Integrated energy system distributed decoupling optimization method and system considering carbon trading

Abstract

The application discloses a distributed decoupling optimization method for a comprehensive energy system considering carbon trading, and comprises the following steps: establishing a centralized optimization framework of an electrically coupled system, initializing global data and information of a power system and a gas system; constructing a centralized model of a regional comprehensive energy system, wherein an objective function of the model comprises the power system, the gas system and carbon emission cost, and corresponding operation constraints are added to the objective function; converting an original non-convex problem into a mixed integer second-order cone programming based on SOCP relaxation, and performing reactive power optimization by using an ADMM consistent distributed algorithm; introducing consensus variables to represent the synergistic effect between the power and natural gas networks based on the ADMM method of consistent variables, so as to solve a distributed optimization problem of the regional comprehensive energy system; and finally, a case analysis of a regional electric and gas comprehensive energy integrated system is performed, and the distributed decoupling optimization of the system is realized by using the ADMM method of consistency. The application also comprises a distributed decoupling optimization system for a comprehensive energy system considering carbon trading.

Description

Technical Field

[0001] This invention relates to a distributed decoupling optimization method and system for an integrated energy system that takes carbon trading into account. Background Technology

[0002] With the significant increase in the installed capacity of new energy units and multi-energy units, the coupling of multiple energy forms and the scheduling problems in regional integrated energy systems are becoming increasingly difficult, making the research on distributed control and scheduling methods particularly important. Compared with traditional coal-fired units, gas-fired units have advantages such as high thermal efficiency, lower carbon emissions, and stronger unit adjustability. With the increasing environmental regulations restricting carbon emissions and the phasing out of old and inefficient units, Chinese society is further promoting the transition from coal-fired to gas-fired power generation units. Under the current central government's dual-carbon strategy, researching integrated energy systems to achieve the transformation and coordinated supply of traditional energy sources into multiple clean energy forms is an inevitable trend.

[0003] Gas turbine units enable the organic coupling of gas and electricity networks, while also promoting the high integration of heterogeneous multi-energy systems and significantly increasing system complexity. Traditionally, power systems and natural gas networks are designed and operated separately, with corresponding dispatch decisions made independently, often neglecting the coupling between the two networks. In reality, the price, cost, and usage of power and gas systems can be mutually complementary. With the increasing integration and coupling of power and natural gas networks, there is an urgent need to establish a collaborative working model to meet the economic, safe, and reliable operation requirements of the entire network.

[0004] Traditional centralized energy flow optimization is no longer suitable for multi-decision-agent system architectures. With the emergence of new intelligent algorithms such as cloud storage computing and data mining, distributed optimization and control theory has been further developed and has penetrated into various aspects such as scientific research, engineering empirical applications, and residential and commercial applications. Distributed intelligent algorithms complete the refined modeling and efficient solution of large-scale optimization problems through multi-agent cooperation. The research focus of its control optimization algorithms also includes developing efficient solution algorithms and proving their feasibility and stability. Unlike general centralized algorithms, distributed methods need to consider the communication problem between distributed agent nodes, such as studying the stability of communication networks using mathematical graph theory. Domestic and foreign scholars have proposed a variety of distributed methods or frameworks to solve integrated energy system optimization problems, including dual methods, augmented Lagrange methods, and alternating multiplier direction methods (ADMM). Among them, the dual ascent method requires the objective function to be strictly convex and requires the selection of an appropriate iteration step size; the augmented Lagrange method is indecomposable and cannot be parallelized, while the ADMM method integrates the decomposability of the dual ascent method and the excellent convergence of the augmented Lagrange multiplier method, which can both decompose the original function and augment the function. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention provides a distributed decoupling optimization method and system for integrated energy systems that take carbon trading into account.

[0006] This invention focuses on utilizing Active Dynamics Modeling (ADMM) to achieve coordinated operation of power and natural gas networks in a distributed manner and effectively reduce carbon emissions. Specifically, the coordinated power and gas networks are modeled as a centralized optimal energy flow problem. Furthermore, a distributed ADMM method based on consistent variables is developed to solve centralized problems with multiple decision-makers, aiming to achieve optimal operation and scheduling of the integrated energy system as a whole.

[0007] To achieve the above objectives, the technical solution of the present invention includes the following steps:

[0008] A distributed decoupling optimization method for an integrated energy system considering carbon trading includes the following steps:

[0009] S1: Establish a centralized optimization framework for the electrical coupling system. The centralized optimization framework for the electrical coupling system mainly consists of the power system, gas system, gas turbine, and computing center. Initialize the global data and information of the power system and gas system.

[0010] S2: Construct a centralized model of a regional integrated energy system. Its objective function mainly includes the power system, gas system, and carbon emission costs, and impose corresponding operational constraints on the objective function.

[0011] S3: Based on the relaxation of second-order cone programming (SOCP), the original non-convex problem is transformed into mixed-integer second-order cone programming (MISOCP), and reactive power optimization is performed using the ADMM consistent distributed algorithm;

[0012] S4: The ADMM method based on consensus variables introduces consensus variables to represent the synergistic effect between the power and natural gas networks, thereby solving the distributed optimization problem of the regional integrated energy system;

[0013] S5: The system determines whether the convergence requirement has been met. If yes, the final system scheduling scheme is output as the optimization result, and the solution is complete. If no, the updated consensus variables and multipliers are sent to the lower-level power system and gas system for the next iteration.

[0014] Furthermore, in step S2, constructing a centralized model of the regional integrated energy system includes the following processes:

[0015] S2-1: The centralized optimization framework for the electrical coupling system mainly consists of the power system, gas system, gas turbine, and computing center. The objective function of the regional integrated energy system mainly includes the power system, gas system, and carbon emission costs. Specifically, the total system cost is defined as Cost, which is composed of three parts:

[0016] Cost = Cost1 + Cost2 + Cost3 (1)

[0017] Cost1, Cost2, and Cost3 represent the costs of the power system, gas system, and carbon trading, respectively. The composition of each cost component will be explained in detail below.

[0018] (P1) Calculate the cost in the power system, defined as Cost1:

[0019]

[0020] Electricity costs are primarily generated by gas-fired and coal-fired power units, and their cost function is generally defined as a quadratic function. It is important to note that the specific α values ​​vary depending on the type of gas-fired or coal-fired power unit. i β i γ i All three parameters are different.

[0021] (P2) Calculate the cost of using the gas system, defined as Cost2:

[0022]

[0023] Where R is the gas price. Real-time gas consumption

[0024] (P3) Integrated energy companies currently generally adopt a carbon quota trading method, which means that the remaining carbon emissions after deducting a certain amount of carbon quotas need to be purchased with carbon credits at the equivalent cash value. The carbon trading cost Cost3 is defined as being related to the active power transmission of the power system and the gas consumption of the gas system.

[0025]

[0026] Where R c To represent carbon trading prices, Ω c ξ represents the total carbon emissions of the system. E With ξ G Carbon emission quota coefficients corresponding to the power system and gas system, respectively

[0027] S2-2: After establishing the objective function, it should be constrained to conform to the actual situation.

[0028] (Q1) Corresponding to the power system operating cost, the relevant operating constraints mainly include linear power flow constraints, which are expressed in a centralized manner as follows:

[0029]

[0030] in, V0 = const, ∈ = 0.05. These are decision variables.

[0031] Define the upper and lower limits of active power transmission on the line and the ramping constraints of coal-fired units respectively:

[0032]

[0033]

[0034] in and These represent the minimum and maximum active power transmission, respectively. and These represent the minimum and maximum climbing power, respectively.

[0035] (Q2) The relevant gas system operating constraints mainly include:

[0036] ∑G ab -∑G ba =G p -G c (8)

[0037] g + +g - =1 (9)

[0038]

[0039]

[0040] Θ b ≤Υ·Θ a (12)

[0041] Θ min ≤Θ a ≤Θ max (13)

[0042]

[0043]

[0044] Equation (8) represents the nodal input and output power balance equation of the gas system. Equation (9) is g + With g -The direction of gas flow in the pipeline is indicated by a binary variable 0 or 1. Formula (10) is the Weymouth equation, where ω is the Weymouth coefficient, applicable to pipelines with a wall roughness k of 20-30 μm; Formula (11) indicates that the positive or negative value of the gas flow corresponds to the direction of gas transmission. Formula (12) indicates the pressure coefficient ratio of the gas node equipped with a compressor; Formula (13) limits the upper and lower limits of the pressure coefficient of the pipeline; Formulas (14) and (15) are the upper and lower limits of the production and consumption of gas well n, respectively.

[0045] (Q3) In a real regional integrated energy system, the gas energy consumed by the gas turbine unit is converted into energy output in the form of a quadratic function, thus there exists a corresponding coupling relationship between the electrical and gas systems. This coupling relationship can be expressed by the following formula:

[0046]

[0047] In step S3, the transformation of the non-convex problem based on SOCP relaxation includes the following process:

[0048] S3-1: Considering the non-convexity of the quadratic equality constraint (16), and that the dimension of the optimization model is proportional to the total number of nodes in the power grid, bus and gas network, large-scale systems are prone to problems such as the curse of optimization dimension. By using SOCP relaxation to transform the constraints, the original non-convex problem can be reformulated as mixed integer second-order cone programming (MISOCP), which can be solved using mature commercial software such as Cplex.

[0049] A general expression for quadratic convex programming is as follows:

[0050] X T AX+q T x+c≤0 (17)

[0051] Transforming it into the following general second-order cone form allows us to solve it using the second-order cone rule:

[0052]

[0053] Based on this, further relaxation of the equation (16) using a second-order cone yields:

[0054]

[0055] The linear and quadratic terms in the objective function (16) of the original optimization problem reflect the coupling between the electric and gas networks, where ρ>0 represents a constant. The original gas consumption is non-convex, but can be relaxed to inequality constraints to obtain SOCP relaxation. Equation (20) can be obtained by scaling down the above equation (10) in the same way:

[0056]

[0057] As mentioned above, the Weymouth equation (10) can be relaxed by second-order cone constraints to maintain the solvability of its convex function.

[0058] S3-2: ADMM Distributed Reactive Power Optimization:

[0059] The above formula (11) expresses the linear power flow constraints in the power system in a centralized form. The corresponding ADMM consistent distributed algorithm (local variables are...) Global variable P j (As is known) is represented as:

[0060]

[0061] Define the Lagrange function as:

[0062]

[0063]

[0064] S3-3: The specific ADMM consistent distributed algorithm steps are as follows:

[0065] (T1) Each node solves its own optimization problem (updating local variables):

[0066]

[0067] (T2) Update global variables Q and U. This step requires communication with neighboring nodes to exchange their local variables in order to update the global variables. The global variables are then averaged based on the local variables of the nodes.

[0068]

[0069] (T3) Each node locally updates the Lagrange multipliers:

[0070]

[0071] The consensus algorithm leads to the convergence of these local variables among adjacent nodes, thereby finding the global optimum. Once the algorithm converges, the local variables actually correspond to the optimal feasible solution of the problem, that is, the actual reactive power can be obtained from the local variables and substituted into the power system:

[0072]

[0073] In step S4, the ADMM method based on consensus variables introduces consensus variables to specifically solve the distributed optimization problem of the regional integrated energy system, including the following process:

[0074] S4-1: The ADMM method considering consistency variables is applied to a regional integrated energy system. When using the ADMM method, the subsystems can be modeled and solved using SOCP relaxation on the subproblems of the electricity and gas networks. For privacy reasons, the power grid company and the gas operator have complete information about their own networks but cannot access detailed information about other networks. To decompose the original optimization problem, the natural gas consumption variable of the gas turbine units is copied and defined as follows:

[0075] A i =B n (28)

[0076] Equation (28) ensures the consistency of natural gas consumption variables for each natural gas unit in the natural gas and electricity networks. By adopting the standard ADMM algorithm, the centralized optimal energy optimization problem considering carbon emissions can be reformulated as an electricity network optimization problem and a gas network optimization problem. The data exchange required between electricity and natural gas operators involves only natural gas consumption and Lagrange multipliers, and data interaction and update iteration are carried out through a distributed management center.

[0077] S4-2: Specific implementation of distributed optimization of regional integrated energy systems considering the consistency variable ADMM:

[0078] Introducing consensus variable φ k This is used to represent the synergy between electricity and natural gas networks;

[0079] A i -φ k =0,B n -φ k =0 (29)

[0080] The sub-problems of the power system and the gas system are calculated separately.

[0081] (M1) Power network optimization problem, obtained from CO and φ k It obtains the power output of all units by local optimization and is responsible for transmitting the calculated natural gas losses of the gas turbines. To CO:

[0082]

[0083] (M2) Natural gas network optimization problem, from CO2 acquisition and φ k Information is used to locally optimize the production of natural gas wells and the natural gas consumption of gas turbines. And Passed to CO:

[0084]

[0085] (M3) Distributed computing center optimization problem; the upper-level distributed control center is responsible for handling the coupling constraints between the two networks. In each iteration, the distributed control center is responsible for receiving data, updating multipliers, and verifying convergence criteria. The control center obtains data from the power system and the gas system. and The information is used to determine whether the original residual and the dual residual are within the tolerance range, i.e.:

[0086]

[0087]

[0088] If the stopping criterion is not met, the control center will update the consensus variables and multipliers. If the residual discriminants in formulas (32) and (33) are both satisfied, the iteration stops; otherwise, the Lagrange multipliers are updated, and the ADMM iteration steps are returned.

[0089]

[0090] The updated consensus variables and multipliers are sent to the lower-level power and gas systems for the next iteration.

[0091] A distributed decoupling optimization method for integrated energy systems considering carbon trading includes the following steps: establishing a centralized optimization framework for the electrical coupling system and initializing global data and information for the power system and gas system; constructing a centralized model of the regional integrated energy system, whose objective function mainly includes the power system, gas system, and carbon emission costs, and imposing corresponding operational constraints on the objective function; transforming the original non-convex problem into a mixed-integer second-order cone programming problem (MISOCP) based on SOCP relaxation, and using the ADMM consistent distributed algorithm for reactive power optimization; using the ADMM method based on consensus variables, introducing consensus variables to represent the synergistic effect between the power and gas networks, thereby solving the distributed optimization problem of the regional integrated energy system; finally, using a case study of a regional integrated power and gas energy system, the distributed decoupling optimization of the system is achieved using the consistent ADMM method, proving the effectiveness of the proposed method. This invention considers that the ADMM method based on consensus variables is suitable for hierarchical collaboration between upper-level distributed managers and lower-level gas companies and power operators, enabling collaboration between the power and gas networks without the need for centralized management.

[0092] A system for implementing the distributed decoupling optimization method of an integrated energy system considering carbon trading according to the present invention includes: a centralized optimization framework establishment module for an electrical coupling system, a centralized model construction module for a regional integrated energy system, a mixed integer second-order cone programming transformation and reactive power optimization module, a module for representing the synergistic effect between power and natural gas networks, and a convergence judgment module.

[0093] The module for establishing a centralized optimization framework for the electrical coupling system establishes a centralized optimization framework for the electrical coupling system, which consists of a power system, a gas system, a gas turbine, and a computing center, and initializes the global data and information of the power system and the gas system.

[0094] The module for constructing a centralized model of a regional integrated energy system builds a centralized model of the regional integrated energy system. Its objective function includes the power system, gas system, and carbon emission costs, and applies corresponding operational constraints to the objective function.

[0095] The mixed-integer second-order cone programming transformation and reactive power optimization module transforms the original non-convex problem into mixed-integer second-order cone programming (MISOCP) based on second-order cone programming (SOCP) relaxation, and uses the ADMM consistent distributed algorithm for reactive power optimization;

[0096] The module representing the synergy between power and natural gas networks is based on the ADMM method with consensus variables. It introduces consensus variables to represent the synergy between power and natural gas networks, thereby solving the distributed optimization problem of the regional integrated energy system.

[0097] The convergence judgment module determines whether the convergence requirement has been met. If so, it outputs the final system scheduling scheme as the optimization result, and the solution is completed. If not, the updated consensus variables and multipliers are sent to the lower-level power system and gas system for the next iteration.

[0098] The beneficial effects of this invention are:

[0099] 1. In-depth exploration of distributed optimization, especially the application scenarios of the ADMM method in regional integrated energy systems;

[0100] 2. The overall economic optimization problem is modeled using a centralized method, decomposing it into three parts: electricity cost, gas cost, and carbon trading cost, combined with corresponding operational constraints. Furthermore, considering that the quadratic equations of the electricity and gas systems with the gas turbine as the coupling hub, and the higher-order nonlinear parts of the Weymouth equations in the gas system, cannot be directly solved, a relaxation approach using SCOP second-order cone programming is employed to resolve the issue.

[0101] 3. Considering the synergistic effect between the power and natural gas networks, distributed control is implemented based on the consensus-based ADMM method. By introducing consensus variables to reflect the iterative process between upper and lower level operators, in each iteration, the upper-level computation center checks convergence and updates the consensus variables, while the lower-level power and gas systems solve their respective local sub-optimization problems. Attached Figure Description

[0102] Figure 1 This is a flowchart of the distributed decoupling optimization method for a comprehensive energy system considering carbon trading, as described in this invention.

[0103] Figure 2 This is a centralized optimization framework diagram of the electrical coupling system of the present invention.

[0104] Figure 3 This is a framework diagram of the integrated energy system for the electric and gas coupling region of the present invention.

[0105] Figure 4 This is a graph showing the change in the total cost of the present invention.

[0106] Figure 5 This is a schematic diagram of the iterative process of the ADMM method of the present invention.

[0107] Figure 6 This is a diagram showing the power output variation of the electrical unit according to the present invention.

[0108] Figure 7 This is a graph showing the output variation of gas wells according to the present invention. Detailed Implementation

[0109] The invention will now be further described with reference to the accompanying drawings.

[0110] Reference Figures 1 to 7 A distributed decoupling optimization method for an integrated energy system considering carbon trading, comprising the following steps:

[0111] S1: Establish a centralized optimization framework for the electrical coupling system. The centralized optimization framework for the electrical coupling system mainly consists of the power system, gas system, gas turbine, and computing center. Initialize the global data and information of the power system and gas system.

[0112] S2: Construct a centralized model of a regional integrated energy system. Its objective function mainly includes the power system, gas system, and carbon emission costs, and impose corresponding operational constraints on the objective function.

[0113] S3: Based on the relaxation of second-order cone programming (SOCP), the original non-convex problem is transformed into mixed-integer second-order cone programming (MISOCP), and reactive power optimization is performed using the ADMM consistent distributed algorithm;

[0114] S4: The ADMM method based on consensus variables introduces consensus variables to represent the synergistic effect between the power and natural gas networks, thereby solving the distributed optimization problem of the regional integrated energy system;

[0115] S5: The system determines whether the convergence requirement has been met. If yes, the final system scheduling scheme is output as the optimization result, and the solution is complete. If no, the updated consensus variables and multipliers are sent to the lower-level power system and gas system for the next iteration.

[0116] Furthermore, in step S2, constructing a centralized model of the regional integrated energy system includes the following processes:

[0117] S2-1: The centralized optimization framework for the electrical coupling system mainly consists of the power system, gas system, gas turbine, and computing center. The objective function of the regional integrated energy system mainly includes the power system, gas system, and carbon emission costs. Specifically, the total system cost is defined as Cost, which is composed of three parts:

[0118] Cost = Cost1 + Cost2 + Cost3 (1)

[0119] Cost1, Cost2, and Cost3 represent the costs of the power system, gas system, and carbon trading, respectively. The composition of each cost component will be explained in detail below.

[0120] (P1) Calculate the cost in the power system, defined as Cost1:

[0121]

[0122] Electricity costs are primarily generated by gas-fired and coal-fired power units, and their cost function is generally defined as a quadratic function. It is important to note that the specific α values ​​vary depending on the type of gas-fired or coal-fired power unit. i β i γ i All three parameters are different.

[0123] (P2) Calculate the cost of using the gas system, defined as Cost2:

[0124]

[0125] Where R is the gas price. Real-time gas consumption

[0126] (P3) Integrated energy companies currently generally adopt a carbon quota trading method, which means that the remaining carbon emissions after deducting a certain amount of carbon quotas need to be purchased with carbon credits at the equivalent cash value. The carbon trading cost Cost3 is defined as being related to the active power transmission of the power system and the gas consumption of the gas system.

[0127]

[0128] Where R c To represent carbon trading prices, Ω c ξ represents the total carbon emissions of the system. E With ξ G Carbon emission quota coefficients corresponding to the power system and gas system, respectively

[0129] S2-2: After establishing the objective function, it should be constrained to conform to the actual situation.

[0130] (Q1) Corresponding to the power system operating cost, the relevant operating constraints mainly include linear power flow constraints, which are expressed in a centralized manner as follows:

[0131]

[0132] in, V0 = const, ∈ = 0.05. These are decision variables.

[0133] Define the upper and lower limits of active power transmission on the line and the ramping constraints of coal-fired units respectively:

[0134]

[0135]

[0136] in and These represent the minimum and maximum active power transmission, respectively. and These represent the minimum and maximum climbing power, respectively.

[0137] (Q2) The relevant gas system operating constraints mainly include:

[0138] ∑G ab -∑G ba =G p -G c (8)

[0139] g + +g - =1 (9)

[0140]

[0141]

[0142] Θ b ≤Υ·Θ a (12)

[0143] Θ min ≤Θ a ≤Θ max (13)

[0144]

[0145]

[0146] Equation (8) represents the nodal input and output power balance equation of the gas system. Equation (9) is g + With g - The direction of gas flow in the pipeline is indicated by a binary variable 0 or 1. Formula (10) is the Weymouth equation, where ω is the Weymouth coefficient, applicable to pipelines with a wall roughness k of 20-30 μm; Formula (11) indicates that the positive or negative value of the gas flow corresponds to the direction of gas transmission. Formula (12) indicates the pressure coefficient ratio of the gas node equipped with a compressor; Formula (13) limits the upper and lower limits of the pressure coefficient of the pipeline; Formulas (14) and (15) are the upper and lower limits of the production and consumption of gas well n, respectively.

[0147] (Q3) In a real regional integrated energy system, the gas energy consumed by the gas turbine unit is converted into energy output in the form of a quadratic function, thus there exists a corresponding coupling relationship between the electrical and gas systems. This coupling relationship can be expressed by the following formula:

[0148]

[0149] In step S3, the transformation of the non-convex problem based on SOCP relaxation includes the following process:

[0150] S3-1: Considering the non-convexity of the quadratic equality constraint (16), and that the dimension of the optimization model is proportional to the total number of nodes in the power grid, bus and gas network, large-scale systems are prone to problems such as the curse of optimization dimension. By using SOCP relaxation to transform the constraints, the original non-convex problem can be reformulated as mixed integer second-order cone programming (MISOCP), which can be solved using mature commercial software such as Cplex.

[0151] A general expression for quadratic convex programming is as follows:

[0152] X T AX+q T x+c≤0 (17)

[0153] Transforming it into the following general second-order cone form allows us to solve it using the second-order cone rule:

[0154]

[0155] Based on this, further relaxation of the equation (16) using a second-order cone yields:

[0156]

[0157] The linear and quadratic terms in the objective function (16) of the original optimization problem reflect the coupling between the electric and gas networks, where ρ>0 represents a constant. The original gas consumption is non-convex, but can be relaxed to inequality constraints to obtain SOCP relaxation. Equation (20) can be obtained by scaling down the above equation (10) in the same way:

[0158]

[0159] As mentioned above, the Weymouth equation (10) can be relaxed by second-order cone constraints to maintain the solvability of its convex function.

[0160] S3-2: ADMM Distributed Reactive Power Optimization:

[0161] The above formula (11) expresses the linear power flow constraints in the power system in a centralized form. The corresponding ADMM consistent distributed algorithm (local variables are...) Global variable P j (As is known) is represented as:

[0162]

[0163] Define the Lagrange function as:

[0164]

[0165]

[0166] S3-3: The specific ADMM consistent distributed algorithm steps are as follows:

[0167] (T1) Each node solves its own optimization problem (updating local variables):

[0168]

[0169] (T2) Update global variables Q and U. This step requires communication with neighboring nodes to exchange their local variables in order to update the global variables. The global variables are then averaged based on the local variables of the nodes.

[0170]

[0171] (T3) Each node locally updates the Lagrange multipliers:

[0172]

[0173] The consensus algorithm leads to the convergence of these local variables among adjacent nodes, thereby finding the global optimum. Once the algorithm converges, the local variables actually correspond to the optimal feasible solution of the problem, that is, the actual reactive power can be obtained from the local variables and substituted into the power system:

[0174]

[0175] In step S4, the ADMM method based on consensus variables introduces consensus variables to specifically solve the distributed optimization problem of the regional integrated energy system, including the following process:

[0176] S4-1: The ADMM method considering consistency variables is applied to a regional integrated energy system. When using the ADMM method, the subsystems can be modeled and solved using SOCP relaxation on the subproblems of the electricity and gas networks. For privacy reasons, the power grid company and the gas operator have complete information about their own networks but cannot access detailed information about other networks. To decompose the original optimization problem, the natural gas consumption variable of the gas turbine units is copied and defined as follows:

[0177] A i =B n (28)

[0178] Equation (28) ensures the consistency of natural gas consumption variables for each natural gas unit in the natural gas and electricity networks. By adopting the standard ADMM algorithm, the centralized optimal energy optimization problem considering carbon emissions can be reformulated as an electricity network optimization problem and a gas network optimization problem. The data exchange required between electricity and natural gas operators involves only natural gas consumption and Lagrange multipliers, and data interaction and update iteration are carried out through a distributed management center.

[0179] S4-2: Specific implementation of distributed optimization of regional integrated energy systems considering the consistency variable ADMM:

[0180] Introducing consensus variable φ k This is used to represent the synergy between electricity and natural gas networks;

[0181] A i -φ k =0,B n -φ k =0 (29)

[0182] The sub-problems of the power system and the gas system are calculated separately.

[0183] (M1) Power network optimization problem, obtained from CO and φ kIt obtains the power output of all units by local optimization and is responsible for transmitting the calculated natural gas losses of the gas turbines. To CO:

[0184]

[0185] (M2) Natural gas network optimization problem, from CO2 acquisition and φ k Information is used to locally optimize the production of natural gas wells and the natural gas consumption of gas turbines. And Passed to CO:

[0186]

[0187] (M3) Distributed computing center optimization problem; the upper-level distributed control center is responsible for handling the coupling constraints between the two networks. In each iteration, the distributed control center is responsible for receiving data, updating multipliers, and verifying convergence criteria. The control center obtains data from the power system and the gas system. and The information is used to determine whether the original residual and the dual residual are within the tolerance range, i.e.:

[0188]

[0189]

[0190] If the stopping criterion is not met, the control center will update the consensus variables and multipliers. If the residual discriminants in formulas (32) and (33) are both satisfied, the iteration stops; otherwise, the Lagrange multipliers are updated, and the ADMM iteration steps are returned.

[0191]

[0192] The updated consensus variables and multipliers are sent to the lower-level power and gas systems for the next iteration.

[0193] A system for implementing a distributed decoupling optimization method for an integrated energy system considering carbon trading, as proposed by the present invention, includes: a centralized optimization framework establishment module for an electrical coupling system, a centralized model construction module for a regional integrated energy system, a mixed-integer second-order cone programming transformation and reactive power optimization module, a module for representing the synergistic effect between power and natural gas networks, and a convergence judgment module. These modules correspond sequentially to steps S1 to S5 of the method of the present invention.

[0194] To enable those skilled in the art to better understand the present invention, the applicant uses a regional integrated energy system combining electricity and gas as an example to verify the effectiveness of the decoupling optimization method proposed in this project.

[0195] I. Test System and Parameter Settings

[0196] The case study of this invention employs a regional integrated electricity and gas energy system with a 6-bus grid and a 7-node gas network, as shown in the attached figure. Figure 3 As shown, G2 is a non-gas turbine unit, and the two gas turbine units (G1 and G3) are located on bus lines 1 and 6, respectively. The gas network has one compressor, five pipelines, and two natural gas wells. Natural gas loads 1 and 3 correspond to gas turbine units G1 and G3, respectively. The correlation matrix of the power system and related system parameters are shown in Tables 1 and 2.

[0197] Table 1 Power System Correlation Matrix

[0198]

[0199] Table 2 Generator Set System Parameters

[0200]

[0201] The correlation matrix and well parameters of the relevant natural gas wells are shown in Table 3, where the initial values ​​of gas consumption and multiplier are set to zero.

[0202] Table 3 Natural Gas Well Parameters

[0203]

[0204] In this test system, the performance of the ADMM method based on consistency variables was compared with that of traditional standalone optimization and MISOCP centralized optimization. The SOCP relaxation model was used for the sub-problems of the power and gas networks in the centralized optimization, and the calculation results of standalone optimization and MISOCP methods are presented.

[0205] All numerical tests were performed on a 4.0GHz desktop PC with four Intel Core cores, eight threads, and 12GB of RAM. The algorithm was coded using CPLEX 12.6 MATLAB R2016a, and the CPLEX solver was used to solve the centralized MISOCP and ADMM problems respectively.

[0206] II. Simulation Results and Analysis

[0207] This invention discusses the application of a distributed method based on consistent Active Variable Model (ADMM) in solving the optimal scheduling problem of a regional integrated energy system that takes carbon trading costs into account. This method is applicable to electrically coupled integrated energy systems with multiple decision-makers (i.e., gas operators, electricity operators, and a higher-level distributed control center), where each decision-maker may have its own independent cost function and constraint variables. The ADMM method based on consistent variables enables coordination between the upper-level coordinating operator and the lower-level gas and electricity operators. Experimental results show that the ADMM-based method has better performance and superior economic indicators than traditional centralized methods based on MISCOP and individual optimization methods. Specific optimization results for three case studies are shown in Table 4.

[0208] Table 4 Optimization results of three algorithm cases

[0209]

[0210] Table 4 compares the cost, number of iterations, and CPU computation time of the three methods used to solve the regional integrated energy system scheduling problem. N represents the number of iterations, and the first and second rows show the solutions generated by individual optimization and centralized MISOCP, respectively. Centralized MISOCP outperforms individual optimization in terms of solution accuracy. Therefore, the solution obtained by centralized MISOCP is selected as a reference to evaluate the optimality of the solution generated by the distributed method. (See Table 4 and Appendix...) Figure 4 As can be seen, the accuracy loss of individual optimization is mainly due to the poor solution quality of gas production variables, while the ADMM algorithm based on consistent variables has better economic indicators and algorithm performance.

[0211] Although the ADMM-based method is implemented in a distributed manner using second-order cone relaxation, its operating cost is essentially the same as the centralized MISOCP method. However, this ADMM-based method requires fewer iterations and computation time than methods based on general augmented Lagrange sequences; the ADMM method takes 38.74 seconds to compute 20 iterations. (Appendix) Figure 5The term "ADMM" represents the iterative process of the primary and dual residuals following the threshold in the ADMM method. The reason why consensus-based ADMM converges slower than ordinary ADMM is that consensus-based ADMM requires a distributed management center to handle the coupling variables between gas and electricity operators. In this small integrated energy system case, the centralized method is faster than the ADMM-based method, but this does not mean that the centralized method is faster than the ADMM-based method in all other cases. On the one hand, as the system dimension increases, the computational difficulty of centralized control and scheduling explodes exponentially. On the other hand, centralized methods are generally only suitable for situations where the gas and electricity networks are centrally operated by a higher level. In reality, in most countries and localities, gas networks and electricity systems are operated by different companies. Therefore, the consensus-based ADMM method proposed in this invention is applicable to real-world architectures involving multiple distributed decision-makers.

[0212] Appendix Figure 6 and attached Figure 7 The figures show the iterative changes in output power for the electrical generator unit EG and the gas well GW, respectively. The X-axis represents the node number, the Y-axis represents the iteration number, and the Z-axis represents the output power (kW) of the electrical generator unit and the production value of the gas well, respectively. The three electrical generator units show power output changes at nodes 1, 2, and 6, and converged in approximately 20 iterations. Compared to centralized methods, the consensus-based ADMM method avoids oscillations and has a significant advantage in convergence. The gas wells 4 and 6 show production output changes, but the degree of change is significantly smaller than that of the electrical generator units.

[0213] In summary, the ADMM-based method of this invention exhibits better convergence performance and economic indicators, including carbon emission costs, compared to traditional subsystem-by-subsystem optimization methods and centralized MISOCP methods. However, compared to ordinary ADMM iterative methods, the ADMM method with consistent variable updates used in this invention leads to an increase in the number of iterations and a decrease in optimization speed. Future work will focus on the security constraints of regional integrated energy systems and the scalability of the ADMM method, with the aim of applying it to large-scale integrated energy systems.

[0214] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A distributed decoupling optimization method for an integrated energy system considering carbon trading, characterized in that, Includes the following steps: S1: Establish a centralized optimization framework for the electrical coupling system, consisting of a power system, a gas system, a gas turbine, and a computing center, and initialize the global data and information of the power system and the gas system; S2: Construct a centralized model of a regional integrated energy system. Its objective function includes the electricity system, gas system, and carbon emission costs. Appropriate operational constraints are imposed on the objective function. The operational constraints for the gas system include: ∑G ab -∑G ba =G p -G c (8) g + +g - =1 (9) I b ≤Y·Θ a (12) I min ≤Θ a ≤Θ max (13) Wherein, formula (8) represents the node input and output power balance equation of the gas system; formula (9) is g + With g - The direction of gas flow in the pipeline is indicated by the binary variable 0 or 1; Formula (10) is the Weymouth equation, where ω is the Weymouth coefficient, which is applicable to pipelines with a wall roughness k of 20 to 30 μm; Formula (11) indicates that the positive and negative values ​​of the gas flow value correspond to the direction of gas transmission; Formula (12) indicates the pressure coefficient ratio of the gas node equipped with a compressor; Formula (13) limits the upper and lower limits of the pressure coefficient of the pipeline; Formulas (14) and (15) are the upper and lower limits of the production and consumption of gas well n, respectively; In a real regional integrated energy system, the gas energy consumed by the gas turbine unit is converted into energy output in the form of a quadratic function, thus there exists a corresponding coupling relationship between the electrical and gas systems; this coupling relationship can be expressed by the following formula: S3: Based on the relaxation of second-order conical programming (SOCP), the original non-convex problem is transformed into mixed-integer second-order conical programming (MISOCP), and reactive power optimization is performed using the ADMM consistent distributed algorithm; specifically including: S3-1: Considering the non-convexity of the quadratic equality constraint, and that the dimension of the optimization model is proportional to the total number of nodes in the power grid, bus and gas networks, large-scale systems are prone to the curse of optimization dimension. By using SOCP relaxation to transform the constraint, the original non-convex problem is reformulated as mixed integer second-order cone programming (MISOCP), which is solved using the mature commercial software Cplex. A general quadratic convex programming expression is as follows: X T AX+q T x+c≤0 (17) Transforming it into the following general second-order cone form allows us to solve it using the second-order cone rule: Based on this, further relaxation of the equation (16) using a second-order cone yields: The linear and quadratic terms in the objective function (16) of the original optimization problem reflect the coupling between the electric and gas networks, where ρ>0 represents a constant; the original gas consumption is non-convex, but can be relaxed to inequality constraints to obtain SOCP relaxation; by scaling Equation (10) in the same way, Equation (20) can be obtained: The Weymouth equation (10) is relaxed by second-order cone constraints to preserve the solvability of its convex function. S3-2: ADMM Distributed Reactive Power Optimization: Formula (11) expresses the linear power flow constraints in the power system in a centralized form, and the corresponding ADMM consistent distributed algorithm is expressed as formula (21); where the local variables are Global variable P j It is known; Define the Lagrange function as: S3-3: The specific ADMM consistent distributed algorithm steps are as follows: (T1) Each node solves its own optimization problem, i.e., updates its local variables: (T2) Update global variables Q and U. This step requires communication with neighboring nodes to exchange their local variables in order to update the global variables. The global variables are averaged based on the local variables of the nodes. (T3) Each node locally updates the Lagrange multipliers: The consensus algorithm leads to the convergence of these local variables between adjacent nodes, thereby finding the global optimum. Once the algorithm converges, the local variables actually correspond to the optimal feasible solution of the problem, that is, the actual reactive power can be obtained from the local variables and substituted into the power system. S4: The ADMM method based on consensus variables introduces consensus variables to represent the synergistic effect between the power and natural gas networks, thereby solving the distributed optimization problem of the regional integrated energy system; S5: The system determines whether the convergence requirement has been met. If yes, the final system scheduling scheme is output as the optimization result, and the solution is completed. If no, the updated consensus variables and multipliers are sent to the lower-level power system and gas system for the next iteration.

2. The distributed decoupling optimization method for an integrated energy system considering carbon trading as described in claim 1, characterized in that: In step S2, constructing a centralized model of the regional integrated energy system includes the following processes: S2-1: The objective function of a regional integrated energy system mainly includes the electricity system, gas system, and carbon emission costs; specifically, the total cost of the entire system is defined as Cost, which consists of the sum of three parts: Cost=Cost1+Cost2+Cost3 (1) Cost1, Cost2, and Cost3 represent the costs of the electricity system, gas system, and carbon trading, respectively. The composition of each cost component will be explained in detail below. (P1) Calculate the cost in the power system, defined as Cost1: Electricity costs are primarily generated by gas-fired and coal-fired power units, and their cost functions are generally defined as quadratic functions. It is important to note that the specific α values ​​vary depending on the type of gas-fired or coal-fired power unit. i β i γ i All three parameters are different; (P2) Calculate the cost of using the gas system, defined as Cost2: Where R is the gas price. This represents real-time gas consumption. (P3) Integrated energy companies currently generally adopt the carbon quota trading method, that is, the remaining carbon emissions after deducting a certain carbon quota need to be purchased with equivalent cash in the form of carbon credits; the carbon trading cost Cost3 is defined as being related to the active power transmission of the power system and the gas consumption of the gas system. Where R c To represent carbon trading prices, Ω c ξ represents the total carbon emissions of the system. E With ξ G These correspond to carbon emission quota coefficients for the power system and the gas system, respectively. S2-2: After establishing the objective function, it is necessary to constrain it to conform to the actual situation; (Q1) Corresponding to the power system operating cost, the relevant operating constraints mainly include linear power flow constraints, which are expressed in a centralized manner as follows: in, V0 = const, ∈ = 0.05; For decision variables; Furthermore, the upper and lower limits of active power transmission on the line and the ramping constraints of coal-fired units are defined respectively: in and These represent the minimum and maximum active power transmission, respectively. and These represent the minimum and maximum climbing power, respectively.

3. The distributed decoupling optimization method for an integrated energy system considering carbon trading as described in claim 1, characterized in that, In step S4, the ADMM method based on consensus variables introduces consensus variables to specifically solve the distributed optimization problem of the regional integrated energy system, including the following steps: S4-1: The ADMM method considering consistency variables is applied to a regional integrated energy system; when using the ADMM method, the subsystem can use SOCP relaxation to model and solve the subproblems of the power and gas networks; for privacy protection purposes, the power grid company and the gas operator have complete information about their own networks, but cannot access detailed information about other networks; in order to decompose the original optimization problem, the natural gas consumption variable of the gas turbine unit is copied and introduced into the definition: A i =B n (28) Equation (28) can guarantee the consistency of natural gas consumption variables for each natural gas unit in the natural gas and power networks; by adopting the standard ADMM algorithm, the centralized optimal energy optimization problem considering carbon emissions is reformulated as a power network optimization problem and a gas network optimization problem; the data exchange required between power and natural gas operators only involves natural gas consumption and Lagrange multipliers, and data interaction and update iteration are carried out through a distributed management center; S4-2: Specific implementation of distributed optimization of regional integrated energy systems considering the consistency variable ADMM: Introducing consensus variable φ k This is used to represent the synergy between electricity and natural gas networks; A i -f k =0, B n -f k =0 (29) The sub-problems of the power system and the gas system are calculated separately. (M1) Power network optimization problem, obtained from CO and φ k It obtains the power output of all units by local optimization and is responsible for transmitting the calculated natural gas losses of the gas turbines. To CO: (M2) Natural gas network optimization problem, from CO2 acquisition and φ k Information is used to locally optimize the production of natural gas wells and the natural gas consumption of gas turbines. And Passed to CO: (M3) Distributed computing center optimization problem; the upper-level distributed control center is responsible for handling the coupling constraints between the two networks; in each iteration, the distributed control center is responsible for receiving data and updating multipliers, and verifying convergence criteria; the control center obtains data from the power system and gas system. and The information is used to determine whether the original residual and the dual residual are within the tolerance range, i.e.: If the stopping criterion is not met, the control center will update the consensus variables and multipliers; if the residual discriminants in formulas (32) and (33) are both satisfied, the iteration stops; otherwise, the Lagrange multipliers will continue to be updated, and the ADMM iteration execution step (1) will be returned. The updated consensus variables and multipliers are sent to the lower-level power and gas systems for the next iteration.

4. A system for implementing the distributed decoupling optimization method for an integrated energy system considering carbon trading as described in claim 1, characterized in that: include: The module includes a centralized optimization framework for electrical coupling systems, a centralized model for regional integrated energy systems, a mixed-integer second-order cone programming transformation and reactive power optimization module, a module for representing the synergistic effect between power and natural gas networks, and a convergence judgment module. The module for establishing a centralized optimization framework for the electrical coupling system establishes a centralized optimization framework for the electrical coupling system, which consists of a power system, a gas system, a gas turbine, and a computing center, and initializes the global data and information of the power system and the gas system. The module for constructing a centralized model of a regional integrated energy system builds a centralized model of the regional integrated energy system. Its objective function includes the power system, gas system, and carbon emission costs, and applies corresponding operational constraints to the objective function. The mixed-integer second-order cone programming transformation and reactive power optimization module transforms the original non-convex problem into a mixed-integer second-order cone programming problem based on second-order cone programming SOCP relaxation, and uses the ADMM consistent distributed algorithm for reactive power optimization. The module representing the synergy between power and natural gas networks is based on the ADMM method with consensus variables. It introduces consensus variables to represent the synergy between power and natural gas networks, thereby solving the distributed optimization problem of the regional integrated energy system. The convergence judgment module determines whether the convergence requirement has been met. If so, it outputs the final system scheduling scheme as the optimization result, and the solution is completed. If not, the updated consensus variables and multipliers are sent to the lower-level power system and gas system for the next iteration.

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