Quantitative method for coordination of frequency stability of hybrid power system supported by grid-connected and grid-forming devices

Abstract

The application discloses a kind of mixed support power system frequency coordination quantization methods of net type and network type equipment, comprising the following steps: constructing electromagnetic transient simulation model to simulate dynamic response under disturbance, obtain the frequency and frequency deviation time series of GFM unit and GFL unit;The standardized frequency sequence of each unit is time-lag embedded, and the phase space trajectory vector is constructed;Recurrence matrix is constructed based on time lag recursive method;Coupling state recurrence index is calculated;Coordination decay rate and coordination half-life index are calculated.The coupling state recurrence index, coordination decay rate and coordination half-life index calculated by the application constitute the index system of quantifying frequency coordination support, support the planning configuration, stability evaluation and operation control of high proportion new energy power system.

Description

Technical Field

[0001] This invention relates to the field of power system stability analysis and control technology, specifically to a quantitative method for the frequency coordination of a power system supported by a combination of grid-connected and grid-building equipment. Background Technology

[0002] With the large-scale grid connection of new energy sources such as wind power and photovoltaics, the penetration rate of inverter-based power generation resources in the power system is constantly increasing. The power system is gradually transforming from the traditional structure dominated by synchronous generators to a new structure supported by a hybrid of grid-forming converters (GFM) and grid-following converters (GFL). Grid-forming converters simulate the characteristics of synchronous generators, autonomously establish and support grid voltage and frequency, and exhibit voltage source characteristics. On the other hand, grid-following converters rely on phase-locked loops to track grid synchronization signals and exhibit current source characteristics. The two have fundamental differences in control mechanisms, inertial response, primary frequency regulation, and other time scales, resulting in complex multi-time-scale transient interactions in the frequency dynamics of the hybrid system, which brings unprecedented challenges to the coordinated analysis and evaluation of system frequency stability.

[0003] With a high proportion of renewable energy integration, it is difficult to balance system stability, economy, and grid support performance using a single grid-following or grid-building control mode. Therefore, the hybrid configuration of GFM and GFL has become an inevitable trend in the development of current power systems. However, when these two devices operate in the same system, their dynamic interaction mechanism is extremely complex. When the system is disturbed, the fast tracking behavior of GFL devices relying on phase-locked loops and the frequency support behavior autonomously established by GFM devices may produce constructive synergistic effects or may trigger destructive coupled oscillations. This hybrid but not integrated phenomenon has become a potential risk point threatening the safe and stable operation of new power systems.

[0004] Currently, research on hybrid GFM and GFL systems has become a cutting-edge hot topic in the international academic community. The focus of research is gradually shifting from early single-device control to multi-device collaborative optimization, and from qualitative analysis to quantitative evaluation. However, existing quantitative evaluation methods still have significant shortcomings:

[0005] (1) The inertial center model is over-aggregated and cannot depict the details of the interaction between heterogeneous devices;

[0006] (2) Small signal analysis relies on accurate linearization models and parameters, which makes it difficult to handle strong nonlinear effects, and accurate parameters are often not easy to obtain in actual systems.

[0007] (3) Although traditional data-driven methods (such as deep learning models and physical information neural networks) can achieve trajectory prediction, they often focus on minimizing prediction errors and fail to effectively preserve and reveal the inherent physical stability mechanism of the system, resulting in poor interpretability and unclear physical meaning of the evaluation results.

[0008] In summary, when the power system is subjected to disturbances, there is still a lack of corresponding quantitative assessment methods for the synergistic effect of the frequency support behavior autonomously established by grid-connecting equipment. Summary of the Invention

[0009] To overcome the defects and shortcomings of existing technologies, this invention provides a quantitative method for the frequency coordination of power systems supported by a combination of grid-connected and grid-building equipment. Based on the CSR-Koopman analysis framework, which combines the Coupled State Recursion (CSR) method with the Koopman operator, this invention constructs a multi-dimensional quantitative evaluation index system to achieve quantitative analysis of the frequency coordination of power systems supported by grid-connected and grid-building equipment, and guides the optimal configuration of GFM and GFL equipment.

[0010] To achieve the above objectives, the present invention adopts the following technical solution:

[0011] This invention provides a quantitative method for the frequency coordination of a power system supported by a combination of grid-connected and grid-building equipment, comprising the following steps:

[0012] An electromagnetic transient simulation model was constructed to simulate the dynamic response under disturbance, and the frequency and frequency deviation time series of the GFM and GFL elements were obtained.

[0013] Time-delay embedding is performed on the normalized frequency sequence of each unit to construct the phase space trajectory vector;

[0014] Constructing a recursive matrix based on a time-lag recursive method;

[0015] Calculate the recursive index of coupling state;

[0016] Calculate the coordinated decay rate and coordinated half-life indices.

[0017] As a preferred technical solution, the frequency and frequency deviation time series of the GFM unit and the GFL unit are obtained, specifically including:

[0018] The frequency is decomposed into globally slow-changing and locally fast-changing signals, and the deviation between the instantaneous frequency and the rated frequency in the power grid is calculated.

[0019] The deviation between the instantaneous frequency and the rated frequency in the power grid is standardized.

[0020] As a preferred technical solution, the frequency is decomposed into globally slow-changing and locally fast-changing signals, and the deviation between the instantaneous frequency and the rated frequency in the power grid is calculated, expressed as:

[0021] ;

[0022] in, This represents the deviation between the measured instantaneous frequency and the rated frequency at node i in the power grid at time t. This represents the inertial weighted average frequency. Reflects the interactions caused by rapid coupling;

[0023] From the total power balance, we get:

[0024] ;

[0025] in, and Represents the overall inertia and damping of the system. Distinguish between relative synchronization and global drift.

[0026] As a preferred technical solution, the deviation between the instantaneous frequency and the rated frequency in the power grid is standardized, specifically including:

[0027] make After standardization, it is represented as:

[0028] ;

[0029] in, , These are the mean and standard deviation of the local frequency deviation, respectively.

[0030] As a preferred technical solution, the standardized frequency sequence of each unit is time-delayed embedded to construct a phase space trajectory vector, which is represented as:

[0031] ;

[0032] Where d is the embedding dimension, Due to time lag, Represents a normalized frequency sequence. This represents the phase space trajectory vector.

[0033] As a preferred technical solution, a recursion matrix is ​​constructed based on the time-lag recursion method, and is represented as follows:

[0034] ;

[0035] in, For the Heaviside function, For density invariance threshold, and These are the local fast-changing frequency signals of unit u at times t and s, respectively.

[0036] As a preferred technical solution, the calculation of the coupling state recursion index specifically includes:

[0037] Construct a joint recursive matrix by performing a Hadamard product on the recursive matrices of the GFM and GFL elements;

[0038] Calculate the recursion rate of the coupled state;

[0039] The time-delay recursion rate of GFM and GFL cells is calculated respectively using the time-delay recursion method.

[0040] Calculate the coordination gain.

[0041] As a preferred technical solution, the joint recursive matrix is ​​represented as follows:

[0042] ;

[0043] in, This indicates that the GFM and GFL cells simultaneously return to their previous states at times t and s, suggesting that phase space trajectories have locked. , These are the recursion matrices for the GFM and GFL units, respectively;

[0044] The recursion rate of the coupled state is expressed as:

[0045] ;

[0046] in, Represents the recursion rate of the coupled state. To predict the time lag window, It is a joint recursive matrix The set of recursive points related to time point t, yes The number of elements in the set. It is a joint recursive matrix In and at time point The relevant set of recursive points, It can last The collaborative recursive event of the step;

[0047] The coordination gain is expressed as:

[0048] ;

[0049] in, This indicates that the joint dynamics of the grid-connected converter and the integrated grid-connected converter are more predictable than when they are independent, meaning that constructive synchronous coupling exists. This indicates that the two units are independent. This indicates that the interaction between the two units produces a hindering synchronous coupling. , These represent the time-delay recursion rates of the GFM and GFL cells, respectively.

[0050] As a preferred technical solution, the calculation of the coordinated decay rate and coordinated half-life indices specifically includes:

[0051] A deep Koopman network with embedded CSR physical information is trained based on electromagnetic transient simulation data to align the Koopman matrix with the power system physical information. The obtained Koopman matrix is ​​then decomposed into eigenvalues ​​to obtain the dominant non-unit eigenvalues, which correspond to the slowest decaying oscillation modes in the system.

[0052] Calculate the coordinated decay rate and coordinated half-life.

[0053] As a preferred technical solution, the coordinated attenuation rate is expressed as:

[0054] ;

[0055] in, The sampling interval is... Dominant non-unit eigenvalues;

[0056] Coordinated half-life is expressed as:

[0057] ;

[0058] in, The duration of the coordinated dynamics.

[0059] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0060] This invention proposes a coupled state recursion (CSR) method based on the time-lagged recurrence (TLR) approach. This method quantifies the supporting frequency coordination characteristics of the ground fault current generator (GFM) and ground fault current generator (GFL), providing a scientific basis for the optimized configuration of GFL / GFM equipment in high-proportion renewable energy power systems. The invention divides the frequency deviation data of each GFM and GFL generating unit into globally slow-changing and locally fast-changing signals. It collects and standardizes the locally fast-changing signals of each GFM and GFL generating unit through electromagnetic transient simulation, using these signals as the research object. A recursion matrix is ​​constructed, and the coupled state recursion rate is calculated. Coordination gain index Simultaneously, a deep Koopman network with deep CSR consistency regularization was constructed and trained to obtain a linear evolution model with interpretable physical mechanisms. The coordinated half-life index can be extracted from the model. The three indicators calculated above constitute an indicator system for quantifying the supporting role of frequency coordination, supporting the planning, configuration, stability assessment and operation control of high-proportion new energy power systems. Attached Figure Description

[0061] Figure 1 This is a flowchart illustrating the quantitative method for the hybrid support of grid-type and grid-structured equipment for power system frequency coordination according to the present invention.

[0062] Figure 2 This is a schematic diagram of the recursive calculation process of the present invention;

[0063] Figure 3 This is a schematic diagram of the process for calculating the recursive index of coupling state in this invention;

[0064] Figure 4 This is a schematic diagram of the improved IEEE 14 bus system. Detailed Implementation

[0065] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0066] Example

[0067] like Figure 1 As shown, this embodiment provides a quantitative method for the frequency coordination of a power system supported by a combination of grid-connected and grid-building equipment, including the following steps:

[0068] S1: Data acquisition and preprocessing;

[0069] S11: Build an electromagnetic transient simulation model on the MATLAB / Simulink platform to simulate the dynamic response of the system under typical disturbances, such as load step change, power generation failure, and high-voltage DC blockage.

[0070] S12: The frequency and frequency deviation time series of the GFM and GFL elements are obtained through electromagnetic transient simulation model, specifically including:

[0071] The frequency is dynamically decomposed into globally slow-changing and locally fast-changing signals;

[0072] To decouple multi-timescale dynamics, the center of inertia (COI) signal is used as an analytical reference to decompose local frequency deviations, as follows:

[0073] ;

[0074] in, The effective inertia of the GFL element is set to the inertial weighted average frequency, according to analysis convention. This decomposition reflects that the overall inertial response of the system is mainly dominated by the GFM source. This decomposition is only used to distinguish between global inertial drift and relative synchronization dynamics. It reflects the interactions caused by rapid coupling (such as tracking deviation caused by PLL). It refers to the deviation between the measured instantaneous frequency at node i at time t in the power grid and the rated frequency of the system;

[0075] From the total power balance, we can obtain:

[0076] ;

[0077] in, and Represents the overall inertia and damping of the system. Distinguish between relative synchronization (such as GFM-GFL interaction) and global drift;

[0078] make Standardization is performed to eliminate the influence of dimensions:

[0079] ;

[0080] in, , These are the mean and standard deviation of the local frequency deviation of the unit, respectively;

[0081] The data used in subsequent steps is a standardized local fast-frequency signal. ;

[0082] S2: Perform phase space reconstruction and recursive matrix construction;

[0083] In this embodiment, the normalized frequency sequence of each unit is time-delayed embedded to construct a phase space trajectory vector, represented as:

[0084] ;

[0085] Where d is the embedding dimension, It is a time lag;

[0086] Coupled-State Recursion (CSR) is based on Time-Lagged Recurrence (TLR). TLR eliminates the reliance on system models, directly extracting local predictability information from observational data. Its core principle is to quantify system stability through the recurrence of states in phase space. Specifically, for a reference state B, its neighboring states (called recurrence points) are first identified, and then these neighboring states are tracked within a future time window. The evolutionary trajectory within a time frame, if most neighboring trajectories are within a certain time frame... If the future position is still close to the reference state, it indicates that the state has high predictability; otherwise, it means that it has low predictability.

[0087] like Figure 2 As shown, the implementation process of the TLR method includes:

[0088] Recursive point identification: Utilizing extreme value theory, neighboring points of the reference state (e.g., ...) are filtered using quantile thresholds of the distance distribution. Figure 2 (The blue solid dots in the image) are to avoid noise interference;

[0089] Future state tracking: Evolving the recursion point forward to the time window Generate forward recursion points (e.g.) Figure 2 (blue hollow points in the image), and the future neighborhood of the reference state (such as...) Figure 2 Match the orange hollow dots in the image;

[0090] Predictability quantification: Calculate the matching ratio (i.e., the proportion of intersection between the forward recursion point and the future neighborhood), defined as the local predictability index. The closer this value is to 1, the higher the local predictability of the state. The local predictability index is expressed as:

[0091] ;

[0092] In this embodiment, the TLR adaptively adjusts the neighborhood scale through a quantile threshold, revealing predictability characteristics at different spatial scales. For example, a small-scale neighborhood may reflect the impact of short-term disturbances, while a large-scale neighborhood corresponds to the stability of the system's long-term evolution.

[0093] This embodiment calculates the recursion matrix of the GFM or GFL element u based on the local fast-changing frequency data obtained through simulation and processing. The recursive matrix is ​​constructed based on the TLR method. The formula for calculating the recursive matrix of cell u is as follows:

[0094] ;

[0095] in, For the Heaviside function, The density-invariant threshold (fixed at the 10th percentile of the pairwise distance) is used. and These are the local fast-changing frequency signals of unit u at times t and s, respectively;

[0096] S3: As Figure 3 As shown, the calculation of the Coupled State Recursion (CSR) index specifically includes:

[0097] S31: Select a pair of GFM unit i and GFL unit j. To quantify the coordination between these two units, construct a joint recurrence plot (JRP) by performing a Hadamard product on their recurrence matrices.

[0098] ;

[0099] in, This indicates that the two subsystems simultaneously return to their previous states at times t and s, suggesting that the phase space trajectories have locked. , These are the recursion matrices for GFM unit i and GFL unit j, respectively;

[0100] S32: Calculate the recursion rate of the coupled state :

[0101] ;

[0102] The above formula indicates whether, at time t, GFM and GFL are simultaneously in a recursive state, meaning they have both returned to states they previously experienced. The recursion rate of coupled states is a statistical indicator that measures the predictability of coordination in a hybrid system. To predict the time lag window, It is a joint recursive matrix The set of recursive points related to time point t, yes The number of elements in the set. It is a joint recursive matrix In and at time point The relevant set of recursive points, It can last Step-by-step collaborative recursive events, When larger The reading remains high, indicating that the synchronization between the two units is very persistent and stable;

[0103] S33: Calculate the time delay recursion rate of GFM and GFL cells respectively using the TLR method. , , , This represents its own predictability;

[0104] S34: Calculate the coordination gain :

[0105] ;

[0106] in, This indicates that the joint dynamics of the two units, the grid-connected converter and the integrated grid-connected converter, are more predictable than when they are independent, meaning that constructive synchronous coupling (coordinated gain) exists. This indicates that the two units are basically independent. This indicates that their interaction produces hindering synchronous coupling;

[0107] S4: Calculate the coordinated decay rate and coordinated half-life indices

[0108] S41: Establishment The theoretical boundary relating the decay rate to the Koopman operator spectral gap, and the exponential decay of CSR. Structurally related to the spectral properties of the Koopman operator, according to the ergodic theory of hybrid systems. The coupling recursive decay rate is limited by the spectral gap of the Koopman operator K:

[0109] ;

[0110] in This represents the invariant joint recursive measure under a stationary distribution. It is the dominant non-unit eigenvalue. In practical applications, this stationary measure is empirically approximated using long-term EMT trajectories. M is a positive constant (M>0) derived from the coefficients of the spectral decomposition.

[0111] Therefore, from Empirical decay rate derived from curve This is called the coordinated decay rate, which is statistically consistent. Alternative metrics that can reflect the dominant physical attenuation rate associated with the Koopman spectral gap.

[0112] S42: Train a deep Koopman network embedding CSR physical information using electromagnetic transient simulation data, aligning the Koopman matrix with the actual physical information of the power system. Then, analyze the obtained Koopman matrix... Eigenvalue decomposition is performed to obtain the dominant non-unit eigenvalues. The eigenvalue decomposition formula is:

[0113] ;

[0114] Where V is the eigenvector of the Koopman matrix. Given the eigenvalues ​​of the Koopman matrix, extract all eigenvalues ​​from the diagonal matrix. (i=1,2,...,m), sorted by real part in descending order. Dominant non-unit eigenvalues: selection (exclude The corresponding steady-state mode corresponds to the slowest decaying oscillation mode in the system.

[0115] S43: Calculate the coordinated decay rate and coordinated half-life

[0116] The coordinated attenuation rate is expressed as:

[0117] ;

[0118] in, The sampling interval (e.g., 1 ms) reflects the physical decay rate of the system's oscillation mode.

[0119] Coordinated half-life is expressed as:

[0120] ;

[0121] in, The duration of the coordinated dynamics is represented in milliseconds (ms).

[0122] like Figure 4 As shown, to verify the effectiveness of the proposed framework and indicator system, an experiment was conducted on an improved IEEE 14 bus system. In the figure, red graphics represent follow-the-network devices, and blue graphics represent network-building devices. The power generation system was configured with five GFM units (located at bus positions 1, 2, 3, 6, and 8) and three GFL units (located at bus positions 11, 12, and 13). Three representative node pairs were selected for the indicator system calculation: distant nodes 1-11, medium-distance nodes 3-11, and near-distance nodes 6-11. During indicator calculation... =100m, the calculation results of each index are shown in Table 1 below. Based on the data in the table, a detailed analysis of system coordination can be performed, such as... The coordination duration range is a highly sensitive indicator of impedance distance. The far-end bus (buses 1-11) exhibits a longer duration range (approximately 2000 milliseconds), reflecting the slow and persistent interaction that maintains coordination under a soft coupling mechanism. Conversely, the near-end bus (buses 6-11) shows rapid decay (≈430 milliseconds), exhibiting hard coupling characteristics, where local deviations are immediately suppressed. This can be seen in the table... This indicates that under different GFM penetration rates, the combined dynamics of the two units, the grid-type converter and the integrated grid-type converter, are more predictable than when they are independent.

[0123] Table 1. Schematic diagram of CSR-based measurement calculation results based on coordination analysis.

[0124]

[0125] Wherein, GFM (%) represents the percentage of GFM capacity in the entire network.

[0126] This invention proposes a coupled-state recursive method based on the time-delay recursion approach. It quantifies the supporting frequency coordination characteristics of GFM and GFL, providing a scientific basis for the optimized configuration of GFL / GFM equipment in high-proportion renewable energy power systems. This invention divides the frequency deviation data of each GFM and GFL generating unit into globally slow-changing and locally fast-changing signals. It collects and standardizes the locally fast-changing signals of each GFM and GFL generating unit through electromagnetic transient simulation, using them as the research object. A recursion matrix is ​​constructed, and the coupled-state recursion rate is calculated. Coordination gain index Simultaneously, a deep Koopman network with deep CSR consistency regularization was constructed and trained to obtain a linear evolution model with interpretable physical mechanisms. The coordinated half-life index can be extracted from the model. The three indicators calculated above constitute an indicator system for quantifying the supporting role of frequency coordination, supporting the planning, configuration, stability assessment and operation control of high-proportion new energy power systems.

[0127] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A quantitative method for the frequency coordination of a power system supported by a hybrid network of grid-connected and grid-building equipment, characterized in that, Includes the following steps: An electromagnetic transient simulation model was constructed to simulate the dynamic response under disturbance, and the frequency and frequency deviation time series of the GFM and GFL elements were obtained. Time-delay embedding is performed on the normalized frequency sequence of each unit to construct the phase space trajectory vector; Constructing a recursive matrix based on a time-lag recursive method; Calculate the recursive index of coupling state; Calculate the coordinated decay rate and coordinated half-life indices.

2. The method for quantifying the frequency coordination of a power system supported by a hybrid network of grid-connected and grid-building equipment as described in claim 1, characterized in that, Obtain the frequency and frequency deviation time series of GFM and GFL cells, specifically including: The frequency is decomposed into globally slow-changing and locally fast-changing signals, and the deviation between the instantaneous frequency and the rated frequency in the power grid is calculated. The deviation between the instantaneous frequency and the rated frequency in the power grid is standardized.

3. The method for quantifying the frequency coordination of a power system supported by a hybrid network of grid-connected and grid-building equipment as described in claim 2, characterized in that, The frequency is decomposed into globally slow-changing and locally fast-changing signals. The deviation between the instantaneous frequency and the rated frequency in the power grid is calculated and expressed as: ； in, This represents the deviation between the measured instantaneous frequency and the rated frequency at node i in the power grid at time t. This represents the inertial weighted average frequency. Reflects the interactions caused by rapid coupling; From the total power balance, we get: ； in, and Represents the overall inertia and damping of the system. Distinguish between relative synchronization and global drift.

4. The method for quantifying the frequency coordination of a power system supported by a hybrid network-following and network-building equipment according to claim 3, characterized in that, The deviation between the instantaneous frequency and the rated frequency in the power grid is standardized, specifically including: make After standardization, it is represented as: ； in, , These are the mean and standard deviation of the local frequency deviation, respectively.

5. The method for quantifying the frequency coordination of a power system supported by a hybrid network-following and network-building equipment according to claim 1, characterized in that, For each unit, the normalized frequency sequence is time-delayed embedded to construct a phase space trajectory vector, represented as: ； Where d is the embedding dimension, Due to time lag, Represents a normalized frequency sequence. This represents the phase space trajectory vector.

6. The method for quantifying the frequency coordination of a power system supported by a combination of grid-connected and grid-building equipment according to claim 1, characterized in that, The recursion matrix is ​​constructed based on the time lag recursion method and is represented as follows: ； in, For the Heaviside function, For density invariance threshold, and These are the local fast-changing frequency signals of unit u at times t and s, respectively.

7. The method for quantifying the frequency coordination of a power system supported by a combination of grid-connected and grid-building equipment according to claim 1, characterized in that, The calculation of the coupling state recursion index specifically includes: Construct a joint recursive matrix by performing a Hadamard product on the recursive matrices of the GFM and GFL elements; Calculate the recursion rate of the coupled state; The time-delay recursion rate of GFM and GFL cells is calculated respectively using the time-delay recursion method. Calculate the coordination gain.

8. The method for quantifying the frequency coordination of a power system supported by a hybrid network of grid-connected and grid-building equipment as described in claim 7, characterized in that, The joint recursive matrix is ​​represented as: ； in, This indicates that the GFM and GFL cells simultaneously return to their previous states at times t and s, suggesting that phase space trajectories have locked. , These are the recursion matrices for the GFM and GFL units, respectively; The recursion rate of the coupled state is expressed as: ； in, Represents the recursion rate of the coupled state. To predict the time lag window, It is a joint recursive matrix The set of recursive points related to time point t, yes The number of elements in the set. It is a joint recursive matrix In and at time point The relevant set of recursive points, It can last The collaborative recursive event of the step; The coordination gain is expressed as: ； in, This indicates that the joint dynamics of the grid-connected converter and the integrated grid-connected converter are more predictable than when they are independent, meaning that constructive synchronous coupling exists. This indicates that the two units are independent. This indicates that the interaction between the two units produces a hindering synchronous coupling. , These represent the time-delay recursion rates of the GFM and GFL cells, respectively.

9. The method for quantifying the frequency coordination of a power system supported by a combination of grid-connected and grid-building equipment according to claim 1, characterized in that, The calculation of the coordinated decay rate and coordinated half-life indices includes: A deep Koopman network with embedded CSR physical information is trained based on electromagnetic transient simulation data to align the Koopman matrix with the power system physical information. The obtained Koopman matrix is ​​then decomposed into eigenvalues ​​to obtain the dominant non-unit eigenvalues, which correspond to the slowest decaying oscillation modes in the system. Calculate the coordinated decay rate and coordinated half-life.

10. The method for quantifying the frequency coordination of a power system supported by a hybrid network-following and network-building equipment according to claim 9, characterized in that, The coordinated attenuation rate is expressed as: ； in, The sampling interval is... Dominant non-unit eigenvalues; Coordinated half-life is expressed as: ； in, The duration of the coordinated dynamics.

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