Frequency response modeling method for high-proportion new energy power system and application

Abstract

The application discloses a high-proportion new energy power system frequency response modeling method and application, and the method comprises the following steps: dividing all nodes in a power system into active nodes and passive nodes; establishing a linearized power flow model of the power system; reducing the linearized power flow model to obtain an equivalent active node power injection power expression; respectively establishing frequency-active response models of various power resources in the active nodes and the passive nodes; combining the equivalent active node power injection power expression with the frequency-active response models to construct a unified linearized state space model taking phase angles and frequencies of the active nodes as state variables; and calculating frequency responses of the power system based on the unified linearized state space model. The unified linearized state space model constructed by the method can realize more rapid and more accurate simulation and stability analysis of frequency dynamics of the high-proportion new energy power system, and is suitable for rapid simulation and online analysis of large-scale systems.

Description

Technical Field

[0001] This invention relates to the field of new energy power system technology, and in particular to a method and application for frequency response modeling of high-proportion new energy power systems. Background Technology

[0002] With the advancement of the decarbonization process of the power system, the integration ratio of renewable energy sources such as wind power, photovoltaics, and energy storage is continuously increasing. Most new energy power generation units are connected to the grid through power electronic inverters. Based on different control methods, inverters can generally be divided into two categories: grid-following (GFL) and grid-forming (GFM). Grid-following inverters track the grid frequency and voltage through phase-locked loops, exhibiting current source characteristics and primarily relying on the external grid for power injection. In contrast, grid-forming inverters use algorithms such as power-frequency droop control to form voltage source characteristics, enabling them to actively establish voltage and frequency references and achieve grid-forming capabilities similar to synchronous machines.

[0003] With the integration of high-proportion renewable energy sources, power system frequency response modeling and frequency stability analysis face new challenges. Traditional modeling methods are typically based on the oscillation equations of synchronous machines, describing the active power-frequency dynamic relationship through the rotational inertia characteristics of the generator rotor, the droop control characteristics of the speed regulation system, and the active power output characteristics. This method is simple in structure and clear in physical meaning, and has long been widely used in systems dominated by synchronous machines. However, as the proportion of inverter power sources increases, the system inertia decreases significantly, and the oscillation equations can hardly accurately characterize the frequency behavior under inverter control dynamics.

[0004] To capture the unique rapid dynamic response characteristics of inverters, researchers have proposed various inverter power supply frequency response models based on joint electrical-control modeling. Some studies accurately simulate the dynamic characteristics of GFLs and GFMs by establishing positive-sequence equivalent models or analytical controller frameworks for transient analysis and frequency support capability assessment. While these models can reflect the impact of control loops on system frequency, they are complex in structure, have numerous parameters, and incur a significant computational burden, making them unsuitable for rapid simulation or online analysis in large-scale systems. Between complex electromagnetic transient models and simplified average models, some studies have attempted to employ linearized oscillation equation models or system inertia optimization models in system planning and frequency scheduling scenarios, shaping the overall frequency trajectory by optimizing parameters such as the system's equivalent inertia and frequency droop coefficient. However, these models typically still assume a uniform frequency across the entire system and do not distinguish the differential impacts of GFLs and GFMs on local node frequencies.

[0005] In traditional unified frequency models, the system is equivalent to a single-node or "Centre of Inertia (COI)" model, assuming that all generators rotate synchronously and the system frequency is uniform. However, in high-proportion renewable energy power systems, the spatial distribution of inertia is uneven, and renewable energy power plants are usually located in remote areas far from load centers, resulting in significant differences in frequency response between different regions. The real-time frequency deviation, rate of change, and time of occurrence of the frequency minimum point are inconsistent at different nodes, and the global average frequency model can hardly reflect this spatial inconsistency.

[0006] Therefore, with the increasing penetration rate of new energy sources, the frequency response of power systems exhibits significant heterogeneity and regional differences. Existing modeling methods are insufficient in distinguishing the dynamic characteristics of different types of inverters and describing the frequency differences among multiple nodes. They cannot fully reflect the complex frequency dynamics caused by differences in control structure, topology location, and inertia distribution in actual systems, thus affecting the accuracy of system frequency stability analysis.

[0007] It should be noted that the information disclosed in the background section above is only for understanding the background of this application, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0008] The purpose of this invention is to solve the technical problems in the prior art that it is difficult to balance the accuracy and computational efficiency of power system frequency response models, and that it is impossible to effectively characterize the non-consistency of frequency response space. The invention proposes a frequency response modeling method and application for high-proportion new energy power systems.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] A method for modeling the frequency response of a high-proportion renewable energy power system includes the following steps:

[0011] S1: Divide all nodes in the power system into active nodes and passive nodes; active nodes are those whose frequency dynamics can be described by differential equations, including synchronous generator nodes and grid-connected inverter nodes; passive nodes are those whose frequency dynamics cannot be directly described by differential equations, including grid-connected inverter nodes, load nodes, and intermediate nodes; S2: Establish a linearized power flow model of the power system to obtain the phase angle vectors of active nodes. d A and passive node power injection vector P P Active node power flow injection power vector P A S3: Reduce the linearized power flow model and eliminate the passive node phase angle vector. dP This yields a phase angle vector containing only the active nodes. d A and passive node power injection vector P P S4: Establish the equivalent active node power flow injection power expression; S5: Combine the equivalent active node power flow injection power expression with the frequency-active response model to construct a unified linearized state space model with the active node phase angle and frequency as state variables; S6: Calculate the frequency response of the power system based on the unified linearized state space model.

[0012] In some embodiments, the linearized power flow model in step S2 is:

[0013]

[0014] Where L is the Laplace matrix of the system power flow, L AA L represents the power flow relationship between two active nodes. AP L represents the power flow relationship from passive nodes to active nodes. PA L represents the power flow relationship from the active node to the passive node. PP This indicates the power flow relationship between two passive nodes.

[0015] In some embodiments, the reduction in step S3 is a Kron reduction, and the equivalent active node power flow injection power expression after reduction is:

[0016]

[0017] in, , is the equivalent Laplace matrix; , where is the power distribution matrix.

[0018] In some embodiments, establishing the frequency-active power response model in step S4 includes: establishing the oscillation equation model of the synchronous generator node; establishing the droop control model of the grid-connected inverter node; establishing the phase-locked loop frequency measurement and damping control model of the grid-connected inverter node; and establishing the frequency response model of the load node.

[0019] In some embodiments, the unified linearized state-space model described in step S5 takes the form of:

[0020]

[0021] in, A sys This represents the system state matrix, which consists of the dynamic matrices of each power source and the Laplace matrix.X It is a vector of state variables, including the phase angle of the active node, the frequency of the active node, and the intermediate state variables of each power supply regulation system; B sys This indicates the channel through which the frequency control command input is applied. U This is the frequency control command vector; P d The disturbance power vector; y This is the output vector; C sys The output channel represents the state variable; D sys This represents the output channel of the input variable.

[0022] In some embodiments, step S6 is followed by: S7: performing frequency stability analysis on the power system based on the unified linearized state-space model.

[0023] In some embodiments, the frequency stability analysis includes at least one of time-domain dynamic performance analysis, eigenvalue and modal analysis.

[0024] In some embodiments, the method further includes: S8: generating stability improvement measures for the power system based on the results of frequency stability analysis.

[0025] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, performs the steps of the method as described in any of the preceding claims.

[0026] The present invention also provides a computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the steps of the method as described in any of the preceding claims.

[0027] This invention also provides a frequency response simulation system for a high-proportion renewable energy power system, comprising: a data input module for acquiring parameters of the power system; a model building module for executing the method described in any of the preceding items to construct a unified linearized state-space model of the power system; a simulation calculation module for performing frequency response simulation based on the model; and a result output module for outputting the frequency response simulation results.

[0028] The present invention also provides a stability control device for a high-proportion renewable energy power system, comprising: a frequency response simulation system for a high-proportion renewable energy power system as described above; an analysis and decision module for performing stability analysis based on simulation results and generating control commands; and a control output interface for sending the control commands to the execution devices in the power system.

[0029] The present invention also provides a planning and design platform for a high-proportion renewable energy power system, which integrates the frequency response simulation system for a high-proportion renewable energy power system as described above, for evaluating the frequency stability of the power system under different planning schemes.

[0030] The present invention also provides a control system for an inverter, including a local controller configured to: receive global information from the power grid; calculate local control parameters based on a simplified frequency response model constructed or pre-set by the high-proportion new energy power system frequency response modeling method described in any of the preceding claims; and adjust the active power output of the inverter to participate in power system frequency regulation.

[0031] The present invention also provides a frequency stability analysis method for high-proportion renewable energy power systems. The method uses the frequency response simulation system for high-proportion renewable energy power systems described above to generate a power system model, and performs eigenvalue analysis on the model to identify the oscillation modes and stability of the power system.

[0032] This invention also provides a frequency monitoring method for a high-proportion renewable energy power system based on digital twins, comprising: acquiring power system operation data in real time; establishing and updating a unified linearized state-space model of the power system in real time using the frequency response modeling method for a high-proportion renewable energy power system as described in any of the preceding claims; performing real-time simulation based on the updated model to predict the frequency dynamics of the power system; and issuing an early warning when a frequency stability risk is predicted.

[0033] The beneficial effects of this invention compared to the prior art include:

[0034] The frequency response modeling method for high-proportion new energy power systems provided by this invention divides nodes into active nodes and passive nodes according to their frequency response capabilities, establishes a linearized power flow model of the system, and simplifies it into an equivalent model that is only related to active nodes. It also systematically establishes frequency-active response models for various heterogeneous power resources, integrates the network power flow model with various resource response models, and finally constructs a unified linearized state space model. This modeling approach firstly achieves a refined characterization of the differentiated frequency response characteristics of heterogeneous resources such as synchronous generators, grid-connected inverters, grid-linked inverters, and loads, solving the model error problem caused by the neglect of resource heterogeneity in traditional models. Secondly, through the active node framework and frequency allocation matrix, it effectively characterizes the frequency differences between multiple nodes while ensuring model simplicity, overcoming the shortcomings of traditional single-node or COI models in reflecting the inconsistency of frequency response space. Finally, the synergistic effect of the above intermediate effects enables the unified linearized state-space model provided by this invention to achieve faster and more accurate simulation and stability analysis of the frequency dynamics of high-proportion new energy power systems, while having significant advantages in computational complexity and simulation efficiency compared with detailed electromagnetic transient models. This provides an efficient and reliable theoretical tool for system planning, operation, and control.

[0035] By introducing a frequency stability analysis step, the system stability can be comprehensively evaluated from multiple dimensions, including the time and frequency domains, based on a refined model, and effective stability improvement measures can be generated.

[0036] By integrating the method into electronic devices, storage media, simulation systems, control devices, planning and design platforms, inverter control systems, and digital twin monitoring methods, the application scenarios of the modeling method are expanded, enabling efficient monitoring, accurate analysis, and effective control of power system frequency stability.

[0037] Other beneficial effects of the embodiments of the present invention will be further described below. Attached Figure Description

[0038] Figure 1 This is a flowchart of the frequency response modeling method for high-proportion new energy power systems in an embodiment of the present invention.

[0039] Figure 2 This is a schematic diagram of the frequency response model structure of a high-proportion new energy power system in an embodiment of the present invention.

[0040] Figure 3 This is a simulation example of the frequency response of a high-proportion new energy power system in an embodiment of the present invention.

[0041] Figure 4 This is a simulation example of the phase angle response of a high-proportion new energy power system in an embodiment of the present invention.

[0042] Figure 5 This is a flowchart illustrating the programming implementation of frequency response modeling for a high-proportion renewable energy power system according to an embodiment of the present invention. Detailed Implementation

[0043] The present invention will be further described below with reference to the accompanying drawings and preferred embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other.

[0044] It should be noted that the directional terms such as left, right, up, down, top, and bottom used in this embodiment are only relative concepts or are based on the normal use of the product, and should not be considered as restrictive.

[0045] The refined modeling of the frequency response of heterogeneous power resources in high-proportion renewable energy power systems is the main technical problem addressed in this invention. With the increasing penetration rate of renewable energy generation in new power systems, the characteristics of system frequency response are undergoing profound changes. Renewable energy sources connected to the grid using grid-connected inverters and grid-connected inverters exhibit greater flexibility and vulnerability compared to traditional synchronous generator units, and these two types of grid-connected resources also possess different frequency-active power response characteristics. Traditional power system frequency modeling methods fail to distinguish the frequency response output characteristics of different types of power resources, resulting in significant errors between the obtained system frequency state trajectories and the actual values. This affects the reliability of grid frequency stability analysis and frequency control. Therefore, a modeling method that considers the frequency regulation response characteristics of heterogeneous resources is needed.

[0046] How to model the frequency response of multiple nodes in a power system separately is another technical problem addressed by the embodiments of this invention. Some existing modeling methods employ a system-wide uniform frequency modeling approach, that is, using a single ordinary differential equation to describe the system frequency. However, the frequency response of different nodes in a power system exhibits significant differences during the transient phase after a fault / disturbance, with variations in indicators such as the rate of frequency change and frequency deviation. Furthermore, the frequencies of nodes containing grid-connected renewable energy sources and demand response loads are difficult to model directly using differential equations; models constructed from algebraic equations have a substantial computational burden.

[0047] How to conduct accurate and comprehensive frequency stability analysis on power systems with a high proportion of new energy sources is another technical problem addressed by the embodiments of this invention. Existing analysis methods fail to be based on refined frequency response models, are insufficient in characterizing the stability characteristics of the two types of inverters, and fail to achieve a comprehensive assessment of frequency stability from multiple dimensions. Therefore, there is a need for methods that can refine the modeling of the frequency response of power systems with multiple resource types and multiple nodes, as well as a complete frequency stability analysis method.

[0048] This invention proposes a frequency response modeling method for high-proportion renewable energy power systems. Its core principle lies in: firstly, classifying power system nodes into active and passive nodes based on their frequency response capabilities; and systematically analyzing the frequency-active response characteristics of common resources in new power systems (synchronous generators, grid-forming (GFM) inverter power supplies, grid-following (GFL) inverter power supplies, and demand-response loads), thereby establishing response models for these four resource types. Secondly, this invention utilizes the Laplace matrix of power network flow to establish a linearized small-signal power flow model to describe the relationship between power flow and frequency deviation. Kronenstein reduction eliminates the algebraic equations of passive nodes, ultimately unifying them into the differential equation framework of active nodes, thus constructing a unified linearized state-space model that can distinguish resource heterogeneity and reflect frequency differences between nodes.

[0049] like Figure 1 As shown in the figure, the frequency response modeling method for high-proportion renewable energy power systems provided in this embodiment of the invention includes the following steps:

[0050] S1: All nodes in the power system are divided into active nodes and passive nodes; active nodes are those whose frequency dynamics can be described by differential equations, including synchronous generator nodes and grid-connected inverter nodes; passive nodes are those whose frequency dynamics cannot be directly described by differential equations, including grid-connected inverter nodes, load nodes, and intermediate nodes.

[0051] S2: Establish a linearized power flow model of the power system to obtain the phase angle vectors of active nodes. d A and passive node power injection vector P P Active node power flow injection power vector P A The expression for linearized power flow is:

[0052]

[0053] Where L is the Laplace matrix of the system power flow, L AA L represents the power flow relationship between two active nodes. AP L represents the power flow relationship from passive nodes to active nodes. PA L represents the power flow relationship from the active node to the passive node. PP This indicates the power flow relationship between two passive nodes.

[0054] S3: Reduce the linearized power flow model by eliminating the phase vectors of passive nodes. dP This yields a phase angle vector containing only the active nodes. d A and passive node power injection vector P P The equivalent active node power injection power expression is obtained. This is reduced to a Kron reduction, and the reduced equivalent active node power injection power expression is:

[0055]

[0056] in, , is the equivalent Laplace matrix; , where is the power distribution matrix.

[0057] S4: Establish frequency-active response models for various power resources in both active and passive nodes. Establishing these models includes: establishing the oscillation equation model for synchronous generator nodes; establishing the droop control model for grid-connected inverter nodes; establishing the phase-locked loop frequency measurement and damping control model for grid-connected inverter nodes; and establishing the frequency response model for load nodes.

[0058] S5: Combine the equivalent active node power flow injection expression with the frequency-active response model to construct a unified linearized state-space model with the active node phase angle and frequency as state variables. The unified linearized state-space model has the following form:

[0059]

[0060] in, A sys This represents the system state matrix, which consists of the dynamic matrices of each power source and the Laplace matrix. X It is a vector of state variables, including the phase angle of the active node, the frequency of the active node, and the intermediate state variables of each power supply regulation system; B sys This indicates the channel through which the frequency control command input is applied. U This is the frequency control command vector; P d The disturbance power vector; y This is the output vector; C sys The output channel represents the state variable; D sys This represents the output channel of the input variable.

[0061] S6: Calculate the frequency response of the power system based on the unified linearized state-space model.

[0062] S7: Based on the unified linearized state-space model, perform frequency stability analysis on the power system. Frequency stability analysis includes at least one of time-domain dynamic performance analysis, eigenvalue analysis, and modal analysis.

[0063] S8: Based on the results of the frequency stability analysis, generate measures to improve the stability of the power system.

[0064] This invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps of the high-proportion new energy power system frequency response modeling method as described in any of the preceding embodiments.

[0065] This invention also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the high-proportion renewable energy power system frequency response modeling method as described in any of the preceding embodiments.

[0066] This invention also provides a frequency response simulation system for a high-proportion renewable energy power system, comprising: a data input module for acquiring parameters of the power system; a model building module for executing the frequency response modeling method for a high-proportion renewable energy power system as described in any of the preceding embodiments to construct a unified linearized state-space model of the power system; a simulation calculation module for performing frequency response simulation based on the model; and a result output module for outputting the frequency response simulation results.

[0067] This invention also provides a stability control device for a high-proportion renewable energy power system, comprising: a frequency response simulation system for a high-proportion renewable energy power system as described above; an analysis and decision module for performing stability analysis based on simulation results and generating control commands; and a control output interface for sending the control commands to the execution devices in the power system.

[0068] This invention also provides a high-proportion renewable energy power system planning and design platform, which integrates the high-proportion renewable energy power system frequency response simulation system described above, for evaluating the frequency stability of the power system under different planning schemes.

[0069] This invention also provides a control system for an inverter, including a local controller configured to: receive global information from the power grid; calculate local control parameters based on a simplified frequency response model constructed or pre-set by the high-proportion renewable energy power system frequency response modeling method described in any of the preceding claims; and adjust the active power output of the inverter to participate in power system frequency regulation.

[0070] This invention also provides a method for frequency stability analysis of high-proportion renewable energy power systems. The method uses the frequency response simulation system for high-proportion renewable energy power systems described above to generate a power system model, and performs eigenvalue analysis on the model to identify the oscillation modes and stability of the power system.

[0071] This invention also provides a frequency monitoring method for a high-proportion renewable energy power system based on digital twins, comprising: acquiring power system operation data in real time; establishing and updating a unified linearized state-space model of the power system in real time using the frequency response modeling method for a high-proportion renewable energy power system as described in any of the preceding embodiments; performing real-time simulation based on the updated model to predict the frequency dynamics of the power system; and issuing an early warning when a frequency stability risk is predicted.

[0072] The following describes specific embodiments of the present invention.

[0073] The frequency response modeling method for high-proportion renewable energy power systems provided in this embodiment includes the following steps:

[0074] Step 1: Establish power system node and line models

[0075] The power system frequency response model was constructed based on the following assumptions:

[0076] (1) There is no power consumption in the power network line, that is, the line resistance is zero.

[0077] (2) Ignore reactive power flow and injection.

[0078] (3) Active power and voltage angle are decoupled from each other.

[0079] (4) The steady-state voltage phase angle difference at each node satisfies ± π Within the range of / 2.

[0080] (5) Loads and power sources can exist in the same grid node. For a node connected to a power source, it is assumed that only one type of power source is connected, including synchronous generator sets, wind power, photovoltaic or energy storage units.

[0081] (6) Ignore the dynamic performance of the inverter’s inner loop voltage and current control circuit.

[0082] The above assumptions significantly simplify the form of the system power flow and frequency dynamic equations, allowing the model to focus on the main coupling relationship between active power and frequency, thus facilitating the analysis of the system's frequency response characteristics under disturbances. These assumptions are widely used in traditional synchronous machine-dominated power systems, and their errors are usually negligible.

[0083] In high-proportion power electronic systems, the inverter's control characteristics and variations in line impedance ratio cause reactive power and voltage dynamics to have a certain impact on the frequency response. Ignoring reactive power and network losses may lead to model biases in the following aspects:

[0084] (1) Dynamic amplitude error: The active coupling caused by voltage change is ignored, which may lead to an underestimation of the frequency deviation amplitude.

[0085] (2) Phase response error: When the assumption that the line impedance angle is close to 90° no longer holds, the power angle-power linearization deviation increases.

[0086] (3) Stability boundary offset: Under low short-circuit ratio or weak power grid conditions, neglecting reactive power may overestimate the system damping and stability margin.

[0087] Therefore, this method is mainly applicable to transmission networks with medium to high short-circuit ratios and relatively low line resistance; and to scenarios where the frequency response analysis timescale is on the order of seconds and focuses on active power dynamics. This method is used in the initial stage of frequency stability analysis, in scenarios with small disturbances, and under normal stable operating conditions. Its advantage lies in its high computational efficiency, making it suitable for rapid evaluation in planning, scheduling, and online analysis, rather than replacing detailed electromagnetic transient simulation.

[0088] When reactive power dynamics are significant in the system (such as in weak grids or high-proportion grid-connected inverter power supply operation), the accuracy can be improved by introducing voltage-reactive power coupling equations or extending the model using complex power forms. Furthermore, when large disturbances occur in the system leading to excessive power angle differences or when the system is nearing voltage instability, the accuracy of this linearized model will decrease, requiring a more detailed nonlinear model for analysis.

[0089] 1.1 Classification of Power System Nodes

[0090] Consider a n A power system consisting of nodes, the topology of which is a set of nodes , and edge set constitute. i, j Both represent the index of the node, and The index of the system's transmission lines consists of unordered pairs. This indicates that the transmission line { i, j} connects two adjacent nodes in the system i and j The above-mentioned graph model connects nodes and lines. Describe the power system.

[0091] Depending on the type of power source contained in the nodes, the power system contains:

[0092] (1) Synchronous machine nodes, i.e., nodes containing synchronous generators, are denoted by the set denoted as . , n G The number of synchronization machine nodes;

[0093] (2) Grid-type nodes, which are nodes containing power sources connected to the grid by grid-type inverters (referred to as grid-type power sources), are denoted as . , n FM The number of nodes in the network structure;

[0094] (3) Grid-connected nodes, which are nodes that include power sources connected to the grid via grid-connected inverters (referred to as grid-connected power sources), are denoted as . , n FL The number of nodes in the network;

[0095] (4) Load nodes, i.e., nodes that contain only loads, are denoted as . , n L The number of load nodes;

[0096] (5) Intermediate nodes, i.e., grid nodes that are not connected to any power source or load, are denoted as […]. , n N This represents the number of intermediate nodes.

[0097] Based on the frequency response capabilities of the above-mentioned types of nodes, n The system nodes are divided into n A One "active node" and n P One "passive node":

[0098] (1) Active Nodes: Active nodes include synchronous machine nodes and network-type nodes, and their set yes and The union of, i.e. The number of them n A = n G + n FM ;

[0099] (2) Passive Nodes: Passive nodes include network nodes, load nodes, and intermediate nodes, and their set is as follows: yes , and The union of, i.e. The number of them n P= n FL + n L + n N .

[0100] This node classification method is based on the frequency response capability of the power resources connected to each node: synchronous generators and grid-connected inverters on active nodes can spontaneously adjust the frequency dynamics of their respective nodes, and their frequency dynamics can be described by differential equations (oscillation equations); loads and grid-connected inverters on passive nodes adjust active power output according to the measured frequency signal, and cannot spontaneously adjust the frequency of their respective nodes. Intermediate nodes have neither spontaneous frequency regulation capability nor additional active power regulation capability, so the frequency dynamics of passive nodes cannot be directly modeled by differential equations.

[0101] 1.2 Establishing a linearized power flow model

[0102] node i Current injection power p i Expressed as equation (1):

[0103] (1)

[0104] in, V i , V j They are nodes i and nodes j voltage amplitude, B ij For the line The imaginary part of the admittance, d i , d j They are nodes i and nodes j The voltage phase angle.

[0105] By performing small-signal linearization with the system equilibrium point as the center, the linearized power flow equation (2) can be obtained:

[0106] (2)

[0107] in, P A , P P Let represent the linear approximate power injection vectors of the active and passive nodes, respectively; secondly, d A , d PThese are the phase angle vectors of the active node and the passive node, respectively, determined by the voltage phase angle belonging to either the active or passive node. d i composition: , Matrix L is the Laplace matrix of the system power flow, which consists of four blocks representing the power coupling relationships between different types of nodes. AA L represents the power flow relationship between two active nodes. AP L represents the power flow relationship from passive nodes to active nodes. PA L represents the power flow relationship from the active node to the passive node. PP This represents the power flow relationship between two passive nodes. The matrix elements in matrix L represent the power flow relationship between them. L i,j The expression for is shown in equation (3). Here, we will explain its calculation method. The formulas in the subsequent steps will all appear in the overall form of matrix L.

[0108]

[0109] in, For partial derivative operators, and They represent p i about d i and d j The partial derivative of .

[0110] Since the frequency of the passive node cannot be directly modeled using differential equations, the phase vector of the passive node in equation (2) is eliminated by the Kronek reduction method. d P The linear approximate power flow injection vector of the active node is established as shown in equation (4):

[0111] (4)

[0112] in, For L PP The inverse matrix. The first term on the right-hand side of equation (4) represents the equivalent power flow injection active power between active nodes. The equivalent Laplace matrix of the system is defined as follows: The equivalent power flow between active nodes can be simply represented as J. d A The second term on the right-hand side of equation (4) represents the active power injection from the passive node to the active node. The power distribution matrix of the passive node is defined as follows: The active power injection from a passive node to an active node can be simply represented as W. P PFinally, equation (4) can be simplified to: The purpose of establishing a linear approximation of equation (4) is to facilitate the use of known vectors. d A and P P Calculate the power flow injection power of the active nodes, and finally construct the frequency response state space model of the auxiliary system in step 3.

[0113] Step 2: Establish frequency modulation response models for various power supplies

[0114] 22.1 Response Model of Thermal Power Unit Nodes

[0115] Synchronous generator nodes are active nodes, and their frequency dynamics can be described by differential equations. Common synchronous generator sets mainly include thermal power units and hydropower units. The frequency regulation response of hydropower units is similar to that of thermal power units in principle, only the model of the turbine response part is different. In this embodiment, thermal power units are used as an example for modeling. The frequency response model of the synchronous generator node of a thermal power unit follows the oscillation equation (5):

[0116] (5)

[0117] in, Active node i frequency, M i For nodes i The inertia constant of thermal power units. For nodes i Frequency-regulated power response, For nodes i The disturbance power, p i For nodes i The power injected by the current, D i For nodes i The damping constant, This indicates that the node belongs to the set of synchronization machine nodes.

[0118] The active power response of thermal power units adopts the transfer function model (6), which defines... s For the Laplace operator in the complex frequency domain, where T 1i , T 2i , T 3i Thermal power nodes i The governor valve lag time constant, the turbine lead time constant, and the reheat time constant. Frequency regulation power response. This includes the droop response of the speed controller and secondary frequency modulation, among whichR Gi This is the governor droop coefficient. u Gi This is a secondary frequency modulation control command.

[0119] (6)

[0120] Define and describe thermal power nodes i intermediate variable of the unit's regulating valve The frequency regulation response model of the thermal power unit node can be written as the state-space expression as Equation (7).

[0121] (7)

[0122] 2.2 Response Model of Grid-Based Inverter Nodes

[0123] The grid-connected power source is regarded as a voltage source, and the grid-connected node is an active node. Its frequency dynamics can be described by differential equations. The GFM inverter controls the voltage and frequency of the active grid connection point. This scheme assumes that the energy storage unit is connected to the grid through the GFM inverter and uses droop control as a way to synchronize with the main grid. Its dynamics are described by equations (8)–(11).

[0124] (8)

[0125] (9)

[0126] (10)

[0127] (11)

[0128] Equation (8) defines a grid-type inverter. i (abbreviated as GFM) i Output power deviation , For GFM i 'output power' For GFM i The power reference value, For GFM i The set value of the frequency-regulated power response. In equation (9), For GFM i The low-pass filtered power deviation signal, oh fi For GFM i The filter bandwidth. Equation (10) describes the GFM. i Frequency deviation of the node The relationship between the power deviation signal and the low-pass filtered signal. RFMi For GFM i The droop control coefficient. Substituting equations (8) and (9) into equation (10) in turn, we can obtain equation (11) for the dynamic relationship between power deviation and frequency adjustment. The equivalent inertia constant and damping constant of the node where the grid-type power source is located are respectively determined by... , calculate.

[0129] Linearize equation (11) to eliminate steady-state values ​​and construct a network of nodes. The frequency response model can be expressed as equation (12):

[0130] (12)

[0131] in, For nodes i The disturbance power, p i For nodes i The power is injected by the current.

[0132] For GFM i Secondary frequency modulation control command u FMi , Described using a first-order inertial element, GFM i The control time constant is T FMi The expression is as shown in equation (13):

[0133] (13)

[0134] 2.3 Response Model of Grid-connected Inverter Nodes

[0135] In grid-connected power sources, the power supply is considered a current source, and grid-connected nodes are passive nodes. GFL inverters cannot spontaneously adjust the grid connection frequency, therefore their frequency dynamics cannot be directly described by differential equations. GFL inverters synchronize with the system via a phase-locked loop (PLL), and the estimated node frequency is obtained from the PLL estimation. When frequency regulation is required, active power is injected through additional damping control. This scheme assumes that wind turbines and photovoltaics are connected to the grid via GFL inverters, each node connects to only one type of power source, and several identical grid-connected power sources are equivalently aggregated into a single power source. (Grid-connected node) The disturbance power caused by fluctuations in new energy sources and load is denoted as .

[0136] Frequency-regulated power response model of mesh nodes See equation (14).

[0137] (14)

[0138] in D FLi This is the damping control coefficient. T FLi The control time constant for the grid-connected inverter.

[0139] The dynamic model of the node frequency estimated by the PLL of the GFL inverter is given by equation (15). , These are the equivalent proportional and integral control gains for phase-locked loop synchronous control, respectively. oh Pi Passive node i The true value of the frequency.

[0140] (15)

[0141] To facilitate modeling, intermediate variables for phase-locked loop control are defined. and The frequency estimation signal can be written as a linear combination of equation (16), and further transformed into a state-space model equation (17).

[0142]

[0143] (16)

[0144]

[0145] It is important to note that this model is based on the assumptions of normal grid voltage and PLL in a linearly locked state. Nonlinear dynamics during grid faults are not considered in this model. Furthermore, conventionally, this scheme assumes that grid-connected renewable energy operates in maximum power output mode. For wind power grid-connected nodes, the wind turbine can release rotor kinetic energy through pitch angle control to temporarily provide frequency regulation power, thus achieving damping control. However, this is not sustainable and lacks additional frequency regulation capacity for secondary frequency regulation. In contrast, photovoltaic (PV) power does not have additional frequency regulation capacity; therefore, the frequency regulation power response of grid-connected nodes containing PV power is... =0.

[0146] 2.4 Response Model of Load Nodes

[0147] The node containing the load is a passive node, and like other nodes, it cannot spontaneously adjust the frequency of its grid connection point; therefore, its frequency dynamics cannot be directly described using differential equations. Load frequency control adjusts active power through demand response, and the frequency control command is... u Li The process adopts the following: The frequency-regulated power response is described by a first-order inertial element with a time constant as follows: The expression is as shown in equation (18).

[0148] (18)

[0149] In addition, load nodes The disturbance power caused by load fluctuations is denoted as .

[0150] Step 3: Establish the phase angle and frequency response model of the power system

[0151] In the coordinate system of the center of inertia, the voltage phase angle vector of the active node d A The dynamic model is defined by equation (19).

[0152] (19)

[0153] Where matrix E is the active node frequency vector in the inertial center coordinate system. oh A phase angle vector d A The linear mapping matrix. In the expression for calculating matrix E, For dimension is n A The identity matrix has 1s on its diagonal and 0s on the rest; the matrix on the right-hand side of the equation has dimensions of . n A A square matrix of all 1s.

[0154] Define the system active frequency vector In order from n G A frequency variable belonging to the synchronizer node and n FM Frequency variables belonging to network nodes Composition. The frequency response of the active nodes in the power system has been given in step 2, namely the frequency response equation (5) of the synchronous machine node in step 2.1 and the frequency response equation (12) of the network-type node in step 2.2. The frequency responses of the two types of nodes can be summarized as the system active frequency vector. oh A The general frequency response model is expressed as shown in equation (20).

[0155] (20)

[0156] in, For all active nodes The inertia constant is the system inertia diagonal matrix composed of elements, M —1 Let M be the inverse matrix. Active node The damping constant is the system damping diagonal matrix composed of elements; and Active nodes With passive nodes The frequency-regulated power is a frequency-modulated power vector composed of elements, and its expression is: , The specific expressions for each type of element have been given in step 2. and The analytical form is about the frequency vector of the active nodes. oh A and frequency control command vector The linear model. Finally. and The disturbance power vector consists of the disturbance power of the active node and the passive node, respectively. It should be noted that the node power flow injection power in equations (5) and (12) is... p i When expressed in vector form in equation (20), a linear approximation of the power flow injection vector is used. P A Substituting into equation (4) in step 1 P A The expression, that is, the expression in equation (20) is obtained. part.

[0157] Combining equations (19) and (20), the state-space model of the phase angle and frequency response of all active nodes in the system can be expressed as equation (21).

[0158] (twenty one)

[0159] Based on the frequency model of the active nodes, the frequencies of the passive nodes can be further calculated. The frequency allocation matrix is ​​defined as follows: Its physical meaning reflects the relationship between the network topology and impedance between active and passive nodes, and the frequency of the passive node. oh P Based on the frequency of active nodes oh A The result is obtained through linear expression calculation, as shown in equation (22):

[0160] (twenty two)

[0161] It should be noted that formula (22) is essentially a mathematical method for effectively estimating the frequency of passive nodes and is only used as a tool for simulation analysis.

[0162] A schematic diagram of the power system frequency response model is shown below. Figure 2 As shown. The system power flow model in step 1, the response model of the active node in step 2, and the response model of the passive node together constitute the system frequency response model, which is presented in a closed-loop form. System input W is the equivalent perturbation vector of the active node after system elimination, and W is the power distribution matrix of the passive node defined in step 1; the green boxes in the forward path of the structure diagram represent active node 1 to active node 2. n The model is represented by equations (5) and (6) of the thermal power unit node response model in step 2.1 and equations (12) and (13) of the grid-connected inverter node response model in step 2.2. p The input vector is the power bias of the active node, and the output is the frequency vector of the active node. oh A Passive node 1 to passive node 2 (red box) in the inner feedback channel of the structure diagram. n The model is represented by equations (14) and (15) of the grid-connected inverter node response model in step 2.3 and equation (18) of the load node response model in step 2.4, and its input is the passive node frequency vector defined by equation (22). oh P =F oh A Output W P P The equivalent injected power vector for the passive node; the network dynamics J / s in the blue box on the outer feedback channel of the structure diagram represents the frequency from the active node. oh A To the trend J d A The mapping.

[0163] Step 4: Program simulation of system frequency and phase angle:

[0164] The modeling method proposed in this embodiment can be implemented using mainstream programming software (such as Visual Studio Code, MATLAB) and programming languages ​​(such as Python and MATLAB). This example uses Python to illustrate the implementation method. Scientific computing and system simulation libraries such as NumPy, Pandas, and the Control Systems Library should be pre-installed in the computing environment to enable matrix calculations, state-space model construction, and dynamic response simulation. The specific implementation steps are as follows.

[0165] 4.1 Data Reading and Initialization

[0166] 4.1.1 Read system-related data from power system model files (e.g., .xlsx format). Typically, data tables from different categories are stored in different worksheets within the same .xlsx file. The first row of each worksheet usually contains data labels (numbers and variable names), and the remaining data is stored in columns. The main data considered in this modeling method is as follows:

[0167] • Node data table: contains node number, initial voltage v 0 and initial phase angle a 0;

[0168] • Line data table: contains the starting node from_bus, the destination node to_bus, and the line resistance. r ij With line reactance x ij ;

[0169] • Generator and governor data sheets: provide the inertia, damping and governor parameters of the synchronous generator;

[0170] • GFM control and GFL control data sheets: provide control parameters for grid-connected and grid-linked inverters.

[0171] 4.1.2 After reading is complete, an index array is built based on the node number, and the total number of nodes is calculated. n Number of synchronous generators n G Number of grid-connected inverters n FM and the number of grid-connected inverters n FL .

[0172] 4.1.3 Based on the system and power supply parameters read from the table, construct parameter matrices such as the system inertia diagonal matrix M and the system damping diagonal matrix D to form the basic parameter array for subsequent state equations.

[0173] 4.2 Construction and Reduction of the Power Flow Laplace Matrix

[0174] 4.2.1 The admittance matrix of the network is constructed based on the line data, which is implemented in the program through a user-defined function. This function takes the line parameters as input, first merging parallel lines according to the node pairs (from_bus, to_bus), then iterates through the line data table, filling the corresponding position of the admittance matrix with the susceptance value of each line, and accumulating the diagonal elements to calculate the susceptance value of each line. .

[0175] 4.2.2 Under the assumption of lossless line, calculate the Laplace matrix L of the system power flow, where the diagonal and off-diagonal elements represent the self-admittance and mutual admittance of the nodes, respectively.

[0176] 4.2.3 The nodes are divided into "active nodes" (i.e., synchronous generator and grid-connected inverter nodes) and "passive nodes" (i.e., load and grid-connected inverter nodes). The system Laplace matrix J, power distribution matrix W and frequency allocation matrix F after Kron reduction are calculated according to the block matrix formula. These are used to establish the linear mapping relationship of power transfer between active nodes and passive nodes.

[0177] 4.3 Establish dynamic models of power supply and load

[0178] 4.3.1 Synchronous Generator Model: Based on step 2.1, state variables are constructed using the governor and turbine parameters of the thermal power unit. , The corresponding array of second-order state-space models, inertia M i With damping D i This constitutes an array that describes the frequency dynamics of the synchronizer nodes.

[0179] 4.3.2 Grid-type inverter model: According to step 2.2, a low-pass filter bandwidth is adopted. oh fi and droop coefficient R FMi Calculate equivalent inertia With damping This constitutes an array that describes the frequency dynamics of network nodes.

[0180] 4.3.3 Grid-connected inverter model: Based on the phase-locked loop frequency measurement equation and GFL damping control loop in step 2.3, a three-state variable model is constructed. This corresponds to a proportional-integral PLL control and a first-order low-pass filter control. Its state equation is derived from the control parameters. Sure.

[0181] 4.3.4 Load Frequency Response Model: Based on step 2.4, a time constant is used. T Li The first-order inertial element describes the active response of the load to frequency deviation.

[0182] 4.4 Assembly of the System State-Space Model

[0183] 4.4.1 Combine the state variables in the system into a unified state vector. This includes the phase angles of the active nodes. d A Active node frequency ohA Step 2.1 Response variable of regulating valve in thermal power unit The vector formed Step 2.1 Frequency regulation power response variable of thermal power unit The vector formed Step 2.2 Frequency regulation power of the grid inverter The vector formed Intermediate variables in phase-locked loop control in step 2.3 and The vectors formed respectively Step 2.3 involves adjusting the frequency power of the network nodes. The vector formed :

[0184]

[0185] 4.4.2 Constructing the state-space model of the system's closed-loop frequency response:

[0186]

[0187] Among them, the system state matrix A sys It consists of the dynamic matrices of each power source and the Laplace matrices J, W, and F. B sys The channel that reflects the effect of frequency control command input. U It is the frequency control command vector in step 3. B d The channel that reflects the effect of disturbance power injection. P d This is a vector composed of the perturbation variables of each node in step 3; y For the output vector, C sys It is an output channel that reflects state variables. D sys It is the output channel that reflects the input variables.

[0188] 4.4.3 The system object `system` is created using the Control library function `ss(A_sys, B_sys, C_sys, D_sys)` for time-domain simulation.

[0189] 4.5 Simulation Implementation of Frequency and Phase Response

[0190] Taking the simulation results of a two-region 10-node power system as an example, there are two thermal power unit nodes, one grid-type power supply node and one grid-connected power supply node in the system. The remaining nodes are load nodes or intermediate nodes. The node, line and power supply parameters related to the frequency response modeling of this system are shown in Tables 1-5.

[0191] Table 1 System Node Parameters

[0192]

[0193] Table 2 System Line Parameters

[0194]

[0195] Table 3 Parameters of Thermal Power Units

[0196]

[0197] Table 4 Parameters of Grid-connected Inverters

[0198]

[0199] Table 5 Parameters of Grid-Connected Inverters

[0200]

[0201] The simulation experiment was conducted using Visual Studio Code and Python version 3.12. The simulation duration was 100 seconds, the sampling period was 0.02 seconds, and all state variables were initialized to 0. This embodiment only verifies the system's spontaneous frequency response, i.e., the vector formed by the frequency control commands of each power supply. U The element in the value is 0. Simulation time t When the phase angle is 0, a step power disturbance with an amplitude of +0.5 pu (per unit) is applied at node 5. The forced response of the system under the disturbance is solved using the forced_response() function in the Python ControlSystems Library, and the changes in node frequency and phase angle are plotted using the Matplotlib library.

[0202] The program's average computation time for modeling and simulation is 0.464 seconds. The frequency response and phase response of the four system power nodes are as follows: Figure 3 and Figure 4 As shown. Figure 3 In oh 1- oh 4 represents the frequency trajectories of thermal power unit 1, thermal power unit 2, grid-connected inverter 1, and grid-linked inverter 1, respectively. Figure 4 In d 1- d 4 represents the phase angle deviation trajectories of thermal power unit 1, thermal power unit 2, grid-connected inverter 1, and grid-following inverter 1, respectively.

[0203] The flowchart of the programming implementation of the frequency response modeling method for high-proportion renewable energy power systems proposed in this embodiment is as follows: Figure 5 As shown.

[0204] Step 5: Stability analysis of power system frequency:

[0205] 5.1 Time-Domain Dynamic Performance Analysis

[0206] Time-domain dynamic performance analysis is used to evaluate the transient frequency response characteristics of a system under conditions such as power disturbances, generator failures, and changes in inverter control parameters, including indicators such as frequency deviation, frequency recovery time, and damping performance.

[0207] Based on the system frequency time-domain simulation results obtained in step 4.5, the dynamic performance indicators such as the maximum frequency change rate, the lowest frequency point (frequency valley), the frequency recovery time, and the steady-state deviation of each node can be calculated, and the influence of system inertia and control characteristics on the overall frequency stability can be analyzed.

[0208] 5.2 Eigenvalue and Modal Analysis

[0209] Eigenvalue and modal analysis methods are used to evaluate the linear stability and dynamic modal characteristics of a system under small disturbance conditions, and to determine the dominant modes and damping characteristics that affect the frequency oscillation of the system.

[0210] Based on the system state matrix obtained in step 4.4.2 A sys Calculate its eigenvalues l The system's natural frequency and damping ratio are determined by analyzing the corresponding eigenvectors. The rule for determining eigenvalues ​​is as follows: when all eigenvalues ​​have negative real parts, the system is stable under small disturbances; negative eigenvalues ​​with larger real parts correspond to fast-decaying modes, while eigenvalues ​​with larger imaginary parts correspond to low-frequency oscillation modes. This method is used to analyze the participation factors of key modes and identify the dominant oscillation source and its associated node or device type.

[0211] Eigenvalue and modal analysis can utilize numerical linear algebra functions (such as numpy.linalg.eig() in Python's NumPy library or eig() in MATLAB) to calculate system eigenvalues. By plotting system modal diagrams or damping distribution diagrams, the dynamic modes of the system and their changing trends can be visually displayed.

[0212] 5.3 Comprehensive Analysis and Frequency Stability Improvement Measures

[0213] By combining time-domain and eigenvalue analysis results, the frequency dynamic stability of the system and the sensitivity of each control parameter under different operating conditions can be comprehensively evaluated. By comparing frequency response indicators and characteristic mode changes under different scenarios, key factors affecting system frequency stability can be identified, providing a basis for parameter optimization and control strategy design.

[0214] First, sensitivity analysis is used to calculate the impact of changes in power resource control parameters (such as equivalent inertia constant, damping coefficient, droop coefficient, control time constant, etc.) on frequency valleys, damping ratio, and steady-state error, thus determining the parameter range most sensitive to system frequency stability. Then, based on the analysis results, targeted parameter adjustments or structural optimizations are performed on the system. Typical adjustment and treatment measures are as follows:

[0215] 5.3.1 Adjustment measures based on time-domain response results

[0216] When the steady-state frequency deviation of a node is large or the recovery time is too long, the droop control coefficient of the grid-type power supply can be appropriately reduced (i.e., the active power-frequency regulation strength can be increased) to improve the node's ability to correct frequency deviation.

[0217] If the frequency response curve shows obvious oscillations or overshoot, the system oscillations can be suppressed by increasing the damping coefficient of the grid-connected power supply and the grid-connected power supply or by introducing additional damping control elements.

[0218] If the rate of frequency change is too large, the system can have a smoother dynamic response by increasing the equivalent inertia constant of the grid-type power supply or by adding synchronous generators.

[0219] When the frequency deviation of a local node is large while other regions are relatively stable, the inverter output regulation rate of that node can be increased, or coordinated control can be introduced to improve the power support distribution between regions.

[0220] 5.3.2 Adjustment measures based on eigenvalue and modal analysis results

[0221] If there is a mode with a large imaginary part of the eigenvalue (corresponding to low frequency or regional oscillation), it indicates that the system has a strong oscillation mode. The damping ratio of the oscillation mode can be improved by increasing the damping control of the power supply related to the mode or adjusting the controller time constant.

[0222] When the real part of a partial mode is close to zero, it indicates that the system is at the critical stability boundary. The system stability can be enhanced by increasing the active-frequency droop coefficient of the dominant node of that mode or by reducing the control delay.

[0223] If analysis shows that multiple modes are concentrated in a specific frequency band, mode separation can be achieved by optimizing the bandwidth configuration of different types of inverters (such as the low-pass filter frequency of the GFM control loop) to avoid resonance.

[0224] 5.3.3 Measures to Improve Power System Operation

[0225] In addition to parameter adjustment, improvement measures at the power system operation level can be taken based on the analysis results, including:

[0226] (1) Parallel impedance configuration: Damping resistors or impedance branches are connected in parallel at critical nodes to suppress the propagation of oscillation energy;

[0227] (2) Oscillation source isolation: When modal analysis determines that a power supply or control unit is an oscillation source, the oscillation source can be temporarily cut off or the control mode can be adjusted (such as switching from GFM to GFL).

[0228] (3) Power redistribution: By adjusting the power transmitted or the direction of power flow through the tie line, the amplification effect of frequency disturbance in a certain area can be reduced;

[0229] (4) Control coordination optimization: Optimize the frequency support sharing ratio among different types of power sources through centralized or distributed coordination strategies.

[0230] Through the above comprehensive analysis and improvement measures, the frequency stability performance of the power system can be analyzed in the simulation verification platform, providing a theoretical basis and experimental foundation for power resource parameter tuning, frequency control strategy optimization, and power system operation mode adjustment.

[0231] In step 1.1 of this embodiment, based on the differences in the frequency response characteristics of power resources, a classification method suitable for system frequency modeling and analysis is proposed, dividing system nodes containing different types of power sources and loads into active nodes and passive nodes. The linearized small-signal power flow model proposed in step 1.2 can calculate the active power exchange value on transmission lines between interconnected nodes in the power system, and eliminates passive node vectors using the Kron reduction method, retaining the power flow injection model of active nodes. In step 2, the frequency-active response models of common power resource types such as synchronous generator units, grid-connected renewable energy, grid-linked renewable energy, and demand-response loads are refined. In step 3, the response models of various power resources are substituted into the system power flow model in step 1 to obtain the phase angle and frequency response models of active nodes. The frequency of passive nodes, which is difficult to model directly using differential equations, is solved through linear operations of the frequency allocation matrix, realizing frequency response modeling of heterogeneous power resources in multi-node interconnected power systems. Step 4 provides an explanation and examples of program simulation. Finally, based on the proposed refined frequency response model, step 5 proposes a system of methods for power system frequency stability analysis, further realizing the application of the refined frequency response model.

[0232] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, several equivalent substitutions or obvious modifications can be made without departing from the concept of the present invention, and all such modifications, achieving the same performance or purpose, should be considered within the scope of protection of the present invention.

Claims

1. A method for modeling the frequency response of a high-proportion renewable energy power system, characterized in that, Includes the following steps: S1: All nodes in the power system are divided into active nodes and passive nodes; the active nodes are those whose frequency dynamics can be described by differential equations, including synchronous generator nodes and grid-connected inverter nodes; the passive nodes are those whose frequency dynamics cannot be directly described by differential equations, including grid-connected inverter nodes, load nodes and intermediate nodes. S2: Establish a linearized power flow model of the power system, obtaining the phase angle vectors of the active nodes. δ A and passive node power injection vector P P Active node power flow injection power vector P A The expression; S3: Reduce the linearized power flow model by eliminating the phase vectors of passive nodes. δ P This yields a phase angle vector containing only the active nodes. δ A and passive node power injection vector P P The equivalent active node power flow injection power expression; S4: Establish frequency-active response models for various power resources in the active and passive nodes respectively; S5: Combine the equivalent active node power flow injection expression with the frequency-active response model to construct a unified linearized state-space model with active node phase angle and frequency as state variables. S6: Calculate the frequency response of the power system based on the unified linearized state-space model.

2. The method according to claim 1, characterized in that, The linearized power flow model mentioned in step S2 is as follows: Where L is the Laplace matrix of the system power flow, L AA L represents the power flow relationship between two active nodes. AP L represents the power flow relationship from passive nodes to active nodes. PA L represents the power flow relationship from the active node to the passive node. PP This indicates the power flow relationship between two passive nodes.

3. The method according to claim 2, characterized in that, The reduction described in step S3 is the Kron reduction, and the equivalent active node power injection power expression after reduction is: in, , is the equivalent Laplace matrix; , where is the power distribution matrix.

4. The method according to claim 1, characterized in that, Step S4, establishing the frequency-active response model, includes: establishing the swing equation model of the synchronous generator node; establishing the droop control model of the grid-connected inverter node; establishing the phase-locked loop frequency measurement and damping control model of the grid-connected inverter node; and establishing the frequency response model of the load node.

5. The method according to claim 1, characterized in that, The unified linearized state-space model described in step S5 is in the following form: in, A sys The system state matrix is ​​represented by the dynamic and Laplace matrices of the synchronous generator, grid-connected inverter, grid-linked inverter, and load. X It is a vector of state variables, including the phase angle of the active node, the frequency of the active node, and the intermediate state variables of the synchronous generator, the grid-connected inverter, the grid-connected inverter, and the load regulation system; B sys This indicates the channel through which the frequency control command input is applied. U This is the frequency control command vector; P d The disturbance power vector; y This is the output vector; C sys The output channel represents the state variable; D sys This represents the output channel of the input variable.

6. The method according to claim 1, characterized in that, Step S6 is followed by: S7: Based on the unified linearized state-space model, perform frequency stability analysis on the power system.

7. The method according to claim 6, characterized in that, The frequency stability analysis includes at least one of time-domain dynamic performance analysis, eigenvalue and modal analysis.

8. The method according to claim 7, characterized in that, The method further includes: S8: Based on the results of the frequency stability analysis, generate measures to improve the stability of the power system.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method as described in any one of claims 1 to 8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method as described in any one of claims 1 to 8.

11. A frequency response simulation system for a high-proportion renewable energy power system, characterized in that, include: The data input module is used to acquire parameters of the power system; The model building module is used to execute the method as described in any one of claims 1 to 8 to build a unified linearized state-space model of the power system; the simulation calculation module is used to perform frequency response simulation based on the model. The results output module is used to output the frequency response simulation results.

12. A stability control device for a high-proportion new energy power system, characterized in that, include: The frequency response simulation system for a high proportion of new energy power systems as described in claim 11; The analysis and decision module is used to perform stability analysis based on simulation results and generate control commands; the control output interface is used to send the control commands to the execution devices in the power system.

13. A planning and design platform for a high-proportion new energy power system, characterized in that, It integrates the frequency response simulation system for high-proportion new energy power systems as described in claim 11, and is used to evaluate the frequency stability of power systems under different planning schemes.

14. A control system for an inverter, characterized in that, The system includes a local controller configured to: receive global information from the power grid; calculate local control parameters based on a simplified frequency response model constructed or preset by the method described in any one of claims 1-8; and adjust the active power output of the inverter to participate in power system frequency regulation.

15. A method for frequency stability analysis of a high-proportion renewable energy power system, characterized in that, A power system model is generated using the high-proportion new energy power system frequency response simulation system as described in claim 11, and eigenvalue analysis is performed on the model to identify the oscillation mode and stability of the power system.

16. A frequency monitoring method for a high-proportion renewable energy power system based on digital twins, characterized in that, include: Real-time acquisition of power system operation data; Using the method described in any one of claims 1-8, a unified linearized state-space model of the power system is established and updated in real time; real-time simulation is performed based on the updated model to predict the frequency dynamics of the power system; and an early warning is issued when a frequency stability risk is predicted.

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