A transient stability constrained optimal power flow determination method containing wind power grid connection

CN122801283APending Publication Date: 2026-09-22CHINA THREE GORGES UNIV
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Patent Information

Application Number
CN202610900842.5
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2026-06-22
Publication Date
2026-09-22

AI Technical Summary

Technical Problem

[0005]本发明的目的是为了解决现有技术中单一概率分布模型难以精准刻画多风场间复杂相关性、常规时域仿真数据处理负荷大,且场景缩减操作易丢失极端工况信息的问题,从而导致含风电并网的暂态稳定约束最优潮流评估模型输入与实际工况存在严重偏差、模型求解效率与极端场景适应性低下,进而导致电力系统或电网调度系统在面临风电随机波动时,难以兼顾高精度建模与实时快速响应,极易因暂态失稳而引发系统脱网、大面积停电或底层电气设备损坏的技术问题,而提出了本发明提供的一种含风电并网的暂态稳定约束最优潮流确定方法

Benefits of technology

1)本发明通过引入Pair-Copula函数构建联合概率分布模型,克服了传统单一概率模型的局限性,很好的描述了多风电场预测出力误差之间的复杂空间相关性,解决了模型输入端与实际工况脱节的问题,为电力系统提供了更贴近真实物理运行状态的基础数据;

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Abstract

A transient stability constraint optimal power flow determination method containing wind power grid connection, comprising the following steps: step 1: based on historical data, a joint distribution model under wind power grid connection is constructed by using Pair-Copula function; step 2: a transient stability constraint optimal power flow (CC-TSCOPF) model containing chance constraint is constructed, and PI-seq2seq model and transient stability index (TSI) are used to construct transient stability constraint; step 3: through principal component analysis (PCA) method in Lite polynomial chaos expansion (Lite-PCE) method and Rosenblatt inverse transformation, high-dimensional random variables are converted into a single highly correlated random variable, and the CC-TSCOPF model is determined; step 4: the improved osprey optimization algorithm (IOOA) is used to solve the transformed CC-TSCOPF model.
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Description

Technical Field

[0001] This invention relates to the fields of new energy and power system technology, and in particular to power system transient stability analysis, wind power output power model establishment and optimal power flow acquisition technology, specifically to a method for determining optimal power flow with transient stability constraints including wind power grid connection. Background Technology

[0002] With the accelerated transformation of the energy structure, wind power, as an important form of clean and renewable energy, is experiencing a continuous increase in its grid connection penetration rate. However, wind power output exhibits strong randomness and volatility, posing a severe challenge to the safe and stable operation and economic dispatch of the power system. Optimal power flow technology is a core means to achieve efficient operation of the power system and optimize resource allocation. Incorporating transient stability constraints into the optimal power flow model and constructing a transient stability-constrained optimal power flow model is a key technical path to ensure the safe and economical operation of power systems with high wind power penetration.

[0003] Patent application CN118611066A discloses a transient stability-constrained optimal power flow calculation method for wind power integration into a power system. This method first establishes a probabilistic model of wind power output based on the Weibull distribution, generates wind power scenarios through Latin hypercube sampling, and simplifies the number of scenarios using a synchronous back-substitution reduction method. Then, it constructs transient stability constraints using an input convex neural network, embeds them into the optimal power flow model, and completes the model solution through a search space reduction algorithm. However, this method has certain limitations. It uses only a single Weibull distribution to describe the characteristics of wind power output, failing to accurately characterize the complex correlation of predicted output errors among multiple wind farms, leading to deviations between the model input and actual operating conditions. Furthermore, the synchronous back-substitution reduction method, when simplifying scenarios, removes some low-probability but high-impact extreme scenarios, reducing the model's adaptability to extreme system conditions. Patent application CN104766142A discloses a transient stability-constrained optimal power flow calculation method based on EEAC and trajectory sensitivity. This method starts with the conventional optimal power flow solution and classifies anticipated faults through transient time-domain simulation and equivalent operations using the Extended Equal Area Criteria (EEAC). Subsequently, transient stability constraints are constructed based on trajectory sensitivity analysis, and the constraints are embedded into the optimal power flow model for iterative solution. However, this method has certain limitations. It relies on traditional time-domain simulation and EEAC equivalent operations, requiring individual simulation analysis for each anticipated fault, resulting in high computational cost and long processing time. Furthermore, trajectory sensitivity analysis is suitable for deterministic scenarios; in scenarios with random fluctuations in wind power output, the sensitivity coefficient fluctuates significantly with changes in random variables, leading to constraint failure.

[0004] In summary, this study proposes an optimal power flow approach with transient stability constraints for wind power grid integration, aiming to ensure the transient stability of the power system under the condition of gradually increasing wind power grid integration penetration. This research not only addresses the problem of insufficient modeling accuracy caused by the randomness of wind power output, but also efficiently constructs transient stability constraints to meet the timeliness requirements of power system operation, thereby improving the transient stability level and economic efficiency of power systems with wind power grid integration. Summary of the Invention

[0005] The purpose of this invention is to address the problems in existing technologies, such as the difficulty of accurately depicting the complex correlations between multiple wind farms using a single probability distribution model, the heavy processing load of conventional time-domain simulation data, and the easy loss of extreme operating condition information during scenario reduction operations. These problems lead to serious deviations between the input of the transient stability constraint optimal power flow evaluation model containing wind power grid connection and the actual operating conditions, as well as low model solution efficiency and adaptability to extreme scenarios. Consequently, when facing random fluctuations in wind power, power systems or grid dispatching systems struggle to achieve both high-precision modeling and real-time rapid response, making them highly susceptible to system disconnection, large-scale power outages, or damage to underlying electrical equipment due to transient instability. Therefore, this invention proposes a transient stability constraint optimal power flow determination method for wind power grid connection.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A method for determining optimal power flow with transient stability constraints including wind power grid connection includes the following steps: Step 1: Obtain historical wind speed data of the wind farm, determine the wind power output prediction result based on the historical wind speed data, and then determine the joint probability distribution model of the wind power output prediction error; Step 2: Based on the joint probability distribution model output in Step 1, and combining the optimal power flow objective function with chance constraints and the operating boundary, the PI-seq2seq model is introduced to determine the mapping conditions between the active power output of the generator group and the transient stability index, and finally the mathematical expression of the transient stability optimal power flow with chance constraints is obtained. Step 3: For the optimal power flow mathematical expression output in Step 2, perform Lite polynomial chaotic expansion dimensionality reduction operation to transform the high-dimensional random variable into a single-dimensional deterministic polynomial expression step by step, thereby transforming the chance constraint into a deterministic constraint. Step 4: Receive the deterministic constraints output from Step 3, perform iterative optimization, and finally obtain the optimal active power parameters for power system dispatch control.

[0007] Step 1 specifically includes the following sub-steps: Step 1-1: Input the acquired historical wind speed data into the kernel limit learning machine for feature processing, and the kernel limit learning machine outputs wind power output prediction data; Step 1-2: Collect the wind power output prediction data output in Step 1-1 and collect the corresponding real data to determine the prediction deviation data; input the prediction deviation data of different wind farms into the Pair-Copula function to capture the spatial correlation of prediction deviations between wind farms and output the joint probability distribution model of prediction output error.

[0008] In steps 1-2, the joint probability distribution formula used for processing with the Pair-Copula function is expressed as follows: (1); In the formula: For wind farm Predicted output error; For wind farm The predicted output error; For wind farm Predicted output; For wind farm Predicted output; for The probability density function; For wind farm Actual output; For wind farm The actual output.

[0009] Step 2 specifically includes the following sub-steps: Step 2-1: Combining the physical operating boundary of the power grid, construct the total generation cost objective function of the optimal power flow, the power flow balance equality constraints of the conventional power grid, and the inequality chance constraints to generate the basic optimal power flow structure; Step 2-2: Input the system operating state characteristics into the pre-trained PI-seq2seq model to replace the traditional transient stability numerical simulation process, and output the maximum power angle difference prediction value corresponding to each fault scenario in the expected fault set; calculate the transient stability index TSI based on the maximum power angle difference prediction value, and embed it as a transient stability constraint into the optimal power flow model, and finally construct a transient stability constraint optimal power flow model with chance constraints.

[0010] In step 2-1, the objective function and constraints are specifically as follows: 1) Objective function: (2); In the formula: Total power generation cost; This is the expected value; This represents the total number of synchronous generators. , , For the first Cost coefficient of a generator; For the first The active power of the synchronous generator.

[0011] 2) Equality constraints: (3); In the formula: , This refers to the active and reactive power of the system's wind turbine generators. , The active and reactive power of the system load; This refers to the reactive power of the system's synchronous generator. , For nodes , The voltage amplitude; , For nodes , The real and imaginary parts of the line admittance; For nodes , The phase angle difference between them; This represents the total number of nodes.

[0012] 3) Inequality constraints: (4); In the formula: The probability function that satisfies the inequality; , These represent the upper and lower limits of the generator's active power. , These represent the upper and lower limits of the generator's reactive power. , These are the upper and lower bounds of the node voltage; , For the line The meritorious current and its upper limit; , , , These are the set active power, reactive power, node voltage, and line voltage of the thermal power generator. The confidence level of the positive trend.

[0013] 4) Transient stability constraints: In step 2-2, the implicit mapping processing operation of the PI-seq2seq model uses the following formula: (5); In the formula: This is the trained PI-seq2seq model; , , Input for the PI-seq2seq model; Output the power angle for the model.

[0014] The formula used to determine the transient stability index is: (6); In the formula: Let be the maximum power angle difference between any two generators; when When the system is stable; when At that time, the system became unstable.

[0015] Step 3 specifically includes the following steps: Step 3-1: Perform principal component analysis and orthogonalization feature extraction on high-dimensional random variables with chance constraints to reduce dimensionality; Step 3-2: Use the inverse Copula transform to reproject the dimension-reduced variables output in Step 3-1 into transition variables with strong correlation characteristics; Step 3-3: Perform a second principal component analysis projection operation on the transition variables output in Step 3-2 to select the first principal component in order to compress the data space into a single-dimensional structure; Step 3-4: Construct the Lite polynomial chaotic expansion based on the single variable output in Step 3-3; Steps 3-5: Use the least squares method to find the expansion coefficients and substitute them back into the expansion formula to complete step 3. Finally, the mathematical expression of the optimal power flow is transformed into a deterministic constraint of deterministic polynomial expansion.

[0016] In step 3-1, the formula used to perform the dimensionality reduction operation is: (7); In the formula: These are the orthogonal principal component vectors after dimensionality reduction; Represents the PCA transform operator; Centered data matrix for power prediction bias; for The transpose of a matrix composed of vectors.

[0017] In step 3-2, the formula used for the inverse transformation mapping operation is: (8); In the formula: These are highly correlated variables; This represents the Copula-based inverse Rosenblatt transformation operator.

[0018] In step 3-3, the formula used for the second principal component projection operation is: (9); In the formula: for The transpose matrix of the eigenvectors; Principal component projection, and the first principal component can be directly selected. It is a single variable.

[0019] In steps 3-4, the formula used for generating the expansion is: (10); In the formula: The output will be random. This is the polynomial truncation number, usually taken as 8 to 10; PCE coefficient; It is an orthogonal basis; obey A uniform distribution on the surface.

[0020] In steps 3-5, the formula used to solve for the expansion coefficients is: (11); (12); In the formula: It is a polynomial basis matrix; For matrix The transpose of the matrix; This represents the number of samples.

[0021] Step 4 specifically includes the following sub-steps: Step 4-1: Collect the line parameters, node data, and generator foundation output parameters of the actual power system, and load the collected parameters together with the output boundary conditions determined in Step 1 into the input of the improved Osprey optimization algorithm. Step 4-2: Initialize the parameters of the improved Osprey optimization algorithm, set the Osprey population size and maximum number of iterations, generate the initial position of each independent individual in the population, and set the initial position as the control variable of the deterministic constraint; Step 4-3: Import the location information of each independent entity into deterministic constraints for power flow calculation, judge the execution result based on the physical constraints of the power grid, and extract the fitness variable representing the scheduling quality as the output; Step 4-4: Based on the fitness variable, compare the positions of different individuals, introduce the Cauchy mutation perturbation mechanism and the reverse learning strategy to break out of local constraints, instruct the population to update and generate a new generation of individual positions; Step 4-5: Verify whether the algorithm has reached the maximum number of iterations. If not, backtrack the position of the new generation of individuals to step 4-3 for repeated evaluation. If it has reached the maximum number of iterations, terminate the optimization process and output the historical global optimal position.

[0022] Compared with the prior art, the present invention has the following technical effects: 1) This invention introduces a Pair-Copula function to construct a joint probability distribution model, which overcomes the limitations of traditional single probability models, effectively describes the complex spatial correlation between the predicted output errors of multiple wind farms, solves the problem of the model input being disconnected from the actual operating conditions, and provides basic data for the power system that is closer to the real physical operating state. 2) This invention uses the PI-seq2seq model to replace the traditional numerical solution process of differential algebraic equations, and establishes an end-to-end mapping relationship between generator output and transient stability index. This feature eliminates the massive and time-consuming traditional time-domain simulation process, and shortens the processing time to the millisecond level while ensuring the accuracy of transient stability constraints, effectively meeting the high timeliness operation requirements of modern power systems. 3) This invention innovatively adopts the Lite-PCE method to reduce the dimensionality of high-dimensional random variables and transform them into deterministic ones; this avoids the information loss caused by the forced elimination of low-probability extreme scenarios in traditional scenario reduction methods, and retains the randomness characteristics of the entire working condition, so that the final generated scheduling scheme still has good system anti-disturbance capability when facing extreme wind power fluctuations. 4) For the high-complexity optimal power flow model after deterministic transformation, this invention configures IOA. By introducing reverse learning and mutation strategies, it effectively escapes the local optimum trap and ensures that the system scheduling system can still quickly and stably search for the globally feasible solution under strict transient stability constraints, thus ensuring the stable operation of the power grid. Attached Figure Description

[0023] 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 improved IEEE 39-node system in an example of the present invention; Figure 3 This is a dynamic response curve of the generator power angle of the improved IEEE 39-bus system in this invention example without using the method of this invention; Figure 4 This is the dynamic response curve of the generator power angle obtained by the method of this invention; Figure 5 This is a flowchart of the algorithm for solving TSCOPF in this invention. Detailed Implementation

[0024] like Figure 1 As shown, a method for determining the optimal power flow under transient stability constraints involving wind power grid connection includes the following steps: Step 1: Obtain historical wind speed data of the wind farm, determine the wind power output prediction result based on the historical wind speed data, and then determine the joint probability distribution model of the wind power output prediction error; Step 2: Based on the joint probability distribution model output in Step 1, and combining the optimal power flow objective function with chance constraints and the operating boundary, the PI-seq2seq model is introduced to determine the mapping conditions between the active power output of the generator group and the transient stability index, and finally the mathematical expression of the transient stability optimal power flow with chance constraints is obtained. Step 3: For the optimal power flow mathematical expression output in Step 2, perform Lite polynomial chaotic expansion dimensionality reduction operation to transform the high-dimensional random variable into a single-dimensional deterministic polynomial expression step by step, thereby transforming the chance constraint into a deterministic constraint. Step 4: Receive the deterministic constraints output from Step 3, perform iterative optimization, and finally obtain the optimal active power parameters for power system dispatch control.

[0025] In step 1: Based on historical data, a joint distribution model for wind power grid connection is constructed using the Pair-Copula function; Step 2: Construct a ChanceConstraintTransient Stability Constrained Optimal Power Flow (CC-TSCOPF) model, and use the PI-seq2seq model and the Transient Stability Index (TSI) to construct transient stability constraints; Step 3: Using the Principal Component Analysis (PCA) and Rosenblatt inverse transformation in the Lite Polynomial Chaos Expansion (Lite-PCE) method, the high-dimensional random variables are transformed into a single highly correlated random variable, thus performing a deterministic transformation on the CC-TSCOPF model. Step 4: Solve the transformed CC-TSCOPF model using the Improved Osprey Optimization Algorithm (IOOA); Further: In step 1, to ultimately obtain the joint probability distribution model of the prediction error, the following sub-steps are specifically included: Step 1-1: Input the acquired historical wind speed data into the kernel limit learning machine for feature processing, and the kernel limit learning machine outputs wind power output prediction data; Step 1-2: Collect the wind power output prediction data output in Step 1-1 and collect the corresponding real data to determine the prediction deviation data; input the prediction deviation data of different wind farms into the Pair-Copula function to capture the spatial correlation of prediction deviations between wind farms, and output the joint probability distribution model of prediction output error to overcome the limitations of traditional single probability models, accurately characterize the complex spatial correlation between prediction output errors of multiple wind farms, and provide basic data for the power system that closely reflects the real physical operating state.

[0026] In steps 1-2, the joint probability distribution formula used for processing with the Pair-Copula function is expressed as follows: (1); In the formula: For wind farm Predicted output error; For wind farm The predicted output error; For wind farm Predicted output; For wind farm Predicted output; for The probability density function; For wind farm Actual output; For wind farm The actual output.

[0027] Step 2 specifically includes the following sub-steps: Step 2-1: Combining the physical operating boundary of the power grid, construct the total generation cost objective function of the optimal power flow, the power flow balance equality constraints of the conventional power grid, and the inequality chance constraints to generate the basic optimal power flow structure; Step 2-2: Input the system operating state characteristics into the pre-trained PI-seq2seq model to replace the traditional transient stability numerical simulation process, and output the maximum power angle difference prediction value corresponding to each fault scenario in the expected fault set; calculate the transient stability index TSI based on the maximum power angle difference prediction value, and embed it as a transient stability constraint into the optimal power flow model, and finally construct a transient stability constraint optimal power flow model with chance constraints.

[0028] In step 2-1, the objective function and constraints are specifically as follows: 1) Objective function: (2); In the formula: Total power generation cost; This is the expected value; This represents the total number of synchronous generators. , , For the first Cost coefficient of a generator; For the first The active power of the synchronous generator.

[0029] 2) Equality constraints: (3); In the formula: , This refers to the active and reactive power of the system's wind turbine generators. , The active and reactive power of the system load; This refers to the reactive power of the system's synchronous generator. , For nodes , The voltage amplitude; , For nodes , The real and imaginary parts of the line admittance; For nodes , The phase angle difference between them; This represents the total number of nodes.

[0030] 3) Inequality constraints: (4); In the formula: The probability function that satisfies the inequality; , These represent the upper and lower limits of the generator's active power. , These represent the upper and lower limits of the generator's reactive power. , These are the upper and lower bounds of the node voltage; , For the line The meritorious current and its upper limit; , , , These are the set active power, reactive power, node voltage, and line voltage of the thermal power generator. The confidence level of the positive trend.

[0031] 4) Transient stability constraints: The transient stability constraints in the TSCOPF model are generally represented by a set of differential-algebraic equations: (5); (6); In the formula: For state variables; For algebraic variables; For control variables; To describe the dynamic differential equation; This is the power balance algebraic equation.

[0032] In step 2-2, the implicit mapping processing operation of the PI-seq2seq model uses the following formula: (7); In the formula: This is the trained PI-seq2seq model; , , Input for the PI-seq2seq model; Output the power angle for the model.

[0033] The formula used to determine the transient stability index is: (8); In the formula: Let be the maximum power angle difference between any two generators; when When the system is stable; when At that time, the system became unstable.

[0034] In step 3, to eliminate the random variables in the optimal power flow mathematical expression obtained in step 2, the following steps are specifically included: Step 3-1: Perform principal component analysis and orthogonalization feature extraction on high-dimensional random variables with chance constraints to reduce dimensionality; Step 3-2: Use the inverse Copula transform to reproject the dimension-reduced variables output in Step 3-1 into transition variables with strong correlation characteristics; Step 3-3: Perform a second principal component analysis projection operation on the transition variables output in Step 3-2 to select the first principal component in order to compress the data space into a single-dimensional structure; Step 3-4: Construct the Lite polynomial chaotic expansion based on the single variable output in Step 3-3; Steps 3-5: Use the least squares method to find the expansion coefficients and substitute them back into the expansion formula to complete step 3. Finally, the optimal power flow mathematical expression is transformed into deterministic constraints of deterministic polynomial expansion to avoid information loss caused by the forced elimination of low-probability extreme scenarios by traditional scenario reduction methods, retain the randomness characteristics of the entire operating condition, and comprehensively improve the robustness of the power system in response to extreme weather and operating conditions.

[0035] In step 3-1, the formula used to perform the dimensionality reduction operation is: (9); In the formula: These are the orthogonal principal component vectors after dimensionality reduction; Represents the PCA transform operator; Centered data matrix for power prediction bias; for The transpose of a matrix composed of vectors.

[0036] In step 3-2, the formula used for the inverse transformation mapping operation is: (10); In the formula: These are highly correlated variables; This represents the Copula-based inverse Rosenblatt transformation operator.

[0037] In step 3-3, the formula used for the second principal component projection operation is: (11); In the formula: for The transpose matrix of the eigenvectors; Principal component projection, and the first principal component can be directly selected. It is a single variable.

[0038] In steps 3-4, the formula used for generating the expansion is: (12); In the formula: The output will be random. This is the polynomial truncation number, usually taken as 8 to 10; PCE coefficient; It is an orthogonal basis; obey A uniform distribution on the surface.

[0039] In steps 3-5, the formula used to solve for the expansion coefficients is: (13); (14); In the formula: It is a polynomial basis matrix; For matrix The transpose of the matrix; This represents the number of samples.

[0040] Step 4 specifically includes the following sub-steps: Step 4-1: Collect the line parameters, node data, and generator foundation output parameters of the actual power system, and load the collected parameters together with the output boundary conditions determined in Step 1 into the input of the improved Osprey optimization algorithm. Step 4-2: Initialize the parameters of the improved Osprey optimization algorithm, set the Osprey population size and maximum number of iterations, generate the initial position of each independent individual in the population, and set the initial position as the control variable of the deterministic constraint; Step 4-3: Import the location information of each independent entity into deterministic constraints for power flow calculation, judge the execution result based on the physical constraints of the power grid, and extract the fitness variable representing the scheduling quality as the output; Step 4-4: Based on the fitness variable, compare the positions of different individuals, introduce the Cauchy mutation perturbation mechanism and the reverse learning strategy to break out of local constraints, instruct the population to update and generate a new generation of individual positions, so as to ensure that under the strict transient stability constraints, the scheduling system can quickly and stably search for the global feasible solution and improve the efficiency of obtaining the global optimal solution under complex high-dimensional constraints. Step 4-5: Verify whether the algorithm has reached the maximum number of iterations. If not, backtrack the position of the new generation of individuals to step 4-3 for repeated evaluation. If it has reached the maximum number of iterations, terminate the optimization process and output the historical global optimal position. Finally, convert the optimal position into the optimal active power parameters at the bottom layer of the power grid to execute generator scheduling, thereby ensuring the stable and safe operation of the power grid with a high proportion of wind power penetration.

[0041] Example: To verify the effectiveness of this invention, it was tested on the IEEE 39-bus system. Two synchronous generators located at nodes 5 and 16 were replaced with wind turbines with rated capacities of 250MW and 300MW, respectively. The remaining eight synchronous generators maintained their original parameters. Based on the historical power output data of the two wind farms, point prediction models for wind power output were constructed using a kernel extreme learning machine, and the prediction errors were calculated. The prediction errors of the two wind farms were modeled using a Pair-Copula function to jointly assess their probability distribution, fully considering the spatial correlation between the wind farms.

[0042] Table 1. Accuracy of Wind Power Output Prediction:

[0043] A three-phase short-circuit fault was set up on the transmission line between nodes 21 and 22. The fault occurred for 0.1 seconds and was cleared after 0.15 seconds. A simulation analysis was performed on the fault for 20 seconds. Using the ANDES time-domain simulation tool, TSI samples were generated under different generator output combinations to train a PI-seq2seq model and establish the mapping relationship between generator output and system transient stability. The model input was the active power output of 8 generators, and the output was the maximum power angle difference under the corresponding fault, which served as the basis for judging transient stability constraints.

[0044] The aforementioned wind power scenario and transient stability constraints were embedded into the CC-TSCOPF model. The Lite-PCE method was used to reduce the dimensionality of the high-dimensional random variables and transform them into deterministic values. Subsequently, the IOOA algorithm was used to solve the transformed optimized model. During the solution process, the algorithm population size was set to 50, and the maximum number of iterations was 200.

[0045] Table 2 Comparison of transient stability results before and after optimization:

[0046] Simulation results show that without the method of this invention, the system experiences transient instability after a fault occurs, the generator power angle difference continues to increase, and the system cannot recover stability. However, after optimization using the method of this invention, the power angle response curve gradually converges after the fault is cleared, all generators maintain synchronous operation, and the system maintains transient stability.

[0047] Table 3. Calculation results of the steady-state power angle curve:

[0048] Compared with existing technologies, the method of this invention still shows good adaptability in the IEEE 39-bus system containing wind farms. The Pair-Copula function effectively characterizes the correlation of the output errors of the two wind farms, the PI-seq2seq model accurately fits the transient stability constraints, the Lite-PCE method avoids information loss caused by scene reduction, and the IOOA algorithm can still efficiently search for feasible solutions under complex constraints.

Claims

1. A method for determining optimal power flow under transient stability constraints involving wind power grid connection, characterized in that, Includes the following steps: Step 1: Obtain historical wind speed data of the wind farm, determine the wind power output prediction result based on the historical wind speed data, and then determine the joint probability distribution model of the wind power output prediction error; Step 2: Based on the joint probability distribution model output in Step 1, and combining the optimal power flow objective function with opportunity constraints and the operating boundary, the PI-seq2seq model is introduced to determine the mapping conditions between the active power output of the generator group and the transient stability index, and finally the mathematical expression of the optimal power flow with opportunity constraints and transient stability constraints is obtained. Step 3: For the optimal power flow mathematical expression output in Step 2, perform Lite polynomial chaotic expansion dimensionality reduction operation to transform the high-dimensional random variable into a single-dimensional deterministic polynomial expression step by step, thereby transforming the chance constraint into a deterministic constraint. Step 4: Receive the deterministic constraints output from Step 3, perform iterative optimization, and finally obtain the optimal power output scheme for power system dispatch control.

2. The method according to claim 1, characterized in that, Step 1 specifically includes the following sub-steps: Step 1-1: Input the acquired historical wind speed data into the kernel limit learning machine for feature processing, and the kernel limit learning machine outputs wind power output prediction data; Step 1-2: Collect the wind power output prediction data output in Step 1-1 and collect the corresponding real data to determine the prediction deviation data; input the prediction deviation data of different wind farms into the Pair-Copula function to capture the spatial correlation of prediction deviations between wind farms and output the joint probability distribution model of prediction output error.

3. The method according to claim 2, characterized in that, In steps 1-2, the joint probability distribution formula used for processing with the Pair-Copula function is expressed as follows: (1); In the formula: For wind farm Predicted output error; For wind farm The predicted output error; For wind farm Predicted output; For wind farm Predicted output; for The probability density function; For wind farm Actual output; For wind farm The actual output.

4. The method according to claim 1, characterized in that, Step 2 specifically includes the following sub-steps: Step 2-1: Combining the physical operation boundary of the power grid, construct the total generation cost objective function of the optimal power flow, the power flow balance equality constraints including wind power grid connection, and the inequality chance constraints to generate the basic optimal power flow structure; Step 2-2: Input the system operating state characteristics into the pre-trained PI-seq2seq model to replace the traditional transient stability numerical simulation process, and output the maximum power angle difference prediction value corresponding to each fault scenario in the expected fault set; calculate the transient stability index TSI based on the maximum power angle difference prediction value, and embed it as a transient stability constraint into the optimal power flow model, and finally construct a transient stability constraint optimal power flow model with chance constraints.

5. The method according to claim 4, characterized in that, In step 2-1, the aim is to minimize the expected power generation cost of conventional units, while simultaneously satisfying deterministic power balance constraints taking into account wind power injection, probabilistic chance constraints for the risk of operating variables exceeding limits, and transient stability constraints characterized by differential algebraic equations.

6. The method according to claim 4, characterized in that, In step 2-2, the implicit mapping processing operation of the PI-seq2seq model uses the following formula: (2); In the formula: This is the trained PI-seq2seq model; , , Input for the PI-seq2seq model; Output the power angle for the model; The formula used to determine the transient stability index is: (3); In the formula: The maximum power angle difference between any two generators; when When the system is stable; when At that time, the system became unstable.

7. The method according to any one of claims 1 to 6, characterized in that, Step 3 specifically includes the following steps: Step 3-1: Perform principal component analysis and orthogonalization feature extraction on high-dimensional random variables with chance constraints to reduce dimensionality; Step 3-2: Use the inverse Copula transform to reproject the dimension-reduced variables output in Step 3-1 into transition variables with strong correlation characteristics; Step 3-3: Perform a second principal component analysis projection operation on the transition variables output in Step 3-2 to select the first principal component in order to compress the data space into a single-dimensional structure; Step 3-4: Construct the Lite polynomial chaotic expansion based on the single variable output in Step 3-3; Steps 3-5: Use the least squares method to find the expansion coefficients and substitute them back into the expansion formula to complete step 3. Finally, the mathematical expression of the optimal power flow is transformed into a deterministic constraint of deterministic polynomial expansion.

8. The method according to claim 7, characterized in that, In step 3-1, the formula used for dimensionality reduction is: (4); In the formula: These are the orthogonal principal component vectors after dimensionality reduction; Represents the PCA transform operator; Centered data matrix for power prediction bias; for The transpose of the matrix formed by the vectors; In step 3-2, the formula used for the inverse transformation mapping operation is: (5); In the formula: These are highly correlated variables; This represents the Copula-based inverse Rosenblatt transformation operator.

9. The method according to claim 8, characterized in that, In step 3-3, the formula used for the second principal component projection operation is: (6); In the formula: for The transpose matrix of the eigenvectors; Principal component projection, and the first principal component can be directly selected. It is a single variable; In steps 3-4, the formula used for generating the expansion is: (7); In the formula: The output will be random. This is the polynomial truncation number, usually taken as 8 to 10; PCE coefficient; It is an orthogonal basis; obey Uniform distribution on; In steps 3-5, the formula used to solve for the expansion coefficients is: (8); (9); In the formula: It is a polynomial basis matrix; For matrix The transpose of the matrix; This represents the number of samples.

10. The method according to claim 1, 2, 3, 4, 5, 6, 8, or 9, characterized in that, Step 4 specifically includes the following sub-steps: Step 4-1: Collect the line parameters, node data, and generator foundation output parameters of the actual power system, and load the collected parameters together with the output boundary conditions determined in Step 1 into the input of the improved Osprey optimization algorithm. Step 4-2: Initialize the parameters of the improved Osprey optimization algorithm, set the Osprey population size and maximum number of iterations, generate the initial position of each independent individual in the population, and set the initial position as the control variable of the deterministic constraint; Step 4-3: Import the location information of each independent entity into deterministic constraints for power flow calculation, judge the execution result based on the physical constraints of the power grid, and extract the fitness variable representing the scheduling quality as the output; Step 4-4: Based on the fitness variable, compare the positions of different individuals, introduce the Cauchy mutation perturbation mechanism and the reverse learning strategy to break out of local constraints, instruct the population to update and generate a new generation of individual positions; Step 4-5: Verify whether the algorithm has reached the maximum number of iterations. If not, backtrack the position of the new generation of individuals to step 4-3 for repeated evaluation. If the optimal position is reached, the optimization process is terminated and the historical global optimal position is output. Finally, this optimal position is transformed into the optimal active power parameters at the bottom layer of the power grid to execute generator scheduling.

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