output characteristic model and the SOFC nonlinear degradation cost model, and describing the operation and degradation effect of the SOFC; further, adopting a piecewise linearization method to linearize the ETC model, so as to facilitate the solution of the IES optimization scheduling problem. The application facilitates the scheduling personnel of the IES to formulate a safe and economic SOFC operation strategy.

Description

Technical Field

[0001] This invention relates to the field of integrated energy system automation technology, and in particular to an IES scheduling method, system and medium based on the SOFC electrochemical-thermal coupling model. Background Technology

[0002] In recent years, technological innovation and institutional reforms in the energy sector have permeated the entire process of human societal development. However, the rapid development of social productivity has led to a sharp increase in energy demand. Traditional fossil fuels face serious problems of over-exploitation and depletion, resulting in increasingly severe environmental pollution. The transformation and upgrading of traditional energy systems is urgently needed. Therefore, Integrated Energy Systems (IES) are widely considered an important means to solve this problem. Meanwhile, solid oxide fuel cells (SOFCs) have significant potential for integration into IESs due to their advantages of low pollution, high efficiency, and high energy density. In IESs, SOFCs can exchange heat with the external environment through controlled auxiliary equipment, thereby flexibly meeting the electricity and heating needs of different users. Modeling the operation and degradation performance of SOFCs under different operating conditions is a key technology for ensuring the healthy and economical operation of SOFCs and has become a current research focus.

[0003] In existing IES (Environmentally Modulated Systems) optimization scheduling research, some studies use constant efficiency models to model SOFCs, assuming that SOFCs always output electrical and thermal power at a constant efficiency. Other studies treat SOFC efficiency as a univariate function of output electrical power and use polynomial functions to fit its characteristics. These studies fail to grasp the operational characteristics of SOFCs from the perspective of their operating mechanisms, neglecting the significant impact of environmental factors such as temperature and the amount of input hydrogen on their energy conversion efficiency. Furthermore, a constant electrothermal output ratio is not conducive to the flexible operation of SOFCs. At the same time, most studies simply assume that SOFC degradation costs are proportional to operating time. In reality, the electrochemical performance degradation process of SOFCs involves a complex degradation mechanism and does not degrade at a constant rate. Therefore, proposing an electrochemical-thermal coupling model for SOFCs suitable for IES optimization scheduling is of positive significance and important practical value for the economic and healthy operation of SOFCs. Summary of the Invention

[0004] The main objective of this invention is to provide a method, system, and medium for formulating SOFC operation strategies based on the SOFO electrochemical-thermal coupling model. In particular, a modeling and scheduling method is designed to address the complex operation and decay characteristics caused by the coupling of SOFC electrochemical and thermodynamic processes, aiming to facilitate IES schedulers in formulating safe and economical SOFC operation strategies.

[0005] To achieve the above objectives, this invention proposes an IES scheduling method based on an SOFC electrochemical-thermal coupling model, which includes the following steps:

[0006] Step S10: Model the electrochemical and thermodynamic processes of the battery cells and SOFC auxiliary equipment in SOFC respectively, and combine them to obtain the SOFC nonlinear output characteristic model to represent the relationship between SOFC output electric power, thermal power and operating state.

[0007] Step S20: Based on the degradation effect of SOFC under different working conditions, establish a nonlinear degradation cost model for SOFC to include the asset loss caused by the degradation process in the cost.

[0008] Step S30: Construct an ETC model based on the SOFC nonlinear output characteristic model and the SOFC nonlinear degradation cost model to comprehensively describe the operation and degradation effects of SOFC.

[0009] Step S40: The ETC model is linearized using a piecewise linearization method to facilitate the solution of the IES optimization scheduling problem.

[0010] A further technical solution of the present invention is that step S10 includes:

[0011] Step S110: The nonlinear relationship between the electrical power generated by the SOFC, the hydrogen consumption rate, and the operating temperature is derived from the semi-empirical formula of the SOFC single cell output voltage.

[0012] Step S120: Derive the nonlinear relationship between the thermal power generated by the SOFC, the hydrogen consumption rate, and the operating temperature.

[0013] In step S130, taking into account the heat exchange effect of auxiliary equipment and heat dissipation to the outside, the change of SOFC operating temperature is described by heat transfer differential equation.

[0014] A further technical solution of the present invention is that, in step S110, the step of deriving the electrical power generated by the SOFC from the semi-empirical formula of the SOFC single cell output voltage includes:

[0015] First, a semi-empirical formula is used to indirectly calculate the output voltage of a single cell in a SOFC. Using standard state voltage The actual output voltage V is evaluated by summing multiple deviation voltages caused by various operating parameters deviating from standard conditions. SOFC Assuming the SOFC's operating pressure and positive / negative electrode composition are controlled within standard conditions, only the deviation voltage caused by the operating temperature deviating from the standard temperature is considered. Based on this assumption, in the proposed METC model, the specific formula for the output voltage of a single battery cell in SOFC is simplified as shown in equation (1):

[0016]

[0017] Among them, i SOFC This is the current density of the SOFC; T SOFC This is the actual operating temperature of the SOFC; The standard operating temperature of SOFC is 850℃; the current density of SOFC is determined by the rate at which SOFC consumes hydrogen, as shown in equation (2):

[0018]

[0019] Where F is the Faraday constant, taken as 96485 C / mol; n SOFC The SOFC hydrogen consumption rate is the amount of hydrogen flowing into the SOFC per unit time. For SOFC fuel utilization rate; N SOFC A represents the number of battery cells in an SOFC. SOFC This represents the cross-sectional area of ​​the SOFC.

[0020] Finally, by combining equations (1) and (2), we can obtain the expression for the output power of the SOFC:

[0021] P sOFC (n SOFC T SOFC ) = N SOFC ·V SOFC (n SOFC T SOFC )·I sOFC (n SOFC (3)

[0022] Among them, P SOFC This refers to the output electrical power of the SOFC, which is related to the SOFC hydrogen consumption rate n. SOFC and the actual operating temperature T of SOFC SOFC A bivariate nonlinear function.

[0023] A further technical solution of the present invention is that, in step S110, after a portion of the hydrogen energy in the SOFC is converted into electrical energy, the remaining majority is converted into usable thermal energy. The usable thermal power generated simultaneously by the output electrical power of the SOFC can be calculated by equation (4):

[0024]

[0025] Among them, H SOFCIt is the thermal power generated by the SOFC, and it relates to the SOFC hydrogen consumption rate n. SOFC and the actual operating temperature T of SOFC SOFC A bivariate nonlinear function; It has the low calorific value of hydrogen. This refers to the thermal energy utilization efficiency of the SOFC. The heat exchange process between the SOFC and the external environment can be controlled via the Organic Rankine Cycle (ORC), thereby controlling the operating temperature of the SOFC. According to the heat transfer theorem, the temperature change of the SOFC can be described by equation (5):

[0026]

[0027] Among them, C SOFC The heat capacity of SOFC; H SOFC，re For the heat exchanged with SOFC, H SOFC，re When H > 0, SOFC outputs heat power externally. SOFC，re When <0, SOFC absorbs heat power from the outside, H SOFC，re When H = 0, SOFC does not exchange heat with the outside environment; Loss To dissipate heat and meet H Loss =(T SOFC -T ext ) / R SOFC T ext Let the ambient temperature be the external temperature; equation (5) can be discretized as:

[0028]

[0029] Where Δt is the scheduling step size.

[0030] A further technical solution of the present invention is that step S20 includes:

[0031] Step S210: The degradation cost of SOFC operating at different hydrogen consumption rates and temperatures is derived from the SOFC output voltage degradation rate formula.

[0032] A further technical solution of the present invention is that step S210 includes:

[0033] The voltage decay rate is calculated using a local degradation model, as shown in equation (7):

[0034]

[0035] Where, r SOFC，de The voltage decay rate of the SOFC is expressed in units of 100% / kh; further, the degradation cost of the SOFC is obtained, as shown in equation (8):

[0036]

[0037] in, The degradation cost of SOFC can also be viewed as a factor related to the SOFC hydrogen consumption rate n. SOFC and the actual operating temperature T of SOFC SOFC A bivariate nonlinear function; r SOFC，p·u. The minimum allowable output voltage for normal SOFC operation; Cap SOFC This refers to the one-time investment cost of SOFC equipment.

[0038] A further technical solution of the present invention is that the step of linearizing the ETC model using a piecewise linearization method in step S40 includes:

[0039] To linearize the nonlinear operating characteristics of SOFC, the feasible region of SOFC operation is divided into K triangular subdomains, and the nonlinear characteristics are approximated by linear characteristics in each subdomain; the specific formula is shown in equation (9):

[0040]

[0041] in, and These are the linear coefficients of the approximate nonlinear characteristic of the output electric power over subdomain k; and Let A and B be the linear coefficients of the approximate attenuation cost nonlinearity characteristic over subdomain k; matrix A. k And vector b k The determined polyhedron A k x≤b k The subdomain k was determined; n SOFC , and T SOFC These are the upper and lower limits of the SOFC hydrogen consumption rate and operating temperature, respectively; for the purpose of optimizing scheduling, they are further converted into hybrid linear constraints, as shown in equation (10):

[0042]

[0043] in, and x SOFC Auxiliary variables introduced; P SOFC , and C SOFC，de, respectively, represent the upper and lower limits of SOFC output power and SOFC attenuation cost; m is a vector in which each component is a sufficiently large positive number, used to relax constraints in other subdomains outside the subdomain where the operating point is located.

[0044] A further technical solution of the present invention is that the step of formulating the IES scheduling strategy in step S40 includes formulating a safe and economical SOFC operation strategy by the IES scheduler.

[0045] To achieve the above objectives, the present invention also proposes an IES scheduling system based on the SOFC electrochemical-thermal coupling model. The system includes a memory, a processor, and an IES scheduler based on the SOFC electrochemical-thermal coupling model stored on the processor. The IES scheduler based on the SOFC electrochemical-thermal coupling model is executed by the processor to perform the steps of the method described above.

[0046] To achieve the above objectives, the present invention also proposes a computer-readable storage medium, characterized in that the computer-readable storage medium stores an IES scheduler based on the SOFC electrochemical-thermal coupling model, wherein the IES scheduler based on the SOFC electrochemical-thermal coupling model is executed by a processor to perform the steps of the method described above.

[0047] The beneficial effects of the IES scheduling method, system, and medium based on the SOFC electrochemical-thermal coupling model of this invention are:

[0048] 1) This invention establishes an ETC model to describe the output and degradation characteristics of SOFC under different operating conditions (hydrogen flow rate and temperature). Semi-empirical algebraic formulas are used to comprehensively reveal the effects of different operating conditions (hydrogen flow rate and temperature) on the voltage and voltage degradation rate of SOFC single cells, ensuring sufficient accuracy while avoiding complex mechanistic modeling of electrochemical and degradation processes.

[0049] 2) This invention linearizes the nonlinear, even nonconvex, ETC model piecewise. By introducing auxiliary variables, it transforms the nonlinear constraints between SOFC output power, degradation cost, and operating state into a set of hybrid linear constraints that can be used for system-level scheduling. This enables SOFC-related optimization scheduling problems to be solved quickly and accurately by commercial solvers. Attached Figure Description

[0050] Figure 1 This is a flowchart illustrating a preferred embodiment of the IES scheduling method based on the SOFC electrochemical-thermal coupling model of the present invention.

[0051] Figure 2 This is a schematic diagram of the SOFC principle;

[0052] Figure 3 This invention presents the output characteristic model of SOFC.

[0053] Figure 4 This invention presents a degradation cost model for SOFC.

[0054] Figure 5 This is a block diagram of the SOFC ETC model proposed in this invention;

[0055] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. Detailed Implementation

[0056] It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

[0057] To address the problems in existing technologies, this invention proposes an IES scheduling method based on an SOFC electrochemical-thermal coupling model. The electrochemical-thermal coupling (ETC) model incorporates the complex coupled electrochemical reactions and degradation processes of SOFCs. First, the electrochemical and thermodynamic processes of the battery cells and SOFC auxiliary equipment in the SOFC are modeled separately, resulting in a nonlinear output characteristic model of the SOFC to represent the relationship between the SOFC's output electrical and thermal power and its operating state. Based on this, considering the degradation characteristics of the SOFC under different operating states, a nonlinear degradation cost model is established to include the asset losses caused by degradation in the cost. The output characteristic model and the degradation model together constitute the ETC model, which can effectively describe the operation and degradation process of the SOFC. To meet the scheduling requirements of the IES system where the SOFC is located, a piecewise linearization method is used to linearize the ETC model. The ETC model and linearization help IES schedulers formulate safe and economical SOFC operation strategies and can be applied to practical engineering.

[0058] Specifically, such as Figure 1 As shown, a preferred embodiment of the IES scheduling method based on the SOFC electrochemical-thermal coupling model of the present invention includes the following steps:

[0059] Step S10: Model the electrochemical and thermodynamic processes of the battery cells and SOFC auxiliary equipment in SOFC, and combine them to obtain the SOFC nonlinear output characteristic model to represent the relationship between SOFC output electrical power, thermal power and operating state.

[0060] Specifically, step S10 includes:

[0061] Step S110: The nonlinear relationship between the electrical power generated by the SOFC, the hydrogen consumption rate, and the operating temperature is derived from the semi-empirical formula of the SOFC single cell output voltage.

[0062] The semi-empirical formula for the output voltage of a single SOFC cell can well represent its output characteristics. However, as the current density increases, the output voltage decreases rapidly, exhibiting a significant nonlinearity. This further leads to nonlinearities in the electrical and thermal power generated by the SOFC.

[0063] The semi-empirical formula for the output voltage of a single SOFC cell incorporates operating temperature, which is reflected in the inclusion of a cross term for temperature and current density in the formula. Specifically, the higher the current density of a single SOFC cell, the greater the impact of operating temperature on its output voltage.

[0064] SOFCs can only convert a portion of the chemical energy contained in the hydrogen gas they consume into electrical energy through electrochemical reactions; the remainder diffuses as heat into the surrounding insulated space. The addition of auxiliary equipment makes it possible to utilize this heat energy. To describe the effect of this process on the critical factor of operating temperature, a heat transfer differential equation was established to lumped out the heat transfer process, which can effectively reflect the temperature changes in the SOFC.

[0065] In step S110, the effects of external pressure and the composition of positive and negative electrode gases on the output voltage are ignored because these influencing factors are easy to control and have little impact on the output voltage of SOFC single cells.

[0066] Step S110 involves a method for calculating the output power of an SOFC. The steps in step S110 that derive the power generated by the SOFC from a semi-empirical formula based on the output voltage of a single SOFC cell include:

[0067] First, a semi-empirical formula is used to indirectly calculate the output voltage of a single cell in a SOFC. Using standard state voltage The actual output voltage V is evaluated by summing multiple deviation voltages caused by various operating parameters deviating from standard conditions. SOFC Assuming the SOFC's operating pressure and positive / negative electrode composition are controlled within standard conditions, only the deviation voltage caused by the operating temperature deviating from the standard temperature is considered. Based on this assumption, in the proposed ETC model, the specific formula for the output voltage of a single battery cell in SOFC is simplified as shown in equation (1):

[0068]

[0069] Among them, i SOFC This is the current density of the SOFC; T SOFC This is the actual operating temperature of the SOFC; The standard operating temperature of SOFC is 850℃; the current density of SOFC is determined by the rate at which SOFC consumes hydrogen, as shown in equation (2):

[0070]

[0071] Where F is the Faraday constant, taken as 96485 C / mol; n SOFC The SOFC hydrogen consumption rate is the amount of hydrogen flowing into the SOFC per unit time. For SOFC fuel utilization rate; N SOFC A represents the number of battery cells in an SOFC. SOFC This represents the cross-sectional area of ​​the SOFC.

[0072] Finally, by combining equations (1) and (2), we can obtain the expression for the output power of the SOFC:

[0073] P sOFC (n SOFC T SOFC ) = N sOFC ·V sOFe (n SOFC T SOFC )·I SOFC (n SOFC (3)

[0074] Among them, P SOFC This refers to the output electrical power of the SOFC, which is related to the SOFC hydrogen consumption rate n. SOFC and the actual operating temperature T of SOFC SOFC A bivariate nonlinear function.

[0075] Step S110 also involves a method for calculating the SOFC operating temperature. During the process of converting chemical energy into electrical energy, another portion of the energy exists in the form of waste heat. Due to the extremely high operating temperature of the SOFC and the addition of a well-insulated outer shell, some of the waste heat can be converted into high-quality heat energy that can be utilized.

[0076] In step S110, considering the ultra-high operating temperature and good thermal insulation performance of SOFC, after part of the hydrogen energy in SOFC is converted into electrical energy, the remaining majority is converted into usable thermal energy. The usable thermal power generated by the SOFC outputting electrical power can be calculated by equation (4):

[0077]

[0078] Among them, H sOFC It refers to the thermal power generated by the SOFC, and is related to the SOFC hydrogen consumption rate. SOFC and the actual operating temperature T of SOFCSOFC A bivariate nonlinear function; It has the low calorific value of hydrogen. This refers to the thermal energy utilization efficiency of the SOFC. The heat exchange process between the SOFC and the external environment can be controlled via the Organic Rankine Cycle (ORC), thereby controlling the operating temperature of the SOFC. According to the heat transfer theorem, the temperature change of the SOFC can be described by equation (5):

[0079]

[0080] Among them, C SOFC The heat capacity of SOFC; H SOFC，re For the heat exchanged with SOFC, H SOFC，re When H > 0, SOFC outputs heat power externally. SOFC，re When <0, SOFO absorbs heat power from the outside, H SOFC，re When H = 0, SOFC does not exchange heat with the outside environment; Loss To dissipate heat and meet H Loss =(T SOFC -T ext ) / R SOFC T ext Let the ambient temperature be the external temperature; equation (5) can be discretized as:

[0081]

[0082] Where Δt is the scheduling step size.

[0083] Step S120: Derive the nonlinear relationship between the thermal power generated by the SOFC, the hydrogen consumption rate, and the operating temperature.

[0084] In step S130, taking into account the heat exchange effect of auxiliary equipment and heat dissipation to the outside, the change of SOFC operating temperature is described by heat transfer differential equation.

[0085] Step S20: Based on the degradation effect of SOFC under different operating conditions, establish a nonlinear degradation cost model for SOFC to include the asset loss caused by the degradation process in the cost.

[0086] Step S20 specifically includes:

[0087] Step S210: The degradation cost of SOFC operating at different hydrogen consumption rates and temperatures is derived from the SOFC output voltage degradation rate formula.

[0088] In step S210, the SOFC voltage degradation rate is used to measure the degree of SOFC degradation. Taking into account the minimum voltage required for normal operation of SOFC and the one-time investment cost of SOFC, the SOFC voltage degradation rate is converted into degradation cost.

[0089] Step S210 involves the method for calculating the degradation cost of an SOFC system, specifically including:

[0090] The voltage decay rate is calculated using a local degradation model, as shown in equation (7):

[0091]

[0092] Where, r SOFC，de The voltage decay rate of the SOFC is given in % / kh; further, the degradation cost of the SOFC is obtained as shown in equation (8):

[0093]

[0094] in, The degradation cost of SOFC can also be viewed as a factor related to the SOFC hydrogen consumption rate n. SOFC and the actual operating temperature T of SOFC SOFC A bivariate nonlinear function; r SOFC，p·u. The minimum allowable output voltage (pu) for normal SOFC operation; Cap SOFC This represents the one-time investment cost of the SOFC equipment. SOFC degradation takes thousands of hours to significantly impact its operation; therefore, the ETC model is considered a time-invariant system within the scheduling cycle.

[0095] Step S30: Construct the ETC model based on the SOFC nonlinear output characteristic model and the SOFC nonlinear degradation cost model to comprehensively describe the operation and degradation effects of SOFC.

[0096] Step S40: The ETC model is linearized using a piecewise linearization method to facilitate the solution of the IES optimal scheduling problem and to formulate an IES optimal scheduling strategy.

[0097] The ETC model can be easily incorporated into optimization scheduling problems. When considering the nonlinear characteristics of SOFCs in optimization scheduling problems, the degradation cost of SOFCs and other necessary expenses (such as fuel costs) can be directly added to the original objective function, and the constraints of SOFC output characteristics and other necessary constraints (such as power balance constraints) can be added to the original constraints. In other words, the SOFC operation plan can be obtained by solving the optimization problem.

[0098] For the significant nonlinear characteristics of SOFC's electrical and thermal power generation and degradation costs, a piecewise linearization method is used to transform them into linear features. The linearized model can more accurately characterize the impact of temperature on SOFC operating status. This invention employs techniques such as the Big M method to transform linear characteristics into mixed-integer linear constraints that can be used for optimized scheduling.

[0099] The segmentation in step S40 actually refers to dividing the SOFC operating domain into triangular subdomains, and using planes on multiple triangular subdomains to approximate the surface characteristics of the electrical and thermal power generated by the SOFC.

[0100] The triangular shape of the subdomains means that the approximate plane can be uniquely determined by the three vertices, and this plane necessarily passes through the three vertices, i.e., there is no deviation at the three vertices. Moreover, since every two adjacent subdomains share an edge, the linearized approximate function is continuous. This choice of subdomain shape can yield an approximate function with better properties, ensuring the rationality of the optimized scheduling results.

[0101] Step S40 involves a piecewise linearization method for the ETC model suitable for IES optimized scheduling. The specific steps in step S40 for linearizing the ETC model using the piecewise linearization method include:

[0102] To linearize the nonlinear operating characteristics of SOFC, the feasible region of SOFC operation is divided into K triangular subdomains, and the nonlinear characteristics are approximated by linear characteristics in each subdomain; the specific formula is shown in equation (9):

[0103]

[0104] in, and These are the linear coefficients of the approximate nonlinear characteristic of the output electric power over subdomain k; and Let A and B be the linear coefficients of the approximate attenuation cost nonlinearity characteristic over subdomain k; matrix A. k And vector b k The determined polyhedron A k x≤b k The subdomain k was determined; n SOFC , and T SOFC These are the upper and lower limits of the SOFC hydrogen consumption rate and operating temperature, respectively; for the purpose of optimizing scheduling, they are further converted into hybrid linear constraints, as shown in equation (10):

[0105]

[0106] in, and Auxiliary variables introduced; P SOFC , and C SOFC，de , respectively, represent the upper and lower limits of SOFC output power and SOFC attenuation cost; m is a vector in which each component is a sufficiently large positive number, used to relax constraints in other subdomains outside the subdomain where the operating point is located.

[0107] Step S40, which involves developing an IES scheduling strategy, includes having IES schedulers develop a safe and economical SOFC operation strategy.

[0108] The following provides a detailed description of the SOFC electrochemical-thermal coupling model for IES optimization scheduling proposed in this invention.

[0109] This invention relates to an electrochemical-thermal coupling model for SOFCs suitable for IES (Environmental Engineering Systems) optimal scheduling. First, an output characteristic model is established: based on a semi-empirical formula for SOFC output voltage, the nonlinear relationship between its output electrical power, hydrogen consumption rate, and operating temperature is obtained. Furthermore, the relationship between the SOFC's generated heat power, output electrical power, hydrogen consumption rate, and operating temperature is derived. The heat transfer process of the SOFC is further analyzed, yielding a heat transfer differential equation to reveal the temperature variation law of the SOFC. Next, a degradation cost model is established. A semi-empirical formula for SOFC voltage degradation rate is used to derive the hourly degradation cost of the SOFC under different operating conditions. The resulting degradation cost model and output characteristic model together constitute the electrochemical-thermal coupling model of the SOFC. Finally, to adapt to the needs of IES optimal scheduling, the obtained nonlinear electrochemical-thermal coupling model is piecewise linearized and converted into mixed-integer linear constraints common in optimization scheduling problems, which can be easily processed by commercial optimization solvers. The model is simple in form and computationally fast, and can be applied to practical engineering projects including IES optimal scheduling and real-time operation control of SOFCs.

[0110] This invention is a modeling of the operation and degradation process of SOFC. A schematic diagram of the SOFC structure is shown in the figure, including:

[0111] like Figure 2 As shown, SOFC converts the chemical energy contained in hydrogen into electrical energy through an electrochemical reaction. Simultaneously, due to its high operating temperature, SOFC generates different levels of waste heat, which can be recovered and reused to achieve combined heat and power (CHP). Therefore, an ORC system is installed as auxiliary equipment, mainly composed of pumps and heat exchangers, to utilize waste heat in a timely manner or control the SOFC operating temperature.

[0112] like Figure 3 As shown, in the MTC model, the output electrical and thermal power of the SOFC are both bivariate functions of the hydrogen consumption rate and the operating temperature. The SOFC operating domain is determined by the following two equipment operating constraints:

[0113] 3458mol / h≤ SOFC ≤10375mol / h;

[0114] 800℃≤T sOFC ≤900℃

[0115] Within the operating domain, at a constant temperature, the output thermal power increases rapidly with increasing hydrogen consumption rate; the output electrical power increases monotonically with increasing hydrogen consumption rate at higher temperatures, and initially increases then decreases with increasing hydrogen consumption rate at lower temperatures. At a constant hydrogen consumption rate, the output electrical power increases with rising temperature, while the output thermal power decreases with rising temperature. Therefore, the SOFC's electrothermal ratio, i.e., the output electrical power and output thermal power, varies considerably at different temperatures.

[0116] like Figure 4 As shown, in the ETC model, the SOFC degradation cost is a bivariate function of hydrogen consumption rate and operating temperature. Within the operating domain, the degradation cost increases with increasing temperature and hydrogen consumption rate. In particular, the degradation cost is significantly higher at lower operating temperatures and higher hydrogen consumption rates than under other operating conditions.

[0117] like Figure 5 As shown, the ETC model is based on T SOFC n is a state variable. SOFC and H SOFC，re For input variables, P SOFC and C SOFC，de A two-input, two-output autonomous nonlinear system with output variables can be represented by the following state-space equations:

[0118]

[0119] [P SOFC C SOFC，de ] = G(T SOFC ;n SOFC H SOFC，re )

[0120] To facilitate the solution of the IES optimization scheduling problem, it is necessary to optimize P. SOFC (n SOFC T SOFC ), H SOFC (n SOFC T SOFC ) and C sOFC，de (n SOFC T SOFC The three nonlinear bivariate functions are piecewise linearized. Figures 3 to 5 The four vertices and center point of the operating domain are selected, and a linear subdomain is defined for every three adjacent points, thus dividing the operating domain into four subdomains. Each subdomain approximates the surface corresponding to the original function through a plane defined by the three vertices. Based on this piecewise approximation function, a linearized SOFC system is obtained. This system reflects the performance of SOFC under different operating conditions and has a certain degree of accuracy, making it suitable for tasks such as optimization scheduling.

[0121] The beneficial effects of the IES scheduling method based on the SOFC electrochemical-thermal coupling model in this invention are:

[0122] 1) This invention establishes an ETC model to describe the output and degradation characteristics of SOFC under different operating conditions (hydrogen flow rate and temperature). Semi-empirical algebraic formulas are used to comprehensively reveal the effects of different operating conditions (hydrogen flow rate and temperature) on the voltage and voltage degradation rate of SOFC single cells, ensuring sufficient accuracy while avoiding complex mechanistic modeling of electrochemical and degradation processes.

[0123] 2) This invention linearizes the nonlinear, even nonconvex, ETC model piecewise. By introducing auxiliary variables, it transforms the nonlinear constraints between SOFC output power, degradation cost, and operating state into a set of hybrid linear constraints that can be used for system-level scheduling. This enables SOFC-related optimization scheduling problems to be solved quickly and accurately by commercial solvers.

[0124] To achieve the above objectives, the present invention also proposes an IES scheduling system based on the SOFC electrochemical-thermal coupling model. The system includes a memory, a processor, and an IES scheduler based on the SOFC electrochemical-thermal coupling model stored on the processor. When the processor runs the IES scheduler based on the SOFC electrochemical-thermal coupling model, it executes the steps described in the above embodiments, which will not be repeated here.

[0125] To achieve the above objectives, the present invention also proposes a computer-readable storage medium storing an IES scheduler based on the SOFC electrochemical-thermal coupling model. When the processor runs the IES scheduler based on the SOFC electrochemical-thermal coupling model, it executes the steps described in the above embodiments, which will not be repeated here.

[0126] The above description is only a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural changes made based on the content of the present invention specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for IES scheduling based on a SOFC electrochemical-thermodynamic coupling model, characterized in that, The method comprises the following steps: Step S10, modeling the electrochemical process and the thermodynamic process of the cell units and the SOFC auxiliary equipment respectively, and obtaining a SOFC nonlinear output characteristic model to represent the relationship between the SOFC output electric power, the heat power and the working state; Step S20, establishing a SOFC nonlinear degradation cost model to count the asset loss caused by the degradation process into the cost based on the degradation effect of the SOFC under different working states; Step S30, constructing an ETC model according to the SOFC nonlinear output characteristic model and the SOFC nonlinear degradation cost model to comprehensively describe the operation and the degradation effect of the SOFC; Step S40, linearizing the ETC model by using a piecewise linearization method to facilitate the solution of the IES optimization scheduling problem; The step S10 comprises: Step S110, deriving the nonlinear relationship between the electric power and the hydrogen consumption rate and the operating temperature of the SOFC from a semi-empirical formula of the SOFC single cell output voltage; Step S120, deriving the nonlinear relationship between the heat power and the hydrogen consumption rate and the operating temperature of the SOFC; Step S130, taking into account the heat exchange action of the auxiliary equipment and the heat dissipation to the outside world, and using a heat transfer differential equation to describe the change of the SOFC operating temperature; In the step S110, the step of deriving the electric power of the SOFC from the semi-empirical formula of the SOFC single cell output voltage comprises: First, the output voltage of a single cell in SOFC is indirectly calculated by using semi-empirical formula The standard state voltage and the sum of several deviation voltages caused by various operating parameters deviating from the standard state to evaluate the actual output voltage V SOFC , assuming that the operating pressure of SOFC and the composition of positive and negative electrodes are controlled at the standard state, only considering the deviation voltage caused by the operating temperature deviating from the standard temperature Based on this assumption, in the proposed ETC model, the specific formula of the output voltage of a single cell in SOFC is simplified as formula (1): wherein, i SOFC is the current density of the SOFC; T SOFC is the actual operating temperature of the SOFC; is the standard operating temperature of the SOFC, which is 850°C; the current density of the SOFC is determined by the rate at which the SOFC consumes hydrogen gas, as in equation (2): wherein F is Faraday's constant, taken as 96485 C / mol; n SOFC is the hydrogen consumption rate of the SOFC, i.e., the amount of hydrogen that flows into the SOFC per unit time; is the fuel utilization of the SOFC; N SOFC is the number of cell units in the SOFC; A SOFC is the cross-sectional area of the SOFC; Finally, by combining formula (1) and formula (2), the expression of the SOFC output electric power can be obtained: P SOFC (n SOFC , T SOFC ) = N SOFC · V SOFC (n SOFC , T SOFC ) · I SOFC (n SOFC ) (3) Among them, P SOFC This refers to the output electrical power of the SOFC, which is related to the SOFC hydrogen consumption rate n. SOFC and the actual operating temperature T of SOFC SOFC A bivariate nonlinear function.

2. The IES scheduling method based on SOFC electro-thermodynamic coupling model according to claim 1, characterized in that, In the step S110, after the hydrogen energy is partially converted into electric energy, most of the remaining hydrogen energy is converted into usable heat energy, and the usable heat power generated simultaneously with the SOFC output electric power can be calculated by formula (4): wherein H SOFC is the thermal power generated by the SOFC, is a binary nonlinear function of the hydrogen consumption rate n SOFC and the actual operating temperature T SOFC of the SOFC; is the low calorific value of hydrogen; is the thermal energy utilization efficiency of the SOFC; the heat exchange process between the SOFC and the outside world is controlled by the organic Rankine cycle, thereby controlling the operating temperature of the SOFC; according to the heat transfer theorem, the SOFC temperature change can be described by formula (5): where C SOFC is the heat capacity of the SOFC; H SOFC re is the heat exchanged with the SOFC, H SOFC re > 0, the SOFC outputs heat power to the outside, H SOFC,re < 0, the SOFC absorbs heat power from the outside, H SOFC,re = 0, the SOFC does not exchange heat with the outside; H Loss is the dissipated heat power, satisfying H Loss = (T SOFC - T ext ) / R SOFC , T ext is the outside temperature; formula (5) can be discretized as: Where Δt is the scheduling step length.

3. The IES scheduling method based on SOFC electro-thermodynamic coupling model according to claim 2, characterized in that, The step S20 comprises: Step S210, deriving the degradation cost of the SOFC under different hydrogen consumption rates and temperatures from a SOFC output voltage degradation rate formula.

4. The IES scheduling method based on SOFC electro-thermodynamic coupling model according to claim 3, characterized in that, The step S210 comprises: The voltage decay rate is calculated by using a local degradation model, as shown in formula (7): where r SOFC,de is the voltage decay rate of the SOFC in 100% / kh; and further the degradation cost of the SOFC is obtained as in equation (8): where C SOFC,de is the degradation cost of SOFC, which can also be seen as a binary nonlinear function of SOFC hydrogen consumption rate n SOFC and actual operating temperature T SOFC of SOFC; r SOFC,p.u. is the minimum output voltage allowed for SOFC to operate normally; Cap SOFC is the one-time investment cost of SOFC equipment.

5. The IES scheduling method based on SOFC electro-thermodynamic coupling model according to claim 4, characterized in that, The step of linearizing the ETC model by using a piecewise linearization method in the step S40 comprises: In order to linearize the nonlinear operation characteristics of the SOFC, the feasible region of the SOFC operation is divided into K triangular sub-regions, and the nonlinear characteristics are approximated by linear characteristics in each sub-region; the specific formula is shown in formula (9): wherein, and are the linear coefficients of the approximated nonlinear characteristic of the output electrical power in the sub-domain k; and are the linear coefficients of the approximated nonlinear characteristic of the decay cost in the sub-domain k; the matrix A k and the vector b k are determined polyhedrons determines the sub-domain k; n SOFC , and T SOFC are the upper and lower limits of the hydrogen consumption rate and the operating temperature of the SOFC, respectively; they are further converted into mixed linear constraints for the need of optimization scheduling implementation, as in equation (10): wherein and x SOFC are auxiliary variables introduced; P SOFC , and C SOFC,de are the upper and lower limits of the SOFC output electric power and the upper and lower limits of the SOFC degradation cost, respectively; m is a vector of sufficiently large positive numbers for each component, used to relax the constraints of other sub-domains outside the sub-domain where the operating point lies. 6.The IES scheduling method based on SOFC electrochemical-thermodynamic coupling model of claim 1, wherein, The step of formulating the IES scheduling strategy in the step S40 comprises formulating a safe and economic SOFC operation strategy by the scheduling personnel of the IES.

7. An IES scheduling system based on SOFC electro-thermodynamic coupling model, characterized in that, The system comprises a memory, a processor, and an IES scheduling program based on a SOFC electrochemical-thermodynamic coupling model stored on the processor, and the IES scheduling program based on the SOFC electrochemical-thermodynamic coupling model performs the steps of the method according to any one of claims 1 to 6 when the IES scheduling program is run by the processor.

8. A computer-readable storage medium, characterized in that, The computer readable storage medium stores an SOFC electro-thermodynamic coupling model based IES scheduler, which, when executed by the processor, performs the steps of the method of any one of claims 1 to 6.

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