A method for constructing a safety boundary of an electric-carbon coupled system considering source-load uncertainty

Abstract

The application discloses a kind of considering source load uncertainty electric carbon coupling system safety boundary construction method, it is related to power system operation and control technical field, including the following steps: S1. establish electric carbon coupling system linearization model, S2. based on data distribution robust fuzzy set is constructed, S3. optimization problem is established with distribution robust chance constraint, S4. CVaR approximation is used with dual theory is transformed into deterministic programming, S5. the explicit expression of dynamic safety boundary is obtained by iterative algorithm.The application generates the intersection of dynamic safety boundary which is physical safety domain and low-carbon feasible region by deeply embedding carbon emission flow dynamic tracking mechanism into the whole process of safety boundary construction, and the out-of-limit risk of line power, node voltage and node carbon potential can be directly monitored by dispatcher, so that the unified, quantitative and visualized representation of electric-carbon dual safety state of system is realized, and the operation risk caused by ignoring carbon constraint is fundamentally avoided.

Description

Technical Field

[0001] This invention relates to the field of power system operation and control technology, specifically to a method for constructing a safety boundary for an electric-carbon coupled system that considers source-load uncertainty. Background Technology

[0002] As global efforts to address climate change deepen, "carbon peaking and carbon neutrality" have become the core constraints for the development of the energy and power industry. As a key sector for carbon emissions, the power system is undergoing a profound transformation from a "high-carbon power system" to a "new type of power system with new energy as the main body." Against this backdrop, the physical properties of electricity and its environmental properties (carbon emissions) exhibit a close coupling relationship, namely, the electricity-carbon coupling characteristic. Traditional power system dispatch and control mainly focus on the physical flow of electrical energy, and analyze the physical safety boundaries of the system such as voltage, frequency, and thermal stability through power flow calculations. However, with the establishment of the carbon trading market and the tightening of carbon emission reduction policies, the power system must not only meet physical safety constraints, but also low-carbon safety constraints such as carbon emission intensity and carbon quotas. The electric carbon coupling system requires the ability to track the transfer process of carbon emission flow from the generation side to the load side in real time and incorporate carbon emission indicators into the construction of the safety domain. At the same time, the operating environment of the new power system is becoming increasingly complex. The core challenge lies in the uncertainty on both the source and load sides. On the power source side, the output of renewable energy sources such as wind power and photovoltaics has strong randomness, volatility and intermittency. Its probability distribution often changes dynamically with weather conditions and is difficult to describe with a single deterministic model. On the load side, the large-scale access of electric vehicles, distributed energy storage and demand response resources makes the load side exhibit strong initiative and uncertainty. Currently, research on power system safety boundaries mainly focuses on the physical level, such as static voltage stability boundaries and transient power angle stability boundaries. Commonly used methods include fitting techniques, analytical methods, and data-driven methods. For handling uncertainties, robust optimization or stochastic programming is often used. Robust optimization usually constructs a fixed set of uncertainties, which ensures safety under the worst-case scenario, but is often too conservative. Stochastic programming relies on accurate probability distribution assumptions, and when the actual distribution deviates significantly from the assumptions, the calculation results may become invalid. Furthermore, most existing safety boundary construction technologies neglect the impact of "carbon flow." In the context of electric-carbon coupling, the safe operating domain of the system should be the intersection of the "physical safety domain" and the "low-carbon feasible domain." The lack of consideration for the dynamic characteristics of carbon emission flow makes the existing scheduling boundary unable to effectively guide low-carbon operation and easily leads to the risk of carbon emission exceeding the standard. Therefore, there is an urgent need for a dynamic safety boundary construction technology that can simultaneously encompass physical constraints and carbon emission constraints and accurately characterize the uncertainty of source and load based on real-time data features.

[0003] The existing drawbacks of electro-carbon coupling systems that consider source-load uncertainty are: 1. Patent CN120509514A discloses a low-carbon operation method for gas-electricity-hydrogen coupled distribution networks using a two-stage P2G model with a distributed broom. "This invention relates to the field of integrated energy system optimization and operation technology, and discloses a low-carbon operation method for gas-electricity-hydrogen coupled distribution networks using a two-stage P2G model with a distributed broom. A refined P2G model considering the two-stage processes of water electrolysis for hydrogen production and hydrogen methanation is established. A model is constructed with the objective function of minimizing the operating cost of the gas-electricity-hydrogen coupled distribution network system. The low-carbon operation optimization model is transformed into a mixed-integer second-order cone programming model for solution. Uncertainty scenarios related to wind power output and load fluctuations are obtained, and based on..." KL divergence is used to construct a fuzzy set of probability distribution of uncertain parameters, and to establish a low-carbon operation model of gas-electricity-hydrogen coupled distribution network considering source-load uncertainty. This invention can improve the flexibility and environmental friendliness of system scheduling, and obtain the optimal operation decision that balances economy and safety while ensuring the safe operation of the system. However, the above documents often separate physical safety from low-carbon goals. The dispatcher can only see the physical safety boundary, but it is difficult to intuitively see the carbon safety boundary. This leads to the technical problem that the system is physically safe, but violates environmental regulations or causes high carbon tax costs due to the instantaneous carbon emission intensity exceeding the standard. Summary of the Invention

[0004] The purpose of this invention is to provide a method for constructing a safety boundary for an electro-carbon coupling system that considers source-load uncertainty, so as to solve the technical problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for constructing a safety boundary for an electro-carbon coupling system considering source-charge uncertainty, comprising the following steps: S1. Establish a linear sensitivity model for the electro-carbon coupling system. The model is used to establish a linear mapping relationship between the node injection power change and the branch power flow and node carbon potential change. S2. Based on historical source load observation data, construct a data-driven sub-Bruker fuzzy set using Wasserstein distance; S3. Based on the linearized sensitivity model and the sub-Bruker fuzzy set, define the optimization problem of the dynamic safety boundary, and express the system safety constraints in the form of sub-Bruker chance constraints; S4. The conditional value at risk (CVaR) is used to make a convex approximation of the chance constraints of the sub-Bruker bar, and the optimization problem is reconstructed into a deterministic linear programming problem using Wasserstein strong duality theory. S5. Solve the linear programming problem using an iterative algorithm based on adaptive polyhedral projection to obtain an explicit analytical expression for the dynamic safety boundary, characterized by a set of linear inequalities.

[0006] Preferably, S1 specifically includes: S11. Establish a linear power flow model based on the power transfer distribution factor (PTDF), specifically as follows:

[0007] in, Represents the branch power flow vector. Represents the PTDF matrix. Let represent the active power vector injected into the node, and:

[0008] in, These represent the power vectors of conventional generating units, new energy sources, and loads, respectively. These represent the node association matrices corresponding to conventional generating units, new energy sources, and loads, respectively, and are all 0-1 matrices; S12. Based on the principle of proportional sharing in carbon emission flow theory, establish nodal carbon potential. The matrix-based model is as follows:

[0009] in, This represents a vector representing the carbon potential of each node in the entire network. Represents the diagonal matrix of total flux at nodes. Represents the power flow distribution matrix. Represents the generator carbon injection flow vector; S13. Derive the sensitivity matrix of nodal carbon potential to nodal injection power. and nodes carbon potential In uncertain scenarios The lower linearization is expressed as:

[0010] in, Represents the node at the reference operating point Carbon potential, Representing nodes respectively The sensitivity coefficient vector of carbon potential to conventional units, new energy sources, and load. This represents the planned output vector of a conventional generating unit. This represents the predicted power output vector of the new energy source. Represents the load forecast vector. The total vector representing the uncertainty of the source load.

[0011] Preferably, in S13, the sensitivity matrix The derivation formula is as follows: =

[0012] in, This represents the inherent carbon emission intensity vector of the generator. This represents the node carbon potential of each node in the entire network.

[0013] Preferably, in S2, the fuzzy set is divided into two parts. Represented as:

[0014] in, Represents the true probability distribution. Indicates support set The set of all probability distributions above, Represents the first-order Wasserstein distance. Indicates the number of historical data samples. Indicates by Historical observation samples The constructed discrete empirical distribution, The Wasserstein radius is the total vector of the source load uncertainty. .

[0015] Preferably, in step S3, the dynamic safety boundary is defined as the feasible region of the system control variables under the premise of satisfying system safety constraints. This region is described by a set of hyperplanes: in, Represents the safety boundary variable to be determined. Indicates the number of system control variables. Indicates the first The normal vector and intercept of each hyperplane. The total number of hyperplanes representing the boundary; The chance constraint of the Blue bar is expressed as:

[0016] in, This indicates the permissible probability of default. Denotes the constraint function, and , Indicates the first The coefficient vector corresponding to each constraint. Indicates the first The upper limit of a constraint.

[0017] Preferably, S4 specifically includes: S41. Using Conditional Value at Risk (CVaR) to constrain the opportunities of the sub-Bruker:

[0018] in, Auxiliary variables representing CVaR; S42. Based on the strong duality theory of Wasserstein distance, the convex constraint is transformed into the following equivalent constraint containing the supremum operator: For each historical sample There are auxiliary variables Satisfy the following robust constraints:

[0019] Simultaneously satisfy:

[0020] in, Indicates dual multipliers. Indicating uncertainty support set Auxiliary variables within; S43. Linearizing the constraints that include the supremum operator and the 1-norm yields the following deterministic linear constraint system:

[0021]

[0022] in, Indicates the first The constraint on the first The absolute value of the sensitivity of an uncertain source, where K is the total dimension of the uncertain variables.

[0023] Preferably, in the optimization problem of S3, the total vector is used to address the uncertainty of the source load. The resulting power deviation is addressed by employing an affine regulation strategy to adjust the output of conventional units. Make real-time adjustments:

[0024] in, Represents the total vector under source load uncertainty. The conventional unit power vector of the generator set, This represents the day-ahead scheduling plan value for the generator set. This represents the unit participation factor vector for automatic generation control. The predicted vector value represents the uncertainty of the source load.

[0025] Preferably, in step S5, the iterative algorithm for adaptive polyhedral projection iterates by alternately solving the following main problem and sub-problems: S51. Solving the main problem: Following the preset search direction Solve for safe distance The optimization problem with the objective of maximizing yields candidate boundary points. And the mathematical model of the main problem is:

[0026] in, Let represent the boundary point vector to be determined, which is a point on the safety boundary; S52. Subproblem Solving: For candidate boundary points To verify security, the subproblem is a two-level optimization problem aimed at finding the worst-case uncertainty scenario and calculating the maximum default amount. The mathematical model is as follows:

[0027] in, Represents the objective function value of the subproblem, when This indicates that there is an out-of-bounds error. This means that the system remains secure even under the worst-case scenario. This indicates outer-layer optimization, which aims to find the worst-case uncertainty scenarios. This indicates inner-layer optimization, simulating how a dispatcher, when faced with this scenario, adjusts generator output to minimize out-of-limit operations. This represents the default rate function, which calculates the extent to which physical currents or carbon potential exceed the limit.

[0028] Preferably, in step S52, during the solution of the sub-problem, the carbon emission flow equation is processed. bilinear terms in Linearization is performed using the McCormick envelope method for nonlinear terms. Introducing auxiliary variables Replace and construct the following set of linear inequality constraints:

[0029] in, Represents branch power flow variables. node The carbon potential variable, Indicates the upper and lower bounds of the branch current flow. The upper and lower bounds of the estimated carbon potential at the nodes are represented, and the subproblem is transformed into a mixed-integer linear programming problem to be solved.

[0030] Preferably, in step S5, the iterative algorithm further includes the following steps: S53, Cutting plane generation: When the subproblem solution result shows that the current point is unsafe (i.e., ... Then, according to duality theory, a Benders cutting plane is generated and fed back to the main problem to remove the unsafe region:

[0031] in, Indicate the subproblem in The maximum amount of default calculated at that point. This represents the gradient vector of the default amount with respect to the boundary variables; S54. Boundary Fitting: Repeat steps S51 to S53 until convergence, and collect the critical safe points generated in all iterations to form a set. ,and The minimum volume envelope algorithm is used for fitting, and the following optimization problem is solved to obtain the final boundary parameters:

[0032] in, This represents the safety boundary parameters to be determined. This represents the volume function.

[0033] Compared with the prior art, the beneficial effects of the present invention are: 1. This invention deeply embeds the dynamic tracking mechanism of carbon emission flows into the entire process of safety boundary construction. The generated dynamic safety boundary is the intersection of the physical safety domain and the low-carbon feasible domain. The dispatcher can simultaneously and intuitively monitor the risk of exceeding the limits of line power, node voltage and node carbon potential. This achieves a unified, quantitative and visual representation of the dual electrical and carbon safety status of the system, fundamentally avoiding the operational risks caused by ignoring carbon constraints. 2. This invention abandons the fixed geometric uncertainty set in traditional robust optimization and innovatively adopts a data-driven sub-robust fuzzy set based on Wasserstein distance. It can directly learn the probability distribution characteristics of uncertain variables from limited historical or real-time data and generate a distribution sphere with a controllable radius centered on the empirical distribution. This characterization method avoids the strong dependence of stochastic programming on the precise distribution and overcomes the problem of excessive conservatism caused by traditional robust optimization covering extremely low probability events. It makes the constructed safety boundary more realistic and significantly improves the space for new energy consumption and the economic efficiency of system operation. 3. This invention approximates complex nonlinear relationships as linear mappings through a linearized sensitivity model, transforms infinite-dimensional fractional Broglie chance constraints into finite-dimensional linear constraints using CVaR and Wasserstein strong duality theory, and finally achieves efficient solutions by using an adaptive master-subproblem iterative algorithm combined with the McCormick envelope method to handle non-convex terms. This reduces the computational complexity from unacceptable non-convex programming to standard linear or mixed-integer linear programming, shortening the solution time from hours to minutes or even seconds, fully meeting the real-time requirements of online dynamic security analysis and early warning of power grids. 4. Unlike the "black box" neural network method, the final output of this invention is a set of explicit linear hyperplane inequalities with clear physical meaning. The dispatcher can intuitively understand the boundary composition and the relative position of the operating point. At the same time, based on rigorous physical mechanisms and mathematical programming theory, this method has stronger robustness and generalization ability than pure data-driven methods when facing new operating conditions or changes in power grid topology that are not covered by training data, and the decision reliability is higher. Attached Figure Description

[0034] Figure 1 This is a framework diagram for constructing the safety boundary of the electro-carbon coupling system considering source-load uncertainty in this invention; Figure 2 This is a flowchart of the iterative algorithm for adaptive polyhedral projection of the present invention. Detailed Implementation

[0035] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] Please see Figure 1 and Figure 2 The present invention provides an embodiment of a method for constructing a safety boundary for an electro-carbon coupling system considering source-charge uncertainty. Step 1: Establish an electrocarbon coupling linearized sensitivity model (S1) The core of this step is to approximate the complex nonlinear electrocarbon coupling relationship as a linear mapping near the benchmark operating point, laying the foundation for subsequent efficient optimization. S11, Linearized Power Flow Model Based on PTDF Using the DC power flow assumption, neglecting line resistance and voltage amplitude variations, we focus on the distribution of active power flow. Forming the nodal admittance matrix ( (representing the number of nodes) and the product matrix of the branch-node incidence matrix and the line susceptance. ( (Indicates the number of branches); Select a balance node, from Remove the corresponding rows and columns to obtain the row representing the row to remove the balancing node. Reduced admittance matrix after column ; Calculate the power transfer distribution factor matrix: ,matrix The Line number Column elements The physical meaning is: at the node When 1 unit of active power is injected and 1 unit of power is extracted at the slack node, the branch The amount of change in the current; Injecting active power vectors at nodes Composed of various power sources and loads:

[0037] in, These are the active power vectors for conventional generating units, renewable energy generating units, and loads, respectively. This is the corresponding node association matrix (0-1 matrix), used to map devices to their connected physical nodes; Ultimately, the active power flow vector of the branch is... It can be linearly represented as:

[0038] This model can quickly assess the impact of node injection power changes on the overall network power flow. S1.2 Matrix Model of Carbon Emission Flows Based on Proportional Sharing Principle Carbon emission flow theory is used to track the distribution of carbon emissions from the power generation side in the network along with the power flow, based on the principle of proportional power sharing among nodes: Based on current trend results Based on the network topology, construct a diagonal matrix of total flux for each node. and power flow distribution matrix ; Calculate the generator carbon injection flow vector: , This represents the carbon emission intensity vector of the generator; Carbon potential vector of all nodes in the network The following system of linear equations was obtained by solving:

[0039] The solution is:

[0040] This model establishes the power output from the generator. and tidal distribution ( , From the entire network carbon potential Mapping; S13. Derivation and Linearization of Total Differential Sensitivity Linearize the nonlinear mapping in S12 at a given baseline operating point ( , , Perform total differential analysis; For matrix equations Differentiating both sides, we derive the sensitivity matrix of the nodal carbon potential to the nodal injection power:

[0041] The partial derivative terms in this formula need to be determined according to... , and The specific functional relationship is calculated; Based on this sensitivity matrix and node correlation matrix, any node can be extracted. carbon potential Sensitivity coefficient vectors for various power variables: : Output vector of conventional units Sensitivity; : Power output vector of new energy Sensitivity; : For load power vector Sensitivity; Therefore, near the baseline point, the nodal carbon potential can be linearly expressed as:

[0042] in, Representing the baseline carbon potential, and combining it with the power flow linear model of S11, all physical security constraints (line power, voltage) and low-carbon security constraints (node ​​carbon potential) can be uniformly expressed as a total vector concerning the uncertainty of source loads. A linear function, denoted as ; Step 2: Constructing a data-driven sub-Browsing fuzzy set (S2) To accurately describe source load uncertainty The probability characteristics of the distribution avoid the conservatism of traditional methods or their dependence on precise distributions; collect Historical observation samples , constitute discrete empirical distribution ,in Indicates at sample points Dirac measure at the location; The first-order Wasserstein distance is defined to measure the distance between two probability distributions, for discrete empirical distributions. and any possible true distribution Its Wasserstein distance is defined; Build with Centered on, with radius The fuzzy set of the Blue bar:

[0043] in, It is a support set The set of all probability distributions above, with radius The conservatism of the model is controlled, and it can be calibrated using data-driven methods such as cross-validation. This fuzzy set It includes all data that are "similar" to historical empirical distributions (distance from 1 / 2000 to 1 / 3000). The possible true distribution of (within); Step 3: Define the dynamic safety boundary and the chance constraints of the distributed bar (S3) Formalizing the safety boundary: The dynamic safety boundary is defined as the feasible region of the system control variables while satisfying system safety constraints. This region is approximately described by a set of hyperplanes:

[0044] in, Represents the safety boundary variable to be determined. Indicates the number of system control variables. Indicates the first The normal vectors and intercepts of each hyperplane are the solution objectives of this model. The total number of hyperplanes representing the boundary; Affine adjustment strategy: to cope with real-time uncertainty To address the resulting power imbalance, an affine regulation strategy is introduced into the model, whereby the output of conventional units will be adjusted in real time based on the realized value of the uncertainty.

[0045] in, Represents the total vector under source load uncertainty. The actual active power output of the generator unit. This represents the unit participation factor vector for automatic generation control. The predicted vector value represents the uncertainty of the source load. This strategy ensures real-time power balance, and its impact is already reflected in the linear constraint function. coefficient middle; Distributed chance constraint: requires the system to be in a fuzzy set Even under the worst-case probability distribution, the probability of violating each security constraint is still below a given threshold. :

[0046] This constraint is the core of the model's robustness, ensuring that the boundary has a high degree of confidence in its safety under uncertainty; Step 4: Problem Restructuring and Deterministic Transformation (S4) The bibliometric chance constraint is a semi-infinite programming problem that cannot be solved directly. This invention transforms it into a deterministic linear constraint in two steps. S41. Convex approximation based on CVaR Utilizing the property that Conditional Value at Risk (CVaR) is a convex conservative approximation of opportunity constraints, for each constraint Introducing auxiliary variables The original Bruker chance constraint can be transformed into an equivalent convex constraint form:

[0047] S42. Application of Wasserstein's Strong Duality Theory By utilizing the duality of the Wasserstein distance, the aforementioned convex constraints involving the worst-case distribution expectation can be equivalently transformed into a set of constraints associated with each historical sample. Specifically, for each constraint... and each historical sample There are auxiliary variables This makes the original constraint equivalent to satisfying the following two conditions:

[0048] At the same time, for each historical sample Satisfies the robust inequality:

[0049] in, ≥0 indicates dual multipliers. This represents the auxiliary variables within the support set of the uncertainty set; S43. Linearization of Norm Constraints To eliminate the supremum operator supremum and handle the norm term in the above equation, linearization is performed using the norm duality principle. Since... The duality is Norm, therefore we get:

[0050] in, It is a satisfaction Auxiliary dual vectors ≤ 1; To handle the 1-norm To address the nonlinearity, a variable substitution method is introduced, allowing the deviation vector to... Substituting into the above formula, we get:

[0051] in, These represent the offsets of the uncertain variable in the positive and negative directions, respectively. They are vectors and The first in One element; After simplification, a set of linear constraints is obtained:

[0052] in, Indicates the first The constraint on the first The absolute value of the sensitivity of an uncertain source; Step 5: Iterative Solution of Adaptive Polyhedral Projection (S5) The iterative algorithm for adaptive polyhedral projection is performed according to the following steps; S51. Main Problem – Finding Candidate Boundary Points The core task is to explore the maximum safe operating radius of the system along a preset search direction ray, and its mathematical model is constructed as follows:

[0053] in, Indicates the safe distance in the search direction. This represents the current search direction vector. This represents the boundary point vector to be found, where each point is on the safe boundary. This problem is a linear programming problem, and solving it yields candidate boundary points. ; S52, Sub-problem – Key Scenario Identification and Security Verification Obtain candidate boundary points from the main problem. The subproblem then aims to verify whether the point remains safe under the worst-case uncertainty distribution, which is equivalent to solving a bilevel programming problem:

[0054] in, Describe the objective function value of the subproblem, if If, then it indicates that there is an out-of-bounds error. This means that the system remains secure even under the worst-case scenario. This indicates outer-layer optimization, which aims to find the worst-case uncertainty scenarios. This indicates inner-layer optimization, simulating how a dispatcher, when faced with this scenario, adjusts generator output to minimize out-of-limit operations. This represents the default rate function, which calculates the extent to which physical currents or carbon potential exceed the limit. To address the nonconvexity of the electro-carbon coupling, the carbon emission flow equation in the subproblem... Contains bilinear terms This leads to a non-convex model that is difficult to solve. This invention employs a mixed-integer linear programming strategy combining the Big M method and the McCormick envelope method, by introducing auxiliary variables. Substitution of nonlinear terms We construct McCormick convex hull relaxation constraints to transform the bilinear terms into a set of linear inequalities:

[0055] in, Represents branch power flow variables. node The carbon potential variable, Indicates the upper and lower bounds of the branch current flow. Indicates the upper and lower bounds of the estimated nodal carbon potential; Through the above transformation, the nonlinear subproblem is transformed into a standard mixed-integer linear programming problem, which can be solved efficiently using the Gurobi or CPLEX solvers. S53, Generation of Cutting Plane If the solution to the subproblem shows that the current point is unsafe (i.e.) Then, according to duality theory, a Benders cutting plane is generated and fed back to the main problem to remove the unsafe region:

[0056] in, Indicate the subproblem in The maximum amount of default calculated at that point. This represents the gradient vector of the default amount with respect to the boundary variables. It indicates the direction in which moving will most quickly reduce the default amount. This indicates the new boundary point that needs to be found in the next iteration; S54, Boundary Fitting and Output Once the principal subproblem converges iteratively, collect the set of critical safe points generated during all iterations. ,and The final explicit boundary is constructed using the minimum volume envelope algorithm:

[0057] in, The parameters to be determined represent the safety boundary parameters, and together they define the final output dynamic safety domain polyhedron. The goal is to find a convex polyhedron with the smallest volume that encloses all the found safe points, thus obtaining the most compact and accurate boundary description. This represents the set of critical points, which contains all the safe boundary points found by the algorithm in the first few iterations.

[0058] The working principle involves deeply embedding the dynamic carbon emission flow tracking mechanism into the entire process of safety boundary construction. The generated dynamic safety boundary is the intersection of the physical safety domain and the low-carbon feasible domain. Dispatchers can simultaneously and intuitively monitor the risks of exceeding limits for line power, node voltage, and node carbon potential. This achieves a unified, quantitative, and visual representation of the system's dual electrical and carbon safety states, fundamentally avoiding operational risks caused by neglecting carbon constraints. By abandoning the fixed geometric uncertainty set in traditional robust optimization, it innovatively adopts a data-driven sub-robust fuzzy set based on Wasserstein distance. This allows it to directly learn the probability distribution characteristics of uncertain variables from limited historical or real-time data, generating a distribution sphere centered on the empirical distribution with a controllable radius. This characterization method avoids the strong dependence of stochastic programming on precise distributions and overcomes the overly conservative problem caused by traditional robust optimization covering extremely low-probability events. This makes the constructed safety boundary more realistic, significantly improving the space for renewable energy consumption and the economic efficiency of system operation. The personalized sensitivity model approximates complex nonlinear relationships as linear mappings. Utilizing CVaR and Wasserstein strong duality theory, it transforms infinite-dimensional fractional Bruker chance constraints into finite-dimensional linear constraints. Finally, an adaptive master-subproblem iterative algorithm, combined with McCormick's envelope method to handle non-convex terms, achieves efficient solution. This reduces computational complexity from unacceptably complex non-convex programming to standard linear or mixed-integer linear programming, shortening solution time from hours to minutes or even seconds. This fully meets the real-time requirements of online dynamic safety analysis and early warning for power grids. Unlike "black box" neural network methods, this invention outputs a set of explicit linear hyperplane inequalities with clear physical meaning, allowing dispatchers to intuitively understand the boundary composition and relative position of operating points. Furthermore, based on rigorous physical mechanisms and mathematical programming theory, this method exhibits stronger robustness and generalization ability compared to purely data-driven methods when facing new operating conditions or power grid topology changes not covered by training data, resulting in higher decision reliability.

[0059] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, it is intended that all variations falling within the meaning and scope of equivalents of the claims be included within the present invention.

Claims

1. A method for constructing a safety boundary for an electro-carbon coupling system considering source-charge uncertainty, characterized in that: Includes the following steps: S1. Establish a linear sensitivity model for the electro-carbon coupling system. The model is used to establish a linear mapping relationship between the node injection power change and the branch power flow and node carbon potential change. S2. Based on historical source load observation data, construct a data-driven sub-Bruker fuzzy set using Wasserstein distance; S3. Based on the linearized sensitivity model and the sub-Bruker fuzzy set, define the optimization problem of the dynamic safety boundary, and express the system safety constraints in the form of sub-Bruker chance constraints; S4. The conditional value at risk (CVaR) is used to make a convex approximation of the chance constraints of the sub-Bruker bar, and the optimization problem is reconstructed into a deterministic linear programming problem using Wasserstein strong duality theory. S5. Solve the linear programming problem using an iterative algorithm based on adaptive polyhedral projection to obtain an explicit analytical expression for the dynamic safety boundary, characterized by a set of linear inequalities.

2. The method for constructing a safety boundary of an electro-carbon coupling system considering source-charge uncertainty according to claim 1, characterized in that: S1 specifically includes: S11. Establish a linear power flow model based on the power transfer distribution factor (PTDF), specifically as follows: ； in, Represents the branch power flow vector. Represents the PTDF matrix. Let represent the active power vector injected into the node, and: ； in, These represent the power vectors of conventional generating units, new energy sources, and loads, respectively. These represent the node association matrices corresponding to conventional generating units, new energy sources, and loads, respectively, and are all 0-1 matrices; S12. Based on the principle of proportional sharing in carbon emission flow theory, establish nodal carbon potential. The matrix-based model is as follows: ； in, This represents a vector representing the carbon potential of each node in the entire network. Represents the diagonal matrix of total flux at nodes. Represents the power flow distribution matrix. Represents the generator carbon injection flow vector; S13. Derive the sensitivity matrix of nodal carbon potential to nodal injection power. and nodes carbon potential In uncertain scenarios The lower linearization is expressed as: ； in, Nodes at the reference operating point Carbon potential, Representing nodes respectively The sensitivity coefficient vector of carbon potential to conventional units, new energy sources, and load. This represents the planned output vector of a conventional generating unit. This represents the predicted power output vector of the new energy source. Represents the load forecast vector. The total vector representing the uncertainty of the source load.

3. The method for constructing a safety boundary of an electro-carbon coupling system considering source-charge uncertainty according to claim 2, characterized in that: In S13, the sensitivity matrix The derivation formula is as follows: = ； in, This represents the inherent carbon emission intensity vector of the generator. This represents the node carbon potential of each node in the entire network.

4. The method for constructing a safety boundary of an electro-carbon coupling system considering source-charge uncertainty according to claim 1, characterized in that: In S2, the fuzzy set of the sub-Brussels bar is... Represented as: ； in, Represents the true probability distribution. Indicates support set The set of all probability distributions above, Represents the first-order Wasserstein distance. Indicates the number of historical data samples. Indicates by Historical observation samples The constructed discrete empirical distribution, The Wasserstein radius is the total vector of the source load uncertainty. .

5. The method for constructing a safety boundary of an electro-carbon coupling system considering source-charge uncertainty according to claim 1, characterized in that: In S3, the dynamic safety boundary is defined as the feasible region of the system control variables under the premise of satisfying system safety constraints. This region is described by a set of hyperplanes: in, Represents the safety boundary variable to be determined. Indicates the number of system control variables. Indicates the first The normal vector and intercept of each hyperplane. The total number of hyperplanes representing the boundary; The chance constraint of the Blue bar is expressed as: ； in, This indicates the permissible probability of default. Denotes the constraint function, and , Indicates the first The coefficient vector corresponding to each constraint. Indicates the first The upper limit of each constraint.

6. The method for constructing a safety boundary of an electro-carbon coupling system considering source-charge uncertainty according to claim 1, characterized in that: S4 specifically includes: S41. Using Conditional Value at Risk (CVaR) to constrain the opportunities of the sub-Bruker: ； in, Auxiliary variables representing CVaR; S42. Based on the strong duality theory of Wasserstein distance, the convex constraint is transformed into the following equivalent constraint containing the supremum operator: For each historical sample There are auxiliary variables Satisfy the following robust constraints: ； Simultaneously satisfy: ； in, Indicates dual multipliers. Indicating uncertainty support set Auxiliary variables within; S43. Linearizing the constraints that include the supremum operator and the 1-norm yields the following deterministic linear constraint system: ； ； in, Indicates the first The constraint on the first The absolute value of the sensitivity of an uncertain source, where K is the total dimension of the uncertain variables.

7. The method for constructing a safety boundary of an electro-carbon coupling system considering source-charge uncertainty according to claim 1, characterized in that: In the optimization problem of S3, in order to cope with uncertainty... The resulting power deviation is addressed by employing an affine regulation strategy to adjust the output of conventional units. Make real-time adjustments: ； in, Represents the total vector under source load uncertainty. The conventional unit power vector of the generator set, This represents the day-ahead scheduling plan value for the generator set. This represents the unit participation factor vector for automatic generation control. The predicted vector value represents the uncertainty of the source load.

8. The method for constructing a safety boundary of an electro-carbon coupling system considering source-charge uncertainty according to claim 1, characterized in that: In S5, the iterative algorithm for adaptive polyhedral projection iterates by alternately solving the following main problem and sub-problems: S51. Solving the main problem: Following the preset search direction Solve for safe distance The optimization problem with the objective of maximizing yields candidate boundary points. And the mathematical model of the main problem is: ； in, Let represent the boundary point vector to be determined, which is a point on the safety boundary; S52. Subproblem Solving: For candidate boundary points To verify security, the subproblem is a two-level optimization problem aimed at finding the worst-case uncertainty scenario and calculating the maximum default amount. The mathematical model is as follows: ； in, Represents the objective function value of the subproblem, when This indicates that there is an out-of-bounds error. This means that the system remains secure even under the worst-case scenario. This indicates outer-layer optimization, which aims to find the worst-case uncertainty scenarios. This indicates inner-layer optimization, simulating how a dispatcher, when faced with this scenario, adjusts generator output to minimize out-of-limit operations. This represents the default rate function, which calculates the extent to which physical currents or carbon potential exceed the limit.

9. A method for constructing a safety boundary of an electro-carbon coupling system considering source-charge uncertainty according to claim 8, characterized in that: In S52, during the solution of subproblems, the carbon emission flow equation is handled. bilinear terms in Linearization is performed using the McCormick envelope method for nonlinear terms. Introducing auxiliary variables Replace and construct the following set of linear inequality constraints: ； in, Represents branch power flow variables. node The carbon potential variable, Indicates the upper and lower bounds of the branch current flow. The upper and lower bounds of the estimated carbon potential at the nodes are represented, and the subproblem is transformed into a mixed-integer linear programming problem to be solved.

10. The method for constructing a safety boundary of an electro-carbon coupling system considering source-charge uncertainty according to claim 1, characterized in that: In S5, the iterative algorithm further includes the following steps: S53, Cutting plane generation: When the subproblem solution result shows that the current point is unsafe (i.e., ... Then, according to duality theory, a Benders cutting plane is generated and fed back to the main problem to remove the unsafe region: ； in, Indicate the subproblem in The maximum amount of default calculated at that point. This represents the gradient vector of the default amount with respect to the boundary variables; S54. Boundary Fitting: Repeat steps S51 to S53 until convergence, and collect the critical safe points generated in all iterations to form a set. ,and The minimum volume envelope algorithm is used for fitting, and the following optimization problem is solved to obtain the final boundary parameters: ； in, This represents the safety boundary parameters to be determined. This represents the volume function.

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