Transient stability preventive control method for power system with high proportion of wind power integration

Abstract

Aiming at the transient stability preventive control method of power system with high proportion of wind power integration, step 1: for the power system with high proportion of wind power integration, the probability transient stability constraint of unstable mode classification is constructed; step 2: based on the historical operation data and simulation data of power system, the limit cutting time and unstable mode under corresponding fault are determined by time domain simulation method, and the initial sample set is established; step 3: the gradient boosting and step-by-step feature enhancement model are trained offline to form the evaluation model; step 4: for the probability transient stability constraint, the current system operation condition is evaluated to obtain the sensitivity of the probability of meeting the stability index of the limit cutting time of each unstable mode category to the active power generated by the key generator, and the probability transient stability constraint is converted into a set of explicit constraints embedded into the traditional optimal power flow; step 5: the optimal power flow model considering the probability transient stability constraint is solved by using the dynamic inertia weight particle swarm optimization algorithm.

Description

Technical Field

[0001] This invention belongs to the field of power system technology, specifically relating to the field of power system transient stability prevention and control technology, and particularly to a power system transient stability prevention and control method for a high proportion of wind power grid connection. Background Technology

[0002] Typically, research on transient stability prevention and control in power systems involves solving the Transient Stability Constrained Optimal Power Flow (TSCOPF) problem, where the transient stability of the power system is determined by solving a set of differential-algebraic equations representing the system's transient state. However, with the continuous expansion of power system scale, the difficulty of solving these differential-algebraic equations increases significantly. As my country's power system transforms and upgrades towards a new type of power system dominated by renewable energy sources, the uncertainty of power generation output and the complexity of grid interconnection will inevitably increase, undoubtedly raising the risk of grid instability faults. Therefore, considering the dual uncertainties of renewable energy output and system operating state on transient instability faults, and developing targeted prevention and control schemes in the early stages of fault development, is of great significance for suppressing fault propagation and avoiding large-scale blackouts.

[0003] With the application of wide-area measurement systems and synchronous phasor measurement devices, the collection of power system operation data has become increasingly convenient and rapid, and the use of data-driven methods has become increasingly widespread. Data-driven methods mainly include support vector machines, backpropagation neural networks, and deep belief networks. Patent document CN110163540B discloses a power system transient stability prevention and control method and system, which adjusts the active power output of generators based on a generator in a generative adversarial network model. Patent document CN109473977B discloses a risk-based rapid prevention and control method for power systems, considering line failures caused by aging, and formulating a prevention and control model based on DC power flow and branch interruption distribution factors, and solving it using the interior-point method. However, the above methods cannot handle large amounts of sample data, and they cannot independently handle the uncertainty of new energy output.

[0004] In summary, current transient stability prevention and control methods cannot meet the high adaptability and high precision requirements of modern new power systems based on new energy sources for transient stability prevention and control methods. Summary of the Invention

[0005] The purpose of this invention is to address the technical problem, as mentioned in the background section, that existing technologies cannot meet the high adaptability and high precision requirements of modern new power systems based on new energy sources for transient stability prevention and control methods. This invention proposes a high-precision, highly adaptable power system transient stability prediction model considering a high proportion of wind power grid connection, and utilizes optimization algorithms to solve for the optimal power flow considering the uncertainty of wind power output, thereby providing a transient stability prevention and control method for power systems with a high proportion of wind power grid connection.

[0006] The objective of this invention is achieved as follows:

[0007] The transient stability prevention and control method for power systems with a high proportion of wind power grid connection includes the following steps:

[0008] Step 1: Set up a set of anticipated faults. For power systems with a high proportion of wind power connected to the grid, construct a probabilistic transient stability constraint (PTSC) for instability mode (IM) classification.

[0009] Step 2: Based on historical operating data and simulation data of the power system, use time-domain simulation to determine the critical clearing time (CCT) and IM under the corresponding fault, and establish an initial sample set;

[0010] Step 3: Based on the constructed sample set, the Gradient Boosting Enhanced with Step-Wise Feature Augmentation (AugBoost) model is trained offline to form an evaluation model based on AugBoost, and CCT and IM are evaluated online.

[0011] Step 4: Based on the evaluation results, assess the current system operation status for PTSC, calculate the sensitivity of the probability of CCT meeting stability indicators to the active power generated by key generators in each IM category, transform PTSC into a set of explicit constraints, and embed them into the traditional Optimal Power Flow (OPF) model to obtain the PTSCOPF model.

[0012] Step 5: Solve the PTSCOPF model using the Dynamic Inertia Weight Particle Swarm Optimization (DW-PSO) algorithm to obtain the optimal operating point of the power system.

[0013] In step 1, all lines that may cause transient instability are set as the expected fault set, and the PTSC of IM classification is constructed as shown in formula (1):

[0014] ρ(τ((x sol ,y sol ),Ω L ,ζ,u,ε,T)>α)≥β (1)

[0015] In the formula: ρ(·) represents probability; τ represents the relevant stability index CCT; (x sol ,y sol ) represents a control scheme, that is, an algebraic variable of the system state after a certain control; Ω L ζ represents the set of lines; u represents the probability density function of fault occurrence for each line; ε represents the control variables, including the active power output of each synchronous generator; T represents the uncertainty affecting the system operating point, such as the change in power generation of each wind power plant (WPP); T represents the time interval between two consecutive control operations. Since OPF is usually used to solve for one-hour control methods, T is set to one hour; α is the defined CCT threshold. Equation (1) shows that if Ω between two consecutive control operations L If a random fault occurs on the line, considering ζ and ε during this period, the probability that CCT > α must be no less than the safety level β.

[0016] Analyzing each potential fault individually after considering ε is challenging, making formula (1) complex in the OPF problem. Given that a particular control solution may have a similar impact on the system vulnerability to multiple faults triggering the same IM, a more general and manageable approach to PTSC is adopted, as shown in formula (2):

[0017]

[0018] Where: Ω IM k represents the set of all possible IMs in the power grid; k represents Ω. IM The number.

[0019] This approach helps to set flexible probabilistic stability criteria for each IM that needs to be prevented. IMs are similar to coherent generator sets, the main difference being that they contain only two sets of generator sets: critical generator sets and surplus generator sets.

[0020] In step 2, CCT and IM are two important indicators in power system transient stability analysis. The value of CCT determines the relationship between the system's stability level and specific faults, while the identification of IM determines the critical synchronous generator that has lost synchronization. A set of data pairs (CCT, IM) is represented as Ω.CCT,IM This includes CCT and IM for the power system under all possible failure scenarios. Ω CCT,IM It reflects the overall stability level of the power system and identifies generators prone to losing synchronization, providing a basis for further preventive control.

[0021] Power companies and power system simulation software can provide a large amount of historical power system operating data and simulation data. Based on the corresponding historical observation data and simulation data, statistical models are estimated to address various uncertainties (output of each wind turbine, load level, and fault location, etc.). Then, time-domain simulations are performed, sampling uncertainties in the system from the corresponding statistical models in each simulation. Finally, selected features (synchronous generator rotor angle, fault location, active power output of the synchronous generator and wind power plant, and reactive power output of the synchronous generator) and target labels (CCT and IM) are extracted from the simulation results and stored in a sample set.

[0022] In step 3, for a power system with a high proportion of wind power connected to the grid, the potential operating points increase exponentially, making it very time-consuming to calculate the CCT and identify the IM through time-domain simulation. Therefore, the constructed sample set is used to train the AugBoost model to build a mapping relationship between variables and CCT and IM, enabling online evaluation.

[0023] The evaluation models include a regression model (for evaluating the CCT system) and a multi-class classification model (for evaluating the IM system). AugBoost is a machine learning algorithm that can be used in conjunction with many other types of learning algorithms and can be applied to multi-class classification and regression problems. Unlike the regular Gradient Boosting Decision Tree (GBDT) model, AugBoost enhances dataset features between GBDT iterations to achieve better results.

[0024] The AugBoost algorithm mainly consists of two parts: 1) Feature extraction and combination. First, an Artificial Neural Network (ANN) is trained using the original feature data of the power system. The ANN learns the information and extracts a new set of features, which are then combined with the original features; 2) DT-based evaluation model. The combined features are input into the DT model for training, constructing a mapping relationship between feature data and stable evaluation labels.

[0025] In step 4, it is assumed that the probabilistic transient stability level is related to the... There is a quasi-linear relationship between the generated active power. Based on this relationship, in order to satisfy the PTSC shown in formula (1), the active power generated can be calculated from... Transferred to Active power generation. and Let be the set of critical and remaining synchronous generators for the k-th IM. The sensitivity of the probability that the CCT satisfies the stability index to the active power shift from the critical generator to the remaining generators is:

[0026]

[0027] In the formula: ΔP represents the maximum power output change of all synchronous generators between two consecutive iterations.

[0028] Based on the assumed quasi-linear relationship, in order to achieve the required level of stability, from Transferred to Target active power The calculation formula is as follows:

[0029]

[0030] Convert PTSC into a set of explicit constraints:

[0031]

[0032] In the formula: P g P represents the active power output of the g-th synchronous generator; g ' represents the active power output of the g-th synchronous generator before the power transfer.

[0033] Embedding it into the traditional OPF model yields the PTSCOPF model.

[0034] In step 5, the inertia weight ω in PSO reflects the particle's search capability. A high inertia weight indicates strong global search capability, and vice versa. In the standard PSO algorithm, ω is a constant. Although it has strong global capability in the early stages of the search process, its convergence speed is slow in the later stages, and it easily tends to local optima. Therefore, the inertia weight should be adjusted according to the search process to balance convergence speed and global search capability. To overcome the shortcomings of PSO and consider the constraints in the optimization model, a DW-PSO algorithm with a penalty function is proposed to optimize the parameters. When the particle's position does not meet the constraints, the fitness value is set to the maximum value through a penalty function. By setting the penalty function, the constrained optimization problem can be transformed into an unconstrained optimization problem. The DW-PSO algorithm is used to solve PTSCOPF to obtain the optimal operating mode of the power system. The specific steps are as follows:

[0035] (1) Input generator set, transmission line, busbar, and power system load data;

[0036] (2) Input PSO parameter data, namely inertial weight, acceleration constant, number of particles in the swarm, and maximum number of iterations;

[0037] (3) Randomly generate the position and velocity of the initial particle swarm;

[0038] (4) Assume the number of iterations is 0;

[0039] (5) Calculate the total cost of each particle based on the fitness function and check for cases where the constraints are not met. When a particle's position does not meet the constraints, set the fitness value to the maximum value using a penalty function;

[0040] (6) If the fitness of each particle is lower than a certain value, then use that fitness value as the optimal value;

[0041] (7) Update the velocity and position of particles in the particle swarm;

[0042] (8) If the maximum number of iterations has been reached, stop and output the result; otherwise, repeat step (5).

[0043] Compared with the prior art, the present invention has the following technical effects:

[0044] 1) To address the uncertainty of wind power output in power systems with a high proportion of wind power connected to the grid, this invention proposes PTSC based on IM classification, which transforms uncertainty into deterministic constraint expression. It obtains the sensitivity of the probability of CCT satisfying stability index for each IM category to the active power generated by key generators. PTSC is transformed into a set of explicit constraints and embedded into the traditional OPF formula to obtain the PTSCOPF model.

[0045] 2) This invention proposes an effective method for transient stability prevention and control of power systems, achieving rapid evaluation of CCT and IM, as well as rapid solution of PTSCOPF. Compared with traditional data-driven tools, the proposed data-driven method based on AugBoost and DW-PSO overcomes the shortcomings of traditional evaluation models, such as large computational load, local optima, and overfitting. Attached Figure Description

[0046] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0047] Figure 1 This is a flowchart of the method of the present invention;

[0048] Figure 2 This is a schematic diagram of an IEEE 68-node system in an embodiment of the present invention;

[0049] Figure 3 This is a test result diagram of prevention and control using the method of the present invention in an embodiment of the present invention. Detailed Implementation

[0050] A method for preventing and controlling transient stability in power systems with a high proportion of wind power grid connection includes the following steps:

[0051] Step 1: Set up a set of anticipated faults and construct a PTSC with IM classification for power systems with a high proportion of wind power connected to the grid.

[0052] Step 2: Based on historical operating data and simulation data of the power system, determine the CCT and IM under the corresponding fault using the time-domain simulation method, and establish an initial sample set;

[0053] Step 3: Based on the constructed sample set, perform offline training on AugBoost to form an evaluation model based on AugBoost, and perform online evaluation on CCT and IM;

[0054] Step 4: Based on the evaluation results, assess the current system operation status for PTSC, calculate the sensitivity of the probability of CCT meeting stability indicators to the active power generated by key generators in each IM category, transform PTSC into a set of explicit constraints, and embed them into the traditional OPF model to obtain the PTSCOPF model.

[0055] Step 5: Solve the PTSCOPF model using the DW-PSO algorithm to obtain the optimal operating point of the power system.

[0056] In step 1, all lines that may cause transient instability are set as the expected fault set, and the PTSC of IM classification is constructed as shown in formula (1):

[0057] ρ(τ((x sol ,y sol ),Ω L ,ζ,u,ε,T)>α)≥β (1)

[0058] In the formula: ρ(·) represents probability; τ represents the relevant stability index CCT; (x sol ,y sol ) represents a control scheme, that is, an algebraic variable of the system state after a certain control; Ω L ζ represents the set of lines; ζ represents the probability density function of fault occurrence for each line; u represents the control variables, including the active power output of each synchronous generator; ε represents the uncertainty affecting the system operating point, such as the change in power generation for each WPP; T represents the time interval between two consecutive control operations. Since OPF is usually solved for a one-hour control mode, T is set to one hour; α is the defined CCT threshold. Equation (1) shows that if Ω between two consecutive control operations L If a random fault occurs on the line, considering ζ and ε during this period, the probability that CCT > α must be no less than the safety level β.

[0059] Analyzing each potential fault individually after considering ε is challenging, making formula (1) complex in the OPF problem. Given that a particular control solution may have a similar impact on the system vulnerability to multiple faults triggering the same IM, a more general and manageable approach to PTSC is adopted, as shown in formula (2):

[0060]

[0061] Where: Ω IM k represents the set of all possible IMs in the power grid; k represents Ω. IM The number.

[0062] This approach helps to set flexible probabilistic stability criteria for each IM that needs to be prevented. IMs are similar to coherent generator sets, the main difference being that they contain only two sets of generator sets: critical generator sets and surplus generator sets.

[0063] In step 2, CCT and IM are two important indicators in power system transient stability analysis. The value of CCT determines the relationship between the system's stability level and specific faults, while the identification of IM determines the critical synchronous generator that has lost synchronization. A set of data pairs (CCT, IM) is represented as Ω. CCT,IM This includes CCT and IM for the power system under all possible failure scenarios. Ω CCT,IM It reflects the overall stability level of the power system and identifies generators prone to losing synchronization, providing a basis for further preventive control.

[0064] Power companies and power system simulation software can provide a large amount of historical power system operating data and simulation data. Based on the corresponding historical observation data and simulation data, statistical models are estimated to address various uncertainties (output of each wind turbine, load level, and fault location). Then, time-domain simulations are performed, sampling uncertainties in the system from the corresponding statistical models in each simulation. Finally, selected features (synchronous generator rotor angle, fault location, active power output of the synchronous generator and wind power plant, and reactive power output of the synchronous generator) and target labels (CCT and IM) are extracted from the simulation results and stored in a sample set.

[0065] In step 3, for a power system with a high proportion of wind power connected to the grid, the potential operating points increase exponentially, making it very time-consuming to calculate the CCT and identify the IM through time-domain simulation. Therefore, the constructed sample set is used to train the AugBoost model to build a mapping relationship between variables and CCT and IM, enabling online evaluation.

[0066] The evaluation models include a regression model (for evaluating the CCT system) and a multi-class classification model (for evaluating the IM system). AugBoost is a machine learning algorithm that can be used in conjunction with many other types of learning algorithms and can be applied to multi-class classification and regression problems. Unlike the regular GBDT model, AugBoost enhances dataset features between GBDT iterations to achieve better results.

[0067] The AugBoost algorithm mainly consists of two parts: 1) Feature extraction and combination. First, an ANN is trained using the original feature data of the power system. The ANN learns the information and extracts a new set of features. Then, the newly extracted features are combined with the original features; 2) DT-based evaluation model. The combined features are input into the DT model for training, constructing a mapping relationship between feature data and stable evaluation labels.

[0068] In step 4, it is assumed that the probabilistic transient stability level is related to the... There is a quasi-linear relationship between the generated active power. Based on this relationship, in order to satisfy the PTSC shown in formula (1), the active power generated can be calculated from... Transferred to Active power generation. and Let be the set of critical and remaining synchronous generators for the k-th IM. The sensitivity of the probability that the CCT satisfies the stability index to the active power shift from the critical generator to the remaining generators is:

[0069]

[0070] In the formula: ΔP represents the maximum power output change of all synchronous generators between two consecutive iterations.

[0071] Based on the assumed quasi-linear relationship, in order to achieve the required level of stability, from Transferred to Target active power The calculation formula is as follows:

[0072]

[0073] Convert PTSC into a set of explicit constraints:

[0074]

[0075] In the formula: P g P represents the active power output of the g-th synchronous generator; g ' represents the active power output of the g-th synchronous generator before the power transfer.

[0076] Embedding it into the traditional OPF model yields the PTSCOPF model. The other components of the PTSCOPF model are as follows:

[0077] (1) Objective function

[0078] The objective function is to minimize the total operating cost of the synchronous generator.

[0079]

[0080] In the formula: a 2g a 1g and a 0g P represents the power generation cost coefficient of the g-th synchronous generator; g S represents the active power output of the g-th synchronous generator; G It is a generator set that participates in prevention and control.

[0081] (2) Equality constraints

[0082] Power flow equilibrium equation:

[0083]

[0084] In the formula: P Gi and Q Gi P represents the active and reactive power output of the generators on bus i; Li and Q Li It represents the active and reactive loads on bus i; |V i and |V j | represents the voltage amplitude on bus i and j; α ij It is the phase angle difference of the bus voltage; G ij and B ij These are the real and imaginary parts of the line admittance; S n It is a set of busbars.

[0085] (3) Inequality constraints

[0086] Stable operation constraints:

[0087]

[0088] In the formula: and These are the upper and lower limits of the generator's active power output; and The upper and lower limits of the reactive power source output; V i max and V i min These are the upper and lower limits of the bus voltage; and The upper and lower limits of the line thermal stability constraints; S lThis is a set of routes.

[0089] In step 5, the inertia weight ω in PSO reflects the particle's search capability. A high inertia weight indicates strong global search capability, and vice versa. In the standard PSO algorithm, ω is a constant. Although it has strong global capability in the early stages of the search process, its convergence speed is slow in the later stages, and it easily tends to local optima. Therefore, the inertia weight should be adjusted according to the search process to balance convergence speed and global search capability. To overcome the shortcomings of PSO and consider the constraints in the optimization model, a DW-PSO algorithm with a penalty function is proposed to optimize the parameters. When the particle's position does not meet the constraints, the fitness value is set to the maximum value through a penalty function. By setting the penalty function, the constrained optimization problem can be transformed into an unconstrained optimization problem. The DW-PSO algorithm is used to solve PTSCOPF to obtain the optimal operating mode of the power system. The specific steps are as follows:

[0090] (1) Input generator set, transmission line, busbar, and power system load data;

[0091] (2) Input PSO parameter data, namely inertial weight, acceleration constant, number of particles in the swarm, and maximum number of iterations;

[0092] (3) Randomly generate the position and velocity of the initial particle swarm;

[0093] (4) Assume the number of iterations is 0;

[0094] (5) Calculate the total cost of each particle based on the fitness function and check for cases where the constraints are not met. When a particle's position does not meet the constraints, set the fitness value to the maximum value using a penalty function;

[0095] (6) If the fitness of each particle is lower than a certain value, then use that fitness value as the optimal value;

[0096] (7) Update the velocity and position of particles in the particle swarm;

[0097] (8) If the maximum number of iterations has been reached, stop and output the result; otherwise, repeat step (5).

[0098] Example:

[0099] The embodiments used in this invention are based on the IEEE 68-node system, such as... Figure 2As shown, the system comprises 68 nodes, 20 transformers, and 16 generators. This test included all the steps described in the method of this invention, and was conducted on a computer equipped with an Intel Core i7 processor and 16GB of memory. The results were obtained. Five wind farms are located on buses 18, 22, 31, 41, and 42, each with an installed capacity of 800MW; therefore, the wind power installed capacity accounts for approximately 30% of the total load.

[0100] This test generated 6000 initial samples through time-domain simulation. The fault clearing time of the circuit breaker is typically less than 0.2 seconds. The CCT value considered in the simulation is between 0 and 0.25 seconds, meaning that faults with a CCT greater than 0.25 seconds can be considered safe because they can be cleared by the circuit breaker before the system reaches a critical state. The model test used 5x cross-validation.

[0101] The test accuracy of the evaluation model is shown in Table 1, where the test accuracy includes the MSE for evaluating CCT and the classification accuracy (Acc) for evaluating IM. The results verify the high accuracy of the trained model in evaluating CCT and IM. The trained model will be applied to subsequent prevention and control operations.

[0102] Table 1 Evaluation performance of the evaluation model

[0103] Evaluation object CCT IM accuracy <![CDATA[MSE:1.4150×10 -4 ]]> Acc: 99.21%

[0104] The solution obtained in the first iteration by the conventional OPF model does not satisfy PTSC. Using the proposed method, a preventative control solution is found after multiple iterations. The control effect is as follows: Figure 3 As shown, the system remained transiently stable even under fault conditions. The results demonstrate that using sensitivity analysis to address the transient stability prevention and control problem in power systems considering PTSC is feasible.

Claims

1. A method for preventing and controlling transient stability in power systems with a high proportion of wind power grid connection, characterized in that, Step 1: Set up the expected fault set and construct the probabilistic transient stability constraint (PTSC) for unstable mode (IM) classification for power systems with a high proportion of wind power grid connection. Step 2: Based on historical operating data and simulation data of the power system, determine the critical clearing time (CCT) and imminent time (IM) under the corresponding fault using the time-domain simulation method, and establish an initial sample set; Step 3: Based on the constructed sample set, perform offline training on the gradient boosting and stepwise feature enhancement AugBoost model to form an AugBoost-based evaluation model, and perform online evaluation on CCT and IM; Step 4: Based on the evaluation results, assess the current system operation status for PTSC, calculate the sensitivity of the probability of CCT satisfying stability index to the active power generated by key generators in each IM category, transform PTSC into a set of explicit constraints, and embed them into the traditional optimal power flow OPF model to obtain the PTSCOPF model. Step 5: Solve the PTSCOPF model using the Dynamic Inertial Weighted Particle Swarm Optimization (DW-PSO) algorithm to obtain the optimal operating point of the power system.

2. The method of claim 1, wherein, In step 1, the PTSC for IM classification is constructed as shown in formula (1): （1）； In the formula: Represents probability; Represents the relevant stability indicator CCT; It represents a control scheme, that is, an algebraic variable of the system state after a certain control. Representative line set; The probability density function representing the occurrence of faults on each line; Represents control variables, including the active power output of each synchronous generator; This represents the uncertainty affecting the system's operating point, such as the variation in power generation per WPP; T Represents the time interval between two consecutive control operations; It is the defined CCT threshold; Represents the security level; Since a certain control solution may have a similar impact on the system vulnerability to multiple faults that trigger the same IM, a more general and easier-to-handle PTSC is formed, as shown in Equation (2): （2）； In the formulae: represents the set of all IMs that can be present in the power grid; k represents the number of the.

3. The method of claim 1, wherein, In step 2, a set of data pairs (CCT, IM) is represented as , containing the CCT and IM of the power system under all possible fault scenarios, reflecting the overall stability level of the power system and identifying the generators prone to loss of synchronism.

4. The method according to claim 1 or 3, characterized in that, In step 2, when establishing the initial sample set, several historical power system operating point operation data and simulation data are obtained from the power company. Based on the corresponding historical observation data and simulation data, statistical models of various uncertainties are estimated. Then, time-domain simulation is performed. In each simulation, uncertain variables in the system are sampled from the corresponding statistical model. Finally, the selected features and target labels are extracted from the simulation results and stored in the sample set.

5. The method of claim 1, wherein, In step 4, it is assumed that there is a quasi-linear relationship between the probability transient stability level and the generated active power; In step 4, it is assumed that there is a quasi-linear relationship between the probability transient stability level and the generated active power; Based on this relationship, in order to satisfy the PTSC shown in formula (1), it is possible to calculate from Transferred to Active power generation, and They are the first k The sensitivity of the probability that the critical and remaining synchronous generator sets (IMs) meet the stability criteria to the active power shift from the critical generator to the remaining generators is as follows: （3）； wherein: represents the maximum power output change of all synchronous generators between two consecutive iterations; Based on the assumed quasi-linear relationship, to achieve the required level of stability, from is transferred to the target active power The calculation formula is as follows: （4）； Convert PTSC into a set of explicit constraints: （5）； In the formulae: denotes the active output power of the gth synchronous generator; g denotes the active output power of the gth synchronous generator; denotes the active output power of the gth synchronous generator before power transfer. Embedding it into the traditional OPF model yields the PTSCOPF model.

6. The method of claim 5, wherein, The objective function and constraints of the PTSCOPF model are as follows: (1) Objective function The objective function is to minimize the total operating cost of the synchronous generator. （6）； In the formula: , and Representing the g The power generation cost coefficient of a synchronous generator; Representing the g The active power output of the synchronous generator; These are generator sets involved in prevention and control. (2) Equality constraints Power flow equilibrium equation: （7）； In the formula: and It is a busbar i The active and reactive power output of the generator on the platform; and It is a busbar i Active and reactive loads on the load; and It is a busbar i and j Voltage amplitude; It is the phase angle difference of the bus voltage; and These are the real and imaginary parts of the line admittance; It is a set of busbars; (3) Inequality constraints Stable operation constraints: （8）； In the formula: and These are the upper and lower limits of the generator's active power output; and The upper and lower limits of reactive power source output; and These are the upper and lower limits of the bus voltage; and The upper and lower limits of the line thermal stability constraints; This is a set of routes.

7. The method of claim 1, wherein, In step 5, the DW-PSO algorithm is used to solve the PTSCOPF model to obtain the optimal operating point of the power system. To overcome the shortcomings of PSO, such as slow convergence speed and tendency to approach local optima in the later stages of the search process, and considering the constraints in the optimization model, a DW-PSO algorithm with a penalty function is proposed to optimize the parameters. When the particle position does not meet the constraints, the fitness value is set to the maximum value through the penalty function. By setting the penalty function, the constrained optimization problem can be transformed into an unconstrained optimization problem. The specific steps are as follows: (1) Input generator set, transmission line, busbar, and power system load data; (2) Input PSO parameter data, namely inertial weight, acceleration constant, number of particles in the swarm, and maximum number of iterations; (3) Randomly generate the position and velocity of the initial particle swarm; (4) Assume the number of iterations is 0; (5) Calculate the total cost of each particle according to the fitness function and check for non-compliance of constraints; when the position of a particle does not meet the constraints, set the fitness value to the maximum value through the penalty function; (6) If the fitness of each particle is lower than a certain value, then the fitness value is the optimal value; (7) Update the velocity and position of particles in the particle swarm; (8) If the maximum number of iterations has been reached, stop and output the result; otherwise, repeat step (5).

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