Two-stage robust optimization operation method of electricity-hydrogen-heat comprehensive energy system

Abstract

The invention discloses a two-stage robust optimization operation method for an electricity-hydrogen-heat comprehensive energy system, relates to the field of comprehensive energy systems, considers recycling of heat in the process of an alkaline electrolysis hydrogen production system, and recycles heat generated by electricity hydrogen production into a heat supply network through a heat exchanger to improve the energy utilization efficiency. According to the method, the two-stage robust optimization operation model of the electricity-hydrogen-heat comprehensive energy system comprising a wind power system, a photovoltaic-hydrogen system and a heat supply system is constructed, a robust optimization model solving method based on a multi-affine decision rule is provided, and the operation economical efficiency of the electricity-hydrogen-heat comprehensive energy system is improved.

Description

Technical Field

[0001] The present invention relates to the field of electric-hydrogen-heat integrated energy systems, and in particular to a two-stage robust optimization operation method for electric-hydrogen-heat integrated energy systems. Background Art

[0002] As human society pays more and more attention to environmental protection, the proportion of clean and low-carbon hydrogen in the energy system continues to increase, so the scale of electrolytic hydrogen production sites continues to increase. However, about 30% of the energy in the electrolytic hydrogen production process is lost in the form of heat energy. In order to maintain the stable operation of the hydrogen production system, active heat dissipation is usually required to discharge the waste heat. For large-scale electrolytic hydrogen production sites, waste heat recovery is an effective means to reduce the overall energy consumption of the system and improve the overall economic benefits. In this regard, this patent integrates the active distribution network, electrolytic hydrogen production system and regional heating network for integrated scheduling and operation to improve the overall benefits of the electric / hydrogen / heat integrated energy park. In addition, considering that the huge thermal inertia of the alkaline electrolysis system is the main reason for the slow start-up process of the electrolyzer, this chapter attempts to use the power of the heat network to improve the thermal dynamics of the electrolytic hydrogen production system. Therefore, this chapter proposes an operation model of an electric / hydrogen / heat integrated energy system that considers the two-way heat exchange of hydrogen production / heat network, and improves the overall operation level and economic benefits through two-way heat exchange between the heat network and the hydrogen production system.

[0003] In addition, the uncertainty of renewable energy output brings many challenges to the stable operation of power systems and hydrogen production systems. Taking full account of the uncertainty of renewable energy output is an effective measure to enhance the reliability of integrated energy system operation. Among many uncertain optimization methods, robust optimization uses a set of scenarios to characterize the uncertainty of variables, so that the constraints can be met in all uncertain scenarios, and the system can be guaranteed to have sufficient robustness in the day-ahead scheduling stage. Therefore, this chapter aims at the day-ahead scheduling problem of electric / hydrogen / heat / integrated energy parks, and constructs a day-ahead economic scheduling model for electric / hydrogen / heat integrated energy parks based on two-stage robust optimization. Considering the conservative problem 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] There are three problems in the existing research on the electric-hydrogen-heat integrated energy system: 1) Few studies focus on the waste heat recovery of electrolyzers used for regional heating, and lack analysis of the dynamic interaction between the heating system and the electric hydrogen production. 2) The existing operating state model of the electrolytic hydrogen production system is difficult to adapt to the two-way interaction requirements of the hydrogen production system and the heating system. 3) The traditional robust optimization operation method leads to a high degree of conservatism in the operation of the electric-hydrogen-heat integrated energy system. Therefore, the above problems need to be solved urgently. Summary of the invention

[0005] The object of the present invention is to provide a two-stage robust optimization operation method for an integrated power-hydrogen-heat energy system, which improves the energy utilization efficiency and the operation flexibility of the hydrogen production system by bidirectional heat exchange between the hydrogen production system and the heat supply system, and proposes a two-stage robust optimization operation method for the integrated power-hydrogen-heat energy system based on multi-affine decision rules, ensuring the robust and economic operation of the integrated power-hydrogen-heat energy system and solving the problems raised in the above background technology.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A two-stage robust optimization operation method for an integrated power-hydrogen-heat energy system, comprising the following steps:

[0008] ① Construct a multi-state operation model for the alkaline electrolytic hydrogen production system: Divide the state of the alkaline electrolyzer into a shutdown state, a standby state, and a production state. In the shutdown state, the temperature of the alkaline electrolyzer is lower than 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 lower than the minimum operating power; in the production state, the alkaline electrolyzer operates within the allowable temperature and power range, and the conversion between different states includes cold start, hot start, standby, and shutdown. Construct a new state s3,new by combining the cold start and the production state; Figure 2 In, the left part of s3,new represents the cold start process, where the power is limited by a start coefficient a0 (0 < a0 < 1). When the temperature rises to the operating range [Tmin, Tmax], the alkaline electrolyzer will switch to the production state:

[0009]

[0010] Among them, s 1,t , s 2,t , and are binary variables representing the shutdown, standby, and production states; T a is the ambient temperature; and are the electrolysis power and temperature at time t, respectively; P H is the maximum power in the standby state; a t is the scaling factor in the production state; P max is the maximum operating power;

[0011] ② Model the bidirectional heat exchange between the alkaline electrolyzer and the heat supply network;

[0012] The direction of heat transfer is controlled by two valves, denoted as k v1 and k v2 , respectively. When k v1 is open and k v2 is closed, the heat of the alkaline electrolyzer is transferred to the return water of the heat supply network. When kv1 Close and k v2 When turned on, hot water flows into the heat exchanger to heat the electrolyte, and the heat between the alkaline electrolyzer and the heating network is flexibly exchanged according to the following formula:

[0013]

[0014] in, is the heat transferred from the alkaline electrolyzer to the heating network, and is a binary variable representing the switching status of the two valves;

[0015] The alkaline electrolysis system model is constructed as follows:

[0016] P t EL =N c P t cell (0-100)

[0017]

[0018] in, The power consumed by each unit, N c is the number of units, k a , k b , k c are the approximate coefficients of the electrolysis linear model, I EL t is the current of the alkaline electrolytic cell, A m is the membrane area, is the hydrogen production, Δt is the time interval, F is the Faraday constant, and z is the number of electrons transferred;

[0019] The power consumption of alkaline electrolyzer includes the power consumption of electrolyzer and the power consumption of electrolysis auxiliary system:

[0020] P t AC =P t EL +P t BoP (0-104)

[0021]

[0022] in, Indicates the power consumed by the electrolysis auxiliary system, including the circulation pump, temperature regulation, and gas purification system; is the total power consumption of the alkaline electrolyzer system, H dis t is the heat dissipation power, γ BoP is a scaling factor;

[0023] The heat and temperature constraints of an alkaline electrolyser system are as follows:

[0024]

[0025] in, is the heat generated during the hydrogen production process, u tn is the thermal neutral voltage of water electrolysis, C EL and R EL are the heat capacity and resistance of the electrolytic cell, is the maximum heat dissipation of the alkaline electrolyzer system, and are the supply and return water temperatures of the heating network nodes connected to the heat exchanger, respectively;

[0026] Build a power system model:

[0027] The operation constraints of the CHP unit are modeled as follows:

[0028]

[0029] Among them, P CHP t and H CHP t Respectively represent the electrical power and thermal power of the combined heat and power unit, a CHP 、b CHP and d CHP is the vector describing the feasible area of ​​the electrical and thermal energy output of the CHP unit, k CHP t is a binary variable indicating the start and stop status of the cogeneration unit, n NG t is the natural gas consumption rate, η CHP is the conversion efficiency, L NG is the lower calorific value of natural gas, Q CHP t is the reactive power of the combined heat and power unit, λ CHP Q CHP t With P CHP t The proportionality coefficient between

[0030] The power flow and node voltage of the distribution network are modeled based on the linear DistFlow model as follows:

[0031]

[0032] V j,t =V i,t -2(r ij Pij,t +x ij Q ij,t ) (0-116)

[0033]

[0034] V min ≤V j,t ≤V max (0-119)

[0035] Among them, P jk,t and Q jk,t are the active power and reactive power passing through line jk at time t, δ(j) is the set of branch endpoints connected to node j, P RE j,t and Q RE j,t are the active and reactive power of renewable energy at time t, and are active and reactive loads respectively, r ij and x ij are the resistance and reactance of line ij, V j,t is the square value of the voltage at node j, is the maximum active power of the renewable energy unit connected to node j, Q RE j,min and Q RE j,max are the minimum and maximum reactive power of renewable energy at node j, V min and V max are the minimum and maximum values ​​of the squared voltage, respectively;

[0036] Build the district heating system model as follows:

[0037]

[0038] T t,b,end =γ loss L b (T t,b,start -T a )+T a (0-124)

[0039]

[0040] m min ≤m t,b ≤m max (0-129)

[0041] Among them, C h and Cc are the heat capacities of the high temperature side and low temperature side of the heat exchanger, respectively. is the actual heat capacity, and are the input temperatures of the mass flow on the high temperature side and the low temperature side, respectively, H max is the maximum heat exchange power, η HE is the heat transfer efficiency parameter, which is used to determine the actual amount of heat transferred between the high temperature side and the low temperature side of the heat exchanger, m t,b and m t,n denote the mass flow of branch b and node n respectively, A DHN is the incidence matrix, T t,b,start and T t,b,end Respectively represent the temperature of the starting point and the end point of branch b, γ loss is the temperature drop coefficient per unit distance, L b is the length of branch b, m t,j is the mass flow rate of branch j, T t,i is the temperature of node i, T t,j,end is the temperature at the end of branch j, T s i,t , and T ri,t are the temperatures of node i in the supply network and return network, respectively, t,i is the heat load of node i, m min and m max is m b The lower and upper bounds of and The upper and lower temperature bounds for the supply and return networks.

[0042] As a further solution of the present invention, it also includes constructing an operation model of the electric hydrogen heat integrated energy system in the two stages of the day before and the day after:

[0043] ①Construct the day-ahead operation model of the electric, hydrogen and heat integrated energy system

[0044] The day-ahead objective function for building an electric, hydrogen and heat integrated energy system is as follows:

[0045]

[0046] in, and P 0-t are the electricity purchased and sold from the upstream power grid, λ NG , λ H2 Represent the price coefficients of natural gas, electricity purchase, electricity sale and hydrogen respectively. The objective function includes the operating cost of the CHP unit, the cost of purchasing electricity from the upstream power grid, the income from selling electricity to the upstream power grid, and the income from selling hydrogen;

[0047] The day-ahead decision includes the operating status, electrolysis power, electrolysis current, heat dissipation power and temperature of the alkaline electrolyzer, the operating status and heat transfer power of the heat exchanger, the status, electric power and thermal power of the combined heat and power unit, the power purchased or sold from the upstream power grid, the active and reactive power of the renewable energy unit, and the line flow and node voltage of the active distribution network; let x represent the day-ahead decision variable, where the day-ahead decision variable at time t is as follows:

[0048]

[0049] The day-ahead model is expressed in the following compact form:

[0050] mina T x (0-132)

[0051] Ax≤c (0-133)

[0052] Among them, A, a, and c are coefficients obtained from the above model;

[0053] ②Construct a daily operation model for the electric, hydrogen and heat integrated energy system

[0054] The daily objective function of building an electric, hydrogen and heat integrated energy system is as follows:

[0055]

[0056] in

[0057]

[0058] in, It is the adjustment amount of the upstream power grid's electricity purchase and sales cost. is the adjustment amount of the operation cost of the cogeneration unit, is the adjustment amount for the cost of curtailing wind and solar power, is the adjustment amount of the income from selling hydrogen during the day, λ CUR is the price coefficient of the cost of curtailing wind and solar power, and ΔP 0-t are the upward and downward regulation of the upstream power grid power, is the adjustment amount of the electric power of the combined heat and power unit, and r,t are the output change of renewable energy unit r within a day and the deviation of actual output relative to typical output, R is the number of renewable energy units, is the adjustment amount of electrolysis current;

[0059] The constraints for intraday operation are as follows:

[0060]

[0061]

[0062] V t,j,R =V t,i,R -2(r ij P t,ij,R +x ij Q t,ij,R ) (0-148)

[0063]

[0064] P 0,min ≤P t 0+ -P t 0- +ΔP t 0+ -ΔP t 0- ≤P 0,max (0-151)

[0065]

[0066] V min ≤V t,i,R ≤V max (0-153)

[0067] in, and are the temperature and power adjustment of the alkaline electrolyzer, is the change in heat dissipation power of the alkaline electrolytic cell, H HE t,R is the daily heat transfer power, and are the maximum power purchased and sold from the upstream grid, is the reactive power of the renewable energy unit at node j, V t,i,R is the node voltage;

[0068] Let y represent the matrix of intraday decision variables, then the decision vector y at any time t within the day is t The composition is as follows:

[0069]

[0070] Intraday operation problems can be summarized as follows:

[0071]

[0072] Bx+Cy+Dξ≤d (0-156)

[0073] Among them, B, C, D, b and d are coefficient matrices or vectors obtained from the above constraints, and U is the uncertainty set used to describe the output deviation ξ of renewable energy;

[0074] ③Construct a two-stage robust optimization model for the electric, hydrogen and heat integrated energy system

[0075] The day-ahead dispatch determines the operating status, electrical power or thermal power of the alkaline electrolyzer, cogeneration unit, and heat exchanger, as well as the power purchased or sold from the upstream power grid. The intraday operation adjusts the power of the alkaline electrolyzer, cogeneration unit, heat exchanger, and the power from the upstream power grid according to the change in the output of renewable energy relative to the typical output curve to follow the change in the output of renewable energy. The compact form of the two-stage robust optimization problem is constructed as follows:

[0076]

[0077] st(3-41),(3-64)

[0078] Constructing an uncertain set

[0079] First, the multivariate time series K-means clustering method is used to divide the renewable energy output samples into multiple sets. This method establishes sets through iteration. In the nth iteration, the clustering iteration update is as follows:

[0080]

[0081] Among them, c n,i is the center point of set i in the nth iteration, S n,i is the set of samples belonging to set i in the nth iteration, ξ z represents the time series sample of renewable energy output on day z, Ξ is the sample set, Z is the number of days of sample data, and the cluster center is calculated by the following formula:

[0082]

[0083] Among them, n i is the number of samples in set i. The clustering results are updated by iteratively solving equations (3-73) and (3-74) until the clustering set no longer changes;

[0084] Then, for each set of clusters, the uncertainty subset ranges are constructed using the polyhedral uncertainty set:

[0085] U i ={ξ|W i ξ≤w i},i∈{1,2,...,N} (0-159)

[0086] Finally, the uncertain set is constructed as the union of multiple uncertain subsets:

[0087]

[0088] ④Construct a two-stage robust optimization operation problem solving method for the electric-hydrogen-heat integrated energy system based on multiple affine decision rules

[0089] Based on the uncertainty set (3-76), the proposed two-stage robust optimization problem (3-65) is remodeled as follows:

[0090]

[0091] Satisfying constraints (3-41) and:

[0092] Bx+Cy+Dξ≤d (0-162)

[0093] U i ={ξ|W i ξ≤w i},i∈{1,2,…,N} (0-163)

[0094] The second-stage decision variable y is divided into two categories, the first of which is directly replaced by the affine function of the random variable, including The second category is represented as a linear function of the first category variables and random variables, including the remaining decision variables in the second stage. The affine model of the two categories of variables is constructed as follows:

[0095] For the first type of intraday decision variables:

[0096]

[0097] For the second type of intraday decision variables

[0098]

[0099] Among them, W and w are the linear term and constant term coefficients of the affine decision rule for intraday decision variables. So far, all decision variables in the second stage are presented in the form of affine functions:

[0100] y=M i ξ+m i (0-173)

[0101] Among them, M i and m i The subsets U i The affine coefficient matrix and vector of , by replacing y with equation (3-89), problem (3-77) becomes:

[0102]

[0103] st(3-41)

[0104]

[0105] Then, the robust constraint (3-91) is reconstructed into (3-92)-(3-94) through dual theory:

[0106] (w i ) T μ 1,i ≤d-Bx-Cm i (0-176)

[0107] (W i ) T μ 1,i =(CM i +D) T (0-177)

[0108] μ 1,i ≥0 (0-178)

[0109] Among them, μ 1,i is the dual variable matrix;

[0110] The inner maximization problem of (3-90) is converted into a minimization problem through duality theory:

[0111]

[0112] st

[0113]

[0114] μ 2,i ≥0 (0-181)

[0115] Among them, μ 2,i is the dual variable vector of the inner maximization problem, so problems (3-90)-(3-91) are expressed as:

[0116]

[0117] st(3-41),(3-92)-(3-97)

[0118] Problem (3-98) is transformed into (3-99) and solved by a mixed integer linear programming solver;

[0119]

[0120] st

[0121] Θ≥(w i )T μ 2,i +b T m i ,i∈{1,2,...,N} (0-184)

[0122] (3-41),(3-92)-(3-97)

[0123] Among them, Θ is the dual auxiliary variable bv.

[0124] The beneficial effects of the present invention are as follows: the method of the present invention improves the energy utilization efficiency and the operation 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 electric-hydrogen-heat integrated energy system based on multi-affine decision rules, thereby ensuring the robust and economical operation of the electric-hydrogen-heat integrated energy system. BRIEF DESCRIPTION OF THE DRAWINGS

[0125] Figure 1 This is an energy flow diagram of the electric, hydrogen and heat integrated energy system proposed in an embodiment of the present invention.

[0126] Figure 2 This is the operating state model of the alkaline electrolytic cell proposed in the embodiment of the present invention.

[0127] Figure 3 Schematic diagram of heat exchange between the alkaline electrolytic cell and the heating network proposed in an embodiment of the present invention.

[0128] Figure 4 Schematic diagram of the electric, hydrogen and heat integrated energy system in an embodiment of the present invention.

[0129] Figure 5 Schematic diagram of typical wind power and photovoltaic output and electrical and thermal load curves in an embodiment of the present invention.

[0130] Figure 6 It is a comparison diagram of the operating status of the alkaline electrolyzer in the one-way heat exchange mode and the two-way heat exchange mode in the embodiment of the present invention.

[0131] Figure 7 It is a ratio diagram of the alkaline electrolytic cell temperature and the supply and return water temperatures of the heating network in the one-way heat exchange and two-way heat exchange modes in an embodiment of the present invention. DETAILED DESCRIPTION

[0132] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0133] In the embodiments of the present invention, ① considering the operation mode of the integrated electricity-hydrogen-heat energy system with two-way heat exchange between the hydrogen production system and the heat supply system, the following two considerations are taken into account to construct the integrated electricity-hydrogen-heat energy system: 1) The temperature of alkaline electrolysis is about 90 °C, which is usually higher than the return water temperature of the heat supply network; 2) The feed water temperature range of the heat supply network is 80 - 110 °C, so the feed water can be used to heat the electrolyte with a lower temperature. Therefore, the temperature difference between the electrolysis system and the heat supply network enables spontaneous heat exchange between the electrolyte and the heat supply feed water or return water. Therefore, the waste heat of electrolytic hydrogen production can be recovered for district heating, and the heat of the heat network can also be used to accelerate the thermal dynamics of the alkaline electrolyzer.

[0134] Please refer to Figure 1 , in this system, electrolytic hydrogen production is used as the coupling link of the electricity, hydrogen, and heat subsystems, and the hydrogen production power is determined according to the electricity price, electricity load, and hydrogen energy price. The heat exchange direction and power between the hydrogen production system and the heat supply network are determined according to the operation state requirements. Therefore, energy coupling and the uncertainty of renewable energy are transmitted through energy coupling in the integrated energy system.

[0135] Considering that the alkaline electrolyzer continues to work during the cold start process, in this paper, the cold start and production states are constructed into a new state s 3,new . Please refer to Figure 2 , s 3,new 's left part represents the cold start process, where the power is limited by a start coefficient a0 (0 < a0 < 1). When the temperature rises to the operating range [T min , T max , the alkaline electrolyzer will switch to the production state, as shown in the right part of s 3,new . Therefore, the state of the alkaline electrolyzer is modeled as:

[0136]

[0137] where s 1,t , s 2,t , and are binary variables representing the off, standby, and production states; T a is the ambient temperature; and are the electrolysis power and temperature at time t respectively; P H is the maximum power in the standby state; a t is the scaling factor in the production state; P max is the maximum operating power.

[0138] Please refer to Figure 3 , in order to improve the operation flexibility of the alkaline electrolyzer restricted by large thermal inertia, a two-way heat exchange operation scheme between the alkaline electrolyzer and the heat supply network is proposed, as Figure 3The heat transfer direction is controlled by two valves, denoted by k v1 and k v2 When k v1 Open and k v2 When switched off, the heat from the alkaline electrolyser is transferred to the return water of the heating network. v1 Close and k v2 When switched on, hot feed water flows into the heat exchanger to heat the electrolyte. In this way, heat can be flexibly exchanged between the alkaline electrolyser and the heating network according to the following formula:

[0139]

[0140] in, is the heat transferred from the alkaline electrolyzer to the heating network, and is a binary variable representing the switching status of the two valves.

[0141] ②The realization of the coupled operation of the electric-hydrogen-heat integrated energy system depends on the modeling of 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 a heat exchanger. The dynamic modeling of the power system includes the power network and the combined heat and power unit.

[0142] The alkaline electrolysis hydrogen production system is modeled as follows:

[0143] The relationship between the power consumption and hydrogen production of the electrolyzer is modeled as:

[0144] P t EL =N c P t cell (0-192)

[0145]

[0146] in, The power consumed by each unit, N c is the number of units, k a , k b , k c are the approximate coefficients of the electrolysis linear model, I EL t is the current of the alkaline electrolytic cell, A m is the membrane area, is the hydrogen production, Δt is the time interval, F is the Faraday constant, and z is the number of electrons transferred.

[0147] The operation constraints of the combined heat and power system are modeled as follows:

[0148]

[0149] Among them, P CHP t and H CHP t Represent electrical power and thermal power respectively, a CHP 、b CHP and d CHP is the vector describing the feasible area of ​​the electrical and thermal energy output of the CHP unit, k CHP t is a binary variable indicating the start and stop status of the cogeneration unit, n NG t is the natural gas consumption rate, η CHP is the conversion efficiency, L NG is the lower calorific value of natural gas, Q CHP t is the reactive power of the combined heat and power unit, λ CHP Q CHP t With P CHP t The proportionality factor between .

[0150] The power flow and node voltage of the distribution network are modeled based on the linear DistFlow model:

[0151]

[0152] V j,t =V i,t -2(r ij P ij,t +x ij Q ij,t ) (0-201)

[0153]

[0154] V min ≤V j,t ≤V max (0-204)

[0155] Among them, P jk,t and Q jk,t are the active power and reactive power passing through line jk at time t, δ(j) is the set of branch endpoints connected to node j, P RE j,t and Q RE j,t are the active and reactive power of renewable energy at time t, and are active and reactive loads respectively, rij and x ij are the resistance and reactance of line ij, V j,t is the square value of the voltage at node j, is the maximum active power of the renewable energy unit connected to node j, Q RE j,min and Q RE j,max are the minimum and maximum reactive power of renewable energy at node j, V min and V max are the minimum and maximum values ​​of the squared voltage, respectively.

[0156] The heat exchanger is modeled as follows:

[0157]

[0158] Among them, C h and C c are the heat capacities of the high temperature side and low temperature side of the heat exchanger, respectively. is the actual heat capacity, and are the input temperatures of the mass flow on the high temperature side and the low temperature side, respectively, H max is the maximum heat exchange power, η HE is the heat exchange efficiency parameter. The heating network model is as follows:

[0159]

[0160] T t,b,end =γ loss L b (T t,b,start -T a )+T a (0-209)

[0161]

[0162] m min ≤m t,b ≤m max (0-214)

[0163] Among them, m t,b and m t,n denote the mass flow of branch b and node n respectively, A DHN is the incidence matrix, T t,b,start and T t,b,end Respectively represent the temperature of the starting point and the end point of branch b, γ loss is the temperature drop coefficient per unit distance, L b is the length of branch b, m t,j is the mass flow rate of branch j, Tt,i is the temperature of node i, T t,j,end is the temperature at the end of branch j, and are the temperatures of node i in the supply network and return network, respectively, t,i is the heat load of node i, m min and m max is m b The lower and upper bounds of and The upper and lower temperature bounds for the supply and return networks.

[0164] ③The realization of the two-stage robust optimization operation model of the electric-hydrogen-heat integrated energy system depends on the construction of the day-ahead and intraday operation models.

[0165] Based on the typical output curve of renewable energy, the day-ahead operation aims to minimize the operating cost of the electric, hydrogen and heat integrated energy system. The objective function is constructed as follows:

[0166]

[0167] in, and P 0-t are the electricity purchased and sold from the upstream power grid, λ NG , λ H2 Represent the price coefficients of natural gas, electricity purchase, electricity sale and hydrogen respectively. The objective function includes the operating cost of the CHP unit, the cost of purchasing electricity from the upstream power grid, the income from selling electricity to the upstream power grid, and the income from selling hydrogen. It is assumed that all the hydrogen produced is sold, so the income from hydrogen sales is proportional to the amount of hydrogen produced.

[0168] The day-ahead decision includes the operating status, electrolysis power, electrolysis current, heat dissipation power and temperature of the alkaline electrolyzer, the operating status and heat transfer power of the heat exchanger, the status, electrical power and thermal power of the combined heat and power unit, the power purchased or sold from the upstream power grid, the active and reactive power of the renewable energy unit, and the line flow and node voltage of the active distribution network. Let x represent the day-ahead decision variables, where the day-ahead decision variables at time t are as follows:

[0169]

[0170] During the intraday operation phase, the power and heat of the alkaline electrolyzer and the combined heat and power unit, the heat through the heat exchanger, and the power from or delivered to the upstream grid are adjusted to cope with changes in renewable energy output. Intraday operation is based on the plan made for day-ahead operation, and the operation goal is to minimize the redispatch cost under the worst scenario. The objective function for intraday operation is constructed as follows:

[0171]

[0172] in

[0173]

[0174] in, It is the adjustment amount of the upstream power grid's electricity purchase and sales cost. is the adjustment amount of the operation cost of the cogeneration unit, is the adjustment amount for the cost of curtailing wind and solar power, is the adjustment amount of the income from selling hydrogen during the day, λ CUR is the price coefficient of the cost of curtailing wind and solar power, and ΔP 0-t are the upward and downward regulation of the upstream power grid power, is the adjustment amount of the electric power of the combined heat and power unit, and r,t are the output change of renewable energy unit r within a day and the deviation of actual output relative to typical output, R is the number of renewable energy units, is the adjustment value of electrolysis current.

[0175] The constraints for intraday operation are as follows:

[0176]

[0177]

[0178] V t,j,R =V t,i,R -2(r ij P t,ij,R +x ij Q t,ij,R ) (0-231)

[0179]

[0180] P 0,min ≤P t 0+ -P t 0- +ΔP t 0+ -ΔP t 0- ≤P 0,max (0-234)

[0181]

[0182] V min ≤V t,i,R ≤V max(0-236)

[0183] in, and are the temperature and power adjustment of the alkaline electrolyzer, is the change in heat dissipation power of the alkaline electrolytic cell, H HE t,R is the daily heat transfer power, and are the maximum power purchased and sold from the upstream grid, is the reactive power of the renewable energy unit at node j, V t,i,R is the node voltage.

[0184] Let y represent the matrix of intraday decision variables, then the decision vector y at any time t within the day is t The composition is as follows:

[0185]

[0186] Since (3-42)-(3-61) are linear models, the intraday operation problem can be summarized as follows:

[0187]

[0188] Bx+Cy+Dξ≤d (0-239)

[0189] Among them, B, C, D, b and d are coefficient matrices or vectors obtained from (3-43)-(3-61), and U is the uncertainty set used to describe the renewable energy output deviation ξ.

[0190] Finally, the day-ahead and intraday coordinated operation problem is formulated as a two-stage robust optimization problem. Day-ahead scheduling determines the operating status, electrical power or thermal power, and power purchased or sold from the upstream power grid of the alkaline electrolyzer, cogeneration unit, and heat exchanger. Intraday operation adjusts the power of the alkaline electrolyzer, cogeneration unit, heat exchanger, and the power from the upstream power grid according to the change in renewable energy output relative to the typical output curve to follow the change in renewable energy output. The compact form of the two-stage robust optimization problem is constructed as follows:

[0191]

[0192] st(3-41),(3-64)

[0193] ④ Two-stage robust optimization solution method based on multiple affine decision rules

[0194] The decision variables in the second stage are constructed as affine functions of the random variable ξ. The affine decision rule can effectively solve the adjustable robust optimization problem and provide real-time adjustment strategies for intraday operations. [85,83] The affine decision rule is as follows:

[0195] y=y0+Yξξ (0-240)

[0196] Among them, y0 is a constant matrix, and Y is a coefficient matrix of the first-order term. Then the two-stage robust optimization problem (3-21) is transformed into:

[0197]

[0198] Formula (3-66) is called the single affine decision rule (SADR). Since the affine decision rule does not make flexible adjustments to different uncertain scenarios, it may lead to a conservative scheduling strategy. In order to reduce the conservatism of the single affine decision rule, this paper proposes a multi-affine decision rule (MADR) to provide different decision rules in different uncertain scenarios. Assume that the uncertainty set U consists of subsets U1, U2, …, U N For any uncertain subset U i , the second stage decision variables can be expressed as:

[0199] y=y i,0 +Y i ξ (0-242)

[0200] Among them, y i,0 and Y i is the uncertain subset U i The affine coefficients of .

[0201] Next, problem (3-67) is transformed into

[0202]

[0203] First, the renewable energy output samples are divided into multiple sets using the multivariate time series K-means clustering method, which establishes sets through iteration. In the nth iteration, the clustering iteration update is as follows:

[0204]

[0205] Among them, c n,i is the center point of set i in the nth iteration, S n,i is the set of samples belonging to set i in the nth iteration, ξ zrepresents the time series sample of renewable energy output on day z, Ξ is the sample set, and Z is the number of days of sample data. The cluster center is calculated by the following formula:

[0206]

[0207] Among them, n i is the number of samples in set i. The clustering results are updated by iteratively solving equations (3-73) and (3-74) until the clustering set no longer changes.

[0208] Then, for each set of clusters, the uncertainty subset ranges are constructed using the polyhedral uncertainty set:

[0209] U i ={ξ|W i ξ≤w i},i∈{1,2,...,N} (0-246)

[0210] Finally, the uncertain set is constructed as the union of multiple uncertain subsets:

[0211]

[0212] Based on the uncertainty set (3-76), the proposed two-stage robust optimization problem (3-65) can be remodeled as follows:

[0213]

[0214] Constraints (3-41) and:

[0215] Bx+Cy+Dξ≤d(0-249)

[0216] U i ={ξ|W i ξ≤w i},i∈{1,2,…,N} (0-250)

[0217] In order to solve problem (3-77) using multiple affine decision rules, the second-stage decision variables y are divided into two categories. The first category can be directly replaced by the affine function of the random variable, including The second category can be expressed as a linear function of the first category variables and random variables, including the remaining decision variables in the second stage. The affine model of the two categories of variables is constructed as follows:

[0218] For the first type of intraday decision variables:

[0219]

[0220] For the second type of intraday decision variables

[0221]

[0222] Among them, W and w are the linear term and constant term coefficients of the affine decision rule for intraday decision variables. So far, all decision variables in the second stage are presented in the form of affine functions:

[0223] y=M i ξ+m i (0-260)

[0224] Among them, M i and m i The subsets U i The affine coefficient matrix and vector of . By replacing y with equation (3-89), problem (3-77) becomes:

[0225]

[0226] st(3-41)

[0227]

[0228] Then, the robust constraint (3-91) is reconstructed into (3-92)-(3-94) through dual theory:

[0229] (w i ) T μ 1,i ≤d-Bx-Cm i (0-263)

[0230] (W i ) T μ 1,i =(CM i +D) T (0-264)

[0231] μ 1,i ≥0 (0-265)

[0232] Among them, μ 1,i is the dual variable matrix.

[0233] The inner maximization problem of (3-90) is converted into a minimization problem through duality theory:

[0234]

[0235] st

[0236]

[0237] μ 2,i ≥0 (0-268)

[0238] Among them, μ 2,i is the dual variable vector of the inner maximization problem. Therefore, problems (3-90)-(3-91) are expressed as:

[0239]

[0240] st(3-41),(3-92)-(3-97)

[0241] Finally, problem (3-98) is transformed into (3-99) and solved by a mixed integer linear programming solver.

[0242]

[0243] st

[0244] Θ≥(w i ) T μ 2,i +b T m i ,i∈{1,2,...,N} (0-271)

[0245] (3-41),(3-92)-(3-97)

[0246] Among them, Θ is the dual auxiliary variable.

[0247] As a further embodiment of the present invention, please refer to Figure 4 and Figure 5 This embodiment involves the electrolysis of renewable energy to produce hydrogen and recovering waste heat through a heat exchanger for heat supply. The basic parameters of the electrolyzer and system operation in the electric-hydrogen-heat integrated energy system are shown in Tables 1 and 2:

[0248] Table 1 Parameters of the electrolysis hydrogen production system

[0249]

[0250]

[0251] The power system parameter settings in the model are shown in the following table:

[0252] Table 2 Parameters of the electric, hydrogen and heat integrated energy system

[0253]

[0254] Figure 6The status of the alkaline electrolyzer in the one-way heat exchange mode and the two-way heat exchange mode is shown. In the one-way heat exchange mode, the alkaline electrolyzer remained closed for the first two hours due to the slow startup speed. In contrast, in the two-way heat exchange mode, the alkaline electrolyzer was quickly started using the heat of the heating network. During 10:00-11:00 and 18:00-19:00, the alkaline electrolyzer in the two-way heat exchange mode was shut down due to insufficient output of renewable energy, while the alkaline electrolyzer in the one-way heat exchange mode remained on standby to facilitate subsequent hydrogen production, which increased the operating cost of the alkaline electrolyzer.

[0255] Figure 7 The temperature of the alkaline electrolyzer and the associated supply and return water temperatures in the heating network are shown. Heat dissipation indicates the transfer of heat from the alkaline electrolyzer to the heating network, and heat absorption indicates the reverse direction. In the bidirectional heat exchange mode, the alkaline electrolyzer temperature fluctuates more, indicating a faster temperature adjustment. After the initial startup phase, the temperature range in the bidirectional heat exchange mode is between 30°C and 90°C, while the temperature range in the unidirectional heat exchange mode is between 60°C and 90°C. Therefore, more waste heat is recovered in the bidirectional heat exchange mode.

[0256] Table 3 shows the operating costs of the electric-hydrogen-heat integrated energy system in the one-way heat exchange and two-way heat exchange modes. In the one-way heat exchange mode, the largest part of the cost of the CHP unit is borne by district heating. At the same time, the CHP unit generates more electricity to meet the constraints of electricity and heat. Therefore, the cost of purchasing electricity from the upstream power grid is smaller in the one-way heat exchange mode. In the two-way heat exchange mode, more hydrogen is produced due to the enhanced flexibility. At the same time, the recovered heat increases, thereby reducing the district heating cost. In general, the proposed operation model reduces the operating cost of the electric-hydrogen-heat integrated energy system by about 6%.

[0257] Table 3 Comparison of operating costs between one-way heat exchange and two-way heat exchange (￥)

[0258]

[0259] In order to verify the effectiveness of the proposed multi-affine decision rule method, the multi-affine decision rule is compared with the traditional single affine decision rule and deterministic optimization in an out-of-sample test. The test samples are obtained by sampling from a normal distribution. At the same time, 2-10 affine decision rules are set to evaluate the impact of the number of affine decision rules on the total net cost, reliability and calculation 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 power grid within a day. Since a higher penalty cost means that the robustness of the scheduling scheme is lower, this item can be used to reflect the reliability of the robust optimization scheme.

[0260] According to Table 4, the total net cost and penalty cost of deterministic optimization are the highest among the three methods, while the calculation time is the shortest. This is because there is no response to the change of renewable energy output in deterministic optimization, resulting in the highest adjustment cost and the lowest calculation burden in intraday operation. Compared with the single affine decision rule, the multi-affine decision rule provides a more targeted affine decision rule through uncertainty set clustering, thereby reducing the total net cost and penalty cost. Compared with deterministic optimization and single affine decision rule, the total net cost in multi-affine-10 is reduced by about 17.9% and 9.7%, and the penalty cost is reduced by about 96.5% and 93.6%. This shows that the finer division of uncertainty sets effectively reduces operating costs and improves robustness. However, as the number of sets increases, the reduction of penalty costs and total net costs gradually slows down, while the calculation time increases significantly. Among all multi-affine decision rules, multi-affine-5 better balances the total net cost and calculation time. Therefore, the subsequent analysis is based on multi-affine-5.

[0261] Table 4 Comparison of operating costs and calculation time under different methods

[0262]

[0263]

[0264] Note: n in multi-affine-n represents the number of affine decision rules.

[0265] Table 5 presents the operating costs of the out-of-sample tests for deterministic optimization, single affine decision rule, and multi-affine-5. Multi-affine provides similar day-ahead costs compared to single affine decision rule. In the intraday phase, multi-affine has smaller 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 in the average and worst-case scenarios is 4.6% and 4.9% smaller than that of the single affine decision rule, respectively. In addition, the standard deviation of the multi-affine cost is also smaller, indicating that the scheduling strategy is more reliable.

[0266] Table 5 Comparison of out-of-sample test operation costs (￥)

[0267]

[0268] Among the above simulation methods, the one that is original to the present invention, has never been disclosed, and its working method is different from any existing literature records is: the present invention improves the energy utilization level and the operational flexibility of the hydrogen production system by establishing an operating mode of two-way heat exchange between electric hydrogen production and heating system, and considers the volatility of renewable energy output, constructs a two-stage robust optimization operation method for the electric, hydrogen and heat integrated energy system, and proposes multiple affine decision rules for solving it, thereby reducing the conservatism of the robust optimization method.

[0269] It will be apparent to those skilled in the art that the 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 the spirit or essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations falling within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0270] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A two-stage robust optimization operation method for an electric, hydrogen and heat integrated energy system, characterized in that: The steps include: ① Construct a multi-state operation model of the alkaline electrolysis hydrogen production system: the state of the alkaline electrolyzer is divided into the shutdown state, the standby state and the production state. In the shutdown state, the temperature of the alkaline electrolyzer is lower than 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 lower than the minimum working 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 shutdown. The cold start and production states are constructed into a new state s3,new; when the temperature rises to within the operating range [Tmin, Tmax], the alkaline electrolyzer will switch to the production state: Among them, s 1,t ,s 2,t ,and is a binary variable representing shutdown, standby, and production status; T a is the ambient temperature; and are the electrolysis power and temperature at time t respectively; P H is the maximum power in standby mode; a t is the scaling factor in production state; P max is the maximum operating power, a0 is the starting coefficient; ② Bidirectional heat exchange modeling between alkaline electrolyzer and heating network; The heat transfer direction is controlled by two valves, denoted by k v1 and k v2 , when k v1 Open and k v2 When the alkaline electrolyser is switched off, the heat is transferred to the return water of the heating network. v1 Close and k v2 When turned on, hot water flows into the heat exchanger to heat the electrolyte, and the heat between the alkaline electrolyzer and the heating network is flexibly exchanged according to the following formula: in, is the heat transferred from the alkaline electrolyzer to the heating network, and is a binary variable representing the switching status of the two valves; The alkaline electrolysis system model is constructed as follows: P t EL =N c P t cell (0-8) in, The power consumed by each unit, N c is the number of units, k a , k b , k c are the approximate coefficients of the electrolysis linear model, I EL t is the current of the alkaline electrolytic cell, A m is the membrane area, is the hydrogen production, Δt is the time interval, F is the Faraday constant, and z is the number of electrons transferred; The power consumption of alkaline electrolyzer includes the power consumption of electrolyzer and the power consumption of electrolysis auxiliary system: P t AC =P t EL +P t BoP (0-12) in, Indicates the power consumed by the electrolysis auxiliary system, including the circulation pump, temperature regulation, and gas purification system; is the total power consumption of the alkaline electrolyzer system, H dis t is the heat dissipation power, γ BoP is a scaling factor; The heat and temperature constraints of an alkaline electrolyser system are as follows: in, is the heat generated during the hydrogen production process, u tn is the thermal neutral voltage of water electrolysis, C EL and R EL are the heat capacity and resistance of the electrolytic cell, is the maximum heat dissipation of the alkaline electrolyzer system, and are the supply and return water temperatures of the heating network nodes connected to the heat exchanger, respectively; Build a power system model: The operation constraints of the CHP unit are modeled as follows: Among them, P CHP t and H CHP t Respectively represent the electrical power and thermal power of the combined heat and power unit, a CHP , b CHP and d CHP is the vector describing the feasible area of ​​the electrical and thermal energy output of the CHP unit, k CHP t is a binary variable indicating the start and stop status of the cogeneration unit, n NG t is the natural gas consumption rate, η CHP is the conversion efficiency, L NG is the lower calorific value of natural gas, Q CHP t is the reactive power of the combined heat and power unit, λ CHP Q CHP t With P CHP t The proportionality coefficient between The power flow and node voltage of the distribution network are modeled based on the linear DistFlow model as follows: In min ≤V j,t ≤V max (0-27) Among them, P jk,t and Q jk,t are the active power and reactive power passing through line jk at time t, δ(j) is the set of branch endpoints connected to node j, P RE j,t and Q RE j,t are the active and reactive power of renewable energy at time t, and are active and reactive loads respectively, r ij and x ij are the resistance and reactance of line ij, V j,t is the square value of the voltage at node j, is the maximum active power of the renewable energy unit connected to node j, Q RE j,min and Q RE j,max are the minimum and maximum reactive power of renewable energy at node j, V min and V max are the minimum and maximum values ​​of the squared voltage, respectively; Build the district heating system model as follows: m min ≤m t,b ≤m max (0-37) Among them, C h and C c are the heat capacities of the high temperature side and low temperature side of the heat exchanger, respectively. is the actual heat capacity, and are the input temperatures of the mass flow on the high temperature side and the low temperature side, respectively, H max is the maximum heat exchange power, η HE is the heat transfer efficiency parameter, which is used to determine the actual amount of heat transferred between the high temperature side and the low temperature side of the heat exchanger, m t,b and m t,n denote the mass flow of branch b and node n respectively, A DHN is the incidence matrix, T t,b,start and T t,b,end Respectively represent the temperature of the starting point and the end point of branch b, γ loss is the temperature drop coefficient per unit distance, L b is the length of branch b, m t,j is the mass flow rate of branch j, T t,i is the temperature of node i, T t,j,end is the temperature at the end of branch j, and are the temperatures of node i in the supply network and return network, respectively, t,i is the heat load of node i, m min and m max is m b The lower and upper bounds of and The upper and lower temperature bounds for the supply and return networks.

2. According to claim 1, a two-stage robust optimization operation method for an electric-hydrogen-heat integrated energy system is characterized in that: It also includes the construction of the operation model of the electric, hydrogen and heat integrated energy system in the two stages of the day before and the day after: ①Construct the day-ahead operation model of the electric, hydrogen and heat integrated energy system The day-ahead objective function for building an integrated electric, hydrogen and thermal energy system is as follows: in, and P 0-t are the electricity purchased and sold from the upstream power grid, λ NG , λ H2 Represent the price coefficients of natural gas, electricity purchase, electricity sale and hydrogen respectively. The objective function includes the operating cost of the CHP unit, the cost of purchasing electricity from the upstream power grid, the income from selling electricity to the upstream power grid, and the income from selling hydrogen; The day-ahead decision includes the operating status, electrolysis power, electrolysis current, heat dissipation power and temperature of the alkaline electrolyzer, the operating status and heat transfer power of the heat exchanger, the status, electric power and thermal power of the combined heat and power unit, the power purchased or sold from the upstream power grid, the active and reactive power of the renewable energy unit, and the line flow and node voltage of the active distribution network; let x represent the day-ahead decision variable, where the day-ahead decision variable at time t is as follows: The day-ahead model is expressed in the following compact form: min a T x (0-40) Ax≤c (0-41) Among them, A, a, and c are coefficients obtained from the above model; ②Construct a daily operation model for the electric, hydrogen and heat integrated energy system The daily objective function of building an electric, hydrogen and heat integrated energy system is as follows: in in, It is the adjustment amount of the upstream power grid's electricity purchase and sales cost. is the adjustment amount of the operation cost of the cogeneration unit, is the adjustment amount for the cost of curtailing wind and solar power, is the adjustment amount of the income from selling hydrogen during the day, λ CUR is the price coefficient of the cost of curtailing wind and solar power, and ΔP 0-t are the upward and downward regulation of the upstream power grid power, is the adjustment amount of the electric power of the combined heat and power unit, and r,t are the output change of renewable energy unit r within a day and the deviation of actual output relative to typical output, R is the number of renewable energy units, is the adjustment amount of electrolysis current; The constraints for intraday operation are as follows: V t,j,R =V t,i,R -2(r ij P t,ij,R +x ij Q t,ij,R ) (0-56) In min ≤V t,i,R ≤V max (0-61) in, and are the temperature and power adjustment of the alkaline electrolyzer, is the change in heat dissipation power of the alkaline electrolytic cell, H HE t,R is the daily heat transfer power, and are the maximum power purchased and sold from the upstream grid, is the reactive power of the renewable energy unit at node j, V t,i,R is the node voltage; Let y represent the matrix of intraday decision variables, then the decision vector y at any time t within the day is t The composition is as follows: Intraday operation problems can be summarized as follows: Bx+Cy+Dξ≤d (0-64) Among them, B, C, D, b and d are coefficient matrices or vectors obtained from the above constraints, and U is the uncertainty set used to describe the output deviation ξ of renewable energy; ③Construct a two-stage robust optimization model for the electric, hydrogen and heat integrated energy system The day-ahead dispatch determines the operating status, electrical power or thermal power of the alkaline electrolyzer, cogeneration unit, and heat exchanger, as well as the power purchased or sold from the upstream power grid. The intraday operation adjusts the power of the alkaline electrolyzer, cogeneration unit, heat exchanger, and the power from the upstream power grid according to the change in the output of renewable energy relative to the typical output curve to follow the change in the output of renewable energy. The compact form of the two-stage robust optimization problem is constructed as follows: st(3-41),(3-64) Constructing an uncertain set First, the multivariate time series K-means clustering method is used to divide the renewable energy output samples into multiple sets. This method establishes sets through iteration. In the nth iteration, the clustering iteration update is as follows: Among them, c n,i is the center point of set i in the nth iteration, S n,i is the set of samples belonging to set i in the nth iteration, ξ z represents the time series sample of renewable energy output on day z, Ξ is the sample set, Z is the number of days of sample data, and the cluster center is calculated by the following formula: Among them, n i is the number of samples in set i. The clustering results are updated by iteratively solving equations (3-73) and (3-74) until the clustering set no longer changes; Then, for each set of clusters, the uncertainty subset ranges are constructed using the polyhedral uncertainty set: U i ={ξ|W i ξ≤w i },i∈{1,2,...,N} (0-67) Finally, the uncertain set is constructed as the union of multiple uncertain subsets: ④Construct a two-stage robust optimization operation problem solving method for the electric-hydrogen-heat integrated energy system based on multiple affine decision rules Based on the uncertainty set (3-76), the proposed two-stage robust optimization problem (3-65) is remodeled as follows: Satisfying constraints (3-41) and: Bx+Cy+Dξ≤d (0-70) U i ={ξ∣W i ξ≤w i },i∈{1,2,…,N} (0-71) The second-stage decision variable y is divided into two categories, the first of which is directly replaced by the affine function of the random variable, including The second category is represented as a linear function of the first category variables and random variables, including the remaining decision variables in the second stage. The affine model of the two categories of variables is constructed as follows: For the first type of intraday decision variables: For the second type of intraday decision variables Among them, W and w are the linear term and constant term coefficients of the affine decision rule for intraday decision variables. So far, all decision variables in the second stage are presented in the form of affine functions: y=M i ξ+m i (0-81) Among them, M i and m i The subsets U i The affine coefficient matrix and vector of , by replacing y with equation (3-89), problem (3-77) becomes: st(3-41) Then, the robust constraint (3-91) is reconstructed into (3-92)-(3-94) through dual theory: (In i ) T μ 1,i ≤d-Bx-Cm i (0-84) (IN i ) T μ 1,i =(CM i +D) T (0-85) m 1,i ≥0 (0-86) Among them, μ 1,i is the dual variable matrix; The inner maximization problem of (3-90) is converted into a minimization problem through duality theory: st m 2,i ≥0 (0-89) Among them, μ 2,i is the dual variable vector of the inner maximization problem, so problems (3-90)-(3-91) are expressed as: st(3-41),(3-92)-(3-97) Problem (3-98) is transformed into (3-99) and solved by a mixed integer linear programming solver; st Θ≥(w i ) T μ 2,i +b T m i ,i∈{1,2,...,N} (0-92) (3-41),(3-92)-(3-97) Among them, Θ is the dual auxiliary variable bv.

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