Low-inertia operation scene construction method and system based on Frank-Copula function

Abstract

The invention belongs to the technical field of power system planning, and particularly relates to a low-inertia operation scene construction method and system based on an improved Frank-Copula function, and the method comprises the steps: obtaining the probability density distribution of historical low-inertia operation data of a power system through employing a kernel density estimation method; the low-inertia operation data comprises system equivalent inertia and system frequency-time response data, and then generating new low-inertia operation data satisfying power system topology constraints by using a Frank-Copula function based on probability density distribution of the low-inertia operation data; and superposing the obtained new low-inertia operation data and historical low-inertia operation data to generate a plurality of low-inertia operation scenes, and clustering the generated low-inertia operation scenes to obtain a low-inertia operation typical scene. According to the method, the power system topology constraint is introduced when the Frank-Copula function is utilized to generate the low-inertia scene operation data, the low-inertia operation scene of the power grid can be accurately described, and finally the typical scene generation precision is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of power system planning, and in particular relates to a method and system for constructing a low-inertia operation scenario based on a Frank-Copula function. Background Art

[0002] At present, new energy technologies represented by wind power and photovoltaics have been widely used. Since wind power and photovoltaics are affected by ever-changing meteorological conditions, their output has obvious randomness, intermittency and volatility, and they are often connected to the grid through power electronics interfaces, so they are also classified as inverter-based power sources. Among them, wind power is an AC power source, which needs to be fed into the grid after back-to-back power conversion to industrial frequency; while photovoltaic power is a DC power source, which needs to be fed into the grid through a single-stage DC-AC or two-stage DC-DC-AC. Different from the electromechanical coupling and synchronous operation mechanism of traditional synchronous generators, the converter decouples the power supply and the grid, so new energy is a typical non-synchronous power source.

[0003] Wind power and photovoltaic power have low energy density and generally need to be connected to the grid through power electronic interface devices. Therefore, large-scale access to new energy sources has brought a large number of power electronic devices to the power system. The power electronic interface of power sources and the application of DC transmission, DC distribution, DC load and large-scale energy storage have made the power grid develop in the direction of power electronics. However, the access of large-scale new energy sources has impacted the active frequency control system of the power system based on the synchronous mechanism. Power electronic switches have almost no inertia. New energy sources running in maximum power tracking mode do not respond to frequency changes, nor do they actively participate in the dispatch of active balance. At the same time, they bring new uncertainties to the source end of the power system and increase the regulation burden of the remaining synchronous power sources. In order to solve the problem of parallel operation of non-synchronous power sources and synchronous power sources, virtual synchronous machine control technology has been proposed. Its concept is to simulate the external characteristics of synchronous machines so that the grid-connected characteristics of new energy and traditional synchronous generators are compatible.

[0004] Low-inertia scenarios mainly refer to operating states in which the overall inertia level of the power system is reduced due to factors such as the increase in installed capacity of new energy generators (such as wind power and photovoltaics), the decrease in grid strength, and the reduction in the capacity of energy storage systems. In this context, the inertial support role of traditional power systems is weakened, resulting in a decrease in the frequency response capability of the system, which brings greater challenges to the stability and reliability of the power system. Therefore, scientifically generating typical low-inertia operating scenarios is crucial to ensuring the safety, stability and efficient operation of the power system. Traditional methods for generating typical low-inertia operating scenarios are often based on existing operating data, lack effective modeling of the physical topology of the power system, and fail to effectively consider the complex dependencies and nonlinear characteristics between different variables, resulting in insufficient scenario simulation accuracy and poor reliability, especially in the case of fluctuations in new energy output and changes in grid load. Summary of the invention

[0005] The purpose of the present invention is to address the above-mentioned problems existing in the prior art and to provide a method and system for constructing low-inertia operation scenarios based on Frank-Copula functions, which introduces power system topology constraints when generating low-inertia scenario operation data using Frank-Copula functions and effectively models the physical topology structure of the power system, thereby accurately characterizing the low-inertia operation scenarios of the power grid and improving the accuracy of scenario generation.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] In a first aspect, the present invention provides a low inertia running scenario construction method based on a Frank-Copula function, the scenario construction method comprising:

[0008] S1. Obtain historical low-inertia operation data of the power system, and obtain its probability density distribution using a kernel density estimation method; the low-inertia operation data includes system equivalent inertia and system frequency-time response data;

[0009] S2. Based on the probability density distribution of low inertia operation data, the Frank-Copula function is used to generate new low inertia operation data that meets the topology constraints of the power system;

[0010] S3, superimposing the historical low inertia operation data obtained by S1 and the new low inertia operation data obtained by S2 to generate multiple low inertia operation scenarios;

[0011] S4. Cluster the multiple low-inertia running scenarios generated by S3 to obtain a typical low-inertia running scenario.

[0012] The power system topology constraint includes a comprehensive SFR model and a system inertia level model. The comprehensive SFR model includes:

[0013]

[0014] In the above formula, G(s) is the transfer function; H sys represents the system equivalent inertia; s is the Laplace operator; D sys is the system equivalent damping; K L is the frequency regulation coefficient of the load; D is the generator damping; ΔP L is the load disturbance power; Δf is the system frequency; K G is the frequency regulation coefficient of the generator; a 0 、a 1 、b 0 All are fitting parameters;

[0015] The system inertia level model includes:

[0016]

[0017] E sys =E SG +E IM +E RE +E LOAD ;

[0018] In the above formula, P inject Inject power into the system; t is the unit time; E sys is the system equivalent kinetic energy; S sys E is the total rated generating capacity of the system; SG 、E IM 、E RE 、E LOAD They are synchronous kinetic energy, asynchronous kinetic energy, new energy virtual inertia, and static load equivalent inertia.

[0019] The S4 includes:

[0020] S41. For each low inertia running scenario, calculate the Euclidean distance between it and other low inertia running scenarios to obtain the distance vector: LS i ={L i1 , L i2 , …, L ij , …, L iN , j≠i}; where LS i Represents the distance vector of the i-th low inertia running scenario, L ij represents the Euclidean distance between the i-th low inertia running scenario and the j-th low inertia running scenario, and N represents the total number of low inertia running scenarios;

[0021] S42, distance vector LS i Sort in ascending order and select the distance vector LS i The Mth element value in is used as the scene density index of the i-th low inertia running scene i ; Finally, we get the scene density vector index = {index 1 , index 2 , ...index N};

[0022] S43, sorting the scene density vector index in ascending order, selecting the Tth element value in the scene density vector index as the scene threshold; taking all low-inertia running scenes with scene density higher than the scene threshold as a high-density scene set Hindex={index 1 , index 2 , ...index T};

[0023] S44, first select the low-inertia running scene with the highest scene index from the high-density scene set Hindex as the first cluster center, and then select the low-inertia running scene far away from all existing cluster centers from the high-density scene set Hindex as the next cluster center, until the number of existing cluster centers reaches the clustering threshold;

[0024] S45. Each cluster center is updated; the updating strategy is: within each cluster, the low-inertia running scenario with the lowest sum of distances to other low-inertia running scenarios is used as the new cluster center.

[0025] In S44, the clustering threshold K is determined by maximizing the objective function W:

[0026] W = Q - 0.2 * SSE;

[0027]

[0028]

[0029] m=∑ i，j A ij ;

[0030]

[0031] In the above formula, W is the objective function; Q is the clustering modularity; SSE is the sum of squares of clustering errors; |C i | represents the number of scenes in the i-th cluster; is the cluster center ε between the jth scene in the i-th cluster and the i-th cluster i The Euclidean distance between them; m is the total similarity of the similarity matrix A; A ij is an element in the similarity matrix A, indicating the similarity between the i-th scene and the j-th scene; d ij is the Euclidean distance between the i-th scene and the j-th scene; k i is the total similarity of the i-th scene; k j is the total similarity of the jth scene; δ(c i , c j ) is an intermediate variable.

[0032] In a second aspect, the present invention provides a low-inertia operation scenario construction system based on the Frank-Copula function, wherein the scenario construction system includes a data processing module, a data prediction module, a scenario generation module, and a clustering module;

[0033] The data processing module is used to obtain historical low-inertia operation data of the power system and obtain its probability density distribution using a kernel density estimation method, wherein the low-inertia operation data includes system equivalent inertia and system frequency-time response data;

[0034] The data prediction module is used to generate new low inertia operation data that meets the power system topology constraints based on the probability density distribution of the low inertia operation data using the Frank-Copula function;

[0035] The scenario generation module is used to superimpose the obtained historical low inertia operation data with the obtained new low inertia operation data to generate multiple low inertia operation scenarios;

[0036] The clustering module is used to cluster the generated multiple low-inertia running scenarios to obtain a typical low-inertia running scenario.

[0037] The power system topology constraints include a comprehensive SFR model and a system inertia level model; the comprehensive SFR model includes:

[0038]

[0039] In the above formula, G(s) is the transfer function; H sys represents the system equivalent inertia; s is the Laplace operator; D sys is the system equivalent damping; K L is the frequency regulation coefficient of the load; D is the generator damping; ΔP L is the load disturbance power; Δf is the system frequency; K G is the frequency regulation coefficient of the generator; a 0 、a 1 、b 0 All are fitting parameters;

[0040] The system inertia level model includes:

[0041]

[0042] E sys =E SG +E IM +E RE +E LOAD ;

[0043] In the above formula, P inject Inject power into the system; t is the unit time; E sys is the system equivalent kinetic energy; S sys E is the total rated power generation capacity of the system; SG 、E IM 、E RE 、E LOADThey are synchronous kinetic energy, asynchronous kinetic energy, new energy virtual inertia, and static load equivalent inertia.

[0044] The clustering module includes a scene distance calculation module, a scene density calculation module, a high-density scene acquisition module, a cluster center determination module, and an update module.

[0045] The scene distance calculation module is used to calculate the Euclidean distance between each low inertia running scene and other low inertia running scenes to obtain a distance vector: LS i ={L i1 , L i2 , …, L ij , …, L iN , j≠i}; where LS i Represents the distance vector of the i-th low inertia running scenario, L ij represents the Euclidean distance between the i-th low inertia running scenario and the j-th low inertia running scenario, and N represents the total number of low inertia running scenarios;

[0046] The scene density calculation module is used to calculate the distance vector LS i Sort in ascending order and select the distance vector LS i The Mth element value in is used as the scene density index of the i-th low inertia running scene i ; Finally, we get the scene density vector index = {index 1 , index 2 , ...index N};

[0047] The high-density scene acquisition module is used to sort the scene density vector index in ascending order, select the Tth element value in the scene density vector index as the scene threshold; and take all low-inertia running scenes with scene density higher than the scene threshold as a high-density scene set Hindex={index 1 , index 2 , ...index T};

[0048] The cluster center determination module is used to first select the low-inertia running scene with the highest scene index from the high-density scene set Hindex as the first cluster center, and then select the low-inertia running scene far away from all existing cluster centers from the high-density scene set Hindex as the next cluster center until the number of existing cluster centers reaches the clustering threshold;

[0049] The updating module is used to update each cluster center; the updating strategy is: within each cluster, the low-inertia running scene with the lowest sum of distances to other low-inertia running scenes is used as the new cluster center.

[0050] The cluster center determination module is also used to determine the clustering threshold K by maximizing the objective function W:

[0051] W = Q - 0.2 * SSE;

[0052]

[0053] m=∑ i，j A ij ;

[0054]

[0055] In the above formula, W is the objective function; Q is the clustering modularity; SSE is the sum of squares of clustering errors; |C i | represents the number of scenes in the i-th cluster; is the cluster center ε between the jth scene in the i-th cluster and the i-th cluster i The Euclidean distance between them; m is the total similarity of the similarity matrix A; A ij is an element in the similarity matrix A, indicating the similarity between the i-th scene and the j-th scene; d ij is the Euclidean distance between the i-th scene and the j-th scene; k i is the total similarity of the i-th scene; k j is the total similarity of the jth scene; δ(c i , c j ) is an intermediate variable.

[0056] In a third aspect, the present invention provides a low-inertia running scenario construction device based on the Frank-Copula function, the scenario construction device comprising a memory and a processor; the memory is used to store computer program code and transfer the computer program code to the processor; the processor is used to execute the aforementioned scenario construction method according to the instructions in the computer program code.

[0057] In a fourth aspect, the present invention provides a computer-readable storage medium having a computer program stored thereon, and the computer program implements the aforementioned scene construction method when executed by a processor.

[0058] Compared with the prior art, the present invention has the following beneficial effects:

[0059] 1. A method for constructing a low-inertia operation scenario based on the Frank-Copula function of the present invention, firstly, the probability density distribution of the historical low-inertia operation data of the power system is obtained by using the kernel density estimation method, the low-inertia operation data includes the system equivalent inertia and the system frequency-time response data, and then based on the probability density distribution of the low-inertia operation data, the Frank-Copula function is used to generate new low-inertia operation data that meets the topological constraints of the power system, and then the obtained new low-inertia operation data is superimposed with the historical low-inertia operation data to generate multiple low-inertia operation scenarios, and the typical low-inertia operation scenario is obtained by clustering the generated multiple low-inertia operation scenarios; the above-mentioned design introduces the topological constraints of the power system when using the Frank-Copula function to generate the low-inertia scenario operation data, and effectively models the physical topological structure of the power system, so as to accurately characterize the low-inertia operation scenario of the power grid, and finally improve the generation accuracy of the typical scenario. Therefore, the present invention can improve the generation accuracy of the typical low-inertia operation scenario of the power grid.

[0060] 2. The present invention provides a method for constructing low-inertia operation scenarios based on the Frank-Copula function, which determines the clustering threshold by maximizing the objective function formed by the clustering modularity and the sum of squared clustering errors; this is because the sum of squared clustering errors usually decreases with the increase of the clustering threshold, but in practical applications such as voltage regulation in distribution networks, excessively increasing the number of clusters will reduce the number of scenarios within each cluster, thereby reducing the flexibility of voltage regulation auxiliary services within the cluster, thereby weakening the practical value of clustering; the above design combines clustering modularity with the sum of squared clustering errors, and a higher modularity means that the clusters are closely connected, while the connections between different clusters are sparse, that is, the clustering division is more reasonable, thereby achieving a balance between the SSE value and the number of clusters through modularity. Therefore, the present invention can reasonably determine the clustering threshold, thereby reasonably performing clustering division. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 The present invention is a flowchart of the scene construction method.

[0062] Figure 2 This is a structural block diagram of the scene construction system described in the present invention.

[0063] Figure 3 The present invention provides a structural block diagram of the scene construction device described in the present invention.

[0064] Figure 4 This is a curve showing the change of clustering modularity with clustering threshold.

[0065] Figure 5 This is a curve showing the change of the sum of squares of clustering errors with the clustering threshold.

[0066] Figure 6These are typical low-inertia operation scenarios under three circumstances: increased penetration of new energy, decreased grid strength, and the addition of energy storage modules.

[0067] Figure 7 This is the topological structure diagram of the power system model. DETAILED DESCRIPTION

[0068] The present invention is further described in detail below in conjunction with specific implementations and drawings.

[0069] Embodiment 1:

[0070] See also Figure 1 , a method for constructing a low inertia running scenario based on the Frank-Copula function, follows the following steps in sequence:

[0071] S1. In the power system considering the influence of multiple factors of "source-grid-load-storage", by simulating the increase of new energy penetration rate, the decrease of grid strength, the addition of energy storage modules, etc., the system equivalent inertia and frequency-time response data of the power system are obtained, which are used as the historical low inertia operation data of the power system; the probability density distribution of the historical low inertia operation data is obtained by using the kernel density estimation method;

[0072] Suppose that sample X is extracted from historical low inertia running data 1 , X 2 , …, X n , n is the number of samples. In the kernel density estimation method, f(x) is the probability density function that X meets. By calculating the distance between each point in the neighborhood of x and point x, the distance between each point and point x is analyzed, and then the estimated values ​​of these point pairs are determined. The contribution degree of

[0073]

[0074] In the above formula, K( ) represents the kernel function, which can be a Gaussian function; h is the window width, which can be optimized by minimizing the integrated mean square error MISE(h) between the estimated value and the actual value. E is the weight matrix;

[0075] After completing the fitting of the probability density function, the Pearson chi-square and KS value can be used to test the fitting effect;

[0076] S2. Based on the probability density distribution of low inertia operation data, the predicted low inertia operation data is generated by using the Frank-Copula function, and the data in the predicted low inertia operation data that meets the power system topology constraints is used as the new low inertia operation data; the power system topology constraints include a comprehensive SFR model and a system inertia level model, and satisfying the power system topology constraints means that the comprehensive SFR model and the system inertia level model are established after substituting the low inertia operation data; the comprehensive SFR model is based on Figure 7 The power system model shown is obtained. The power system model is built based on the inertia characteristics of the generator and is suitable for power systems containing a large amount of renewable energy generation. In this power system model, ΔP L is the load disturbance power, ΔP m is the mechanical power stored in the generator, Δf is the system frequency, G m (s) is the equivalent model of various prime movers and speed regulators in the system; the comprehensive SFR model constructed includes:

[0077]

[0078] In the above formula, G(s) is the transfer function; H sys represents the system equivalent inertia; s is the Laplace operator; D sys is the system equivalent damping; K L is the frequency regulation coefficient of the load; D is the generator damping; ΔP L is the load disturbance power; Δf is the system frequency; K G is the frequency regulation coefficient of the generator; ΔP m The mechanical power stored for the generator; a 0 、a 1 , b 0 are all fitting parameters, and the sum of squares of fitting errors is used as the objective function Parameter fitting is performed by minimizing the objective function, where subscript c represents the frequency-time response data calculated by the comprehensive SFR model, subscript m represents the frequency-time response data obtained by actual measurement, and N represents the number of data used for fitting;

[0079] The system inertia level model includes:

[0080]

[0081]

[0082] E sys =E SG +E IM +E RE +E LOAD ;

[0083] In the above formula, P inject Inject power into the system; t is the unit time; E sys is the system equivalent kinetic energy; S sys E is the total rated power generation capacity of the system; SG 、E IM 、E RE 、E LOAD They are synchronous kinetic energy, asynchronous kinetic energy, new energy virtual inertia, and static load equivalent inertia;

[0084] S3, superimposing the historical low inertia running data obtained by S1 and the new low inertia running data obtained by S2, that is, merging the historical low inertia running data set and the new low inertia running data set to generate multiple low inertia running scenarios;

[0085] S4. Cluster the multiple low-inertia running scenarios generated in S3 to obtain typical low-inertia running scenarios. The specific clustering process is as follows:

[0086] S41. For each low inertia running scenario, calculate the Euclidean distance between it and other low inertia running scenarios to obtain the distance vector: LS i ={L i1 , L i2 , …, L ij , …, L iN , j≠i}; where LS i Represents the distance vector of the i-th low inertia operation scenario, L ij represents the Euclidean distance between the i-th low inertia running scenario and the j-th low inertia running scenario, and N represents the total number of low inertia running scenarios;

[0087] S42, distance vector LS i Sort in ascending order and select the distance vector LS i The Mth element value in is used as the scene density index of the i-th low inertia running scene i ; Finally, we get the scene density vector index = {index 1 , index 2 , ...index N};

[0088] S43, sorting the scene density vector index in ascending order, selecting the Tth element value in the scene density vector index as the scene threshold; taking all low-inertia running scenes with scene density higher than the scene threshold as a high-density scene set Hindex={index 1 , index 2 , ...index T};

[0089] S44, first select the low-inertia running scene with the highest scene index from the high-density scene set Hindex as the first cluster center, and then select the low-inertia running scene far away from all existing cluster centers from the high-density scene set Hindex as the next cluster center, until the number of existing cluster centers reaches the clustering threshold;

[0090] Specifically, the clustering threshold K is determined by maximizing the objective function W:

[0091] W = Q - 0.2 * SSE;

[0092]

[0093] m=∑ i，j A ij ;

[0094]

[0095] In the above formula, W is the objective function; Q is the clustering modularity; SSE is the sum of squares of clustering errors; |C i | represents the number of scenes in the i-th cluster; is the cluster center ε between the jth scene in the i-th cluster and the i-th cluster i The Euclidean distance between them; m is the total similarity of the similarity matrix A; A ij is an element in the similarity matrix A, indicating the similarity between the i-th scene and the j-th scene; d ij is the Euclidean distance between the i-th scene and the j-th scene; k i is the total similarity of the i-th scene; k j is the total similarity of the jth scene; δ(c i , c j ) is an intermediate variable;

[0096] In this embodiment, the curves of clustering module degree changing with clustering threshold and the curves of clustering error sum changing with clustering threshold are obtained as follows: Figure 4 , Figure 5 As shown in the figure, the sum of squares of clustering errors reaches an inflection point as the number of clusters increases. After this inflection point, the continued increase in the number of clusters will not cause the SSE to continue to drop significantly, and the number of modules reaches the maximum at this time. Therefore, the optimal clustering threshold is set to 5;

[0097] S45, updating each cluster center; the updating strategy is: within each cluster, the low-inertia running scenario with the lowest sum of distances to other low-inertia running scenarios is used as a new cluster center;

[0098] In this embodiment, taking the frequency-time response data as an example, the typical low inertia operation scenarios obtained in the three scenarios of increased new energy penetration, decreased grid strength, and added energy storage modules are as follows: Figure 6 As shown in Figures (a), (b) and (c), each situation has five typical scenes.

[0099] Performance Verification:

[0100] Taking the frequency-time response data as an example, the Kendall rank correlation coefficient, Spearman rank correlation coefficient and square Euclidean distance are used to judge the goodness of fit of different Copula functions. The correlation coefficient judgment method is to compare the rank correlation coefficients of different Copula functions with the rank correlation coefficients of sample data. The closer the rank correlation coefficients are, the better the goodness of fit is. The corresponding Copula function is the optimal one. The Euclidean distance judgment method is to compare the square Euclidean distances of different Copula functions and the empirical Copula function of sample data. The smaller the square Euclidean distance is, the better the goodness of fit is. The calculation results are shown in Table 1:

[0101] Table 1 Goodness of fit of different Copula functions

[0102]

[0103] As can be seen from Table 1, the frequency-time response data generated by the improved Frank-Copula using the power system topology constraint of the present invention is relatively close to the rank correlation coefficients of the sample data, and its square Euclidean distance is the smallest among all the results. This is because the Frank-Copula function can simultaneously consider the non-negative and negative correlations of the variables, and the wind power output and photovoltaic output are complementary and negatively correlated. Although the rank correlation coefficients of other Copula functions are also relatively good, their square Euclidean distances are too large, indicating that the fitting effects of other types of Copula functions are not good. In summary, the present invention selects the improved Frank-Copula using the power system topology constraint for data fitting, which can ensure the fitting accuracy, and the generated prediction data is closest to the low-inertia historical operation scenario data, indicating that it has the highest accuracy and reliability in generating low-inertia prediction operation scenarios.

[0104] Embodiment 2:

[0105] See also Figure 2A low inertia operation scenario construction system based on Frank-Copula function includes a data processing module, a data prediction module, a scenario generation module, and a clustering module; the data processing module is used to obtain historical low inertia operation data of the power system, and obtain its probability density distribution by using the kernel density estimation method, the low inertia operation data includes system equivalent inertia and system frequency-time response data; the data prediction module is used to generate new low inertia operation data that meets the topology constraints of the power system by using the Frank-Copula function based on the probability density distribution of the low inertia operation data; the power system topology constraints include a comprehensive SFR model and a system inertia level model; the comprehensive SFR model includes:

[0106]

[0107] In the above formula, G(s) is the transfer function; H sys represents the system equivalent inertia; s is the Laplace operator; D sys is the system equivalent damping; K L is the frequency regulation coefficient of the load; D is the generator damping; ΔP L is the load disturbance power; Δf is the system frequency; K G is the frequency regulation coefficient of the generator; a 0 、a 1 、b 0 All are fitting parameters;

[0108] The system inertia level model includes:

[0109]

[0110] E sys =E SG +E IM +E RE +E LOAD ;

[0111] In the above formula, P inject Inject power into the system; t is the unit time; E sys is the system equivalent kinetic energy; S sys E is the total rated generating capacity of the system; SG 、E IM 、E RE 、E LOAD They are synchronous kinetic energy, asynchronous kinetic energy, new energy virtual inertia, and static load equivalent inertia;

[0112] The scenario generation module is used to superimpose the historical low inertia operation data obtained with the new low inertia operation data obtained to generate multiple low inertia operation scenarios; the clustering module includes a scenario distance calculation module, a scenario density calculation module, a high-density scenario acquisition module, a cluster center determination module, and an update module. The scenario distance calculation module is used to calculate the Euclidean distance between each low inertia operation scenario and other low inertia operation scenarios to obtain a distance vector: LS i ={L i1 , L i2 ,,…,L ij , …, L iN , j≠i}; where LS i Represents the distance vector of the i-th low inertia running scenario, L ij represents the Euclidean distance between the i-th low inertia running scenario and the j-th low inertia running scenario, and N represents the total number of low inertia running scenarios; the scenario density calculation module is used to calculate the distance vector LS i Sort in ascending order and select the distance vector LS i The Mth element value in is used as the scene density index of the i-th low inertia running scene i ; Finally, we get the scene density vector index = {index 1 , index 2 , ...index N}; The high-density scene acquisition module is used to sort the scene density vector index in ascending order, select the Tth element value in the scene density vector index as the scene threshold; all low-inertia running scenes with scene density higher than the scene threshold are taken as a high-density scene set Hindex = {index 1 , index 2 , ...index T}; The cluster center determination module is used to first select the low-inertia running scene with the highest scene index from the high-density scene set Hindex as the first cluster center, and then select the low-inertia running scene far away from all existing cluster centers from the high-density scene set Hindex as the next cluster center, until the number of existing cluster centers reaches the clustering threshold; The update module is used to update each cluster center; The update strategy is: within each cluster, the low-inertia running scene with the lowest sum of distances to other low-inertia running scenes is used as the new cluster center;

[0113] The cluster center determination module is also used to determine the clustering threshold K by maximizing the objective function W:

[0114] W = Q - 0.2 * SSE;

[0115]

[0116] m=∑ i，j A ij ;

[0117]

[0118] In the above formula, W is the objective function; Q is the clustering modularity; SSE is the sum of squares of clustering errors; |C i | represents the number of scenes in the i-th cluster; is the cluster center ε between the jth scene in the i-th cluster and the i-th cluster i The Euclidean distance between them; m is the total similarity of the similarity matrix A; A ij is an element in the similarity matrix A, indicating the similarity between the i-th scene and the j-th scene; d ij is the Euclidean distance between the i-th scene and the j-th scene; k i is the total similarity of the i-th scene; k j is the total similarity of the jth scene; δ(c i , c j ) is an intermediate variable;

[0119] The clustering module is used to cluster the generated multiple low-inertia running scenarios to obtain a typical low-inertia running scenario.

[0120] Embodiment 3:

[0121] See also Figure 3 , a low-inertia running scene construction device based on Frank-Copula function, comprising a memory and a processor; the memory is used to store computer program code and transmit the computer program code to the processor; the processor is used to execute the scene construction method as described in Example 1 according to the instructions in the computer program code.

[0122] Embodiment 4:

[0123] A computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the scene construction method as described in Example 1.

[0124] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0125] The present application is described with reference to flowcharts and / or block diagrams of methods, devices (systems) and computer program products according to embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0126] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0127] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0128] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A low-inertia running scenario construction method based on the Frank-Copula function, characterized by: The scene construction method comprises: S1. Obtain historical low-inertia operation data of the power system, and obtain its probability density distribution using a kernel density estimation method; the low-inertia operation data includes system equivalent inertia and system frequency-time response data; S2. Based on the probability density distribution of low inertia operation data, the Frank-Copula function is used to generate new low inertia operation data that meets the topology constraints of the power system; S3, superimposing the historical low inertia operation data obtained by S1 and the new low inertia operation data obtained by S2 to generate multiple low inertia operation scenarios; S4. Cluster the multiple low-inertia running scenarios generated by S3 to obtain a typical low-inertia running scenario.

2. The method for constructing a low-inertia running scenario based on the Frank-Copula function according to claim 1, characterized in that: The power system topology constraint includes a comprehensive SFR model and a system inertia level model. The comprehensive SFR model includes: In the above formula, G(s) is the transfer function; H sys represents the system equivalent inertia; s is the Laplace operator; D sys is the system equivalent damping; K L is the frequency regulation coefficient of the load; D is the generator damping; ΔP L is the load disturbance power; Δf is the system frequency; K G is the frequency adjustment coefficient of the generator; a0, a1, b0 are all fitting parameters; The system inertia level model includes: AND sys =And SG +E IM +E RE +E LOAD ; In the above formula, P inject Inject power into the system; t is the unit time; E sys is the system equivalent kinetic energy; S sys E is the total rated power generation capacity of the system; SG 、E IM 、E RE 、E LOAD They are synchronous kinetic energy, asynchronous kinetic energy, new energy virtual inertia, and static load equivalent inertia.

3. The method for constructing a low-inertia running scenario based on the Frank-Copula function according to claim 1, characterized in that: The S4 includes: S41. For each low inertia running scenario, calculate the Euclidean distance between it and other low inertia running scenarios to obtain the distance vector: LS i ={L i1 , L i2 , …, L ij , …, L iN , j≠i}; where LS i Represents the distance vector of the i-th low inertia running scenario, L ij represents the Euclidean distance between the i-th low inertia running scenario and the j-th low inertia running scenario, and N represents the total number of low inertia running scenarios; S42, distance vector LS i Sort in ascending order and select the distance vector LS i The Mth element value in is used as the scene density index of the i-th low inertia running scene i ; Finally, we get the scene density vector index = {index1, index2, ...index N }; S43, sorting the scene density vector index in ascending order, selecting the Tth element value in the scene density vector index as the scene threshold; and treating all low-inertia running scenes with scene density higher than the scene threshold as a high-density scene set Hindex = {index1, index2, ...index T }; S44, first select the low-inertia running scene with the highest scene index from the high-density scene set Hindex as the first cluster center, and then select the low-inertia running scene far away from all existing cluster centers from the high-density scene set Hindex as the next cluster center, until the number of existing cluster centers reaches the clustering threshold; S45. Each cluster center is updated; the updating strategy is: within each cluster, the low-inertia running scenario with the lowest sum of distances to other low-inertia running scenarios is used as the new cluster center.

4. The method for constructing a low-inertia running scenario based on the Frank-Copula function according to claim 3 is characterized in that: In S44, the clustering threshold K is determined by maximizing the objective function W: W = Q - 0.2 * SSE; m=∑ i，j A ij ; In the above formula, W is the objective function; Q is the clustering modularity; SSE is the sum of squares of clustering errors; |C i | represents the number of scenes in the i-th cluster; is the cluster center ε between the jth scene in the i-th cluster and the i-th cluster i The Euclidean distance between them; m is the total similarity of the similarity matrix A; A ij is an element in the similarity matrix A, indicating the similarity between the i-th scene and the j-th scene; d ij is the Euclidean distance between the i-th scene and the j-th scene; k i is the total similarity of the i-th scene; k j is the total similarity of the jth scene; δ(c i , c j ) is an intermediate variable.

5. A low-inertia running scenario construction system based on the Frank-Copula function, characterized by: The scenario construction system includes a data processing module, a data prediction module, a scenario generation module, and a clustering module; The data processing module is used to obtain historical low-inertia operation data of the power system and obtain its probability density distribution using a kernel density estimation method, wherein the low-inertia operation data includes system equivalent inertia and system frequency-time response data; The data prediction module is used to generate new low inertia operation data that meets the power system topology constraints based on the probability density distribution of the low inertia operation data using the Frank-Copula function; The scenario generation module is used to superimpose the obtained historical low inertia operation data with the obtained new low inertia operation data to generate multiple low inertia operation scenarios; The clustering module is used to cluster the generated multiple low-inertia running scenarios to obtain a typical low-inertia running scenario.

6. The method for constructing a low-inertia running scenario based on the Frank-Copula function according to claim 5, characterized in that: The power system topology constraints include a comprehensive SFR model and a system inertia level model; the comprehensive SFR model includes: In the above formula, G(s) is the transfer function; H sys represents the system equivalent inertia; s is the Laplace operator; D sys is the system equivalent damping; K L is the frequency regulation coefficient of the load; D is the generator damping; ΔP L is the load disturbance power; Δf is the system frequency; K G is the frequency adjustment coefficient of the generator; a0, a1, b0 are all fitting parameters; The system inertia level model includes: AND sys =And SG +E IM +E RE +E LOAD ; In the above formula, P inject Inject power into the system; t is the unit time; E sys is the system equivalent kinetic energy; S sys E is the total rated power generation capacity of the system; SG 、E IM 、E RE 、E LOAD They are synchronous kinetic energy, asynchronous kinetic energy, new energy virtual inertia, and static load equivalent inertia.

7. The method for constructing a low-inertia running scenario based on the Frank-Copula function according to claim 5, characterized in that: The clustering module includes a scene distance calculation module, a scene density calculation module, a high-density scene acquisition module, a cluster center determination module, and an update module. The scene distance calculation module is used to calculate the Euclidean distance between each low inertia running scene and other low inertia running scenes to obtain a distance vector: LS i ={L i1 , L i2 ,,…,L ij , …, L iN , j≠i}; where LS i Represents the distance vector of the i-th low inertia running scenario, L ij represents the Euclidean distance between the i-th low inertia running scenario and the j-th low inertia running scenario, and N represents the total number of low inertia running scenarios; The scene density calculation module is used to calculate the distance vector LS i Sort in ascending order and select the distance vector LS i The Mth element value in is used as the scene density index of the i-th low inertia running scene i ; Finally, we get the scene density vector index = {index1, index2, ...index N }; The high-density scene acquisition module is used to sort the scene density vector index in ascending order, select the Tth element value in the scene density vector index as the scene threshold; and take all low-inertia running scenes with scene density higher than the scene threshold as a high-density scene set Hindex={index1, index2, ...index T }; The cluster center determination module is used to first select the low-inertia running scene with the highest scene index from the high-density scene set Hindex as the first cluster center, and then select the low-inertia running scene far away from all existing cluster centers from the high-density scene set Hindex as the next cluster center until the number of existing cluster centers reaches the clustering threshold; The updating module is used to update each cluster center; the updating strategy is: within each cluster, the low-inertia running scene with the lowest sum of distances to other low-inertia running scenes is used as the new cluster center.

8. The method for constructing a low-inertia running scenario based on the Frank-Copula function according to claim 7, characterized in that: The cluster center determination module is also used to determine the clustering threshold K by maximizing the objective function W: W = Q - 0.2 * SSE; m=∑ i，j A ij ; In the above formula, W is the objective function; Q is the clustering modularity; SSE is the sum of squares of clustering errors; |C i | represents the number of scenes in the i-th cluster; is the cluster center ε between the jth scene in the i-th cluster and the i-th cluster i The Euclidean distance between them; m is the total similarity of the similarity matrix A; A ij is an element in the similarity matrix A, indicating the similarity between the i-th scene and the j-th scene; d ij is the Euclidean distance between the i-th scene and the j-th scene; k i is the total similarity of the i-th scene; k j is the total similarity of the jth scene; δ(c i , c j ) is an intermediate variable.

9. Low inertia running scenario construction equipment based on Frank-Copula function, characterized by: The scene construction device includes a memory and a processor; the memory is used to store computer program code and transmit the computer program code to the processor; the processor is used to execute the scene construction method as described in claims 1-4 according to instructions in the computer program code.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the scene construction method according to claims 1-4 is implemented.

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