Multi-park integrated energy system collaborative optimization method based on equivalent projection theory

Abstract

The invention discloses a multi-park integrated energy system collaborative optimization method based on an equivalent projection theory. The method comprises the following steps: establishing a park integrated energy system scheduling model considering fuel gas hydrogen doping; establishing a park integrated energy system robust collaborative scheduling model participating in the multi-park integrated energy system alliance by considering the uncertainty of hydrogen energy interaction and energy load; the established double-layer region integrated energy system robust collaborative scheduling model is equivalent to a single-layer mixed integer programming collaborative scheduling model based on an equivalent projection theory; deriving a decentralized solution of the established mixed integer programming collaborative scheduling model by using a dual decomposition algorithm; and establishing a multi-park integrated energy system collaborative optimization model based on the feasible region equivalent projection and solving the multi-park integrated energy system collaborative optimization model. According to the method, a two-stage robust problem is converted into an MILP type robust optimization problem through feasible region projection, the converted model does not need to be iteratively solved, and the solving time is greatly shortened compared with that of a traditional iterative method; and a decentralized solution is derived by using a dual decomposition algorithm, so that the convergence and optimality of the result are ensured.

Description

Technical Field

[0001] The present invention relates to the field of collaborative optimization of integrated energy systems, and specifically to a collaborative optimization method for multi-park integrated energy systems based on equivalent projection theory. Background Art

[0002] With the increasing penetration and utilization of new energy sources, building an integrated energy system centered on multi-energy coupling is crucial for improving energy efficiency and enhancing carbon sequestration capacity. Integrated park energy systems, encompassing electricity, heat, hydrogen, and gas, play a crucial role in current energy systems. They not only promote the development of multi-energy coupling systems but also provide an effective means for absorbing renewable energy.

[0003] Most of the existing research on the collaborative optimization of multi-park integrated energy systems considering uncertainty is based on the idea of ​​centralized optimization. For example, the literature [1]: "Zhao Mingxin, Ding Baodi, Wu Yiheng, et al. Robust flexibility evaluation of integrated energy systems based on conservative adaptive optimization [J / OL]. Power System Technology, 1-13 [2024-12-05]" proposed to improve the conservative constraint conditions of the traditional robust optimization model and proposed an adaptive optimization method for the robust conservative parameters of the integrated energy system. However, different entities only exchange shared information that is not related to privacy, but the centralized optimization framework achieves complete information disclosure. To solve this problem, the distributed optimal scheduling of regional integrated energy systems (PIES) has flourished in the past few years. For the collaborative operation of multi-park integrated energy systems under wind power uncertainty, the alternating direction multiplier method and the column sum constraint algorithm can be combined to establish a decentralized two-stage robust model. Reference [2]: "Zhai Xiangyu, Li Zening, Xue Yixun, et al. Distributed energy management strategy for electric-thermal integrated energy system considering building height [J / OL]. Power System Technology, 1-14 [2024-12-05]" comprehensively considers the constraints of the power and thermal systems and integrates them into the PIES operation model, and proposes a three-stage accelerated alternating direction multiplier method to decompose the original optimization problem into sub-problems of the distribution network and the heat network for distributed solution. Since the computational efficiency of the mainstream distributed algorithm (ADMM) is not high, reference [3] "Luo Qingju, Zhu Jizhong. Distributed optimization scheduling of linear electric-gas integrated energy system based on multi-parameter planning improved ADMM [J / OL]. Transactions of the Chinese Society of Electrical Engineering, 1-13 [2024-12-05]" has improved the ADMM algorithm. However, the classic distributed optimization method cannot fully guarantee the convergence and optimality of the solution to this complex robust problem, which hinders its practicality in real situations. Summary of the Invention

[0004] In order to solve the problem that the current multi-park integrated energy system robust collaborative optimization cannot fully guarantee the convergence and optimality of the solution to complex robust problems when using traditional solutions. This paper proposes a multi-park integrated energy system collaborative optimization method based on equivalent projection theory. This method transforms the two-stage robust problem into a MILP type robust optimization problem through feasible region projection. The transformed model does not require iterative solution, and the solution time is greatly reduced compared with the traditional iterative method. The dual decomposition algorithm is used to derive a decentralized solution, ensuring the convergence and optimality of the result.

[0005] The technical solution adopted by the present invention is:

[0006] The collaborative optimization method of multi-park integrated energy system based on equivalent projection theory includes the following steps:

[0007] Step 1: By integrating the coupling of multiple energy flows, a park integrated energy system scheduling model considering natural gas hydrogen blending was established. Step 2: Considering the hydrogen energy interaction and energy load uncertainty of multi-park integrated energy systems, a robust collaborative scheduling model for park integrated energy systems participating in a multi-park integrated energy system alliance was established based on the park integrated energy system scheduling model established in Step 1.

[0008] Step 3: Based on the equivalent projection theory, the two-layer district integrated energy system robust coordinated scheduling model established in step 2 is equivalent to a single-layer mixed integer programming coordinated scheduling model;

[0009] Step 4: Use the dual decomposition algorithm to derive the decentralized solution of the mixed integer programming collaborative scheduling model established in step 3;

[0010] Step 5: Establish and solve the collaborative optimization model of multi-park integrated energy system based on the equivalent projection of the feasible domain.

[0011] In step 1, the establishment of a comprehensive energy system scheduling model for a park considering hydrogen-blended natural gas is as follows:

[0012] The objective function of the park integrated energy system scheduling model considering hydrogen blending of natural gas is as follows:

[0013] The Park Integrated Energy System (PIES) aims to minimize total operating costs. Before hydrogen energy interaction, the total operating costs of each Park Integrated Energy System i are divided into three parts: electricity purchase costs from the grid, gas purchase costs from the gas grid, and energy storage costs, as shown below:

[0014]

[0015] In formula (1), is the total cost of independent operation of the i-th PIES without considering hydrogen energy interaction, is the electricity purchase cost of the i-th PIES grid, is the cost of purchasing gas from the i-th PIES gas network, is the energy storage cost of the i-th PIES; p buy 、p sell Respectively represent the price of buying and selling electricity from the main grid; p gas represents the price of natural gas; represents the gas consumption of the i-th PIES cogeneration unit at time t; represents the gas consumption of the i-th PIES gas boiler unit at time t; α EES Indicates the cost coefficient of energy storage battery utilization; They represent the ESS charge and discharge capacity of the i-th PIES at time t; They represent the amount of electricity purchased and sold by the i-th PIES to the main network at time t, respectively; t is the index of the current scheduling time, and T is the total number of time steps in the scheduling cycle.

[0016] The operational constraints of the integrated energy system scheduling model for the park considering hydrogen blending with natural gas include: the operational constraints of the cogeneration unit, the electricity-hydrogen conversion device, the gas boiler, the energy storage battery, and the energy balance constraints, which are as follows:

[0017] 1) Operational constraints of cogeneration units:

[0018]

[0019] In formula (2), represents the power generation capacity of the i-th PIES cogeneration unit at time t, represents the heat production capacity of the i-th PIES cogeneration unit at time t; represents the natural gas consumption of the ith PIES cogeneration unit at time t, represents the hydrogen consumption of the i-th PIES cogeneration unit at time t; Indicates the maximum power generation of the cogeneration unit; represents the efficiency coefficient of natural gas power generation; represents the power generation efficiency coefficient of hydrogen; Indicates the heating efficiency coefficient of natural gas; Indicates the heating efficiency coefficient of hydrogen.

[0020] 2) Operational constraints of the electric-hydrogen conversion device:

[0021]

[0022] In formula (3), represents the hydrogen production of the electric-hydrogen conversion device in the P2H operation mode of the i-th PIES at time t; represents the hydrogen consumption of the electric-hydrogen conversion device in the H2P operation mode of the i-th PIES at time t; represents the power consumption of the electric-hydrogen conversion device in the P2H operation mode of the i-th PIES at time t; represents the power generation of the electric-hydrogen conversion device in the H2P operation mode of the i-th PIES at time t; They represent the upper and lower limits of the power input of the electric-hydrogen conversion device in the P2H mode respectively; A 0-1 indicator variable representing the P2H operation mode of the electric-to-hydrogen converter of the i-th PIES at time t; A 0-1 indicator variable representing the H2P operation mode of the electric-hydrogen conversion device of the i-th PIES at time t; They represent the upper and lower limits of the power output of the electric-hydrogen conversion device in the H2P mode respectively; Indicates the electricity-to-hydrogen conversion coefficient of the electricity-to-hydrogen conversion device in the P2H operating state; Indicates the hydrogen-to-electricity conversion coefficient of the electric-hydrogen conversion device in the P2H operating state.

[0023] 3) Operation constraints of gas boiler units:

[0024]

[0025] In formula (4), represents the heat production capacity of the i-th PIES gas boiler unit at time t; represents the natural gas consumption of the i-th PIES gas boiler unit at time t; Indicates the upper limit of the heat production capacity of the gas boiler unit; α GB Indicates the operation coefficient of the gas boiler unit.

[0026] 4) Operational constraints of energy storage batteries:

[0027]

[0028] In formula (5), Respectively represent the upper limit of charge and discharge of ESS; represents the storage capacity of the i-th PIES energy storage battery at time t; represents the storage capacity of the i-th PIES energy storage battery at time t-1; A 0-1 indicator variable representing the charging status of the i-th PIES energy storage battery at time t; η is a 0-1 indicator variable representing the discharge state of the i-th PIES energy storage battery at time t; ch ,η dis Respectively represent the charging and discharging efficiency of the energy storage battery; They respectively represent the upper and lower limits of the energy storage capacity of the energy storage battery.

[0029] 5) Energy balance constraints:

[0030]

[0031] In the above formula, represents the renewable energy output power of the i-th PIES at time t; They represent the electrical load and thermal load of the i-th PIES at time t, respectively.

[0032] In step 2, the establishment of a robust coordinated scheduling model for a multi-park integrated energy system is as follows:

[0033] The mass of hydrogen in the hydrogen storage tank in one day is expressed as:

[0034]

[0035] In formula (8), is the mass of hydrogen stored in the i-th system hydrogen storage tank at time t+1; is the mass of hydrogen stored in the i-th system hydrogen storage tank at time t. Since hydrogen delivery is delayed by 1 hour, the hydrogen transported at time t-1 is transported to the system hydrogen storage tank for storage at time t. Therefore, It represents the amount of hydrogen purchased by the i-th system from the j-th system through the l-th hydrogen vehicle at time t-1, and arriving at time t; represents the amount of hydrogen sold by the i-th system to the j-th system through the l-th hydrogen vehicle at time t; i and j are the indexes of the park's integrated energy system number; △t represents the time of a scheduling period; N l Indicates the number of long tube trailers in the multi-park integrated energy system alliance;

[0036] In addition, hydrogen vehicles for hydrogen transportation need to meet the constraints shown in the following equation (9):

[0037]

[0038] In formula (9), represents the hydrogen storage capacity of the lth hydrogen vehicle at time t, Indicates the hydrogen storage capacity of the lth hydrogen vehicle at time t-1; Indicates the upper limit of hydrogen storage capacity of hydrogen vehicles; A 0-1 indicator variable representing the hydrogen charging status of the lth hydrogen vehicle at time t; represents the hydrogen discharge state of the lth hydrogen vehicle at time t (0-1 indicator variable); η represents the hydrogen charging and discharging efficiency; It represents the maximum amount of hydrogen charged by the lth hydrogen vehicle at time t within a single dispatch period △t; It represents the maximum amount of hydrogen released by the lth hydrogen vehicle at time t within a single scheduling period △t;

[0039] In addition, the number of long-tube trailers within the multi-park integrated energy system alliance is limited. The number of hydrogen vehicles between each park integrated energy system (PIES) in a day is also restricted. In addition, the hydrogen storage state of the hydrogen storage tanks has certain requirements and needs to operate within a certain hydrogen storage range.

[0040]

[0041] In formula (10), N l Indicates the number of long tube trailers in the multi-park integrated energy system alliance; is the mass of hydrogen stored in the i-th system hydrogen storage tank at time t. are the maximum and minimum hydrogen storage capacities of the hydrogen storage tank, respectively. The first equation in (10) indicates that the number of hydrogen vehicles in operation needs to be limited to a certain number, and the second equation indicates that the hydrogen storage tank of the i-th PIES needs to operate within a certain range.

[0042] After hydrogen energy interaction, each PIES will conduct peer-to-peer hydrogen energy transactions through cooperation. The hydrogen energy interaction cost of each PIES is shown in the following formula.

[0043]

[0044] In formula (11), represents the hydrogen energy interaction cost of the i-th PIES; Respectively represent the purchase and sale prices of hydrogen energy when each PIES conducts peer-to-peer transactions;

[0045] Collaborative sharing effectively takes into account the unity of individual interests and overall interests. Therefore, based on the independent PIES objective function of formula (1), the overall objective function based on the PIES collaborative scheduling model is established as shown in the following formula (12):

[0046]

[0047] In formula (12), N represents the total dispatch cost of the i-th PIES after participating in the PIES alliance of hydrogen energy interaction; g Indicates the number of PIES in the park integrated energy system alliance.

[0048] In addition, considering the fluctuation range of new energy output and load power is located in the box-type uncertainty set Ω constructed by formula (13) u Inside:

[0049]

[0050] In formula (13) It is the predicted value of new energy output; is the predicted value of electric load output; is the predicted value of heat load output; The maximum fluctuation deviation of the predicted value of renewable energy output; is the maximum fluctuation deviation of the electric load forecast value; is the maximum fluctuation deviation of the heat load prediction value; Ω u An uncertainty set constructed to account for uncertain variables.

[0051] After considering the uncertainty of the system as shown in formula (13), the goal of the present invention becomes to find the uncertainty of the variables in the uncertainty set Ω u The optimal scheduling solution of the multi-PIES alliance when the internal changes towards the worst scenario is as follows:

[0052]

[0053] In formula (14): and Represents the coefficient matrix associated with the objective function in a compact form; the variable x i Represents all scheduling and operating status variables of the i-th PIES; variable y i represents the procurement of electricity, natural gas and equipment scheduling and operation plan of the i-th PIES; u i represents the uncertain variable of the i-th PIES source load;

[0054] x i 、y i and u i Specifically, they are shown in the following formulas (15) to (17):

[0055]

[0056] Equation (14) is essentially a two-level game between the system operator and nature: the operator first makes an irreversible decision x i , then nature never determines the set Ω u Select the worst scenario u i To maximize the total cost, the operator finally adjusts the decision y i Minimize the loss in this scenario. After considering the system uncertainty, to facilitate subsequent explanation and model solvability, the objective function (14), the constraints (2) to (10), and the uncertainty constraint (13) are rewritten into the compact form of the following two-stage robust optimization model, as shown in (18) and (19).

[0057] The first-stage optimization model determines the operation plan, as shown in formula (18):

[0058]

[0059] In formula (18), It is reconstructed from formula (12);

[0060] C i x i，t +D i y i，t ≤b i is the independent constraint of each system i, including equations (2) to (7);

[0061] is the coupling constraint between different PIES systems, mainly hydrogen energy interaction constraint, including equations (8) to (10); C i 、D i and b i The coefficient matrix representing the independent constraints of the park integrated energy system i;

[0062] E i and d i The coefficient matrix representing the coupling constraints of the integrated energy systems of different parks;

[0063] The second-stage optimization model is established to find the worst-case scenario for purchasing natural gas and utilizing energy storage batteries under an uncertain source load set. As shown in Equation (19):

[0064]

[0065] In formula (19), It is to add the corresponding slack variables to each constraint and sum up all the slack variables;

[0066] G i z i +ξ i ≤h i -L i u i -M i x i -N i y i To consider the independent constraints of each system i under uncertain variables, including equations (2)-(7) and (13);

[0067] In order to consider the coupling constraints between different PIES systems under uncertain variables, including equations (8) to (10); Φ(x i ,y i ) represents the decision x of the given first-stage optimization model i Under the worst uncertainty scenario u i By optimizing and adjusting y i The minimum constraint violation that must be tolerated after The maximum value of

[0068] ξ i represents the slack variable vector of the objective function of the i-th PIES under robust optimization at time t;

[0069] L i 、M i 、N i 、h i The coefficient matrix of the compact form of the independent constraints of the system considering uncertainty;

[0070] K i 、g i The coefficient matrix of the compact form of the coupling constraints for different systems considering uncertainties;

[0071] In step 3, the second-stage optimization model of the robust coordinated scheduling model of the multi-park integrated energy system established in step 2 is optimized. This is essentially a feasibility check problem, that is, for the optimal result of the first-stage optimization model, for any scenario in the uncertainty set, y i，t The solution always exists, so the second-stage optimization model (lower-layer model) of the robust coordinated scheduling model of the multi-park integrated energy system as shown in formula (19) can be written as follows:

[0072]

[0073] In formula (20), Indicates the existence of y i The constraints in formula (20) can be satisfied; (x i ,y i ) means that for any uncertain variable u i Feasible scenarios for the second-stage optimization model (lower-level model);

[0074] Based on Fourier-Motzkin elimination, the above formula (20) is projected onto the space defined by the variables and uncertain variables of the first-stage optimization model, thereby eliminating the decision variables of the second-stage optimization model and obtaining the following constraints.

[0075]

[0076] In formula (21), V i X 、V i Y 、V i U and f i is the parameter matrix generated by Fourier-Motzkin elimination;

[0077] Furthermore, the following formula (22) can be guaranteed to hold true for any uncertain variables.

[0078]

[0079] In formula (22), and represents the constant matrix related to the uncertainty concentration constraint of the i-th PIES; [V i U ] k represents the coefficient of the uncertain variable in the kth constraint after Fourier-Motzkin elimination; V i U represents the coefficient matrix of uncertain variables after Fourier-Motzkin elimination; Ω i represents all scenarios of the uncertain set; [χ i ] k represents the dual variable of the kth constraint; χ i The dual variable matrix of the constraint; k represents the kth constraint in the compact constraint form of equation (19);

[0080] After the equivalent transformation process of the above formula (20) to formula (22), the original second-stage optimization model (lower-layer model) shown in formula (19) can be equivalent to the constraints shown in formula (23):

[0081]

[0082] Therefore, the original two-stage robust optimization problem shown in Equation (18) and Equation (19) is finally transformed into a mixed integer programming (MILP) problem as shown in Equation (24):

[0083]

[0084] In step 4, since the mixed integer programming (MILP) model converted in step 3 involves multiple different stakeholders, the information that can be transmitted to each other is limited. In addition, the established MILP model is a non-convex model, and the commonly used distributed algorithm may not be able to find an exact solution for it. The decomposition technology is used to divide the overall Lagrangian dual problem of coordinated scheduling of multi-park integrated energy systems into a single-park integrated energy system problem, and the subgradient algorithm is used to update the dual variables, thereby obtaining a convergent distributed solution to the dual problem. The contraction coefficient is introduced to restore the feasible original solution and ensure the feasibility of the dual solution;

[0085] After introducing the shrinkage coefficient ρ, the mixed integer programming (MILP) obtained in step 3 can be reconstructed into the following model.

[0086]

[0087] In formula (25), δ i is the shrinkage coefficient, In order to introduce the compact form of the multi-PIES coupling constraint after the shrinkage coefficient is introduced, its Lagrangian dual formula is derived as follows:

[0088]

[0089] In formula (26), λ T (d i -δ) indicates that the coupling constraint The marginal opportunity cost contribution to the original problem objective function; δ represents the shrinkage coefficient; λ T Constrained The transpose of the dual variable of ;

[0090] Where λ is the dual variable of the coupling constraint, and the contraction coefficient is defined by the following equation (27):

[0091]

[0092] In formula (27), q is the shrinkage factor, n is the row of the coupling constraint matrix; [E i ] nk Indicates the specific coefficient of the kth variable in the nth coupling constraint among different PIES coupling variables, which is used to calculate the marginal contribution. i is the coefficient matrix of different PIES coupling variables.

[0093] After obtaining the initial dual variable λ j and the contraction coefficient δ i After RIES i According to the Park Integrated Energy System Alliance, RIES is removed i All other RIES j Transmitted Lambda j , according to the weight factor γ ij Compute the other PIES dual variables λ j The average value of the dual variable θ passed in i , as shown below:

[0094]

[0095] In formula (28), k is the number of iterations. Based on the average value, RIES i Fix the dual variable to θ i (k), and perform the following minimum optimization problem.

[0096]

[0097] In formula (29), y i (k+1) represents y after the k+1th iteration i The specific value of θ i (k)T It represents the average value of the dual variables passed to the i-th PIES by other PIES except the i-th PIES in the k-th iteration.

[0098] After performing the above minimum optimization problem, a tentative solution y can be obtained i (k+1), according to E i y i (k+1) calculate PIES i The worst contribution to the coupling constraint can then be updated with the following maximum consensus strategy: i The shrinkage coefficient.

[0099]

[0100] In formula (30), φ i (k) is the maximum value of all contraction coefficients transferred from subsystem j except subsystem i itself; δ j (k) indicates that the source is not PIES i Other PIES j The transferred shrinkage coefficient; Represents the maximum value of all contraction coefficients transferred from other subsystems j; It is represented as the auxiliary record variable with the worst contribution upper limit in the k+1th iteration; Auxiliary record variable for the worst contribution upper limit in the kth iteration; It is represented as the auxiliary record variable with the worst contribution lower bound in the k+1th iteration; Auxiliary record variable for the worst contribution lower limit; δ i (k+1) represents the specific value of the shrinkage coefficient after the k+1th iteration obtained by the maximum consensus strategy shown in formula (30); k represents the number of iterations.

[0101] Finally, the dual variables are updated with subgradients as follows:

[0102] λ i (k+1)=[θ i (k)+ω(E i y i (k+1)-(d i -δ i (k+1)) / N g ] + (31);

[0103] In formula (31), λ i (k+1) represents the specific value of the dual variable of the coupling constraint after the k+1th iteration after the subgradient update; ω is the update step size, [·] + represents the projection on the q-dimensional non-negative orthogonal; Ng The number of PIES in the park integrated energy system alliance; each PIES only i (k) and δ i (k) interact with other PIES, so no private information is disclosed. In step 5, a multi-park integrated energy system collaborative optimization model based on the feasible domain equivalent projection is established. Specifically, the program is written in the Matlab 2020 environment and the GUROBI solver is called based on the YALMIP platform to solve the problem. The details are as follows:

[0104] First, based on the Matlab2020 environment, all optimization variables are classified into equations (15) to (17), and according to the objective function equation (12) and the constraints equations (2) to (10), a two-stage robust optimization problem of the multi-park integrated energy system is constructed as shown in equations (18) and (19);

[0105] Then, using the feasible region projection theory formulas (20) to (22) proposed in step 3, the lower layer problem of the two-stage robust problem of the original model shown in formula (19) is converted into the constraints shown in formula (23) and introduced into the first stage optimization model of the original two-stage robust problem (18), thereby converting it into the model shown in formula (24);

[0106] Finally, the dual decomposition algorithm proposed in step 4 is used to split the centralized MILP model shown in Equation (22) into sub-problems for each park through Lagrangian relaxation. The distributed optimization framework of Equations (25) to (31) is used to solve the problem by calling the GUROBI solver based on the YALMIP platform.

[0107] The present invention provides a collaborative optimization method for a multi-park integrated energy system based on equivalent projection theory, and the technical effects are as follows:

[0108] 1) Step 1 of the present invention establishes a comprehensive energy system scheduling model for a park that considers hydrogen blending with natural gas by integrating the coupling of multiple energy flows. Enhancing the coupling between energy sources helps to reduce the volatility of renewable energy, improve the overall energy efficiency of the system, and lay a solid foundation for subsequent scheduling.

[0109] 2) Step 2 of the present invention considers the hydrogen energy interactions and energy load uncertainty of multi-park integrated energy systems and establishes a robust coordinated scheduling model for multi-park integrated energy systems based on the model in step 1. This improves the reliability and stability of the power system and enables energy complementarity and coordinated operation between different types of PIES. This reduces the amount of electricity PIES purchases from large power grids, lowering the operating costs of the PIES alliance.

[0110] 3) Step 3 of the present invention converts the robust collaborative scheduling model established in step 2 into a mixed integer programming collaborative scheduling model. Converting the iterative optimization problem into a non-iterative optimization problem reduces the time required for solution and can be better applied to actual projects.

[0111] 4) Step 4 of the present invention uses a dual decomposition algorithm to derive a decentralized solution to the mixed-integer collaborative scheduling model proposed in step 3. This algorithm, without requiring a virtual optimization center, guarantees convergence and optimality for decentralized decomposition of non-convex problems, and is of great significance for collaborative optimization scheduling of non-convex problems.

[0112] 5) Step 5 of the present invention establishes a multi-park integrated energy system collaborative optimization model based on equivalent projection theory, realizes the non-iterative solution of the two-stage robust model, greatly reduces the model solution time, is conducive to making full use of various distributed energy sources, and protects the data privacy of each subject. BRIEF DESCRIPTION OF THE DRAWINGS

[0113] The present invention will be further described below with reference to the accompanying drawings and examples:

[0114] Figure 1 This is the distributed algorithm flow chart.

[0115] Figure 2 This is the energy coupling structure diagram of the park’s integrated energy system.

[0116] Figure 3 This is a diagram of the operation model of the multi-park integrated energy system alliance.

[0117] Figure 4 This is the source-load prediction curve for the integrated energy system of each park.

[0118] Figure 5 This is the result diagram of the power optimization scheduling of the park’s integrated energy system 1.

[0119] Figure 6 This is the result diagram of thermal energy optimization scheduling of the park's integrated energy system 1.

[0120] Figure 7 Schematic diagram of the iteration of the method proposed in the present invention. DETAILED DESCRIPTION

[0121] A collaborative optimization method for multi-park integrated energy systems based on equivalent projection theory involves the field of collaborative optimization of multi-park integrated energy systems. The method includes the following steps: by integrating the coupling of multiple energy flows and considering the uncertainty of energy loads, a robust scheduling model for the integrated energy system of a park considering hydrogen blending with natural gas is established; by considering the hydrogen energy interaction of multi-park integrated energy, a collaborative scheduling model for the integrated energy system of a park is established; based on equivalent projection theory, the two-stage robust model is equivalent to a mixed integer programming model, and the dual decomposition algorithm is used to derive the decentralized solution of multiple PIES. The model is solved by calling the GUROBI solver on the YALMIP platform in the Matlab2020a environment. This method solves the robust optimization model of the multi-park integrated energy system in a non-iterative manner, significantly reducing the solution time compared to traditional iterative methods, and uses the dual decomposition algorithm to derive decentralized solutions, ensuring the convergence and optimality of the results.

[0122] The collaborative optimization method of multi-park integrated energy system based on equivalent projection theory includes the following steps:

[0123] Step 1: By integrating the coupling of multiple energy flows, a park integrated energy system scheduling model considering natural gas hydrogen blending was established. Step 2: Considering the hydrogen energy interaction and energy load uncertainty of multi-park integrated energy systems, a robust collaborative scheduling model for park integrated energy systems participating in a multi-park integrated energy system alliance was established based on the park integrated energy system scheduling model established in Step 1.

[0124] Step 3: Based on the equivalent projection theory, the two-layer district integrated energy system robust coordinated scheduling model established in step 2 is equivalent to a single-layer mixed integer programming coordinated scheduling model;

[0125] Step 4: Use the dual decomposition algorithm to derive the decentralized solution of the mixed integer programming collaborative scheduling model established in step 3;

[0126] Step 5: Establish and solve the collaborative optimization model of multi-park integrated energy system based on the equivalent projection of the feasible domain.

[0127] In step 1, the establishment of a comprehensive energy system scheduling model for a park considering hydrogen-blended natural gas is as follows:

[0128] The objective function of the park integrated energy system scheduling model considering hydrogen blending of natural gas is as follows:

[0129] The Park Integrated Energy System (PIES) takes minimizing the total operating cost as its optimization goal. Before hydrogen energy interaction, the total operating cost of each Park Integrated Energy System i is composed of three parts: the cost of purchasing electricity from the power grid, the cost of purchasing gas from the gas grid, and the cost of energy storage, as shown below;

[0130]

[0131] In formula (1), is the total cost of independent operation of the i-th PIES without considering hydrogen energy interaction, is the electricity purchase cost of the i-th PIES grid, is the cost of purchasing gas from the i-th PIES gas network, is the energy storage cost of the i-th PIES; p buy 、p sell Respectively represent the price of buying and selling electricity from the main grid; p gas represents the price of natural gas; represents the gas consumption of the i-th PIES cogeneration unit at time t; represents the gas consumption of the i-th PIES gas boiler unit at time t; α EES Indicates the cost coefficient of energy storage battery utilization; They represent the ESS charge and discharge capacity of the i-th PIES at time t; They represent the amount of electricity purchased and sold by the i-th PIES to the main network at time t, respectively; t is the index of the current scheduling time, and T is the total number of time steps in the scheduling cycle.

[0132] The operational constraints of the integrated energy system scheduling model for the park considering hydrogen blending with natural gas include: the operational constraints of the cogeneration unit, the electricity-hydrogen conversion device, the gas boiler, the energy storage battery, and the energy balance constraints, which are as follows:

[0133] 1) Operational constraints of cogeneration units:

[0134]

[0135] In formula (2), represents the power generation capacity of the i-th PIES cogeneration unit at time t, represents the heat production capacity of the i-th PIES cogeneration unit at time t; represents the natural gas consumption of the ith PIES cogeneration unit at time t, represents the hydrogen consumption of the i-th PIES cogeneration unit at time t; Indicates the maximum power generation of the cogeneration unit; represents the efficiency coefficient of natural gas power generation; represents the power generation efficiency coefficient of hydrogen; Indicates the heating efficiency coefficient of natural gas; Indicates the heating efficiency coefficient of hydrogen.

[0136] 2) Operational constraints of the electric-hydrogen conversion device:

[0137]

[0138] In formula (3), represents the hydrogen production of the electric-hydrogen conversion device in the P2H operation mode of the i-th PIES at time t; represents the hydrogen consumption of the electric-hydrogen conversion device in the H2P operation mode of the i-th PIES at time t; represents the power consumption of the electric-hydrogen conversion device in the P2H operation mode of the i-th PIES at time t; represents the power generation of the electric-hydrogen conversion device in the H2P operation mode of the i-th PIES at time t; They represent the upper and lower limits of the power input of the electric-hydrogen conversion device in the P2H mode respectively; A 0-1 indicator variable representing the P2H operation mode of the electric-to-hydrogen converter of the i-th PIES at time t; A 0-1 indicator variable representing the H2P operation mode of the electric-hydrogen conversion device of the i-th PIES at time t; They represent the upper and lower limits of the power output of the electric-hydrogen conversion device in the H2P mode respectively; Indicates the electricity-to-hydrogen conversion coefficient of the electricity-to-hydrogen conversion device in the P2H operating state; Indicates the hydrogen-to-electricity conversion coefficient of the electric-hydrogen conversion device in the P2H operating state.

[0139] 3) Operation constraints of gas boiler units:

[0140]

[0141] In formula (4), represents the heat production capacity of the i-th PIES gas boiler unit at time t; represents the natural gas consumption of the i-th PIES gas boiler unit at time t; Indicates the upper limit of the heat production capacity of the gas boiler unit; α GB Indicates the operation coefficient of the gas boiler unit.

[0142] 4) Operational constraints of energy storage batteries:

[0143]

[0144] In formula (5), Respectively represent the upper limit of charge and discharge of ESS; represents the storage capacity of the i-th PIES energy storage battery at time t; represents the storage capacity of the i-th PIES energy storage battery at time t-1; A 0-1 indicator variable representing the charging status of the i-th PIES energy storage battery at time t; η is a 0-1 indicator variable representing the discharge state of the i-th PIES energy storage battery at time t; ch ,η disRespectively represent the charging and discharging efficiency of the energy storage battery; They respectively represent the upper and lower limits of the energy storage capacity of the energy storage battery.

[0145] 5) Energy balance constraints:

[0146]

[0147] In the above formula, represents the renewable energy output power of the i-th PIES at time t; They represent the electrical load and thermal load of the i-th PIES at time t, respectively.

[0148] In step 2, the establishment of a robust coordinated scheduling model for a multi-park integrated energy system is as follows:

[0149] Each Park Integrated Energy System (PIES) can achieve point-to-point hydrogen energy interaction with other Park Integrated Energy Systems (PIES) through hydrogen vehicle transportation. The geographical distance between Park Integrated Energy Systems (PIES) cannot be ignored. When limiting the hydrogen content in the energy storage process, it is necessary to consider the hydrogen transportation time. Therefore, the hydrogen mass in the hydrogen storage tank in one day can be expressed as:

[0150]

[0151] In formula (8), is the mass of hydrogen stored in the i-th system hydrogen storage tank at time t+1; is the mass of hydrogen stored in the i-th system hydrogen storage tank at time t. Since hydrogen delivery is delayed by 1 hour, the hydrogen transported at time t-1 is transported to the system hydrogen storage tank for storage at time t. Therefore, It represents the amount of hydrogen purchased by the i-th system from the j-th system through the l-th hydrogen vehicle at time t-1, and arriving at time t; represents the amount of hydrogen sold by the i-th system to the j-th system through the l-th hydrogen vehicle at time t; i and j are the indexes of the park's integrated energy system number; △t represents the time of a scheduling period; N l Indicates the number of long tube trailers in the multi-park integrated energy system alliance;

[0152] In addition, hydrogen vehicles for hydrogen transportation need to meet certain constraints, as shown in the following equation (9):

[0153]

[0154] In formula (9), represents the hydrogen storage capacity of the lth hydrogen vehicle at time t, Indicates the hydrogen storage capacity of the lth hydrogen vehicle at time t-1; Indicates the upper limit of hydrogen storage capacity of hydrogen vehicles; A 0-1 indicator variable representing the hydrogen charging status of the lth hydrogen vehicle at time t; represents the hydrogen discharge state of the lth hydrogen vehicle at time t (0-1 indicator variable); η represents the hydrogen charging and discharging efficiency; It represents the maximum amount of hydrogen charged by the lth hydrogen vehicle at time t within a single dispatch period △t; It represents the maximum amount of hydrogen released by the lth hydrogen vehicle at time t within a single scheduling period △t;

[0155] In addition, the number of long-tube trailers within the multi-park integrated energy system alliance is limited. The number of hydrogen vehicles between each park integrated energy system (PIES) in a day is also restricted. In addition, the hydrogen storage state of the hydrogen storage tanks has certain requirements and needs to operate within a certain hydrogen storage range.

[0156]

[0157] In formula (10), N l Indicates the number of long tube trailers in the multi-park integrated energy system alliance; is the mass of hydrogen stored in the i-th system hydrogen storage tank at time t. are the maximum and minimum hydrogen storage capacities of the hydrogen storage tank, respectively. The first equation in (10) indicates that the number of hydrogen vehicles in operation needs to be limited to a certain number, and the second equation indicates that the hydrogen storage tank of the i-th PIES needs to operate within a certain range.

[0158] After hydrogen energy interaction, each PIES will conduct peer-to-peer hydrogen energy transactions through cooperation. The hydrogen energy interaction cost of each PIES is shown in the following formula.

[0159]

[0160] In formula (11), represents the hydrogen energy interaction cost of the i-th PIES; Respectively represent the purchase and sale prices of hydrogen energy when each PIES conducts peer-to-peer transactions;

[0161] Collaborative sharing effectively takes into account the unity of individual interests and overall interests. Therefore, based on the independent PIES objective function of formula (1), the overall objective function based on the PIES collaborative scheduling model is established as shown in the following formula (12):

[0162]

[0163] In formula (12), N represents the total dispatch cost of the i-th PIES after participating in the PIES alliance of hydrogen energy interaction; g Indicates the number of PIES in the park integrated energy system alliance.

[0164] In addition, in actual systems, renewable energy output Electrical load demand and heat load requirements It is susceptible to prediction errors and manifests as uncertainty. The solutions obtained by the deterministic optimization model often appear too "risky" and the impact of uncertainty needs to be taken into account in the model. Considering the fluctuation range of renewable energy output and load power is located in the box-type uncertainty set Ω constructed by formula (13) u Inside:

[0165]

[0166] In formula (13) It is the predicted value of new energy output; is the predicted value of electric load output; is the predicted value of heat load output; The maximum fluctuation deviation of the predicted value of renewable energy output; is the maximum fluctuation deviation of the electric load forecast value; is the maximum fluctuation deviation of the heat load prediction value; Ω u An uncertainty set constructed to account for uncertain variables.

[0167] After considering the uncertainty of the system as shown in formula (13), the goal of the present invention becomes to find the uncertainty of the variables in the uncertainty set Ω u The optimal scheduling solution of the multi-PIES alliance when the internal changes towards the worst scenario is as follows:

[0168]

[0169] In formula (14): and Represents the coefficient matrix associated with the objective function in a compact form; the variable x i Represents all scheduling and operating status variables of the i-th PIES; variable y i represents the procurement of electricity, natural gas and equipment scheduling and operation plan of the i-th PIES; u i represents the uncertain variable of the i-th PIES source load.

[0170] x i 、y i and u i Specifically, they are shown in the following formulas (15) to (17):

[0171]

[0172]

[0173] Equation (14) is essentially a two-level game between the system operator and nature: the operator first makes an irreversible decision x i , then nature never determines the set Ω u Select the worst scenario u i To maximize the total cost, the operator finally adjusts the decision y i Minimize the loss in this scenario. After considering the system uncertainty, to facilitate subsequent explanation and model solvability, the objective function (14), the constraints (2) to (10), and the uncertainty constraint (13) are rewritten into the compact form of the following two-stage robust optimization model, as shown in (18) and (19).

[0174] The first-stage optimization model determines the operation plan, as shown in formula (18):

[0175]

[0176] In formula (18), It is reconstructed from formula (12);

[0177] C i x i，t +D i y i，t ≤b i is the independent constraint of each system i, including equations (2) to (7);

[0178] is the coupling constraint between different PIES systems, mainly hydrogen energy interaction constraint, including equations (8) to (10); C i 、D i and b i The coefficient matrix representing the independent constraints of the park integrated energy system i;

[0179] E i and d i The coefficient matrix representing the coupling constraints of the integrated energy systems of different parks;

[0180] The second-stage optimization model is established to find the worst-case scenario for purchasing natural gas and utilizing energy storage batteries under an uncertain source load set. As shown in Equation (19):

[0181]

[0182] In formula (19), It is to add the corresponding slack variables to each constraint and sum up all the slack variables;

[0183] G i z i +ξ i ≤hi -L i u i -M i x i -N i y i To consider the independent constraints of each system i under uncertain variables, including equations (2)-(7) and (13);

[0184] In order to consider the coupling constraints between different PIES systems under uncertain variables, including equations (8) to (10); Φ(x i ,y i ) represents the decision x of the given first-stage optimization model i Under the worst uncertainty scenario u i By optimizing and adjusting y i The minimum constraint violation that must be tolerated after The maximum value of

[0185] ξ i represents the slack variable vector of the objective function of the i-th PIES under robust optimization at time t;

[0186] L i 、M i 、N i 、h i The coefficient matrix of the compact form of the independent constraints of the system considering uncertainty;

[0187] K i 、g i The coefficient matrix of the compact form of the coupling constraints for different systems considering uncertainties;

[0188] In step 2, the objective function of the robust coordinated scheduling model of the multi-park integrated energy system is formula (14), and the constraints are formulas (2)-(11) and (13); under uncertain conditions, in order to make the model solvable, it is expressed as a two-stage robust coordinated scheduling model of the multi-park integrated energy system as shown in formulas (18) and (19), where formula (18) is the decision-making operation mode of the first-stage optimization model, and the second-stage optimization model shown in formula (19) is to find the worst scenario of purchasing natural gas and utilizing energy storage batteries under an uncertain source load set.

[0189] In step 3, the second-stage optimization model of the robust coordinated scheduling model of the multi-park integrated energy system established in step 2 is optimized. This is essentially a feasibility check problem, that is, for the optimal result of the first-stage optimization model, for any scenario in the uncertainty set, y i，tThe solution always exists, so the second-stage optimization model (lower-layer model) of the robust coordinated scheduling model of the multi-park integrated energy system as shown in formula (19) can be written as follows:

[0190]

[0191] In formula (20), Indicates the existence of y i The constraints in formula (20) can be satisfied; (x i ,y i ) means that for any uncertain variable u i Feasible scenarios for the second-stage optimization model (lower-level model);

[0192] Based on Fourier-Motzkin elimination, the above formula (20) is projected onto the space defined by the variables and uncertain variables of the first-stage optimization model, thereby eliminating the decision variables of the second-stage optimization model and obtaining the following constraints.

[0193]

[0194] In formula (21), V i X 、V i Y 、V i U and f i is the parameter matrix generated by Fourier-Motzkin elimination;

[0195] Furthermore, the following formula (22) can be guaranteed to hold true for any uncertain variables.

[0196]

[0197] In formula (22), and represents the constant matrix related to the uncertainty concentration constraint of the i-th PIES; [V i U ] k represents the coefficient of the uncertain variable in the kth constraint after Fourier-Motzkin elimination; V i U represents the coefficient matrix of uncertain variables after Fourier-Motzkin elimination; Ω i represents all scenarios of the uncertain set; [χ i ] k represents the dual variable of the kth constraint; χ i The dual variable matrix of the constraint; k represents the kth constraint in the compact constraint form of equation (19);

[0198] After the equivalent transformation process of the above formula (20) to formula (22), the original second-stage optimization model (lower-layer model) shown in formula (19) can be equivalent to the constraints shown in formula (23):

[0199]

[0200] Therefore, the original two-stage robust optimization problem shown in Equation (18) and Equation (19) is finally transformed into a mixed integer programming (MILP) problem as shown in Equation (24):

[0201]

[0202] The mixed integer programming collaborative scheduling model in step 3 is obtained by equivalently transforming the original two-stage robust optimization model shown in equations (18) and (19). Specifically, the second-stage optimization model shown in equation (19) is equivalently transformed. The second-stage optimization model shown in equation (19) is transformed into the constraints shown in equation (23) through the method of equations (20)-(22), and then embedded in the first-stage optimization model shown in (18), becoming the MILP model shown in equation (24). This eliminates the need for iterative solution and speeds up computational efficiency.

[0203] In step 4, since the mixed integer programming (MILP) model converted in step 3 involves multiple different stakeholders, the information that can be transmitted to each other is limited. In addition, the established MILP model is a non-convex model, and the commonly used distributed algorithm may not be able to find an exact solution for it. The decomposition technology is used to divide the overall Lagrangian dual problem of coordinated scheduling of multi-park integrated energy systems into a single-park integrated energy system problem, and the subgradient algorithm is used to update the dual variables, thereby obtaining a convergent distributed solution to the dual problem. The contraction coefficient is introduced to restore the feasible original solution and ensure the feasibility of the dual solution;

[0204] After introducing the shrinkage coefficient ρ, the mixed integer programming (MILP) obtained in step 3 can be reconstructed into the following model.

[0205]

[0206] In formula (25), δ i is the shrinkage coefficient, In order to introduce the compact form of the multi-PIES coupling constraint after the shrinkage coefficient is introduced, its Lagrangian dual formula is derived as follows:

[0207]

[0208] In formula (26), λ T (d i -δ) indicates that the coupling constraint The marginal opportunity cost contribution to the original problem objective function; δ represents the shrinkage coefficient; λ T Constrained The transpose of the dual variable of ; E i The meaning of representation is the same as mentioned above, both are compact form matrices.

[0209] Where λ is the dual variable of the coupling constraint, and the contraction coefficient can be defined by the following equation (27):

[0210]

[0211] In formula (27), q is the shrinkage factor, n is the row of the coupling constraint matrix; [E i ] nk Indicates the specific coefficient of the kth variable in the nth coupling constraint among different PIES coupling variables, which is used to calculate the marginal contribution. i is the coefficient matrix of different PIES coupling variables.

[0212] After obtaining the initial dual variable λ j and the contraction coefficient δ i After RIES i According to the Park Integrated Energy System Alliance, RIES is removed i All other RIES j Transmitted Lambda j , according to the weight factor γ ij Compute the other PIES dual variables λ j The average value of the dual variable θ passed in i , as shown below:

[0213]

[0214] In formula (28), k is the number of iterations. Based on the average value, RIES i Fix the dual variable to θ i (k), and perform the following minimum optimization problem.

[0215]

[0216] In formula (29), y i (k+1) represents y after the k+1th iteration i The specific value of θ i (k) T It represents the average value of the dual variables passed to the i-th PIES by other PIES except the i-th PIES in the k-th iteration.

[0217] After performing the above minimum optimization problem, a tentative solution y can be obtained i(k+1), according to E i y i (k+1) calculate PIES i The worst contribution to the coupling constraint can then be updated with the following maximum consensus strategy: i The shrinkage coefficient.

[0218]

[0219] In formula (30), φ i (k) is the maximum value of all contraction coefficients transferred from subsystem j except subsystem i itself; δ j (k) indicates that the source is not PIES i Other PIES j The transferred shrinkage coefficient; Represents the maximum value of all contraction coefficients transferred from other subsystems j; It is represented as the auxiliary record variable with the worst contribution upper limit in the k+1th iteration; Auxiliary record variable for the worst contribution upper limit in the kth iteration; It is represented as the auxiliary record variable with the worst contribution lower bound in the k+1th iteration; Auxiliary record variable for the worst contribution lower limit; δ i (k+1) represents the specific value of the shrinkage coefficient after the k+1th iteration obtained by the maximum consensus strategy shown in formula (30); k represents the number of iterations.

[0220] Finally, the dual variables are updated with subgradients as follows:

[0221] λ i (k+1)=[θ i (k)+ω(E i y i (k+1)-(d i -δ i (k+1)) / N g ] + (31);

[0222] In formula (31), λ i (k+1) represents the specific value of the dual variable of the coupling constraint after the k+1th iteration after the subgradient update; ω is the update step size, [·] + represents the projection on the q-dimensional non-negative orthogonal; N g The number of PIES in the park integrated energy system alliance; each PIES only i (k) and δ i(k) interact with other PIES, so no private information will be disclosed. In step 5, a multi-park integrated energy system collaborative optimization model based on the feasible domain equivalent projection is established. Specifically, the formula programmed in the Matlab2020 environment is:

[0223] Write a program in the Matlab 2020 environment and call the GUROBI solver based on the YALMIP platform for solution, as follows:

[0224] First, based on the Matlab2020 environment, all optimization variables are classified into equations (15) to (17), and according to the objective function equation (12) and the constraints equations (2) to (10), a two-stage robust optimization problem of the multi-park integrated energy system is constructed as shown in equations (18) and (19);

[0225] Then, using the feasible region projection theory formulas (20) to (22) proposed in step 3, the lower layer problem of the two-stage robust problem of the original model shown in formula (19) is converted into the constraints shown in formula (23) and introduced into the first stage optimization model of the original two-stage robust problem (18), thereby converting it into the model shown in formula (24);

[0226] Finally, the dual decomposition algorithm proposed in step 4 is used to split the centralized MILP model shown in Equation (22) into sub-problems for each park through Lagrangian relaxation. The distributed optimization framework of Equations (25) to (31) is used to solve the problem by calling the GUROBI solver based on the YALMIP platform.

[0227] Verification example:

[0228] An integrated energy system alliance consisting of three park integrated energy systems was built. All models and algorithms were programmed and implemented on MATLAB 2021a and solved using Gurobi 10.0.2.

[0229] The structure of the park's comprehensive energy system considering the integration of multiple energy flows and hydrogenation of natural gas is as follows: Figure 2 As shown in the figure, the multi-alliance cooperation model considering hydrogen energy interaction is as follows Figure 3 The electricity price of the external grid is 0.38 yuan / kW from 00:00 to 07:00, 0.45 yuan / kW from 23:00 to 24:00, and 0.56 yuan / kW at other times. Other system parameters are shown in Table 1. The system parameters and algorithm parameters of all PIES are consistent. The load and renewable energy output forecast curves of each PIES are shown in Figure 4 As shown, the uncertainty set is defined as a 10% fluctuation in its predicted value.

[0230] Table 1 System parameters

[0231]

[0232] Based on the above system parameters, taking PIES1 as an example, the scheduling and operation plan is as follows Figure 5 and Figure 6 As shown. Figure 5 As can be seen, in terms of power dispatch planning, internal wind and solar power generation is prioritized within the system, ensuring full utilization of renewable energy. The system meets power demand through a variety of methods, including power exchange, combined heat and power (CHP) generation, energy storage discharge, power generation from the power-to-hydrogen converter, and external power purchases. Between 00:00 and 07:00, when electricity prices are low, the system purchases a large amount of power from the grid. Considering system optimization over the entire timeframe, the EES requires significant power during charging between 13:00 and 14:00 and 19:00 and 22:00. When electricity prices peak and load is high, the power-to-hydrogen converter and energy storage system release significant amounts of power to meet demand. From 23:00 to 24:00, when electricity prices drop slightly and load is low, the system deactivates the energy storage system and continues to increase power purchases from the grid. Any power shortfalls in the system throughout the day are supplemented by power generation from the CHP units.

[0233] Depend on Figure 6 As can be seen, the heat supply within the system is relatively simple, with heat generated by the cogeneration unit and a small amount by the gas boiler, sufficient to meet the system's heat needs. The optimal dispatch cost for PIES1 is 16,527.46 yuan, which includes 7,258.16 yuan for electricity purchase, 8,433.27 yuan for gas purchase, 598.52 yuan for EES operation, and 437.52 yuan for hydrogen energy interaction.

[0234] The above analysis of typical days shows that the integrated energy system proposed in the present invention can fully utilize renewable energy for power generation and heat production, realize timely energy conversion and storage through the coupling of multiple energy sources, and reduce the energy purchase demand during the system peak period through efficient multi-energy storage and supply, gas-hydrogen blending, and other methods, thereby fully tapping the potential of hydrogen energy.

[0235] To compare and analyze the effectiveness of the gas-hydrogen blending mechanism and the hydrogen energy interactive and synergistic operation mode, four comparison scenarios were set up. Case 1 serves as the baseline case, while Cases 2 and 3 are used to verify the effectiveness of the gas-hydrogen blending mechanism and the hydrogen energy interactive mode, respectively. Case 4 further analyzes the economic efficiency and flexibility of the integrated energy system under these two scenarios.

[0236] Scenario 1: In a traditional integrated energy system, each integrated energy system operates independently, and natural gas is delivered to the cogeneration unit without hydrogen.

[0237] Scenario 2: In an integrated energy system with a gas-hydrogen blending mechanism, each integrated energy system operates independently, but hydrogen is blended into the natural gas and delivered to the cogeneration unit.

[0238] Scenario 3: In an integrated energy system under the hydrogen energy interaction mode, each integrated energy system can transport stored hydrogen through the hydrogen network, and natural gas is delivered to the cogeneration unit without hydrogen.

[0239] Scenario 4: In an integrated energy system with a gas-hydrogen blending mechanism and a hydrogen energy interaction mode, each integrated energy system can transport stored hydrogen through the hydrogen network, and hydrogen blended in natural gas can be delivered to the cogeneration unit.

[0240] Table 2 shows the dispatch costs for the four comparison scenarios. First, due to the utilization of gas-hydrogen blending, Scenario 2 reduces the total cost by 5.0% compared to Scenario 1, demonstrating the economic efficiency of the comprehensive utilization of hydrogen energy. In Scenario 1, hydrogen can only be burned in the electricity-to-hydrogen conversion system, resulting in low combustion efficiency. The coupling characteristics of hydrogen and natural gas are not considered. Therefore, during peak thermal loads, PIES needs to purchase additional electricity from the upstream power grid and gas grid to ensure system supply and demand balance, resulting in increased energy transaction costs. Scenario 2, on the other hand, incorporates the gas-hydrogen blending mechanism, enabling hydrogen to be used both in the electricity-to-hydrogen conversion system and in the combined heat and power (CHP) unit. This enhances energy coupling and improves energy efficiency while also modifying the combustion characteristics of natural gas. However, due to this energy coupling, hydrogen can be better utilized to provide thermal energy, resulting in a slight reduction in electricity supply, leading to a slight increase in electricity purchase and storage costs, but overall costs remain on a downward trend.

[0241] After considering peer-to-peer hydrogen energy exchange transactions, the total costs of Scenarios 3 and 4 are 9.6% and 8.3% lower than those of Scenarios 1 and 2, respectively. The inclusion of hydrogen energy exchange can mitigate the underutilization of renewable energy caused by the spatiotemporal mismatch between sources and loads in the integrated energy system, reduce the energy dependence of each integrated energy system on the parent network, and achieve a mutually beneficial and win-win situation for multiple integrated energy systems. Compared to Scenarios 1 and 2, Scenarios 3 and 4 consider cooperation among integrated energy systems. Table 2 shows that the gas purchase costs of PIES1 and PIES3 decreased, while those of PIES2 increased. This is because PIES2, in order to earn more profit from hydrogen energy exchange, reduced its own hydrogen reserves, thereby purchasing natural gas from the parent gas grid to smooth its own load fluctuations. In contrast, PIES1 and PIES3 reduce their energy purchase costs by partially sharing energy with PIES2 instead of purchasing energy from the parent energy system, resulting in a reduction in the amount of energy purchased. Considering hydrogen energy interoperability point-to-point trading can help promote complementary energy surpluses and shortages among PIES, increase energy trading profits, and reduce reliance on parent system resources, thereby significantly reducing energy trading costs. Furthermore, Scheme 4, which combines optimization with gas hydrogen blending and hydrogen energy interoperability point-to-point trading, reduces total costs by 6.7% and 1.9% compared to Schemes 2 and 3, respectively. This is higher than the combined cost-effectiveness of these two options considered separately. This demonstrates that considering both gas hydrogen blending and hydrogen energy sharing can further enhance hydrogen energy dispatchability and help reduce total costs.

[0242] Table 2 Dispatch costs of multi-integrated energy systems under different scenarios

[0243]

[0244] The iterative situation of decentralized optimization using the method proposed in this invention is as follows: Figure 7 As shown in the figure, the decentralized optimization iteration converges after 10 iterations, and the total solution time is 14.3s. This method realizes the multi-RIEHS robust optimization scheduling under decentralized scheduling conditions, and its running time fully meets the requirements of day-ahead scheduling in the current market environment.

[0245] To further demonstrate the superiority of the method of the present invention, the following four different methods are used to compare with the method proposed in the present invention. The best results of various optimization methods are shown in Table 3. The comparison scheme is as follows:

[0246] Case 1: Aiming at the uncertainty of the integrated energy system, a traditional two-stage robust model is established and solved using centralized scheduling.

[0247] Case 2: Aiming at the uncertainty of the integrated energy system, a MILP robust scheduling model based on feasible domain projection is established, and a centralized scheduling solution is adopted.

[0248] Case 3: Aiming at the uncertainty of the integrated energy system, a traditional two-stage robust model is established and the ADMM algorithm is used for decentralized solution.

[0249] Case 4: Aiming at the uncertainty of the integrated energy system, a MILP robust scheduling model based on feasible domain projection is established, and the ADMM algorithm is used for decentralized solution.

[0250] Case 5: Aiming at the uncertainty of the integrated energy system, a MILP robust scheduling model based on feasible domain projection is established, and the algorithm proposed in this paper is used for decentralized solution.

[0251] Table 3 Optimization results under different optimization methods

[0252]

[0253] As can be seen from Table 3, the optimal total costs obtained for Case 1 and Case 2 are the same, indicating that the feasible domain equivalent projection can accurately transform the two-stage robust problem into an equivalent MILP problem solution.

[0254] Furthermore, the equivalent MILP problem based on the feasible region does not require the two-stage iterations of the C&CG algorithm. Therefore, the solution rate is significantly improved compared to the two-stage robust model. For the decentralized solution of this equivalent MILP robust model, this method achieves the optimal total cost, which is close to the centralized optimal solution result with only a 0.26% error. The ADMM-based decomposition improves the total cost by 1.8%. These results clearly show that the dual decomposition effectively decouples the multi-integrated energy system coupling model without sacrificing optimality. Furthermore, the ADMM-based MILP robust model requires 21 iterations to converge. This is because the multiplier updates in the ADMM are not in the gradient descent direction as in the dual decomposition, resulting in slower convergence. Furthermore, the average runtime per iteration of the ADMM algorithm is 4.06 seconds, which is 2.84 times longer than the average runtime of the dual decomposition algorithm of the present invention. This is because the ADMM repeatedly solves the binary fixation and relaxation problem in each iteration to deal with the undesirable non-convexity, which significantly increases the solution burden.

[0255] In summary, the equivalent MILP robust model based on feasible domain projection and the dual decomposition algorithm proposed in the present invention have superior computational performance, which is conducive to the online implementation of the decentralized robust scheduling and decision-making method.

Claims

1. A collaborative optimization method for multi-park integrated energy systems based on equivalent projection theory, characterized by The following steps are involved: Step 1: By integrating the coupling of multiple energy flows, a comprehensive energy system scheduling model for the park considering hydrogen blending of natural gas was established; Step 2: Considering the hydrogen energy interaction and energy load uncertainty of the multi-park integrated energy system, based on the park integrated energy system scheduling model established in step 1, a robust coordinated scheduling model for the park integrated energy system participating in the multi-park integrated energy system alliance is established; Step 3: Based on the equivalent projection theory, the two-layer district integrated energy system robust coordinated scheduling model established in step 2 is equivalent to a single-layer mixed integer programming coordinated scheduling model; Step 4: Use the dual decomposition algorithm to derive the decentralized solution of the mixed integer programming collaborative scheduling model established in step 3; Step 5: Establish and solve the collaborative optimization model of multi-park integrated energy system based on the equivalent projection of the feasible domain.

2. The method for collaborative optimization of a multi-park integrated energy system based on equivalent projection theory according to claim 1 is characterized by: In step 1, the establishment of a comprehensive energy system scheduling model for a park considering hydrogen-blended natural gas is as follows: The park integrated energy system takes minimizing the total operating cost as its optimization goal. Before hydrogen energy interaction, the total operating cost of each park integrated energy system i is composed of three parts: the electricity purchase cost from the power grid, the gas purchase cost from the gas grid, and the energy storage cost, as shown below; In formula (1), is the total cost of independent operation of the i-th PIES without considering hydrogen energy interaction, is the electricity purchase cost of the i-th PIES grid, is the cost of purchasing gas from the i-th PIES gas network, is the energy storage cost of the i-th PIES; p buy 、p sell Respectively represent the price of buying and selling electricity from the main grid; p gas represents the price of natural gas; represents the gas consumption of the i-th PIES cogeneration unit at time t; represents the gas consumption of the i-th PIES gas boiler unit at time t; α EES Indicates the cost coefficient of energy storage battery utilization; They represent the ESS charge and discharge capacity of the i-th PIES at time t; They represent the amount of electricity purchased and sold by the i-th PIES to the main network at time t, respectively; t is the index of the current scheduling time, and T is the total number of time steps in the scheduling cycle.

3. The method for collaborative optimization of multi-park integrated energy systems based on equivalent projection theory according to claim 2 is characterized by: The operational constraints of the integrated energy system scheduling model for the park considering hydrogen blending with natural gas include: the operational constraints of the cogeneration unit, the electricity-hydrogen conversion device, the gas boiler, the energy storage battery, and the energy balance constraints, which are as follows: 1) Operational constraints of cogeneration units: In formula (2), represents the power generation capacity of the i-th PIES cogeneration unit at time t, represents the heat production capacity of the i-th PIES cogeneration unit at time t; represents the natural gas consumption of the ith PIES cogeneration unit at time t, represents the hydrogen consumption of the i-th PIES cogeneration unit at time t; Indicates the maximum power generation of the cogeneration unit; represents the efficiency coefficient of natural gas power generation; represents the power generation efficiency coefficient of hydrogen; Indicates the heating efficiency coefficient of natural gas; Indicates the heating efficiency coefficient of hydrogen; 2) Operational constraints of the electric-hydrogen conversion device: In formula (3), represents the hydrogen production of the electric-hydrogen conversion device in the P2H operation mode of the i-th PIES at time t; represents the hydrogen consumption of the electric-hydrogen conversion device in the H2P operation mode of the i-th PIES at time t; represents the power consumption of the electric-hydrogen conversion device in the P2H operation mode of the i-th PIES at time t; represents the power generation of the electric-hydrogen conversion device in the H2P operation mode of the i-th PIES at time t; They represent the upper and lower limits of the power input of the electric-hydrogen conversion device in the P2H mode respectively; A 0-1 indicator variable representing the P2H operation mode of the electric-to-hydrogen converter of the i-th PIES at time t; A 0-1 indicator variable representing the H2P operation mode of the electric-hydrogen conversion device of the i-th PIES at time t; They represent the upper and lower limits of the power output of the electric-hydrogen conversion device in the H2P mode respectively; Indicates the electricity-to-hydrogen conversion coefficient of the electricity-to-hydrogen conversion device in the P2H operating state; Indicates the hydrogen-to-electricity conversion coefficient of the electric-hydrogen conversion device in the P2H operating state; 3) Operation constraints of gas boiler units: In formula (4), represents the heat production capacity of the i-th PIES gas boiler unit at time t; represents the natural gas consumption of the i-th PIES gas boiler unit at time t; Indicates the upper limit of the heat production capacity of the gas boiler unit; α GB Indicates the operation coefficient of the gas boiler unit; 4) Operational constraints of energy storage batteries: In formula (5), Respectively represent the upper limit of charge and discharge of ESS; represents the storage capacity of the i-th PIES energy storage battery at time t; represents the storage capacity of the i-th PIES energy storage battery at time t-1; A 0-1 indicator variable representing the charging state of the i-th PIES energy storage battery at time t; η is a 0-1 indicator variable representing the discharge state of the i-th PIES energy storage battery at time t; ch ,η dis Respectively represent the charging and discharging efficiency of the energy storage battery; Respectively represent the upper and lower limits of the energy storage capacity of the energy storage battery; 5) Energy balance constraints: In the above formula, represents the renewable energy output power of the i-th PIES at time t; They represent the electrical load and thermal load of the i-th PIES at time t, respectively.

4. The method for collaborative optimization of multi-park integrated energy systems based on equivalent projection theory according to claim 3 is characterized by: In step 2, the establishment of a robust coordinated scheduling model for a multi-park integrated energy system is as follows: The mass of hydrogen in the hydrogen storage tank in one day is expressed as: In formula (8), is the mass of hydrogen stored in the i-th system hydrogen storage tank at time t+1; is the mass of hydrogen stored in the i-th system hydrogen storage tank at time t; since hydrogen delivery is delayed by 1 hour, the hydrogen transported at time t-1 is transported to the system hydrogen storage tank for storage at time t, therefore, It represents the amount of hydrogen purchased by the i-th system from the j-th system through the l-th hydrogen vehicle at time t-1, and arriving at time t; represents the amount of hydrogen sold by the i-th system to the j-th system through the l-th hydrogen vehicle at time t; i and j are the indexes of the park's integrated energy system number; △t represents the time of a scheduling period; N l Indicates the number of long tube trailers in the multi-park integrated energy system alliance; In addition, the hydrogen vehicle for hydrogen transportation satisfies the constraints as shown in the following equation (9): In formula (9), represents the hydrogen storage capacity of the lth hydrogen vehicle at time t, Indicates the hydrogen storage capacity of the lth hydrogen vehicle at time t-1; Indicates the upper limit of hydrogen storage capacity of hydrogen vehicles; A 0-1 indicator variable representing the hydrogen charging status of the lth hydrogen vehicle at time t; represents the hydrogen discharge state of the lth hydrogen vehicle at time t (0-1 indicator variable); η represents the hydrogen charging and discharging efficiency; It represents the maximum amount of hydrogen charged by the lth hydrogen vehicle at time t within a single dispatch period △t; It represents the maximum amount of hydrogen released by the lth hydrogen vehicle at time t within a single scheduling period △t; In addition, the number of long-tube trailers within the multi-park integrated energy system alliance is limited. The number of hydrogen vehicles between each park integrated energy system PIES in a day is also restricted. In addition, the hydrogen storage state of the hydrogen storage tank has certain requirements and needs to operate within a certain hydrogen storage range. In formula (10), N l Indicates the number of long tube trailers in the multi-park integrated energy system alliance; is the mass of hydrogen stored in the i-th system hydrogen storage tank at time t; are the maximum and minimum hydrogen storage capacities of the hydrogen storage tank, respectively; the first formula in formula (10) indicates that the number of hydrogen vehicles in operation needs to be limited to a certain number, and the first formula indicates that the hydrogen storage tank of the i-th PIES needs to work within a certain range; After hydrogen energy interaction, each PIES will conduct peer-to-peer hydrogen energy transactions through cooperation. The hydrogen energy interaction cost of each PIES is shown in the following formula: In formula (11), represents the hydrogen energy interaction cost of the i-th PIES; Respectively represent the purchase and sale prices of hydrogen energy when each PIES conducts peer-to-peer transactions; Collaborative sharing effectively takes into account the unity of individual interests and overall interests. Therefore, based on the independent PIES objective function of formula (1), the overall objective function based on the PIES collaborative scheduling model is established as shown in the following formula (12): In formula (12), N represents the total dispatch cost of the i-th PIES after participating in the PIES alliance of hydrogen energy interaction; g Indicates the number of PIES in the park integrated energy system alliance.

5. The method for collaborative optimization of multi-park integrated energy systems based on equivalent projection theory according to claim 4 is characterized by: Considering the fluctuation range of new energy output and load power is located in the box-type uncertainty set Ω constructed by formula (13) u Inside: In formula (13) It is the predicted value of new energy output; is the predicted value of electric load output; is the predicted value of heat load output; The maximum fluctuation deviation of the predicted value of renewable energy output; is the maximum fluctuation deviation of the electric load forecast value; is the maximum fluctuation deviation of the heat load prediction value; Ω u Uncertainty sets constructed to account for uncertain variables; After considering the uncertainty of the system as shown in Equation (13), the goal becomes to find the variables with uncertainty in the uncertainty set Ω u The optimal scheduling solution of the multi-PIES alliance when the internal changes towards the worst scenario is as follows: In formula (14): and Represents the coefficient matrix associated with the objective function in a compact form; the variable x i Represents all scheduling and operating status variables of the i-th PIES; variable y i represents the procurement of electricity, natural gas and equipment scheduling and operation plan of the i-th PIES; u i represents the uncertain variable of the i-th PIES source load; x i 、y i and u i Specifically, they are shown in the following formulas (15) to (17): Equation (14) essentially represents a two-level game between the system operator and nature: the operator first makes an irreversible decision x i , then nature never determines the set Ω u Select the worst scenario u i To maximize the total cost, the operator finally adjusts the decision y i Minimize the losses in this scenario.

6. The method for collaborative optimization of multi-park integrated energy systems based on equivalent projection theory according to claim 5 is characterized by: After considering the uncertainty of the system, the objective function (14), the constraints (2) to (10), and the uncertain constraint (13) are rewritten into the compact form of the following two-stage robust optimization model, as shown in (18) and (19); The first-stage optimization model determines the operation plan, as shown in formula (18): In formula (18), It is reconstructed from formula (12); C i x i，t +D i y i,t ≤b i is the independent constraint of each system i, including equations (2) to (7); is the coupling constraint between different PIES systems, including equations (8) to (10); C i 、D i and b i The coefficient matrix representing the independent constraints of the integrated energy system i of the park; E i and d i The coefficient matrix representing the coupling constraints of the integrated energy systems of different parks; The second-stage optimization model is established to find the worst-case scenario for purchasing natural gas and utilizing energy storage batteries under an uncertain source load set, as shown in Equation (19): In formula (19), It is to add the corresponding slack variables to each constraint and sum all the slack variables; G i z i +ξ i ≤h i -L i u i -M i x i -N i y i To consider the independent constraints of each system i under uncertain variables, including equations (2)-(7) and (13); In order to consider the coupling constraints between different PIES systems under uncertain variables, including equations (8) to (10); Φ(x i ,y i ) represents the decision x of the given first-stage optimization model i Under the worst uncertainty scenario u i By optimizing and adjusting y i The minimum constraint violation that must be tolerated after The maximum value of ξ i represents the slack variable vector of the objective function of the i-th PIES under robust optimization at time t; L i 、M i 、N i 、h i The coefficient matrix of the compact form of the independent constraints of the system considering uncertainty; K i 、g i is the coefficient matrix of the compact form of the coupling constraints for different systems considering uncertainties.

7. The method for collaborative optimization of multi-park integrated energy systems based on equivalent projection theory according to claim 6 is characterized by: In step 3, the second-stage optimization model of the multi-park integrated energy system robust coordinated scheduling model established in step 2 is optimized. For the optimal result of the first-stage optimization model, for any scenario in the uncertainty set, y i,t The solution always exists, so the second-stage optimization model of the robust coordinated scheduling model of the multi-park integrated energy system shown in formula (19) is written as follows: In formula (20), Indicates the existence of y i Satisfy the constraints in formula (20); (x i ,y i ) means that for any uncertain variable u i The feasible scenarios of the second stage optimization model; Based on Fourier-Motzkin elimination, the above formula (20) is projected onto the space defined by the variables and uncertain variables of the first-stage optimization model, thereby eliminating the decision variables of the second-stage optimization model, and thus obtaining the following constraints; In formula (21), V i X 、V i Y 、V i U and f i is the parameter matrix generated by Fourier-Motzkin elimination; In addition, the following formula (22) can be guaranteed to hold true for any uncertain variables; In formula (22), and represents the constant matrix related to the uncertainty concentration constraint of the i-th PIES; [V i U | k represents the coefficient of the uncertain variable in the kth constraint after Fourier-Motzkin elimination; V i U represents the coefficient matrix of uncertain variables after Fourier-Motzkin elimination; Ω i represents all scenarios of the uncertain set; [χ i ] k represents the dual variable of the kth constraint; χ i The dual variable matrix of the constraint; k represents the kth constraint in the compact constraint form of equation (19); After the equivalent transformation process of the above formula (20) to formula (22), the original second-stage optimization model shown in formula (19) can be equivalent to the constraints shown in formula (23): Therefore, the original two-stage robust optimization problem shown in Equation (18) and Equation (19) is finally transformed into a mixed integer programming (MILP) problem as shown in Equation (24): s.t.C i x i +D i y i ≤b i 8. The method for collaborative optimization of multi-park integrated energy systems based on equivalent projection theory according to claim 7 is characterized by: In step 4, since the mixed integer programming (MILP) model converted in step 3 involves multiple different stakeholders and the information that can be transmitted between them is limited, and the established MILP model is a non-convex model, the decomposition technique is used to divide the overall Lagrangian dual problem of coordinated scheduling of multi-park integrated energy systems into a single-park integrated energy system problem, and the subgradient algorithm is used to update the dual variables, thereby obtaining a convergent distributed solution to the dual problem; And the shrinkage coefficient is introduced to recover the feasible original solution and ensure the feasibility of the dual solution; After introducing the shrinkage coefficient ρ, the mixed integer programming (MILP) obtained in step 3 can be reconstructed into the following model; s.t.C i x i +D i y i ≤b i In formula (25), δ i is the shrinkage coefficient, In order to introduce the compact form of the multi-PIES coupling constraint after the shrinkage coefficient is introduced, its Lagrangian dual formula is derived as follows: In formula (26), λ T (d i -δ) indicates that the coupling constraint The marginal opportunity cost contribution to the objective function of the original problem; δ represents the shrinkage coefficient; λ T Constrained The transpose of the dual variable of ; Where λ is the dual variable of the coupling constraint, and the contraction coefficient is defined by the following equation (27): In formula (27), q is the shrinkage factor, n is the row of the coupling constraint matrix; [E i ] nk Indicates the specific coefficient of the kth variable in the nth coupling constraint among different PIES coupling variables, which is used to calculate the marginal contribution; E i is the coefficient matrix of different PIES coupling variables.

9. The method for collaborative optimization of multi-park integrated energy systems based on equivalent projection theory according to claim 8 is characterized by: After obtaining the initial dual variable λ j and the contraction coefficient δ i After RIES i According to the Park Integrated Energy System Alliance, RIES is removed i All other RIES j Transmitted Lambda j , according to the weight factor γ ij Compute the other PIES dual variables λ j The average value of the dual variable θ passed in i , as shown below: In formula (28), k is the number of iterations. Based on the average value, RIES i Fix the dual variable to θ i (k), and perform the following minimum optimization problem; In formula (29), y i (k+1) represents y after the k+1th iteration i The specific value of θ i (k) T represents the average value of the dual variables passed to the i-th PIES by other PIES except the i-th PIES in the k-th iteration; After performing the above minimum optimization problem, a tentative solution y can be obtained i (k+1), according to which E i y i (k+1) calculate PIES i The worst contribution to the coupling constraint is then updated using the following maximum consensus strategy: i The shrinkage coefficient; In formula (30), φ i (k) is the maximum value of all contraction coefficients transferred from subsystem j except subsystem i itself; δ j (k) indicates that the source is not PIES i Other PIES j The transferred shrinkage coefficient; Represents the maximum value of all contraction coefficients transferred from other subsystems j; It is represented as the auxiliary record variable of the worst contribution upper limit in the k+1th iteration; Auxiliary record variable for the worst contribution upper limit in the kth iteration; It is represented as the auxiliary record variable with the worst contribution lower bound in the k+1th iteration; Auxiliary record variable for the worst contribution lower limit; δ i (k+1) represents the specific value of the shrinkage coefficient after the k+1th iteration obtained by the maximum consensus strategy shown in formula (30); k represents the number of iterations; Finally, the dual variables are updated with subgradients as follows: l i (k+1)=[θ i (k)+ω(E i y i (k+1)-(d i -d i (k+1)) / N g ] + (31); In formula (31), λ i (k+1) represents the specific value of the dual variable of the coupling constraint after the k+1th iteration after the subgradient update; ω is the update step size, [·] + represents the projection on the q-dimensional non-negative orthogonal; N g The number of PIES in the park integrated energy system alliance; each PIES only i (k) and δ i (k) Interact with other PIES.

10. The method for collaborative optimization of multi-park integrated energy systems based on equivalent projection theory according to claim 9 is characterized in that: In step 5, a multi-park integrated energy system collaborative optimization model based on the feasible region equivalent projection is established, as follows: First, based on the Matlab2020 environment, all optimization variables are classified into equations (15) to (17), and according to the objective function equation (12) and the constraints equations (2) to (10), a two-stage robust optimization problem of the multi-park integrated energy system is constructed as shown in equations (18) and (19); Then, using the feasible region projection theory formulas (20) to (22) proposed in step 3, the lower layer problem of the two-stage robust problem of the original model shown in formula (19) is converted into the constraints shown in formula (23) and introduced into the first stage optimization model of the original two-stage robust problem (18), thereby converting it into the model shown in formula (24); Finally, the dual decomposition algorithm proposed in step 4 is used to split the centralized MILP model shown in Equation (22) into sub-problems for each park through Lagrangian relaxation. The distributed optimization framework of Equations (25) to (31) is used to solve the problem by calling the GUROBI solver based on the YALMIP platform.

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