A distributed algorithm for integrated energy system considering uncertainty of offshore wind power

Abstract

The application discloses a kind of integrated energy system distributed algorithm considering offshore wind power uncertainty, it includes the following steps: step 1: data preparation stage;Step 2: based on the basic data set prepared in data stage, construct the scheduling model of electric-gas integrated energy system under data center access;Step 3: two-stage distribution robust optimization model establishment stage;Step 4: two-stage distribution robust optimization model is solved using C&CG-ADMM algorithm;The application is analyzed to offshore wind farm historical output data set based on the K-medoids clustering method of Wasserstein distance, and a discrete scenario set containing multiple typical output modes is constructed;Further, on this basis, the two-stage distribution robust optimization model of electric-gas integrated energy system considering wind power uncertainty containing data center is established;Original C&CG algorithm is used as outer framework to reconstruct C&CG-ADMM algorithm.

Description

Technical Field

[0001] This invention relates to the field of integrated energy system modeling and optimization technology, and in particular to a distributed algorithm for integrated energy systems that takes into account the uncertainties of offshore wind power. Background Technology

[0002] Driven by the accelerating global energy transition and the demand for low-carbon development, the proportion of renewable energy integrated into power systems is gradually increasing. Electricity-gas integrated energy systems, with their multi-energy flow synergy and complementarity, have demonstrated significant advantages in improving energy efficiency and addressing supply-side uncertainties in energy networks, becoming an important carrier supporting clean and low-carbon energy systems. However, the inherent intermittency and volatility of renewable energy output pose a severe challenge to system balance. Traditional dispatching relies on the start-up and shutdown of gas turbines and the "pipeline storage effect" of natural gas networks for buffering, but limited by mechanical inertia and economic constraints, its response speed is insufficient to meet the needs of scenarios with rapid power fluctuations. Frequent start-ups and shutdowns also accelerate equipment aging and affect unit lifespan.

[0003] As peak-shaving costs on the power generation side rise, the value of demand-side resources is becoming increasingly prominent. Internet data centers, as a new type of digital infrastructure, possess significant spatiotemporal elasticity in their computing load: task scheduling can dynamically migrate between geographically distributed computing nodes and can be flexibly adjusted across different time slots. This characteristic provides an efficient demand-side flexibility supplement to integrated energy systems. By constructing a spatiotemporal migration model for computing tasks, the power load of data centers can be proactively reshaped, thereby reducing the overall operating costs of the system; and by guiding users to shift tasks to peak renewable energy output periods, the local consumption capacity of green electricity can be improved. The portability of data centers aligns perfectly with multi-energy complementarity, making them a crucial resource for solving the challenge of absorbing a high proportion of renewable energy.

[0004] The increasing penetration of renewable energy sources such as offshore wind power has exacerbated supply-side uncertainties in the system, placing higher demands on optimization decision-making methods. Traditional methods mainly include stochastic optimization and robust optimization: the former relies on prior probability distribution assumptions and struggles to reflect the non-Gaussian nature and spatiotemporal correlation of wind power output; the latter defines the fluctuation range through geometric sets, possessing strong robustness but often sacrificing economic efficiency due to excessive defense against extreme scenarios. To balance robustness and economy, sub-stochastic optimization has gradually gained attention. It seeks the optimal solution under the worst-case probability distribution by constructing a probabilistic fuzzy set containing the true distribution, thereby achieving a coordinated trade-off between risk aversion and economic efficiency. Probabilistic fuzzy sets constructed based on discrete scenarios have strong engineering application value. By employing data-driven methods such as K-medoids to extract historical typical power output patterns and combining 1-norm and ∞-norm to jointly constrain the offset range of probability weights, it enhances the ability to characterize tail-end extreme risks while considering computational feasibility.

[0005] While the Column Constraint Generation (C&CG) algorithm can efficiently solve mixed-integer linear problems in two-stage Bruker optimization, the standard C&CG algorithm requires transparent sharing of global information within the system. The power and gas subsystems need to expose complete model parameters and operating states, which fundamentally conflicts with privacy requirements in a multi-stakeholder environment. Therefore, this paper uses the original C&CG algorithm as its outer architecture. Based on its interactive iteration of the main problem and subproblems, it focuses on solving the main power system problem in the day-ahead phase of the two-stage Bruker optimization model, and introduces the ADMM algorithm in the intra-day phase to achieve distributed solution between the power and gas subsystems, thus constructing the C&CG-ADMM algorithm. This enables distributed collaborative computation between the power and gas subsystems, achieving efficient optimization while ensuring information isolation.

[0006] Therefore, improvements to existing technologies are still needed. Summary of the Invention

[0007] The purpose of this invention is to provide a distributed algorithm for integrated energy systems that takes into account the uncertainties of offshore wind power. This is aimed at addressing the inherent randomness and uncertainty of renewable energy sources such as offshore wind power. Existing research often uses a two-stage distributed bar optimization model to characterize these uncertainties and employs the C&CG algorithm for solution. However, the centralized solution mechanism of the standard C&CG algorithm requires all entities in the system to fully share system parameters and operational data, which conflicts with the practical needs of integrated energy systems where multiple entities operate independently and data privacy and trade secrets are emphasized.

[0008] To achieve the above objectives, the technical solution of this invention is as follows: This invention analyzes the historical power output dataset of offshore wind farms using the K-medoids clustering method based on Wasserstein distance, constructing a discrete scenario set containing multiple typical power output modes; furthermore, based on this, a two-stage sub-Bruker optimization model of an integrated electric-gas energy system including data centers and considering wind power uncertainties is established, and simulation experiments are conducted using a case study consisting of a 6-node electric system, a 7-node natural gas system, and 3 data centers. To quantify the accuracy loss that may be introduced by distributed solutions, this invention uses the centralized C&CG algorithm as a benchmark, comparing and analyzing the convergence accuracy and computational efficiency of the proposed algorithm.

[0009] This invention discloses a distributed algorithm for a comprehensive energy system that takes into account the uncertainties of offshore wind power, which includes the following steps: Step 1: Data preparation stage; this involves acquiring operating parameters of the power subsystem, natural gas subsystem, data center, and historical power output data of offshore wind power to form the basic dataset of the integrated energy system. Step 2: Based on the aforementioned basic dataset, construct a scheduling model for the integrated electricity-gas energy system under data center access, including the system objective function and operating constraints, and perform piecewise linearization on the nonlinear relationships in the model; Step 3: Two-stage sub-Brussels bar optimization model establishment stage; The historical offshore wind power output data mentioned in Step 1 is processed, and the K-medoids clustering method based on Wasserstein distance is used to reduce the dimensionality of the wind power output scenarios to obtain a reduced set of typical scenarios; Based on the set of typical scenarios and combined with the synthesis norm constraint, a probabilistic fuzzy set of offshore wind power output is constructed; According to whether the model variables and constraints are affected by uncertainty, the scheduling problem is divided into day-ahead stage and intraday stage, and a two-stage sub-Brussels bar optimization model is established. Step 4: Solve the two-stage biscayne bar optimization model using the C&CG-ADMM algorithm. The specific steps include: S40: Solve the main power system problem involving uncertainties at the day-ahead stage; S41: Construct an electro-gas coupled distributed subproblem during the daytime phase and solve it in a distributed manner using the ADMM algorithm, while simultaneously performing parallel computation on each scenario subproblem; S42: Based on the probability distribution of the worst-case scenario obtained from the sub-problem identification, add corresponding optimality constraints and second-stage decision variables to the main problem; S43: Repeat the iteration until the upper and lower bounds meet the preset convergence conditions, and output the final scheduling result.

[0010] In the aforementioned distributed algorithm for an integrated energy system that considers the uncertainties of offshore wind power, the objective function in the construction of a deterministic scheduling model for the electricity-gas integrated energy system under data center access includes: a. Data center time and space migration cost; that is, the data center transforms the originally rigid power demand into flexible load by migrating computing tasks in time and space, so as to participate in the integrated energy system scheduling as a flexible resource, in order to reduce the impact of load demand fluctuations and the uncertainty of offshore wind power output, and reduce the pressure on coal-fired and gas-fired units caused by frequent peak shaving; its load migration will generate corresponding economic costs, which consist of two parts: time migration cost and space migration cost. In terms of time migration, workload is redistributed across different time periods within the same data center. The cost of this migration is reflected in the penalty for failing to complete the task within the agreed timeframe. : (1) In the formula: A collection of data centers; For data centers From the initial time period t to the target time period The amount of work transferred out; The unit latency cost factor, i.e., data center The cost of breach of contract that needs to be paid to the user for a delay of one hour in processing a unit of workload; T It represents the set of all time periods within the scheduling period; In terms of space migration, the workload is not directly migrated between data centers. Instead, a dynamic resource allocation strategy is used to enable the target center to take over the incremental requests from the original center in subsequent periods. The resulting space transfer cost is manifested as the communication overhead between data centers. Since data centers of the same operator are usually interconnected through private leased lines, while cross-operator communication requires transmission through the public network and incurs additional traffic costs, communication paths are classified according to operator affiliation, and transfer costs are calculated differently for different paths. Under the same operator, based on the considered day-to-day timescale, the cost of building the network between data centers is a sunk cost and is not included in the consideration of a single decision; in this case, the additional electricity cost generated by the network equipment forwarding data should be taken into account. : (2) In the formula: Within time period t, from the data center Transfer to data center The workload; For the same operator from data center To data center Additional cost coefficient when transferring out a unit of work; However, when using different carriers, communication must be conducted via the public network; this incurs cross-carrier workload transfer costs. It can be represented as: (3) In the formula: To from data center To data center The unit traffic cost coefficient that needs to be paid to the public network when transferring out a unit of workload; In other words, the cost of migrating data center loads in the context of scheduling the integrated power and gas energy system for data center access. for: (4) b. Unit start-up and shutdown costs (5) In the formula: Representative generator set Startup cost coefficient Representative generator set The downtime cost coefficient; , , Collectively referred to as generator units The start / stop variables, when 1, represent the unit being in the running, start-up, and shutdown states during the time period t, respectively; Represents a collection of coal-fired power units. Represents a collection of gas turbine units. This represents the set of thermal power units in the system; c. Production costs of natural gas suppliers (6) In the formula: Represents a collection of natural gas wells; Representing natural gas suppliers The production cost coefficient; For suppliers The natural gas supply flow rate during time period t; d. Operating costs of coal-fired power units (7) In the formula: Represents the piecewise linearized i Section coal-fired power unit Operating cost coefficient; The number of segments for piecewise linearization; Representative coal-fired power units In time period t The active power output of a segment that is higher than its minimum output value. To achieve piecewise linearization, only coal-fired power units are involved. Costs related to start-up and shutdown status; e. Non-fuel operating costs of gas turbine units (8) In the formula: Represents the piecewise linearized i-th Sectional gas turbine unit Operating cost coefficient; Represents gas turbine units In time period t Duan's merits and contributions; To achieve piecewise linearization, only the gas turbine unit is involved. Costs related to start-up and shutdown status; f. Carbon emission costs System scheduling based solely on economic considerations cannot achieve carbon emission reduction. Therefore, this paper establishes a carbon emission cost model, which incorporates carbon emission costs into the objective function. : (9) In the formula: For carbon price; This represents the carbon emissions of the power generation entity within one day. The initial one-day carbon allowance is allocated free of charge to power generation entities; considering the current annual carbon allowance allocation, the accounting scale is converted to the day-ahead level; the carbon allowance covers fossil fuel combustion emissions, and the definition of the free initial allowance obtained by each power generation entity is as follows: (10) The total carbon emissions that the system can generate in a single day are: (11) In the formula: For offshore wind farms; This serves as the baseline value for carbon emissions from coal-fired power units. This serves as the baseline value for carbon emissions from gas turbine units; The direct carbon emission factor corresponding to a unit of electricity generated by a coal-fired power unit. The direct carbon emission factor corresponding to the unit power generation of the gas turbine unit; The carbon footprint factor generated by offshore wind turbines during their life cycle; Represents generator sets; Representative unit Active power output that is higher than its minimum output value during time period t. For the unit The minimum active power, Representative unit The binary variable representing the operating status, where a value of 1 indicates that the unit is in operation; In summary, under data center access, the total cost of each sub-module in the system during the scheduling cycle is: (12) In the formula: Represents the cost of the power subsystem. This represents the cost of the natural gas subsystem.

[0011] The aforementioned distributed algorithm for a comprehensive energy system considering the uncertainties of offshore wind power, wherein the constraints in step 2 include: 1) Data center constraints Data center workload constraints The workloads received by data centers are typically categorized into two types based on latency sensitivity: latency-sensitive workloads and latency-tolerant workloads. Latency-sensitive workloads include interactive services with stringent response speed requirements, such as online transactions and real-time streaming media. Latency-tolerant workloads include computationally intensive tasks such as batch data processing and machine learning training, which have longer execution cycles and less stringent real-time constraints, thus exhibiting higher latency tolerance. In this invention, the schedulable and migrateable workloads originate only from latency-tolerant workloads. (13) In the formula: The total number of data centers. This is the ratio of transferable workload to total workload. This is the ratio of the amount of work that can be migrated in space per unit time period to the upper limit of processing capacity; and Data Center The workload required to be processed before and after time period t is adjusted; For data centers From time period The workload will be transferred to the next time period t. For data centers From time period t to time period The amount of work transferred out, Within time period t, from the data center Transferred to data center The workload, Within time period t, from the data center To data center The amount of work transferred out; For data centers The maximum workload to be processed in time period t; t is the index number of the current time period. This is the index number of the time period from which the workload originates. This is the index number for the time period where the workload is directed. For the current data center's index number, This refers to the index number of the data center from which the workload originates. The index number for the workload to be directed to the data center; When data center workloads are migrated at the time level, the constraint that the target time period of the workload is later than the source time period must also be met; that is, for any data center of and Its timing index should also satisfy: (14) Data center energy consumption constraints The energy consumption of a data center mainly includes IT equipment, cooling systems, and auxiliary facilities such as lighting. For modeling the relationship between IT equipment energy consumption and total data center energy consumption, a linear approximation method based on server utilization is adopted. (15) In the formula: and Data Center Peak power and idle power; Data center before time period t adjustment The resulting IT equipment energy consumption, Data center after time period t adjustment The resulting IT equipment energy consumption; Data center before time period t adjustment The total energy consumption generated Data center after time period t adjustment Total energy consumption generated; For data centers The efficiency of electricity use; For each data center, the total energy consumption of its IT equipment is related to the power consumption of its servers as follows: (16) In the formula: The peak power of a single server used in a data center. The idle power of a single server used in a data center. For data centers The total number of servers; Data center user satisfaction constraints Considering the computing limitations of data center servers, there is an upper limit to the amount of work they can process during each scheduling period, which must meet utilization constraints: (17) In the formula: For data centers Average service utilization rate during time period t This represents the upper limit of server utilization. For data centers The number of active servers during time period t; This refers to the workload processing capacity of a single server within a given time period. When optimizing data center power load, workload transmission and queuing delays should not exceed the maximum delay time specified in the service level agreement. The constraints can be expressed as follows: (18) 2) Power system constraints Unit start-up and shutdown constraints: (19) In the formula: The start / stop variable represents the operating status of the unit during time period t-1. A value of 1 indicates that the unit is in operation during time period t-1, and a value of 0 indicates that the unit is not in operation during time period t-1. Minimum start-up / shutdown time constraints for generator sets: The formula for the minimum power-on time constraint is: (20) The formula for the minimum downtime constraint is: (twenty one) In the formula: This is a time index, representing the starting time period of the summation calculated by taking the maximum value on the right side of the equation; Let C be the minimum start-up time of generator set C. For generator sets Minimum downtime; Bus power balance constraints: (twenty two) In the formula: busbar The load demand of the data center; busbar To meet other load demands; For connecting nodes and The susceptance of the transmission lines; busbar The phase angle within time interval t busbar The phase angle within time interval t; It is the set of nodes in a power system; For connection to the busbar A collection of generator sets; Generator capacity constraints: (twenty three) In the formula: For generator sets Minimum active power output during operation For generator sets Maximum active power output during operation; Generator ramping constraints: (twenty four) In the formula: For generator sets Maximum climbing rate; Representative unit The active power output that is higher than its minimum output value during the time period t-1; System spin-off standby constraints: (25) In the formula: Reserve power for the system's upward rotation. Reserve power for the system's downward rotation; Transmission line capacity constraints: (26) In the formula: For connecting bus and busbar The maximum transmission capacity of the transmission lines between them; The reference bus voltage phase angle is zero constraint: (27) In the formula: The voltage phase angle of the reference bus during time period t; 3) Natural gas system constraints Node airflow balance constraints: For node m, its nodal airflow balance constraint is written as follows (28); the left side of equation (28) is the sum of the airflow flowing into node m, and the right side is the sum of the airflow flowing out of node m: (28) In the formula: This is the set of natural gas nodes currently undergoing gas flow balance analysis. This is the set of natural gas nodes that exchange gas with node n; For the collection of gas turbine units, A collection of natural gas compression stations; A generator set at node m that uses natural gas as fuel The fuel flow rate consumed within time period t; To inject into the compressor during time period t Natural gas flow rate in Indicates compressor The air intake port; Let t be the flow rate of natural gas from node m to node n through the pipeline during time period t; Let be the natural gas demand flow rate at node m during time period t, which is independent of power generation. To obtain from the compressor within time period t The flow rate of natural gas flowing out of the middle Indicates compressor The air outlet port; Let t be the flow rate of natural gas from node n to node m through the pipeline during time period t; For the gas source at node m during time period t The flow rate of supplied natural gas; Average flow rate in the pipeline and pressure constraints at both ends: (29) In the formula: For the pipe connecting nodes m and n, For pipeline collection, For pipelines The Weymouth constant, For node m, the air pressure during time period t Let n be the air pressure at time t. For pipelines The average natural gas flow rate; since the Weymouth equation is a nonlinear constraint, it needs to be linearized, and nodes are set. m and n The square vectors of air pressure are respectively , Then the original expression can be transformed into: (30) In the formula: Let be the squared difference in air pressure between node m and node n; based on the first-order Taylor expansion, the nonlinear term of the above equation (30) can be relaxed into the following piecewise linear form: (31) In the formula: This represents the total number of sampling points for linearizing the Weymouth equation. The first of the pressure differences between nodes m and n Each segment is determined by the upper and lower limits of air pressure at both ends of the pipeline; The midpoint of each segment can be chosen; a penalty term needs to be added to the objective function. To minimize Tighten the inequality constraint (31), where It is a small positive number; Constraints on the hourly variation of storage and flow: (32) In the formula: For pipelines within time period t The amount of natural gas stored in the pipeline is called pipeline storage; Pipeline within time period t-1-1 The amount of natural gas stored therein; Compressor station loss constraints: (33) In the formula: For compressor Consumption factor; For the flow into the compressor during time period t Natural gas flow rate; For the compressor to flow out during time period t Natural gas flow rate; Compression ratio constraint: (34) In the formula: This refers to the intake pressure at both ends of the natural gas compressor. The outlet pressure at both ends of the natural gas compressor; This refers to the compression ratio; Flow constraints: (35) In the formula: For compressor The maximum gas flow rate that can be processed within time period t; This represents the upper limit of natural gas flow from node m to node n within time period t; This represents the upper limit of natural gas flow from node n to node m within time period t; Natural gas well output constraints: (36) In the formula: natural gas supplier The provided lower limit of natural gas flow rate, natural gas supplier The maximum natural gas flow rate provided; Nodal pressure constraints: (37) In the formula: Let m be the air pressure at node m during time period t. The lower limit of pressure at node m The upper limit of pressure for node m; Storage range constraints: (38) In the formula: For pipelines The minimum storage capacity, For pipelines Maximum storage capacity; 4) System coupling constraints The gas turbine unit is the only coupling device between the electrical subsystem and the natural gas subsystem, and there is a fuel conversion constraint relationship between them: (39) In the formula: For gas turbine units Thermal efficiency.

[0012] The aforementioned distributed algorithm for a comprehensive energy system that takes into account the uncertainties of offshore wind power, wherein step 3 specifically comprises the following steps: S30. Clustering of multiple wind farm output scenarios based on K-medoids; To address the issue of outliers in offshore wind power output due to wind speed fluctuations, K-medoids clustering is used to extract typical scenarios; Taking the combined power output of several offshore wind farms as the analysis object, the offshore wind power output sequence is modeled as a two-dimensional probability distribution consisting of time and wind farm dimensions, with time index and wind farm number forming a discrete grid coordinate system. The power transmission cost in the time dimension is determined by the time interval, while a discrete equidistant metric is used in the wind farm dimension. That is, the transportation cost within the same wind farm is zero, and the transportation cost between different wind farms is uniformly set as a unit constant. Based on this, the actual wind power output is normalized and used as probabilistic quality to participate in optimal transmission. This metric can consider both the influence of the output amplitude of offshore wind farms and reflect the output time sequence characteristics of different time periods, thus comprehensively evaluating the scenario similarity based on the minimum transportation cost between distributions. For the two normalized offshore wind power distributions... and Its two-dimensional Wasserstein distance is expressed as: (40) In the formula: Represents probability distribution and The second-order Wasserstein distance between them; For all and The set of joint distributions of marginal distributions; From coordinates To coordinates The joint distribution function for probabilistic mass transport; These represent the hourly and wind farm location coordinates in two-dimensional space, respectively. For the corresponding space transportation cost, coordinates and The formula is: (41) In the formula: For probability distribution The time index corresponding to the scene. For probability distribution The time index corresponding to the scene. For probability distribution The corresponding wind farm number in the scenario. For probability distribution The corresponding wind farm number in the scenario; this two-dimensional Wasserstein distance metric can be used to calculate the similarity between different wind power output scenarios; in distribution-based K-medoids clustering studies, the squared Wasserstein distance is usually directly used as the optimization objective, i.e.: (42) At this point, the centers of the K-medoids cluster are: (43) In the formula: Indicates the first Each cluster corresponds to a set of historical offshore wind power output scenarios; The squared Wasserstein distance between the two scenes; This is a typical scenario obtained from K-medoids clustering based on Wasserstein distance; S31. Construction of fuzzy sets for offshore wind power output based on the synthesis norm; A fuzzy set of offshore wind power output is constructed, and the scenario probability distribution is constrained by a composite norm based on the 1-norm and ∞-norm, thereby obtaining the worst-case probability distribution for each typical scenario; its probability confidence interval is shown below: (44) In the formula: The total number of historical scene samples. Let be the total number of discrete typical scenarios; then let the probability confidence level on the right side of the above equation be denoted as . and Then it can be transformed into: (45) This leads to the uncertain confidence set of the scene probability distribution. as follows: (46) in, For the first Probabilistic decision variables for a typical scenario The first one obtained based on historical data statistics Reference probability distribution for a typical scenario; This is a bias tolerance parameter based on the 1-norm, used to limit the overall range of deviation of the probability distribution relative to the reference distribution; This is a bias tolerance parameter based on the ∞-norm, used to limit the maximum component deviation of the probability distribution relative to a reference distribution; the allowable bias is determined by adjusting the 1-norm and the ∞-norm. and To control the fluctuation range of the probability distribution; S32. Construct a two-stage sub-Bruker optimization model; Based on the constraint of the fluctuation range of scene probability using the synthesis norm, the general formula of the data-driven TSDRO model is as follows: (47) In the formula: These are the decision variables for the first stage. Its feasible region; For the decision variables in the second stage, the subscripts are... Representing the An index of typical scenarios is used for differentiation. One possible offshore wind power output state; For the second stage decision variables The feasible domain; Parameters for typical offshore wind power output scenarios A constant coefficient vector, For the second stage decision variables A constant coefficient vector, Decision variables for the first stage A vector of constant coefficients; Decision variables in the first stage constraints The constant coefficient matrix, Decision variables in the second stage constraints The constant coefficient matrix, Parameters for typical offshore wind power output scenarios in the second phase of constraints The constant coefficient matrix, Decision variables in inter-stage inequality constraints The constant coefficient matrix, Decision variables in inter-stage inequality constraints The constant coefficient matrix, Decision variables in inter-stage equality constraints The constant coefficient matrix, Decision variables in inter-stage equality constraints The constant coefficient matrix; This is a constant vector in the first-stage constraints. is a constant vector in the inter-stage inequality constraints. This is a constant vector in the inter-stage equality constraints; Corresponding to the integrated energy system model adopted in this invention, it can be reformulated as follows: (48) In the formula: This represents the total cost of the first phase. This represents the total cost of the second phase.

[0013] The aforementioned distributed algorithm for a comprehensive energy system considering the uncertainties of offshore wind power, wherein the specific steps of using the C&CG-ADMM algorithm to solve the two-stage sub-Bruker optimization model are as follows: In the integrated electric-gas energy system, the power system and natural gas system with data center access belong to different operating entities, and there are privacy requirements for data protection. The model represented by formula (47) has a three-layer structure of min-max-min, which cannot be solved directly. Therefore, in the previous uncertainty scheduling methods for such systems, the two-stage model is usually divided into the main problem, that is, solving the max and the sub-problem, that is, solving the max-min, and then the C&CG algorithm is used to iteratively solve the problem. However, the C&CG algorithm relies on global information aggregation and centralized solution, which inevitably exposes the operating parameters and business secrets of each subsystem, making it difficult to meet the core requirements of modern energy systems for privacy protection and data sovereignty. Therefore, the C&CG-ADMM algorithm is proposed on this basis. As can be seen from formula (47), in the second stage of the max-min two-level problem, the variables... and variables The problems are independent of each other; therefore, the original innermost problem is actually related to the first... Solve the minimization problem of the form (49) independently in a typical scenario: (49) In the formula: For the second stage decision variables constant coefficient vector Transpose of; Parameters for typical offshore wind power output scenarios constant coefficient vector The transpose of ; by solving the minimization problem of the form of formula (49), respectively obtain Let's assume the system cost corresponding to a typical scenario, and let the first... The optimal cost for the second stage corresponding to each typical scenario is: The objective function of the subproblem that the C&CG algorithm needs to solve is expressed as: (50) at this time Should be considered as a variable Given the coefficients, formula (50) is the fuzzy set of the probability distribution in a typical scenario. Under constraints, find a probability distribution that maximizes the total cost of the second stage in the current scenario set; because Representing the A typical offshore wind power output scenario. Since is a constant, and thanks to the previous linearization and convex relaxation operations, the minimization problem represented by formula (49) is actually a linear programming problem, which is also known as linear programming (LP). Obviously, the maximization problem represented by formula (50) is also LP. Formula (49) can be rewritten as: (51) right By decomposing it, it can be reformulated as the second-stage variables of the power subsystem. and natural gas subsystem variables , Then formula (51) becomes: (52) In the formula: These represent the constant coefficients of the power subproblem in the objective function. Let the constant coefficients of the natural gas quantum problem in the objective function be represented; This represents the optimal solution to the main problem during each iteration of the C&CG algorithm; therefore, the innermost min problem can be reformulated as: (53) In the formula: the first constraint is the system coupling constraint explicitly expressed after dividing the power subsystem and the natural gas subsystem, where For power subsystem variables The constant coefficient matrix, For natural gas subsystem variables The constant coefficient matrix, Let be the constant vector of the first constraint; the fourth equality constraint can be represented by two equivalent inequalities: (54) Formula (54) and the third constraint in Formula (53) have the same algebraic form. Therefore, the algebraic expressions of the three are uniformly adjusted as follows: (55) In the formula: optimal solution to the main problem The constant coefficient matrix, Decision variables The constant coefficient matrix, The adjusted constant vector; note that the second constraint in formula (53) and formula (55) have the same direction, so we can apply the inequality addition to get: (56) For the natural gas subsystem, since it has no first-stage variables and does not involve uncertain variables, the simplified formula (56) is the constraint for the natural gas subproblem: (57) In the formula: The constant coefficient matrix of the natural gas system subproblem. For the constant vector of the natural gas system subproblem; the natural gas subsystem only participates in the optimization in the second stage of the original TSDRO model; For the power subsystem, due to the first-stage variable term involved in formula (56) and uncertain scenario items Since all terms are constants, formula (56) can be rearranged to a form similar to formula (57) by transposing terms: (58) In the formula: The constant coefficient matrix of the power system subproblem For a constant vector of a subproblem in a power system; Then, formula (53) can be restated into a standard form that can be solved by the ADMM algorithm as follows: (59) Its augmented Lagrangian function can be expressed as: (60) In the formula: For penalty parameters, ; Let be the Lagrange multiplier vector; formula (59) can be decomposed into a power system subproblem (61) and a natural gas system subproblem (62): (61) (62) After iterating through formulas (61) and (62) alternately once, update the Lagrange multipliers. for: (63) In the formula, superscript and They represent the first The second iteration and the first The variable values ​​corresponding to each iteration; the original residuals during the iteration process. and dual residual They are respectively: (64) In the formula: For the original residual The convergence threshold; For dual residuals The convergence threshold; when the original residual and dual residual Each less than the set convergence threshold and When the iteration converges: (65) Different penalty parameters can be used in each iteration. To reduce the impact of the initial selection of the penalty parameter on the algorithm's performance and improve the convergence speed of ADMM, a commonly effective method for updating the penalty parameter is: (66) In the formula: , The ADMM algorithm is also known as Variable Penalty Parameter ADMM.

[0014] Beneficial Effects: This invention uses the original C&CG algorithm as its outer architecture. Based on the interactive iteration of its main problem and subproblems, it focuses on solving the main problem of the power system in the day-ahead stage of the two-stage distributed bar optimization model, and introduces the ADMM algorithm in the intra-day stage to realize distributed solutions between the electrical and gas subsystems, thus constructing the C&CG-ADMM algorithm. This invention further provides a convergence proof of the proposed algorithm, ensuring its reliability and effectiveness while considering the uncertainties of the integrated energy system and the need for multi-agent privacy protection. Attached Figure Description

[0015] Figure 1 This invention relates to the complete process of a two-stage sub-Blu-ray bar optimization scheduling problem for an integrated electric-gas energy system that takes into account the uncertainties of offshore wind power.

[0016] Figure 2 It is a network structure of an integrated electricity-gas energy system connected to a data center.

[0017] Figure 3 The results are based on clustering using Wasserstein distance.

[0018] Figure 4 The convergence plot of the C&CG-ADMM iteration.

[0019] Figure 5 This diagram illustrates the effect of spatiotemporal transferability on unit fluctuation mitigation. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the present invention clearer and more explicit, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0021] To address the inherent stochasticity and uncertainty of renewable energy sources such as offshore wind power, existing research often employs a two-stage sub-Bruker optimization model and the C&CG algorithm for solution. However, the centralized solution mechanism of the standard C&CG algorithm requires all entities in the system to fully share system parameters and operational data, which conflicts with the practical needs of integrated energy systems where multiple entities operate independently, emphasizing data privacy and protecting trade secrets. Therefore, this invention uses the original C&CG algorithm as its outer architecture. Based on the interactive iteration of its master problem and sub-problems, it centrally solves the main power system problem in the day-ahead phase of the two-stage sub-Bruker optimization model, and introduces the ADMM algorithm in the intra-day phase to achieve distributed solution between the electrical and gas subsystems, thus constructing the C&CG-ADMM algorithm. This invention provides a convergence proof of the proposed algorithm, ensuring its reliability and effectiveness while balancing the uncertainties of integrated energy systems and the privacy protection requirements of multiple entities.

[0022] like Figure 1 As shown, this invention discloses an analysis of historical power output datasets from offshore wind farms using the K-medoids clustering method based on Wasserstein distance, constructing a discrete scenario set containing multiple typical power output modes. Based on this, a two-stage sub-Bruker optimization model of an integrated electric-gas energy system, including a data center and considering wind power uncertainties, is established. Simulation experiments are conducted using a case study consisting of a 6-node electric system, a 7-node natural gas system, and 3 data centers. To quantify the potential accuracy loss introduced by distributed solutions, this invention uses a centralized C&CG algorithm as a benchmark, comparing and analyzing the convergence accuracy and computational efficiency of the proposed algorithm.

[0023] The invention discloses a distributed algorithm for a comprehensive energy system that takes into account the uncertainties of offshore wind power, which includes the following steps: Step 1: Data preparation stage; this involves acquiring operating parameters of the power subsystem, natural gas subsystem, data center, and historical power output data of offshore wind power to form the basic dataset of the integrated energy system. Step 2: Based on the aforementioned basic dataset, construct a scheduling model for the integrated electricity-gas energy system under data center access, including the system objective function and operating constraints, and perform piecewise linearization on the nonlinear relationships in the model; Step 3: Two-stage sub-Brussels bar optimization model establishment stage; The historical offshore wind power output data mentioned in Step 1 is processed, and the K-medoids clustering method based on Wasserstein distance is used to reduce the dimensionality of the wind power output scenarios to obtain a reduced set of typical scenarios; Based on the set of typical scenarios and combined with the synthesis norm constraint, a probabilistic fuzzy set of offshore wind power output is constructed; According to whether the model variables and constraints are affected by uncertainty, the scheduling problem is divided into day-ahead stage and intraday stage, and a two-stage sub-Brussels bar optimization model is established. Step 4: Solve the two-stage biscayne bar optimization model using the C&CG-ADMM algorithm. The specific steps include: S40: Solve the main power system problem involving uncertainties at the day-ahead stage; S41: Construct an electro-gas coupled distributed subproblem during the daytime phase and solve it in a distributed manner using the ADMM algorithm, while simultaneously performing parallel computation on each scenario subproblem; S42: Based on the probability distribution of the worst-case scenario obtained from the sub-problem identification, add corresponding optimality constraints and second-stage decision variables to the main problem; S43: Repeat the iteration until the upper and lower bounds meet the preset convergence conditions, and output the final scheduling result.

[0024] This invention addresses the optimization scheduling problem of an integrated electricity-gas energy system with data center access considering the uncertainties of offshore wind power. By constructing a two-stage bibloc robust optimization model and designing a C&CG-ADMM distributed solution algorithm, it can improve the scheduling robustness and solution efficiency of integrated energy systems with a high proportion of offshore wind power while balancing system economy, operational security, and privacy protection requirements. Specifically: 1. Unified Modeling of Multi-Source Data: This invention integrates historical data from the power subsystem, natural gas subsystem, data center, and offshore wind power to fully characterize the actual operating characteristics of the integrated power-gas energy system under data center access, providing comprehensive data support for scheduling decisions; 2. Data Center Flexibility Exploration: This invention improves the overall system flexibility by introducing the spatiotemporal migration characteristics of data center workloads and using them as schedulable resources on the load side to participate in system optimization. 3. Uncertainty characterization: This invention characterizes the uncertainty of offshore wind power through a data-driven approach, uses K-medoids clustering based on Wasserstein distance for scenario dimensionality reduction, and constructs a probabilistic fuzzy set by combining synthesis norm constraints, thereby ensuring the robustness of the solution while avoiding overly conservative scheduling results. 4. Distributed Solution Architecture: This invention proposes the C&CG-ADMM algorithm, which uses the outer C&CG framework to identify the probability distribution of the most unfavorable scenario and the inner ADMM algorithm to solve the power and natural gas subsystems in a distributed manner. This achieves privacy protection among different entities within the system while considering the impact of uncertainty on the system.

[0025] In the aforementioned distributed algorithm for an integrated energy system that considers the uncertainties of offshore wind power, the objective function in the construction of a deterministic scheduling model for the electricity-gas integrated energy system under data center access includes: a. Data center time and space migration cost; that is, the data center transforms the originally rigid power demand into flexible load by migrating computing tasks in time and space, so as to participate in the integrated energy system scheduling as a flexible resource, in order to reduce the impact of load demand fluctuations and the uncertainty of offshore wind power output, and reduce the pressure on coal-fired and gas-fired units caused by frequent peak shaving; its load migration will generate corresponding economic costs, which consist of two parts: time migration cost and space migration cost. In terms of time migration, workload is redistributed across different time periods within the same data center. The cost of this migration is reflected in the penalty for failing to complete the task within the agreed timeframe. : (1) In the formula: A collection of data centers; For data centers From the initial time period t to the target time period The amount of work transferred out; The unit latency cost factor, i.e., data center The cost of breach of contract that needs to be paid to the user for a delay of one hour in processing a unit of workload; T It represents the set of all time periods within the scheduling period; In terms of space migration, the workload is not directly migrated between data centers. Instead, a dynamic resource allocation strategy is used to enable the target center to take over the incremental requests from the original center in subsequent periods. The resulting space transfer cost is manifested as the communication overhead between data centers. Since data centers of the same operator are usually interconnected through private leased lines, while cross-operator communication requires transmission through the public network and incurs additional traffic costs, communication paths are classified according to operator affiliation, and transfer costs are calculated differently for different paths. Under the same operator, based on the considered day-to-day timescale, the cost of building the network between data centers is a sunk cost and is not included in the consideration of a single decision; in this case, the additional electricity cost generated by the network equipment forwarding data should be taken into account. : (2) In the formula: Within time period t, from the data center Transfer to data center The workload; For the same operator from data center To data center Additional cost coefficient when transferring out a unit of work; However, when using different carriers, communication must be conducted via the public network; this incurs cross-carrier workload transfer costs. It can be represented as: (3) In the formula: To from data center To data center The unit traffic cost coefficient that needs to be paid to the public network when transferring out a unit of workload; In other words, the cost of migrating data center loads in the context of scheduling the integrated power and gas energy system for data center access. for: (4) b. Unit start-up and shutdown costs (5) In the formula: Representative generator set Startup cost coefficient Representative generator set The downtime cost coefficient; , , Collectively referred to as generator units The start / stop variables, when 1, represent the unit being in the running, start-up, and shutdown states during the time period t, respectively; Represents a collection of coal-fired power units. Represents a collection of gas turbine units. This represents the set of thermal power units in the system; c. Production costs of natural gas suppliers (6) In the formula: Represents a collection of natural gas wells; Representing natural gas suppliers The production cost coefficient; For suppliers The natural gas supply flow rate during time period t; d. Operating costs of coal-fired power units (7) In the formula: Represents the piecewise linearized i-th Section coal-fired power unit Operating cost coefficient; The number of segments for piecewise linearization; Representative coal-fired power units In time period t The active power output of a segment that is higher than its minimum output value. To achieve piecewise linearization, only coal-fired power units are involved. Costs related to start-up and shutdown status; e. Non-fuel operating costs of gas turbine units (8) In the formula: Represents the piecewise linearized i-th Sectional gas turbine unit Operating cost coefficient; Represents gas turbine units In time period t Duan's merits and contributions; To achieve piecewise linearization, only the gas turbine unit is involved. Costs related to start-up and shutdown status; f. Carbon emission costs System scheduling based solely on economic considerations cannot achieve carbon emission reduction. Therefore, this paper establishes a carbon emission cost model, which incorporates carbon emission costs into the objective function. : (9) In the formula: For carbon price; This represents the carbon emissions of the power generation entity within one day. The initial one-day carbon allowance is allocated free of charge to power generation entities; considering the current annual carbon allowance allocation, the accounting scale is converted to the day-ahead level; the carbon allowance covers fossil fuel combustion emissions, and the definition of the free initial allowance obtained by each power generation entity is as follows: (10) The total carbon emissions that the system can generate in a single day are: (11) In the formula: For offshore wind farms; This serves as the baseline value for carbon emissions from coal-fired power units. This serves as the baseline value for carbon emissions from gas turbine units; The direct carbon emission factor corresponding to a unit of electricity generated by a coal-fired power unit. The direct carbon emission factor corresponding to the unit power generation of the gas turbine unit; The carbon footprint factor generated by offshore wind turbines during their life cycle; Represents generator sets; Representative unit Active power output that is higher than its minimum output value during time period t. For the unit The minimum active power, Representative unit The binary variable representing the operating status, where a value of 1 indicates that the unit is in operation; In summary, under data center access, the total cost of each sub-module in the system during the scheduling cycle is: (12) In the formula: Represents the cost of the power subsystem. This represents the cost of the natural gas subsystem.

[0026] The aforementioned distributed algorithm for a comprehensive energy system considering the uncertainties of offshore wind power, wherein the constraints in step 2 include: 1) Data center constraints Data center workload constraints The workloads received by data centers are typically categorized into two types based on latency sensitivity: latency-sensitive workloads and latency-tolerant workloads. Latency-sensitive workloads include interactive services with stringent response speed requirements, such as online transactions and real-time streaming media. Latency-tolerant workloads include computationally intensive tasks such as batch data processing and machine learning training, which have longer execution cycles and less stringent real-time constraints, thus exhibiting higher latency tolerance. In this invention, the schedulable and migrateable workloads originate only from latency-tolerant workloads. (13) In the formula: The total number of data centers. This is the ratio of transferable workload to total workload. This is the ratio of the amount of work that can be migrated in space per unit time period to the upper limit of processing capacity; and Data Center The workload required to be processed before and after time period t is adjusted; For data centers From time period The workload will be transferred to the next time period t. For data centers From time period t to time period The amount of work transferred out, Within time period t, from the data center Transferred to data center The workload, Within time period t, from the data center To data center The amount of work transferred out; For data centers The maximum workload to be processed in time period t; t is the index number of the current time period. This is the index number of the time period from which the workload originates. This is the index number for the time period where the workload is directed. For the current data center's index number, This refers to the index number of the data center from which the workload originates. The index number for the workload to be directed to the data center; When data center workloads are migrated at the time level, the constraint that the target time period of the workload is later than the source time period must also be met; that is, for any data center of and Its timing index should also satisfy: (14) Data center energy consumption constraints The energy consumption of a data center mainly includes IT equipment, cooling systems, and auxiliary facilities such as lighting. For modeling the relationship between IT equipment energy consumption and total data center energy consumption, a linear approximation method based on server utilization is adopted. (15) In the formula: and Data Center Peak power and idle power; Data center before time period t adjustment The resulting IT equipment energy consumption, Data center after time period t adjustment The resulting IT equipment energy consumption; Data center before time period t adjustment The total energy consumption generated Data center after time period t adjustment Total energy consumption generated; For data centers The efficiency of electricity use; For each data center, the total energy consumption of its IT equipment is related to the power consumption of its servers as follows: (16) In the formula: The peak power of a single server used in a data center. The idle power of a single server used in a data center. For data centers The total number of servers; Data center user satisfaction constraints Considering the computing limitations of data center servers, there is an upper limit to the amount of work they can process during each scheduling period, which must meet utilization constraints: (17) In the formula: For data centers Average service utilization rate during time period t This represents the upper limit of server utilization. For data centers The number of active servers during time period t; This refers to the workload processing capacity of a single server within a given time period. When optimizing data center power load, workload transmission and queuing delays should not exceed the maximum delay time specified in the service level agreement. The constraints can be expressed as follows: (18) 2) Power system constraints Unit start-up and shutdown constraints: (19) In the formula: The start / stop variable represents the operating status of the unit during time period t-1. A value of 1 indicates that the unit is in operation during time period t-1, and a value of 0 indicates that the unit is not in operation during time period t-1. Minimum start-up / shutdown time constraints for generator sets: The formula for the minimum power-on time constraint is: (20) The formula for the minimum downtime constraint is: (twenty one) In the formula: This is a time index, representing the starting time period of the summation calculated by taking the maximum value on the right side of the equation; Let C be the minimum start-up time of generator set C. For generator sets Minimum downtime; Bus power balance constraints: (twenty two) In the formula: busbar The load demand of the data center; busbar To meet other load demands; For connecting nodes and The susceptance of the transmission lines; busbar The phase angle within time interval t busbar The phase angle within time interval t; It is the set of nodes in a power system; For connection to the busbar A collection of generator sets; Generator capacity constraints: (twenty three) In the formula: For generator sets Minimum active power output during operation For generator sets Maximum active power output during operation; Generator ramping constraints: (twenty four) In the formula: For generator sets Maximum climbing rate; Representative unit The active power output that is higher than its minimum output value during the time period t-1; System spin-off standby constraints: (25) In the formula: Reserve power for the system's upward rotation. Reserve power for the system's downward rotation; Transmission line capacity constraints: (26) In the formula: For connecting bus and busbar The maximum transmission capacity of the transmission lines between them; The reference bus voltage phase angle is zero constraint: (27) In the formula: The voltage phase angle of the reference bus during time period t; 3) Natural gas system constraints Node airflow balance constraints: For node m, its nodal airflow balance constraint is written as follows (28); the left side of equation (28) is the sum of the airflow flowing into node m, and the right side is the sum of the airflow flowing out of node m: (28) In the formula: This is the set of natural gas nodes currently undergoing gas flow balance analysis. This is the set of natural gas nodes that exchange gas with node n; For the collection of gas turbine units, A collection of natural gas compression stations; A generator set at node m that uses natural gas as fuel The fuel flow rate consumed within time period t; To inject into the compressor during time period t Natural gas flow rate in Indicates compressor The air intake port; Let t be the flow rate of natural gas from node m to node n through the pipeline during time period t; Let be the natural gas demand flow rate at node m during time period t, which is independent of power generation. To obtain from the compressor within time period t The flow rate of natural gas flowing out of the middle Indicates compressor The air outlet port; Let t be the flow rate of natural gas from node n to node m through the pipeline during time period t; For the gas source at node m during time period t The flow rate of supplied natural gas; Average flow rate in the pipeline and pressure constraints at both ends: (29) In the formula: For the pipe connecting nodes m and n, For pipeline collection, For pipelines The Weymouth constant, For node m, the air pressure during time period t Let n be the air pressure at time t. For pipelines The average natural gas flow rate; since the Weymouth equation is a nonlinear constraint, it needs to be linearized, and nodes are set. m and n The square vectors of air pressure are respectively , Then the original expression can be transformed into: (30) In the formula: Let be the squared difference in air pressure between node m and node n; based on the first-order Taylor expansion, the nonlinear term of the above equation (30) can be relaxed into the following piecewise linear form: (31) In the formula: This represents the total number of sampling points for linearizing the Weymouth equation. The first of the pressure differences between nodes m and n Each segment is determined by the upper and lower limits of air pressure at both ends of the pipeline; The midpoint of each segment can be chosen; a penalty term needs to be added to the objective function. To minimize Tighten the inequality constraint (31), where It is a small positive number; Constraints on the hourly variation of storage and flow: (32) In the formula: For pipelines within time period t The amount of natural gas stored in the pipeline is called pipeline storage; Pipeline within time period t-1-1 The amount of natural gas stored therein; Compressor station loss constraints: (33) In the formula: For compressor Consumption factor; For the flow into the compressor during time period t Natural gas flow rate; For the compressor to flow out during time period t Natural gas flow rate; Compression ratio constraint: (34) In the formula: This refers to the intake pressure at both ends of the natural gas compressor. The outlet pressure at both ends of the natural gas compressor; This refers to the compression ratio; Flow constraints: (35) In the formula: For compressor The maximum gas flow rate that can be processed within time period t; This represents the upper limit of natural gas flow from node m to node n within time period t; This represents the upper limit of natural gas flow from node n to node m within time period t; Natural gas well output constraints: (36) In the formula: natural gas supplier The provided lower limit of natural gas flow rate, natural gas supplier The maximum natural gas flow rate provided; Nodal pressure constraints: (37) In the formula: Let m be the air pressure at node m during time period t. The lower limit of pressure at node m The upper limit of pressure for node m; Storage range constraints: (38) In the formula: For pipelines The minimum storage capacity, For pipelines Maximum storage capacity; 4) System coupling constraints The gas turbine unit is the only coupling device between the electrical subsystem and the natural gas subsystem, and there is a fuel conversion constraint relationship between them: (39) In the formula: For gas turbine units Thermal efficiency.

[0027] The aforementioned distributed algorithm for a comprehensive energy system that takes into account the uncertainties of offshore wind power, wherein step 3 specifically comprises the following steps: S30. Clustering of multiple wind farm output scenarios based on K-medoids; To address the issue of outliers in offshore wind power output due to wind speed fluctuations, K-medoids clustering is used to extract typical scenarios; Taking the combined power output of several offshore wind farms as the analysis object, the offshore wind power output sequence is modeled as a two-dimensional probability distribution consisting of time and wind farm dimensions, with time index and wind farm number forming a discrete grid coordinate system. The power transmission cost in the time dimension is determined by the time interval, while a discrete equidistant metric is used in the wind farm dimension. That is, the transportation cost within the same wind farm is zero, and the transportation cost between different wind farms is uniformly set as a unit constant. Based on this, the actual wind power output is normalized and used as probabilistic quality to participate in optimal transmission. This metric can consider both the influence of the output amplitude of offshore wind farms and reflect the output time sequence characteristics of different time periods, thus comprehensively evaluating the scenario similarity based on the minimum transportation cost between distributions. For the two normalized offshore wind power distributions... and Its two-dimensional Wasserstein distance is expressed as: (40) In the formula: Represents probability distribution and The second-order Wasserstein distance between them; For all and The set of joint distributions of marginal distributions; From coordinates To coordinates The joint distribution function for probabilistic mass transport; These represent the hourly and wind farm location coordinates in two-dimensional space, respectively. For the corresponding space transportation cost, coordinates and The formula is: (41) In the formula: For probability distribution The time index corresponding to the scene. For probability distribution The time index corresponding to the scene. For probability distribution The corresponding wind farm number in the scenario. For probability distribution The corresponding wind farm number in the scenario; this two-dimensional Wasserstein distance metric can be used to calculate the similarity between different wind power output scenarios; in distribution-based K-medoids clustering studies, the squared Wasserstein distance is usually directly used as the optimization objective, i.e.: (42) At this point, the centers of the K-medoids cluster are: (43) In the formula: Indicates the first Each cluster corresponds to a set of historical offshore wind power output scenarios; The squared Wasserstein distance between the two scenes; This is a typical scenario obtained from K-medoids clustering based on Wasserstein distance; S31. Construction of fuzzy sets for offshore wind power output based on the synthesis norm; A fuzzy set of offshore wind power output is constructed, and the scenario probability distribution is constrained by a composite norm based on the 1-norm and ∞-norm, thereby obtaining the worst-case probability distribution for each typical scenario; its probability confidence interval is shown below: (44) In the formula: The total number of historical scene samples. Let be the total number of discrete typical scenarios; then let the probability confidence level on the right side of the above equation be denoted as . and Then it can be transformed into: (45) This leads to the uncertain confidence set of the scene probability distribution. as follows: (46) in, For the first Probabilistic decision variables for a typical scenario The first one obtained based on historical data statistics Reference probability distribution for a typical scenario; This is a bias tolerance parameter based on the 1-norm, used to limit the overall range of deviation of the probability distribution relative to the reference distribution; This is a bias tolerance parameter based on the ∞-norm, used to limit the maximum component deviation of the probability distribution relative to a reference distribution; the allowable bias is determined by adjusting the 1-norm and the ∞-norm. and To control the fluctuation range of the probability distribution; S32. Construct a two-stage sub-Bruker optimization model; Based on the constraint of the fluctuation range of scene probability using the synthesis norm, the general formula of the data-driven TSDRO model is as follows: (47) In the formula: These are the decision variables for the first stage. Its feasible region; For the decision variables in the second stage, the subscripts are... Representing the An index of typical scenarios is used for differentiation. One possible offshore wind power output state; For the second stage decision variables The feasible domain; Parameters for typical offshore wind power output scenarios A constant coefficient vector, For the second stage decision variables A constant coefficient vector, Decision variables for the first stage A vector of constant coefficients; Decision variables in the first stage constraints The constant coefficient matrix, Decision variables in the second stage constraints The constant coefficient matrix, Parameters for typical offshore wind power output scenarios in the second phase of constraints The constant coefficient matrix, Decision variables in inter-stage inequality constraints The constant coefficient matrix, Decision variables in inter-stage inequality constraints The constant coefficient matrix, Decision variables in inter-stage equality constraints The constant coefficient matrix, Decision variables in inter-stage equality constraints The constant coefficient matrix; This is a constant vector in the first-stage constraints. is a constant vector in the inter-stage inequality constraints. This is a constant vector in the inter-stage equality constraints; Corresponding to the integrated energy system model adopted in this invention, it can be reformulated as follows: (48) In the formula: This represents the total cost of the first phase. This represents the total cost of the second phase.

[0028] The aforementioned distributed algorithm for a comprehensive energy system considering the uncertainties of offshore wind power, wherein the specific steps of using the C&CG-ADMM algorithm to solve the two-stage sub-Bruker optimization model are as follows: In the integrated electric-gas energy system, the power system and natural gas system with data center access belong to different operating entities, and there are privacy requirements for data protection. The model represented by formula (47) has a three-layer structure of min-max-min, which cannot be solved directly. Therefore, in the previous uncertainty scheduling methods for such systems, the two-stage model is usually divided into the main problem, that is, solving the max and the sub-problem, that is, solving the max-min, and then the C&CG algorithm is used to iteratively solve the problem. However, the C&CG algorithm relies on global information aggregation and centralized solution, which inevitably exposes the operating parameters and business secrets of each subsystem, making it difficult to meet the core requirements of modern energy systems for privacy protection and data sovereignty. Therefore, the C&CG-ADMM algorithm is proposed on this basis. As can be seen from formula (47), in the second stage of the max-min two-level problem, the variables... and variables The problems are independent of each other; therefore, the original innermost problem is actually related to the first... Solve the minimization problem of the form (49) independently in a typical scenario: (49) In the formula: For the second stage decision variables constant coefficient vector Transpose of; Parameters for typical offshore wind power output scenarios constant coefficient vector The transpose of ; by solving the minimization problem of the form of formula (49), respectively obtain Let's assume the system cost corresponding to a typical scenario, and let the first... The optimal cost for the second stage corresponding to each typical scenario is: The objective function of the subproblem that the C&CG algorithm needs to solve is expressed as: (50) at this time Should be considered as a variable Given the coefficients, formula (50) is the fuzzy set of the probability distribution in a typical scenario. Under constraints, find a probability distribution that maximizes the total cost of the second stage in the current scenario set; because Representing the A typical offshore wind power output scenario. Since is a constant, and thanks to the previous linearization and convex relaxation operations, the minimization problem represented by formula (49) is actually a linear programming problem, which is also known as linear programming (LP). Obviously, the maximization problem represented by formula (50) is also LP. Formula (49) can be rewritten as: (51) right By decomposing it, it can be reformulated as the second-stage variables of the power subsystem. and natural gas subsystem variables , Then formula (51) becomes: (52) In the formula: These represent the constant coefficients of the power subproblem in the objective function. Let the constant coefficients of the natural gas quantum problem in the objective function be represented; This represents the optimal solution to the main problem during each iteration of the C&CG algorithm; therefore, the innermost min problem can be reformulated as: (53) In the formula: the first constraint is the system coupling constraint explicitly expressed after dividing the power subsystem and the natural gas subsystem, where For power subsystem variables The constant coefficient matrix, For natural gas subsystem variables The constant coefficient matrix, Let be the constant vector of the first constraint; the fourth equality constraint can be represented by two equivalent inequalities: (54) Formula (54) and the third constraint in Formula (53) have the same algebraic form. Therefore, the algebraic expressions of the three are uniformly adjusted as follows: (55) In the formula: optimal solution to the main problem The constant coefficient matrix, Decision variables The constant coefficient matrix, The adjusted constant vector; note that the second constraint in formula (53) and formula (55) have the same direction, so we can apply the inequality addition to get: (56) For the natural gas subsystem, since it has no first-stage variables and does not involve uncertain variables, the simplified formula (56) is the constraint for the natural gas subproblem: (57) In the formula: The constant coefficient matrix of the natural gas system subproblem. For the constant vector of the natural gas system subproblem; the natural gas subsystem only participates in the optimization in the second stage of the original TSDRO model; For the power subsystem, due to the first-stage variable term involved in formula (56) and uncertain scenario items Since all terms are constants, formula (56) can be rearranged to a form similar to formula (57) by transposing terms: (58) In the formula: The constant coefficient matrix of the power system subproblem For a constant vector of a subproblem in a power system; Then, formula (53) can be restated into a standard form that can be solved by the ADMM algorithm as follows: (59) Its augmented Lagrangian function can be expressed as: (60) In the formula: For penalty parameters, ; Let be the Lagrange multiplier vector; formula (59) can be decomposed into a power system subproblem (61) and a natural gas system subproblem (62): (61) (62) After iterating through formulas (61) and (62) alternately once, update the Lagrange multipliers. for: (63) In the formula, superscript and They represent the first The second iteration and the first The variable values ​​corresponding to each iteration; the original residuals during the iteration process. and dual residual They are respectively: (64) In the formula: For the original residual The convergence threshold; For dual residuals The convergence threshold; when the original residual and dual residual Each less than the set convergence threshold and When the iteration converges: (65) Different penalty parameters can be used in each iteration. To reduce the impact of the initial selection of the penalty parameter on the algorithm's performance and improve the convergence speed of ADMM, a commonly effective method for updating the penalty parameter is: (66) In the formula: , The ADMM algorithm is called the Variable Penalty Parameter ADMM (VPP-ADMM).

[0029] This invention uses the original C&CG algorithm as its outer architecture. Based on the interactive iteration of its main problem and subproblems, it focuses on solving the main problem of the power system in the day-ahead phase of the two-stage distributed bar optimization model, and introduces the ADMM algorithm in the intra-day phase to realize distributed solution between the electric and gas subsystems, thus constructing the C&CG-ADMM algorithm. This paper further provides a convergence proof of the proposed algorithm, ensuring its reliability and effectiveness while taking into account the uncertainties of the integrated energy system and the need for multi-agent privacy protection.

[0030] This invention addresses the uncertainties brought about by the large-scale integration of offshore wind power in the construction of new power systems. To overcome the bottleneck of traditional centralized C&CG algorithms, which rely on global information aggregation and struggle to protect the privacy of multiple stakeholders, this invention innovatively proposes a C&CG-ADMM distributed collaborative optimization algorithm. This algorithm, within the classic two-stage bibliometric optimization framework, embeds the Alternating Directional Multiplier Method (ADMM) at the sub-problem level, achieving decoupled solution and parallel computation between the power and natural gas subsystems, thus avoiding the risk of cross-stakeholder transmission of sensitive information. For uncertainty characterization, a data-driven fuzzy set of wind power output is constructed using K-medoids clustering combined with the synthesis norm, establishing a two-stage bibliometric optimization model. Furthermore, rigorous convergence analysis provides a theoretical guarantee for the proposed algorithm. This scheme effectively addresses the volatility of wind power while achieving localized processing of multi-stakeholder privacy information through a distributed computing architecture, providing reliable technical support for the safe and economical dispatch of integrated power-gas energy systems with a high proportion of renewable energy integration.

[0031] To verify the effectiveness and reliability of the C&CG-ADMM algorithm, this invention analyzes historical power output datasets of offshore wind farms using the K-medoids clustering method based on Wasserstein distance, constructing a discrete scenario set containing multiple typical power output modes. Based on this, a two-stage sub-Bruker optimization model of an integrated electric-gas energy system, including data centers and considering wind power uncertainties, is established. Simulation experiments are conducted using a case study consisting of a 6-node electric system, a 7-node natural gas system, and 3 data centers. To quantify the accuracy loss that may be introduced by distributed solutions, this invention uses the centralized C&CG algorithm as a benchmark, comparing and analyzing the convergence accuracy and computational efficiency of the proposed algorithm.

[0032] To verify the effectiveness of this invention, a simulation was performed using an integrated energy system consisting of a 6-bus power system, a 7-node natural gas system, and 3 data centers belonging to 2 different operators. The network structure diagram is shown below. Figure 2 As shown.

[0033] In small-scale systems, DC1 and DC3 belong to the same operator; therefore, in Figure 2 In the diagram, DC1 and DC3 are connected by a dark blue line representing a "dedicated direct connection"; while communication with DC2 requires forwarding through the public network, so a light blue line with a cloud symbol is used to represent it.

[0034] All experiments in this invention were conducted on a computer equipped with an Intel Core i7-12700H@3.20Hz CPU and 16GB DDR5 4800MHz RAM using Matlab 2022b and Gurobi 12.0.2. To quantitatively evaluate the regulatory potential of spatiotemporal transferability in data centers, the following four comparative strategies were designed: Strategy 1: Ignore the spatiotemporal transferability of data centers; Strategy 2: Only consider the spatial portability of the data center; Strategy 3: Only consider the time-transferable characteristics of data centers; Strategy 4: Simultaneously consider the spatiotemporal transferability of data centers.

[0035] 3.2.4.1 Dimensionality reduction of historical offshore wind power output data is achieved using the K-medoids clustering method based on Wasserstein distance. The historical offshore wind power output data was reduced in dimensionality using the K-medoids clustering method based on Wasserstein distance, resulting in five clusters. The variation of total offshore wind power output with scheduling periods under different scenarios can be plotted as follows: Figure 3 As shown.

[0036] analyze Figure 3 As shown, typical offshore wind power output scenarios obtained based on Wasserstein distance exhibit significant differences in intraday temporal patterns and fluctuation structures. Different scenarios can reflect the diverse dynamic patterns of output from multiple wind farms. In power system dispatching, unit standby and ramp-up constraints are highly sensitive to output changes. Therefore, preserving the temporal structure characteristics of wind power output helps to more accurately characterize system operational risks and provides representative input scenarios for the subsequent two-stage Bruker bar optimization model. The output patterns of the five scenarios can be summarized as follows: Scenario 1: The output is moderate to high throughout the day with minimal fluctuations, exhibiting a steady-state high output mode; Scenario 2: Output is high from early morning to noon, then drops in the afternoon with significant fluctuations, exhibiting a high output and high volatility pattern; Scenario 3: Low output in the early stage, rapid rise after noon and fall back in the evening, showing an evening peak pattern; Scenario 4: The average output is low throughout the day, with near-zero output during many periods, exhibiting a nighttime hibernation mode; Scenario 5: Output is mainly concentrated from early morning to noon, and then continuously decreases, showing a single-peak decreasing pattern of early start and late stop.

[0037] To further quantify the differences between clustering results, the mean and standard deviation of different scenarios within the scheduling cycle can be recorded as shown in Tables 1 to 3: Table 1 Comparison of mean values ​​for sea breeze output clustering scenarios

[0038] Table 2 Comparison of volatility (standard deviation) in sea breeze output clustering scenarios

[0039] Table 3 Percentage of Each Scenarios

[0040] Analysis of Tables 1-3 reveals significant differences in average power output across the typical scenarios. The distribution of mean wind power output across different scenarios demonstrates good discriminative power, effectively reflecting the operational status at different output levels. Furthermore, the scenarios exhibit significant differences in volatility indicators (standard deviation), with some scenarios showing substantial fluctuations. This indicates that the constructed typical scenarios effectively reflect the random fluctuations in offshore wind power output on an intraday scale. Historically, the probability weight distribution for different output modes is reasonable, with typical high-output scenarios accounting for a high proportion (41.82%), while low-output scenarios also maintain a certain weight, reflecting the long-term statistical characteristics of wind power operation.

[0041] It is evident that the obtained clustering scenario is not only representative in terms of power output level, but also accurately reflects the uncertainty characteristics of offshore wind power output in terms of fluctuation structure and probability distribution, providing input data with discriminative characteristics and conforming to statistical laws for subsequent two-stage split-bulb optimization scheduling.

[0042] 3.2.4.2 Comparison of results between C&CG-ADMM algorithm and C&CG algorithm To verify the effectiveness of the proposed C&CG-ADMM distributed algorithm, strategy 4 is used as an example, and it is compared and analyzed with the traditional C&CG algorithm. The economic indicators and computation time of the two algorithms in solving the TSDRO model are statistically analyzed, and the results are summarized in Table 4: Table 4 Comparison of results between C&CG-ADMM algorithm and C&CG algorithm

[0043] This demonstrates the application of the MATLAB Parallel Computing Toolbox to accelerate the solution through parallel computing technology.

[0044] As shown in Table 4, the C&CG-ADMM algorithm proposed in this paper maintains strict consistency with the traditional centralized C&CG algorithm in terms of the total cost of the final model and the costs at each stage, down to the integer part. Further analysis reveals a difference between the two algorithms at the decimal part, but this error is extremely small relative to the scale analyzed in this paper, and their economic results remain equivalent at the engineering decision-making level. To systematically evaluate the source and propagation mechanism of this error, this paper subsequently conducts a sensitivity analysis of the C&CG-ADMM algorithm parameters.

[0045] Regarding solution time, because C&CG-ADMM embeds the ADMM iterative coordination mechanism in the solution of subproblems, although each scenario is still a linear programming problem, the actual solution complexity increases significantly. In the "serial mode" without parallel acceleration, its total solution time is as high as 1839.79% longer than that of centralized C&CG.

[0046] Clearly, the number of scenarios introduced in the TSDRO model is one of the significant computational bottlenecks in the solution algorithm. While the centralized solution time also increases with the number of scenarios, this is relatively insignificant due to the simple structure of its subproblems. Distributed algorithms, however, are inherently less efficient than centralized algorithms because they require coordination between two subsystems. The scenario-parallel acceleration strategy introduced in this paper reduces the solution time by 75.87% compared to the serial version. By amortizing the waiting overhead of a single scenario, the overall solution efficiency of the subproblems is significantly improved. Thus, while maintaining solution accuracy, the efficiency disadvantage of the distributed architecture is partially offset.

[0047] Further plotting the iterative convergence graph of the C&CG-ADMM algorithm is as follows: Figure 4 As shown.

[0048] analyze Figure 4 As can be seen, the outer C&CG algorithm converges to the optimal value after two iterations, with a final convergence tolerance of 0. The inner ADMM algorithm exhibits different iteration counts in different scenarios, with all scenarios having fewer than 100 iterations, indicating good numerical stability and convergence efficiency under the selected parameters. To further explore the impact of the ADMM algorithm's convergence accuracy on the final result of the C&CG-ADMM algorithm in the subproblems, the convergence thresholds of the primal and dual residuals were adjusted, and the above experiment was repeated, recording the model's total cost deviation and solution time as shown in Tables 5 and 6 below: Table 5. Deviation of total model cost under different convergence thresholds

[0049] Table 6 Solution time under different convergence thresholds

[0050] In Tables 5 and 6, each column represents a different initial residual convergence threshold, and each row represents a different dual residual convergence threshold. To quantify the difference in solution accuracy between the distributed C&CG-ADMM algorithm and the centralized algorithm, the tables show the absolute deviation obtained by subtracting the total cost of the centralized algorithm from the total cost of the distributed algorithm. The centralized algorithm, rounded to four decimal places, yields a result of 685220.9578. When At that time, the absolute deviation of the total cost reached single digits, but the relative error compared to the centralized result was only 0.0004%, indicating a high degree of consistency in solution accuracy between the two methods. This shows that the solution quality of the distributed algorithm is not sensitive to convergence accuracy and has good stability and robustness. However, the solution time shows a significant change, especially when the strict convergence condition is met. , Relax to In this case, the solution time was reduced by 63.22%. This is because solving the ADMM subproblems is the most computationally burdensome part of the overall algorithm, and its convergence speed directly determines the global solution efficiency; while the total cost of the model is more determined by the structure of the main problem and the C&CG main framework, and is robust to changes in the accuracy of the subproblems.

[0051] Therefore, in practical engineering applications, the convergence threshold can be appropriately relaxed while ensuring the quality of the solution, in order to shorten the solution time and improve the practicality and deployment efficiency of the algorithm.

[0052] 3.2.4.3 Analysis of Results of Two-Stage Broken Bar Optimization Model Based on the verification of the effectiveness of the C&CG-ADMM algorithm, this paper further analyzes the role of data center access in mitigating turbine output fluctuations and improving system economics in an integrated electric-gas energy system considering the uncertainties of offshore wind power. This paper calculates the standard deviation of turbine output under different strategies for various scenarios, and records strategies 1 and 4 in Tables 7 and 8: Table 7 Strategy 1 Unit Fluctuations

[0053] Table 8 Strategy 4 Unit Fluctuations

[0054] Analysis of Tables 7 and 8 shows that, considering the spatiotemporal transferability of data centers, the overall fluctuation in unit output shows a downward trend. The percentage change in standard deviation for each unit under each scenario when changing from Strategy 1 to Strategy 4 is calculated and plotted as shown in Tables 7 and 8. Figure 5 As shown: exist Figure 5 In the graph, red indicates a decrease in the standard deviation of unit output, meaning reduced volatility; green indicates an increase in the standard deviation of unit output, meaning increased volatility. Analysis Figure 5As can be seen, when considering the spatiotemporal transferability of data centers, all scenarios showed varying degrees of load fluctuations, with the largest decrease observed in GFU1 in scenario 4, reaching 31.73%. GFU1 also experienced the most frequent decreases, showing a downward trend across all scenarios. Only GFU2 in scenario 5 and CFU2 in scenario 2 showed fluctuating increases, with the largest increase being only 5.07%. Further analysis reveals that the fluctuations in load capacity are closely related to their operating characteristics. GFUs, with their fast response speed and primary peak-shaving capabilities, benefit most from the load migration effect after the data center acquires spatiotemporal transferability, resulting in a significant decrease in fluctuations in most scenarios. In contrast, CFUs have weaker regulation capabilities and exhibit smaller overall fluctuations. The results indicate that the flexible load of data centers, to some extent, replaces the peak-shaving function of the load cells, effectively mitigating fluctuations in load cell output.

[0055] Tables 9 and 10 record the total system cost and the time taken by the C&CG-ADMM algorithm to solve the problem for each scenario under different strategies: Table 9 Total Costs for Different Scenarios under Various Strategies / $

[0056] Table 10 Total time spent under different strategies (s)

[0057] Analysis of Tables 9 and 10 shows that the total costs of strategies 2, 3, and 4 all decreased to varying degrees compared to strategy 1, with strategy 4 showing the largest decrease. This indicates that utilizing the spatiotemporal portability of data centers helps improve the system's economics. In the next section, the analysis of typical daily operating results, this paper will conduct a more detailed analysis of the changes in different cost items.

[0058] Regarding algorithm efficiency, the solution time for strategies 2, 3, and 4 increased by 4.81%, 249.88%, and 299.34% respectively compared to strategy 1. However, the solution time for all strategies was effectively controlled within 50 seconds. This indicates that although the introduction of spatiotemporal transferability makes the model exhibit more complex spatiotemporal coupling characteristics and increases computational complexity, the parallel accelerated C&CG-ADMM algorithm adopted in this paper can still keep the total time within a reasonable range, further verifying its effectiveness and engineering applicability in dealing with complex uncertainty scenarios.

[0059] The above are merely preferred embodiments of the present invention, and should not be construed as limiting the scope of the present invention. It should be noted that for those skilled in the art, any modifications or equivalent substitutions to the technical solutions of the present invention without creative effort do not depart from the protection scope of the technical solutions of the present invention.

Claims

1. A distributed algorithm for a comprehensive energy system that considers the uncertainties of offshore wind power, characterized in that, Includes the following steps: Step 1: Data preparation stage; this involves acquiring operating parameters of the power subsystem, natural gas subsystem, data center, and historical power output data of offshore wind power to form the basic dataset of the integrated energy system. Step 2: Based on the aforementioned basic dataset, construct a scheduling model for the integrated electricity-gas energy system under data center access, including the system objective function and operating constraints, and perform piecewise linearization on the nonlinear relationships in the model; Step 3: Two-stage sub-Brussels bar optimization model establishment stage; The historical offshore wind power output data mentioned in Step 1 is processed, and the K-medoids clustering method based on Wasserstein distance is used to reduce the dimensionality of the wind power output scenarios to obtain a reduced set of typical scenarios; Based on the set of typical scenarios and combined with the synthesis norm constraint, a probabilistic fuzzy set of offshore wind power output is constructed; According to whether the model variables and constraints are affected by uncertainty, the scheduling problem is divided into day-ahead stage and intraday stage, and a two-stage sub-Brussels bar optimization model is established. Step 4: Solve the two-stage biscayne bar optimization model using the C&CG-ADMM algorithm. The specific steps include: S40: Solve the main power system problem involving uncertainties at the day-ahead stage; S41: Construct an electro-gas coupled distributed subproblem during the daytime phase and solve it in a distributed manner using the ADMM algorithm, while simultaneously performing parallel computation on each scenario subproblem; S42: Based on the probability distribution of the worst-case scenario obtained from the sub-problem identification, add corresponding optimality constraints and second-stage decision variables to the main problem; S43: Repeat the iteration until the upper and lower bounds meet the preset convergence conditions, and output the final scheduling result.

2. The distributed algorithm for a comprehensive energy system considering the uncertainties of offshore wind power according to claim 1, characterized in that, The objective function in the deterministic scheduling model of the integrated electricity-gas energy system under data center access includes: a. Data center time and space migration cost; that is, the data center transforms the originally rigid power demand into flexible load by migrating computing tasks in time and space, so as to participate in the integrated energy system scheduling as a flexible resource, in order to reduce the impact of load demand fluctuations and the uncertainty of offshore wind power output, and reduce the pressure on coal-fired and gas-fired units caused by frequent peak shaving; its load migration will generate corresponding economic costs, which consist of two parts: time migration cost and space migration cost. In terms of time migration, workload is redistributed across different time periods within the same data center. The cost of this migration is reflected in the penalty for failing to complete the task within the agreed timeframe. : （1） In the formula: A collection of data centers; For data centers From the initial time period t to the target time period The amount of work transferred out; The unit latency cost factor, i.e., data center The cost of breach of contract that needs to be paid to the user for a delay of one hour in processing a unit of workload; T It represents the set of all time periods within the scheduling period; In terms of space migration, the workload is not directly migrated between data centers. Instead, a dynamic resource allocation strategy is used to enable the target center to take over the incremental requests from the original center in subsequent periods. The resulting space transfer cost is manifested as the communication overhead between data centers. Since data centers of the same operator are usually interconnected through private leased lines, while cross-operator communication requires transmission through the public network and incurs additional traffic costs, communication paths are classified according to operator affiliation, and transfer costs are calculated differently for different paths. Under the same operator, based on the considered day-to-day timescale, the cost of building the network between data centers is a sunk cost and is not included in the consideration of a single decision; in this case, the additional electricity cost generated by the network equipment forwarding data should be taken into account. : (2) In the formula: Within time period t, from the data center Transfer to data center The workload; For the same operator from data center To data center Additional cost coefficient when transferring out a unit of work; However, when using different carriers, communication must be conducted via the public network; this incurs cross-carrier workload transfer costs. It can be represented as: （3） In the formula: To from data center To data center The unit traffic cost coefficient that needs to be paid to the public network when transferring out a unit of workload; In other words, the data center load migration cost that needs to be paid in the context of scheduling the integrated power and gas energy system for data center access. for: （4） b. Unit start-up and shutdown costs （5） In the formula: Representative generator set Startup cost coefficient Representative generator set The downtime cost coefficient; , , Collectively referred to as generator units The start / stop variables, when 1, represent the unit being in the running, start-up, and shutdown states during the time period t, respectively; Represents a collection of coal-fired power units. Represents a collection of gas turbine units. This represents the set of thermal power units in the system; c. Production costs of natural gas suppliers （6） In the formula: Represents a collection of natural gas wells; Representing natural gas suppliers The production cost coefficient; For suppliers The natural gas supply flow rate during time period t; d. Operating costs of coal-fired power units （7） In the formula: Represents the piecewise linearized i-th Section coal-fired power unit Operating cost coefficient; The number of segments for piecewise linearization; Representative coal-fired power units In time period t The active power output of a segment that is higher than its minimum output value. To achieve piecewise linearization, only coal-fired power units are involved. Costs related to start-up and shutdown status; e. Non-fuel operating costs of gas turbine units （8） In the formula: Represents the piecewise linearized i-th Sectional gas turbine unit Operating cost coefficient; Represents gas turbine units In time period t Duan's merits and contributions; To achieve piecewise linearization, only the gas turbine unit is involved. Costs related to start-up and shutdown status; f. Carbon emission costs System scheduling based solely on economic considerations cannot achieve carbon emission reduction. Therefore, this paper establishes a carbon emission cost model, which incorporates carbon emission costs into the objective function. : （9） In the formula: For carbon price; This represents the carbon emissions of the power generation entity within one day. The initial one-day carbon allowance is allocated free of charge to power generation entities; considering the current annual carbon allowance allocation, the accounting scale is converted to the day-ahead level; the carbon allowance covers fossil fuel combustion emissions, and the definition of the free initial allowance obtained by each power generation entity is as follows: （10） The total carbon emissions that the system can generate in a single day are: （11） In the formula: For offshore wind farms; This serves as the baseline value for carbon emissions from coal-fired power units. This serves as the baseline value for carbon emissions from gas turbine units; The direct carbon emission factor corresponding to a unit of electricity generated by a coal-fired power unit. The direct carbon emission factor corresponding to the unit power generation of the gas turbine unit; The carbon footprint factor generated by offshore wind turbines during their life cycle; Represents generator sets; Representative unit Active power output that is higher than its minimum output value during time period t. For the unit The minimum active power, Representative unit The binary variable representing the operating status, where a value of 1 indicates that the unit is in operation; In summary, under data center access, the total cost of each sub-module in the system during the scheduling cycle is: （12） In the formula: Represents the cost of the power subsystem. This represents the cost of the natural gas subsystem.

3. The distributed algorithm for a comprehensive energy system considering the uncertainties of offshore wind power according to claim 2, characterized in that, The constraints in step 2 include: 1) Data center constraints Data center workload constraints Data center workloads are typically categorized into two types based on latency sensitivity: latency-sensitive workloads and latency-tolerant workloads. Latency-sensitive workloads include interactive services with stringent response speed requirements, such as online transactions and real-time streaming media. Latency-tolerant workloads include computationally intensive tasks such as batch data processing and machine learning training, which have longer execution cycles and less stringent real-time constraints, thus exhibiting higher latency tolerance. Scheduled and migrateable workloads originate solely from latency-tolerant workloads. (13) In the formula: The total number of data centers. This is the ratio of transferable workload to total workload. This is the ratio of the amount of work that can be migrated in space per unit time period to the upper limit of processing capacity. and Data Center The workload required to be processed before and after time period t is adjusted; For data centers From time period The workload will be transferred to the next time period t. For data centers From time period t to time period The amount of work transferred out, Within time period t, from the data center Transferred to data center The workload, Within time period t, from the data center To data center The amount of work transferred out; For data centers The maximum workload to be processed in time period t; t is the index number of the current time period. This is the index number of the time period from which the workload originates. This is the index number for the time period where the workload is directed. For the current data center's index number, This refers to the index number of the data center from which the workload originates. The index number for the workload to be directed to the data center; When data center workloads are migrated at the time level, the constraint that the target time period of the workload is later than the source time period must also be met; that is, for any data center of and Its timing index should also satisfy: (14) Data center energy consumption constraints The energy consumption of a data center mainly consists of IT equipment, cooling systems, and auxiliary facilities such as lighting. For modeling the relationship between IT equipment energy consumption and total data center energy consumption, a linear approximation method based on server utilization is adopted. (15) In the formula: and Data Center Peak power and idle power; Data center before time period t adjustment The resulting IT equipment energy consumption, Data center after time period t adjustment The resulting IT equipment energy consumption; Data center before time period t adjustment The total energy consumption generated Data center after time period t adjustment Total energy consumption generated; For data centers The efficiency of electricity use; For each data center, the total energy consumption of its IT equipment is related to the power consumption of its servers as follows: (16) In the formula: The peak power of a single server used in a data center. The idle power of a single server used in a data center. For data centers The total number of servers; Data center user satisfaction constraints Considering the computing limitations of data center servers, there is an upper limit to the amount of work they can process during each scheduling period, which must meet utilization constraints: (17) In the formula: For data centers Average service utilization rate during time period t This represents the upper limit of server utilization. For data centers The number of active servers during time period t; This refers to the workload processing capacity of a single server within a given time period. When optimizing data center power load, the transmission and queuing delays of the workload should not exceed the maximum delay time specified in the service level agreement. The constraints can be expressed as follows: (18) 2) Power system constraints Unit start-up and shutdown constraints: (19) In the formula: The start / stop variable represents the operating status of the unit during time period t-1. A value of 1 indicates that the unit is in operation during time period t-1, and a value of 0 indicates that the unit is not in operation during time period t-1. Minimum start-up / shutdown time constraints for generator sets: The formula for the minimum power-on time constraint is: (20) The formula for the minimum downtime constraint is: (21) In the formula: This is a time index, representing the starting time period of the summation calculated by taking the maximum value on the right side of the equation; Let C be the minimum start-up time of generator set C. For generator sets Minimum downtime; Bus power balance constraints: (22) In the formula: busbar The load demand of the data center; busbar To meet other load demands; For connecting nodes and The susceptance of the transmission lines; busbar The phase angle within time interval t busbar The phase angle within time interval t; It is the set of nodes in a power system; For connection to the busbar A collection of generator sets; Generator capacity constraints: (23) In the formula: For generator sets Minimum active power output during operation For generator sets Maximum active power output during operation; Generator ramping constraints: (24) In the formula: For generator sets Maximum climbing rate; Representative unit The active power output that is higher than its minimum output value during the time period t-1; System spin-off standby constraints: (25) In the formula: Reserve power for the system's upward rotation. Reserve power for the system's downward rotation; Transmission line capacity constraints: (26) In the formula: For connecting bus and busbar The maximum transmission capacity of the transmission lines between them; The reference bus voltage phase angle is zero constraint: (27) In the formula: The voltage phase angle of the reference bus during time period t; 3) Natural gas system constraints Node airflow balance constraints: For node m, its nodal airflow balance constraint is written as follows (28); the left side of equation (28) is the sum of the airflow flowing into node m, and the right side is the sum of the airflow flowing out of node m: (28) In the formula: This is the set of natural gas nodes currently undergoing gas flow balance analysis. This is the set of natural gas nodes that exchange gas with node n; For the collection of gas turbine units, A collection of natural gas compression stations; A generator set at node m that uses natural gas as fuel The fuel flow rate consumed within time period t; To inject into the compressor during time period t Natural gas flow rate in Indicates compressor The air intake port; Let t be the flow rate of natural gas from node m to node n through the pipeline during time period t; Let be the natural gas demand flow rate at node m that is unrelated to power generation during time period t; To obtain from the compressor within time period t The flow rate of natural gas flowing out of the middle Indicates compressor The air outlet port; Let t be the flow rate of natural gas from node n to node m through the pipeline during time period t; For the gas source at node m during time period t The flow rate of supplied natural gas; Average flow rate in the pipeline and pressure constraints at both ends: (29) In the formula: For the pipe connecting nodes m and n, For pipeline collection, For pipelines The Weymouth constant, For node m, the air pressure during time period t Let n be the air pressure at time t. For pipelines The average natural gas flow rate; since the Weymouth equation is a nonlinear constraint, it needs to be linearized, and nodes are set. m and n The square vectors of air pressure are respectively , Then the original expression can be transformed into: (30) In the formula: Let be the squared difference in air pressure between node m and node n; based on the first-order Taylor expansion, the nonlinear term in the above equation (30) can be relaxed to the following piecewise linear form: (31) In the formula: This represents the total number of sampling points for linearizing the Weymouth equation. The first of the pressure differences between nodes m and n Each segment is determined by the upper and lower limits of air pressure at both ends of the pipeline; The midpoint of each segment can be chosen; a penalty term needs to be added to the objective function. To minimize Tighten the inequality constraint (31), where It is a small positive number; Constraints on the hourly variation of storage and flow: (32) In the formula: For pipelines within time period t The amount of natural gas stored in the pipeline is called pipeline storage; Pipeline within time period t-1-1 The amount of natural gas stored therein; Compressor station loss constraints: (33) In the formula: For compressor Consumption factor; For the flow into the compressor during time period t Natural gas flow rate; For the compressor to flow out during time period t Natural gas flow rate; Compression ratio constraint: (34) In the formula: This refers to the intake pressure at both ends of the natural gas compressor. The outlet pressure at both ends of the natural gas compressor; This refers to the compression ratio; Flow constraints: (35) In the formula: For compressor The maximum gas flow rate that can be processed within time period t; This represents the upper limit of the natural gas flow rate from node m to node n within time period t; This represents the upper limit of natural gas flow from node n to node m within time period t; Natural gas well output constraints: (36) In the formula: natural gas supplier The provided lower limit of natural gas flow rate, natural gas supplier The maximum natural gas flow rate provided; Nodal pressure constraints: (37) In the formula: Let m be the air pressure at node m during time period t. The lower limit of pressure at node m The upper limit of pressure for node m; Storage range constraints: (38) In the formula: For pipelines The minimum storage capacity, For pipelines Maximum storage capacity; 4) System coupling constraints The gas turbine unit is the only coupling device between the electrical subsystem and the natural gas subsystem, and there is a fuel conversion constraint relationship between them: （39） In the formula: For gas turbine units Thermal efficiency.

4. The distributed algorithm for a comprehensive energy system considering the uncertainties of offshore wind power according to claim 3, characterized in that, The specific steps of step 3 are as follows: S30. Clustering of multiple wind farm output scenarios based on K-medoids; To address the issue of outliers in offshore wind power output due to wind speed fluctuations, K-medoids clustering is used to extract typical scenarios; Taking the combined power output of several offshore wind farms as the analysis object, the offshore wind power output sequence is modeled as a two-dimensional probability distribution consisting of time and wind farm dimensions, with time index and wind farm number forming a discrete grid coordinate system. The power transmission cost in the time dimension is determined by the time interval, while a discrete equidistant metric is used in the wind farm dimension. That is, the transmission cost within the same wind farm is zero, and the transmission cost between different wind farms is uniformly set as a unit constant. Based on this, the actual wind power output is normalized and used as a probabilistic quality to participate in optimal transmission. This metric can take into account the influence of the power output amplitude of offshore wind farms. It can also reflect the power output time sequence characteristics at different times, thus comprehensively evaluating the scenario similarity based on the minimum transportation cost between distributions; for the two normalized offshore wind power distributions and Its two-dimensional Wasserstein distance is expressed as: （40） In the formula: Represents probability distribution and The second-order Wasserstein distance between them; For all and The set of joint distributions of marginal distributions; From coordinates To coordinates The joint distribution function for probabilistic mass transport; These represent the hourly and wind farm location coordinates in two-dimensional space, respectively. For the corresponding space transportation cost, coordinates and The formula is: （41） In the formula: For probability distribution The time index corresponding to the scene. For probability distribution The time index corresponding to the scene. For probability distribution The corresponding wind farm number in the scenario. For probability distribution The corresponding wind farm number in the scenario; this two-dimensional Wasserstein distance metric can be used to calculate the similarity between different wind power output scenarios; in distribution-based K-medoids clustering studies, the squared Wasserstein distance is usually directly used as the optimization objective, i.e.: （42） At this point, the centers of the K-medoids cluster are: （43） In the formula: Indicates the first Each cluster corresponds to a set of historical offshore wind power output scenarios; The squared Wasserstein distance between the two scenes; This is a typical scenario obtained from K-medoids clustering based on Wasserstein distance; S31. Construction of fuzzy sets for offshore wind power output based on the synthesis norm; A fuzzy set of offshore wind power output is constructed, and the scenario probability distribution is constrained by the synthetic norm based on the 1-norm and the ∞-norm, so as to obtain the worst possible probability distribution of each typical scenario. The probability confidence intervals are shown below: （44） In the formula: The total number of historical scene samples. Let be the total number of discrete typical scenarios; then let the probability confidence level on the right side of the above equation be denoted as . and Then it can be transformed into: （45） This leads to the uncertain confidence set of the scene probability distribution. as follows: （46） in, For the first Probabilistic decision variables for a typical scenario The first one obtained based on historical data statistics Reference probability distribution for a typical scenario; This is a bias tolerance parameter based on the 1-norm, used to limit the overall range of deviation of the probability distribution relative to the reference distribution; This is a bias tolerance parameter based on the ∞-norm, used to limit the maximum component deviation of the probability distribution relative to a reference distribution; the allowable bias is determined by adjusting the 1-norm and the ∞-norm. and To control the fluctuation range of the probability distribution; S32. Construct a two-stage sub-Bruker optimization model; Based on the constraint of the fluctuation range of scene probability using the synthesis norm, the general formula of the data-driven TSDRO model is as follows: （47） In the formula: These are the decision variables for the first stage. Its feasible region; For the decision variables in the second stage, the subscripts are... Representing the An index of typical scenarios is used for differentiation. One possible offshore wind power output state; For the second stage decision variables The feasible domain; Parameters for typical offshore wind power output scenarios A constant coefficient vector, For the second stage decision variables A constant coefficient vector, Decision variables for the first stage A vector of constant coefficients; Decision variables in the first stage constraints The constant coefficient matrix, Decision variables in the second stage constraints The constant coefficient matrix, Parameters for typical offshore wind power output scenarios in the second phase of constraints The constant coefficient matrix, Decision variables in inter-stage inequality constraints The constant coefficient matrix, Decision variables in inter-stage inequality constraints The constant coefficient matrix, Decision variables in inter-stage equality constraints The constant coefficient matrix, Decision variables in inter-stage equality constraints The constant coefficient matrix; This is a constant vector in the first-stage constraints. is a constant vector in the inter-stage inequality constraints. This is a constant vector in the inter-stage equality constraints; Corresponding to the integrated energy system model adopted in this invention, it can be re-expressed as: （48） In the formula: This represents the total cost of the first phase. This represents the total cost of the second phase.

5. The distributed algorithm for a comprehensive energy system considering the uncertainties of offshore wind power according to claim 4, characterized in that, The C&CG-ADMM algorithm is used to solve the two-stage partial blue bar optimization model as follows: In the integrated electric-gas energy system, the power system and natural gas system with data center access belong to different operating entities, and there are privacy requirements for data protection; the model represented by formula (47) has a three-layer structure of min-max-min, which cannot be solved directly; Therefore, in previous uncertain scheduling methods for such systems, the two-stage model is usually divided into a main problem, namely solving the max problem and a subproblem, i.e., solving the max-min problem, and then the C&CG algorithm is used for iterative solution. However, the C&CG algorithm relies on global information aggregation and centralized solution, which inevitably exposes the operating parameters and trade secrets of each subsystem, making it difficult to meet the core requirements of modern energy systems for privacy protection and data sovereignty. Therefore, the C&CG-ADMM algorithm is proposed based on this. As can be seen from formula (47), in the second stage of the max-min two-level problem, the variables... and variables The problems are independent of each other; therefore, the original innermost problem is actually related to the first... Solve the minimization problem of the form (49) independently in a typical scenario: （49） In the formula: For the second stage decision variables constant coefficient vector transpose; Parameters for typical offshore wind power output scenarios constant coefficient vector The transpose of ; by solving the minimization problem of the form of formula (49), respectively obtain Let's assume the system cost corresponding to a typical scenario, and let the first... The optimal cost for the second stage corresponding to each typical scenario is: The objective function of the subproblem that the C&CG algorithm needs to solve is expressed as: （50） at this time Should be considered as a variable Given the coefficients, formula (50) is the fuzzy set of the probability distribution in a typical scenario. Under constraints, find a probability distribution that maximizes the total cost of the second stage in the current scenario set; because Representing the A typical offshore wind power output scenario. Since is a constant, and thanks to the previous linearization and convex relaxation operations, the minimization problem represented by formula (49) is actually a linear programming problem, which is also known as linear programming (LP). Obviously, the maximization problem represented by formula (50) is also LP. Formula (49) can be rewritten as: （51） right By decomposing it, it can be reformulated as the second-stage variables of the power subsystem. and natural gas subsystem variables , Then formula (51) becomes: （52） In the formula: These represent the constant coefficients of the electric subproblem in the objective function. Let the constant coefficients of the natural gas quantum problem in the objective function be represented; This represents the optimal solution to the main problem during each iteration of the C&CG algorithm; therefore, the innermost min problem can be reformulated as: （53） In the formula: the first constraint is the system coupling constraint explicitly expressed after dividing the power subsystem and the natural gas subsystem, where For power subsystem variables The constant coefficient matrix, For natural gas subsystem variables The constant coefficient matrix, Let be the constant vector of the first constraint; the fourth equality constraint can be represented by two equivalent inequalities: （54） Formula (54) and the third constraint in Formula (53) have the same algebraic form. Therefore, the algebraic expressions of the three are uniformly adjusted as follows: （55） In the formula: optimal solution to the main problem The constant coefficient matrix, Decision variables The constant coefficient matrix, The adjusted constant vector; note that the second constraint in formula (53) and formula (55) have the same direction, so we can apply the inequality addition to get: （56） For the natural gas subsystem, since it has no first-stage variables and does not involve uncertain variables, the simplified formula (56) is the constraint for the natural gas subproblem: （57） In the formula: The constant coefficient matrix of the natural gas system subproblem. For the constant vector of the natural gas system subproblem; the natural gas subsystem only participates in the optimization in the second stage of the original TSDRO model; For the power subsystem, due to the first-stage variable term involved in formula (56) and uncertain scenario items Since all terms are constants, formula (56) can be rearranged to a form similar to formula (57) by transposing terms: （58） In the formula: The constant coefficient matrix of the power system subproblem For a constant vector of a subproblem in a power system; Then, formula (53) can be restated into a standard form that can be solved by the ADMM algorithm as follows: （59） Its augmented Lagrangian function can be expressed as: （60） In the formula: For penalty parameters, ; Let be the Lagrange multiplier vector; formula (59) can be decomposed into a power system subproblem (61) and a natural gas system subproblem (62): （61） （62） After iterating through formulas (61) and (62) alternately once, update the Lagrange multipliers. for: （63） In the formula, superscript and They represent the first The second iteration and the first The variable values ​​corresponding to each iteration; the original residuals during the iteration process. and dual residual They are respectively: （64） In the formula: For the original residual The convergence threshold; For dual residuals The convergence threshold; when the original residual and dual residual Each less than the set convergence threshold and When the iteration converges: （65） Different penalty parameters can be used in each iteration. To reduce the impact of the initial selection of the penalty parameter on the algorithm's performance and improve the convergence speed of ADMM, a commonly effective method for updating the penalty parameter is: （66） In the formula: , The ADMM algorithm is also known as Variable Penalty Parameter ADMM.

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