A low-frequency power frequency system coupling stability modeling method and system

Abstract

The application discloses a low-frequency power-frequency system coupling stability modeling method and system, relates to the technical field of power system modeling, and comprises the following steps: performing system division on an electric network to be analyzed and establishing a unified port variable set, and defining the unified port variable set at an interface position; constructing a multi-frequency reference coupling small disturbance model based on the unified port variable set, respectively establishing a low-frequency reference dynamic model and a power-frequency reference dynamic model, establishing a frequency transformation and control coupling relationship in an interface subsystem, forming a unified coupling state space model, and constructing an energy-consistent impedance mapping model based on a port power conjugate variable; passively detecting the impedance mapping model and performing passive repair processing, identifying a passive destruction channel by performing positive reality judgment on an impedance matrix, performing local energy shaping repair to obtain an impedance model satisfying a passivity constraint, and substituting the repaired impedance model into a phasor domain and a state space model to perform cross-model consistency checking.

Description

Technical Field

[0001] This invention relates to the field of power system modeling technology, specifically to a method and system for modeling the coupling stability of low-frequency power frequency systems. Background Technology

[0002] With the large-scale integration of new energy power generation and power electronic equipment, the traditional power system structure is gradually evolving from a single power frequency AC system to a multi-frequency coupled system. In some long-distance transmission, offshore wind power aggregation, and specific industrial power supply scenarios, low-frequency AC transmission technology has been proposed and gradually applied. This technology reduces line reactance and increases transmission capacity by lowering the system operating frequency. In this context, low-frequency systems and traditional power frequency grids are typically interconnected through frequency converter interface devices, forming a low-frequency-power frequency hybrid power system structure. For such systems, not only is dynamic characteristic analysis necessary, but also effective stability control strategies need to be constructed to suppress the oscillation risks caused by cross-frequency coupling and improve system operational safety. Therefore, to achieve a unified analysis of system stability and control behavior, a unified modeling method is needed that can simultaneously describe the dynamic behavior and control coupling relationships of different frequency subsystems. Currently, common modeling methods mainly include phasor domain modeling methods, state-space modeling methods, and frequency domain modeling methods based on impedance characteristics. These methods have been widely used in the stability analysis, controller design, and stability control strategy evaluation of single-frequency power systems.

[0003] However, in scenarios where low-frequency and power-frequency systems are coupled, existing modeling methods still have shortcomings in supporting stability analysis and strategy design. Traditional phasor domain or state-space modeling methods typically build models for single-frequency systems, making it difficult to simultaneously describe the dynamic coupling relationships between low-frequency systems, power-frequency systems, and their interface control systems within a unified mathematical framework. This limits the ability to uniformly design and verify stability strategies across frequency-crossing systems. Existing impedance modeling methods often establish port impedance models based on single-system frequency assumptions. When mapping these models to low-frequency-power-frequency coupled systems, inconsistencies in port power representation can easily arise, leading to inconsistent stability assessments of the same control strategy under different models. During the mapping from state-space models to impedance models, the impedance matrix may exhibit non-passive characteristics in certain frequency ranges, meaning the system displays energy gain within a specific frequency range. This not only violates the positive reality condition upon which impedance stability analysis relies but may also cause stability strategies designed based on impedance criteria to fail or misjudge. Existing technologies typically lack a unified processing mechanism for such problems, making it difficult to passively repair the impedance model while maintaining model energy consistency and ensuring consistency in the response of different models to stability strategies. Therefore, how to construct a coupled modeling method that can uniformly describe the dynamic coupling behavior of low-frequency and power-frequency systems, support the design of stability control strategies and consistency assessment, and ensure the consistency of power expression and the passivity of impedance during model mapping has become a key technical problem in the analysis and stability control of low-frequency-power-frequency coupled power systems. Summary of the Invention

[0004] In view of the above-mentioned problems, the present invention is proposed.

[0005] Therefore, the technical problem solved by this invention is: existing low-frequency-power frequency coupled power system modeling methods have problems such as inconsistent cross-frequency system model structure, inconsistent power expression in impedance model mapping process, and the impedance matrix may have non-passive characteristics, which leads to reduced reliability of stability analysis and stability control strategy evaluation. The problem is how to construct a coupled modeling method that can uniformly describe the dynamic coupling behavior of low-frequency system and power frequency system, support stability control strategy design and consistency evaluation, and ensure the energy consistency and passivity of impedance model.

[0006] To address the aforementioned technical problems, this invention provides the following technical solution: a method for modeling the coupling stability of a low-frequency power frequency system, comprising: dividing the power grid to be analyzed into a system partition and establishing a unified set of port variables; defining the unified set of port variables at the interface location; constructing a multi-frequency reference coupled small-disturbance model based on the unified set of port variables; establishing a low-frequency reference dynamic model and a power frequency reference dynamic model respectively; establishing frequency transformation and control coupling relationships in the interface subsystem to form a unified coupled state space model; and constructing an energy-consistent impedance mapping model based on the port power conjugate variables; performing passive detection and passive repair processing on the impedance mapping model; identifying passively disrupted channels by judging the positive and real nature of the impedance matrix and performing local energy shaping repair to obtain an impedance model that satisfies passive constraints; and substituting the repaired impedance model back into the phasor domain and state space model for cross-model consistency verification.

[0007] As a preferred embodiment of the low-frequency power frequency system coupling stability modeling method described in this invention, the system partitioning includes: acquiring power grid topology data and equipment parameter data, and classifying power grid equipment according to the rated operating frequency, control method, and electrical connection relationship of the equipment; transmission lines, cables, collection networks, and related compensation equipment with rated operating frequencies lower than the power frequency are classified as low-frequency AC subsystems; the main grid system, synchronous generators, loads, and grid-connected power electronic equipment with rated operating frequencies of the power frequency are classified as power frequency AC subsystems; and frequency converters, interface transformers, and corresponding control systems connecting the low-frequency system and the power frequency system are classified as low-frequency-power frequency interface subsystems; constructing the system topology based on the network node connection relationship, and identifying cross-frequency connection nodes by traversing the node connection relationship; when a node is detected to be simultaneously connected to low-frequency system equipment and power frequency system equipment, the corresponding node is marked as an interface node; and forming a system regional partitioning structure based on the interface node set to obtain the system partitioning structure of the low-frequency system region, the power frequency system region, and the interface region.

[0008] As a preferred embodiment of the low-frequency power frequency system coupling stability modeling method described in this invention, the establishment of a unified port variable set includes: setting up a port voltage measurement unit and a port current measurement unit at each interface node; calculating the port power exchange relationship by collecting port voltage and port current information; establishing a unified power direction convention based on the system power flow direction, defining the direction as positive power when power is transmitted from the low-frequency system to the power frequency system, and defining the direction as negative power when power is transmitted from the power frequency system to the low-frequency system; and uniformly organizing the voltage variables, current variables, and power variables of each interface node into a port variable set, and using the port variable set as a unified input / output interface.

[0009] As a preferred embodiment of the low-frequency power frequency system coupling stability modeling method described in this invention, the construction of the multi-frequency reference coupled small disturbance model includes: forming a low-frequency system state equation based on the low-frequency reference frequency by describing the dynamic relationship between low-frequency network voltage, current, and control state; forming a power frequency system state equation based on the power frequency reference frequency by describing the dynamic relationship between power frequency grid operating state variables; establishing a frequency converter control model in the low-frequency-power frequency interface subsystem, describing the dynamic coupling relationship between frequency systems by constructing a proportional mapping relationship between the low-frequency side phase change and the power frequency side phase change, and embedding the frequency mapping relationship into the interface subsystem dynamic model to form a unified coupled state space model that uniformly describes the coupling dynamic characteristics of the low-frequency system, power frequency system, and interface system.

[0010] As a preferred embodiment of the low-frequency power frequency system coupling stability modeling method described in this invention, the construction of an energy-consistent impedance mapping model includes: converting port voltage variables and port current variables into power conjugate variables characterizing power exchange relationships; performing frequency domain transformation on the system according to the unified coupled state space model to obtain the frequency domain relationship between port voltage and port current, and establishing the port impedance matrix of the system; judging energy consistency by comparing the port power increment change relationship before and after model mapping, calculating the port power change before and after mapping respectively, and judging the energy error by the difference between the port power change before and after mapping; when the energy error is less than a preset threshold, the model is determined to meet the energy consistency condition; when the energy error exceeds the threshold, the impedance model is reconstructed by adjusting the variable mapping relationship until the energy consistency constraint condition is met.

[0011] As a preferred embodiment of the low-frequency power frequency system coupling stability modeling method described in this invention, the passive detection of the impedance mapping model includes: performing frequency scanning analysis on the impedance matrix, calculating the energy dissipation characteristics of the impedance matrix at multiple frequency points, and determining whether the system meets the passive condition by analyzing the response of the impedance matrix to input power disturbances. When the system exhibits energy gain at any frequency point, it is determined to be a passive failure, and the frequency point exhibiting energy gain and the corresponding port channel are marked as a control intervention candidate set. After detecting passive failure, the corresponding frequency range and port channel position are identified by matrix eigenvalue analysis, and the corresponding degree of failure is recorded. Based on the degree of failure, each port channel is sorted and priority adjustment channels are selected. When the degree of failure exceeds a set threshold, a passive repair process is triggered.

[0012] As a preferred embodiment of the low-frequency power frequency system coupling stability modeling method described in this invention, the following steps are included: The local energy shaping and repair process involves introducing an equivalent virtual damping structure into the identified passively damaged channels, calculating virtual damping parameters based on the degree of damage to the corresponding channels, mapping the virtual damping parameters to the impedance correction amount of the corresponding ports, and correcting the impedance matrix by adding dissipation channels to the impedance model of the corresponding ports. After completing the virtual damping injection, the passivity index of the impedance matrix is ​​recalculated. Repair is considered complete when the passivity condition is met across all frequency ranges; otherwise, the virtual damping parameters are readjusted and the impedance matrix is ​​iteratively updated based on the remaining frequency points that do not meet the passivity condition. The repaired impedance model is then substituted back into the original coupling model framework, and model consistency is judged by comparing the changes in system oscillation modes. The mode change results are used as constraints for updating the virtual damping parameters in the next round of parameter calculation. Model consistency is confirmed when the changes in the key oscillation modes of the system before and after repair are within the allowable range; otherwise, the virtual damping parameters are adjusted until the consistency condition is met.

[0013] Another objective of this invention is to provide a coupling stability modeling system for low-frequency power frequency systems.

[0014] As a preferred embodiment of the low-frequency power frequency system coupling stability modeling system described in this invention, it includes: a partitioning module, a frequency analysis module, and a detection module; the partitioning module is used to partition the power grid to be analyzed and establish a unified set of port variables, defining the unified set of port variables at the interface location; the frequency analysis module is used to construct a multi-frequency reference coupled small disturbance model based on the unified set of port variables, by establishing a low-frequency reference dynamic model and a power frequency reference dynamic model respectively, and establishing frequency transformation and control coupling relationships in the interface subsystem to form a unified coupled state space model, and constructing an energy-consistent impedance mapping model based on the port power conjugate variables; the detection module is used to passively detect the impedance mapping model and perform passive repair processing, by identifying passively damaged channels by judging the positive and real nature of the impedance matrix and performing local energy shaping repair to obtain an impedance model that satisfies passive constraints, and substituting the repaired impedance model back into the phasor domain and state space model for cross-model consistency verification.

[0015] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement a method for modeling the coupling stability of a low-frequency power frequency system.

[0016] A computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of a method for modeling the coupling stability of a low-frequency power frequency system.

[0017] The beneficial effects of this invention are as follows: The low-frequency power frequency system coupling stability modeling method provided by this invention achieves a clear expression of the energy exchange boundary between the low-frequency system and the power frequency system through system partitioning and interface node identification, and establishes a unified set of port variables at the interface location. This gives the voltage, current, and power variables between different frequency subsystems a unified physical meaning. By constructing a multi-frequency coupled small-disturbance model of the low-frequency system, the power frequency system, and the interface control system, and introducing a frequency mapping relationship to establish a unified state-space model, while using port power conjugate variables to construct an energy-consistent impedance mapping model, a unified expression between the state-space model and the impedance model is achieved, thereby ensuring that the power expression and dynamic characteristics of different analysis models remain consistent. By performing frequency scanning and passivity detection on the impedance model, and using a local energy shaping method with virtual damping injection to repair non-passive channels, combined with a modal change consistency verification mechanism, it is ensured that the repaired impedance model satisfies the passivity constraints without destroying the original system dynamic characteristics. Attached Figure Description

[0018] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 The above is an overall flowchart of a low-frequency power frequency system coupling stability modeling method provided in Embodiment 1 of the present invention.

[0020] Figure 2 Impedance mapping diagram for a low-frequency power frequency system coupling stability modeling method provided in Embodiment 1 of the present invention. Detailed Implementation

[0021] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0022] Example 1, referring to Figures 1-2 As an embodiment of the present invention, a method for modeling the coupling stability of a low-frequency power frequency system is provided, comprising: S1: Divide the power grid to be analyzed into a system and establish a unified set of port variables. Define the unified set of port variables at the interface location.

[0023] Furthermore, the system partitioning includes acquiring power grid topology data and equipment parameter data, and classifying power grid equipment according to the rated operating frequency, control method, and electrical connection relationship. Transmission lines, cables, collection networks, and related compensation equipment with rated operating frequencies lower than the power frequency are classified as low-frequency AC subsystems; the main grid system, synchronous generators, loads, and grid-connected power electronic equipment with rated operating frequencies at the power frequency are classified as power frequency AC subsystems; and frequency converters, interface transformers, and corresponding control systems connecting the low-frequency system and the power frequency system are classified as low-frequency-power frequency interface subsystems. The system topology is constructed based on the network node connection relationship, and cross-frequency connection nodes are identified by traversing the node connection relationship. When a node is detected to be simultaneously connected to low-frequency system equipment and power frequency system equipment, the corresponding node is marked as an interface node. The system's regional partitioning structure is formed based on the interface node set, resulting in a system partitioning structure of low-frequency system region, power frequency system region, and interface region.

[0024] It should also be noted that a preferred scheme for system partitioning of the power grid to be analyzed specifically includes first obtaining the basic system data of the power grid to be analyzed, and then organizing the basic data into the following system data set: , in, This represents the total set of input data for the power grid to be analyzed. Let represent the set of system nodes, and any node in the set be denoted as . subscript For node index, the value range is: , Indicates the total number of system nodes; Let represent the set of system branches, and any branch in the set be denoted as . subscript This is a branch index, with a value range of [value range missing]. , Indicates the total number of branches in the system; Let represent the set of system devices, and let any device in the set be denoted as . subscript For device index, the value range is: , This represents the total number of devices in the system. For any given device... Furthermore, its core attributes related to this invention are extracted and represented as follows: , in, Indicates equipment The set of attributes, This indicates the rated operating frequency of the equipment. This indicates the control method of the device. This indicates the node number to which the device is connected. The device attributes are limited to rated operating frequency, control method, and connection node because the system partitioning in this invention needs to distinguish between low-frequency and power-frequency devices, and also identify interface devices that perform cross-frequency coupling functions. Therefore, frequency attributes, electrical connection attributes, and control attributes must all be included in a unified processing procedure. After obtaining the set of device attributes, in order to partition the system into a low-frequency AC subsystem, a power-frequency AC subsystem, and a low-frequency-power-frequency interface subsystem, a unified power-frequency reference standard needs to be provided first. Let the system power-frequency reference frequency be... , representing the standard power grid frequency. Based on this, a device frequency classification function is constructed: , in, Indicates equipment The system type identifier, This represents a classification mapping function that takes the equipment's rated operating frequency as input. Specifically, when the equipment's rated operating frequency... satisfy At that time, the device was identified as a low-frequency system device, and ordered... .

[0025] When the rated operating frequency of the equipment meets At that time, the device was identified as a power frequency system device, and ordered .

[0026] When a device simultaneously serves as a connection and conversion device between low-frequency and power-frequency systems, meaning it constitutes part of a cross-frequency energy exchange link, the device is classified as an interface device, and... .

[0027] Based on the above classification rules, we can further obtain three sets of devices, represented as follows: , , , in, This represents a collection of low-frequency AC subsystem devices. This represents the collection of equipment in the power frequency AC subsystem. This represents the set of low-frequency to power frequency interface devices. The purpose of this approach is to first establish a preliminary distinction of system functional roles at the device level, creating conditions for subsequent identification of cross-frequency connection boundaries at the node level. In other words, while it's known which devices belong to low-frequency, power frequency, and interface categories, it's not yet determined which specific nodes are located at the boundary between the two systems; therefore, further topology-level identification is required. After device classification, based on the system node set... and branch road collection Construct the topological connections of the power grid. To this end, the system adjacency matrix is ​​defined as follows: , in, Represents the adjacency matrix of the power grid topology. Represents a node With nodes The connection status between nodes. When nodes With nodes When there is an electrical connection, let .

[0028] When node With nodes When there is no electrical connection between them, let .

[0029] The dimension of the adjacency matrix is Therefore, it can completely reflect whether any two nodes in the system are directly connected. Based on this adjacency matrix, the set of adjacent nodes for each node can be further obtained, represented as: , in, Represents a node The set of adjacent nodes, the elements in the set For nodes There are nodes with direct electrical connections. Using this topological representation, the access status of devices at different frequencies can be determined at the node level, rather than simply at the device classification level.

[0030] To identify the actual coupling points between the low-frequency system and the power frequency system, this embodiment further defines a set of frequency attributes for each node, represented as follows: , in, Indicates a connection at the node The complete set of device type identifiers on the device. For the aforementioned equipment type identifier, Indicates equipment Access Node The practical significance of this definition lies in the fact that by grouping the device types connected to the same node, it's possible to determine whether the node simultaneously supports both low-frequency and power-frequency devices, thereby identifying whether it belongs to the low-frequency-power-frequency connection boundary. A node is identified as an interface node when it meets the following conditions: and and ;in, Represents a node The number of elements in the device type set, condition This indicates that the node has connected to at least two different types of devices, and and This indicates that the node is connected to both low-frequency system equipment and power frequency system equipment. The set of nodes satisfying the above conditions is defined as: , in, This represents the set of low-frequency to power frequency interface nodes. Through this step, the nodes that actually perform cross-frequency connection functions in the system are clearly identified, and these nodes will directly serve as the locations for establishing subsequent unified port variables. After identifying the interface node set, it is necessary to further complete the system region division so that subsequent model construction can clearly identify which nodes belong to the low-frequency system, which nodes belong to the power frequency system, and which nodes belong to the interface region. Therefore, the low-frequency system node set and the power frequency system node set are defined as follows: , , in, This represents a set of nodes that connect only to low-frequency devices. This represents the set of nodes that connect only to power frequency equipment, while the aforementioned This represents the set of interface nodes that simultaneously connect low-frequency and power-frequency equipment. At this point, the entire power grid is divided into three parts: the low-frequency system region, the power-frequency system region, and the low-frequency-power-frequency interface region. This division is not simply a matter of region naming, but rather a way to ensure that subsequent establishment of a multi-frequency coupled state-space model can be directly based on... , and To determine the state boundaries and coupling boundaries of different subsystems.

[0031] It should be noted that establishing a unified set of port variables includes setting up port voltage measurement units and port current measurement units at each interface node, calculating port power exchange relationships by collecting port voltage and port current information; establishing a unified power direction convention based on the system power flow direction, defining positive power direction when power is transmitted from the low-frequency system to the power frequency system, and negative power direction when power is transmitted from the power frequency system to the low-frequency system; and organizing the voltage, current, and power variables of each interface node into a unified set of port variables, using the set of port variables as a unified input / output interface.

[0032] It should also be noted that a preferred approach to defining a unified set of port variables at the interface location specifically includes, in this embodiment, establishing a unified set of port variables at each interface node after completing interface node identification. The rationale behind this design is that regardless of whether a phasor domain model, state-space model, or impedance model is subsequently used, all cross-frequency interactions ultimately return to the voltage, current, and power relationships at the interface; therefore, a unified variable representation must first be established at the interface node. For any interface node… Define the port variable set as follows: , in, Represents a node The set of local port variables at that location. This represents the port voltage variable of the node. This represents the port current variable of the node. This represents the port power variable of the node. and All data originates from measurement or simulation sampling data at the interface nodes. The power relationship between the voltage and current at the interface is calculated and expressed as follows: , in, Indicates interface node Instantaneous power exchange quantity, This indicates the voltage amplitude at the node port. This represents the amplitude of the port current at the node. The voltage and current at the interface are uniformly mapped to power exchange quantities, thus providing a unified physical measure for the interaction between the low-frequency system and the power-frequency system. It should be noted that power magnitude alone is insufficient to support subsequent unified modeling, as the symbolic definition of power flow direction may differ across models. Therefore, after establishing the port power variables, a unified power direction convention needs to be further defined. For this purpose, a power direction function is defined: , in, Indicates interface node Power direction indicator, This represents the direction determination function with the port power exchange state as input. When power flows from the low-frequency system to the power-frequency system, the following is taken: .

[0033] When power flows from the mains frequency system to the low frequency system, take .

[0034] Based on this, the port power under the unified direction convention is defined as: , in, This represents the interface power variable with a uniform sign and direction. (This is achieved by introducing...) This ensures that different models maintain a consistent definition of the positive and negative power values ​​for the same interface, avoiding additional errors caused by inconsistent power directions during model mapping and consistency checks. Finally, all port variables established at all interface nodes are organized into a unified system-level port variable set. , in, This represents the unified set of port variables for the entire low-frequency to power-frequency coupled system, which includes the port voltage variables at all interface nodes. Port current variables and port power variables under a unified direction agreement The purpose of this set of variables is to serve as a unified input interface, providing boundary variables for establishing small disturbance models of low-frequency and power-frequency subsystems, and also providing basic variables for the port power conjugate relationship in subsequent impedance mapping.

[0035] It should also be noted that by dividing the power grid under analysis into a system and establishing a unified set of port variables, structured identification and unified modeling boundary definition of the low-frequency system, the power frequency system, and the low-frequency-power frequency interface system are achieved. Specifically, by acquiring power grid topology data and equipment parameter data, and classifying system equipment based on equipment rated operating frequency, control method, and electrical connection relationship, the entire power grid can be divided into a low-frequency AC subsystem, a power frequency AC subsystem, and a low-frequency-power frequency interface subsystem. Furthermore, by analyzing the node adjacency matrix, interface nodes that simultaneously connect equipment of different frequencies are identified, thereby clarifying the location where energy exchange actually occurs between the low-frequency system and the power frequency system. Subsequently, a unified set of port variables is established at the interface nodes, and a unified interface variable representation is constructed through port voltage, port current, and port power variables. At the same time, a unified power direction convention is introduced to ensure that the positive and negative definitions of port power remain consistent in different models. On the one hand, it can accurately identify cross-frequency coupling boundaries at the system topology level, giving the coupling relationship between low-frequency systems and power frequency systems a clear structural expression; on the other hand, it establishes a unified input and output interface through a unified set of port variables, providing a unified physical variable basis for the subsequent construction of multi-frequency coupled dynamic models and impedance model mapping, thereby avoiding additional errors caused by inconsistent variable definitions between different modeling methods, and ultimately improving the physical consistency and model scalability in the modeling process of low-frequency-power frequency coupled systems.

[0036] S2: Construct a multi-frequency reference coupled small disturbance model based on a unified set of port variables. By establishing a low-frequency reference dynamic model and a power frequency reference dynamic model respectively, and establishing frequency transformation and control coupling relationship in the interface subsystem, a unified coupled state space model is formed, and an energy-consistent impedance mapping model is constructed based on the port power conjugate variables.

[0037] Furthermore, the construction of a multi-frequency reference coupled small-disturbance model includes: forming a low-frequency system state equation based on a low-frequency reference frequency by describing the dynamic relationship between low-frequency network voltage, current, and control state; forming a power frequency system state equation based on a power frequency reference frequency by describing the dynamic relationship between power frequency grid operating state variables; establishing a frequency converter control model in the low-frequency-power frequency interface subsystem, describing the dynamic coupling relationship between frequency systems by constructing a proportional mapping relationship between the phase change on the low-frequency side and the phase change on the power frequency side, and embedding the frequency mapping relationship into the dynamic model of the interface subsystem to form a unified coupled state space model that uniformly describes the coupled dynamic characteristics of the low-frequency system, the power frequency system, and the interface system.

[0038] It should also be noted that a preferred scheme for constructing a multi-frequency reference coupled small perturbation model based on a unified set of port variables specifically includes, firstly, targeting the obtained low-frequency system node set... Establish a dynamic model of the low-frequency system. Assume the operating reference frequency of the low-frequency system is . This represents the angular frequency reference of the low-frequency system, and its value is equal to the operating frequency of the low-frequency system multiplied by . .

[0039] To describe the dynamic behavior of low-frequency systems under small disturbance conditions, a state variable vector for the low-frequency system is introduced. This indicates that the low-frequency system is at time... The state variable vector contains low-frequency system node voltages, currents, and control state variables.

[0040] The input variables of a low-frequency system are defined as follows: This represents the input variables of a low-frequency system, which mainly consist of interface node voltage variables. and current variables composition.

[0041] Under small disturbance conditions, the dynamic relationship of a low-frequency system can be expressed as the following linear state equation: , in, Represents the state variable with respect to time The derivative of Represents the state matrix of a low-frequency system. This represents the input coupling matrix. The state equation reflects the dynamic coupling relationship between the voltage, current, and control variables of the low-frequency network. Meanwhile, the output variables of the low-frequency system are defined as: , in This represents the output variable of the low-frequency system. This represents the output matrix.

[0042] After completing the low-frequency system modeling, it is necessary to address the resulting power frequency system node set. Establish a dynamic model of the power frequency system. Assume the reference angular frequency of the power frequency system is ω. This represents the operating angular frequency of the power frequency system, and its value is equal to the rated frequency of the power frequency system multiplied by 0. .

[0043] Similarly, a state variable vector for the power frequency system is introduced. , representing the state variable vector of the power frequency system, which includes the voltage and current of the power frequency grid nodes and the control states of electromechanical or power electronic equipment. The input variables of the power frequency system are represented as... This represents the input variables of the power frequency system, which mainly originate from the port variables at the interface nodes. and Dynamic behavior of power frequency system under small disturbance conditions It can be represented as: , in Represents the state matrix of the power frequency system. This represents the input coupling matrix. The output variables of the power frequency system are represented as: , in This represents the output matrix and output variables. Used to describe the dynamic response of a power frequency system at the interface node.

[0044] Since the low-frequency system and the power frequency system operate at different frequencies, a frequency mapping relationship must be established through the interface subsystem to achieve dynamic coupling between the two systems.

[0045] Let the phase variable of the low-frequency system be... Let the phase variable of the power frequency system be... Since the two systems have different frequencies, their phase change rates satisfy the following relationship: , , in, This represents the phase change rate of a low-frequency system. This represents the phase change rate of a power frequency system. To describe the phase correspondence between two frequency systems, a frequency mapping coefficient is introduced: , in This represents the frequency ratio coefficient from the low-frequency system to the power frequency system.

[0046] This yields the interface phase mapping relationship: , This mapping relationship describes the equivalent effect of low-frequency side phase changes on power-frequency side phase changes. In the interface control system, this frequency mapping relationship is embedded into the interface state equation to obtain the interface dynamic model: , in, Represents the state variables of the interface subsystem Regarding time The first derivative, which is the rate of change of the interface system state. Represents the state variables of the interface subsystem. Indicates the interface input variables, matrix and These represent the interface system state matrix and input matrix, respectively.

[0047] After completing the low-frequency system model, the power frequency system model, and the interface model, the unified coupled state-space model combines the three subsystems into a unified coupled model. The overall system state variables are defined as follows: , Define system input variables: , The entire low-frequency-power-frequency coupled system can then be represented as a unified state-space model: , in, This indicates the rate at which the state variables of the interface subsystem change over time. The system coupling state matrix, The input matrix is ​​used for the system. This unified model can simultaneously describe the dynamic coupling behavior between low-frequency systems, power frequency systems, and interface control systems.

[0048] It should be noted that constructing an energy-consistent impedance mapping model includes: converting port voltage and port current variables into power conjugate variables that characterize the power exchange relationship; performing a frequency domain transformation on the system based on the unified coupled state-space model to obtain the frequency domain relationship between port voltage and port current, and establishing the system's port impedance matrix; judging energy consistency by comparing the port power increment changes before and after model mapping, calculating the port power changes before and after mapping respectively, and judging the energy error by the difference between the port power changes before and after mapping. When the energy error is less than a preset threshold, the model is determined to meet the energy consistency condition. When the energy error exceeds the threshold, the impedance model is reconstructed by adjusting the variable mapping relationship until the energy consistency constraint condition is met.

[0049] It should also be noted that the reference Figure 2 A preferred scheme for constructing an energy-consistent impedance mapping model based on port power conjugate variables specifically includes, after obtaining the unified state-space model, establishing an impedance model. Since the impedance model needs to maintain consistency in power expression, the port variables are first converted into power conjugate variables. Let the interface node port voltage vector... for: , in, Indicates the first Port voltage variables of each interface node This indicates a transpose operation, setting the port current vector. for: , in, Indicates the first Port current variables of each interface node This indicates the number of interface nodes. Port power can be expressed as: , in This represents the total power exchange at the interface. This variable conversion ensures that the relationship between voltage and current directly reflects power changes.

[0050] Based on the unified state-space model, a frequency domain transformation is performed on the system. Let the complex frequency domain variables be... Applying the Laplace transform to the state equation yields: , in This represents the frequency domain representation of state variables. This represents the frequency domain expression of the input variables. The voltage-current relationship can be obtained from the output equation: , in Represents the system port impedance matrix. This represents the port current vector of the interface node in the frequency domain (complex frequency domain). The representation in ).

[0051] To ensure a consistent power expression between the impedance model and the original state-space model, an energy consistency check is required during the mapping process. Let the change in port power before mapping be... Let the port power change calculated by the impedance model be... The energy error is defined as: , in This indicates power mapping error. The allowable error threshold is set to... ;when When the impedance model is satisfied, the energy uniformity condition is determined.

[0052] when At that time, the impedance model is recalculated by adjusting the mapping relationship of the power conjugate variables until the energy consistency condition is met.

[0053] It should also be noted that by constructing a multi-frequency reference coupled small-disturbance model based on a unified set of port variables, and establishing dynamic models for low-frequency systems, power-frequency systems, and interface coupling models respectively, the dynamic behavior description of power systems at different frequencies under a unified mathematical framework is realized. By establishing state equations for the low-frequency system and the power-frequency system respectively, the dynamic coupling relationship between system node voltages, currents, and control state variables can be characterized under their respective operating frequency references. Simultaneously, a frequency mapping relationship is introduced into the low-frequency-power-frequency interface subsystem. By constructing a proportional mapping coefficient between the low-frequency phase change and the power-frequency phase change, the phase dynamic relationship between the two different frequency systems can be expressed in the unified model, thus forming a unified coupled state-space model including the low-frequency subsystem, the power-frequency subsystem, and the interface control system. Based on this, by converting port voltage and current variables into power conjugate variables, and using the unified state-space model for frequency domain transformation to establish the system port impedance matrix, and by comparing the port power changes before and after model mapping to determine energy consistency, it can be ensured that the impedance model maintains a power expression relationship consistent with the original state-space model during the mathematical transformation process. On the one hand, it realizes a unified mapping between the dynamic model and the impedance model of the multi-frequency system, enabling different analysis methods to perform stability analysis on the same physical basis; on the other hand, it avoids the power expression distortion problem that may occur in the traditional impedance modeling process through the energy consistency judgment mechanism, thereby improving the consistency and reliability of the stability analysis results of the low-frequency-power frequency coupled system.

[0054] S3: Passive detection and passive repair processing are performed on the impedance mapping model. By judging the positive and real nature of the impedance matrix, passive destruction channels are identified and local energy shaping and repair are performed to obtain an impedance model that meets the passive constraints. The repaired impedance model is then substituted back into the phasor domain and state space model for cross-model consistency verification.

[0055] Furthermore, the passive detection of the impedance mapping model includes performing frequency scanning analysis on the impedance matrix, calculating the energy dissipation characteristics of the impedance matrix at multiple frequency points, and determining whether the system meets the passive condition by analyzing the response of the impedance matrix to input power disturbances. When the system exhibits energy gain at any frequency point, it is determined to be a passive failure, and the frequency point with energy gain and the corresponding port channel are marked as a candidate set for control intervention. After detecting passive failure, the corresponding frequency range and port channel position are identified by matrix eigenvalue analysis, and the corresponding degree of failure is recorded. Based on the degree of failure, each port channel is sorted and the priority adjustment channel is selected. When the degree of failure exceeds a set threshold, the passive repair process is triggered.

[0056] It should also be noted that a preferred scheme for passive detection using the impedance mapping model specifically includes, in order to detect the energy characteristics of the impedance matrix at different frequencies, first analyzing the system port impedance matrix. Perform a frequency scan. Let the set of scan frequencies be: , in Represents the frequency scan set, Indicates the first Each scanning frequency point, This represents the number of scanned frequency points. For each frequency point, the complex frequency domain variable is set as: , Thus, the impedance matrix at the corresponding frequency is obtained. ,in This represents the imaginary unit. To evaluate the energy dissipation characteristics of the system at this frequency, it is necessary to construct the energy criterion matrix of the impedance matrix: , in The symmetric energy matrix representing the impedance matrix, denoted by [symbol]. This represents the conjugate transpose of a matrix. This matrix is ​​used to characterize the system at certain frequencies. Energy exchange characteristics under [condition].

[0057] If matrix If the matrix is ​​positive definite, it indicates that the system exhibits energy dissipation characteristics at that frequency; if negative eigenvalues ​​exist, it indicates that the system may generate energy gain at that frequency. To identify the channels generating energy gain, the matrix needs to be analyzed. Perform eigenvalue analysis: , in Representation matrix The 1 eigenvalue, For eigenvalue indices. The number of eigenvalues ​​equals the dimension of the impedance matrix. When there exists When, it indicates that the system is at a certain frequency. Passive damage exists. To quantify the degree of passive damage, a damage index is introduced: , in Indicates frequency The passive damage intensity corresponding to the characteristic direction. The larger this value, the stronger the energy gain of the system.

[0058] Furthermore, for the same port channel The maximum damage index at the port level is obtained by summing the damage intensity at all frequency points. , is represented as: , in, Indicates port The corresponding virtual damping coefficient, and based on Sort all port channels and select those that meet the requirements. The ports constitute a priority adjustment channel set .

[0059] Set a passive judgment threshold When satisfied When the corresponding frequency point and characteristic direction are found to be severely passively damaged, the corresponding frequency range and port channel number are recorded.

[0060] It should be noted that the local energy shaping and repair process includes: introducing an equivalent virtual damping structure into the identified passive damage channels; calculating virtual damping parameters based on the degree of damage to the corresponding channels; mapping the virtual damping parameters to the impedance correction amount of the corresponding ports; and correcting the impedance matrix by adding dissipation channels to the impedance model of the corresponding ports. After completing the virtual damping injection, the passivity index of the impedance matrix is ​​recalculated. The repair is considered complete when the passivity condition is met in all frequency ranges; otherwise, the virtual damping parameters are readjusted and the impedance matrix is ​​iteratively updated based on the remaining frequency points that do not meet the passivity condition. The repaired impedance model is then substituted back into the original coupled model framework, and the model consistency is judged by comparing the changes in the system's oscillation modes. The results of the mode changes are used as constraints for updating the virtual damping parameters in the next round of parameter calculation. When the changes in the key oscillation modes of the system before and after the repair are within the allowable range, the model consistency is confirmed; otherwise, the virtual damping parameters are adjusted until the consistency condition is met.

[0061] It should also be noted that a preferred scheme for substituting the repaired impedance model back into the phasor domain and state space model for cross-model consistency verification specifically includes performing local energy shaping and repair on the impedance model when a passively damaged channel is detected. This embodiment achieves energy repair by introducing an equivalent virtual damping structure in the corresponding port channel.

[0062] Let the virtual damping matrix be , This is a diagonal matrix, where the diagonal elements represent the equivalent damping parameters at each port. The modified impedance model is obtained by superimposing this damping matrix onto the original impedance matrix. , in This represents the corrected system impedance matrix. Each diagonal element of the virtual damping matrix is ​​adjusted according to the passive failure intensity at the corresponding frequency point, specifically: , in This is the proportional adjustment coefficient. This method allows for the introduction of additional dissipation in port channels with high energy gain, thereby reducing the system energy gain. After introducing virtual damping, the energy determination matrix of the impedance matrix needs to be recalculated: , in, Let represent the symmetric energy matrix of the updated impedance matrix, and then recalculate the updated eigenvalues. : , If satisfied If the condition is met at that frequency, it indicates that the system has satisfied the passivity condition at that frequency point. When all frequency points satisfy the above condition, the passive repair of the impedance model is considered complete.

[0063] When it still exists At that time, for the corresponding port The virtual damping parameters are iteratively updated: , in, Indicates the first After the next iteration update, the port The corresponding virtual damping parameter values, Indicates the first After the next iteration update, the port The corresponding virtual damping parameter values, Indicates the port in the current iteration The remaining passive damage intensity.

[0064] To ensure that the impedance repair process does not disrupt the original dynamic characteristics of the system, the repaired impedance model needs to be substituted back into the unified state-space model of step S2 for consistency verification. Let the system modal eigenvalues ​​be... , indicating the system's first Eigenvalues ​​of each oscillation mode. Modal changes before and after repair. Defined as: , in This represents the modal eigenvalues ​​of the system before repair. This represents the modal characteristic values ​​of the system after repair. Set the allowable error threshold. When satisfied At that time, it is determined that the repaired impedance model is consistent with the dynamic characteristics of the original system. If there is... Then the modal variation Used as a feedback constraint to correct port damping parameters The impedance repair and passivity testing process described above is repeated until both the passivity constraint and modal consistency constraint are simultaneously satisfied. This yields a modified impedance model that satisfies the passivity constraint. This model ensures that the system port impedance meets the energy dissipation condition and maintains the same dynamic characteristics as the original state-space model, thus providing a reliable model basis for the stability analysis and control strategy design of low-frequency-power-frequency coupled systems.

[0065] It should also be noted that by passively detecting and performing passive repair on the impedance mapping model, the stability characteristics of the impedance model are corrected while maintaining the model's energy consistency. By performing frequency scanning analysis on the system port impedance matrix and calculating the energy determination matrix of the impedance matrix at multiple frequency points, the energy dissipation characteristics of the system in different frequency ranges can be determined. When negative eigenvalues ​​are detected at certain frequency points, the port channels generating energy gain and their corresponding frequency intervals can be identified, thus accurately locating the passive impedance failure point. After identifying the passive failure channel, an equivalent virtual damping structure is introduced into the corresponding port channel, and a virtual damping matrix is ​​constructed to perform local energy shaping and repair on the original impedance matrix, enabling the system port impedance to once again satisfy the passive constraint conditions. Furthermore, by substituting the repaired impedance model back into the original unified state-space model and performing consistency verification through the system oscillation mode changes, it can be ensured that the passive repair process does not damage the original dynamic characteristics of the system. It can not only solve the non-passive problem that may occur in the traditional impedance modeling process, but also maintain the authenticity of the model's dynamic characteristics while ensuring the effectiveness of the system stability criterion, thus providing a reliable model basis for the stability analysis, control strategy design and stability control system parameter optimization of low-frequency-power frequency coupled systems.

[0066] Example 2, an embodiment of the present invention, provides a low-frequency power frequency system coupling stability modeling system, including a partitioning module, a frequency analysis module, and a detection module.

[0067] The partitioning module is used to partition the power grid to be analyzed and establish a unified set of port variables, defining the unified set of port variables at the interface location. The frequency analysis module is used to construct a multi-frequency reference coupled small disturbance model based on the unified set of port variables. By establishing a low-frequency reference dynamic model and a power frequency reference dynamic model respectively, and establishing frequency transformation and control coupling relationships in the interface subsystem, a unified coupled state space model is formed, and an energy-consistent impedance mapping model is constructed based on the port power conjugate variables. The detection module is used to perform passive detection and passive repair processing on the impedance mapping model. By judging the positive and real nature of the impedance matrix, passive damage channels are identified and local energy shaping repair is performed to obtain an impedance model that meets the passive constraints. The repaired impedance model is then substituted back into the phasor domain and state space model for cross-model consistency verification.

Claims

1. A method for modeling the coupling stability of a low-frequency power frequency system, characterized in that, include: The power grid to be analyzed is divided into a system and a unified set of port variables is established. The unified set of port variables is defined at the interface location. A multi-frequency reference coupled small disturbance model is constructed based on a unified set of port variables. By establishing a low-frequency reference dynamic model and a power frequency reference dynamic model respectively, and establishing frequency transformation and control coupling relationship in the interface subsystem, a unified coupled state space model is formed, and an energy-consistent impedance mapping model is constructed based on the port power conjugate variables. The impedance mapping model is subjected to passive detection and passive repair. By judging the positive and real nature of the impedance matrix, passively damaged channels are identified and local energy shaping and repair are performed to obtain an impedance model that meets the passive constraints. The repaired impedance model is then substituted back into the phasor domain and the state space model for cross-model consistency verification.

2. The low-frequency power frequency system coupling stability modeling method as described in claim 1, characterized in that: The system partitioning includes, Acquire power grid topology data and equipment parameter data, and classify power grid equipment according to the rated operating frequency, control method, and electrical connection relationship; Transmission lines, cables, collection networks and related compensation equipment with rated operating frequencies lower than the power frequency are classified as low-frequency AC subsystems. Main grid systems, synchronous generators, loads and grid-connected power electronic equipment with rated operating frequencies of the power frequency are classified as power frequency AC subsystems. Variable frequency converters, interface transformers and corresponding control systems that connect the low-frequency system and the power frequency system are classified as low-frequency-power frequency interface subsystems. The system topology is constructed based on the network node connection relationship, and cross-frequency connection nodes are identified by traversing the node connection relationship. When a node is detected to be connected to both low-frequency system equipment and power frequency system equipment, the corresponding node is marked as an interface node. Based on the set of interface nodes, a regional division structure of the system is formed, resulting in a system partition structure of low-frequency system region, power frequency system region, and interface region.

3. The low-frequency power frequency system coupling stability modeling method as described in claim 2, characterized in that: The establishment of a unified port variable set includes, A port voltage measurement unit and a port current measurement unit are set at each interface node. The port power exchange relationship is calculated by collecting port voltage and port current information. A unified power direction convention is established based on the system power flow direction. When power is transmitted from the low-frequency system to the power frequency system, it is defined as positive power direction, and when power is transmitted from the power frequency system to the low-frequency system, it is defined as negative power direction. The voltage, current, and power variables of each interface node are organized into a unified port variable set, which is then used as a unified input / output interface.

4. The low-frequency power frequency system coupling stability modeling method as described in claim 3, characterized in that: The construction of the multi-frequency reference coupled small perturbation model includes, Based on a low-frequency reference frequency, the state equation of the low-frequency system is formed by describing the dynamic relationship between the low-frequency network voltage, current and control state. Based on the power frequency reference frequency, the power frequency system state equation is formed by describing the dynamic relationship between the power frequency power grid operation state variables. A frequency conversion control model is established in the low-frequency-power frequency interface subsystem. The dynamic coupling relationship between the frequency systems is described by constructing a proportional mapping relationship between the phase change on the low-frequency side and the phase change on the power frequency side. The frequency mapping relationship is then embedded into the dynamic model of the interface subsystem, forming a unified coupled state space model that describes the coupling dynamic characteristics of the low-frequency system, the power frequency system, and the interface system.

5. The low-frequency power frequency system coupling stability modeling method as described in claim 4, characterized in that: The construction of an energy-consistent impedance mapping model includes... The port voltage and port current variables are converted into power conjugate variables that characterize the power exchange relationship; The system is frequency-domain transformed according to the unified coupled state-space model to obtain the frequency-domain relationship between port voltage and port current, and the port impedance matrix of the system is established. Energy consistency is determined by comparing the changes in port power increments before and after model mapping. The changes in port power before and after mapping are calculated respectively, and the energy error is determined by the difference between the changes in port power before and after mapping. When the energy error is less than a preset threshold, the model is determined to meet the energy consistency condition. When the energy error exceeds the threshold, the impedance model is reconstructed by adjusting the variable mapping relationship until the energy consistency constraint condition is met.

6. The low-frequency power frequency system coupling stability modeling method as described in claim 5, characterized in that: The passive detection of the impedance mapping model includes, Frequency scanning analysis is performed on the impedance matrix to calculate the energy dissipation characteristics of the impedance matrix at multiple frequency points. The system is judged to meet the passive condition by analyzing the response of the impedance matrix to the input power disturbance. When the system exhibits energy gain at any frequency point, it is determined to be a passive failure. The frequency point where energy gain occurs and the corresponding port channel are marked as a candidate set for control intervention. After detecting passive damage, the corresponding frequency range and port channel location are identified by matrix eigenvalue analysis, and the corresponding degree of damage is recorded. Based on the degree of damage, each port channel is sorted and the channel to be adjusted first is selected. When the degree of damage exceeds the set threshold, the passive repair process is triggered.

7. The low-frequency power frequency system coupling stability modeling method as described in claim 6, characterized in that: The execution of local energy shaping and repair includes, An equivalent virtual damping structure is introduced into the identified passive damage channels, and the virtual damping parameters are calculated according to the degree of damage of the corresponding channels. The virtual damping parameters are mapped to the impedance correction amount of the corresponding port, and the impedance matrix is ​​corrected by adding dissipation channels in the impedance model of the corresponding port. After completing the virtual damping injection, the passivity index of the impedance matrix is ​​recalculated. When the passivity condition is met in all frequency ranges, the repair is considered complete. Otherwise, the virtual damping parameters are readjusted and the impedance matrix is ​​iteratively updated based on the remaining frequency points that do not meet the passivity condition. The repaired impedance model is substituted back into the original coupled model framework, and the consistency of the model is judged by comparing the changes in the system's oscillation modes. The results of the mode changes are used as constraints for updating the virtual damping parameters in the next round of parameter calculation. When the changes in the key oscillation modes of the system before and after the repair are within the allowable range, the model consistency is confirmed. Otherwise, the virtual damping parameters are adjusted until the consistency condition is met.

8. A low-frequency power frequency system coupling stability modeling system, employing the low-frequency power frequency system coupling stability modeling method as described in any one of claims 1 to 7, characterized in that: It includes a partitioning module, a frequency analysis module, and a detection module; The partitioning module is used to partition the power grid to be analyzed into a system and establish a unified set of port variables. The unified set of port variables is defined at the interface position. The frequency analysis module is used to construct a multi-frequency reference coupled small disturbance model based on a unified set of port variables. By establishing a low-frequency reference dynamic model and a power frequency reference dynamic model respectively, and establishing frequency transformation and control coupling relationship in the interface subsystem, a unified coupled state space model is formed, and an energy-consistent impedance mapping model is constructed based on the port power conjugate variables. The detection module is used to perform passive detection and passive repair processing on the impedance mapping model. By judging the positive and real nature of the impedance matrix, it identifies passively damaged channels and performs local energy shaping repair to obtain an impedance model that meets the passive constraints. The repaired impedance model is then substituted back into the phasor domain and state space model for cross-model consistency verification.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the low-frequency power frequency system coupling stability modeling method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the low-frequency power frequency system coupling stability modeling method according to any one of claims 1 to 7.

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