A transient stability constrained optimal power flow method based on semi-definite programming convex relaxation

Abstract

A transient stability constraint-based optimal power flow method based on semidefinite programming and convex relaxation includes the following steps: Step 1: Establish a Gaussian mixture model (GMM) for wind power output prediction based on historical wind speed and direction data, generate wind power output scenarios using Latin hypercube sampling (LHS), and reduce the scenarios using K-means++ clustering to obtain the final scenario set; Step 2: Based on the GMM constructed in Step 1 and the final scenario set, establish a transient stability optimal power flow model (TSCOPF), obtain the trajectory sensitivity matrix using the trajectory sensitivity method (TST), and construct linear inequality constraints based on the trajectory sensitivity matrix; Step 3: Reconstruct the model including the above linear inequality constraints into a semidefinite programming form (SDP), add a penalty term based on the matrix second-order minor to the objective function, and perform penalized SDP relaxation; Step 4: Solve using the MOSEK solver to obtain feasible power flow and unit output schemes.

Description

Technical Field

[0001] This invention relates to the fields of power systems and new energy technologies, and particularly to transient stability analysis of power systems, establishment of wind power output models, and semidefinite programming convex relaxation calculation techniques. Specifically, it relates to a method for solving the optimal power flow problem under transient stability constraints based on semidefinite programming convex relaxation. Background Technology

[0002] Current power generation relies on fossil fuels, but fossil fuel reserves are limited, and carbon emissions from thermal power generation cause environmental pollution. In contrast, the global theoretical reserves of wind energy are about 10 times the current electricity demand. Wind power is clean and safe, and is receiving increasing attention from countries around the world. However, wind power output is intermittent and random, which introduces uncertainties into the operation and control of the power system.

[0003] Patent document CN202311837330A discloses an optimal power flow model and calculation method considering the transient stability constraints of renewable energy access. The method includes: establishing an optimal power flow model considering the uncertainty of renewable energy; constructing transient stability constraints based on a single-machine infinite bus system and embedding them into the optimal power flow model to form a TSCOPF model; applying semidefinite programming relaxation to convexize the TSCOPF model; establishing a joint probability distribution function of wind-solar coupled output power, and using Monte Carlo simulation sampling and K-means clustering algorithm for scene reduction; and combining Benders decomposition algorithm and branch-bound algorithm to refine the convexized model. The patent document with application publication number CN202311795526A discloses a method for solving the optimal power flow solution with probabilistic transient stability constraints that takes into account wind load uncertainty. This method includes: establishing a probability distribution model of wind power output and load injection; performing equivalent analysis on the transient stability constraints based on the single-machine equivalent method, transforming them into algebraic transient stability constraints; establishing an optimal power flow model with probabilistic transient stability constraints that takes into account wind load uncertainty; using sensitivity analysis based on the digital characteristics of the wind load probability distribution model to perform a deterministic transformation of the probabilistic constraints; and solving the deterministically transformed model based on an improved semidefinite programming relaxation and sequential quadratic programming algorithm. However, neither of these methods introduces a penalty term in the convex relaxation framework, making it difficult to guarantee the physical feasibility of the relaxed solution. Furthermore, the processing of transient stability constraints contains simplification errors, failing to provide a high-precision optimal power flow solution that satisfies the transient stability constraints.

[0004] Therefore, the applicant proposes a research method for optimal power flow under transient stability constraints based on semidefinite programming and convex relaxation, considering the total power generation cost, and finding the optimal output scheme of the computer group under the premise of ensuring the transient stability of the power system with wind power integration. Summary of the Invention

[0005] The purpose of this invention is to address the technical shortcomings of existing transient stability-constrained optimal power flow calculation methods that consider renewable energy access. These shortcomings include the failure to introduce penalty terms into the convex relaxation framework and the oversimplification of transient stability constraint processing. Consequently, these methods suffer from difficulties in guaranteeing the physical feasibility of relaxed solutions, low solution accuracy, and the inability to provide high-precision scheduling schemes. This invention provides a transient stability-constrained optimal power flow calculation method based on semidefinite programming convex relaxation. This method can improve the physical feasibility of relaxed solutions and the accuracy of optimal power flow calculation while ensuring the transient stability of the wind power access system.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A study on transient stability constraints for optimal power flow based on definite programming convex relaxation includes the following steps: Step 1: Based on historical data of wind speed and direction, establish a Gaussian Mixture Model (GMM) for wind power output prediction. Combine this with Latin Hypercube Sampling (LHS) to generate wind power output scenarios. Use K-means++ clustering to reduce the scenarios and obtain the final scenario set. Step 2: Based on the GMM constructed in Step 1 and the final scenario set, establish a Transient Stability Constrained Optimal Power Flow (TSCOPF) model, use the Trajectory Sensitivity Technique (TST) to obtain the trajectory sensitivity matrix, and construct linear inequality constraints based on the trajectory sensitivity matrix. Step 3: Reconstruct the model, which includes the linear inequality constraints mentioned above, into a semidefinite programming (SDP) form. Add a penalty term based on the second-order submatrix of the matrix to the objective function to perform penalized SDP relaxation. Step 4: Solve using the MOSEK solver.

[0007] Step 1 specifically includes the following sub-steps: Step 1-1: Establish a GMM for wind power output prediction based on historical data of wind speed and wind direction.

[0008] Get continuous Historical data on wind speed and direction for a given period, wind speed sequence Wind direction sequence and the corresponding measured wind power output sequence ,in Regarding wind direction Perform a sine-cosine mapping to obtain two-dimensional loop variables. ,form 3D feature sample set ,in , For historical sample size, Establishing a GMM for wind power output forecasting: (1); In the formula: For the sample The joint probability density function; The total number of Gaussian components; For the first Gaussian component mixing weights , ; , The first The mean vector and covariance matrix of each Gaussian component; For the first The probability density function of Gaussian components.

[0009] Step 1-2: Divide the probability interval Divided into Each interval Wind power output scenarios are generated using LHS: (2); (3); In the formula: In the first The interval is the first The original samples obtained from sampling at each time period; For wind power output quantile function; For the first The sample scenario in the first The probability level for each time period; , The first Wind speed and direction at different times; For the generated scene set, containing A scene vector; For scene vectors with spatiotemporal correlation, .

[0010] Steps 1-3: Use K-means++ clustering to reduce the number of scenes, resulting in the final scene set: (4); In the formula: This is the final set of scenes after reduction; For the first The centroid of the nth cluster class, i.e., the nth A typical scenario; For the first The weight of the typical scenario, i.e., belonging to the first... The ratio of the number of LHS samples in each cluster to the total number of samples; To reduce the number of scenes, .

[0011] Step 2 specifically includes the following sub-steps: Step 2-1: Establish the TSCOPF model.

[0012] 1) Objective function: (5); In the formula: This refers to the collection of all conventional generators in the system. For nodes The active power of the generator; , , These are the quadratic coefficient, primary coefficient, and constant term of the generator cost, respectively.

[0013] 2) Static power flow equations: (6); (7); In the formula: , They are nodes The injected active and reactive power; For nodes The reactive power of the generator; , They are nodes The active and reactive power output of the load; 3) Operating limits: (8); (9); In the formula: , They are nodes The lower and upper limits of the generator's active power; , They are nodes The lower and upper limits of voltage.

[0014] 4) Swing equation: (10); (11); In the formula: , The first Rotor angle and angular velocity of a generator; Synchronous angular velocity; , These are the inertial time constant and the damping coefficient, respectively. , The first The mechanical power and electromagnetic power of the generator; This represents the rotor angle vector for all generators.

[0015] 5) Transient stability constraints: (12); In the formula: This refers to the fault clearance time. , The first Taiwan, No. A generator in The rotor angle at any given moment; As the critical relative angle, take rad.

[0016] Step 2-2: Obtain the sensitivity matrix based on TST: (13); (14); In the formula: Rotor angular vector For control vector Matrix; relative angles exist The sensitivity row vector at time step.

[0017] Step 2-3: Construct linear inequality constraints based on the sensitivity matrix: (15); (16); Step 3 specifically includes the following sub-steps: Step 3-1: Reconstruct the TSCOPF model, which includes the objective function, static power flow equations, running limits, swing equations, and the aforementioned linear inequality constraints, into a semidefinite programming form: For all nodes Construct the nodal voltage outer product matrix : (17); In the formula: The total number of nodes; , They are nodes The real and imaginary parts of voltage; It is the voltage outer product matrix of all nodes, containing all quadratic forms of voltage.

[0018] Non-convex rank 1 constraint Relaxation is semidefinite; reconstruct the objective function as a function of... Affine function To obtain the standard SDP: (18); In the formula: Representation matrix It is a positive semi-definite matrix. , These are the generator's active power and its lower and upper limits, respectively; , These are the lower and upper limits of the voltage, respectively.

[0019] Step 3-2: Add a penalty term based on the second-order minor of the matrix to the objective function: (19); In the formula: for all Master-subordinate determinant; The penalty coefficient increases adaptively with iteration. This formula maintains convexity while driving the solution towards rank 1, thus reducing the relaxation gap.

[0020] Step 4: Use sparse chordal decomposition technology to reduce the dimensionality of the penalized semidefinite programming model, and perform iterative calculation by adaptively updating the penalty coefficients. After the iteration is completed, enter the rank-1 repair module to complete the repair of semidefinite constraints. Finally, use the MOSEK solver to output the scheduling scheme.

[0021] Compared with the prior art, the present invention has the following technical effects: 1) To address the computational challenges of massive scenarios arising from the uncertainty of new energy output, this invention (corresponding to step 1) employs a typical scenario generation and clustering reduction method based on a combination of wind speed-wind direction GMM and LHS. After reduction, only a small number of scenarios need to be retained (e.g., This approach can cover over 95% of the probability space in typical scenarios (as defined in the sample). While preserving the core statistical characteristics of wind power output, it significantly reduces the scale of stochastic optimization and substantially improves the computational efficiency of subsequent optimal power flow. 2) To address the technical problem of low accuracy caused by oversimplification of transient stability constraint processing in existing technologies (such as single-machine equivalence), this invention (corresponding to step 2) introduces a linearized inequality constraint constructed based on the Trajectory Sensitivity Method (TST). This method effectively avoids the errors caused by equivalent analysis and can strictly satisfy the stability criterion of "any generator relative rotor angle difference ≤ 180°" under the N-1 fault set in a few optimizations. It can provide a high-precision transient stability scheduling scheme without repeated iterative verification. 3) To address the technical deficiency of existing convex relaxation frameworks, which suffer from poor physical feasibility of relaxation solutions due to the lack of a penalty term, this invention (corresponding to steps 3 and 4) proposes a semidefinite programming (SDP) relaxation method based on a second-order submatrix penalty term. This method successfully transforms the non-convex TSCOPF model into a convex optimization problem. The penalty term effectively ensures that the relaxation result satisfies the non-convex rank-1 constraint, ensuring that the unit output scheme obtained after iteration by a solver (such as MOSEK) not only has global optimality but also physical feasibility for implementation in actual power systems. Attached Figure Description

[0022] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a flowchart of a method for studying transient stability constraints and optimal power flow based on semidefinite programming with convex relaxation. Figure 2 This is a schematic diagram of the IEEE 39-node system in an example of the present invention; Figure 3 This is a relative rotor angle diagram of the IEEE 39-node system in an example of the present invention when a three-phase short-circuit fault occurs at branch 28-29; Figure 4 The relative rotor angle diagram is calculated by the IEEE 39-bus system in the example of this invention using the proposed optimal power flow optimization method based on semidefinite programming convex relaxation and transient stability constraints. Figure 5 This is a flowchart of the algorithm for solving TSCOPF in this invention. Detailed Implementation

[0023] like Figure 1 As shown, a method for studying transient stability constraints and optimal power flow based on semidefinite programming convex relaxation includes the following steps: Step 1: Based on historical data of wind speed and direction, establish a Gaussian Mixture Model (GMM) for wind power output prediction, combine it with Latin Hypercube Sampling (LHS) to generate wind power output scenarios, and use K-means++ clustering to reduce the scenarios. Step 2: Based on the GMM constructed in Step 1, establish a Transient Stability Constrained Optimal Power Flow (TSCOPF) model, use the Trajectory Sensitivity Technique (TST) to obtain the trajectory sensitivity matrix, and construct linear inequality constraints based on the trajectory sensitivity matrix. Step 3: Reconstruct the model into a semidefinite programming (SDP) form, add a penalty term based on matrix second-order minors to the objective function, and perform penalized SDP relaxation; Step 4: Solve using the MOSEK solver.

[0024] In step 1, a GMM for wind power output prediction is established based on historical wind speed and direction data. Wind power output scenarios are generated by combining LHS data, and K-means++ clustering is used to reduce the number of scenarios. The specific process is as follows: Step 1-1: Establish a GMM for wind power output prediction based on historical data of wind speed and wind direction.

[0025] Get continuous Historical data on wind speed and direction for a given period, wind speed sequence Wind direction sequence and the corresponding measured wind power output sequence ,in Regarding wind direction Perform a sine-cosine mapping to obtain two-dimensional loop variables. ,form 3D feature sample set ,in , For historical sample size, Establishing a GMM for wind power output forecasting: (1); In the formula: For the sample The joint probability density function; The total number of Gaussian components. For the first Gaussian component mixing weights , ; , The first The mean vector and covariance matrix of each Gaussian component; For the first The probability density function of Gaussian components.

[0026] Step 1-2: Divide the probability interval Divided into Each interval Wind power output scenarios are generated using LHS: (2); (3); In the formula: In the first The interval is the first The original samples obtained from sampling at each time period; For wind power output quantile function; For the first The sample scenario in the first The probability level for each time period; , The first Wind speed and direction at different times; For the generated scene set, containing A scene vector; For scene vectors with spatiotemporal correlation, .

[0027] Steps 1-3: Use K-means++ clustering to reduce the number of scenes, resulting in the final scene set: (4); In the formula: This is the final set of scenes after reduction; For the first The centroid of the nth cluster class, i.e., the nth A typical scenario; For the first The weight of the typical scenario, i.e., belonging to the first... The ratio of the number of LHS samples in each cluster to the total number of samples; To reduce the number of scenes, .

[0028] In step 2, a TSCOPF model is established, the trajectory sensitivity matrix is ​​obtained using TST, and linear inequality constraints are constructed based on the trajectory sensitivity matrix. The specific process is as follows: Step 2-1: Establish the TSCOPF model.

[0029] 1) Objective function: (5); In the formula: This refers to the collection of all conventional generators in the system. For nodes The active power of the generator; , , These are the quadratic coefficient, primary coefficient, and constant term of the generator cost, respectively.

[0030] 2) Static power flow equations: (6); (7); In the formula: , They are nodes The injected active and reactive power; For nodes The reactive power of the generator; , They are nodes The active and reactive power output of the load; 3) Operating limits: (8); (9); In the formula: , They are nodes The lower and upper limits of the generator's active power; , They are nodes The lower and upper limits of voltage.

[0031] 4) Swing equation: (10); (11); In the formula: , The first Rotor angle and angular velocity of a generator; Synchronous angular velocity; , These are the inertial time constant and the damping coefficient, respectively. , The first The mechanical power and electromagnetic power of the generator; This represents the rotor angle vector for all generators.

[0032] 5) Transient stability constraints: (12); In the formula: This refers to the fault clearance time. , The first Taiwan, No. A generator in The rotor angle at any given moment; As the critical relative angle, take rad.

[0033] Step 2-2: Obtain the sensitivity matrix based on TST: (13); (14); In the formula: Rotor angular vector For control vector Matrix; relative angles exist The sensitivity row vector at time step.

[0034] Step 2-3: Construct linear inequality constraints based on the sensitivity matrix: (15); (16); In step 3, the model is reconstructed into a semidefinite programming form, and a penalty term based on matrix second-order minors is added to the objective function to perform penalized SDP relaxation. The specific process is as follows: Step 3-1: Reconstruct the model into a semidefinite programming form: For all nodes Construct the nodal voltage outer product matrix : (17); In the formula: The total number of nodes; , They are nodes The real and imaginary parts of voltage; It is the voltage outer product matrix of all nodes, containing all quadratic forms of voltage.

[0035] Non-convex rank 1 constraint Relaxation is semidefinite; reconstruct the objective function as a function of... Affine function To obtain the standard SDP: (18); In the formula: Representation matrix It is a positive semi-definite matrix. , These are the generator's active power and its lower and upper limits, respectively; , These are the lower and upper limits of the voltage, respectively.

[0036] Step 3-2: Add a penalty term based on the second-order minor of the matrix to the objective function: (19); In the formula: for all Master-subordinate determinant; The penalty coefficient increases adaptively with iteration. This formula maintains convexity while driving the solution towards rank 1, thus reducing the relaxation gap.

[0037] In step 4, the penalized semidefinite programming model is solved using the MOSEK solver.

[0038] Step 4-1: Initialize parameters and set penalty coefficient Maximum number of iterations ; Step 4-2: Check the sum of the absolute values ​​of all principal determinants. ,like If the iteration fails, stop; otherwise, increase the penalty coefficient, making... Continue iterating; among them, The absolute value of the determinant of the master matrix; The rank criterion tolerance; Step 4-3: Output the optimal solution ,right Eigenvalue decomposition is performed, and the principal eigenvectors are used to recover the voltage phasors, yielding feasible power flow and unit output schemes; among which... These are the optimal matrix variables after SDP relaxation; The optimal control variable after SDP relaxation.

[0039] Example: This invention is based on the IEEE 39-node system, which contains 39 buses and 10 synchronous generators. In this example, the synchronous generator at node 32 is replaced with a wind farm, with a total installed capacity of approximately 6150MW. The synchronous generator uses a fourth-order transient model, and the state variables include rotor angle. angular velocity Direct-axis transient potential and cross-axis transient potential This method can accurately characterize the electromechanical transient process after a fault. The load adopts a constant power model with a power factor of 0.85. The load level fluctuates continuously in 5% increments within the 80%–120% range. System transient stability is determined by the relative rotor angles of any two generators, with a stability threshold set to 180°. To verify the effectiveness of this invention and its adaptability to wind power uncertainties, a 600MW equivalent wind farm is connected at node 32. The wind turbine parameters are set as follows: cut-in wind speed 4 m / s, rated wind speed 16 m / s, and cut-out wind speed 25 m / s. The prediction time domain is... Hour.

[0040] An electromechanical transient model incorporating wind power was established on the MATLAB R2018b / Simscape Electrical platform. The anticipated fault settings are shown in Table 1, with a three-phase ground fault occurring at the beginning of branch 28-29. First, conventional optimal power flow and time-domain simulation calculations were performed. At the instant the fault was cleared, the maximum relative rotor angle difference between the generators exceeded 200°, exceeding the 180° stability threshold, causing the system to experience initial instability. The waveform is shown in [Figure 1]. Figure 3 Subsequently, using the method proposed in this invention, 800 spatiotemporally relevant wind power scenarios are first generated by combining wind speed-direction joint GMM with LHS. K-means++ clustering is then used to reduce these scenarios to 20 typical scenarios, which are then weighted probabilities using a Gaussian mixture distribution. Based on this, an equivalent transient stability constraint optimal power flow model is established, with the objective function being the minimum expected generation cost. The rotor angle constraint after a fault is then linearized using TST, and a convex optimization model is formed through penalized semidefinite relaxation. The penalty coefficient is adaptively increased and initially set to 10. -3 After iterating using the MOSEK solver, the obtained generator active and reactive power values ​​and node voltage amplitudes are then used for a 0-10s fault simulation. The optimized actual output of each generator under a typical high-wind power processing scenario is shown in Table 2. The maximum relative rotor angle difference between generators is reduced to within 140°, and the system remains transiently stable. The waveforms are shown in Table 2. Figure 4 .

[0041] Table 1

[0042] Table 2

[0043] This embodiment demonstrates that the proposed method can complete the entire process from modeling to constraint linearization, solution, and verification at a 39-node scale. First, this method generates spatiotemporally relevant wind power scenarios based on a joint GMM and LHS for wind speed and direction. Then, K-means++ clustering is used to reduce these scenarios to 20 typical scenarios, and probability weights are calculated, achieving modeling and dimensionality reduction of wind power uncertainties. Second, TST is used to transform the nonlinear rotor angle constraint after a fault into a linear inequality constraint, avoiding the huge computational burden of repeated iterations in time-domain simulation in traditional methods. Finally, the nonconvex TSCOPF model is transformed into a convex optimization problem through penalized semidefinite relaxation, and solved using the MOSEK solver. The solution process is described in [link to solution process]. Figure 5 Compared with traditional deterministic methods, this invention is more effective and superior, and has practical significance for the dispatching of high-proportion renewable energy power systems.

Claims

1. A transient stability constraint-based optimal power flow method based on semidefinite programming and convex relaxation, characterized in that, Includes the following steps: Step 1: Based on historical data of wind speed and direction, establish a Gaussian mixture model (GMM) for wind power output prediction, combine it with Latin hypercube sampling (LHS) to generate wind power output scenarios, and use K-means++ clustering to reduce the scenarios to obtain the final scenario set. Step 2: Based on the GMM constructed in Step 1 and the final scenario set, establish the Transient Stable Optimal Power Flow Model (TSCOPF), use the Trajectory Sensitivity Method (TST) to obtain the trajectory sensitivity matrix, and construct linear inequality constraints based on the trajectory sensitivity matrix. Step 3: Reconstruct the model, which includes the linear inequality constraints mentioned above, into a semidefinite programming form (SDP). Add a penalty term based on the second-order submatrix of the matrix to the objective function to perform penalized SDP relaxation. Step 4: Use the solver to obtain feasible power flow and unit output schemes.

2. The method according to claim 1, characterized in that: Step 1 specifically includes the following sub-steps: Step 1-1: Establish a GMM for wind power output prediction based on historical wind speed and direction data; Step 1-2: Divide the probability interval Divided into In each interval, wind power output scenarios are generated using LHS; Steps 1-3: Use K-means++ clustering to reduce the number of scenes to obtain the final scene set.

3. The method according to claim 2, characterized in that: In step 1-1, the specific procedure is as follows: Get continuous Historical data on wind speed and direction for a given period, wind speed sequence Wind direction sequence and the corresponding measured wind power output sequence ,in ; Regarding wind direction Perform a sine-cosine mapping to obtain two-dimensional loop variables. ,form 3D feature sample set ,in , For historical sample size, Establishing a GMM for wind power output forecasting: （1）； In the formula: For the sample The joint probability density function; The total number of Gaussian components; For the first Gaussian component mixing weights , ; , The first The mean vector and covariance matrix of each Gaussian component; For the first The probability density function of Gaussian components.

4. The method according to claim 3, characterized in that: Step 1-2: Divide the probability interval Divided into In each interval, wind power output scenarios are generated using LHS: （2）； （3）； In the formula: In the first The interval is the first The original samples obtained from sampling at each time period; For wind power output quantile function; For the first The sample scenario in the first The probability level for each time period; , The first Wind speed and direction at different times; For the generated scene set, containing A scene vector; For scene vectors with spatiotemporal correlation, .

5. The method according to claim 4, characterized in that: Steps 1-3: Use K-means++ clustering to reduce the number of scenes, resulting in the final scene set: （4）； In the formula: This is the final set of scenes after reduction; For the first The centroid of the nth cluster class, i.e., the nth A typical scenario; For the first The weight of the typical scenario, i.e., belonging to the first typical scenario The ratio of the number of LHS samples in each cluster to the total number of samples; This is to reduce the number of scenes.

6. The method according to any one of claims 1 to 5, characterized in that: Step 2 specifically includes the following sub-steps: Step 2-1: Establish the TSCOPF model; Step 2-2: Obtain the sensitivity matrix based on TST; Steps 2-3: Construct linear inequality constraints based on the sensitivity matrix; In step 2-1, the TSCOPF model includes: 1) Objective function: （5）； In the formula: This refers to the collection of all conventional generators in the system. For nodes The active power of the generator; , , These are the quadratic coefficient, the primary coefficient, and the constant term for the generator cost, respectively. 2) Static power flow equations: （6）； （7）； In the formula: , They are nodes The injected active and reactive power; For nodes The reactive power of the generator; , They are nodes The active and reactive power output of the load; 3) Operating limits: （8）； （9）； In the formula: , They are nodes The lower and upper limits of the generator's active power; , They are nodes Lower and upper voltage limits; 4) Swing equation: （10）； （11）； In the formula: , The first Rotor angle and angular velocity of a generator; Synchronous angular velocity; , These are the inertial time constant and the damping coefficient, respectively. , The first The mechanical power and electromagnetic power of the generator; This represents the rotor angle vector of all generators; 5) Transient stability constraints: （12）； In the formula: This refers to the fault clearance time; , The first Taiwan, No. A generator in The rotor angle at any given moment; As the critical relative angle, take rad.

7. The method according to claim 6, characterized in that, In step 2-2, the sensitivity matrix obtained based on TST is: （13）； （14）； In the formula: Rotor angular vector For control vector Matrix; relative angles exist The sensitivity row vector at time step; In step 2-3: the linear inequality constraints constructed based on the sensitivity matrix are: （15）； （16）； In the formula, This indicates the magnitude of the adjustment made to the current system control state.

8. The method according to claim 7, characterized in that: Step 3 specifically includes the following sub-steps: Step 3-1: Reconstruct the TSCOPF model, which includes the objective function, static power flow equations, running limits, swing equations, and the aforementioned linear inequality constraints, into a semidefinite programming form, i.e., a semidefinite programming model: For all nodes Construct the nodal voltage outer product matrix : （17）； In the formula: The total number of nodes; , They are nodes The real and imaginary parts of voltage; It is the voltage outer product matrix of all nodes, containing all quadratic forms of voltage; Non-convex rank 1 constraint Relaxation is semidefinite; reconstruct the objective function as a function of... Affine function To obtain the standard SDP: （18）； In the formula: Representation matrix It is a positive semi-definite matrix. , These are the generator's active power and its lower and upper limits, respectively; , These are the lower and upper limits of the voltage, respectively. Step 3-2: Add a penalty term based on the second-order minor of the matrix to the objective function: （19）； In the formula: for all Master-subordinate determinant; The penalty coefficient increases adaptively with iteration; this formula maintains convexity while driving the solution to tend towards rank 1, thus reducing the relaxation gap.

9. The method according to claim 8, characterized in that: Step 4: Use sparse chordal decomposition technology to reduce the dimensionality of the penalized semidefinite programming model, and perform iterative calculation by adaptively updating the penalty coefficients. After the iteration is completed, enter the rank-1 repair module to complete the repair of semidefinite constraints. Finally, use the MOSEK solver to output the scheduling scheme.

10. The method according to claim 9, characterized in that: In step 4, the penalized semidefinite programming model is solved using the MOSEK solver. The specific steps are as follows: Step 4-1: Initialize parameters and set penalty coefficient Maximum number of iterations ; Step 4-2: Check the sum of the absolute values ​​of all principal determinants. ,like If the iteration fails, stop; otherwise, increase the penalty coefficient, making... Continue iterating; among them, The absolute value of the determinant of the master matrix; The rank criterion tolerance; Step 4-3: Output the optimal solution ,right Eigenvalue decomposition is performed, and the principal eigenvectors are used to recover the voltage phasors, yielding feasible power flow and unit output schemes; among which... These are the optimal matrix variables after SDP relaxation; These are the optimal control variables after SDP relaxation.

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