Power system region division method considering frequency space-time distribution characteristics

Abstract

The invention discloses a power system region division method considering frequency space-time distribution characteristics. The method comprises the following steps: modeling a device side and a network side of the new energy power system respectively to obtain a system closed-loop frequency response model, and decomposing frequency response into a plurality of components based on spectral decomposition of a system return difference matrix; analyzing response characteristics such as a frequency lowest point and an average change rate of each frequency component to quantify a frequency space-time distribution characteristic; the method comprises the following steps: measuring the frequency of a PMU configuration node through simulation when disturbance occurs at different positions of a system, and constructing a similarity matrix and a Laplacian matrix by using an actually measured frequency response curve after modal decomposition and an improved spectral clustering algorithm to extract a feature vector of modal frequency; and finally, the frequency curves with high similarity are gathered together by adopting a DBSCAN clustering algorithm to realize partitioning of the system. According to the method, the real-time partitioning result of the system can be quickly and accurately given, and the consistency of regional frequency response under various disturbances is ensured.

Description

Technical Field

[0001] The present invention relates to the field of spatio-temporal distribution characteristics of the frequency of a new power system, and particularly to a method for partitioning a power system region considering spatio-temporal distribution characteristics of the frequency. Background Art

[0002] There is a spatio-temporal distribution phenomenon in the frequency response of a power system. New energy sources such as wind turbines and photovoltaics cannot actively provide inertia support to the system. After the access of new energy to the system, the inertia distribution becomes more uneven, and the spatio-temporal distribution characteristics of the frequency after the system is disturbed are more obvious. Existing inertia assessment has started to shift from the system side to the regional side. Accurately partitioning the system is a prerequisite for realizing regional inertia assessment. Therefore, a real-time partitioning method that can be fully programmed is needed to quickly and accurately give the real-time partitioning result of the system and ensure the consistency of the regional frequency response under various disturbances.

[0003] In existing partitioning methods, most of them divide regions according to the degree of correlation of the frequency response characteristics between generators, and group the unit nodes with similar frequency responses into one region. However, most of these methods do not consider the system partitioning situation after the access of new energy. With the increase of new energy units in the system, this partitioning method based on generator coherence is gradually limited. To ensure the accuracy of the regional partitioning result, it is necessary to consider the influence of the system operating conditions and the location of the disturbance on the partitioning, so as to perform real-time partitioning. By analyzing the spatio-temporal distribution characteristics of the frequency response of the power system, the influence of the disturbance type and location on the frequency response of each unit can be pointed out. Through simulation, the frequency of the PMU configuration nodes when disturbances occur at different positions of the system can be measured. Using the measured frequency response curve after modal decomposition, a similarity matrix and a Laplacian matrix are constructed through an improved spectral clustering algorithm, and the eigenvectors of the modal frequencies are extracted. Subsequently, the DBSCAN clustering algorithm is used to cluster and partition the system, and the frequency curves with high similarity are grouped together, thereby realizing system partitioning. Summary of the Invention

[0004] The object of the present invention is to overcome the defects in the above background art. The present invention proposes a method for partitioning a power system region considering spatio-temporal distribution characteristics of the frequency. The method measures the frequencies of PMU configuration nodes when disturbances occur at different positions of the system through simulation under the condition of considering the influence of the system operating conditions and the location of the disturbance on the partitioning. Using the measured frequency response curve after modal decomposition, a similarity matrix and a Laplacian matrix are constructed through an improved spectral clustering algorithm, and the eigenvectors of the modal frequencies are extracted. Subsequently, the DBSCAN clustering algorithm is used to cluster and partition the system, and the frequency curves with high similarity are grouped together, thereby realizing system partitioning.

[0005] The present invention adopts the following technical solutions to solve the above technical problems:

[0006] A method for partitioning a power system considering the spatio-temporal distribution characteristics of frequency, the steps are as follows:

[0007] Step S1: First, model the equipment side and network side of the new energy power system respectively, and then obtain the system closed-loop frequency response model. Secondly, decompose the frequency response into multiple components based on the spectral decomposition of the system return difference matrix:

[0008] is the common-mode frequency, which is the same for each machine;

[0009] is the differential-mode frequency, with relative oscillation between each machine;

[0010] Step S2: For the modal frequencies decomposed in Step S1, further analyze the response characteristics of the lowest frequency point and the average change rate of each frequency component, and quantify the spatio-temporal distribution characteristics of frequency;

[0011] Step S3: Measure the frequencies of PMU configuration nodes when disturbances occur at different positions of the system through simulation, where the PMU is a synchronized phasor measurement unit; use the measured frequency response curve after modal decomposition, construct a similarity matrix and a Laplacian matrix through an improved spectral clustering algorithm, and extract the eigenvectors of the modal frequencies; subsequently, use the DBSCAN clustering algorithm to cluster and partition the system, and cluster the frequency curves with high similarity together, thereby realizing system partitioning, where DBSCAN is a density-based clustering algorithm.

[0012] Further, the specific content of Step S1 is as follows:

[0013] Step S1-1: First, model the equipment side and network side of the new energy power system respectively, and then obtain the system closed-loop frequency response model. The dynamics of the power generation equipment can all be represented by the transfer function of frequency input - active power output:

[0014]

[0015] Among them, represents the perturbation of the variable; and are the active power vector and the frequency vector respectively, and they take and as elements, , is the number of equipment; is the frequency-active power transfer function matrix of all equipment, and its negative sign is because the active power output of the power generation equipment is positive when the frequency drops;

[0016] Step S1-2: The relationship between the network-side frequency and the active power can be described by the power flow equation, which can be expressed as:

[0017]

[0018] wherein, is the system nominal frequency, is a diagonal matrix with the Laplace operator as the diagonal element, is the network Laplace matrix for eliminating passive nodes;

[0019] Connect the input and output of the device to the network and superimpose a disturbance on the active power of the device , and the closed-loop system frequency response can be obtained:

[0020] .

[0021] Furthermore, the closed-loop system frequency response in step S1-2 is decomposed as follows:

[0022] For the convenience of decomposing the closed-loop system frequency response in Equation (3), rewrite it as:

[0023]

[0024] wherein, is the identity matrix, is the return difference matrix with respect to , and the spectral decomposition of is denoted as:

[0025]

[0026] wherein, are respectively eigenvalues and left and right eigenvectors, , generally the subscript is used to represent the ordinal number of the eigenvalue, which is distinguished from representing the device ordinal number, and they are all functions; 0, and 1 are eigenvalues and left and right eigenvectors; correspondingly, it is easy to know that has the following eigenvalues and eigenvectors:

[0027]

[0028] Substitute Equations (5)-(6) into Equation (4), then the node frequency response can also be decomposed into n components:

[0029]

[0030] Among them, is the change in the global frequency response, representing the consistent part among the frequency responses of all nodes, is the change in the frequency response of the th node, is the total number of nodes, is the weight coefficient, represents the weight coefficient of the th device, is the power change, and respectively are the left and right eigenvectors, is the eigenvalue of the th node, represents the transfer function of the th device, represents the inverse transfer function of the system;

[0031] It can be seen from the above formula that all elements in are the same, so it is the consistent part among the frequency responses of each node, characterizing the global frequency, and the remaining components characterize the frequency distribution difference. Therefore, the first component is called the frequency common-mode component, simply referred to as the common-mode frequency, and the remaining components are collectively referred to as the frequency differential-mode components, simply referred to as the differential-mode frequency.

[0032] Furthermore, the specific process of quantifying the frequency spatio-temporal distribution characteristics in step S2 is as follows:

[0033] Step 2-1: During the period from the initial perturbation moment to the lowest frequency point, the high-order common-mode frequency trajectory is very close to a second-order damped sine curve. The frequency characteristics of the lowest point and the average change rate of the common-mode frequency can be obtained based on the latter. Therefore, the device transfer function structure corresponding to the damped sine curve can be selected to uniformly simplify the models of various devices. This transfer function structure can be expressed as:

[0034]

[0035] Among them, , and are the effective inertia, effective damping, and effective frequency modulation coefficient respectively, is the system common-mode inertia;

[0036] Step S2-2: Solve the unified structure parameters through the following parameter optimization problem, described as:

[0037]

[0038] in, is the initial time of disturbance, is the final moment, which can usually be selected as , is the moment of lowest frequency, For the i Devices at time t The active power change at the moment, u Represents wind power and photovoltaic new energy equipment and nodes; For the i Devices at time t The active power change at the moment, cm represents common mode; and Respectively represent i Device and i Frequency-active power transfer function of wind power and photovoltaic new energy equipment; It represents the change in the common-mode frequency response, that is, the consistent part of the frequency response of all nodes;

[0039] Depend on , as well as The above optimization problem can be described as approximating the linear combination of these three items. , the optimal coefficients are , as well as ;

[0040] Step S2-3: After solving the optimization problem, the equipment is simplified into a unified structure as follows:

[0041]

[0042] In the formula, , as well as They are the system common mode inertia, common mode damping and common mode frequency modulation coefficient respectively; considering the power step disturbance:

[0043]

[0044] in, is the equivalent disturbance size, then equation (10) can be rewritten as:

[0045]

[0046] In the formula The time domain analytical expression can be directly obtained and the lowest frequency point and the average rate of change can be calculated.

[0047] Further, the solution of the lowest point of formula (12) in step S2-3 is as follows:

[0048] According to the relationship between the system common-mode inertia, common-mode damping, and common-mode frequency modulation coefficient in formula (12), the damping ratio, undamped oscillation frequency, damped oscillation frequency, and attenuation coefficient of the second-order system are respectively , , , ;

[0049] Then The moment of reaching the lowest point And the lowest point Are respectively:

[0050]

[0051] In the formula, Represents the initial power of the system, Represents the gain coefficient of the system, Represents the equivalent moment of inertia of the system, Represents the attenuation coefficient of the system, Represents the damped oscillation frequency of the system.

[0052] Further, the calculation method of the average frequency change rate in a certain period is as follows:

[0053] Take , As a positive integer, then at , The average frequency change rate In the time of

[0054]

[0055] In the formula, Represents the initial power of the system, Represents the common-mode inertia of the system, Represents the damping ratio of the system, and e is the base of the natural logarithm.

[0056] Further, the specific process of clustering and partitioning the system in step S3 is as follows:

[0057] Step S3-1: First establish a Laplacian matrix through the spectral clustering algorithm, then standardize the Laplacian matrix, and obtain the eigenvalues of the Laplacian matrix to establish an eigenmatrix;

[0058] Step S3-2: Optimize it using the Harris hawk optimization algorithm;

[0059] Step S3-3: Apply the EDR algorithm to all node frequency curves in the region. Perform deletion, insertion, and replacement operations on two node frequency time series points in the same region under the sampling time window, and compare all nodes in the region one by one using the EDR algorithm. Finally, find the node with the fewest number of operations in the region. The frequency curve can best reflect the dynamic response characteristics of each node's frequency in the region. The EDR algorithm is the reallocation edit distance algorithm, which is an algorithm for measuring the similarity between two time series.

[0060] Step S3-4: Finally, use the DBSCAN clustering algorithm to cluster frequency curves with small distances and high similarities together, thus realizing system partitioning.

[0061] Furthermore, the feature matrix in Step S3-1 is specifically shown as follows:

[0062]

[0063] In the formula: is the admittance of the tie line; Node and node The line conductance between them; is the imaginary unit, used to represent the imaginary part in a complex number; is an element of an adjacency matrix, used to represent whether there is a connection between nodes a and b in the power system; represents the edge set between nodes in the power system, and respectively represent the voltages of nodes a and b ; represents node and node The line conductance between them; is the node and node The line susceptance between them; is the standardized Laplacian matrix; is the identity matrix; is the sum of the admittance matrices of all edges connected to this node; is the degree matrix; is the number of nodes in the region.

[0064] Furthermore, the optimization process of the Harris hawk optimization algorithm includes: first setting the initial population number and the maximum number of iterations, and then traversing all clustering results to save the global maximum silhouette coefficient partitioning result.

[0065] Compared with the prior art by adopting the above technical solutions, the present invention has the following beneficial effects:

[0066] (1) A method for dividing power system regions considering the spatio-temporal distribution characteristics of frequency proposed by the present invention takes into account the modal characteristics of the frequency response of new energy power systems. By modal frequency decomposition, the spatio-temporal distribution characteristics of frequency are quantified, and the response characteristic indexes such as the lowest point and average change rate of each frequency component are further analyzed, and the temporal distribution characteristics of modal frequency components in the power system are quantified.

[0067] (2) A method for dividing power system regions considering the spatio-temporal distribution characteristics of frequency proposed by the present invention measures the frequencies of PMU configuration nodes when disturbances occur at different positions of the system through simulation, and uses the measured frequency response curves after modal decomposition to construct a similarity matrix and a Laplacian matrix through an improved spectral clustering algorithm, and extracts the eigenvectors of modal frequencies.

[0068] (3) A method for dividing power system regions considering the spatio-temporal distribution characteristics of frequency proposed by the present invention uses the DBSCAN clustering algorithm to cluster frequency curves with high similarity together to realize the partitioning of the system. The present invention provides a real-time partitioning method that can be fully programmed to operate, which can quickly and accurately give the real-time partitioning results of the system, and ensure the consistency of regional frequency responses under various disturbance conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 is the flowchart of the steps of the present invention;

[0070] Figure 2 is the closed-loop dynamic response diagram of the frequency of the new energy power system of the present invention;

[0071] Figure 3 is the schematic diagram of the common-mode frequency of the present invention;

[0072] Figure 4 is the schematic diagram of the differential-mode frequency of the present invention;

[0073] Figure 5 is the optimization flowchart of the Harris hawk algorithm of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0074] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0075] A method for partitioning power system regions considering the spatio-temporal distribution characteristics of frequency, the steps are as follows:

[0076] Step S1: First, model the equipment side and network side of the new energy power system respectively, and then obtain the system closed-loop frequency response model. Secondly, decompose the frequency response into multiple components based on the spectral decomposition of the system return difference matrix:

[0077] is the common-mode frequency, which is the same for each machine;

[0078] is the differential-mode frequency, and there is relative oscillation between each machine;

[0079] Step S2: For the modal frequencies decomposed in Step S1, further analyze the response characteristics of the lowest frequency point and average change rate of each frequency component, and quantify the spatio-temporal distribution characteristics of frequency;

[0080] Step S3: Measure the frequencies of PMU configuration nodes when disturbances occur at different positions of the system through simulation, where the PMU is a synchronized phasor measurement unit; use the measured frequency response curve after modal decomposition, construct a similarity matrix and a Laplacian matrix through an improved spectral clustering algorithm, and extract the eigenvectors of the modal frequencies; subsequently, use the DBSCAN clustering algorithm to cluster and partition the system, and gather the frequency curves with high similarity together, thereby realizing system partitioning, where DBSCAN is a density-based clustering algorithm.

[0081] Further, the specific content of Step S1 is as follows:

[0082] Step S1-1: First, model the equipment side and network side of the new energy power system respectively, and then obtain the system closed-loop frequency response model. The dynamics of the power generation equipment can all be represented by the transfer function of frequency input - active power output:

[0083] (1)

[0084] Among them, represents the perturbation of the variable; and are the active power vector and frequency vector respectively, and they are composed of and as elements, , is the number of equipment; is the frequency - active power transfer function matrix of all equipment, and the negative sign is because the active power output of the power generation equipment is positive when the frequency drops;

[0085] Step S1-2: The relationship between the network side frequency and active power can be described by the power flow equation, which can be expressed as:

[0086] (2)

[0087] Wherein, is the system nominal frequency, is a diagonal matrix with the Laplace operator as the diagonal element, is the network Laplace matrix eliminating the passive nodes;

[0088] Connect the input and output of the device to the network and superimpose a perturbation on the active power of the device , and the frequency response of the closed-loop system can be obtained, as Figure 2 shown:

[0089] (3).

[0090] Further, the frequency response of the closed-loop system in the step S1-2 is decomposed as follows:

[0091] For the convenience of decomposing the frequency response of the closed-loop system in Equation (3), rewrite it as:

[0092] (4)

[0093] Wherein, is the identity matrix, is the return difference matrix with respect to , and the spectral decomposition of is denoted as:

[0094] (5)

[0095] Wherein, are respectively 's eigenvalues and left and right eigenvectors, , generally represented by the subscript indicating the ordinal number of the eigenvalue, which is distinguished from representing the device ordinal number, and they are all 's functions; 0, and 1 are 's eigenvalues and left and right eigenvectors; correspondingly, it is easy to know that has the following eigenvalues and eigenvectors:

[0096] (6)

[0097] Substitute Equations (5)-(6) into Equation (4), then the node frequency response can also be decomposed into n components:

[0098] (7)

[0099] Wherein, is the change in the global frequency response, representing the consistent part among the frequency responses of all nodes. is the change in the frequency response of the th node, is the total number of nodes, is the weight coefficient, representing the weight coefficient of the th device, is the power change, and are the left and right eigenvectors of respectively, is the eigenvalue of the th node, represents the transfer function of the th device,

[0100] From the above formula, it can be seen that all elements in are the same. Therefore, it is the consistent part among the frequency responses of each node, characterizing the global frequency, and the remaining components characterize the frequency distribution differences. So, the first component is called the frequency common-mode component, simply referred to as the common-mode frequency as Figure 3 shown, and the remaining components are collectively referred to as the frequency differential-mode components, simply referred to as the differential-mode frequency as Figure 4 shown.

[0101] Furthermore, the specific process of quantifying the frequency spatio-temporal distribution characteristics in step S2 is as follows:

[0102] Step 2-1: During the period from the initial perturbation moment to the lowest frequency point, the high-order common-mode frequency trajectory is very close to a second-order damped sine curve. The frequency characteristics of the lowest point and the average change rate of the common-mode frequency can be obtained based on the latter. Therefore, the transfer function structure corresponding to the damped sine curve can be selected to uniformly simplify the models of various devices, and this transfer function structure can be expressed as:

[0103] (8)

[0104] where , and are the effective inertia, effective damping, and effective frequency modulation coefficient respectively;

[0105] Step S2-2: Solve the unified structure parameters through the following parameter optimization problem, described as:

[0106] (9)

[0107] where is the initial perturbation moment, is generally selected as , is the moment of the lowest frequency point;

[0108] It consists of , and . The above optimization problem can be described as approximating using a linear combination of these three terms. The optimal coefficients are respectively , and ;

[0109] After solving the optimization problem in step S2 - 3, the device is simplified to a unified structure as follows:

[0110] (10)

[0111] In the formula, , and are the system's common - mode inertia, common - mode damping, and common - mode frequency - modulation coefficient respectively. Considering the power - step disturbance:

[0112] (11)

[0113] Among them, is the magnitude of the equivalent disturbance. Then formula (10) can be rewritten as:

[0114] (12)

[0115] In the formula the time - domain analytical formula can be directly obtained, and the lowest frequency point and the average change rate can be calculated.

[0116] Furthermore, the solution of the lowest point of formula (12) in step S2 - 3 is as follows:

[0117] Based on the relationships of the system's common - mode inertia, common - mode damping, and common - mode frequency - modulation coefficient in formula (12), the damping ratio, undamped oscillation frequency, damped oscillation frequency, and attenuation coefficient of the second - order system are respectively , , , ;

[0118] Then the moment when it reaches the lowest point and the lowest point

[0119] (13)

[0120] In the formula, Represents the initial power of the system, Represents the gain coefficient of the system, Represents the equivalent moment of inertia of the system, Represents the attenuation coefficient of the system, Represents the damped oscillation frequency of the system.

[0121] Furthermore, the calculation method of the average frequency change rate over a certain period is as follows:

[0122] Take , as a positive integer, then at , the average frequency change rate within the time

[0123] is:

[0124] In the formula, represents the initial power of the system, represents the common-mode inertia of the system, represents the damping ratio of the system, and e is the base of the natural logarithm.

[0125] Furthermore, the specific process of clustering and partitioning the system in step S3 is as follows:

[0126] Step S3-1: First establish a Laplacian matrix through the spectral clustering algorithm, then standardize the Laplacian matrix, and obtain the eigenvalues of the Laplacian matrix to establish an eigenmatrix;

[0127] Step S3-2: Optimize it using the Harris hawk optimization algorithm;

[0128] Step S3-3: Apply the EDR algorithm to the frequency curves of all nodes in the region, perform deletion, insertion, and replacement operations on the frequency time series points of two nodes in the same region under the sampling time window, compare all nodes in the region one by one using the EDR algorithm, and finally find the node with the least number of operations; the frequency curve can best reflect the dynamic response characteristics of the frequencies of each node in the region, and the EDR algorithm is the reassignment edit distance algorithm, which is an algorithm for measuring the similarity between two time series;

[0129] Step S3-4: Finally, use the DBSCAN clustering algorithm to cluster the frequency curves with small distances and high similarities together, thereby realizing system partitioning.

[0130] Furthermore, the eigenmatrix in step S3-1 is specifically shown as the following formula:

[0131] (15)

[0132] In the formula: is the admittance of the tie line; node and node The line conductance between them; is the imaginary unit, used to represent the imaginary part in a complex number; represents the edge set between nodes in the power system; represents node and node The line conductance between them; is the node and node The line susceptance between them; is the standardized Laplacian matrix; is the identity matrix; is the sum of the admittance matrices of all the edges connected to this node; is the degree matrix; is the number of nodes in the region.

[0133] Furthermore, the optimization process of the Harris hawk optimization algorithm includes; first set the initial population number and the maximum number of iterations, then traverse all clustering results, and save the global maximum silhouette coefficient partition result. The specific process is as Figure 5 shown.

[0134] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for dividing power system regions considering the spatio-temporal distribution characteristics of frequency, characterized in that The method includes the following steps: Step S1: First, model the device side and network side of the new energy power system respectively, and then obtain the system closed-loop frequency response model. Secondly, decompose the frequency response into multiple components based on the spectral decomposition of the system return difference matrix: is the common-mode frequency, which is kept consistent for each machine; is the differential mode frequency, with relative oscillation between each machine; Step S2: For the modal frequencies decomposed in Step S1, further analyze the response characteristics of the lowest frequency point and average change rate of each frequency component, and quantify the frequency spatio-temporal distribution characteristics; Step S3: Measure the frequencies of PMU configuration nodes when disturbances occur at different positions of the system through simulation. The PMU is a synchronized phasor measurement unit. Using the measured frequency response curve after modal decomposition, construct a similarity matrix and a Laplacian matrix through an improved spectral clustering algorithm, and extract the eigenvectors of the modal frequencies. Subsequently, use the DBSCAN clustering algorithm to cluster and partition the system, and gather the frequency curves with high similarity together to achieve system partitioning. The DBSCAN is a density-based clustering algorithm.

2. The power system regional division method considering the spatio-temporal distribution characteristics of frequency according to claim 1, wherein The specific content of Step S1 is as follows: Step S1-1: First, model the device side and network side of the new energy power system respectively, and then obtain the system closed-loop frequency response model. The dynamics of the power generation equipment are all represented by the transfer function of frequency input - active power output: ， Among them, represents the perturbation of the variable; and are the active power vector and the frequency vector respectively, and they are and as elements, , is the number of devices; is the frequency-active power transfer function matrix of all devices, and the negative sign is because the active power output of the power generation device is positive when the frequency drops; The relationship between the network side frequency and active power is described by the power flow equation, expressed as: ， In the formula, is the system nominal frequency, is a diagonal matrix with the Laplace operator as the diagonal element, is the network Laplace matrix after eliminating the passive nodes; Connect the input and output of the device to the network and superimpose a disturbance on the active power of the device , to obtain the frequency response of the closed-loop system: 。 3. A method for dividing power system regions considering the spatio-temporal distribution characteristics of frequency, as claimed in claim 2, wherein The decomposition of the closed-loop system frequency response in Step S1-2 is as follows: To facilitate the decomposition of the closed-loop system frequency response in Equation (3), rewrite it as: ， In the formula, is the identity matrix, is the backlash matrix with respect to The spectral decomposition of is denoted as: ， wherein, are respectively the eigenvalue and the left and right eigenvectors, , generally the subscript is used to represent the ordinal number of the eigenvalue, which is distinguished from representing the ordinal number of the device, and they are all functions of; 0, and 1 are the eigenvalue and the left and right eigenvectors; correspondingly, it is easy to know that has the following eigenvalues and eigenvectors: ， Substituting Eqs. (5)-(6) into Eq. (4), the node frequency response is also decomposed into n components: ， Among them, is the change in the global frequency response, representing the consistent part among the frequency responses of all nodes. is the change in the frequency response of the -th node. is the total number of nodes. is the weight coefficient. represents the weight coefficient of the -th device. is the change in power. and are the left and right eigenvectors of respectively. is the eigenvalue of the -th node. represents the transfer function of the -th device. represents the inverse transfer function of the system. As can be seen from the above formula, all elements in are the same, which is the consistent part in the frequency responses of each node and represents the global frequency. The remaining components represent the frequency distribution differences. Therefore, the first component is called the frequency common-mode component, simply referred to as the common-mode frequency, and the remaining components are collectively referred to as the frequency differential-mode components, simply referred to as the differential-mode frequency.

4. A method for partitioning power system regions considering the spatio-temporal distribution characteristics of frequency, characterized in that, The specific process of quantifying the frequency spatio-temporal distribution characteristics in Step S2 is as follows: Step 2-1: During the period from the initial moment of the disturbance to the lowest frequency point, the high-order common-mode frequency trajectory is very close to the second-order damped sine curve. Based on the latter, obtain the frequency characteristics of the more accurate common-mode frequency lowest point and average change rate. Select the device transfer function structure corresponding to the damped sine curve to uniformly simplify the models of various devices. This transfer function structure is expressed as: ， Among them, , and are the effective inertia, effective damping, and effective frequency modulation coefficient respectively, is the system common-mode inertia; Step S2-2: Solve the unified structure parameters through the following parameter optimization problem, described as: ， Among them, is the initial moment of perturbation, is the final moment, which can generally be selected as , is the moment of the lowest frequency point, is the i th device's active power change at time t ; u represents wind power and photovoltaic new energy devices and nodes; is the i th device's active power change at time t ; cm represents common mode; and respectively represent the frequency-active power transfer functions of the i th device and the i th wind power and photovoltaic new energy device; represents the change in common mode frequency response, that is, the consistent part among all node frequency responses; consisting of , and , the above optimization problem is described as approximating using a linear combination of these three terms, and the optimal coefficients are respectively , and ; After the optimization problem is solved, the device is simplified to the unified structure as follows: ， wherein, , and are the system common-mode inertia, common-mode damping, and common-mode frequency modulation coefficient, respectively; considering a power step disturbance: ， wherein, is the equivalent disturbance magnitude, then Equation (10) is rewritten as: ， wherein directly obtain the time-domain analytical formula and calculate the lowest frequency point and the average rate of change.

5. A method for partitioning power system regions considering the spatio-temporal distribution characteristics of frequency, characterized in that, The specific solution of the lowest point of Equation (12) in Step S2-3 is as follows: Based on the relationships among the system common-mode inertia, common-mode damping, and common-mode frequency modulation coefficient in Equation (12), the damping ratio, undamped oscillation frequency, damped oscillation frequency, and attenuation coefficient of the second-order system are respectively , , , ; Then The moment of reaching the lowest point and the lowest point are respectively ， In the formula, represents the initial power of the system, represents the gain coefficient of the system, represents the equivalent moment of inertia of the system, represents the attenuation coefficient of the system, represents the damped oscillation frequency of the system.

6. A method for partitioning power system regions considering the spatio-temporal distribution characteristics of frequency, characterized in that, The calculation method of the average change rate of frequency during a certain period is as follows: Take , is a positive integer, then at , the average rate of change of frequency within the time is: ， wherein, represents the initial power of the system, represents the common-mode inertia of the system, represents the damping ratio of the system, and e is the base of the natural logarithm.

7. A method for dividing power system regions considering the spatio-temporal distribution characteristics of frequency, characterized in that, The specific process of clustering and partitioning the system in Step S3 is as follows: Step S3-1: First, establish a Laplacian matrix through the spectral clustering algorithm, then standardize the Laplacian matrix, and obtain the eigenvalue of the Laplacian matrix to establish an eigenmatrix; Step S3-2: Optimize it using the Harris hawk optimization algorithm; Step S3-3: Apply the EDR algorithm to all node frequency curves in the region. Perform deletion, insertion, and replacement operations on the frequency time series points of two nodes in the same region under the sampling time window, and compare all nodes in the region one by one using the EDR algorithm. Finally, find the node with the fewest number of operations in the region; The frequency curve can best reflect the dynamic response characteristics of frequencies of each node in the region. The EDR algorithm is the reallocation edit distance algorithm, which is an algorithm for measuring the similarity between two time series; Step S3-4: Finally, use the DBSCAN clustering algorithm to cluster the frequency curves with small distances and high similarities together, so as to realize system partitioning.

8. A method for partitioning power system regions considering the spatio-temporal distribution characteristics of frequency, characterized in that, The feature matrix in step S3-1 is specifically shown as follows: ， Where: is the admittance of the tie line; node and node is the line conductance between them; is the imaginary unit, used to represent the imaginary part in a complex number; is an element of an adjacency matrix, used to represent whether there is a connection between nodes a and b in the power system; represents the edge set between nodes in the power system, and respectively represent the voltages of nodes a and b ; represents the line conductance between node and node ; is the line susceptance between node and node ; is the normalized Laplacian matrix; is the identity matrix; is the sum of the admittance matrices of all edges connected to this node; is the degree matrix; is the number of nodes in the area.

9. A method for dividing power system regions considering the spatio-temporal distribution characteristics of frequency, as claimed in claim 7, wherein The optimization process of the Harris hawk optimization algorithm includes: first setting the initial population number and the maximum number of iterations, then traversing all clustering results, and saving the global maximum silhouette coefficient partitioning result.

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