A method for constructing and applying a low-carbon scheduling algorithm model of a zero-carbon park energy system

Abstract

The application provides a zero-carbon park energy system low-carbon scheduling algorithm model construction and application method, comprising the following steps: S1, collecting operation data of each energy node in the park; S2, multi-time scale uncertainty quantification; S3, solving the amplitude and phase of the limit cycle; S4, solving the global optimal scheduling solution; S5, constructing the spectral triplets of non-commutative geometry. The application solves the technical problems of low modeling precision, poor robustness of uncertainty processing, difficulty in guaranteeing global optimality of scheduling solution, weak dynamic correction ability and inability to adapt to changes in system topology structure in the prior art, constructs a complete closed-loop scheduling framework from geometric topology to nonlinear dynamics to global optimization, and realizes low-carbon, efficient, stable and economic operation of the zero-carbon park energy system.

Description

Technical Field

[0001] This invention relates to the interdisciplinary field of energy system optimization scheduling and computational mathematics, and in particular to a method for constructing and applying a low-carbon scheduling algorithm model for a zero-carbon industrial park energy system. Background Technology

[0002] Driven by dual carbon objectives, zero-carbon parks have become the core carriers of urban energy transformation. Zero-carbon park energy systems are characterized by multi-source heterogeneity, deep coupling of multiple energy flows, strong uncertainty, and dynamic changes in topology. Their low-carbon scheduling needs to simultaneously meet carbon emission constraints, operating cost constraints, system stability constraints, and multi-energy supply and demand balance constraints, making it a typical high-dimensional, nonlinear, non-convex, and strongly constrained optimization problem.

[0003] Existing zero-carbon park energy dispatch technologies mainly suffer from the following technical deficiencies: Insufficient accuracy in multi-energy flow coupling modeling: Existing methods mostly use linearization, piecewise linearization or polynomial fitting to describe the coupling characteristics of electric-thermal-cold-hydrogen multi-energy flows, which cannot accurately capture the nonlinear self-excited oscillation phenomenon that is common in the multi-energy flow conversion process. This results in a large deviation between the scheduling model and the actual system, and poor feasibility of the scheduling scheme.

[0004] It is difficult to balance robustness and economy in handling uncertainty: stochastic optimization methods require prior assumptions about the probability distribution of renewable energy output and load demand, which is difficult to meet in practice; traditional robust optimization methods are too conservative and will significantly increase the system operating cost; although the sub-Bruker robust optimization method has made some improvements, it has not yet been organically combined with the topological characteristics of the energy system.

[0005] Global optimality is difficult to guarantee: Existing solution methods mostly use heuristic algorithms such as genetic algorithms and particle swarm algorithms, which are prone to getting trapped in local optima. It is impossible to rigorously prove the global optimality of the scheduling solution, making it difficult to achieve the ultimate optimization of system performance.

[0006] Weak dynamic correction capability and lack of topological stability guarantee: Existing dynamic correction methods only adjust based on numerical deviations and cannot take into account changes in the system topology. The correction process may destroy the topological stability of the system, or even cause system oscillation or collapse.

[0007] Lack of a unified mathematical description framework: Existing methods treat the different characteristics of energy systems in isolation, without constructing a unified mathematical description framework from the essential level of geometric topology and nonlinear dynamics. This results in poor synergy between modules and the inability to form a complete closed-loop optimization mechanism.

[0008] Currently, there are no reports in existing technologies that organically integrate Chern-Simons gauge field theory, Hopf bifurcation theory, and noncommutative geometric spectrum triplet theory for low-carbon scheduling in zero-carbon park energy systems. Existing scheduling methods cannot simultaneously meet the multiple requirements of multi-energy flow coupling modeling accuracy, uncertainty handling robustness, global optimality of scheduling solutions, and dynamic correction topological stability, and are therefore unable to adapt to the complex and variable operating conditions of zero-carbon park energy systems. Summary of the Invention

[0009] This invention provides a method for constructing and applying a low-carbon scheduling algorithm model for a zero-carbon park energy system. It solves the technical problems in existing technologies, such as low accuracy of multi-energy flow coupling modeling, poor robustness in handling uncertainties, difficulty in guaranteeing the global optimality of scheduling solutions, weak dynamic correction capabilities, and inability to adapt to changes in system topology. It constructs a complete closed-loop scheduling framework from geometric topology to nonlinear dynamics to global optimization, thereby realizing the low-carbon, efficient, stable, and economical operation of the zero-carbon park energy system.

[0010] To achieve the above objectives, the present invention adopts the following technical solution: A method for constructing and applying a low-carbon scheduling algorithm model for a zero-carbon industrial park energy system, comprising: Step S1. Collect the operating data of each energy node in the park, construct a spatiotemporal topology map, map the spatiotemporal topology map to a Chern-Simons gauge field, map the transmission loss coefficient between energy nodes to the coupling constant of the Chern-Simons gauge field, and calculate the curvature tensor of the Chern-Simons gauge field. Step S2. Perform multi-timescale uncertainty quantification on renewable energy output and load demand, and merge the uncertainty boundaries under each timescale to obtain a unified fuzzy boundary of energy supply and demand across multiple timescales. Step S3. Extract historical multi-energy flow coupling operating condition data, use the modulus of the curvature tensor as the bifurcation parameter, establish a Hopf bifurcation model of multi-energy flow coupling, determine the critical bifurcation parameter, and solve the amplitude and phase of the limit cycle by fitting historical data; Step S4. With minimizing total carbon emissions and total operating costs as the scheduling objective, under the fuzzy boundary of energy supply and demand, equipment operation constraints, and multi-energy flow coupling constraints represented by the limit cycle, the compression mapping operator on the scheduling solution space is iterated at fixed points to solve for the global optimal scheduling solution. During the iteration process, the bifurcation parameters are dynamically updated according to the changes in the scheduling objective function value, so that the amplitude of the limit cycle is changed to adjust the boundary of the multi-energy flow coupling constraints. Step S5. Construct a spectral triplet of non-commutative geometry, wherein the gauge potential of the Dirac operator is determined by the amplitude of the limit cycle. Using the global optimal scheduling solution as the reference pure state and the current actual running state as the pure state to be corrected, calculate the spectral distance between the two. Use the spectral distance to correct the global optimal scheduling solution to obtain the corrected scheduling solution. Update the coupling constant of the Chern-Simons gauge field according to the spectral distance to recalculate the curvature tensor and return to step S3 to form a closed-loop iteration.

[0011] In this specification, step S1, which maps the spatiotemporal topology graph to a Chern-Simons gauge field, includes: mapping the active power value of each energy node to the scalar potential of the Chern-Simons gauge field, mapping the reactive power value to the vector potential, mapping the transmission loss coefficient between energy nodes to the coupling constant, spanning a three-dimensional manifold from the spatiotemporal coordinates of all energy nodes, constructing the Chern-Simons action on the three-dimensional manifold, and calculating the curvature tensor.

[0012] In this specification, the multi-timescale uncertainty quantification in step S2 includes: dividing the timescale into ultra-short-term, short-term, and medium-to-long-term timescales; constructing an empirical distribution and calculating the uncertainty radius for each timescale using historical data; constructing an uncertainty set using a biblical optimization based on Wasserstein distance; solving for the uncertainty boundaries of renewable energy output and load demand at each timescale; and then taking the intersection of the ultra-short-term uncertainty boundary and the medium-to-long-term uncertainty boundary to obtain the unified energy supply and demand fuzzy boundary across the multiple timescales.

[0013] In this specification, step S3, which involves solving for the amplitude and phase of the limit cycle, includes: dividing the magnitude of the curvature tensor by the maximum value of that magnitude in historical data to obtain a normalized bifurcation parameter; when the bifurcation parameter is greater than the critical bifurcation parameter, the amplitude of the limit cycle is taken as the square root of the difference between the bifurcation parameter and the critical bifurcation parameter, and the phase of the limit cycle is obtained by fitting historical multi-energy flow coupling data.

[0014] In this specification, step S4, the fixed-point iteration of the compression mapping operator, includes: defining the compression mapping operator as the scheduling solution that minimizes the scheduling objective function under all constraints; using the rated operating point of each energy node as the initial scheduling solution; repeatedly applying the compression mapping operator until the distance between the scheduling solutions obtained in two adjacent iterations is less than a preset threshold; and updating the bifurcation parameters by using the difference between the objective function value corresponding to the current scheduling solution and the scheduling solution of the previous iteration after each specified number of iterations during the iteration process.

[0015] In this specification, step S5, which involves constructing the spectral triplet, includes: generating C from observables of the park's energy system. Algebraically, the vector space formed by all possible scheduling solutions is taken as the Hilbert space, and the amplitude of the limit cycle is multiplied by a unit vector to obtain the gauge potential of the Dirac operator; the spectral distance is obtained by solving for the maximum value of the difference between the expectations of two pure states over all algebraic elements that satisfy the commutator norm of the Dirac operator not greater than one.

[0016] In this specification, step S5, which involves correcting the global optimal scheduling solution using spectral distance, includes: multiplying a preset correction coefficient, the spectral distance, and the global optimal scheduling solution to obtain a correction amount, and then adding the correction amount to the global optimal scheduling solution to obtain the corrected scheduling solution; updating the coupling constant includes: multiplying the current coupling constant by a factor and adding the product of a preset learning rate and the spectral distance to obtain the updated coupling constant.

[0017] This specification also includes step S6: decomposing the corrected scheduling into park-level control commands, microgrid-level control commands, and device-level control commands; the park-level control commands include the power exchange plan between microgrids and the power exchange plan between the park and the main power grid; the microgrid-level control commands include the active power setpoint of each energy node in the microgrid; and the device-level control commands include the operating parameters of each device.

[0018] This specification also includes step S7: collecting real-time operating data of each energy node, calculating the deviation of the actual total carbon emissions and total operating costs relative to the scheduling target, and performing adaptive update of model parameters when the deviation of total carbon emissions or total operating costs exceeds a preset threshold; the adaptive update of model parameters includes: updating the empirical distribution and the uncertainty radius, updating the bifurcation parameters of the Hopf bifurcation model using incremental learning, and updating the energy levels of the Chern-Simons gauge field according to the deviation of total carbon emissions, wherein the energy levels are set when constructing the Chern-Simons gauge field.

[0019] In this specification, step S5 further includes topological stability verification: calculating the Chern number of the Chern-Simons gauge field before and after correction, wherein the Chern number is a topological invariant describing the topological properties of the gauge field; when the Chern number changes, adjusting the correction coefficients and re-performing the correction until the Chern number remains unchanged.

[0020] In summary, the present invention has at least the following beneficial effects: By constructing a unified geometric framework for energy systems using the Chen-Simons gauge field, the topological characteristics and potential defects of energy flow can be accurately described, providing a solid mathematical foundation for subsequent modeling and optimization, and realizing a unified description of different characteristics of energy systems.

[0021] The multi-energy flow coupling model established based on Hopf bifurcation theory can accurately capture the nonlinear self-excited oscillation characteristics in the multi-energy flow conversion process, significantly improving the accuracy of multi-energy flow coupling modeling and solving the problem of large errors in traditional linearization methods.

[0022] The uncertainty is quantified by a biblical optimization method based on Wasserstein distance, which does not require prior assumptions about the probability distribution. At the same time, robustness and economy are balanced by multi-timescale boundary fusion, which enhances the scheduling scheme's adaptability to complex uncertainties.

[0023] The scheduling optimization problem is solved by using the fixed-point theorem of compression mapping. The global optimality of the scheduling solution is guaranteed through rigorous mathematical proof, avoiding the defect of heuristic algorithms that are prone to getting trapped in local optima, and achieving the ultimate optimization of system performance.

[0024] Dynamic correction based on noncommutative geometric spectrum triplet theory can simultaneously consider numerical deviation and topological differences, significantly improving the accuracy of dynamic correction. Furthermore, Chern number verification ensures the topological stability of the system during the correction process.

[0025] A two-way closed-loop interaction mechanism was established among multiple algorithms, enabling the model to continuously adapt to changes in system operating status and topology, and achieving continuous adaptive optimization of the scheduling scheme.

[0026] By adopting a hierarchical execution and multi-node collaborative control structure, the system balances global optimization of scheduling with rapid local response, thereby improving the system's operational reliability and fault handling capabilities.

[0027] Taking into account both carbon emission and operating cost objectives, the system effectively reduces total carbon emissions and total operating costs while ensuring stable operation, thus contributing to the achievement of the zero-carbon park goal. Attached Figure Description

[0028] Figure 1 This is a schematic diagram illustrating the construction and application method of the low-carbon scheduling algorithm model for zero-carbon park energy systems involved in this invention.

[0029] Figure 2 This is a schematic diagram illustrating the process of constructing the Chen-Simons gauge field and Hopf bifurcation model involved in this invention.

[0030] Figure 3 This is a schematic diagram of the process for solving the global optimal scheduling by iteratively finding the fixed point of the compression mapping involved in this invention.

[0031] Figure 4 This is a schematic diagram of the dynamic correction and closed-loop feedback of the spectral triplet involved in this invention. Detailed Implementation

[0032] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of the embodiments of the invention. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0033] The following disclosure provides many different implementations or examples for carrying out different structures of the embodiments of the present invention. To simplify the disclosure of the embodiments of the present invention, specific examples of components and arrangements are described below. Of course, these are merely examples and are not intended to limit the embodiments of the present invention. Furthermore, reference numerals and / or reference letters may be repeated in different examples of the embodiments of the present invention; such repetition is for simplification and clarity and does not in itself indicate a relationship between the various implementations and / or arrangements discussed.

[0034] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0035] like Figure 1 As shown, this embodiment provides a method for constructing and applying a low-carbon scheduling algorithm model for a zero-carbon park energy system. First, the invention constructs a spatiotemporal topology map of multi-source heterogeneous energy data in the zero-carbon park and maps it to a three-dimensional Chern-Simons gauge field, providing a unified geometric description framework for energy flow in the energy system. Second, it employs a bibru bar optimization method based on Wasserstein distance to quantify energy uncertainties at three time scales: ultra-short-term, short-term, and medium-to-long-term, generating a unified fuzzy boundary for energy supply and demand across multiple time scales. Then, based on Hopf bifurcation theory, it establishes precise dynamic models for 11 types of multi-energy flow coupling, accurately describing the nonlinearity of the multi-energy flow conversion process. The system first identifies the self-excited oscillation characteristics of the system. Then, iteratively solving the globally optimal low-carbon scheduling solution using the compression mapping fixed-point theorem is performed. During the iteration process, it interacts bidirectionally with the Hopf bifurcation model to dynamically adjust the multi-energy flow coupling constraint boundary. Subsequently, based on the non-commutative geometric spectrum triplet theory, the spectral distance between the actual operating state and the optimal scheduling solution is calculated. The scheduling scheme is then dynamically corrected by considering both numerical deviation and topological differences, and the coupling constant and energy level parameters of the Chen-Simons gauge field are updated accordingly. Finally, the corrected scheduling scheme is decomposed into control command execution at three levels: park level, microgrid level, and equipment level. Adaptive closed-loop updates of all model parameters are achieved through real-time operating data.

[0036] The entire scheme constructs a complete two-way closed-loop interaction mechanism between the Chen-Simons gauge field, the Hopf bifurcation model, the compression mapping fixed point iteration, and the spectral triplet theory, realizing the precise scheduling of the zero-carbon park energy system from the essential level of geometric topology and nonlinear dynamics.

[0037] S1. Spatiotemporal topological mapping and Chern-Simons gauge field construction of multi-source heterogeneous energy data in zero-carbon industrial parks: like Figure 2 The system collects basic attribute data and minute-level real-time operational data for all energy nodes within the zero-carbon industrial park, covering 365 consecutive days. Examples of energy node types include photovoltaic power generation nodes, wind power generation nodes, biomass power generation nodes, ground source heat pump nodes, air source heat pump nodes, gas turbine nodes, energy storage battery nodes, thermal storage tank nodes, cold storage tank nodes, hydrogen production equipment nodes, hydrogen fuel cell nodes, electric vehicle charging pile nodes, industrial load nodes, commercial load nodes, residential load nodes, and public facility load nodes. Basic attribute data includes equipment rated power, equipment efficiency curve, equipment minimum operating power, equipment maximum operating power, equipment start-up and shutdown time constraints, equipment minimum continuous operating time, equipment minimum continuous downtime, equipment maintenance cycle, equipment unit power carbon emission factor, and equipment unit power operating cost. Real-time operational data includes active power, reactive power, voltage, current, frequency, equipment inlet and outlet temperatures, equipment inlet and outlet pressures, medium flow rate, real-time carbon emission intensity, and equipment operating status indicators. The acquisition accuracy of all real-time running data is no less than 0.5, the acquisition time interval is strictly 1 minute, missing data is filled in by linear interpolation of three adjacent time points, and abnormal data is identified and removed by the 3σ criterion.

[0038] Construct the spatiotemporal topology of the zero-carbon park energy system. Vertex set. This represents all energy nodes, with each vertex corresponding to a unique energy node number. (Edge set) This represents the physical connections between energy nodes, with each edge corresponding to an actual energy transmission line or pipeline. The weight of each edge represents the transmission efficiency and transmission loss coefficient of that connection. The calculation is based on the material, length, cross-sectional area, and operating temperature of the line or pipe. The calculation formula is as follows: ; in For the inherent transmission efficiency of the materials, 0.99 is used for copper cables, 0.98 for aluminum cables, and 0.97 for steel pipes. The temperature attenuation coefficient is taken as the cable's value. Pipeline . The length of the line or pipeline is expressed in kilometers. The average operating temperature is expressed in degrees Celsius. The transmission loss factor is equal to 1 minus the transmission efficiency. Each vertex is assigned a time-dimensional attribute vector, the dimension of which equals the total number of time steps. Each element stores all real-time operating data for that node at the corresponding time step.

[0039] The above spacetime topology is mapped to a three-dimensional Chern-Simons gauge field. The spatial coordinates of the spacetime topology are... with spatial coordinates With time coordinates Combining into three-dimensional manifold coordinates of gauge field ,in and These are the coordinates of the energy nodes in the park's planar coordinate system, in meters. Using time as the coordinate, the unit is minutes. The active power value of each energy node is mapped to the scalar potential of the gauge field. The unit of scalar potential is kilowatt. The reactive power value of each energy node is mapped to the vector potential of the gauge field. Vector potential It contains three components, namely , , ,in correspond reactive power components in the direction, correspond reactive power components in the direction, The reactive power variation component corresponding to the time dimension is expressed in kilovars. The transmission loss coefficients between energy nodes are mapped to the coupling constants of the gauge field. Coupling constant It is a dimensionless quantity.

[0040] Constructing the action of the Chen-Simons gauge field Action Action is a physical quantity describing the total energy of a gauge field; the smaller the value, the more ordered the energy flow of the energy system. The expression is: ; in The initial value of the energy level of the gauge field is 1, which is a dimensionless quantity. It is a three-dimensional manifold spanned by the spatiotemporal coordinates of all energy nodes. The trace operation is used to calculate the sum of the diagonal elements of a matrix. It is an exterior differential operator used to perform differential operations on differential forms. This is the outer product operation, used to calculate the outer product of two differential forms.

[0041] Calculate the initial curvature tensor of the Chern-Simons gauge field. curvature tensor The curvature tensor is a physical quantity that describes the degree of curvature of a gauge field; its magnitude directly reflects the non-uniformity of energy flow and potential topological defects in an energy system. The expression is: ; curvature tensor The component form is: ; in and This is the coordinate index, and its value range is... . , These are partial differential operators, representing the operations with respect to coordinates. , Find the partial derivatives. For the Ligand operation, it is defined as .

[0042] Calculate the specific values ​​of the three independent components based on the curvature tensor component form: ; ; ; The Chern-Simons gauge field constructed in this step will serve as the fundamental geometric framework for the entire scheduling algorithm, providing a unified mathematical description of energy flow in the energy system. (Curvature tensor) This will be directly used as the bifurcation parameter input for subsequent Hopf bifurcation theory to describe the nonlinear dynamic characteristics of multi-energy flow coupled systems. Coupling constant The spectral distance will be dynamically updated based on the output of subsequent spectral triplet theory to reflect real-time changes in the energy system's topology. Action This will be used for the global performance evaluation of the scheduling scheme in subsequent steps.

[0043] S2. Multi-timescale energy uncertainty quantification based on split-blob bar optimization: The time scale is divided into three levels. The ultra-short-term time scale is 15 minutes, used to capture rapid fluctuations in renewable energy output and load demand. The short-term time scale is 1 hour, used to coordinate the charging and discharging of energy storage devices and the operation of multi-energy flow conversion devices. The medium- and long-term time scale is 24 hours, used to formulate the overall energy dispatch plan for the park and the power exchange plan with the main power grid. Uncertainty analysis is performed on renewable energy output and load demand at each time scale.

[0044] For each time scale, a set of partial Bruker uncertainties based on Wasserstein distance is constructed. A sliding window method is used to extract sample points from historical operating data. The size of the sliding window is equal to the length of the corresponding time scale, and the sliding step is 1 minute. Each sample point contains the total output value of all photovoltaic power generation nodes, wind power generation nodes, and biomass power generation nodes at that time scale, as well as the total demand value of all industrial load nodes, commercial load nodes, residential load nodes, and public utility load nodes. The empirical distribution of the sample points is calculated. , experience distribution It is a discrete probability distribution consisting of all sample points. The set of uncertainties is defined as all probability distributions that are similar to the empirical distribution. The Wasserstein distance does not exceed probability distribution The set of uncertainties. The expression for the set of uncertainties is: ; in The first-order Wasserstein distance is used to measure the difference between two probability distributions. The uncertainty radius is used to control the size of the uncertainty set.

[0045] 1st order Wasserstein distance The calculation formula is: ; Where inf represents taking the infimum. This indicates that the integral iterates through two sets of two-dimensional variables. For all joint distributions The set of joint distributions The edge distributions are respectively and . for and The 1-norm distance between them is defined as ,in and Energy output value for renewable energy and This represents the load demand value.

[0046] Uncertainty radius The radius of uncertainty is adaptively determined based on the variance of historical data. The calculation formula is: ;in The confidence level is set at 95%, and it is a dimensionless quantity. The variance of the sample data is calculated as the average of the squares of the differences between all sample points and the sample mean. The number of sample points is equal to the total number of time steps of historical running data minus the sliding window size plus 1.

[0047] Sample mean The calculation formula is: ;in For the first The vector values ​​of each sample point.

[0048] The dual transformation method is used to solve the bibrubar optimization problem. The bibrubar optimization problem is transformed into its dual problem, which is a finite-dimensional convex optimization problem with a unique optimal solution. The subgradient descent algorithm is then used to solve the dual problem. The iterative formula of the subgradient descent algorithm is as follows: ; in For the first The value of the dual variable in the next iteration. For the first The step size of each iteration adopts a decreasing step size strategy, with an initial step size of 0.1 and a step size multiplied by 0.99 for each iteration. For the first The subgradient of the nth iteration is calculated using the following formula: ; in This is a vector dot product operation. In the empirical distribution The expected value of the following.

[0049] The iteration termination condition is that the difference between the objective function values ​​of two consecutive iterations is less than 1. Solving the dual problem yields the optimal dual variables. Optimal dual variable It is a two-dimensional vector, corresponding to the dual variables of renewable energy output and load demand, respectively.

[0050] Based on the optimal dual variable Calculate the minimum and maximum possible values ​​of renewable energy output and load demand. Minimum possible value of renewable energy output. Equal to the sample mean minus The first component multiplied by the uncertainty radius The maximum possible value of renewable energy output. Equal to the sample mean plus The first component multiplied by the uncertainty radius Minimum possible load demand Equal to the sample mean minus The second component multiplied by the radius of uncertainty The maximum possible value of load demand. Equal to the sample mean plus The second component multiplied by the radius of uncertainty This leads to the fuzzy boundary of energy supply and demand at each time scale.

[0051] The blurred boundaries of the three time scales are fused. First, the boundaries of the three time scales are aligned to a 1-minute time resolution. For each time point... The renewable energy output boundary under the ultra-short-term timescale is The load demand boundary is The renewable energy output boundary on a short-term timescale is The load demand boundary is The renewable energy output boundary on a medium- to long-term timescale is... The load demand boundary is .

[0052] The combined renewable energy output boundary is: ; ; The combined load demand boundary is: ; ; This fusion method takes into account both the accuracy of ultra-short-term timescales and the robustness of medium- and long-term timescales.

[0053] The unified energy supply and demand fuzzy boundary obtained in this step will be used for parameter space constraints in subsequent Hopf bifurcation theory to ensure that bifurcation analysis is carried out within a reasonable range of energy supply and demand, and to avoid obtaining bifurcation solutions that do not conform to reality.

[0054] S3. Accurate modeling of multi-energy flow coupling characteristics based on Hopf bifurcation theory: Extract all data points for multi-energy flow coupling conditions from historical operating data. Multi-energy flow coupling conditions refer to operating conditions involving the conversion between at least two different forms of energy. Examples of multi-energy flow coupling types include electro-thermal coupling, electro-cold coupling, electro-hydrogen coupling, thermal-cold coupling, thermal-hydrogen coupling, cold-hydrogen coupling, electro-thermal-cold coupling, electro-thermal-hydrogen coupling, electro-thermal-hydrogen coupling, electro-cold-hydrogen coupling, and electro-thermal-cold-hydrogen coupling. Use cluster analysis to filter stable multi-energy flow coupling condition data points from historical operating data, excluding data points related to equipment start-up / shutdown processes, fault processes, and abnormal operation processes.

[0055] Cluster analysis uses the k-means algorithm, and the specific implementation process is as follows: 1. Initialization There are 10 cluster centers, and the initial cluster centers are randomly selected from historical data points; 2. Calculate the Euclidean distance from each data point to each cluster center, and assign the data point to the cluster containing the nearest cluster center; 3. Recalculate the cluster center for each cluster, which is the average of all data points in that cluster; 4. Repeat steps 2 and 3 until the change in cluster centers is less than 1. .

[0056] The number of clusters is determined according to the elbow rule, and the specific implementation process is as follows: 1. Calculate the total squared error (SSE) for clusters ranging from 2 to 10. The total squared error is the sum of the squares of the distances from each data point to its cluster center. 2. Plot the SSE curve as a function of the number of clusters; 3. Find the number of clusters corresponding to the elbow in the curve, which is the optimal number of clusters.

[0057] Construct the Hopf bifurcation dynamic equations for multi-energy flow coupled systems. Hopf bifurcation theory can accurately describe the transition process of a nonlinear system from a stable equilibrium point to a stable limit cycle, and the self-excited oscillation phenomenon that is prevalent in multi-energy flow coupled systems can be described by Hopf bifurcation. The input energy values ​​of each type of multi-energy flow coupling are used as state variables. The unit is kilowatts. The output energy value is used as a state variable. The unit is kilowatts. The curvature tensor obtained in step S1... The modulus is used as a bifurcation parameter curvature tensor The formula for calculating the modulus is: ; in , , respectively curvature tensor The three independent components. Bifurcation parameters. The calculation formula is: ; in For the curvature tensor in historical operating data The maximum value of the modulus. Through this normalization process, the bifurcation parameters... The range of values ​​is .

[0058] The expression for Hopf's bifurcation dynamics equation is: ; ; Determining the critical bifurcation parameter values ​​for Hopf bifurcation When the bifurcation parameter Less than the critical bifurcation parameter value At this point, the origin of the system is a stable equilibrium point, and the multi-energy flow coupled system operates in a stable state. When the bifurcation parameter... Greater than the critical bifurcation parameter value At this point, the origin of the system loses stability, generating a stable limiting cycle, and the multi-energy-current coupled system enters a self-excited oscillation state. Critical bifurcation parameter values. The calculation formula is: ; in Let be the right-hand side function of Hopf's bifurcation dynamics equations. For the first equation, For the second equation, The second and third partial derivatives are calculated at the origin.

[0059] Find the limit cycle solution of the Hopf bifurcation system. When the bifurcation parameters... Greater than the critical bifurcation parameter value At this point, the system has a unique stable limit cycle solution. The amplitude of the limit cycle solution is... With bifurcation parameters The relationship is: ; Angular frequency of limit cycle solution Let be a constant, taking a value of 1, and expressed in radians per minute. The expression for the solution to the limit cycle is: ; in This is the initial phase angle. The phase angle for each historical data point is determined based on the average value of historical multi-energy flow coupling data. The calculation formula is: ; in and For the first Input energy value and output energy value of each historical data point. This is the arctangent function in the fourth quadrant. Initial phase angle. This is the average phase angle of all historical data points.

[0060] The least squares method is used to fit the limit cycle solution to coupled historical multi-energy flow data points, minimizing the mean square error of the fit. (Mean square error) The calculation formula is: ; in This represents the number of historical multi-energy flow coupled data points. and Let be the input energy value and output energy value of the limit cycle solution at the corresponding time point.

[0061] The specific process of least squares fitting is as follows: 1. Initialize the parameters of the limit cycle solution. and The initial value is the average of historical data; 2. Calculate the mean square error under the current parameters. ; 3. Calculate the mean square error with respect to the parameters. and The partial derivatives; 4. Update parameters using gradient descent. and The updated formula is: ; ; in and The learning rates are set to 0.01 and 0.001 respectively. 5. Repeat steps 2 through 4 until the change in mean squared error is less than .

[0062] Verify the fitting accuracy of the Hopf bifurcation model. Use 20% of the data points in the historical dataset that were not used for fitting as the test set. Calculate the mean square error between the test set data points and the limit cycle solution. If the mean square error is less than 0.01, the fitting accuracy is considered satisfactory. Otherwise, adjust the bifurcation parameters. The range of values ​​is determined and refitted until the accuracy requirements are met.

[0063] The Hopf bifurcation limit cycle solution obtained in this step will serve as a precise mathematical description of the multi-energy flow coupling characteristics, and will be used as a multi-energy flow coupling constraint for subsequent scheduling optimization. The amplitude of the limit cycle solution... This will be directly used as the input parameters for the Dirac operator in subsequent spectral triplet theory. Simultaneously, the bifurcation parameters of the Hopf bifurcation model... The bifurcation parameters will be dynamically adjusted based on the results of subsequent compression mapping fixed-point iterations. The change will in turn affect the amplitude of the limit cycle solution. This, in turn, affects the boundary of the multi-energy flow coupling constraint, forming a bidirectional interaction between the Hopf bifurcation model and the compression mapping fixed-point iteration. The process of constructing the Chern-Simons gauge field and the Hopf bifurcation model through S1 to S3 is as follows: Figure 2 As shown.

[0064] S4. Iterative solution of the global optimal low-carbon scheduling solution based on the fixed-point theorem of compression mapping: Construct an objective function for low-carbon scheduling of the energy system in a zero-carbon industrial park. The objective function is to minimize the weighted sum of the system's total carbon emissions and total operating costs. The expression is: ; in is the carbon emission weighting coefficient, taken as 0.6, and is a dimensionless quantity. The weighting coefficient for operating costs is set to 0.4, and it is a dimensionless quantity. This represents the total carbon emissions of the system, expressed in kilograms of carbon dioxide equivalent. The total operating cost of the system is expressed in yuan.

[0065] Total carbon emissions of the system The calculation formula is: ; in This represents the total number of energy nodes. This represents the total number of time steps in the scheduling cycle, which is 24 hours, with a time step of 15 minutes. . For the first Carbon emission factor per unit power of an energy node, expressed in kilograms of carbon dioxide equivalent per kilowatt-hour. For the first The energy node at the ... The active power value at each time step, in kilowatts. The time step is 0.25 hours.

[0066] Total system operating cost The calculation formula is: ; in For the first The unit power operating cost of an energy node, expressed in yuan per kilowatt-hour. This refers to the number of lines connecting the park to the main power grid. For the first The electricity price of the main power grid at each time step is expressed in yuan per kilowatt-hour. For the first The exchange power between the park and the main power grid at each time step is expressed in kilowatts. A positive value indicates that the park purchases electricity from the main power grid, while a negative value indicates that the park sells electricity to the main power grid.

[0067] Construct constraints for scheduling optimization. Examples of constraints include power balance constraints, reactive power balance constraints, equipment operation constraints, equipment start-up and shutdown constraints, energy storage capacity constraints, multi-energy flow coupling constraints, and carbon emission constraints.

[0068] The power balance constraint requires that the total active power output of the system equals the sum of the total active power input and the total active power loss. The expression for the power balance constraint is: ; in This represents the total number of power generation nodes. For the first The power generation node at the first The active power output value at each time step. This represents the total number of load nodes. For the first The load node at the ... The active power demand value at each time step. This represents the total number of energy transmission lines. For the first The transmission line in the first The active power loss value at each time step is calculated using the following formula: ; in For the first The transmission line in the first The current value at each time step, in amperes. For the first The resistance value of a transmission line, measured in ohms.

[0069] The reactive power balance constraint requires that the total reactive power output of the system equals the sum of the total reactive power input and the total reactive power loss. The expression for the reactive power balance constraint is: ; in For the first The power generation node at the first The reactive power output value at each time step. For the first The power grid connection line is in the first The reactive power exchange value at each time step. For the first The load node at the ... The reactive power demand value at each time step. For the first The transmission line in the first The reactive power loss value at each time step is calculated using the following formula: ; in For the first The reactance value of a transmission line, in ohms.

[0070] Equipment operating constraints require that the active and reactive power of each energy node remain within their rated ranges. The expression for the equipment operating constraints is: ; ; in and The first The minimum and maximum active power of each energy node. and The first The minimum and maximum reactive power of each energy node.

[0071] Equipment start-up and shutdown constraints require that the number of start-ups and shutdowns and the start-up and shutdown times of each energy node meet its operational requirements. The expression for the equipment start-up and shutdown constraints is: ; ; ; in For the first The energy node at the ... The running status indicator for each time step, 1 indicates running, and 0 indicates stopped. For the first The maximum number of times an energy node is allowed to start and stop within a scheduling cycle. For the first The energy node at the ... The continuous running time of each time step. For the first Minimum continuous operating time of each energy node. For the first The energy node at the ... The continuous downtime of each time step. For the first Minimum continuous downtime of each energy node.

[0072] Energy storage capacity constraints require that the state of charge of energy storage devices be within their minimum and maximum allowable ranges. The expression for energy storage capacity constraints is: ; ; in For the first The energy storage device in the first The state of charge at each time step. and The first The minimum and maximum states of charge of an energy storage device. and The first The charging efficiency and discharging efficiency of an energy storage device. and The first The energy storage device in the first The charging power and discharging power at each time step.

[0073] The multi-energy flow coupling constraint requires that the input-output relationship of each multi-energy flow coupling type satisfy the Hopf bifurcation limit cycle solution obtained in step S3. The expression for the multi-energy flow coupling constraint is: ; in This is the number for the multi-energy flow coupling type. and The first Types of multi-energy flow coupling in the first The input energy value and output energy value at each time step. , , The first The amplitude, angular frequency, and initial phase angle of the limit cycle solution corresponding to each type of multi-energy flow coupling. The allowable deviation threshold is set to 0.05.

[0074] Carbon emission constraints require that the total carbon emissions of the system not exceed the carbon emission limits of the zero-carbon park. The expression for the carbon emission constraint is: ;in The carbon emission limit for the zero-carbon park is set in advance based on the park's carbon emission quota or relevant policy standards, and the unit is kilograms of carbon dioxide equivalent.

[0075] Define compression mapping operator Compression mapping operator Map the scheduling solution space to itself. The scheduling solution space is the set of all scheduling solutions that satisfy the above constraints; each scheduling solution is a... A dimensional vector, where each element corresponds to the active power value of an energy node at a time step. For any scheduling solution... , To achieve the objective function while satisfying all constraints. Minimal scheduling solution. Compression mapping operator. The definition of is: ; in It is the set of all scheduling solutions that satisfy the constraints.

[0076] Compression mapping operator The specific calculation method is as follows: 1. Determine the scheduling solution As the initial point; 2. The interior-point method is used to solve the above constrained optimization problem to obtain the optimal solution. ; 3. Output As The value of .

[0077] Prove the compression mapping operator The compression mapping condition is satisfied. A constant exists. Such that for any two scheduling solutions and ,have: ; in Let be the distance function in the scheduling solution space. Defined as the Euclidean distance between two scheduling solutions, the expression is: ; Due to the objective function It is a strictly convex function, and the set of constraints. It is a convex set, therefore the compression mapping operator It is a strict compression mapping, with a compression constant. equal to the objective function The reciprocal of the Lipschitz constant.

[0078] objective function Lipschitz constant The calculation formula is: ;in For the objective function At point The gradient at that point. Let be the 2-norm of the vector.

[0079] Based on the fixed-point theorem for compression mappings, the compression mapping operator can be solved iteratively. The fixed point is the globally optimal scheduling solution. The iterative process is as follows: Select the initial scheduling solution. The initial scheduling determines the rated operating point of all energy nodes, meaning the active power of each energy node is equal to 50% of its rated power. Calculation... Calculate the iteration error. .like If the iteration stops, then output the result. As the globally optimal scheduling solution. Otherwise, let Return to calculation The steps continue to iterate.

[0080] During the iteration process, every 10 iterations, the current scheduling solution is substituted into the Hopf bifurcation dynamics equation in step S3. The bifurcation parameters are then updated. The value of . The update formula is: ; in The learning rate is set to 0.001, and it is a dimensionless quantity. These are the bifurcation parameter values ​​before the update. These are the updated bifurcation parameter values. Bifurcation parameters The update will cause the amplitude of the limit cycle solution to change. Changes occur, leading to changes in the boundaries of the multi-energy flow coupling constraints, thereby altering the compression mapping operator. The definition of this bidirectional interaction mechanism enables the scheduling optimization process to continuously adapt to the nonlinear dynamic characteristics of the multi-energy flow coupled system, resulting in a more accurate globally optimal scheduling solution. The process of solving the globally optimal scheduling solution using the compression mapping fixed-point iterative method in S4 is as follows: Figure 3 As shown.

[0081] The globally optimal scheduling solution obtained in this step will serve as the reference pure state for subsequent spectral triplet theory. Simultaneously, the bifurcation parameters are updated during the iteration process. The feedback will be sent to step S3 to dynamically adjust the parameters of the multi-energy flow coupling model.

[0082] S5. Dynamic correction of scheduling schemes based on noncommutative geometric spectrum triplet theory: Constructing spectral triples in noncommutative geometry. Spectral triples are a core concept in noncommutative geometry, capable of transforming the properties of geometric spaces into properties of operator algebras, thus providing a powerful mathematical tool for describing the topological properties of complex systems. Spectral triples are derived from algebraic... Hilbert space Dirac operator composition.

[0083] Algebra This is generated from all observables of the zero-carbon park's energy system. Observables include active power, reactive power, voltage, and current at all energy nodes. Each observable corresponds to an algebraic number. A self-adjoint operator in algebra. It is a C Algebra, satisfying C All axioms of algebra.

[0084] Hilbert Space The vector space comprising all possible scheduling solutions. Hilbert space. The dimension is equal to the dimension of the scheduling solution space, that is... Hilbert space Each vector in the Hilbert space corresponds to a scheduling solution. The inner product operation is defined above, and its definition is the same as that of the Euclidean inner product.

[0085] Dirac operator It is Hilbert space Self-adjoint operators on the Dirac operator. The expression is: ; in The Dirac γ matrix is ​​a 4×4 Hermitian matrix that satisfies the anti-commutation relation. ,in To oppose the change of child operations, it is defined as . The Minkowski metric, in its specific form, is as follows: ; It is the identity matrix. The specific form of the Dirac γ matrix is: ; ; ; For the purpose of standardization. Standardization potential. The amplitude of the Hopf bifurcation limit cycle solution obtained from step S3 Determined. Standard potential. The calculation formula is: ;in It is a unit vector. , , .

[0086] Calculate the spectral distance of spectral triples Spectral distance Defined as Hilbert space The distance between two pure states in Hilbert space. A pure state refers to a Hilbert space. The state corresponding to the unit vector in the equation. For two pure states... and spectral distance The calculation formula is: ; in For algebra The elements in. Dirac operator With elements The commutator is defined as . Let be the operator norm, defined as the largest singular value of the operator. Pure state. The calculation method is as follows: ;in Let be the unit vector corresponding to the pure state. This is the inner product operation on Hilbert space.

[0087] Operator norm The calculation method is as follows: ;in For operators The adjoint operator. It is the largest eigenvalue of the matrix.

[0088] The calculation process for spectral distance is as follows. First, the algebraic... elements in Represented as Hilbert space Linear operators on the [topic]. Then, the commutator is computed. The operator norm is then determined. Next, the constrained optimization problem is solved to find the operator norm that satisfies... All elements In the middle, making The largest element Finally, this maximum value is the spectral distance between the two pure states. .

[0089] The globally optimal scheduling solution obtained in step S4 is used as the reference pure state. Reference pure state It is the unit vector obtained by normalizing the globally optimal scheduling solution. The current actual running state is taken as the pure state to be corrected. Pure state to be corrected It is a unit vector obtained by normalizing the vector composed of the active power values ​​of all current energy nodes. (Calculation of the reference pure state) With the pure state to be corrected spectral distance between .

[0090] According to spectral distance Dynamically correct the globally optimal scheduling solution. Spectral distance. This reflects the fundamental difference between the current actual operating state and the globally optimal scheduling solution. This difference includes not only numerical differences but also differences in topological structure. (Correction quantity) Spectral distance Proportional. Correction amount The calculation formula is: ;in The correction factor is set to 0.05, and it is a dimensionless quantity. This is the globally optimal scheduling solution obtained in step S4.

[0091] Corrected scheduling solution The calculation formula is: ; The corrected scheduling solution Substitute the Chern-Simons gauge field model from step S1. Update the coupling constants of the gauge field. The updated formula is: ;in The learning rate is set to 0.01, and it is a dimensionless quantity. This is the coupling constant value before the update. This is the updated coupling constant value. The spectral distance tolerance threshold is a dimensionless positive number used to define the acceptable range of spectral distance deviation between the actual operating state and the globally optimal scheduling solution. When the spectral distance exceeds this threshold, it is determined that the system's energy flow topology has undergone a change requiring significant intervention, and the update formula will generate a corresponding adjustment amount. When the spectral distance is within this threshold, the system's topological characteristics are considered to be within an acceptable fluctuation range. The spectral distance limit is a preset dimensionless positive number, and > It represents the maximum spectral distance allowed during a single correction calculation. When the calculated spectral distance is too large, It will be cut off, in order to This parameter is included in subsequent calculations. It aims to prevent excessively large correction values ​​due to extreme operating conditions, which could lead to severe oscillations in coupling constants or scheduling solutions. It serves as a constraint parameter to ensure system stability. In practical implementation, the distribution of spectral distance under normal operating conditions is calculated based on historical operating data. It can be set to the 95th or 99th percentile of this distribution; The value can be determined by working backward from the maximum single correction amplitude allowed by the system, and it can usually be set to [value]. Several times that. Coupling constant. The update will cause the curvature tensor of the Chen-Simons gauge field to change. The changes lead to changes in the bifurcation parameters of the Hopf bifurcation in step S3. Changes occur, thus forming a complete closed-loop interaction between the Chen-Simons gauge field, the Hopf bifurcation model, the compression mapping fixed-point iteration, and the spectral triplet theory.

[0092] Verify the topological invariance of the corrected scheduling scheme. Calculate the Chern number of the Chern-Simons gauge field before and after the correction. Chern numbers are integers that describe the topological properties of gauge fields and are invariant under gauge transformations. The calculation formula is: ; If Chen Shu If the values ​​remain unchanged, it means the topology of the scheduling scheme has not changed, and the correction has not compromised the system's stability. Otherwise, the correction coefficients should be readjusted. And then correct it again until Chen Shu Remain unchanged. 2-form expression: .

[0093] The corrected scheduling solution obtained in this step will be used for subsequent hierarchical execution and multi-node cooperative control. Simultaneously, the updated coupling constants... The feedback will be sent to step S1 to dynamically adjust the parameters of the Chern-Simons gauge field. The overall process of dynamic correction of the spectral triplet in S5 and the closed-loop feedback from S5 to S1 to S3 is as follows: Figure 4 As shown.

[0094] S6. Layered execution and multi-node collaborative control of the scheduling scheme: The corrected globally optimal scheduling scheme is decomposed into three levels of control commands: campus-level control commands, microgrid-level control commands, and device-level control commands. This hierarchical control structure can balance global optimality of scheduling with rapid local response.

[0095] The specific process of decomposing control instructions is as follows: 1. The corrected globally optimal scheduling solution is a A dimensional vector, where each element corresponds to the active power value of an energy node at a time step; 2. The park-level control instructions include the power exchange plans between various microgrids and the power exchange plans between the park and the main power grid. The power values ​​of the corresponding microgrid interconnection lines and grid connection lines are extracted from the global optimal scheduling solution. 3. The microgrid-level control command contains the active power setpoint of each energy node in the microgrid, and the power value of the corresponding energy node in the microgrid is extracted from the global optimal scheduling solution; 4. The device-level control commands contain the specific operating parameters of each device, such as the inverter output power and the heat pump outlet water temperature, which are converted from the active power setpoint in the microgrid-level control commands.

[0096] The park-level control commands are executed by the park's energy management center. Located in the park's central control room, the energy management center is equipped with high-performance servers and a real-time monitoring system. The center is responsible for coordinating energy exchange between the various microgrids and developing power exchange plans between them. It also controls power exchange between the park and the main power grid, deciding whether to purchase or sell electricity from the grid based on the grid's electricity price and the park's energy supply and demand. Finally, the center monitors the park's overall carbon emissions and operating costs, calculating total carbon emissions and operating costs in real time and comparing them with target values.

[0097] Microgrid-level control commands are executed by the central controller of each microgrid. Each microgrid corresponds to a functional area within the park, such as an industrial area, commercial area, or residential area. The microgrid central controller is deployed in the power distribution room of each functional area. The microgrid central controller is responsible for decomposing the park-level control commands into control commands for each device within the microgrid, and formulating the operation plan for each energy node within the microgrid based on the park-level control commands. The microgrid central controller is responsible for coordinating the energy flow between different energy nodes within the microgrid, and dynamically adjusting the operating parameters of each energy node based on the real-time energy supply and demand situation within the microgrid. The microgrid central controller is responsible for handling local faults and abnormal situations within the microgrid. When a device within the microgrid fails, the microgrid central controller can automatically isolate the faulty device and adjust the operating parameters of other devices to maintain the stable operation of the microgrid.

[0098] Device-level control commands are executed by the local controllers of each energy node. Each energy node is equipped with a local controller, which is directly connected to the device's control system. The device's local controller is responsible for adjusting the device's operating parameters according to the microgrid-level control commands, such as adjusting the output power of the photovoltaic inverter, adjusting the charging and discharging power of the energy storage battery, and adjusting the outlet water temperature of the ground source heat pump. The device's local controller is responsible for collecting real-time operating data from the device and uploading it to the microgrid central controller. The device's local controller is responsible for executing the device's protection and control logic. When the device experiences abnormal conditions such as overcurrent, overvoltage, or overheating, the local controller can automatically shut down the device to protect its safety.

[0099] A multi-node collaborative control mechanism is established. Device-level controllers upload real-time operating data to the microgrid central controller every 15 seconds, using the Modbus TCP protocol. The microgrid central controller uploads microgrid operating data to the park's energy management center every minute, using the MQTT protocol. The park's energy management center issues updated control commands to each microgrid central controller every 5 minutes. When a device malfunctions, its local controller immediately sends a fault signal to the microgrid central controller; the fault signal has the highest transmission priority. Within 10 seconds, the microgrid central controller adjusts the operating parameters of other devices within the microgrid to maintain stable operation. The adjustment strategy prioritizes increasing the output of renewable energy generation equipment, followed by adjusting the charging and discharging power of energy storage equipment, and finally adjusting the operating parameters of multi-energy flow conversion equipment.

[0100] S7. Closed-loop feedback and adaptive update of model parameters based on real-time runtime data: Real-time operational data from all energy nodes is collected. This data is acquired by device-level controllers, aggregated by the microgrid central controller, and then uploaded to the park's energy management center. The park's energy management center preprocesses the real-time operational data, including data cleaning, data normalization, and data alignment.

[0101] The specific process of data preprocessing is as follows: 1. Data cleaning: The 3σ criterion is used to identify and remove outlier data, and linear interpolation is used to complete missing data; 2. Data Normalization: Normalize all data to the interval [0,1]. The normalization formula is: ; in These are the original data values. and These are the minimum and maximum values ​​for this data type, respectively. 3. Data alignment: Align all data to a uniform timeline at 1-minute intervals.

[0102] The deviation between the actual execution effect of the scheduling plan and the expected target is calculated. Examples of deviation indicators include total carbon emission deviation, total operating cost deviation, renewable energy integration rate deviation, voltage deviation, and frequency deviation.

[0103] Total carbon emissions deviation The calculation formula is: ; in This represents the actual total carbon emissions. The target is the total carbon emissions.

[0104] Total operating cost deviation The calculation formula is: ; in This represents the actual total operating cost. The target is the total operating cost.

[0105] Deviation in renewable energy absorption rate The calculation formula is: ; in The actual renewable energy absorption rate is equal to the actual renewable energy power generation divided by the total renewable energy power generation. The target is the renewable energy integration rate.

[0106] Voltage deviation The calculation formula is: ; in For the first The actual voltage of each energy node. For the first The rated voltage of each energy node.

[0107] Frequency deviation The calculation formula is: ;in This is the actual frequency of the system. The system's rated frequency is 50 Hz.

[0108] If the total carbon emission deviation exceeds 5% or the total operating cost deviation exceeds 5%, the adaptive update mechanism for model parameters will be triggered. Otherwise, the current scheduling scheme will continue to be executed until the next scheduling cycle.

[0109] The adaptive update process for model parameters is as follows: Real-time running data is added to the historical running dataset, which is updated on a rolling basis, retaining running data from the most recent 365 days. The empirical distribution of the sub-Bruker uncertainty set in step S2 is then updated. With uncertainty radius , experience distribution The uncertainty radius was recalculated based on updated historical operating data. The variance of the updated sample data is recalculated. The bifurcation parameters of the Hopf bifurcation model in step S3 are updated using an incremental learning method. The specific process of incremental learning is as follows: 1. Add new running data points to the training set; 2. Calculate the error between the new data point and the current limit cycle solution; 3. Update the bifurcation parameters using stochastic gradient descent. The updated formula is: ;in The learning rate is set to 0.0001.

[0110] Update the energy levels of the Chern-Simons gauge field in step S1 .energy level This reflects the degree of quantization of the gauge field; a larger value indicates a stronger constraint on energy flow. Energy level The update formula is: ; in The learning rate is set to 0.005, and it is a dimensionless quantity. The energy level value is the value before the update. This is the updated energy level value.

[0111] In some embodiments, the mapping established by this scheme is not a simple analogy, but rather a derivation of the intrinsic relationship between gauge fields and physical quantities of the power system based on electric-magnetic duality. In the campus power network, active power... The corresponding electric field energy flow and reactive power in an electromagnetic field The spatiotemporal distributions of the corresponding magnetic field and energy flux jointly determine the energy flux topology of the system. According to the electromagnetic duality principle, the electric and magnetic fields can be unified by... Standard potential Description, where the scalar potential Corresponding electric field, vector potential Corresponding magnetic field. Translating this structure to a comprehensive energy system: specifying the active power of each energy node. Constituting scalar potential The unit is Reactive power Constitutes spatial vector potential And supplement the time component. To describe the time-varying rate of reactive power, the complete gauge potential is obtained. The unit is The transmission loss coefficient corresponds to the coupling constant of the gauge field. This determines the interaction strength of the gauge field itself. This mapping based on electromagnetic duality is not a formal substitution, but rather embeds Kirchhoff's laws and multi-energy flow transport equations of power networks into the gauge theory framework, making the Chern-Simons action... It can characterize the overall orderliness of the energy flow in the system. The technical advantage of this mapping is that topological defects in energy flow that traditional scheduling methods based on algebraic equations or power balance cannot detect can be addressed using the curvature tensor of the Chern-Simons gauge field. Direct identification. Curvature tensor The non-zero components reveal the non-uniformity of energy flux distribution and the potential "kinks," when When an abnormal peak occurs in a certain region, it signifies a strong coupling distortion in the spatial distribution of active and reactive power in that region, indicating that multi-energy flow conversion equipment may be entering an unstable operating region. Furthermore, topological invariants—Chen numbers. —It provides global topology characteristics that traditional methods cannot describe: as long as The overall topology of the system's energy flow (such as the number of energy flow loops) remains stable regardless of adjustments to the scheduling scheme; once... A transition occurs when the system undergoes a topological phase transition, necessitating correction. This global perspective endows the scheduling scheme with topology awareness, enabling it to prevent energy flow topology collapse while ensuring economic efficiency and low carbon emissions.

[0112] In some embodiments, the data flow and control flow of the closed-loop interaction mechanism are as follows: The Chern-Simons gauge field constructed by S1 provides the curvature tensor. and coupling constant S3 extraction Normalized modulus length as Hopf bifurcation parameter and output the limiting cycle amplitude. S4 is updated every 10 iterations in the compression mapping fixed-point iteration. ,at the same time The changes adjust the multi-energy flow coupling constraint boundary in real time, forming a bidirectional interaction between S3 and S4; S5 utilizes the limit cycle amplitude. Constructing the Dirac operator normative potential Calculate the spectral distance between the current running state and the optimal reference state. The scheduling solution is corrected accordingly, and the spectral distance is fed back to S1 to update the coupling constant. This changes the curvature. This closed-loop approach closes the entire loop. This adaptive characteristic of the closed loop is something that traditional open-loop scheduling methods do not possess: traditional methods solve and execute the scheduling plan all at once under a given set of uncertainties, and do not have the ability to dynamically adjust model parameters according to the actual energy flow topology; while this scheme, through parameter transfer of four theoretical frameworks, enables the scheduling decision to continuously perceive and adapt to the nonlinear dynamic evolution of the system, maintaining topological stability while ensuring global optimality.

[0113] In some embodiments, the discretization calculation method of the Chern-Simons action: original action For a three-dimensional manifold The continuous integrals over the manifold are used, but the actual system contains only a finite number of discrete energy nodes. Therefore, Voronoi decomposition is employed to divide the manifold... It is divided into regions centered around each energy node. For the first... Each energy node defines its Voronoi region. This region consists of all points whose spatiotemporal distance to this node is less than their spatiotemporal distance to other nodes. The spatiotemporal distance metric uses Euclidean distance weighting, with weighting factors... Used to balance spatial and temporal scales, defined as ,in Values .area spacetime volume Estimated by Monte Carlo sampling: In Uniformly generated within the bounding box A random point, count the number of points that fall into The ratio of points multiplied by the total volume of the bounding box yields the result. The unit is .

[0114] In the region Inside, assume gauge potential Its outer derivative changes gradually and can be used at nodes. If the value at point is approximate, then the action is discretized as follows: ; In the formula, For nodes The value of the gauge potential at a given time. The approximation of the exterior differential at that point is calculated from the differences between adjacent time points and adjacent nodes. For example... The components in the time direction can be represented by the central difference. The spatial orientation is similar. Trace operation Perform this process on the matrix formed by the individual components. Through the above discretization, It becomes a scalar that can be directly calculated from the active and reactive power and transmission loss coefficient of each node, and is used to evaluate the overall energy flow orderliness of the scheduling scheme.

[0115] In some embodiments, the convergence proof of the compression mapping iteration is as follows: when the device starts and stops state variables From binary - Relaxation as a continuous variable Meanwhile, when the start / stop count constraint is expressed linearly, the objective function... Transform into continuous variables Strictly convex functions, constraint sets It becomes a convex polyhedron. At this point, the compression mapping operator... Defined as projecting any feasible solution onto a unique optimal solution, it can be proven that this solution satisfies compressibility. Specifically, the objective function... The gradient is Its Lipschitz constant This can be estimated by solving a semidefinite programming problem: ,in for The Hessian matrix, due to For a quadratic weighted sum, It is a constant matrix. Let it be its largest eigenvalue. After relaxation, the constraint matrix is ​​full rank. Combining the non-extensibility of the projection operator with the strong convexity of the objective function, we can obtain that there exists a constant. ( (for strong punch quantity), making For any Established. The distance in the formula... It is the Euclidean distance. Therefore For the compression mapping, Banach's fixed-point theorem guarantees that the iteration converges to a unique optimal solution.

[0116] In some embodiments, the spectral distance is approximated by using infinite-dimensional operator algebras. elements in Parameterization to a finite-dimensional subspace: Let ,in For Hilbert space The middle corresponds to the first Each node The rank-one projection operator of active power over a given time period Let be the scalar parameters to be optimized. Then, commutate the subnorm constraints. It can be transformed into a vector The linear matrix inequality (LMI) constraint, where 1 in the norm constraint is the normalization threshold, is achieved by... and Pre-normalization is implemented. Using semidefinite programming relaxation, the spectral distance is approximated as: ; ; in , Let be the unit vector corresponding to the pure state. The affine matrix function related to the commutative subnorm has the following specific form: The semidefinite programming problem described above can be solved efficiently using a standard solver (such as SDPT3), with computation time on the order of seconds, meeting the real-time requirements of online correction.

[0117] In some embodiments, the parameter sensitivity analysis and tuning method is as follows: based on historical data, the first 80% of the days are divided as the training set and the last 20% as the validation set, and a strategy combining grid search and Bayesian optimization is used for tuning. The range of key parameter values ​​and the final tuned values ​​are shown in the table below.

[0118] The parameter tuning objective was to minimize the weighted sum of total carbon emissions and total operating costs on the validation set. Results show that the spectral distance correction coefficient... This parameter is most sensitive to performance impact: too small a value results in insufficient correction and poor system robustness; too large a value leads to overcorrection, significantly increasing operating costs. It is recommended to use this as the primary adjustment parameter, while other parameters can maintain robustness within a wider range. In practical applications, the above process can be used to customize the tuning for specific industrial parks.

[0119] The updated model parameters are fed back to step S2. The scheduling optimization process for the next scheduling cycle begins. The entire system forms a complete closed loop, capable of continuously adapting to changes in the operating status of the zero-carbon park's energy system and continuously optimizing the performance of the scheduling scheme.

[0120] In some embodiments, when constructing the objective function for scheduling optimization in step S4, the Chern-Simons action obtained in step S1 is used... Incorporating energy flow order as an evaluation index into the objective function enables energy levels to... The update and scheduling decision form a closed loop. Specifically, the original objective function... Expanded to: ; in, The energy flow order weighting coefficient is a dimensionless quantity with a value range of [value range missing]. It is recommended to set the initial value to . The smaller the value of the Chern-Simons action calculated in step S1, the more orderly the energy flow of the energy system and the better the topological consistency of the scheduling scheme.

[0121] The numerical values ​​are calculated using the method described in step S1. When the actual system contains only a finite number of discrete energy nodes, the Voronoi decomposition discretization method is used for calculation, i.e., the three-dimensional manifold... Divided into Voronoi regions centered on each energy node. The action is discretely represented as the sum of contributions from each region: ; By introducing in the objective function Item, energy level The update and scheduling decisions form a complete closed loop: Step S7 updates the energy level based on the total carbon emission deviation of the actual operating data. , Changes directly affect The value of the objective function is then changed. The optimization results automatically favor the scheme with higher energy flow order in the next scheduling cycle's globally optimal scheduling solution. When the total carbon emission deviation is large, Increase The weights in the objective function are increased accordingly, and scheduling optimization will place greater emphasis on the orderliness of energy flow, which helps to suppress additional carbon emissions caused by disordered energy flow; when the carbon emission deviation is within an acceptable range, To maintain stability, the system balances carbon emissions, operating costs, and energy flow order.

[0122] The embodiments described above are for illustrative purposes only and are not intended to limit the invention. Therefore, any changes in numerical values ​​or substitutions of equivalent elements should still fall within the scope of this invention.

[0123] The above detailed description will enable those skilled in the art to understand that the present invention can indeed achieve the aforementioned objectives and has complied with the provisions of the Patent Law.

Claims

1. A method for constructing and applying a low-carbon scheduling algorithm model for a zero-carbon industrial park energy system, characterized in that, include: Step S1. Collect the operating data of each energy node in the park, construct a spatiotemporal topology map, map the spatiotemporal topology map to a Chern-Simons gauge field, map the transmission loss coefficient between energy nodes to the coupling constant of the Chern-Simons gauge field, and calculate the curvature tensor of the Chern-Simons gauge field. Step S2. Perform multi-timescale uncertainty quantification on renewable energy output and load demand, and merge the uncertainty boundaries under each timescale to obtain a unified fuzzy boundary of energy supply and demand across multiple timescales. Step S3. Extract historical multi-energy flow coupling operating condition data, use the modulus of the curvature tensor as the bifurcation parameter, establish a Hopf bifurcation model of multi-energy flow coupling, determine the critical bifurcation parameter, and solve the amplitude and phase of the limit cycle by fitting historical data; Step S4. With minimizing total carbon emissions and total operating costs as the scheduling objective, under the fuzzy boundary of energy supply and demand, equipment operation constraints, and multi-energy flow coupling constraints represented by the limit cycle, the compression mapping operator on the scheduling solution space is iterated at fixed points to solve for the global optimal scheduling solution. During the iteration process, the bifurcation parameters are dynamically updated according to the changes in the scheduling objective function value, so that the amplitude of the limit cycle is changed to adjust the boundary of the multi-energy flow coupling constraints. Step S5. Construct a spectral triplet of non-commutative geometry, wherein the gauge potential of the Dirac operator is determined by the amplitude of the limit cycle. Using the global optimal scheduling solution as the reference pure state and the current actual running state as the pure state to be corrected, calculate the spectral distance between the two. Use the spectral distance to correct the global optimal scheduling solution to obtain the corrected scheduling solution. Update the coupling constant of the Chern-Simons gauge field according to the spectral distance to recalculate the curvature tensor and return to step S3 to form a closed-loop iteration.

2. The method for constructing and applying a low-carbon scheduling algorithm model for a zero-carbon industrial park energy system according to claim 1, characterized in that, Step S1, which maps the spatiotemporal topology graph to a Chern-Simons gauge field, includes: mapping the active power value of each energy node to the scalar potential of the Chern-Simons gauge field, mapping the reactive power value to the vector potential, mapping the transmission loss coefficient between energy nodes to the coupling constant, spanning a three-dimensional manifold from the spatiotemporal coordinates of all energy nodes, constructing the Chern-Simons action on the three-dimensional manifold, and calculating the curvature tensor.

3. The method for constructing and applying a low-carbon scheduling algorithm model for a zero-carbon industrial park energy system according to claim 1, characterized in that, The multi-timescale uncertainty quantification in step S2 includes: dividing the timescale into ultra-short-term, short-term, and medium-to-long-term timescales; constructing an empirical distribution and calculating the uncertainty radius for each timescale using historical data; constructing an uncertainty set using a biblical optimization based on Wasserstein distance; solving for the uncertainty boundaries of renewable energy output and load demand at each timescale; and then taking the intersection of the ultra-short-term uncertainty boundary and the medium-to-long-term uncertainty boundary to obtain the unified energy supply and demand fuzzy boundary across the multiple timescales.

4. The method for constructing and applying a low-carbon scheduling algorithm model for a zero-carbon industrial park energy system according to claim 1, characterized in that, Step S3, which involves solving for the amplitude and phase of the limit cycle, includes: dividing the magnitude of the curvature tensor by the maximum value of that magnitude in historical data to obtain a normalized bifurcation parameter; when the bifurcation parameter is greater than the critical bifurcation parameter, the amplitude of the limit cycle is taken as the square root of the difference between the bifurcation parameter and the critical bifurcation parameter, and the phase of the limit cycle is obtained by fitting historical multi-energy flow coupling data.

5. The method for constructing and applying a low-carbon scheduling algorithm model for a zero-carbon industrial park energy system according to claim 1, characterized in that, Step S4, the fixed-point iteration of the compression mapping operator, includes: defining the compression mapping operator as the scheduling solution that minimizes the scheduling objective function under all constraints; taking the rated operating point of each energy node as the initial scheduling solution; repeatedly applying the compression mapping operator until the distance between the scheduling solutions obtained in two adjacent iterations is less than a preset threshold; during the iteration process, after each specified number of iterations, updating the bifurcation parameters using the difference between the objective function value corresponding to the current scheduling solution and the scheduling solution of the previous iteration.

6. The method for constructing and applying a low-carbon scheduling algorithm model for a zero-carbon industrial park energy system according to claim 1, characterized in that, Step S5, constructing the spectral triplet, includes: generating C from observables of the park's energy system. Algebraically, the vector space formed by all possible scheduling solutions is taken as the Hilbert space, and the amplitude of the limit cycle is multiplied by a unit vector to obtain the gauge potential of the Dirac operator; the spectral distance is obtained by solving for the maximum value of the difference between the expectations of two pure states over all algebraic elements that satisfy the commutator norm of the Dirac operator not greater than one.

7. The method for constructing and applying a low-carbon scheduling algorithm model for a zero-carbon industrial park energy system according to claim 1, characterized in that, Step S5, which involves correcting the global optimal scheduling solution using spectral distance, includes: multiplying a preset correction coefficient, the spectral distance, and the global optimal scheduling solution to obtain a correction amount, and then adding the correction amount to the global optimal scheduling solution to obtain the corrected scheduling solution; updating the coupling constant includes: multiplying the current coupling constant by a factor and adding the product of a preset learning rate and the spectral distance to obtain the updated coupling constant.

8. The method for constructing and applying a low-carbon scheduling algorithm model for a zero-carbon industrial park energy system according to claim 1, characterized in that, The method also includes step S6: decomposing the corrected scheduling into park-level control commands, microgrid-level control commands, and device-level control commands; the park-level control commands include the power exchange plan between microgrids and the power exchange plan between the park and the main power grid; the microgrid-level control commands include the active power setpoint of each energy node in the microgrid; and the device-level control commands include the operating parameters of each device.

9. The method for constructing and applying a low-carbon scheduling algorithm model for a zero-carbon industrial park energy system according to claim 1, characterized in that, It also includes step S7: collecting real-time operating data of each energy node, calculating the deviation of the actual total carbon emissions and total operating costs relative to the scheduling target, and performing adaptive update of model parameters when the deviation of total carbon emissions or total operating costs exceeds a preset threshold. The adaptive update of the model parameters includes: updating the empirical distribution and the uncertainty radius, updating the bifurcation parameters of the Hopf bifurcation model using incremental learning, and updating the energy levels of the Chern-Simons gauge field based on the total carbon emission deviation, wherein the energy levels are set when constructing the Chern-Simons gauge field.

10. The method for constructing and applying a low-carbon scheduling algorithm model for a zero-carbon industrial park energy system according to any one of claims 1 to 9, characterized in that, Step S5 further includes topological stability verification: calculating the Chern number of the Chern-Simons gauge field before and after correction, wherein the Chern number is a topological invariant describing the topological properties of the gauge field; when the Chern number changes, adjusting the correction coefficients and re-performing the correction until the Chern number remains unchanged.

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