A method, system, device and medium for fast calculation of carbon intensity of grid nodes

Abstract

The application discloses a kind of fast calculation method, system, equipment and medium of grid node carbon intensity, and the technical field belongs to low-carbon electric power technical field.The fast calculation method of grid node carbon intensity includes: constructing the scheduling model of power system, and determining power balance constraint and effective inequality constraint;According to the real-time output state of unit and node marginal electricity price, determine marginal unit, and determine the carbon emission coefficient vector corresponding to marginal unit;According to power balance constraint, effective inequality constraint and the cost function of power system, effective feature extraction is carried out, and the sensitivity matrix after dimension reduction and the load disturbance matrix after dimension reduction are obtained;The common mapping matrix after dimension reduction is calculated using the sensitivity matrix after dimension reduction and the load disturbance matrix after dimension reduction;According to the carbon emission coefficient vector corresponding to marginal unit and the common mapping matrix after dimension reduction, the node marginal carbon emission intensity is calculated.The application can accurately and efficiently calculate the grid node carbon intensity.

Description

Technical Field

[0001] This application relates to the field of low-carbon power technology, and in particular to a method, system, device and medium for rapid calculation of carbon intensity at power grid nodes. Background Technology

[0002] The calculation of marginal carbon emission intensity at existing nodes faces a structural contradiction between accuracy and efficiency: the traditional KKT (Karush-Kuhn-Tucker) sensitivity method is constrained by the curse of dimensionality caused by the inversion of the full-dimensional matrix and the dependence on confidential data across the entire network, making it difficult to meet the real-time settlement requirements of the electricity spot market; while data-driven methods, although fast in calculation, have weak physical interpretability and insufficient adaptability to operating conditions.

[0003] Therefore, how to accurately and efficiently calculate the carbon intensity of power grid nodes is a technical problem that needs to be solved by those skilled in the art. Summary of the Invention

[0004] The purpose of this application is to provide a method, system, device, and medium for rapid calculation of carbon intensity at power grid nodes, which can accurately and efficiently calculate the carbon intensity at power grid nodes.

[0005] To address the aforementioned technical problems, this application provides a rapid method for calculating the carbon intensity of power grid nodes, comprising:

[0006] A power system scheduling model is constructed with the goal of minimizing system operating costs, and the power balance constraints and effective inequality constraints of the scheduling model are determined.

[0007] Marginal generating units are determined based on the real-time output status of the generating units and the marginal electricity price at each node in the power system, and the carbon emission coefficient vector corresponding to the marginal generating units is determined based on the index of the marginal generating units.

[0008] Based on the power balance constraint, the effective inequality constraint, and the cost function of the power system, effective feature extraction is performed to obtain the dimension-reduced sensitivity matrix and the dimension-reduced load disturbance matrix.

[0009] The reduced-dimensionality commonality mapping matrix is ​​calculated using the reduced-dimensionality sensitivity matrix and the reduced-dimensionality load perturbation matrix.

[0010] The node marginal carbon emission intensity is calculated based on the carbon emission coefficient vector corresponding to the marginal unit and the dimensionality-reduced commonality mapping matrix.

[0011] Optionally, determining the effective inequality constraints of the scheduling model includes:

[0012] Determine the inequality constraints of the scheduling model;

[0013] The inequality constraint that reaches the boundary value under the real-time output state of the unit is set as the effective inequality constraint.

[0014] Optionally, the effective inequality constraints include blocked line constraints and unit constraints that trigger ramp limits.

[0015] Optionally, the expression for the dimensionality-reduced sensitivity matrix is:

[0016] ;

[0017] in, This represents the sensitivity matrix after dimensionality reduction. This represents the matrix of coefficients of the quadratic term in the cost function. This represents a coefficient matrix containing only valid inequality constraints. This represents the coefficient matrix corresponding to the equality constraints. Indicates transpose. This represents the Lagrange multiplier vector corresponding to the effective inequality constraints. Represents a diagonal matrix. This indicates the real-time output status of the generator unit. Represents a subvector of the complete constant term vector. This represents a submatrix of the complete constraint coefficient matrix. Indicates the nominal load point.

[0018] Optionally, the expression for the dimensionality-reduced load disturbance matrix is:

[0019] ;

[0020] in, This represents the load disturbance matrix after dimensionality reduction. This represents the coefficient matrix under the KKT conditions after differentiation. This represents the Lagrange multiplier vector corresponding to the effective inequality constraints at the nominal load point. This represents the coefficient matrix of the load parameters in the equality constraint.

[0021] Optionally, the dimension-reduced commonality mapping matrix is ​​calculated using the dimension-reduced sensitivity matrix and the dimension-reduced load perturbation matrix, including:

[0022] Substituting the dimension-reduced sensitivity matrix and the dimension-reduced load disturbance matrix into the first preset formula, we obtain the dimension-reduced commonality mapping matrix.

[0023] The preset formula is as follows: ; This represents the commonality mapping matrix after dimensionality reduction. Represents the identity matrix. Indicates transpose. This represents the sensitivity matrix after dimensionality reduction. This represents the load disturbance matrix after dimensionality reduction.

[0024] Optionally, the node marginal carbon emission intensity is calculated based on the carbon emission coefficient vector corresponding to the marginal unit and the dimension-reduced commonality mapping matrix, including:

[0025] Substituting the carbon emission coefficient vector corresponding to the marginal unit and the dimensionality-reduced common mapping matrix into the second preset formula, the marginal carbon emission intensity of the node is obtained;

[0026] The second preset formula is: ; Indicates the marginal carbon emission intensity of a node. This represents the carbon emission coefficient vector corresponding to the marginal unit. Indicates transpose. This represents the commonality mapping matrix after dimensionality reduction.

[0027] This application also provides a rapid calculation system for the carbon intensity of power grid nodes, the system comprising:

[0028] The constraint determination module is used to construct a power system scheduling model with the goal of minimizing system operating costs, and to determine the power balance constraints and effective inequality constraints of the scheduling model.

[0029] The marginal unit determination module is used to determine the marginal units based on the real-time output status of the units in the power system and the nodal marginal electricity price, and to determine the carbon emission coefficient vector corresponding to the marginal unit based on the index of the marginal unit;

[0030] The matrix construction module is used to extract effective features based on the power balance constraints, the effective inequality constraints, and the cost function of the power system to obtain a dimension-reduced sensitivity matrix and a dimension-reduced load disturbance matrix; the matrix construction module is also used to calculate a dimension-reduced commonality mapping matrix using the dimension-reduced sensitivity matrix and the dimension-reduced load disturbance matrix;

[0031] The carbon emission intensity calculation module is used to calculate the node marginal carbon emission intensity based on the carbon emission coefficient vector corresponding to the marginal unit and the dimension-reduced commonality mapping matrix.

[0032] This application also provides a storage medium storing a computer program that, when executed, implements the steps of the above-described method for rapidly calculating the carbon intensity of power grid nodes.

[0033] This application also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor, when calling the computer program in the memory, implements the steps of the above-described method for rapidly calculating the carbon intensity of power grid nodes.

[0034] This application constructs a power system dispatch model with the goal of minimizing system operating costs, and determines the power balance constraints and effective inequality constraints of the dispatch model. It identifies marginal generating units based on real-time unit output and nodal marginal electricity prices, and calculates their carbon emission coefficient vectors. Based on the power balance constraints, effective inequality constraints, and the power system cost function, this application performs effective feature extraction to obtain a dimension-reduced sensitivity matrix and a dimension-reduced load disturbance matrix. Then, it establishes a dimension-reduced common mapping matrix, and calculates the nodal marginal carbon emission intensity based on the carbon emission coefficient vectors corresponding to the marginal generating units and the dimension-reduced common mapping matrix. This application determines the common mapping matrix based on the mathematical isomorphism between nodal marginal electricity prices and nodal marginal carbon emission intensity, and uses the common mapping matrix and the carbon emission coefficient vectors corresponding to the marginal generating units to calculate the nodal marginal carbon emission intensity. This process avoids the complex calculation process of inversely retrieving nodal marginal carbon emissions based on grid physical parameters, and can accurately and efficiently calculate the carbon intensity of grid nodes. This application also provides a fast calculation system for the carbon intensity of power grid nodes, a storage medium, and an electronic device, which have the aforementioned beneficial effects, and will not be elaborated further here. Attached Figure Description

[0035] To more clearly illustrate the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 A flowchart illustrating a rapid calculation method for the carbon intensity of a power grid node, provided as an embodiment of this application;

[0037] Figure 2 A schematic diagram of the structure of a fast calculation device for the carbon intensity of a power grid node based on the marginal electricity price provided in this application embodiment;

[0038] Figure 3 This is a schematic diagram of the structure of a rapid calculation system for the carbon intensity of a power grid node provided in an embodiment of this application. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0040] Please see below. Figure 1 , Figure 1 This is a flowchart illustrating a rapid calculation method for the carbon intensity of a power grid node, as provided in an embodiment of this application.

[0041] Specific steps may include:

[0042] S101: Construct a power system scheduling model with the goal of minimizing system operating costs, and determine the power balance constraints and effective inequality constraints of the scheduling model.

[0043] This embodiment can be applied to electronic devices with data calculation functions, and can improve the efficiency and accuracy of the electronic device in calculating the carbon intensity of power grid nodes.

[0044] This step can obtain system information of the power system (such as network topology and parameters, generator parameters and load information) and establish a scheduling model with the optimization objective of minimizing the total generation cost.

[0045] Power balance constraints are used to ensure that power generation and load in a power system maintain a balance between supply and demand; effective inequality constraints refer to physical limitations that are just in effect at the current operating point, such as transmission lines being fully loaded (power flow reaching the limit) or generating units reaching their upper or lower limits, and their Lagrange multipliers being greater than zero.

[0046] The power system dispatch model includes equality constraints and inequality constraints. The equality constraints include the power balance constraints mentioned above, while the inequality constraints can be determined based on the real-time output status of the power system's units.

[0047] Specifically, the process of determining the effective inequality constraints of the scheduling model includes: determining the inequality constraints of the scheduling model; and setting the inequality constraints that reach the boundary values ​​under the real-time output state of the units as the effective inequality constraints. For example, the effective inequality constraints include blocked line constraints (i.e., line constraints that are in a blocked state or are in a blocked state) and unit constraints that trigger ramp limits.

[0048] S102: Determine the marginal generating units based on the real-time output status of the generating units and the marginal electricity price at the nodes of the power system, and determine the carbon emission coefficient vector corresponding to the marginal generating units based on the index of the marginal generating units.

[0049] Prior to this step, the real-time output status of the power system's generating units (i.e., the current generating unit output status) and the nodal marginal electricity price can be obtained. This step can identify marginal generating units (i.e., units whose actual dispatch results are not at the upper or lower limits of their generating unit output) using the nodal marginal electricity price and the real-time output status of the power system's generating units. After identifying the marginal generating units, the corresponding emission data can be extracted from a pre-set generating unit carbon emission coefficient database based on the index of the marginal generating units in the power system, forming a carbon emission coefficient vector.

[0050] S103: Based on the power balance constraint, the effective inequality constraint, and the cost function of the power system, perform effective feature extraction to obtain the dimension-reduced sensitivity matrix and the dimension-reduced load disturbance matrix.

[0051] In this step, a dimension-reduced KKT system is constructed based on power balance constraints, effective inequality constraints, and the power system cost function. Through effective feature extraction, a commonality mapping matrix is ​​obtained. While the sensitivity matrix and load disturbance matrix can be generated directly using equality constraints, inequality constraints, and the cost function, this step uses power balance constraints, effective inequality constraints, and the cost function to generate the dimension-reduced sensitivity matrix and load disturbance matrix.

[0052] Specifically, the expression for the dimensionality-reduced sensitivity matrix is ​​as follows:

[0053] ;

[0054] in, This represents the sensitivity matrix after dimensionality reduction. This represents the matrix of coefficients of the quadratic term in the cost function. This represents a coefficient matrix containing only valid inequality constraints. This represents the coefficient matrix corresponding to the equality constraints. Indicates transpose. This represents the Lagrange multiplier vector corresponding to the effective inequality constraints. Represents a diagonal matrix. This indicates the real-time output status of the generator unit. Represents a subvector of the complete constant term vector. This represents a submatrix of the complete constraint coefficient matrix. Indicates the nominal load point.

[0055] The matrix describes the coupling relationship between the system decision variables and dual variables in a neighborhood where the current effective constraint set remains unchanged. The dimension depends on the number of effective constraints, not the total number of system constraints.

[0056] Specifically, the expression for the dimensionality-reduced load disturbance matrix is ​​as follows:

[0057] ;

[0058] in, This represents the load disturbance matrix after dimensionality reduction. This represents the coefficient matrix under the KKT conditions after differentiation. This represents the Lagrange multiplier vector corresponding to the effective inequality constraints at the nominal load point. This represents the coefficient matrix of the load parameters in the equality constraint.

[0059] S104: Calculate the dimension-reduced commonality mapping matrix using the dimension-reduced sensitivity matrix and the dimension-reduced load disturbance matrix.

[0060] Among them, the nodal marginal electricity price and the nodal marginal carbon emission intensity are mathematically isomorphic, and they are linear transformations of the unit price vector and the carbon emission coefficient vector onto the same common mapping matrix, respectively. Based on the isomorphism of the nodal marginal electricity price and the nodal marginal carbon emission intensity in terms of mathematical structure, this embodiment can use the dimensionality-reduced sensitivity matrix and the dimensionality-reduced load disturbance matrix to calculate the dimensionality-reduced common mapping matrix.

[0061] Specifically, the process of calculating the dimension-reduced common mapping matrix using the dimension-reduced sensitivity matrix and the dimension-reduced load disturbance matrix is ​​as follows: substituting the dimension-reduced sensitivity matrix and the dimension-reduced load disturbance matrix into the first preset formula to obtain the dimension-reduced common mapping matrix;

[0062] The preset formula is as follows: ; This represents the commonality mapping matrix after dimensionality reduction. Represents the identity matrix. Indicates transpose. This represents the sensitivity matrix after dimensionality reduction. This represents the load disturbance matrix after dimensionality reduction.

[0063] S105: Calculate the node marginal carbon emission intensity based on the carbon emission coefficient vector corresponding to the marginal unit and the dimension-reduced commonality mapping matrix.

[0064] This step involves multiplying the carbon emission coefficient vector of the marginal units with the dimension-reduced commonality mapping matrix to obtain the locational marginal carbon emission intensity. The marginal carbon emission intensity at a node measures the increase in total carbon emissions of the system caused by an increase in the load at a specific node. It is a key indicator for quantifying the carbon footprint of the power grid and guiding a low-carbon response on the demand side.

[0065] Specifically, in this step, the carbon emission coefficient vector corresponding to the marginal unit and the reduced commonality mapping matrix can be substituted into the second preset formula to obtain the marginal carbon emission intensity of the node.

[0066] The second preset formula is: ; Indicates the marginal carbon emission intensity of a node. This represents the carbon emission coefficient vector corresponding to the marginal unit. Indicates transpose. This represents the commonality mapping matrix after dimensionality reduction.

[0067] This embodiment constructs a power system dispatch model with the goal of minimizing system operating costs, and determines the power balance constraints and effective inequality constraints of the dispatch model. Marginal generating units are identified based on real-time unit output and nodal marginal electricity prices, and their carbon emission coefficient vectors are calculated. This embodiment performs effective feature extraction based on the power balance constraints, the effective inequality constraints, and the power system cost function to obtain a dimensionality-reduced sensitivity matrix and a dimensionality-reduced load disturbance matrix. A dimensionality-reduced commonality mapping matrix is ​​then established. The nodal marginal carbon emission intensity is calculated based on the carbon emission coefficient vectors corresponding to the marginal generating units and the dimensionality-reduced commonality mapping matrix. This embodiment determines the commonality mapping matrix based on the isomorphism of the nodal marginal electricity price and the nodal marginal carbon emission intensity in mathematical structure, and uses the commonality mapping matrix and the carbon emission coefficient vectors corresponding to the marginal generating units to calculate the nodal marginal carbon emission intensity. This process avoids the complex calculation process of inversely retrieving nodal marginal carbon emissions based on grid physical parameters, enabling accurate and efficient calculation of grid nodal carbon intensity.

[0068] The process described in the above embodiments is illustrated below through examples in practical applications.

[0069] To build a new power system and promote a green and low-carbon energy transition, new energy sources such as wind and solar power are being connected to the grid on a large scale and in a high proportion. Their inherent intermittency and volatility pose unprecedented challenges to the safe, stable operation and real-time balance of the power grid. Localized absorption of new energy sources has become a bottleneck restricting the development of a high proportion of clean energy. Against this backdrop, establishing a scientific, precise, and transparent carbon measurement system is not only an urgent need for building new energy management capabilities but also a key lever for low-carbon transformation. Nodal marginal carbon emission intensity, as a core indicator, is the technological foundation for achieving transparency of the power grid's carbon footprint in the spatiotemporal dimensions through accurate and rapid calculation. Furthermore, it serves as a crucial guiding signal for stimulating the low-carbon potential of massive demand-side resources.

[0070] However, in related technologies, there are two common methods for calculating nodal marginal carbon emission intensity:

[0071] The first type of method is based on sensitivity analysis using the KKT conditions for optimal power flow across the entire system. As a traditional method for calculating nodal marginal carbon emission intensity, it first formulates the economic dispatch or optimal power flow problem of the electricity market as a linear programming or quadratic programming problem. Then, it establishes the optimality conditions for this optimization problem, constructs a sensitivity matrix by performing total differentials on the nodal load vectors of the entire KKT-condition system, and finally obtains the sensitivity of generator output to load by solving the equations, thereby obtaining the nodal marginal carbon emission intensity.

[0072] The second type of method is the parameter recovery method based on inverse optimization. This method uses publicly available market clearing information to solve a specific linear equation and inversely analyze the key network parameters. After recovering the network parameters, marginal units are identified, and a small-scale equivalent system model containing only marginal units is constructed. The nodal marginal carbon emission intensity is obtained by solving this simplified model. Furthermore, there are also methods in this field that attempt to directly fit the relationship between nodal marginal electricity prices and nodal marginal carbon emission intensity using statistical learning tools such as neural networks.

[0073] Although the aforementioned existing technologies theoretically provide a feasible path for calculating the marginal carbon emission intensity of nodes, they still face the dual dilemmas of computational efficiency and model robustness in practical applications in the electricity spot market.

[0074] Specifically, the first type of method suffers from the curse of dimensionality and data barriers. Because this method requires inverting a massive KKT system matrix encompassing all variables and constraints across the entire network, its computational load is enormous, inefficient, and extremely high when dealing with real-world power grids with thousands of nodes and a vast amount of constraints. This makes it difficult to meet the minute-level real-time settlement requirements of the spot market. Furthermore, the first type of method relies heavily on the complete network topology and internal bidding data of all generating units. This data is highly confidential and difficult to obtain in the decoupled power market environment, resulting in a lack of feasibility for engineering implementation.

[0075] The core flaw of the second type of method mentioned above lies in its lack of mechanism and poor generalization ability. Whether it's the parameter recovery method or the data-driven method, they are essentially fitting or inverting historical operating states. This indirect calculation method is highly dependent on the quality and coverage of historical data samples. Once the power grid operating conditions (such as network topology changes or switching of congested line sets) exceed the range of historical samples, the second type of method exhibits poor generalization ability, unstable prediction results, and cannot guarantee the accuracy and robustness of the calculation results. Its prediction accuracy will drop significantly, failing to provide market participants with reliable and transparent physical guidance signals.

[0076] To address the issues of poor generalization ability, unstable prediction results, and inability to guarantee the accuracy and robustness of calculation results associated with conventional techniques, this embodiment provides a rapid calculation scheme for grid node carbon intensity based on nodal marginal electricity prices. This scheme proposes a rapid calculation method for grid node carbon emission intensity based on nodal marginal electricity prices. Based on multi-parameter programming theory and sensitivity derivation, it establishes the idea and method of an endogenous correlation between nodal marginal electricity prices and nodal marginal carbon emission intensity, along with the core concept of a common mapping matrix. This method relies solely on a dimension-reduced sensitivity analysis framework with effective constraints and, based on the common mapping matrix, provides a direct analytical calculation method and implementation process for nodal marginal carbon emission intensity that avoids the inverse inversion of grid physical parameters.

[0077] This scheme utilizes multi-parameter programming theory to overcome the computational bottleneck of full-dimensional models, enabling real-time and rapid calculation of nodal carbon intensity and identifying the effective constraint set under the current operating state. By constructing a dimensionality-reduced sensitivity matrix based solely on effective constraints, this scheme significantly reduces the computational dimension from the entire system scale to the effective constraint scale, thereby avoiding the curse of dimensionality. It achieves rapid solutions for nodal marginal carbon emission intensity at the second or even millisecond level, perfectly adapting to the rapid clearing pace of the electricity spot market.

[0078] This scheme reveals the isomorphism in mathematical structure between nodal marginal electricity price and nodal marginal carbon emission intensity, avoiding reliance on network-wide data and achieving accurate calculations even with incomplete information. This scheme no longer requires reconstructing the physical parameters of the entire power grid; instead, it directly derives the common mapping matrix shared by both using publicly available market clearing information. This enables the accurate derivation of nodal carbon intensity signals even in open market environments with incomplete information and data privacy protection.

[0079] This scheme establishes an analytical model based on rigorous mathematical derivation, providing a carbon price signal with strong physical interpretability. The commonality mapping matrix calculated by this scheme has clear physical meaning, reflecting the sensitivity impact of minute increases in node load on the scheduling of marginal units in the system. It is not only accurate in calculation but also clearly explains the physical mechanism of the formation of marginal carbon emission intensity at nodes, exhibiting strong robustness and interpretability. This provides a reliable technical basis for low-carbon dispatching and policy formulation in the power grid.

[0080] This scheme establishes a common mapping relationship between nodal marginal electricity price and nodal marginal carbon emission intensity, and its theoretical basis is as follows:

[0081] The economic dispatch or optimal power flow problem of the power grid is formulated as a convex optimization problem with node loads as parameters, aiming to minimize the system operating cost, resulting in the following dispatch model:

[0082] ;

[0083] ;

[0084] ;

[0085] Indicates minimization. Represents the constraints of the optimization problem. It's an optimization problem about parameters. The optimal value function; These are decision variables such as unit output. Indicates transpose; For quotations; The coefficients of the quadratic term in the cost function; A vector of node load parameters; The coefficient matrix representing the inequality constraints, The constant vector representing the inequality constraint, This represents the coefficient matrix of the load parameters in the inequality constraints; The coefficient matrix representing equality constraints The constant vector representing equality constraints The coefficient matrix representing the load parameters in the equality constraints; and Inequality constraints and equality constraints of the system are defined respectively; This represents the coefficient matrix under the KKT conditions after differentiation, and its parameters are the coefficient matrix with respect to the constraints and their slack variables.

[0086] According to multi-parameter programming theory, at a given nominal load point and its corresponding optimal solution (That is, the real-time output status of the unit) ( Indicates at the load point (Lagrange multiplier vectors corresponding to equality constraints) and ( Indicates at the load point In the vicinity of the effective inequality constraints (corresponding to the Lagrange multiplier vectors), the optimal decision variables can be obtained as long as the effective constraint set remains unchanged. And dual variables (Lagrange multipliers) and ;in Lagrange multipliers representing equality constraints with respect to load parameters affine function, Lagrange multipliers representing effective inequality constraints with respect to load parameters The affine function. The above functional relationship can be obtained by solving the differential form of the KKT conditions to obtain the third presupposed formula:

[0087] ;

[0088] This represents the Lagrange multiplier vector corresponding to the effective inequality constraints; Represents the sensitivity matrix; This represents the load disturbance matrix.

[0089] For scheduling models, inequality constraints at the optimal solution When taking strict equality, we name it the effective constraint set and construct the corresponding dimension-reduced system sensitivity matrix. and load disturbance matrix The above process significantly reduces the computational dimensionality by eliminating invalid constraints.

[0090] Let the set of valid inequality constraints identified at the current moment be , i.e., the set of constraints that satisfy inequality constraints. And corresponding to Lagrange multipliers The constraints are used as valid inequality constraints.

[0091] This indicates that it contains only the coefficient matrix corresponding to valid inequality constraints. Represents a vector of complete constant terms A subvector, Represents the complete constraint coefficient matrix A submatrix, This represents the coefficient matrix corresponding to the system's equality constraints. This represents the coefficient matrix of the quadratic term of the system cost function.

[0092] The matrix is ​​essentially the Jacobian matrix of the KKT system under effective constraints. The sensitivity matrix is ​​constructed as follows:

[0093] ;

[0094] The matrix describes the coupling relationship between the system decision variables and dual variables in a neighborhood where the current effective constraint set remains unchanged. The dimension depends on the number of effective constraints, not the total number of system constraints. In real power grids, the number of effective constraints is far less than the total number of constraints, therefore... It is a sparse, small-dimensional, full-rank invertible square matrix.

[0095] The matrix describes the node load parameters. How are changes propagated to the KKT system? The load disturbance matrix is ​​constructed as follows:

[0096] .

[0097] Regarding the common mapping matrix Based on the derivation, this scheme only focuses on decision variables. For load Sensitivity. Separated from the third preset formula. The corresponding row yields:

[0098] ;

[0099] Representing decision variables Regarding parameters The differential, Indicates parameters The differential, Represents the identity matrix.

[0100] This scheme defines this sensitivity matrix as a commonality mapping matrix. .

[0101] Therefore, we can conclude that: .

[0102] For the marginal electricity price at each node, it is defined as the total cost that simplifies and ignores quadratic terms. For load The sensitivity is expressed as:

[0103] ; Indicates the marginal electricity price at the node. This represents the derivative of the total cost.

[0104] The marginal carbon emission intensity of a node is defined as total carbon emissions. For load The sensitivity, of which The carbon emission coefficient vector is represented as:

[0105] ;

[0106] Indicates the marginal carbon emission intensity of a node. This represents the derivative of total carbon emissions.

[0107] The nodal marginal electricity price and the nodal marginal carbon emission intensity are mathematically isomorphic; they are respectively the unit price vectors. and carbon emission coefficient vector For the same commonality mapping matrix Linear transformation.

[0108] The fast calculation method provided in this embodiment utilizes the aforementioned isomorphism to solve for the nodal marginal carbon emission intensity by calculating the common mapping matrix. Specifically, it includes the following steps:

[0109] Step 1: Obtain the operating results of the current electricity market clearing cycle.

[0110] Specifically, this step does not require confidential data from the entire system, but rather the following data from the execution results: the current cleared node marginal electricity price. and the real-time output status of the unit To identify marginal units and verify the accuracy of the common mapping matrix calculation; system power balance constraints ( , ); Effective inequality constraints identified based on actual conditions, such as congested lines under full load or units triggering ramp limits; cost function ( , , ).

[0111] Step 2: Based on the real-time output status of the unit obtained in Step 1 By analyzing the marginal electricity price at each node, the system identifies the set of marginal generating units (i.e., units whose actual dispatch results are not at the upper or lower limits of their output). According to multi-parameter programming theory, the determinism of marginal generating units directly corresponds to the uniqueness of the effective constraint set of the system at the current moment.

[0112] By locking the marginal units, the system can derive the common mapping matrix consisting of the system power balance constraints and the effective inequality constraints of the non-marginal unit operation constraints in the boundary state without traversing all constraints of the entire network.

[0113] Step 3: Construct the sensitivity matrix.

[0114] This step uses the power balance constraint equality constraints and effective inequality constraint set identified in the first two steps, as well as the cost function, to construct the dimension-reduced sensitivity matrix based on the construction forms of the sensitivity matrix and load disturbance matrix. and the reduced load perturbation matrix Compared to previous solutions, this step does not require a full-system KKT matrix or historical data.

[0115] Step 4: Calculate the commonality mapping matrix.

[0116] This step can be used to modify the matrix in step 3. Perform the inversion operation and calculate the commonality mapping matrix after dimensionality reduction. :

[0117] .

[0118] The speed of the above process is manifested in: because The dimension is very small (for example, if the system has 1000 constraints but only 50 effective constraints, then the dimension is close to 50 50, rather than the thousands close to the dimension of the sensitivity matrix in the traditional method thousands), and this step is calculated very quickly.

[0119] Step 5: Obtain the carbon emission coefficient vector after dimension reduction based on the index of the marginal units. Based on the location information of the marginal units, extract the carbon emission coefficient vector corresponding to the marginal units from the carbon emission coefficient vectors of all units This is usually public or based on standard parameters of unit types (such as coal-fired, gas-fired).

[0120] Step 6: Based on the carbon emission coefficient vector indexed by the marginal units in Step 5 and the commonality mapping matrix , calculate the nodal marginal carbon emission intensity, and directly calculate the vector of all nodes:

[0121] .

[0122] To solve the problems of huge computational complexity and curse of dimensionality existing in the existing full-dimensional sensitivity analysis method, this solution is based on the multi-parameter programming theory to accurately identify the effective constraint set at the current operating moment. For the core calculation link, this solution uses the Jacobian matrix corresponding to the effective constraints to construct a reduced-dimensional sensitivity analysis model, replacing the traditional ultra-large-scale matrix inversion process covering all variables and constraints in the whole network. This dimension reduction method significantly reduces the computational complexity from the scale of the whole system to the scale only related to the number of effective constraints, making the calculation time-consuming drop exponentially, realizing the rapid solution of the nodal carbon intensity in seconds or even milliseconds, and effectively overcoming the drawbacks of the traditional method that cannot meet the high-frequency and real-time settlement requirements of the electricity spot market.

[0123] To solve the problem that the traditional method seriously depends on the complete topology of the power grid and the confidential quotation data of units, this solution establishes a direct analysis framework based on the isomorphic representation. This solution reveals the endogenous association between the nodal marginal electricity price and the nodal marginal carbon emission intensity in the mathematical structure, and proves that both are linearly transformed by the same commonality mapping matrix. By directly solving this commonality mapping matrix, this solution can accurately deduce the nodal carbon intensity only by using the public market clearing information without knowing the physical parameters of the whole network or reverse-restoring the network parameters. This mechanism breaks the data barrier, ensures the accuracy and feasibility of the calculation results in the non-complete information environment while protecting the business privacy of market players.

[0124] ​To address the shortcomings of purely data-driven methods, such as a lack of physical context and poor generalization ability, this solution proposes an analytical computation mechanism with strong physical interpretability. This mechanism, through a commonality mapping matrix, clearly traces the formation mechanism of nodal carbon intensity back to specific physical constraints such as congested lines and grid-up units, quantifying the marginal impact of minute load increments on the scheduling of marginal units in the system. This physical mechanism-based modeling approach not only eliminates the uncertainties of neural network-like models and enhances user confidence in carbon price signals, but also maintains high robustness and accuracy even when there are abrupt changes in grid topology or operating modes. Because it is directly based on current effective constraints rather than historical patterns, it transforms fuzzy estimates into guiding signals with clear physical direction.

[0125] Please see Figure 2 , Figure 2 This is a schematic diagram of the structure of a fast calculation device for the carbon intensity of a power grid node based on the marginal electricity price provided in this application embodiment. The device includes a data layer, a multi-parameter sensitivity analysis layer, and an application layer.

[0126] At the data layer, publicly available market data can be transmitted to the multi-parameter sensitivity analysis layer to show the nodal marginal electricity price. The unit's real-time output and power flow data, along with the unit parameter library, can provide carbon emission coefficient vectors to the multi-parameter sensitivity analysis layer and application layer.

[0127] The multi-parameter sensitivity analysis layer includes: a running status acquisition module, an effective constraint identification module, a sensitivity matrix construction module, and a common mapping calculation module. The effective constraint identification module is used to determine effective inequality constraints, the sensitivity matrix construction module is used to construct the dimensionality-reduced sensitivity matrix and the dimensionality-reduced load disturbance matrix, and the common mapping calculation module is used to calculate the dimensionality-reduced common mapping matrix.

[0128] At the application layer, the node carbon intensity calculation module can be used to calculate the marginal carbon emission intensity of nodes in order to output the total carbon emission intensity of the entire network. Information may be displayed on a visual interface.

[0129] The data input and sensing strategy in this embodiment is as follows: First, key operational snapshots of the current clearing cycle are captured in real time from publicly available market data sources, including nodal marginal electricity prices, real-time output values ​​of each generating unit, and line power flow data; simultaneously, carbon emission coefficient vectors for various generating units are retrieved from a pre-set unit parameter library. This step ensures that the system can start up relying only on non-confidential publicly available data, breaking the dependence on private data across the entire network.

[0130] The effective constraint screening and dimensionality reduction strategy in this embodiment is as follows: Using the acquired operating status data and constraint conditions, a logical judgment is made on the current power grid operating status. This embodiment filters out all active inequality constraints to construct an effective constraint set. This process shifts the focus of subsequent calculations from all constraints across the entire system to a few key constraints, achieving a significant reduction in computational dimensionality.

[0131] The mathematical model construction and analysis strategy in this embodiment is as follows: Based on multi-parameter programming theory, the system utilizes only the aforementioned effective constraint set and system equilibrium constraints to numerically construct the dimensionality-reduced system Jacobian matrix and load disturbance matrix according to the matrix definitions described above. Subsequently, the small-scale matrices are inverted and substituted into the commonality mapping matrix. This matrix mathematically quantifies the sensitivity of nodal load changes to the scheduling of marginal units in the system and establishes the correlation between nodal marginal electricity prices and nodal marginal carbon emission intensity.

[0132] The carbon intensity synthesis and output strategy in this embodiment is as follows: After obtaining the common mapping matrix, the system performs a linear transformation on it and the unit carbon emission coefficient vector to directly parse out the marginal carbon emission intensity of each node in the entire network. Finally, the calculation results are output to a visualization interface or data interface to provide real-time and accurate signal support for electricity market settlement, user-side response, and low-carbon dispatch.

[0133] This embodiment utilizes multi-parameter programming theory and, based on the mathematical isomorphism between nodal marginal electricity price and nodal marginal carbon emission intensity, constructs a common mapping matrix that relies solely on effective constraints, thereby achieving rapid analysis of nodal marginal carbon emission intensity that combines physical mechanisms with real-time performance.

[0134] Please see Figure 3 , Figure 3 This is a schematic diagram of a rapid calculation system for the carbon intensity of a power grid node provided in an embodiment of this application. The system may include:

[0135] The constraint determination module 301 is used to construct a power system scheduling model with the goal of minimizing system operating costs, and to determine the power balance constraints and effective inequality constraints of the scheduling model.

[0136] The marginal unit determination module 302 is used to determine the marginal units based on the real-time output status of the units in the power system and the nodal marginal electricity price, and to determine the carbon emission coefficient vector corresponding to the marginal units based on the index of the marginal units.

[0137] The matrix construction module 303 is used to extract effective features based on the power balance constraint, the effective inequality constraint, and the cost function of the power system to obtain the dimension-reduced sensitivity matrix and the dimension-reduced load disturbance matrix; the matrix construction module is also used to calculate the dimension-reduced commonality mapping matrix using the dimension-reduced sensitivity matrix and the dimension-reduced load disturbance matrix;

[0138] The carbon emission intensity calculation module 304 is used to calculate the node marginal carbon emission intensity based on the carbon emission coefficient vector corresponding to the marginal unit and the dimension-reduced commonality mapping matrix.

[0139] This embodiment constructs a power system dispatch model with the goal of minimizing system operating costs, and determines the power balance constraints and effective inequality constraints of the dispatch model. Marginal generating units are identified based on real-time unit output and nodal marginal electricity prices, and their carbon emission coefficient vectors are calculated. This embodiment performs effective feature extraction based on the power balance constraints, the effective inequality constraints, and the power system cost function to obtain a dimensionality-reduced sensitivity matrix and a dimensionality-reduced load disturbance matrix. A dimensionality-reduced commonality mapping matrix is ​​then established. The nodal marginal carbon emission intensity is calculated based on the carbon emission coefficient vectors corresponding to the marginal generating units and the dimensionality-reduced commonality mapping matrix. This embodiment determines the commonality mapping matrix based on the isomorphism of the nodal marginal electricity price and the nodal marginal carbon emission intensity in mathematical structure, and uses the commonality mapping matrix and the carbon emission coefficient vectors corresponding to the marginal generating units to calculate the nodal marginal carbon emission intensity. This process avoids the complex calculation process of inversely retrieving nodal marginal carbon emissions based on grid physical parameters, enabling accurate and efficient calculation of grid nodal carbon intensity.

[0140] Furthermore, the process by which the constraint determination module 301 determines the effective inequality constraints of the scheduling model includes: determining the inequality constraints of the scheduling model; and setting the inequality constraints that reach the boundary values ​​under the real-time output state of the unit as the effective inequality constraints.

[0141] Furthermore, the effective inequality constraints include blocked line constraints and unit constraints that trigger ramp limits.

[0142] Furthermore, the expression for the dimensionality-reduced sensitivity matrix is:

[0143] ;

[0144] in, This represents the sensitivity matrix after dimensionality reduction. This represents the matrix of coefficients of the quadratic term in the cost function. This represents a coefficient matrix containing only valid inequality constraints. This represents the coefficient matrix corresponding to the equality constraints. Indicates transpose. This represents the Lagrange multiplier vector corresponding to the effective inequality constraints. Represents a diagonal matrix. This indicates the real-time output status of the generator unit. Represents a subvector of the complete constant term vector. This represents a submatrix of the complete constraint coefficient matrix. Indicates the nominal load point.

[0145] Furthermore, the expression for the dimensionality-reduced load disturbance matrix is:

[0146] ;

[0147] in, This represents the load disturbance matrix after dimensionality reduction. This represents the coefficient matrix under the KKT conditions after differentiation. This represents the Lagrange multiplier vector corresponding to the effective inequality constraints at the nominal load point. This represents the coefficient matrix of the load parameters in the equality constraint.

[0148] Furthermore, the matrix construction module 303 calculates the dimension-reduced common mapping matrix using the dimension-reduced sensitivity matrix and the dimension-reduced load disturbance matrix, including: substituting the dimension-reduced sensitivity matrix and the dimension-reduced load disturbance matrix into a first preset formula to obtain the dimension-reduced common mapping matrix;

[0149] The preset formula is as follows: ; This represents the commonality mapping matrix after dimensionality reduction. Represents the identity matrix. Indicates transpose. This represents the sensitivity matrix after dimensionality reduction. This represents the load disturbance matrix after dimensionality reduction.

[0150] Furthermore, the process by which the carbon emission intensity calculation module 304 calculates the node marginal carbon emission intensity based on the carbon emission coefficient vector corresponding to the marginal unit and the dimension-reduced common mapping matrix includes: substituting the carbon emission coefficient vector corresponding to the marginal unit and the dimension-reduced common mapping matrix into the second preset formula to obtain the node marginal carbon emission intensity;

[0151] The second preset formula is: ; Indicates the marginal carbon emission intensity of a node. This represents the carbon emission coefficient vector corresponding to the marginal unit. Indicates transpose. This represents the commonality mapping matrix after dimensionality reduction.

[0152] Since the embodiments of the system part correspond to the embodiments of the method part, please refer to the description of the embodiments of the method part for the embodiments of the system part, and they will not be repeated here.

[0153] This application also provides a storage medium on which a computer program is stored, which, when executed, can perform the steps provided in the above embodiments. The storage medium may include various media capable of storing program code, such as a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0154] This application also provides an electronic device that may include a memory and a processor. The memory stores a computer program, and when the processor calls the computer program in the memory, it can implement the steps provided in the above embodiments. Of course, the electronic device may also include various network interfaces, power supplies, and other components.

[0155] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section. It should be noted that those skilled in the art can make various improvements and modifications to this application without departing from the principles of this application, and these improvements and modifications also fall within the protection scope of this application.

[0156] It should also be noted that, in this specification, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

Claims

1. A rapid calculation method for carbon intensity at power grid nodes, characterized in that, include: A power system scheduling model is constructed with the goal of minimizing system operating costs, and the power balance constraints and effective inequality constraints of the scheduling model are determined. Marginal generating units are determined based on the real-time output status of the generating units and the marginal electricity price at each node in the power system, and the carbon emission coefficient vector corresponding to the marginal generating units is determined based on the index of the marginal generating units. Based on the power balance constraint, the effective inequality constraint, and the cost function of the power system, effective feature extraction is performed to obtain the dimension-reduced sensitivity matrix and the dimension-reduced load disturbance matrix. The reduced-dimensionality commonality mapping matrix is ​​calculated using the reduced-dimensionality sensitivity matrix and the reduced-dimensionality load perturbation matrix. The node marginal carbon emission intensity is calculated based on the carbon emission coefficient vector corresponding to the marginal unit and the dimension-reduced common mapping matrix; The step of extracting effective features based on the power balance constraint, the effective inequality constraint, and the cost function of the power system to obtain the dimension-reduced sensitivity matrix and the dimension-reduced load disturbance matrix includes: Based on the construction forms of the sensitivity matrix and the load disturbance matrix, the dimension-reduced sensitivity matrix and the dimension-reduced load disturbance matrix are constructed according to the power balance constraint, the effective inequality constraint and the cost function of the power system. The expression for the dimensionality-reduced sensitivity matrix is: ； in, This represents the sensitivity matrix after dimensionality reduction. This represents the matrix of coefficients of the quadratic term in the cost function. This represents a coefficient matrix containing only valid inequality constraints. This represents the coefficient matrix corresponding to the equality constraints. Indicates transpose. This represents the Lagrange multiplier vector corresponding to the effective inequality constraints. Represents a diagonal matrix. This indicates the real-time output status of the generator unit. Represents a subvector of the complete constant term vector. This represents a submatrix of the complete constraint coefficient matrix. Indicates the nominal load point; The expression for the dimensionality-reduced load disturbance matrix is: ； in, This represents the load disturbance matrix after dimensionality reduction. This represents the coefficient matrix under the KKT conditions after differentiation. This represents the Lagrange multiplier vector corresponding to the effective inequality constraints at the nominal load point. This represents the coefficient matrix of the load parameters in the equality constraint.

2. The rapid calculation method for carbon intensity of power grid nodes according to claim 1, characterized in that, Determining the effective inequality constraints of the scheduling model includes: Determine the inequality constraints of the scheduling model; The inequality constraint that reaches the boundary value under the real-time output state of the unit is set as the effective inequality constraint.

3. The rapid calculation method for the carbon intensity of power grid nodes according to claim 2, characterized in that, The effective inequality constraints include blocked line constraints and unit constraints that trigger ramp limits.

4. The rapid calculation method for the carbon intensity of power grid nodes according to claim 1, characterized in that, The dimension-reduced commonality mapping matrix is ​​calculated using the dimension-reduced sensitivity matrix and the dimension-reduced load disturbance matrix, including: Substituting the dimension-reduced sensitivity matrix and the dimension-reduced load disturbance matrix into the first preset formula, we obtain the dimension-reduced commonality mapping matrix. The preset formula is as follows: ; This represents the commonality mapping matrix after dimensionality reduction. Represents the identity matrix. Indicates transpose. This represents the sensitivity matrix after dimensionality reduction. This represents the load disturbance matrix after dimensionality reduction.

5. The rapid calculation method for carbon intensity of power grid nodes according to claim 1, characterized in that, The node marginal carbon emission intensity is calculated based on the carbon emission coefficient vector corresponding to the marginal unit and the dimensionality-reduced common mapping matrix, including: Substituting the carbon emission coefficient vector corresponding to the marginal unit and the dimensionality-reduced common mapping matrix into the second preset formula, the marginal carbon emission intensity of the node is obtained; The second preset formula is: ; Indicates the marginal carbon emission intensity of a node. This represents the carbon emission coefficient vector corresponding to the marginal unit. Indicates transpose. This represents the commonality mapping matrix after dimensionality reduction.

6. A rapid calculation system for carbon intensity at power grid nodes, characterized in that, include: The constraint determination module is used to construct a power system scheduling model with the goal of minimizing system operating costs, and to determine the power balance constraints and effective inequality constraints of the scheduling model. The marginal unit determination module is used to determine the marginal units based on the real-time output status of the units in the power system and the nodal marginal electricity price, and to determine the carbon emission coefficient vector corresponding to the marginal unit based on the index of the marginal unit; The matrix construction module is used to extract effective features based on the power balance constraints, the effective inequality constraints, and the cost function of the power system to obtain a dimension-reduced sensitivity matrix and a dimension-reduced load disturbance matrix; the matrix construction module is also used to calculate a dimension-reduced commonality mapping matrix using the dimension-reduced sensitivity matrix and the dimension-reduced load disturbance matrix; The carbon emission intensity calculation module is used to calculate the node marginal carbon emission intensity based on the carbon emission coefficient vector corresponding to the marginal unit and the dimension-reduced common mapping matrix. The process by which the matrix construction module extracts effective features based on the power balance constraints, the effective inequality constraints, and the cost function of the power system to obtain the dimension-reduced sensitivity matrix and the dimension-reduced load disturbance matrix includes: Based on the construction forms of the sensitivity matrix and the load disturbance matrix, the dimension-reduced sensitivity matrix and the dimension-reduced load disturbance matrix are constructed according to the power balance constraint, the effective inequality constraint and the cost function of the power system. The expression for the dimensionality-reduced sensitivity matrix is: ； in, This represents the sensitivity matrix after dimensionality reduction. This represents the matrix of coefficients of the quadratic term in the cost function. This represents a coefficient matrix containing only valid inequality constraints. This represents the coefficient matrix corresponding to the equality constraints. Indicates transpose. This represents the Lagrange multiplier vector corresponding to the effective inequality constraints. Represents a diagonal matrix. This indicates the real-time output status of the generator unit. Represents a subvector of the complete constant term vector. This represents a submatrix of the complete constraint coefficient matrix. Indicates the nominal load point; The expression for the dimensionality-reduced load disturbance matrix is: ； in, This represents the load disturbance matrix after dimensionality reduction. This represents the coefficient matrix under the KKT conditions after differentiation. This represents the Lagrange multiplier vector corresponding to the effective inequality constraints at the nominal load point. This represents the coefficient matrix of the load parameters in the equality constraint.

7. An electronic device, characterized in that, It includes a memory and a processor, wherein the memory stores a computer program, and the processor, when calling the computer program in the memory, implements the steps of the method for rapid calculation of the carbon intensity of a power grid node as described in any one of claims 1 to 5.

8. A storage medium, characterized in that, The storage medium stores computer-executable instructions, which, when loaded and executed by a processor, implement the steps of the method for rapidly calculating the carbon intensity of a power grid node as described in any one of claims 1 to 5.

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