Two-stage robust optimization operation method for integrated energy system of electricity, hydrogen and heat

Abstract

The application discloses a two-stage robust optimization operation method of an electric hydrogen heat comprehensive energy system, relates to the field of comprehensive energy systems, and considers the recycling of heat in the process of an alkaline electrolysis hydrogen production system, so that the heat generated in the electric hydrogen production is recycled to a heat supply network through a heat exchanger, so as to improve energy utilization efficiency. The application constructs a two-stage robust optimization operation model of an electric hydrogen heat comprehensive energy system containing wind power, photovoltaic-hydrogen and a heat supply system, proposes a robust optimization model solving method based on a multi-affine decision rule, and improves the operation economy of the electric hydrogen heat comprehensive energy system.

Description

Technical Field

[0001] This invention relates to the field of integrated electric-hydrogen-thermal energy systems, specifically a two-stage robust optimization operation method for integrated electric-hydrogen-thermal energy systems. Background Technology

[0002] As human society places increasing emphasis on environmental protection, the proportion of clean and low-carbon hydrogen energy in the energy system is constantly increasing, leading to a continuous expansion of the scale of hydrogen electrolysis production plants. However, approximately 30% of the energy in the hydrogen electrolysis process is lost as heat. To maintain the stable operation of the hydrogen production system, active heat dissipation is usually required to remove waste heat. For large-scale hydrogen electrolysis production plants, waste heat recovery is an effective means to reduce the overall energy consumption of the system and improve overall economic efficiency. To address this, this patent integrates the active power distribution network, the hydrogen electrolysis production system, and the district heating network for coordinated operation, thereby enhancing the overall efficiency of the integrated electric / hydrogen / heat energy park. Furthermore, considering that the significant thermal inertia of the alkaline electrolysis system is the main reason for the slow start-up process of the electrolyzer, this chapter attempts to utilize the power of the heating network to improve the thermal dynamics of the hydrogen electrolysis production system. Therefore, this chapter proposes an operational model for the integrated electric / hydrogen / heat energy system that considers bidirectional heat exchange between the hydrogen production and heating networks, thereby improving the overall operational level and economic efficiency through bidirectional heat exchange between the heating network and the hydrogen production system.

[0003] Furthermore, the uncertainty of renewable energy output poses numerous challenges to the stable operation of power systems and hydrogen production systems. Fully considering the uncertainty of renewable energy output is an effective measure to enhance the operational reliability of integrated energy systems. Among various uncertainty optimization methods, robust optimization uses a set of scenarios to represent the uncertainty of variables, ensuring that constraints are met under all uncertainty scenarios and guaranteeing sufficient robustness of the system during the day-ahead scheduling phase. Therefore, this chapter addresses the day-ahead scheduling problem of electricity / hydrogen / thermal / integrated energy parks, constructing a day-ahead economic scheduling model for these parks based on two-stage robust optimization. Considering the conservative nature of conventional robust optimization scheduling results, a robust optimization solution strategy based on multi-affine robust decision rules is proposed to reduce the conservatism of the scheduling scheme.

[0004] Existing research on integrated energy systems combining electricity, hydrogen, and heat faces three main problems: 1) Few studies focus on waste heat recovery from electrolyzers used for district heating, and there is a lack of analysis on the dynamic interaction between the heating system and the electrogenerated hydrogen system. 2) Existing operational models for electrolytic hydrogen production systems are ill-suited to the bidirectional interaction between the hydrogen production and heating systems. 3) Traditional robust optimization methods result in a high degree of conservatism in the operation of integrated energy systems combining electricity, hydrogen, and heat. Therefore, these problems urgently need to be addressed. Summary of the Invention

[0005] The purpose of this invention is to provide a two-stage robust optimization operation method for an integrated electric-hydrogen-thermal energy system. By exchanging heat bidirectionally between the hydrogen production system and the heating system, the energy utilization efficiency and operational flexibility of the hydrogen production system are improved. Furthermore, a two-stage robust optimization operation method for an integrated electric-hydrogen-thermal energy system based on multiple affine decision rules is proposed, ensuring the robust and economical operation of the integrated electric-hydrogen-thermal energy system and solving the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A two-stage robust optimization operation method for an integrated electric-hydrogen-thermal energy system includes the following steps: ① Construct a multi-state operation model for the alkaline electrolysis hydrogen production system: The alkaline electrolyzer is divided into three states: off, standby, and production. In the off state, the temperature of the alkaline electrolyzer is below the minimum operating temperature, and the electrolysis power is zero. In the standby state, the temperature of the alkaline electrolyzer is maintained within the operating range, but the electrolysis power is below the minimum operating power. In the production state, the alkaline electrolyzer operates within the allowable temperature and power range. The transitions between different states include cold start, hot start, standby, and off. The cold start and production states are constructed as a new state. ; Figure 2 middle, The left side represents the cold start process, where power is limited by a starting coefficient. a 0(0< a 0<1), when the temperature rises to the operating range During this time, the alkaline electrolyzer will switch to production mode: (2-1) (2-2) (2-3) (2-4) (2-5) in, s 1,t , s 2,t , and Binary variables representing off, standby, and production states; T a Ambient temperature; and They are time t Electrolysis power and temperature at that time; P H This is the maximum power in standby mode; This is the scaling factor in production mode; Pmax Maximum operating power; ② Modeling of bidirectional heat exchange between alkaline electrolytic cells and heating networks; The direction of heat transfer is controlled by two valves, denoted as follows: k v1 and k v2 ,when k v1 Open and k v2 When shut down, the heat from the alkaline electrolyzer is transferred to the return water of the heating network. k v1 Close and k v2 When turned on, high-temperature water flows into the heat exchanger to heat the electrolyte. Heat is flexibly exchanged between the alkaline electrolytic cell and the heating network, as shown in the following formula: (2-6) (2-7) in, The heat transferred from the alkaline electrolyzer to the heating network, and A binary variable representing the switching state of two valves; The alkaline electrolysis system model is constructed as follows: (2-8) (2-9) (2-10) (2-11) in, The power consumed by each unit, N c For the number of units, k a , k b , k c These are the approximation coefficients of the electrolysis linear model. This refers to the current in an alkaline electrolytic cell. A m For membrane area, Hydrogen production, Δ t For time intervals, F It is Faraday's constant. z The number of electrons transferred; The power consumption of an alkaline electrolyzer includes the power consumption of the electrolyzer and the power consumption of the electrolysis auxiliary system: (2-12) (2-13) in, This indicates the power consumed by the electrolysis auxiliary system, including the circulating pump, temperature control, and gas purification system; This represents the total power consumption of the alkaline electrolytic cell system. For heat dissipation power, γ BoP It is a scaling factor; The heat and temperature constraints of the alkaline electrolytic cell system are as follows: (2-14) (2-15) (2-16) (2-17) (2-18) in, The heat generated during hydrogen production. u tn The neutral voltage for electrolytic water electrolysis. C EL and R EL These are the heat capacity and resistance of the electrolytic cell, respectively. This represents the maximum heat dissipation of the alkaline electrolytic cell system. and These are the supply and return water temperatures of the heating network nodes connected to the heat exchanger, respectively. Constructing a power system model: The operating constraints of the combined heat and power (CHP) unit are modeled as follows: (2-19) (2-20) (2-21) in, and These represent the electrical power and thermal power of the combined heat and power unit, respectively. a CHP , b CHP and d CHP A vector describing the feasible region of electrical and thermal energy output of a combined heat and power (CHP) unit. This is a binary variable indicating the start-up and shutdown status of the combined heat and power unit. Natural gas consumption rate ηCHP To improve conversion efficiency, L NG Due to the low calorific value of natural gas, For the reactive power of combined heat and power units, λ CHP for and The proportionality coefficient between them; The power flow and node voltage of the distribution network are modeled based on the linear DistFlow model as follows: (2-22) (2-23) (2-24) (2-25) (2-26) (2-27) in, P jk,t and Q jk,t They are time t Always passing through the line jk Active power and reactive power, δ ( j ) for nodes j The set of endpoints of the connected branches. and They are time t The active and reactive power of renewable energy at any given time. and These are active and reactive loads, respectively. r ij and x ij The lines are respectively ij Resistance and reactance, V j,t For nodes j The square value of the voltage, To connect to the node j The maximum active power of renewable energy units, and They are nodes j The minimum and maximum reactive power of renewable energy sources, V min and V max These are the minimum and maximum values ​​of the square of the voltage, respectively; The district heating system model is constructed as follows: (2-28) (2-29) (2-30) (2-31) (2-32) (2-33) (2-34) (2-35) (2-36) (2-37) in, C h and C c These represent the heat capacities of the high-temperature and low-temperature sides of the heat exchanger, respectively. For the actual heat capacity, and These are the input temperatures of the mass flow on the high-temperature side and the low-temperature side, respectively. H max For maximum heat exchange power, η HE The heat exchange efficiency parameter is used to determine the actual amount of heat transferred between the high-temperature and low-temperature sides of the heat exchanger. m t,b and m t,n Representing branch roads b and nodes n mass flow rate A DHN It is an incidence matrix. T t,b,start and T t,b,end Representing branch roads b Temperature at the starting and ending points, γ loss The temperature drop coefficient per unit distance. L b branch road b Length, m t,j branch road j mass flow rate T t,i For nodes i temperature, T t,j,end branch road j The temperature at the end, and They are nodes i Temperature in the supply and return water networks, H t,i For nodes i heat load, m min and m max for m b The lower and upper bounds, 、 、 、 and The upper and lower temperature limits for the supply and return water networks.

[0007] As a further aspect of the present invention, it also includes constructing an operational model for the integrated electric-hydrogen-thermal energy system in two phases: day-ahead and intraday. ① Construct a day-ahead operation model for an integrated energy system combining electricity, hydrogen, and heat. The objective function for constructing an integrated electric-hydrogen-thermal energy system is shown below: (2-38) in, and These represent the electricity purchased from and sold to the upstream power grid, λ. NG , , , λ H2 These represent the price coefficients for natural gas, electricity purchase, electricity sale, and hydrogen, respectively. The objective function includes the operating cost of the combined heat and power unit, the cost of purchasing electricity from the upstream grid, the revenue from selling electricity to the upstream grid, and the revenue from selling hydrogen. Recent decisions include the operating status, electrolysis power, electrolysis current, heat dissipation power, and temperature of alkaline electrolyzers; the operating status and heat transfer power of heat exchangers; the status, electrical power, and thermal power of combined heat and power units; electricity purchased or sold from the upstream grid; the active and reactive power of renewable energy units; and the line flow and node voltage of the active distribution network. x Denotes the current-day decision variable, where time... t The day-ahead decision variables are shown below: (2-39) The current running model is represented in the following compact form: (2-40) (2-41) in,A , a , c These are coefficients derived from the model described above; ② Construct an intraday operation model for an integrated electric-hydrogen-thermal energy system The intraday objective function for constructing the integrated electric-hydrogen-thermal energy system is shown below: (2-42) in (2-43) (2-44) (2-45) (2-46) in, This is an adjustment amount for the upstream power grid's electricity purchase and sale costs. The adjustment amount for the operating cost of combined heat and power units. This is an adjustment amount for the cost of wind and solar power curtailment. Adjustment amount for revenue from hydrogen sales during the day. λ CUR The price coefficient representing the cost of wind and solar power curtailment. and These represent the upward and downward adjustments to the upstream power grid, respectively. The adjustment amount for the electrical power of the combined heat and power unit. and ξ r,t Renewable energy units for the day r The change in output and the deviation of the actual output from the typical output. R For the number of renewable energy units, This is the adjustment amount of the electrolysis current; The constraints for intraday trading are as follows: (2-47) (2-48) (2-49) (2-50) (2-51) (2-52) (2-53) (2-54) (2-55) (2-56) (2-57) (2-58) (2-59) (2-60) (2-61) in, and These are the temperature and power adjustment amounts for the alkaline electrolytic cell, respectively. This represents the change in heat dissipation power of the alkaline electrolytic cell. This refers to the heat exchange capacity during the day. and These represent the maximum electricity purchased from and sold from the upstream power grid, respectively. For nodes j Reactive power of renewable energy units V t,i,R Node voltage; make y Let the matrix be composed of intraday decision variables, then at any time during the day t Decision vector y t Its composition is as follows: (2-62) The issues encountered during the day can be summarized as follows: (2-63) (2-64) in, B , C , D , b and d The coefficient matrix or vector obtained from the above constraints, U To describe the output deviation of renewable energy ξ An uncertain set; ③ Construct a two-stage robust optimization model for an integrated electric-hydrogen-thermal energy system The daily operation involves determining the operating status, electrical or thermal power of the alkaline electrolyzer, cogeneration unit, and heat exchanger, as well as the electricity purchased or sold from the upstream grid. Based on the daily changes in renewable energy output relative to the typical output curve, the power of the alkaline electrolyzer, cogeneration unit, and heat exchanger, as well as the power from the upstream grid, is adjusted to follow the changes in renewable energy output. The compact form of the two-stage robust optimization problem is as follows: (2-65) Constructing an uncertain set First, the renewable energy output samples are divided into multiple sets using the multivariate time series K-means clustering method. This method establishes the sets iteratively, and at the 1st... n In this iteration, the clustering iterative update is as follows: (2-66) in, c n,i It is the first n In the next iteration, the set i The center point, S n,i It is the first n In the next iteration, it belongs to the set i The sample set, ξ z Indicates the first z Let Ξ be the time series sample of renewable energy output, where Ξ is the sample set. Z The number of days in the sample data is used to calculate the cluster center using the following formula: (2-67) in, n i It is a set i The number of samples in the cluster is updated by iteratively solving equations (2-66) and (2-67) until the cluster set no longer changes; Then, for each cluster set, a subset of uncertainty is constructed using the polyhedral uncertainty set: (2-68) Ultimately, the uncertain set is constructed as the union of multiple uncertain subsets: (2-69); ④ Constructing a two-stage robust optimization operation problem-solving method for an integrated electro-hydrogen-thermal energy system based on multiple affine decision rules Based on the uncertainty set (2-69), the proposed two-stage robust optimization problem (2-65) is remodeled as follows: (2-70) Satisfying constraint (2-41) and: (2-71) (2-72) Second-stage decision variables y They are divided into two categories. The first category directly substitutes the random variable using an affine function, including { , , , , , , The second type is represented by linear functions of the first type of variables and random variables, including the remaining decision variables in the second stage. The affine model of the two types of variables is constructed as follows: For the first type of intraday decision variables: (2-73) (2-74) (2-75) (2-76) (2-77) For the second type of intraday decision variables (2-78) (2-79) (2-80) (2-81) in, W and w The coefficients of the linear and constant terms of the affine decision rule for the intraday decision variables are now presented as affine functions for all decision variables in the second stage. (2-82) in, M i and m i They are subsets U i The affine coefficient matrix and vector are obtained by replacing them with equation (2-82). y Then problem (2-70) becomes: (2-83) st (2-41) (2-84) Then, the robust constraint (2-84) is reconstructed through duality theory as (2-85)-(2-87): (2-85) (2-86) (2-87) in, μ 1,i It is a dual variable matrix; The inner-layer maximization problem of (2-83) is transformed into a minimization problem using duality theory: (2-88) st (2-89) (2-90) in, μ 2,i is the dual variable vector of the inner maximization problem; therefore, problem (2-83)-(2-84) is represented as: (2-91) st (2-41), (2-85)-(2-87), (2-89)-(2-90) Problem (2-91) is transformed into (2-92) and solved using a mixed-integer linear programming solver; (2-92) st (2-93) (2-41), (2-85)-(2-87), (2-89)-(2-90) in, Θ bv is the dual auxiliary variable.

[0008] The beneficial effects of this invention are as follows: the method of this invention improves the energy utilization efficiency and the operational flexibility of the hydrogen production system by bidirectional heat exchange between the hydrogen production system and the heating system, and proposes a two-stage robust optimization operation method for the integrated electric-hydrogen-thermal energy system based on multiple affine decision rules, which ensures the robust and economical operation of the integrated electric-hydrogen-thermal energy system. Attached Figure Description

[0009] Figure 1 This is the energy flow diagram of the integrated electro-hydrogen-thermal energy system proposed in this embodiment of the invention.

[0010] Figure 2 This is the operating state model of the alkaline electrolyzer proposed in the embodiments of the present invention.

[0011] Figure 3 This is a schematic diagram of the heat exchange between the alkaline electrolytic cell and the heating network proposed in this embodiment of the invention.

[0012] Figure 4 This is a schematic diagram of the integrated energy system of electricity, hydrogen, and heat in an embodiment of the present invention.

[0013] Figure 5 This is a schematic diagram of typical wind power and photovoltaic power output and electrical and thermal load curves in an embodiment of the present invention.

[0014] Figure 6 This is a comparison diagram of the operating status of the alkaline electrolyzer under unidirectional and bidirectional heat exchange modes in an embodiment of the present invention.

[0015] Figure 7 This is a diagram showing the temperature ratio of the alkaline electrolytic cell and the supply and return water temperatures of the heating network under unidirectional and bidirectional heat exchange modes in embodiments of the present invention. Detailed Implementation

[0016] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0017] In this embodiment of the invention, ① considering the operation mode of the integrated electro-hydrogen-thermal energy system with bidirectional heat exchange between the hydrogen production system and the heating system, the following integrated electro-hydrogen-thermal energy system is constructed based on the following two considerations: 1) The alkaline electrolysis temperature is approximately 90°C, which is typically higher than the return water temperature of the heating network; 2) The feed water temperature range of the heating network is 80-110°C, therefore the feed water can be used to heat the electrolyte at a lower temperature. Therefore, the temperature difference between the electrolysis system and the heating network allows for spontaneous heat exchange between the electrolyte and the heating feed water or return water. Thus, the waste heat from hydrogen electrolysis can be recovered for district heating, and the heat from the heating network can also be used to accelerate the thermal dynamics of the alkaline electrolyzer.

[0018] Please see Figure 1 In this system, hydrogen electrolysis serves as the coupling link between the electricity, hydrogen, and heat subsystems, and the hydrogen production power is determined based on electricity prices, electricity load, and hydrogen energy prices. The heat exchange direction and power between the hydrogen production system and the heating network are determined based on operational requirements. Therefore, energy coupling and the uncertainty of renewable energy are transmitted through energy coupling within the integrated energy system.

[0019] Considering that the alkaline electrolyzer operates continuously during cold start-up, this paper constructs the cold start-up and production states as a new state. Please see. Figure 2 , The left side represents the cold start process, where power is limited by a starting coefficient. a 0(0< a 0 < 1). When the temperature rises to the operating range [ T min , T max During this period, the alkaline electrolytic cell will switch to production mode, such as... The right side is shown. Therefore, the state of the alkaline electrolyzer is modeled as follows: (2-94) (2-95) (2-96) (2-97) (2-98) in, s 1,t , s 2,t , and Binary variables representing off, standby, and production states; T a Ambient temperature; and They are time t Electrolysis power and temperature at that time; P H This is the maximum power in standby mode; This is the scaling factor in production mode; P max This is the maximum operating power.

[0020] Please see Figure 3 To improve the operational flexibility of alkaline electrolyzers, which are limited by significant thermal inertia, a bidirectional heat exchange operation scheme between the alkaline electrolyzer and the heating network is proposed, such as... Figure 3 As shown. The direction of heat transfer is controlled by two valves, denoted as follows: k v1 and k v2 .when k v1 Open and k v2 When shut down, the heat from the alkaline electrolyzer is transferred to the return water of the heating network. When kv1 Close and k v2 When turned on, hot water flows into the heat exchanger to heat the electrolyte. In this way, heat can be flexibly exchanged between the alkaline electrolyzer and the heating network, as shown in the following formula: (2-99) (2-100) in, The heat transferred from the alkaline electrolyzer to the heating network, and This is a binary variable representing the switching state of two valves.

[0021] ② The realization of the coupled operation of the described electro-hydrogen-thermal integrated energy system relies on modeling the equipment in the hydrogen production system, thermal system, and power system. The hydrogen production system consists of an alkaline electrolyzer, and the thermal system mainly includes a thermal network and heat exchangers. Dynamic modeling of the power system includes the power network and combined heat and power (CHP) units.

[0022] The alkaline electrolysis hydrogen production system is modeled as follows: The relationship between the power consumption of the electrolyzer and the hydrogen production is modeled as follows: (2-101) (2-102) (2-103) (2-104) in, The power consumed by each unit, N c For the number of units, k a , k b , k c These are the approximation coefficients of the electrolysis linear model. This refers to the current in an alkaline electrolytic cell. A m For membrane area, For hydrogen production, Δ t For time intervals, F It is Faraday's constant. z The number of electrons transferred.

[0023] The operational constraints of the combined heat and power system are modeled as follows: (2-105) (2-106) (2-107) in, and These represent electrical power and thermal power, respectively. a CHP , b CHP and d CHP A vector describing the feasible region of electrical and thermal energy output of a combined heat and power (CHP) unit. This is a binary variable indicating the start-up and shutdown status of the combined heat and power unit. The consumption rate of natural gas. η CHP To improve conversion efficiency, L NG Due to the low calorific value of natural gas, For the reactive power of combined heat and power units, λ CHP for and The proportional coefficient between them.

[0024] The power flow and node voltage of the distribution network are modeled based on the linear DistFlow model: (2-108) (2-109) (2-110) (2-111) (2-112) (2-113) in, P jk,t and Q jk,t They are time t Always passing through the line jk Active power and reactive power, δ ( j ) for nodes j The set of endpoints of the connected branches. and They are time t The active and reactive power of renewable energy at any given time. and These are active and reactive loads, respectively. r ij and x ij The lines are respectivelyij Resistance and reactance, V j,t For nodes j The square value of the voltage, To connect to the node j The maximum active power of renewable energy units, and They are nodes j The minimum and maximum reactive power of renewable energy sources, V min and V max These represent the minimum and maximum values ​​of the squared voltage, respectively.

[0025] The heat exchanger model is shown below: (2-114) (2-115) (2-116) in, C h and C c These represent the heat capacities of the high-temperature and low-temperature sides of the heat exchanger, respectively. For the actual heat capacity, and These are the input temperatures of the mass flow on the high-temperature side and the low-temperature side, respectively. H max For maximum heat exchange power, η HE This refers to the heat exchange efficiency parameter.

[0026] The heating network is modeled as follows: (2-117) (2-118) (2-119) (2-120) (2-121) (2-122) (2-123) in, m t,b and m t,n Representing branches b and nodes n mass flow rate ADHN It is an incidence matrix. T t,b,start and T t,b,end Representing branches b Temperature at the starting and ending points, γ loss The temperature drop coefficient per unit distance. L b branch road b Length, m t,j branch road j mass flow rate T t,i For nodes i temperature, T t,j,end branch road j The temperature at the end, and They are nodes i Temperature in the supply and return water networks, H t,i For nodes i heat load, m min and m max for m b The lower and upper bounds, 、 、 、 and The upper and lower temperature limits for the supply and return water networks.

[0027] ③ The realization of the two-stage robust optimization operation model of the integrated electric-hydrogen-thermal energy system depends on the construction of the day-ahead and day-ahead operation models.

[0028] Based on typical output curves of renewable energy sources, day-ahead operation aims to minimize the operating costs of an integrated electricity-hydrogen-thermal energy system. The objective function is constructed as follows: (2-124) in, and These represent the electricity purchased from and sold to the upstream power grid, λ. NG , , , λ H2These represent the price coefficients for natural gas, electricity purchase, electricity sale, and hydrogen, respectively. The objective function includes the operating cost of the combined heat and power (CHP) unit, the cost of purchasing electricity from the upstream grid, the revenue from selling electricity to the upstream grid, and the revenue from selling hydrogen. It is assumed that all produced hydrogen is sold; therefore, the revenue from hydrogen sales is proportional to the amount of hydrogen produced.

[0029] Recent decisions include the operating status, electrolysis power, electrolysis current, heat dissipation power, and temperature of alkaline electrolyzers; the operating status and heat transfer power of heat exchangers; the status, electrical power, and thermal power of combined heat and power units; electricity purchased or sold from the upstream grid; the active and reactive power of renewable energy units; and the line flow and node voltage of the active distribution network. x Denotes the current-day decision variable, where time... t The day-ahead decision variables are shown below: (2-125) The current running model is represented in the following compact form: (2-126) (2-127) in, A , a , c These are the coefficients derived from the model described above; During intraday operation, adjustments are made to the power and heat output of alkaline electrolyzers and combined heat and power (CHP) units, the heat passing through heat exchangers, and the power from or transmitted to the upstream grid to address changes in renewable energy output. Intraday operation is based on the plan established during day-ahead operation, and its objective is to minimize rescheduling costs under the worst-case scenario. The intraday operation objective function is constructed as follows: (2-128) in (2-129) (2-130) (2-131) (2-132) in, This is an adjustment amount for the upstream power grid's electricity purchase and sale costs. The adjustment amount for the operating cost of combined heat and power units. This is an adjustment amount for the cost of wind and solar power curtailment. Adjustment amount for revenue from hydrogen sales during the day. λ CUR The price coefficient representing the cost of wind and solar power curtailment. and These represent the upward and downward adjustments to the upstream power grid, respectively. The adjustment amount for the electrical power of the combined heat and power unit. and ξ r,t Renewable energy units for the day r The change in output and the deviation of the actual output from the typical output. R For the number of renewable energy units, This is the adjustment amount of the electrolysis current.

[0030] The constraints for intraday trading are as follows: (2-133) (2-134) (2-135) (2-136) (2-137) (2-138) (2-139) (2-140) (2-141) (2-142) (2-143) (2-144) (2-145) (2-146) (2-147) in, and These are the temperature and power adjustment amounts for the alkaline electrolytic cell, respectively. This represents the change in heat dissipation power of the alkaline electrolytic cell. This refers to the heat exchange capacity during the day. and These represent the maximum electricity purchased from and sold from the upstream power grid, respectively. For nodes j Reactive power of renewable energy units V t,i,R This represents the node voltage.

[0031] make y Let the matrix be composed of intraday decision variables, then at any time during the day t Decision vector y t Its composition is as follows: (2-148) Since (2-128)-(2-147) is a linear model, the intraday operational issues can be summarized as follows: (2-149) (2-150) in, B , C , D , b and d Let (2-128)-(2-147) be the coefficient matrix or vector obtained from (2-128)-(2-147). U To describe the output deviation of renewable energy ξ An uncertain set.

[0032] Ultimately, the day-ahead and intraday coordinated operation problem was established as a two-stage robust optimization problem. Day-ahead scheduling determines the operating status, electrical or thermal power, and electricity purchased or sold from the upstream grid of the alkaline electrolyzer, cogeneration unit, and heat exchanger. Intraday operation adjusts the power of the alkaline electrolyzer, cogeneration unit, and heat exchanger, as well as the power from the upstream grid, based on changes in renewable energy output relative to the typical output curve, to follow changes in renewable energy output. The compact form of the two-stage robust optimization problem is as follows: (2-151) ④ A two-stage robust optimization solution method based on multiple affine decision rules The decision variables for the second stage are constructed as random variables. ξ The affine function and affine decision rules can effectively solve tunable robust optimization problems and provide real-time adjustment strategies for intraday operations. The affine decision rules are as follows: (2-152) in, y 0 is a constant matrix. Y Let be the coefficient matrix of the first-order terms. Then the two-stage robust optimization problem (2-151) is transformed into: (2-153) Equation (2-153) is referred to as the Single Affine Decision Rule (SADR). Since the SADR does not flexibly adjust to different uncertainty scenarios, it may lead to a conservative scheduling strategy. To reduce the conservatism of the SADR, this paper proposes the Multi-Affine Decision Rule (MADR) to provide different decision rules under different uncertainty scenarios. Assume the uncertainty set... U From subset U 1, U 2,…, U N Composition. For any uncertain subset U i The decision variables for the second stage can be represented as: (2-154) in, y i,0 and Y i It is an indeterminate subset U i The affine coefficients.

[0033] Next, problem (2-153) is transformed into (2-155) First, the renewable energy output samples are divided into multiple sets using the multivariate time series K-means clustering method, which builds the sets iteratively. In the... n In this iteration, the clustering iterative update is as follows: (2-156) in, c n,i It is the first n In the next iteration, the set i The center point, S n,i It is the first n In the next iteration, it belongs to the set i The sample set, ξ z Indicates the first z Let Ξ be the time series sample of renewable energy output, where Ξ is the sample set. Z This refers to the number of days in the sample data. Cluster centers are calculated using the following formula: (2-157) in, n i It is a set iThe number of samples in the cluster is determined. The clustering results are updated by iteratively solving equations (2-156) and (2-157) until the cluster sets no longer change.

[0034] Then, for each cluster set, a subset of uncertainty is constructed using the polyhedral uncertainty set: (2-158) Ultimately, the uncertain set is constructed as the union of multiple uncertain subsets: (2-159) Based on the uncertainty set (2-159), the proposed two-stage robust optimization problem (2-151) can be remodeled as follows: (2-160) Constraint (2-127) must be satisfied, and: (2-161) (2-162) To solve problem (2-160) using multiple affine decision rules, the decision variables for the second stage are... y They are divided into two categories. The first category can be directly replaced by the affine function of the random variable, including { , , , , , , The second type can be represented as a linear function of the first type of variables and random variables, including the remaining decision variables in the second stage. The affine model for the two types of variables is constructed as follows: For the first type of intraday decision variables: (2-163) (2-164) (2-165) (2-166) (2-167) For the second type of intraday decision variables (2-168) (2-169) (2-170) (2-171) in, W and w These are the coefficients of the linear and constant terms of the affine decision rule for the intraday decision variables. At this point, all decision variables in the second stage are presented in the form of affine functions: (2-172) in, M i and m i They are subsets U i The affine coefficient matrix and vector. By replacing with equation (2-172) y Then problem (2-160) becomes: (2-173) st (2-127) (2-174) Then, the robust constraint (2-174) is reconstructed through duality theory as (2-175)-(2-177): (2-175) (2-176) (2-177) in, μ 1,i It is a dual variable matrix.

[0035] The inner-layer maximization problem of (2-173) is transformed into a minimization problem using duality theory: (2-178) st (2-179) (2-180) in, μ 2,i is the dual variable vector of the inner maximization problem. Therefore, problem (2-173)-(2-174) is represented as: (2-181) st (2-127),(2-175)-(2-177),(2-179)-(2-180) Finally, problem (2-181) is transformed into (2-182) and solved by a mixed-integer linear programming solver.

[0036] (2-182) st (2-183) (2-127),(2-175)-(2-177),(2-179)-(2-180) in, Θ It is a dual auxiliary variable.

[0037] As a further embodiment of the present invention, please refer to Figure 4 and Figure 5 This embodiment involves renewable energy electrolysis to produce hydrogen and recovering waste heat from a heat exchanger for heating. The basic parameters of the electrolyzer and system operation in the integrated electro-hydrogen-thermal energy system are shown in Tables 1 and 2: Table 1 Parameters of the Electrolysis Hydrogen Production System The power system parameters in the model are set as shown in the table below: Table 2 Parameters of the Integrated Electric-Hydrogen-Heat Energy System Figure 6 The diagram illustrates the operation of an alkaline electrolyzer under unidirectional and bidirectional heat exchange modes. In unidirectional heat exchange mode, the alkaline electrolyzer remains shut down for the first two hours due to its slower start-up speed. Conversely, in bidirectional heat exchange mode, the alkaline electrolyzer starts up rapidly using heat from the heating network. Between 10:00-11:00 and 18:00-19:00, due to insufficient renewable energy output, the alkaline electrolyzer in bidirectional heat exchange mode is shut down, while the alkaline electrolyzer in unidirectional heat exchange mode remains in standby mode to facilitate subsequent hydrogen production. This increases the operating costs of the alkaline electrolyzer.

[0038] Figure 7 The display shows the temperature of the alkaline electrolyzer and the associated supply and return water temperatures in the heating network. Heat dissipation represents the transfer of heat from the alkaline electrolyzer to the heating network, while heat absorption represents the reverse direction. In bidirectional heat exchange mode, the alkaline electrolyzer temperature fluctuates more significantly, indicating a faster temperature adjustment rate. After the initial start-up phase, the temperature range in bidirectional heat exchange mode is between 30°C and 90°C, while the temperature range in unidirectional heat exchange mode is between 60°C and 90°C. Therefore, more waste heat is recovered in bidirectional heat exchange mode.

[0039] Table 3 shows the operating costs of the integrated electric-hydrogen-thermal energy system under unidirectional and bidirectional heat exchange modes. In the unidirectional heat exchange mode, the largest portion of the cogeneration unit's cost is borne by district heating. Simultaneously, the cogeneration unit generates more electricity to meet electricity and heat constraints. Therefore, the cost of purchasing electricity from the upstream grid is lower under the unidirectional heat exchange mode. In the bidirectional heat exchange mode, more hydrogen is produced due to increased flexibility. At the same time, the recovered heat increases, thereby reducing district heating costs. Overall, the proposed operating model reduces the operating cost of the integrated electric-hydrogen-thermal energy system by approximately 6%.

[0040] Table 3 Comparison of operating costs between unidirectional and bidirectional heat exchange (¥) To verify the effectiveness of the proposed multi-affine decision rule method, out-of-sample tests were conducted to compare the multi-affine decision rule with traditional single-affine decision rules and deterministic optimization. Test samples were obtained through normal distribution sampling. Simultaneously, 2-10 affine decision rules were set to evaluate the impact of the number of affine decision rules on the total net cost, reliability, and computation time of robust optimization. The out-of-sample test results are shown in Table 4. The penalty cost is the incremental cost of purchasing electricity from the upstream grid within a day. Since a higher penalty cost implies lower robustness of the dispatch scheme, this item can be used to reflect the reliability of the robust optimization scheme.

[0041] According to Table 4, deterministic optimization has the highest total net cost and penalty cost among the three methods, but the shortest computation time. This is because deterministic optimization does not address changes in renewable energy output, resulting in the highest adjustment cost during intraday operation and the lowest computational burden. Compared to single affine decision rules, multi-affine decision rules provide more targeted affine decision rules through uncertainty set clustering, thereby reducing total net cost and penalty cost. Compared to deterministic optimization and single affine decision rules, multi-affine-10 reduces total net cost by approximately 17.9% and 9.7%, and penalty cost by approximately 96.5% and 93.6%, respectively. This indicates that finer partitioning of the uncertainty set effectively reduces operating costs and improves robustness. However, as the number of sets increases, the reduction in penalty cost and total net cost gradually slows down, while computation time increases significantly. Among all multi-affine decision rules, multi-affine-5 strikes a good balance between total net cost and computation time. Therefore, subsequent analyses are based on multi-affine-5.

[0042] Table 4 Comparison of operating costs and computation time under different methods Note: In multiple affine-n, n represents the number of affine decision rules.

[0043] Table 5 presents the out-of-sample operating costs for deterministic optimization, single affine decision rules, and multi-affine-5. Multi-affine provides similar day-ahead costs compared to single affine decision rules. During the intraday phase, multi-affine has lower average and worst-case costs because it provides multiple affine decision rules for different realizations of renewable energy output. The total net cost of multi-affine is 4.6% and 4.9% lower than that of single affine decision rules in the average and worst-case scenarios, respectively. Furthermore, the standard deviation of multi-affine costs is also smaller, indicating a more reliable scheduling strategy.

[0044] Table 5 Comparison of Out-of-Sample Test Operating Costs (¥) Among the above simulation methods, the one that is original to this invention, has never been disclosed, and whose working method is different from any existing literature is as follows: This invention improves the energy utilization level and the operational flexibility of the hydrogen production system by establishing a bidirectional heat exchange operation mode for the electric hydrogen production and heating system. Furthermore, considering the fluctuation of renewable energy output, a two-stage robust optimization operation method for the integrated electric-hydrogen-thermal energy system is constructed, and multiple affine decision rules are proposed for solving the problem, thereby reducing the conservatism of the robust optimization method.

[0045] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0046] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A two-stage robust optimization operation method for an integrated electric-hydrogen-thermal energy system, characterized in that, Includes the following steps: ① Construct a multi-state operation model for an alkaline electrolysis hydrogen production system: Divide the state of the alkaline electrolyzer into a shut-off state, a standby state, and a production state. In the shut-off state, the temperature of the alkaline electrolyzer is lower than the minimum operating temperature, and the electrolysis power is zero. In standby mode, the temperature of the alkaline electrolyzer is maintained within the operating range, but the electrolysis power is lower than the minimum operating power. In production mode, the alkaline electrolyzer operates within the allowable temperature and power range. The transitions between different states include cold start, hot start, standby, and shutdown, and the cold start and production states are combined into a new state. ; When the temperature rises to the operating range During this time, the alkaline electrolyzer will switch to production mode: (1-1) (1-2) (1-3) (1-4) (1-5) in, s 1,t , s 2,t , and Binary variables representing off, standby, and production states; T a The ambient temperature; and They are time t Electrolysis power and temperature at that time; P H This is the maximum power in standby mode; This is the scaling factor in production mode; P max For maximum operating power, a 0 represents the starting coefficient; ② Modeling of bidirectional heat exchange between alkaline electrolytic cells and heating networks; The direction of heat transfer is controlled by two valves, denoted as follows: k v1 and k v2 ,when k v1 Open and k v2 When shut down, the heat from the alkaline electrolyzer is transferred to the return water of the heating network. k v1 Close and k v2 When turned on, high-temperature water flows into the heat exchanger to heat the electrolyte. Heat is flexibly exchanged between the alkaline electrolytic cell and the heating network, as shown in the following formula: (1-6) (1-7) in, The heat transferred from the alkaline electrolyzer to the heating network, and A binary variable representing the switching state of two valves; The alkaline electrolysis system model is constructed as follows: (1-8) (1-9) (1-10) (1-11) in, The power consumed by each unit, N c For the number of units, k a , k b , k c These are the approximation coefficients of the electrolysis linear model. This refers to the current in an alkaline electrolytic cell. A m For membrane area, For hydrogen production, Δ t For time intervals, F It is Faraday's constant. z The number of electrons transferred; The power consumption of an alkaline electrolyzer includes the power consumption of the electrolyzer and the power consumption of the electrolysis auxiliary system: (1-12) (1-13) in, This indicates the power consumed by the electrolysis auxiliary system, including the circulating pump, temperature control, and gas purification system; This represents the total power consumption of the alkaline electrolytic cell system. For heat dissipation power, γ BoP It is a scaling factor; The heat and temperature constraints of the alkaline electrolytic cell system are as follows: (1-14) (1-15) (1-16) (1-17) (1-18) in, The heat generated during hydrogen production. u tn The neutral voltage for electrolytic water electrolysis. C EL and R EL These are the heat capacity and resistance of the electrolytic cell, respectively. This represents the maximum heat dissipation of the alkaline electrolytic cell system. and These are the supply and return water temperatures of the heating network nodes connected to the heat exchanger, respectively. Constructing a power system model: The operating constraints of the combined heat and power (CHP) unit are modeled as follows: (1-19) (1-20) (1-21) in, and These represent the electrical power and thermal power of the combined heat and power unit, respectively. a CHP , b CHP and d CHP A vector describing the feasible region of electrical and thermal energy output of a combined heat and power (CHP) unit. This is a binary variable indicating the start-up and shutdown status of the combined heat and power unit. The consumption rate of natural gas. η CHP To improve conversion efficiency, L NG Due to the low calorific value of natural gas, For the reactive power of combined heat and power units, λ CHP for and The proportionality coefficient between them; The power flow and node voltage of the distribution network are modeled based on the linear DistFlow model as follows: (1-22) (1-23) (1-24) (1-25) (1-26) (1-27) in, P jk,t and Q jk,t They are time t Always passing through the line jk Active power and reactive power, δ ( j ) for nodes j The set of endpoints of the connected branches. and They are time t The active and reactive power of renewable energy at any given time. and These are active and reactive loads, respectively. r ij and x ij The lines are respectively ij Resistance and reactance, V j,t For nodes j The square value of the voltage, To connect to the node j The maximum active power of renewable energy units, and They are nodes j The minimum and maximum reactive power of renewable energy sources, V min and V max These are the minimum and maximum values ​​of the square of the voltage, respectively; The district heating system model is constructed as follows: (1-28) (1-29) (1-30) (1-31) (1-32) (1-33) (1-34) (1-35) (1-36) (1-37) in, C h and C c These represent the heat capacities of the high-temperature and low-temperature sides of the heat exchanger, respectively. For the actual heat capacity, and These are the input temperatures of the mass flow on the high-temperature side and the low-temperature side, respectively. H max For maximum heat exchange power, η HE The heat exchange efficiency parameter is used to determine the actual amount of heat transferred between the high-temperature and low-temperature sides of the heat exchanger. m t,b and m t,n Representing branches b and nodes n mass flow rate A DHN It is an incidence matrix. T t,b,start and T t,b,end Representing branches b Temperature at the starting and ending points, γ loss The temperature drop coefficient per unit distance. L b branch road b Length, m t,j branch road j mass flow rate T t,i For nodes i temperature, T t,j,end branch road j The temperature at the end, ,and They are nodes i Temperature in the supply and return water networks, H t,i For nodes i heat load, m min and m max for m b The lower and upper bounds, , , ,and The upper and lower temperature limits for the supply and return water networks.

2. The two-stage robust optimization operation method for the integrated electro-hydrogen-thermal energy system according to claim 1, characterized in that, It also includes the construction of an operational model for the integrated electric-hydrogen-thermal energy system in two phases: day-ahead and intraday. ① Construct a day-ahead operation model for an integrated energy system combining electricity, hydrogen, and heat. The objective function for constructing an integrated electric-hydrogen-thermal energy system is shown below: (1-38) in, and These represent the electricity purchased from and sold to the upstream power grid, λ. NG , , , λ H2 These represent the price coefficients for natural gas, electricity purchase, electricity sale, and hydrogen, respectively. The objective function includes the operating cost of the combined heat and power unit, the cost of purchasing electricity from the upstream grid, the revenue from selling electricity to the upstream grid, and the revenue from selling hydrogen. Recent decisions include the operating status, electrolysis power, electrolysis current, heat dissipation power, and temperature of alkaline electrolyzers; the operating status and heat transfer power of heat exchangers; the status, electrical power, and thermal power of combined heat and power units; electricity purchased or sold from the upstream grid; the active and reactive power of renewable energy units; and the line flow and node voltage of the active distribution network. x Denotes the current-day decision variable, where time... t The day-ahead decision variables are shown below: (1-39) The current running model is represented in the following compact form: (1-40) (1-41) in, A , a , c These are coefficients derived from the model described above; ② Construct an intraday operation model for an integrated electric-hydrogen-thermal energy system The intraday objective function for constructing the integrated electric-hydrogen-thermal energy system is shown below: (1-42) in (1-43) (1-44) (1-45) (1-46) in, This is an adjustment amount for the upstream power grid's electricity purchase and sale costs. The adjustment amount for the operating cost of combined heat and power units. This is an adjustment amount for the cost of wind and solar power curtailment. Adjustment amount for revenue from hydrogen sales during the day. λ CUR The price coefficient representing the cost of wind and solar power curtailment. and These represent the upward and downward adjustments to the upstream power grid, respectively. The adjustment amount for the electrical power of the combined heat and power unit. and ξ r,t Renewable energy units for the day r The change in output and the deviation of the actual output from the typical output. R For the number of renewable energy units, This is the adjustment amount of the electrolysis current; The constraints for intraday trading are as follows: (1-47) (1-48) (1-49) (1-50) (1-51) (1-52) (1-53) (1-54) (1-55) (1-56) (1-57) (1-58) (1-59) (1-60) (1-61) in, and These are the temperature and power adjustment amounts for the alkaline electrolytic cell, respectively. This represents the change in heat dissipation power of the alkaline electrolytic cell. This refers to the heat exchange capacity during the day. and These represent the maximum electricity purchased from and sold from the upstream power grid, respectively. For nodes j Reactive power of renewable energy units V t,i,R Node voltage; make y Let the matrix be composed of intraday decision variables, then at any time during the day t Decision vector y t The structure is as follows: (1-62) The issues encountered during the day can be summarized as follows: (1-63) (1-64) in, B , C , D , b and d The coefficient matrix or vector obtained from the above constraints, U To describe the output deviation of renewable energy ξ An uncertain set; ③ Construct a two-stage robust optimization model for an integrated electric-hydrogen-thermal energy system The daily operation involves determining the operating status, electrical or thermal power of the alkaline electrolyzer, cogeneration unit, and heat exchanger, as well as the electricity purchased or sold from the upstream grid. Based on the daily changes in renewable energy output relative to the typical output curve, the power of the alkaline electrolyzer, cogeneration unit, and heat exchanger, as well as the power from the upstream grid, is adjusted to follow the changes in renewable energy output. The compact form of the two-stage robust optimization problem is as follows: (1-65) Constructing an uncertain set First, the renewable energy output samples are divided into multiple sets using the multivariate time series K-means clustering method. This method establishes the sets iteratively, and at the 1st... n In this iteration, the clustering iterative update is as follows: (1-66) in, c n,i It is the first n In the next iteration, the set i The center point, S n,i It is the first n In the next iteration, it belongs to the set i The sample set, ξ z Indicates the first z Let Ξ be the time series sample of renewable energy output, where Ξ is the sample set. Z The number of days in the sample data is used to calculate the cluster center using the following formula: (1-67) in, n i It is a set i The number of samples in the cluster is updated by iteratively solving equations (1-66) and (1-67) until the cluster set no longer changes; Then, for each cluster set, a subset of uncertainty is constructed using the polyhedral uncertainty set: (1-68) Ultimately, the uncertain set is constructed as the union of multiple uncertain subsets: (1-69)； ④ Constructing a two-stage robust optimization operation problem-solving method for an integrated electro-hydrogen-thermal energy system based on multiple affine decision rules Based on the uncertainty set (1-69), the proposed two-stage robust optimization problem (1-65) is remodeled as follows: (1-70) Satisfying constraint (1-41) and: (1-71) (1-72) Second-stage decision variables y They are divided into two categories. The first category directly substitutes the random variable using an affine function, including { , , , , , , The second type is represented by linear functions of the first type of variables and random variables, including the remaining decision variables in the second stage. The affine model of the two types of variables is constructed as follows: For the first type of intraday decision variables: (1-73) (1-74) (1-75) (1-76) (1-77) For the second type of intraday decision variables (1-78) (1-79) (1-80) (1-81) in, W and w The coefficients of the linear and constant terms of the affine decision rule for the intraday decision variables are now presented as affine functions for all decision variables in the second stage. (1-82) in, M i and m i They are subsets U i The affine coefficient matrix and vector are obtained by replacing them with equation (1-82). y Then problem (1-70) becomes: (1-83) st (1-41) (1-84) Then, the robust constraint (1-84) is reconstructed through duality theory as (1-85)-(1-87): (1-85) (1-86) (1-87) in, μ 1,i It is a dual variable matrix; The inner-layer maximization problem (1-83) is transformed into a minimization problem using duality theory: (1-88) st (1-89) (1-90) in, μ 2,i is the dual variable vector of the inner maximization problem; therefore, problem (1-83)-(1-84) is represented as: (1-91) st (1-41), (1-85)-(1-87), (1-89)-(1-90) Problem (1-91) is transformed into (1-92) and solved using a mixed-integer linear programming solver; (1-92) st (1-93) (1-41)，(1-85)-(1-87)，(1-89)-(1-90) in, Θ bv is the dual auxiliary variable.

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