A power system frequency response consistency partitioning method based on generalized nodal equivalent inertia

Abstract

The application discloses a power system frequency response consistency partitioning method based on generalized node equivalent inertia, and comprises the following steps: firstly, a frequency correlation matrix is constructed; secondly, according to the power distribution relationship at the moment of disturbance and the energy balance relationship in the inertia response stage, and in combination with the frequency correlation matrix, a generalized node equivalent inertia index considering the contribution of the damping term in the swing equation is constructed to represent the comprehensive ability of each node to resist frequency change at the initial stage of disturbance; thirdly, the generalized node equivalent inertia index is used to reflect the inertia similarity between nodes, and in combination with the line reactance to reflect the electrical distance between nodes, an inertia-electricity coupling matrix is constructed to form a partition basis considering the dynamic response characteristics and the network structure characteristics; finally, a random walk normalized Laplacian matrix is constructed according to the inertia-electricity coupling matrix, the original nonlinear partitioning problem is mapped to a spectral space, and the regional frequency consistency partitioning of the new energy power system is realized by clustering the nodes.

Description

Technical Field

[0001] This invention belongs to the field of frequency stability analysis and control technology of new energy power systems. More specifically, it relates to a power system frequency response consistency partitioning method based on generalized node equivalent inertia. Background Technology

[0002] In traditional power systems, frequency stability analysis is typically based on the assumption of a system inertia center, approximating the overall network frequency response as a uniform process. This method is well-suited for scenarios dominated by synchronous machines and with relatively uniform inertia distribution. However, under conditions of high-proportion renewable energy integration, due to uneven spatial distribution of inertia resources, significant differences in grid connection locations, inconsistent control parameters, and network topology constraints, the frequency change rate, frequency drop rate, and phase characteristics of different nodes are no longer consistent in the initial stage of disturbances. Therefore, it is necessary to partition the system and then implement targeted frequency control measures for different regions to ensure the frequency security of local areas.

[0003] Existing system partitioning methods mainly include partitioning methods based on static topology, partitioning methods based on dynamic coherence characteristics, and partitioning methods based on node frequency trajectory similarity. However, partitioning methods based on static topology are difficult to accurately reflect frequency response differences; partitioning methods based on dynamic coherence characteristics are more suitable for synchronous machine-dominated scenarios; partitioning methods based on frequency trajectory similarity usually rely on specific disturbance data or online measurement data, and are easily affected by changes in disturbance location, disturbance type, and operating mode, exhibiting strong scenario dependence. To reduce dependence on measured data, some scholars have proposed partitioning methods based on node equivalent inertia, which can approximately characterize frequency similarity. However, existing methods for characterizing node equivalent inertia only focus on the contribution of the inertia term, while insufficiently considering the role of the damping term in suppressing frequency changes in the early stages of a disturbance, resulting in an inaccurate description of the overall disturbance resistance capability of nodes.

[0004] Therefore, there is an urgent need for a frequency consistency zoning method for new energy power systems that does not rely directly on measured node frequency trajectories and can simultaneously consider inertial response, damping contribution, and electrical coupling relationships, so as to provide a reliable foundation for regional frequency stability analysis and inertial support resource allocation. Summary of the Invention

[0005] This invention provides a power system frequency response consistency partitioning method based on generalized node equivalent inertia to solve the problems of existing partitioning methods being dependent on disturbance scenarios and insufficiently considering the contribution of damping terms.

[0006] To achieve the above-mentioned objectives, the present invention provides a power system frequency response consistency partitioning method based on generalized nodal equivalent inertia, characterized by comprising the following steps:

[0007] S1. Obtain system parameters and construct a frequency correlation matrix;

[0008] S2. Based on the instantaneous power distribution relationship during the disturbance and the energy balance relationship during the inertial response stage, and combined with the frequency correlation matrix, a generalized nodal equivalent inertia index considering the contribution of the damping term in the swing equation is constructed.

[0009] S3. Based on the generalized node equivalent inertia index, the inertia similarity between nodes is characterized, and the line reactance is combined to characterize the electrical distance between nodes, and an inertia-electric coupling matrix is ​​constructed.

[0010] S4. Based on spectral clustering theory, a random walk normalized Laplace matrix is ​​constructed according to the inertia-electric coupling matrix to map the original nonlinear partitioning problem to the spectral space.

[0011] S5. Combine the eigenvalue gap and the contour coefficient to determine the optimal number of partitions, and cluster the nodes to output the region division results.

[0012] The objective of this invention is achieved as follows:

[0013] This invention discloses a power system frequency response consistency partitioning method based on generalized node equivalent inertia. First, it acquires network topology information, line parameters, and inertial and damping parameters of each inertial source in the new energy power system to construct a frequency correlation matrix. Based on the instantaneous power distribution relationship during disturbances and the energy balance relationship during the inertial response stage, and combined with the frequency correlation matrix, a generalized node equivalent inertia index considering the contribution of damping terms in the swing equation is constructed to characterize the comprehensive ability of each node to resist frequency changes in the early stages of disturbances. Further, the generalized node equivalent inertia index is used to reflect the inertia similarity between nodes, and combined with line reactance to reflect the electrical distance between nodes, an inertia-electrical coupling matrix is ​​constructed to form a partitioning basis that considers both dynamic response characteristics and network structure characteristics. Finally, a random walk normalized Laplace matrix is ​​constructed based on the inertia-electrical coupling matrix to map the original nonlinear partitioning problem to the spectral space. By clustering the nodes, regional frequency consistency partitioning of the new energy power system is achieved.

[0014] Meanwhile, the power system frequency response consistency partitioning method based on generalized node equivalent inertia of this invention also has the following beneficial effects:

[0015] (1) Reduce dependence on actual disturbance frequency trajectory data. This invention completes partitioning by using the generalized node equivalent inertia index and system electrical distance, without relying on a large number of online frequency measurement trajectories as input, thus reducing the sensitivity of partitioning results to specific disturbance scenarios.

[0016] (2) More accurate characterization of node anti-disturbance capability. This invention incorporates the contribution of the damping term in the swing equation into the modeling process of the generalized node equivalent inertia index. Compared with the node equivalent inertia index that only considers the inertia term, it can more accurately describe the comprehensive ability of the node to resist rapid frequency changes in the early stage of disturbance.

[0017] (3) Improve the physical rationality and stability of the partitioning results. This invention considers both the similarity of node inertia and the electrical distance coupling relationship, avoiding the boundary deviation caused by partitioning based solely on a single inertia index or a single topology index. Attached Figure Description

[0018] Figure 1 This is a flowchart of a power system frequency response consistency partitioning method based on generalized node equivalent inertia according to the present invention;

[0019] Figure 2 This embodiment illustrates the effect of the damping coefficient on the equivalent inertia and frequency response of the nodes.

[0020] Figure 3 This is a power system topology diagram in this embodiment where the installed capacity of new energy sources accounts for 45.35%.

[0021] Figure 4 This is the frequency curve of some nodes after being disturbed in this embodiment;

[0022] Figure 5 This is a schematic diagram illustrating the determination of the optimal number of partitions based on the feature value gap and the contour coefficient in this embodiment;

[0023] Figure 6 These are the frequency response curves of each region under different disturbances in this embodiment. Detailed Implementation

[0024] To make the objectives, technical solutions, and beneficial effects of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings and examples. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0025] In this embodiment, as Figure 1 As shown, the present invention provides a power system frequency response consistency partitioning method based on generalized node equivalent inertia, comprising the following steps:

[0026] S1. Obtain system parameters and construct a frequency correlation matrix.

[0027] S101. Obtain power system parameters and construct a frequency correlation matrix;

[0028] S101. Obtain synchronous phasor measurement data of each node through the Wide Area Measurement System (WAMS), including node voltage amplitude, node voltage phase angle and node frequency data.

[0029] The power system network topology information and transmission equipment parameter information are obtained through the Energy Management System (EMS), including transmission line connection relationships, line resistance, line reactance, line admittance, transformer turns ratio, and transformer leakage reactance parameters.

[0030] Obtain the generator set inertia coefficient from the equipment parameter database. Damping coefficient Transient reactance ;

[0031] The active power and reactive power operation data of each node are obtained through the scheduling automation system.

[0032] Based on the obtained transmission line parameters, transformer parameters, load parameters, and power system network topology, construct the power system node admittance matrix;

[0033] The transient reactance of each unit is obtained based on the parameters of the units connected to each inertia source node m. These elements are then used sequentially as diagonal elements of the matrix, while all off-diagonal elements are set to 0, thus forming a diagonal matrix. ;

[0034] S102. Constructing the frequency correlation matrix based on the power system node admittance matrix and network equivalent elimination method:

[0035] ;

[0036] in, Let n be the self-admittance of the non-inertial source node. Let m be the self-admittance of the inertia source node. Let n be the mutual admittance of the non-inertia source node and m be the inertia source node. Let m be the mutual admittance of the inertia source node and n be the non-inertia source node. and The values ​​are the same, only the index order is different. The equivalent load admittance for load node l and inertia source node m is given. The equivalent load admittance for load node l and non-inertia source node n. It is a diagonal matrix composed of the transient reactances of the units corresponding to each inertia source node;

[0037] Frequency correlation matrix Stored in the Energy Management System (EMS);

[0038] S2. Based on the instantaneous power distribution relationship during the disturbance and the energy balance relationship during the inertial response stage, and combined with the frequency correlation matrix, a generalized nodal equivalent inertia index considering the contribution of the damping term in the swing equation is constructed.

[0039] S201, Assume the system is at node Active disturbance occurs at the location At the instant of the disturbance, since the frequencies of each inertial source cannot change abruptly, the following condition must be met:

[0040] ;

[0041] in, Indicating inertia source Frequency deviation at the moment of disturbance.

[0042] S202. At the instant of the disturbance, the unbalanced power of the disturbance is distributed according to the synchronization power coefficient between the inertia source and the disturbance node. The change in electromagnetic power undertaken is:

[0043] ;

[0044] in, This is the synchronous power allocation coefficient.

[0045] S203, the synchronous power allocation coefficient The calculation formula is:

[0046] ;

[0047] in, Inertia sources and perturbation nodes voltage amplitude, To shrink to the potential node and perturbation node within the inertial source Equivalent susceptance between them The voltage phase angle difference between the two nodes. This represents the total number of inertia sources in the system.

[0048] S204. In the initial stage after the disturbance, for any inertia source Establish the rotor motion equations that take damping into account:

[0049] ;

[0050] in, The coefficient of inertia, The damping coefficient, For angular velocity deviation, This represents the change in mechanical power. This represents the change in electromagnetic power.

[0051] S205. In the initial stage after a disturbance, since the speed governor has not yet made a significant move, the change in mechanical power is... It is approximately zero. Meanwhile, affected by the disturbance, the change in electromagnetic power of the inertial source can be expressed as the sum of the power exchanged between nodes:

[0052] ;

[0053] in, The exchange power generated by the swaying between units, The unbalanced power is distributed according to the synchronization power allocation factor at the moment of disturbance.

[0054] S206, Take the observation interval as , This indicates the moment when the system frequency drops to its extreme value. Approximately zero, for the rotor motion equation described in S204 in the interval Integrating within the inner, we get:

[0055] ;

[0056] As can be seen from S205, the frequencies of each inertial source cannot change abruptly at the moment of disturbance. Further simplification of the above formula yields:

[0057] ;

[0058] The energy balance equation above shows that the sum of the inertial power and the damping energy dissipation on the left side equals the disturbance power.

[0059] S207. During the inertial response phase after the disturbance, if the inertial source frequency deviation In the interval If the integral term is continuous and monotonically changing, then its time integral term can be approximated using the equivalent area method, i.e.:

[0060] ;

[0061] in, This is the integral correction factor, representing the actual frequency response curve within the interval [missing information]. The area inside and the endpoint value The ratio of the areas of the rectangles formed can take values ​​ranging from 1 to 2. Under typical frequency response characteristics, when the frequency changes approximately linearly, When the frequency decreases approximately parabolically, . Coco can identify or select based on the actual frequency response curve or experience.

[0062] S208, Define the equivalent inertia of a generalized inertia source. According to the principle of energy equivalence, the equivalent kinetic energy released by this generalized inertia should be equal to the disturbance energy on the right side of the S206 formula, satisfying:

[0063] ;

[0064] Substituting formula S207 into the above equation, we obtain the expression for the generalized nodal equivalent inertia of a single inertia source as follows:

[0065] ;

[0066] S209. Construct the frequency correlation between node frequency deviation and inertia source frequency deviation. For any network node Its frequency deviation satisfies:

[0067] ;

[0068] in, The elements in the frequency correlation matrix constructed for S102 represent nodes. With inertia source The degree of frequency coupling correlation between them.

[0069] S208 Substitute the expression into the above formula:

[0070] ;

[0071] S210. To characterize the overall disturbance rejection capability at the node level, a node is introduced. Generalized nodal equivalent inertia index To satisfy:

[0072] ;

[0073] Therefore, we can conclude that:

[0074] ;

[0075] in, Used to characterize nodes in the early stages of disturbance. The overall ability to resist frequency changes.

[0076] S3. To comprehensively characterize the consistency of inertial response and electrical coupling relationship between nodes, the inertial similarity between nodes is characterized based on the generalized node equivalent inertial index, and the electrical distance between nodes is characterized by the line reactance, thereby constructing an inertial-electrical coupling matrix.

[0077] S301. Abstract the power system as an undirected weighted graph. ,in, For a set of nodes, For the collection of routes, Let be the set of edge weights.

[0078] S302, Define the system adjacency matrix for:

[0079] ;

[0080] S303, According to the node and nodes Generalized node equivalent inertia index, constructing inertia similarity weights:

[0081] ;

[0082] in, , The standard deviation represents the generalized nodal equivalent inertia of the entire system. This is the adjustment coefficient.

[0083] S304, According to the node and nodes The equivalent reactance of the lines between them is used to construct the electrical distance weight:

[0084] ;

[0085] in, For nodes and nodes The equivalent reactance of the lines between them, This is the line reactance scaling factor.

[0086] S305. Combining inertia similarity weight and electrical distance weight, the overall coupling weight between nodes is defined as follows:

[0087] ;

[0088] Then, the inertia-electric coupling matrix is ​​constructed. .

[0089] S4. Based on spectral clustering theory, a random walk normalized Laplace matrix is ​​constructed according to the inertia-electric coupling matrix to map the original nonlinear partitioning problem to the spectral space.

[0090] S401, Based on the inertia-electric coupling matrix Construct the degree matrix The degree matrix is ​​a diagonal matrix, and its diagonal elements are:

[0091] ;

[0092] S402. Construct the state transition probability matrix :

[0093] ;

[0094] Among them, matrix elements Indicates a random walk starting from node Transfer to node The probability of.

[0095] S403. Constructing the random walk normalized Laplace matrix :

[0096] ;

[0097] in, It is an identity matrix.

[0098] S404, Normalized Laplace matrix for random walk Perform eigenvalue decomposition to obtain an ascending sequence of eigenvalues: and the corresponding feature vectors ;

[0099] S5. Combine the eigenvalue gap and the contour coefficient to determine the optimal number of partitions, and cluster the nodes to output the region division results;

[0100] S501, S501, Calculate the eigenvalue gap under different numbers of candidate partitions. ;

[0101] ;

[0102] in, This indicates that the system is divided into The spectral gaps corresponding to each region;

[0103] S502. Determine the range of candidate partition numbers based on the eigenvalue gaps, and select the partition numbers corresponding to the top L eigenvalue gaps to form a candidate partition set. ;

[0104] S503, For the set of candidate partition numbers For each candidate partition number k, select the top... Construct a feature matrix from eigenvectors:

[0105] ;

[0106] matrix For N rows A matrix of columns This represents the total number of system nodes.

[0107] With matrix The p-th row is used as the spectral clustering space mapping coordinate of node p;

[0108] The K-means clustering algorithm was used to cluster the spectral space mapping coordinates to obtain the corresponding clustering results;

[0109] S504. Calculate the average profile coefficient based on the corresponding clustering results:

[0110] ;

[0111] Among them, for those already assigned to clusters nodes Its profile coefficient Defined as:

[0112] ;

[0113] in, Represents a node with cluster The average Euclidean distance between all other nodes within the area; Represents a node With the nearest non The average Euclidean distance among all nodes in the cluster;

[0114] S505, in the candidate partition set Within this process, the average profile coefficients corresponding to the number of candidate partitions are compared to determine the optimal number of partitions.

[0115] ;

[0116] S506, Output the optimal number of partitions The corresponding clustering results are generated, and the regional node affiliation is established. The regional node affiliation is then sent to the Energy Management System (EMS) for the construction of regional frequency response models and frequency stability analysis.

[0117] In this embodiment Figure 2 This diagram illustrates the effect of the damping coefficient on the nodal equivalent inertia and frequency response. As the system's equivalent damping coefficient increases, the maximum rate of change of frequency after disturbance gradually decreases, while the lowest frequency point gradually increases. The nodal equivalent inertia, obtained from the ratio of disturbance power to frequency change rate, gradually increases, demonstrating the damping coefficient's suppressive effect on the initial frequency change rate and highlighting the necessity of considering the damping contribution.

[0118] Implement simulation

[0119] Figure 3 This is a topology diagram of a power system where new energy installations account for 45.35% of the total installed capacity.

[0120] To verify the frequency response consistency partitioning method based on generalized node equivalent inertia provided in this invention, a 39-node power system with a renewable energy installed capacity of 45.35% was built on the MATLAB / Simulink simulation platform for simulation verification. The topology is shown below. Figure 3 G4 is a grid-connected photovoltaic power station, G7 is a grid-connected wind power station, G6 and G8 are grid-connected wind power stations without virtual inertia control, and G10 is a grid-connected wind power station with virtual inertia control. The generator simulation parameters in this implementation case are shown in Table 1, and each parameter is normalized to its own rated capacity.

[0121] Table 1 Generator parameters;

[0122]

[0123] Based on the obtained transmission line parameters, transformer parameters, load parameters, and power system network topology, a power system node admittance matrix is ​​constructed. A frequency correlation matrix is ​​then constructed based on the power system node admittance matrix and the network equivalent elimination method. Then, power flow calculations are performed on the system to obtain node voltage magnitudes and phase angles, and the synchronization power factor is calculated. With the synchronous power coefficient matrix; Take 0.6, Taking 0.3 seconds, the generalized nodal equivalent inertia index is calculated according to the S210 formula. Some typical nodes See Table 2, the frequency response curves corresponding to the nodes are as follows: Figure 4 As shown.

[0124] Table 2 Generalized nodal equivalent inertia index H considering damping coefficient GENI,k (Unit: s);

[0125]

[0126] Combine Table 2 and Figure 4 Analysis shows that nodes 4, 6, and 24 are too far from the electrical distances of the new energy power stations without virtual inertia control. The values ​​are 170.498s, 163.880s, and 124.290s, respectively, which are relatively high and similar. Figure 4 These nodes have relatively low initial RoCoF frequencies and similar trajectories. Nodes 30 and 33... The values ​​are 67.030s and 62.537s, which are relatively small and very close in altitude, resulting in a high degree of overlap in the frequency curves shown in the figure, and a relatively large initial RoCoF. Node 35 is directly connected to a GFL-type wind farm without virtual inertia control. The 22.435s time for node 36 and the 30.144s time for node 36 are significantly lower than those of other nodes. Figure 4 The initial RoCoF of the two nodes is the largest, with node 35 being slightly smaller than node 36. (Table 2 and...) Figure 4 The results show that the initial RoCoF spatial distribution characteristics of each node after the disturbance can be determined by the generalized nodal equivalent inertia index. To perform effective characterization.

[0127] It should be noted that, This reflects the comprehensive support contribution of the entire network's inertia resources to that point, and is a coupling performance index rather than an inherent physical constant. Therefore, the values ​​calculated in Table 2... The values ​​are generally higher than the inherent inertial constants of the units listed in Table 1.

[0128] Figure 5 This is a schematic diagram for determining the optimal number of partitions based on eigenvalue gaps and contour coefficients.

[0129] The generalized node equivalent inertia index of each node is retrieved from the Energy Management System (EMS). The inertia-electrical coupling matrix of the transmission line reactance is constructed, and the system is partitioned. The optimal number of partitions is determined based on the eigenvalue gap and profile coefficient. The partitioning results are shown in the diagram. Figure 5 The range of candidate partition numbers is determined based on the eigenvalue gaps, and the top 4 partitions with the largest eigenvalue gaps are selected as the partition set. (k=2~5), for the set of candidate partitions The average profile coefficient was calculated for different partitions. When the number of partitions k=4, =0.912, which is the maximum, therefore the optimal number of partitions is chosen. =4.

[0130] The partitioning effect is evaluated based on the frequency similarity of the perturbed nodes. In the frequency response similarity analysis, mean-removal preprocessing is used to eliminate systematic offsets in the reference frequencies of each node, ensuring that dynamic time warping (DTW) is used to evaluate the dynamic similarity of frequencies. To quantify the performance of the partitioning method, a DTW separation ratio is defined. As a metric for evaluating clustering performance:

[0131] ;

[0132] In the formula, This represents the average DTW distance between regions, characterizing regional differences; This represents the average distance between the DTW frequency curves of nodes within the region, reflecting internal consistency. The larger the value, the better the partitioning effect.

[0133] Table 3. Zoning Results and Indicators;

[0134]

[0135] Table 3 shows the evaluation metrics and final partitioning results for different partition numbers (K=4). The value is 3.347, which is greater than 2.713 for the K=3 scheme. This indicates that the node frequency curves in each region are more consistent under the K=4 partitioning scheme, the frequency differences between regions are greater, and the partitioning effect is better.

[0136] Load disturbances were applied to nodes 9 and 22, respectively. The regional frequency curves under different disturbances are shown below. Figure 6 The node frequency curves in each region are highly consistent, but the frequency differences between regions are large, which verifies the applicability of the proposed method under different perturbations.

[0137] Although the illustrative specific embodiments of the present invention have been described above to enable those skilled in the art to understand the invention, it should be understood that the invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of the present invention are protected.

Claims

1. A power system frequency response consistency partitioning method based on generalized nodal equivalent inertia, characterized in that... This includes the following steps: S1. Obtain power system parameters and construct a frequency correlation matrix; S101. Obtain synchronous phasor measurement data of each node through the Wide Area Measurement System (WAMS), including node voltage amplitude, node voltage phase angle and node frequency data. The power system network topology information and transmission equipment parameter information are obtained through the Energy Management System (EMS), including transmission line connection relationships, line resistance, line reactance, line admittance, transformer turns ratio, and transformer leakage reactance parameters. Obtain the generator set inertia coefficient from the equipment parameter database. Damping coefficient Transient reactance ; The active power and reactive power operation data of each node are obtained through the scheduling automation system. Based on the obtained transmission line parameters, transformer parameters, load parameters, and power system network topology, construct the power system node admittance matrix; The transient reactance of each unit is obtained based on the parameters of the units connected to each inertia source node m. These elements are then used sequentially as diagonal elements of the matrix, while all off-diagonal elements are set to 0, thus forming a diagonal matrix. ; S102. Constructing the frequency correlation matrix based on the power system node admittance matrix and network equivalent elimination method: ； in, Let n be the self-admittance of the non-inertial source node. Let m be the self-admittance of the inertia source node. Let n be the mutual admittance of the non-inertia source node and m be the inertia source node. Let m be the mutual admittance of the inertia source node and n be the non-inertia source node. and The values ​​are the same, only the index order is different. The equivalent load admittance for load node l and inertia source node m is given. The equivalent load admittance for load node l and non-inertia source node n. It is a diagonal matrix composed of the transient reactances of the units corresponding to each inertia source node; Frequency correlation matrix Stored in the Energy Management System (EMS); S2. Based on the frequency dynamic response process of the power system after being disturbed, and combined with the frequency response characteristics of the inertia source node and the frequency correlation matrix, a generalized node equivalent inertia index considering the contribution of the damping term in the swing equation is constructed. S201. Assume the power system under test is at node... Active disturbance occurs at the location At the instant of disturbance, since the frequencies of the units connected to each inertia source node m cannot change abruptly, the following condition must be met: ； in, Indicates the inertia source node Frequency deviation at the moment of disturbance; S202. Obtain the steady-state voltage amplitude and phase angle of each node through power flow calculation; At the instant of the disturbance, the unbalanced power of the disturbance... The inertia source node m is allocated according to the synchronization power coefficient between the inertia source node m and the disturbance node k. The change in electromagnetic power undertaken is: ； in, Let be the synchronization power allocation coefficient between the inertia source node m and the disturbance node k, and its calculation formula is: ； in, Inertia source node voltage amplitude, For the perturbation node voltage amplitude, The internal potential of the contracted inertial source node m and the perturbation node Equivalent susceptance between them The voltage phase angle difference between the inertia source node m and the disturbance node k. The total number of inertia source nodes in the power system under test; S203. For the unit corresponding to the inertia source node m, establish the rotor motion equation considering damping based on its rotor motion characteristics: ； in, Let m be the inertia coefficient of the unit connected to the inertia source node. Let m be the damping coefficient of the unit connected to the inertia source node m. The angular velocity deviation of the unit connected to the inertia source node m. This represents the change in mechanical power of the unit connected to the inertia source node m. The electromagnetic power change of the unit connected to the inertia source node m; S204, Set the observation interval as , This indicates the moment when the frequency of the tested power system drops to an extreme value. when Approximately zero, for the rotor motion equation in S203 in the interval Integrating within the inner, we get: ； As can be seen from S201, at the instant of the disturbance, the frequency at each inertial source node m cannot change abruptly. Further simplification of the above formula yields: ； S205. During the inertial response phase after the disturbance, if the inertial source node... Frequency deviation at In the interval If the integral term is continuous and monotonically changing, then its time integral term can be approximated using the equivalent area method, i.e.: ； in, This is the integral correction factor, representing the actual frequency response curve within the interval [missing information]. The area inside and the endpoint value The ratio of the areas of the rectangles formed can take values ​​ranging from 1 to 2. ; S206. Define the generalized nodal equivalent inertia corresponding to the inertia source node m. : ； Substituting formula S205 into the above equation, we obtain the generalized nodal equivalent inertia expression for a single inertia source node m as follows: ； S207. Retrieve the frequency correlation matrix R from the Energy Management System (EMS) to construct the relationship between node frequency deviation and inertia source frequency deviation; for any disturbed node... Its frequency deviation satisfies: ； in, The element in the k-th row and m-th column of the frequency correlation matrix R represents the perturbation node. With inertia source node The degree of frequency coupling correlation between them; S206 Substituting the expression into the above equation and combining it with the S202 power distribution relationship, we get: ； S208. Based on the generalized nodal equivalent inertia and frequency correlation matrix of the generator sets corresponding to each inertia source node, calculate the generalized nodal equivalent inertia index of each node in the power system. To satisfy: ； Therefore, we can conclude that: ； Generalized nodal equivalent inertia index Stored in an energy management system (EMS); S3. Based on the equivalent inertia index of the generalized nodes of each node and the electrical connection relationship of the transmission network, construct an inertia-electrical coupling relationship matrix that reflects the frequency propagation characteristics of the power system. S301. Call the equivalent inertia index of the generalized node from the energy management system (EMS) and construct the inertia-electrical coupling matrix of the transmission line reactance. Abstracting the power system under test into an undirected weighted graph ,in, For a set of nodes, For the set of routes, The set of edge weights; S302. Define an adjacency matrix that reflects the topological connections of a power system. for: ； S303, Use Gaussian radial basis function to measure nodes Inter-equivalent inertia similarity: ； in, They are nodes The generalized nodal equivalent inertia index , Represents the generalized nodal equivalent inertia of the entire system. standard deviation This is the adjustment coefficient; S304. Define the equivalent reactance based on the transmission line between node p and node q. Electrical distance weighting: ； in, For nodes and nodes The equivalent reactance of the lines between them, For parameters To ensure the adaptability of the weights, the median of the reactance of all lines is selected as the scaling factor. ; S305, combining inertia similarity weight and electrical distance weight, defines nodes. and nodes The overall coupling weight between them is: ； Then, the inertia-electric coupling matrix is ​​constructed. ; S4. Construct a random walk normalized Laplace matrix based on the inertia-electric coupling matrix, and obtain its eigenvalues ​​and corresponding eigenvectors to provide basic data for subsequent determination of the optimal number of partitions and spectral clustering partitions; S401, Based on the inertia-electric coupling matrix Construct the degree matrix The degree matrix It is a diagonal matrix, and its diagonal elements For nodes The sum of the weights of all connected edges: ； S402, Based on Degree Matrix Construct the state transition probability matrix : ； Wherein, the state transition probability matrix Middle elements Indicates from node Jump to node The probability of; S403, Based on the state transition probability matrix Constructing the normalized Laplace matrix for random walks : ； in, It is the identity matrix; S404, Normalized Laplace matrix for random walk Perform eigenvalue decomposition to obtain an ascending sequence of eigenvalues: and the corresponding feature vectors ; S5. Determine the optimal number of partitions by combining eigenvalue gaps and contour coefficients. and output the partitioning results; S501. Calculate the eigenvalue gap under different numbers of candidate partitions. ; ； in, This indicates that the system is divided into The spectral gaps corresponding to each region; S502. Determine the range of candidate partition numbers based on the eigenvalue gaps, and select the partition numbers corresponding to the top L eigenvalue gaps to form a candidate partition set. ; S503, For the set of candidate partition numbers For each candidate partition number k, select the top... Construct a feature matrix from eigenvectors: ； matrix For N rows A matrix of columns, This represents the total number of system nodes. With matrix The p-th row is used as the spectral clustering space mapping coordinate of node p; The K-means clustering algorithm was used to cluster the spectral space mapping coordinates to obtain the corresponding clustering results; S504. Calculate the average profile coefficient based on the corresponding clustering results: ； Among them, for those already assigned to clusters nodes Its profile coefficient Defined as: ； in, Represents a node with cluster The average Euclidean distance between all other nodes within the area; Represents a node With the nearest non The average Euclidean distance among all nodes in the cluster; S505, in the candidate partition set Within this process, the average profile coefficients corresponding to the number of candidate partitions are compared to determine the optimal number of partitions. ； S506, Output the optimal number of partitions The corresponding clustering results are generated, and the regional node affiliation is established. The regional node affiliation is then sent to the Energy Management System (EMS) for the construction of regional frequency response models and frequency stability analysis.

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