A method for solving transient stability constraint optimal power flow with wind power based on second-order cone relaxation

Abstract

The application discloses a second-order cone relaxation-based optimal power flow solving method containing transient stability constraints of wind power, and comprises the following steps: step 1, wind speed is predicted, wind power output scenarios are generated by combining Latin hypercube sampling (LHS), and K-means clustering is used to reduce the scenarios to obtain typical scenarios of wind power output and corresponding occurrence probabilities, so as to represent and process the uncertainty of wind power; step 2, an initial architecture of a transient stability-constrained optimal power flow (TSCOPF) model containing an objective function, static constraints and transient stability constraints is constructed; step 3, a second-order cone relaxation (SOCR) is used for non-convex items in a power balance equation in the TSCOPF model, and a successive inscribed polygon method is used to reduce a relaxation gap, then, the relaxed power balance equation is integrated with linear inequality constraints obtained by transformation in step 2 and other static constraints, and the original TSCOPF model is overall converted into a mixed integer second-order cone programming problem; and step 4, an optimal power flow solving result satisfying the transient stability constraints is obtained.

Description

Technical Field

[0001] This invention relates to the fields of power systems and new energy technologies, and in particular to a power system transient stability analysis and optimal power flow calculation technology; specifically, it relates to an optimal power flow solution method based on second-order cone relaxation with wind power transient stability constraints. Background Technology

[0002] In recent years, with the proposal of dual-carbon goals and the goal of building a new power system dominated by new energy sources, the capacity of new energy sources, represented by wind power and photovoltaics, connected to the power system has grown rapidly. Among these, the intermittency and volatility of wind power generation significantly increase the uncertainty of power system operation, posing new challenges to the safe and stable operation of the power grid. Therefore, conducting research on optimal power flow solutions with wind power transient stability constraints based on second-order cone relaxation is of practical significance for finding the optimal output of generator units, under the premise of safety and economy, and is of practical importance for the safe operation of the system.

[0003] Patent application CN114597902A discloses a power flow calculation method based on convex relaxation. This method first establishes the original power flow equations of the system, then reshapes the original equations based on relaxation variables, transforming them into a linear expression of the relaxation variables. Finally, based on the reshaped power flow equations, the power flow calculation problem is transformed into a convex optimization problem under exact convex relaxation and solved. However, this method has certain limitations; it does not consider the uncertainty of power output from renewable energy sources or the transient stability of the system, and the results may not match the actual operation of the system. Patent application CN118449146A discloses a transient stability constraint-based optimal power flow calculation method with renewable energy access. This method first establishes a probability distribution model of wind and solar power output, and uses a Monte Carlo simulation probabilistic power flow calculation method based on Latin hypercube sampling and scenario reduction technology. Then, based on the relationship between the difference between the rotation angle and the center of inertia angle and the power angle limit, transient stability constraints are established and a transient stability constraint-based optimal power flow is constructed. Finally, the renewable energy access model is incorporated, and the chaotic artificial bee colony algorithm is used to solve the model to obtain the final optimal power flow result. However, this method has certain limitations. It does not consider the influence of non-convex terms in the power flow equation on the obtained optimal power flow result, and cannot guarantee that the obtained optimal power flow result is the global optimal solution.

[0004] In summary, a method for solving optimal power flow with transient stability constraints related to wind power, based on second-order cone relaxation, is proposed. This method aims to provide transient stability assurance for power systems under large-scale grid integration of new energy sources and to seek optimal economic benefits. This research not only improves system operational safety but also provides decision-making basis for optimizing generator output, which is of great significance for promoting the construction of new power systems. Summary of the Invention

[0005] The purpose of this invention is to address the problems of existing optimal power flow solution techniques, such as the difficulty in accurately modeling wind power random fluctuations, nonlinear transient stability constraints, and nonconvex power flow equations. These problems lead to difficulties in model convergence, low computational efficiency, and the inability to guarantee a global optimal solution in optimal power flow solutions with wind power transient stability constraints. In order to accurately capture the time series characteristics of wind speed, avoid generating scenarios that deviate from actual operating conditions, and simultaneously consider computational accuracy and speed, this invention aims to meet the power grid's requirements for safe and stable dispatch.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: The optimal power flow solution method based on second-order cone relaxation with wind power transient stability constraints includes the following steps: Step 1: Based on historical data, the Temporal Pattern Attention-Long Short-Term Memory (TPA-LSTM) model is used to predict wind speed. Combined with Latin Hypercube Sampling (LHS), wind power output scenarios are generated. K-means clustering is used to reduce the scenarios to obtain typical wind power output scenarios and their corresponding probabilities of occurrence, so as to characterize and handle the uncertainty of wind power. Step 2: Based on the reduced typical scenarios and their probabilities output in Step 1, construct the initial architecture of the Transient Stability Constrained Optimal Power Flow (TSCOPF) model, which includes the objective function, static constraints, and transient stability constraints. The extended equal-area criterion (EEAC) is used to calculate the transient stability margin of the system, and sensitivity analysis is combined to transform the nonlinear transient stability constraints in the original TSCOPF model into linear inequality constraints. Step 3: Apply Second-Order Cone Relaxation (SOCR) to the non-convex terms of the power balance equation in the TSCOPF model, and reduce the relaxation gap based on the successive inscribed polygon method. Then, integrate the relaxed power balance equation with the linear inequality constraints obtained in Step 2 and other static constraints to transform the original TSCOPF model into a mixed integer second-order cone programming problem. Step 4: Solve the mixed-integer second-order cone programming problem transformed in Step 3 using the commercial solver Gurobi to obtain the optimal power flow solution that satisfies the transient stability constraints.

[0007] In step 1, the TPA-LSTM model is used to predict wind speed, and LHS and K-means clustering are combined to generate and reduce wind power output scenarios. 1) Wind speed prediction model: remember The wind speed samples are used as input data for the TPA-LSTM model, and the output data is the predicted wind speed.

[0008] The LSTM model selectively retains and updates information through gating mechanisms such as forget gates, input gates, and output gates, effectively solving the problem of long-term dependence. This allows it to accurately capture time-series features from historical wind speed data, providing high-precision wind speed input for wind power output prediction. The model is then connected to the TPA layer, which can identify the most critical time features for the current prediction. The time features are combined with key pattern information filtered by the attention layer and mapped to the final prediction target to obtain the predicted wind speed of the wind turbine generator at the next moment.

[0009] The wind power output can be seen from the wind power-wind speed relationship curve as follows: (1); In the formula: Contribute to wind power forecasting; , , and These are the actual wind speed, cut-in wind speed, cut-out wind speed, and rated wind speed of the fan, respectively. This refers to the rated power of the fan.

[0010] 2) Prediction error probability model: Wind power forecasting has a certain degree of error, and once the market penetration rate reaches a certain level, the impact of this forecasting error becomes significant. Actual wind power output can be expressed as the sum of the predicted output and the forecasting error: (2); In the formula: To contribute actual active power to wind power; This represents the wind power prediction error.

[0011] 3) Wind power output scenario generation and reduction: The initial scenario is generated using LHS: the cumulative distribution function of wind power prediction error is calculated, the range of its cumulative distribution function is divided into several equal parts, the midpoint of each range is taken as the sampling point, the sampling value is calculated by the inverse function to form the initial sampling matrix, and then the correlation between variables is eliminated by arrangement to obtain the sampling matrix.

[0012] K-means clustering is used for scene reduction: the target number of scenes is set, the scenes generated by LHS are used as input, the cluster centers are initialized and iterative clustering is performed, each scene is assigned to the nearest cluster according to the Euclidean distance, and the cluster centers are updated until convergence; finally, each cluster center is used as a representative scene, and its probability is determined according to the proportion of the number of scenes in the cluster to the total number.

[0013] In step 2, a TSCOPF model is constructed for the typical scenario after reduction. The transient stability margin of the system is calculated using EEAC, and the transient stability constraints are transformed into linear inequality constraints by combining sensitivity analysis.

[0014] 1) Objective function: The objective function is defined as minimizing the cost of thermal power generation, as follows: (3); In the formula: Cost of thermal power generation; This represents the total number of scenes after the reduction. For the reduction of the first The probability of each scenario; This represents the total number of thermal power generating units. , and All are the first The fuel coefficient of the generator; For the first The active power of the thermal power generator.

[0015] 2) Power balance constraints: The power balance equation constraint can be expressed as: (4); In the formula: and The first The active and reactive power of the thermal power generator; and These are the active and reactive power of the wind turbine generator set, respectively. and These are the active and reactive power of the load, respectively. This represents the total number of system nodes. and System nodes and The voltage amplitude; For system nodes and The phase angle difference between them; and These are the real and imaginary parts of the nodal admittance matrix, respectively.

[0016] 3) Static stability inequality constraints: (5); In the formula: and These are the lower and upper limits of active power for thermal power generators, respectively. and These are the lower and upper limits of reactive power for thermal power generators, respectively. This is the upper limit of the active power output of the wind turbine generator set; and System nodes The lower and upper limits of the voltage amplitude at that location; and For each system Trends and the upper limit of trends on the line.

[0017] 4) Transient stability constraints: Transient stability constraints describe the transient stability conditions and dynamic processes of the system through a set of differential equations and algebraic equations, respectively. The model is expressed as: (6); In the formula: These are state variables, including the generator rotor angle. Rotation speed wait; As algebraic variables, including the active power of thermal power generating units. and reactive power Active power of wind turbine generator set System node voltage amplitude Phase angle wait; Control variables include the upper and lower limits of active power of thermal power generating units. and Upper and lower limits of reactive power of thermal power generating units and Upper limit of wind turbine generator output wait.

[0018] The transient stability margin of the system is calculated using EEAC, and the transient stability constraints are transformed into linear inequality constraints by combining sensitivity analysis. The specific steps are as follows: Step 2-1: Under the anticipated fault conditions, perform time-domain simulation to obtain the rotor angular trajectory of each generator. and angular velocity ; Step 2-2: Divide the generators into two groups: critical machines (CMs) that lose synchronization after a fault and noncritical machines (NMs) that maintain synchronization. Then, shrink the group down to the generator nodes using the node admittance matrix and calculate the coupling matrix. Identify the clusters with the strongest electrical coupling as candidates for CMs; Steps 2-3: Calculate the combined inertia and center power angle of each aircraft group: (7); In the formula: and These are the aggregate inertia of critical and non-critical machine groups, respectively. and These refer to the number of critical and non-critical clusters, respectively. and These are the equivalent center power angles for critical and non-critical generator groups, respectively. For generator The inertial time constant; For generator Rotor power angle during transient processes.

[0019] Steps 2-4: Construct an equivalent single-machine infinite system, whose equations are: (8); In the formula: The equivalent power angle for a single-machine infinite system; The equivalent inertia of an equivalent single-machine infinite system; This is the equivalent mechanical power of a single-machine system; This is the equivalent electromagnetic power of a stand-alone system; and The first Mechanical power of key machine groups, the first Mechanical power of non-critical machine groups; and The first Electromagnetic power of key machine groups, the first Electromagnetic power of non-critical equipment clusters in Taiwan.

[0020] Steps 2-5: Obtaining data through time-domain simulation , and The curve is obtained, the acceleration and deceleration areas are identified, and the transient stability margin is calculated. ; Steps 2-6: Near the baseline operating point, fine-tune the output of key units, calculate the margin change, and calculate the sensitivity coefficient. ; Steps 2-7: Construct linear transient stability constraints, substitute the EEAC parameters, and obtain the final linearized inequality constraints: (9); In the formula: Fine-tuning values ​​for the output of key generator sets; This is the stability margin threshold; In fault scenarios Transient stability margin; This is the sensitivity coefficient.

[0021] In step 3, the non-convex terms of the power balance equation of the TSCOPF model are subjected to SOCR, and the relaxation gap is reduced based on the successive inscribed polygon method, transforming it into a mixed integer second-order cone programming problem.

[0022] To address the non-convexity in the model and obtain the global optimum, the power balance constraint is improved by introducing intermediate variables to replace non-convex terms such as the square of the voltage: (10); In the formula: , , , and All are intermediate variables, satisfying the following second-order cone constraint: (11); In the formula: It is an intermediate variable.

[0023] At this point, the power balance equation constraint is... It can be rewritten in the following form: (12); The solution obtained after relaxation ,in, , , , All are initial intermediate variables obtained; a relaxation gap is defined, and the relaxation gap is contracted by the method of successive inscribed polygons. By adding additional linear constraints, the feasible region is gradually compressed, forcing the solution to approach the boundary of the original equation. Based on the relaxed initial solution, the normalized variables are calculated. , and according to , The symbol is used to add a linear inscribed polygon constraint, which shrinks the feasible region.

[0024] Based on the relaxed solution obtained after contraction, check whether the maximum relaxation gap is less than the relaxation gap threshold. If the relaxation gap is less than the threshold, the relaxation accuracy requirement is met. If the relaxation gap is greater than the threshold, a second round of feasible region contraction is performed, incorporating octagonal constraints, hexagonal constraints, etc., until the relaxation gap is less than the threshold, thus meeting the relaxation gap requirement.

[0025] By integrating the relaxed second-order cone constraints and the linear inscribed polygon constraints, the original problem is transformed into a mixed-integer second-order cone programming problem.

[0026] In step 4, the TSCOPF model is solved using the commercial solver Gurobi. Gurobi is capable of efficiently solving various types of optimization problems, with its core advantage lying in its ability to solve large-scale, complex mixed-integer programming and convex optimization problems. After the above steps, the TSCOPF problem becomes a mixed-integer second-order cone programming problem, which Gurobi can process directly and efficiently, thus ensuring both efficiency and reliability in the solution.

[0027] Compared with the prior art, the present invention has the following technical effects: 1) This invention captures the long-term dependence and temporal pattern characteristics of wind speed using the TPA-LSTM model, significantly improving the accuracy of wind speed prediction. Furthermore, it combines LHS and K-means clustering algorithms to extract the most representative typical scenarios and probabilities from a large number of possible scenarios. This design effectively compresses the scenario scale while preserving the characteristics of wind power fluctuations, providing high-precision boundary conditions for subsequent calculations and avoiding computational redundancy caused by too many scenarios. 2) To address the nonlinear challenges posed by transient stability differential-algebraic equations, this invention innovatively introduces EEAC (Extended Equivalent-Equivalent-Aggregate) to identify key machine clusters through time-domain simulation and, combined with sensitivity analysis, reduces the dimensionality of highly complex nonlinear transient stability constraints and transforms them into simple linear inequality constraints. This reduces the difficulty of solving the model while also ensuring the transient stability boundary of the system when encountering anticipated faults. 3) To address the non-convexity of the power balance equations in the original TSCOPF model, this invention employs the SOCR technique and uses the successive inscribed polygon method to reduce the relaxation gap, successfully transforming the originally difficult-to-solve non-convex nonlinear problem into an easily solvable mixed-integer second-order cone programming problem. Combined with the commercial Gurobi solver, this scheme avoids the pitfalls of traditional algorithms easily getting trapped in local optima, ensuring stable and efficient acquisition of the global optimal solution for the optimal power flow under complex constraints. Attached Figure Description

[0028] The present invention will be further described below with reference to the accompanying drawings and embodiments: Figure 1 This is a flowchart of the method of the present invention; 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 schematic diagram of the generator power angle dynamic response curve of the IEEE 39-bus system without using the method of this invention in an example of the present invention; Figure 4 This is a schematic diagram of the generator power angle dynamic response curve of the IEEE 39-bus system using the method of this invention in an example of this invention; Figure 5 This is a flowchart of the TSCOPF solution using a solver in this invention. Detailed Implementation

[0029] like Figure 1 As shown, a method for solving optimal power flow with wind power transient stability constraints based on second-order cone relaxation includes the following steps: Step 1: Based on historical data, the TPA-LSTM model is used to predict wind speed. Combined with Latin hypercube sampling (LHS), wind power output scenarios are generated. K-means clustering is used to reduce the scenarios to obtain typical wind power output scenarios and their corresponding occurrence probabilities, so as to characterize and handle the uncertainty of wind power. Step 2: Based on the reduced typical scenarios and their probabilities output in Step 1, construct the initial architecture of the TSCOPF model, which includes the objective function, static constraints, and transient stability constraints; wherein, the transient stability margin of the system is calculated using EEAC, and the nonlinear transient stability constraints in the original TSCOPF model are transformed into linear inequality constraints by combining sensitivity analysis. Step 3: Apply SOCR to the non-convex terms of the power balance equation in the TSCOPF model, and reduce the relaxation gap based on the successive inscribed polygon method. Then, integrate the relaxed power balance equation with the linear inequality constraints obtained in Step 2 and other static constraints to transform the original TSCOPF model into a mixed integer second-order cone programming problem. Step 4: Solve the mixed-integer second-order cone programming problem transformed in Step 3 using the commercial solver Gurobi to obtain the optimal power flow solution that satisfies the transient stability constraints.

[0030] In step 1, the TPA-LSTM model is used to predict wind speed, and LHS and K-means clustering are combined to generate and reduce wind power output scenarios.

[0031] 1) Wind speed prediction model: remember The wind speed samples are used as input data for the TPA-LSTM model, and the output data is the predicted wind speed.

[0032] The LSTM model selectively retains and updates information through gating mechanisms such as forget gates, input gates, and output gates, effectively solving the problem of long-term dependence. This allows it to accurately capture time-series features from historical wind speed data, providing high-precision wind speed input for wind power output prediction. The model is then connected to the TPA layer, which can identify the most critical time features for the current prediction. The time features are combined with key pattern information filtered by the attention layer and mapped to the final prediction target to obtain the predicted wind speed of the wind turbine generator at the next moment.

[0033] The wind power output can be seen from the wind power-wind speed relationship curve as follows: (1); In the formula: Contribute to wind power forecasting; , , and These are the actual wind speed, cut-in wind speed, cut-out wind speed, and rated wind speed of the fan, respectively. This refers to the rated power of the fan.

[0034] 2) Prediction error probability model: Wind power forecasting has a certain degree of error, and once the market penetration rate reaches a certain level, the impact of this forecasting error becomes significant. Actual wind power output can be expressed as the sum of the predicted output and the forecasting error: (2); In the formula: To contribute actual active power to wind power; This represents the wind power prediction error.

[0035] 3) Wind power output scenario generation and reduction: The initial scenario is generated using LHS: the cumulative distribution function of wind power prediction error is calculated, the range of its cumulative distribution function is divided into several equal parts, the midpoint of each range is taken as the sampling point, the sampling value is calculated by the inverse function to form the initial sampling matrix, and then the correlation between variables is eliminated by arrangement to obtain the sampling matrix.

[0036] K-means clustering is used for scene reduction: the target number of scenes is set, the scenes generated by LHS are used as input, the cluster centers are initialized and iterative clustering is performed, each scene is assigned to the nearest cluster according to the Euclidean distance, and the cluster centers are updated until convergence; finally, each cluster center is used as a representative scene, and its probability is determined according to the proportion of the number of scenes in the cluster to the total number.

[0037] In step 2, a TSCOPF model is constructed for the typical scenario after reduction. The transient stability margin of the system is calculated using EEAC, and the transient stability constraints are transformed into linear inequality constraints by combining sensitivity analysis.

[0038] 1) Objective function: The objective function is defined as minimizing the cost of thermal power generation, as follows: (3); In the formula: Cost of thermal power generation; This represents the total number of scenes after the reduction. For the reduction of the first The probability of each scenario; This represents the total number of thermal power generating units. , and All are the first The fuel coefficient of the generator; For the first The active power of the thermal power generator.

[0039] 2) Power balance constraints: The power balance equation constraint can be expressed as: (4); In the formula: and The first The active and reactive power of the thermal power generator; and These are the active and reactive power of the wind turbine generator set, respectively. and These are the active and reactive power of the load, respectively. This represents the total number of system nodes. and System nodes and The voltage amplitude; For system nodes and The phase angle difference between them; and These are the real and imaginary parts of the nodal admittance matrix, respectively.

[0040] 3) Static stability inequality constraints: (5); In the formula: and These are the lower and upper limits of active power for thermal power generators, respectively. and These are the lower and upper limits of reactive power for thermal power generators, respectively. This is the upper limit of the active power output of the wind turbine generator set; and System nodes The lower and upper limits of the voltage amplitude at that location; and For each system Trends and the upper limit of trends on the line.

[0041] 4) Transient stability constraints: Transient stability constraints describe the transient stability conditions and dynamic processes of the system through a set of differential equations and algebraic equations, respectively. The model is expressed as: (6); In the formula: These are state variables, including the generator rotor angle. Rotation speed wait; As algebraic variables, including the active power of thermal power generating units. and reactive power Active power of wind turbine generator set System node voltage amplitude Phase angle wait; Control variables include the upper and lower limits of active power of thermal power generating units. and Upper and lower limits of reactive power of thermal power generating units and Upper limit of wind turbine generator output wait.

[0042] The transient stability margin of the system is calculated using EEAC, and the transient stability constraints are transformed into linear inequality constraints by combining sensitivity analysis. The specific steps are as follows: Step 2-1: Under the anticipated fault conditions, perform time-domain simulation to obtain the rotor angular trajectory of each generator. and angular velocity ; Step 2-2: Divide the generators into two groups: CMs that lose synchronization after a fault and NMs that remain synchronized. Then, shrink the group to the generator nodes using the node admittance matrix and calculate the coupling matrix. Identify the clusters with the strongest electrical coupling as candidates for CMs; Steps 2-3: Calculate the combined inertia and center power angle of each aircraft group: (7); In the formula: and These are the aggregate inertia of critical and non-critical machine groups, respectively. and These refer to the number of critical and non-critical clusters, respectively. and These are the equivalent center power angles for critical and non-critical generator groups, respectively. For generator The inertial time constant; For generator Rotor power angle during transient processes.

[0043] Steps 2-4: Construct an equivalent single-machine infinite system, whose equations are: (8); In the formula: The equivalent power angle of an equivalent single-machine infinite system; The equivalent inertia of an equivalent single-machine infinite system; This is the equivalent mechanical power of a single-machine system; This is the equivalent electromagnetic power of a stand-alone system; and The first Mechanical power of key machine groups, the first Mechanical power of non-critical machine groups; and The first Electromagnetic power of key machine groups, the first Electromagnetic power of non-critical equipment clusters in Taiwan.

[0044] Steps 2-5: Obtaining data through time-domain simulation , and The curve is obtained, the acceleration and deceleration areas are identified, and the transient stability margin is calculated. ; Steps 2-6: Near the baseline operating point, fine-tune the output of key units, calculate the margin change, and calculate the sensitivity coefficient. ; Steps 2-7: Construct linear transient stability constraints, substitute the EEAC parameters, and obtain the final linearized inequality constraints: (9); In the formula: Fine-tuning values ​​for the output of key generator sets; This is the stability margin threshold; In fault scenarios Transient stability margin; This is the sensitivity coefficient.

[0045] In step 3, the non-convex terms of the power balance equation of the TSCOPF model are subjected to SOCR, and the relaxation gap is reduced based on the successive inscribed polygon method, transforming it into a mixed integer second-order cone programming problem.

[0046] To address the non-convexity in the model and obtain the global optimum, the power balance constraint is improved by introducing intermediate variables to replace non-convex terms such as the square of the voltage: (10); In the formula: , , , and All are intermediate variables, satisfying the following second-order cone constraint: (11); In the formula: It is an intermediate variable.

[0047] At this point, the power balance equation constraint is... It can be rewritten in the following form: (12); The solution obtained after relaxation ,in, , , , All are initial intermediate variables obtained; a relaxation gap is defined, and the relaxation gap is contracted by the method of successive inscribed polygons. By adding additional linear constraints, the feasible region is gradually compressed, forcing the solution to approach the boundary of the original equation. Based on the relaxed initial solution, the normalized variables are calculated. , and according to , The symbol is used to add a linear inscribed polygon constraint, which shrinks the feasible region.

[0048] Based on the relaxed solution obtained after contraction, check whether the maximum relaxation gap is less than the relaxation gap threshold. If the relaxation gap is less than the threshold, the relaxation accuracy requirement is met. If the relaxation gap is greater than the threshold, a second round of feasible region contraction is performed, incorporating octagonal constraints, hexagonal constraints, etc., until the relaxation gap is less than the threshold, thus meeting the relaxation gap requirement.

[0049] By integrating the relaxed second-order cone constraints and the linear inscribed polygon constraints, the original problem is transformed into a mixed-integer second-order cone programming problem.

[0050] In step 4, the TSCOPF model is solved using the commercial solver Gurobi. The steps are as follows: Step 4-1: Represent the final mixed-integer second-order cone programming problem model in a Gurobi-recognizable format.

[0051] Step 4-2: Connect to Gurobi through the modeling system, and configure Gurobi's solution parameters according to the problem size and characteristics to improve efficiency and stability.

[0052] Step 4-3: The solver will automatically process the mixed integer second-order cone programming problem and extract the optimal values ​​of all decision variables from the solution output by the solver.

[0053] Example: To verify the effectiveness of this invention, it was tested on the IEEE 39-bus system, which has 39 buses and 10 generators. The synchronous generator model of the system adopts a fourth-order model, such as... Figure 2 As shown. The relative rotor angle of the generators is used to determine the stability of the system. To verify the effectiveness of the invention, the synchronous generators of the 34 nodes in this node system were replaced with 300MW wind turbines. Wind power output was predicted using the TPA-LSTM model. The cut-in wind speed, rated wind speed, and cut-off wind speed of the wind turbines were 3m / s, 12m / s, and 25m / s, respectively. The output of the wind turbines was predicted for one day, and 1500 typical wind power output scenarios were generated and reduced using LHS and K-means clustering.

[0054] The simulation was performed on the MATLAB R2022b platform, setting a three-phase ground fault to occur on bus 15 at 1 second and to disconnect the fault after 0.15 seconds. A simulation analysis of the fault duration of 10 seconds was conducted to obtain the relative rotor angle diagrams of each generator.

[0055] Before optimization using the method of this invention, the power angle diagram of the system generator is as follows: Figure 3 As shown in the figure, when a three-phase short-circuit fault occurs, the relative rotor angles of the system generators increase, the maximum power angle difference between generators exceeds the threshold, and the system loses stability.

[0056] To address this situation, the method of this invention is adopted, and the power angle diagram of the system generator is as follows: Figure 4 As shown, when a three-phase short-circuit fault occurs, the system relative rotor angle fluctuates. After the fault is cleared, the trajectory of the power angle does not continue to increase, but gradually converges and tends to stabilize. The maximum power angle difference between generators does not exceed the threshold, and the system is transiently stable.

[0057] Furthermore, as shown in Table 1, SOCR1 is the untightened SOCR relaxation method, while SOCR2 is the SOCR with successive inscribed polygon tightening proposed in this paper. The relaxation gap of the proposed SOCR method with inscribed polygon tightening is 0.532%, while the relaxation gap of SOCR1 is 15.2%. The relaxation gap is reduced from 15.2% to 0.532%, a reduction of approximately 96.5%. Therefore, SOCR2 can more accurately approximate the global optimum of TSCOPF while maintaining the convex solvability of the problem, effectively avoiding the deviation caused by excessive relaxation gap. In terms of computation time, SOCR2 takes 91.25 seconds, an increase of approximately 43.9% compared to SOCR1's 63.42 seconds. Despite the increase in computation time, the relaxation gap is significantly improved by two orders of magnitude. Taking all factors into account, the proposed SOCR2 method significantly improves the accuracy of convex relaxation while maintaining high computational efficiency, and its converged solution is closer to the true optimum of the original nonconvex mixed-integer nonlinear programming model.

[0058] Table 1

[0059] Compared with existing technologies, the optimal power flow solution based on second-order cone relaxation with wind power transient stability constraints proposed in this invention takes into account the uncertainty of wind power, optimizes the total power generation cost of the system, and ensures the safe and stable operation of the system in the event of a fault. By performing convex approximation on the transient stability constraints, the linearized transient stability constraints are obtained by calculating the sensitivity based on the obtained transient stability margin and combining them with the power balance equation constraints after convex relaxation. This can avoid the optimization scheduling results from getting trapped in local optima and effectively achieve the global optimum of the TSCOPF problem with wind power uncertainty. This is of great significance for ensuring the safe and stable operation of the power system and realizing green and economic development.

Claims

1. A method for solving optimal power flow with wind power transient stability constraints based on second-order cone relaxation, characterized in that, Includes the following steps: Step 1: Based on historical data, the Time Pattern Attention-Long Short-Term Memory (TPA-LSTM) model is used to predict wind speed. Combined with Latin Hypercube Sampling (LHS), wind power output scenarios are generated. K-means clustering is used to reduce the scenarios to obtain typical wind power output scenarios and their corresponding probabilities of occurrence, so as to characterize and handle the uncertainty of wind power. Step 2: For the typical scenarios and their probabilities after reduction output in Step 1, construct the initial architecture of the optimal power flow TSCOPF model, which includes the objective function, static constraints, and transient stability constraints; wherein, the extended equal area criterion EEAC is used to calculate the transient stability margin of the system, and sensitivity analysis is combined to transform the nonlinear transient stability constraints in the original TSCOPF model into linear inequality constraints. Step 3: Apply second-order cone relaxation SOCR to the non-convex terms of the power balance equation in the TSCOPF model, and reduce the relaxation gap based on the successive inscribed polygon method. Then, integrate the relaxed power balance equation with the linear inequality constraints obtained in Step 2 and other static constraints to transform the original TSCOPF model into a mixed integer second-order cone programming problem. Step 4: Solve the mixed-integer second-order cone programming problem transformed in Step 3 to obtain the optimal power flow solution that satisfies the transient stability constraints.

2. The method according to claim 1, characterized in that: In step 1, the specific steps include: 1) Construct a wind speed prediction model; 2) Construct a prediction error probability model; 3) Generate and reduce wind power output scenarios; The wind speed prediction model constructed in step 1) is as follows: （1）； In the formula: Contribute to wind power forecasting; , , and These are the actual wind speed, cut-in wind speed, cut-out wind speed, and rated wind speed of the fan, respectively. This refers to the rated power of the fan.

3. The method according to claim 2, characterized in that: The prediction error probability model constructed in step 2) is as follows: （2）； In the formula: To contribute actual active power to wind power; This represents the wind power prediction error.

4. The method according to claim 3, characterized in that: In step 3), when generating and reducing the wind power output scenario, the following steps are included: The initial scenario is generated using LHS: the cumulative distribution function of wind power prediction error is calculated, the range of its cumulative distribution function is divided into several equal parts, the midpoint of each range is taken as the sampling point, the sampling value is calculated by the inverse function to form the initial sampling matrix, and then the correlation between variables is eliminated by the arrangement to obtain the sampling matrix. K-means clustering is used for scene reduction: the target number of scenes is set, the scenes generated by LHS are used as input, the cluster centers are initialized and iterative clustering is performed, each scene is assigned to the nearest cluster according to the Euclidean distance, and the cluster centers are updated until convergence; finally, each cluster center is used as a representative scene, and its probability is determined according to the proportion of the number of scenes in the cluster to the total number.

5. The method according to any one of claims 1 to 4, characterized in that: In step 2, the initial architecture of the constructed optimal power flow TSCOPF model includes: 1) Objective function: The objective function is defined as minimizing the cost of thermal power generation, as follows: （3）； In the formula: Cost of thermal power generation; This represents the total number of scenes after reduction. For the reduction of the first The probability of each scenario; This represents the total number of thermal power generating units. , and All are the first The fuel coefficient of the generator; For the first The active power of the thermal power generator; 2) Power balance constraints; 3) Static stability inequality constraints; 4) Transient stability constraints.

6. The method according to claim 5, characterized in that: The power balance constraint is specifically as follows: （4）； In the formula: and The first The active and reactive power of the thermal power generator; and These are the active and reactive power of the wind turbine generator set, respectively. and These are the active and reactive power of the load, respectively. This represents the total number of system nodes. and System nodes and The voltage amplitude; For system nodes and The phase angle difference between them; and These are the real and imaginary parts of the nodal admittance matrix, respectively. The static stability inequality constraint is specifically as follows: （5）； In the formula: and These are the lower and upper limits of the active power of thermal power generators, respectively. and These are the lower and upper limits of reactive power for thermal power generators, respectively. This is the upper limit of the active power output of the wind turbine generator set; and System nodes The lower and upper limits of the voltage amplitude at that location; and For each system Trends and the upper limit of trends along the route; The transient stability constraint is specifically as follows: Transient stability constraints describe the transient stability conditions and dynamic processes of the system through a set of differential equations and algebraic equations, respectively. The model is expressed as: （6）； In the formula: These are state variables, including the generator rotor angle. Rotation speed ; As algebraic variables, including the active power of thermal power generating units. and reactive power Active power of wind turbine generator set System node voltage amplitude Phase angle ; Control variables include the upper and lower limits of active power of thermal power generating units. and Upper and lower limits of reactive power of thermal power generating units and Upper limit of wind turbine generator output .

7. The method according to claim 6, characterized in that: In step 2, the transient stability margin of the system is calculated using EEAC, and the transient stability constraints are transformed into linear inequality constraints using sensitivity analysis. The specific steps are as follows: Step 2-1: Under the anticipated fault conditions, perform time-domain simulation to obtain the rotor angular trajectory of each generator. and angular velocity ; Step 2-2: Divide the generators into two groups: critical machine groups (CMs) that lose synchronization after a fault and non-critical machine groups (NMs) that maintain synchronization. Then, shrink the group down to the generator nodes using the node admittance matrix and calculate the coupling matrix. Identify the clusters with the strongest electrical coupling as candidates for CMs; Steps 2-3: Calculate the combined inertia and center power angle of each group of machines; Steps 2-4: Construct an equivalent single-machine infinite system; Steps 2-5: Obtaining data through time-domain simulation , and The curve is obtained, the acceleration and deceleration areas are identified, and the transient stability margin is calculated. ; Steps 2-6: Near the baseline operating point, fine-tune the output of key units, calculate the margin change, and calculate the sensitivity coefficient. ; Steps 2-7: Construct linear transient stability constraints, substitute the EEAC parameters, and obtain the final linearized inequality constraints.

8. The method according to claim 7, characterized in that: In steps 2-3, the calculation of the combined inertia and center power angle of each machine group is as follows: （7）； In the formula: and These are the aggregate inertia of critical and non-critical machine groups, respectively. and These refer to the number of critical and non-critical clusters, respectively. and These are the equivalent center power angles for critical and non-critical generator groups, respectively. For generator The inertial time constant; For generator Rotor power angle during transient processes; In steps 2-4, an equivalent single-machine infinite system is constructed, specifically as follows: （8）； In the formula: The equivalent power angle of an equivalent single-machine infinite system; The equivalent inertia of an equivalent single-machine infinite system; This represents the equivalent mechanical power of a single-machine system. This is the equivalent electromagnetic power of a stand-alone system; and The first Mechanical power of key machine groups, the first Mechanical power of non-critical machine groups; and The first Electromagnetic power of key machine groups, the first Electromagnetic power of non-critical equipment clusters in Taiwan; In steps 2-7, the obtained linearized inequality constraints are: （9）； In the formula: Fine-tuning values ​​for the output of key generator sets; This is the stability margin threshold; In fault scenarios Transient stability margin; This is the sensitivity coefficient.

9. The method according to claim 6, 7, or 8, characterized in that: In step 3, the non-convex terms of the power balance equation of the TSCOPF model are applied using SOCR, and the relaxation gap is reduced based on the successive inscribed polygon method, transforming it into a mixed integer second-order cone programming problem. To address the non-convexity in the model and obtain the global optimum, the power balance constraint is improved by introducing intermediate variables to replace non-convex terms such as the square of the voltage: （10）； In the formula: , , , and All are intermediate variables, satisfying the following second-order cone constraint: （11）； In the formula: As an intermediate variable; At this point, the power balance equation constraint is... It can be rewritten in the following form: （12）； The solution obtained after relaxation ,in, , , , All are initial intermediate variables obtained; a relaxation gap is defined, and the relaxation gap is contracted by the method of successive inscribed polygons. By adding additional linear constraints, the feasible region is gradually compressed, forcing the solution to approach the boundary of the original equation; based on the initial relaxation solution, the normalized variables are calculated. , and according to , Add a linear inscribed polygon constraint to the symbol to shrink the feasible region; Based on the relaxed solution obtained after contraction, check whether the maximum relaxation gap is less than the relaxation gap threshold. If the relaxation gap is less than the threshold, the relaxation accuracy requirement is met. If the relaxation gap is greater than the threshold, a second round of feasible region contraction is performed until the relaxation gap is less than the threshold, thus meeting the relaxation gap requirement. By integrating the relaxed second-order cone constraints and the linear inscribed polygon constraints, the original problem is transformed into a mixed-integer second-order cone programming problem.

10. The method according to claim 9, characterized in that: In step 4, the TSCOPF model is solved using the commercial solver Gurobi. The steps are as follows: Step 4-1: Express the final mixed-integer second-order cone programming problem model in a Gurobi-recognizable format; Step 4-2: Connect to Gurobi through the modeling system, and configure the Gurobi solution parameters according to the problem size and characteristics to improve efficiency and stability; Step 4-3: The solver will automatically process the mixed integer second-order cone programming problem and extract the optimal values ​​of all decision variables from the solution output by the solver.

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