Method and apparatus for tracing power system oscillations with current transformer and synchronous machine

Abstract

This application discloses a method and apparatus for tracing the source of power system oscillations, including converters and synchronous machines. Belonging to the field of power system transmission and distribution technology, the method involves: reducing the order of the power network and constructing its linearized admittance matrix; establishing port admittance matrices for all power supply equipment, including converters and synchronous machines, under small disturbances; establishing the port external admittance matrix of the synchronous machines, taking into account the impedance embedding of the converters, based on the port admittance models of the power supply equipment and the power network; sequentially calculating the port impedance of each synchronous machine and establishing its damping torque model; and identifying the synchronous machine providing negative damping torque based on the phase characteristics of the damping torque model, which is the low-frequency oscillation source of the system. This application does not require internal converter information, can achieve information isolation between different power sources, is applicable to converters with different control strategies, has clear physical meaning, can provide theoretical guidance for oscillation suppression in large-scale multi-machine power systems, and can be embedded in power system analysis software, making it of significant engineering importance.

Description

Technical Field

[0001] This application relates to a method and apparatus for tracing the source of power system oscillations, which includes a converter and a synchronizing machine, and belongs to the field of power system transmission and distribution technology. Background Technology

[0002] With the rapid development of power electronic devices, new energy power generation technologies based on voltage source converters (VSCs) have been widely applied. Compared to converters based on semi-controlled devices, VSCs use fully controlled IGBTs as core components, offering advantages such as flexible control, no need for grid-supplied commutation voltage, independent control of active and reactive power, and the ability to provide synchronous AC power support for passive networks. They also offer the flexibility to reverse power flow. VSCs are widely used in scenarios such as new energy power grid integration, AC grid interconnection, offshore wind power integration, and DC distribution networks, showing great development potential. Meanwhile, as an important asynchronous power source, the converter can replace synchronous power sources in future power systems.

[0003] With the increasing demand for electricity and growing environmental pressures, the need for clean energy is constantly rising, breaking the dominance of traditional synchronous power supplies and leading to profound changes in the dynamic characteristics of power systems. One significant characteristic is the fundamental alteration in the system's synchronous stability, primarily due to two factors. First, physically, converters lack the rotor structure of synchronous machines. Converter integration results in low inertia, weakening the system's ability to withstand disturbances and making it prone to low-frequency oscillations. Second, unlike synchronous machines, converters typically synchronize with the grid through synchronization units, and their synchronization characteristics are determined by the controller. Therefore, the induction and propagation mechanisms of low-frequency oscillations differ from those of synchronous machine-dominated power grids. The complex control characteristics of converter power supplies present significant obstacles and challenges to tracing the source of low-frequency oscillations in power systems containing both converters and synchronous machines.

[0004] Currently, relevant studies have explored oscillation source tracing for multi-machine power systems containing converters and synchronous machines, such as [Sun P, Yao J, Zhao Y, et al. Stability Assessment and Damping Optimization Control of Multiple Grid-connected Virtual Synchronous Generators[J]. IEEE Trans. Energy Conv., 2021, 36(4): 3555-3567.] and [Zong H, Zhang C and Cai X, et al. Oscillation Propagation Analysis of Hybrid AC / DC Grids With High Penetration Renewables[J]. IEEE Trans. Power Syst., 2022, 37(6): 4761-4772.]. Existing oscillation source tracing methods usually require establishing a linearized model of the entire system that includes detailed dynamic characteristics of the converter. However, new energy equipment manufacturers typically provide grid operators with black-box equipment models where internal information such as parameters and control algorithms is unknown, and only port characteristics are known, in order to protect core trade secrets. For power grid operators, the lack of information regarding the converter section makes it impossible to establish a linearized model of the entire system, rendering the aforementioned methods inapplicable. When internal converter information is unavailable and internal parameters cannot be arbitrarily changed, a method for tracing the source of mechanistic low-frequency oscillations in large-scale power systems containing converters and synchronous machines remains lacking, requiring further in-depth research. Summary of the Invention

[0005] This application aims to overcome the shortcomings of existing technologies and proposes a method and apparatus for tracing the source of power system oscillations, including converters and synchronous machines. This method uses the power network as a medium to connect the converters and synchronous machines by reducing the order of the power network and constructing its linearized admittance matrix. Through the power network, the dynamics of all converters are integrated into the port admittance matrix of the synchronous machine. Based on the mapping relationship between the port admittance matrix of the synchronous machine and the torque coefficient, the synchronous machine providing negative damping torque is identified as the low-frequency oscillation source of the system.

[0006] The technical solution adopted by this application to solve its technical problem is: On the one hand, a method for tracing the source of power system oscillations including converters and synchronous machines is provided, including the following steps: Step 1: Reduce the order of the power network and establish the linearized admittance matrix of the reduced-order power network under small disturbances. Y sStep 2: Establish the port admittance matrix of the power supply device under small disturbances. Y d The power supply equipment includes a converter and a synchronous machine; Step 3: Based on the port admittance matrix of the power supply equipment Y d The linearized admittance matrix of the power network Y s Establish a synchronous machine port external admittance matrix that takes into account converter impedance embedding. Y vg Step 4: Based on the external admittance matrix of the synchronous machine port Y vg Calculate the port impedance of each synchronizer. Z gop And based on port impedance Z gop Establish a damping torque model for the synchronous machine. M T Step 5: Based on the damping torque model M T The phase characteristics are used to identify synchronous machines that provide negative damping torque as the oscillation source of the power system.

[0007] Preferably, step 1, which reduces the order of the power network, includes: retaining all power source nodes and eliminating tie nodes to obtain a reduced-order network containing only power source nodes; and linearizing the differential-algebraic equations describing the network dynamics at the steady-state operating point, transforming them to the frequency domain to obtain the node admittance matrix. The linearized admittance matrix of the line is determined based on the line resistance, inductance, and the system's rated angular frequency.

[0008] Preferably, step 2, establishing the port admittance matrix of the converter under small disturbances, includes: injecting an incremental current into the converter port, measuring the incremental voltage at the port, obtaining the internal impedance of the port, and then obtaining the port admittance; no internal parameter information of the converter is required. The port admittance matrix of the synchronous machine is obtained through analytical impedance modeling.

[0009] Preferably, in step 3, a synchronous machine port external admittance matrix considering the converter impedance embedding is established. Y vg Includes: network admittance matrix Y s The system is divided into blocks based on synchronous machine nodes and converter nodes, and then matrix operations are performed. ,in Y ss Let be the self-admittance matrix of the synchronous machine node. Y cc Let be the self-admittance matrix of the converter node. Y cs and Y scThis is the mutual admittance matrix between the synchronous machine node and the converter node; Y dvp For device port admittance matrix Y d The converter port admittance submatrix extracted from it.

[0010] Preferably, the port impedance of each synchronizer is calculated in step 4. Z gop This includes: for the i-th synchronizer, treating the remaining synchronizers as the remaining units, and... Y vg Re-divide into blocks, using the formula Calculate the port impedance, where Y g0 Let be the self-admittance submatrix of the i-th synchronous machine node. Y gr and Y rg For mutually admittance submatrices, Y grsd For the self-admittance submatrix of the remaining unit nodes, Y dgpr This is the equipment port admittance submatrix for the remaining units.

[0011] Preferably, the damping torque model of the synchronizing machine is established in step 4. M T This includes deriving the torque coefficient based on the port impedance of the synchronous machine and the mathematical model of its electrical control system. M T = Δ P g / Δ δ g Its amplitude and phase respectively characterize the synchronous torque and damping torque components.

[0012] Preferably, identifying the synchronizing machine providing negative damping torque in step 5 specifically involves: when the damping torque model... M T phase φ T When the value is less than 0, the synchronizer is determined to provide negative damping torque and is an oscillation source; traverse all synchronizers and output all... φ T Synchronous machines with a value less than 0 are used as a set of oscillation sources.

[0013] On the other hand, a power system oscillation tracing device containing a converter and a synchronous machine is provided, including: a network order reduction module, a device admittance construction module, an external admittance construction module, an impedance torque calculation module, and an oscillation source identification module, each module corresponding to implement the various steps of the above method.

[0014] One of the above technical solutions has the following advantages or beneficial effects: (1) This application provides a feasible method for tracing the source of low-frequency oscillations in large-scale power systems containing converters and synchronous machines. It can couple the dynamic characteristics of the converter with the synchronous machine through network equations, and identify the synchronous machine unit causing the low-frequency oscillations of the system by traversing the damping torque of the synchronous machine. This method has clear physical significance and can guide the design of future engineering projects.

[0015] (2) The method proposed in this application does not require the internal information of the converter and can be extended to the low-frequency oscillation tracing of power systems with converters (such as grid-following type and grid-building type control) and synchronous machines with different control strategies. It has good economic benefits and universality.

[0016] (3) The analytical method proposed in this application can provide theoretical guidance for the design of low-frequency oscillation suppression strategies for large-scale power systems containing converters and synchronous machines, and has good application potential in actual power grids.

[0017] (4) The method proposed in this application does not require converter manufacturers to provide internal information of power equipment to grid dispatchers, nor does it require grid dispatchers to provide grid operation data to converter manufacturers. Therefore, it can achieve effective information shielding and two-way information protection. This application is simple to implement, highly applicable to various operating conditions, and can be embedded in power system analysis software, which has significant practical engineering implications.

[0018] This application organically integrates multiple techniques, including network order reduction, device port admittance modeling, impedance embedded torque modeling, frequency domain analysis, and damped torque analysis. Network order reduction and the construction of a linearized admittance matrix provide a foundation for analyzing the coupling characteristics between power sources; the device port admittance model eliminates the need for internal parameters, solving the problem of black-box analysis; matrix operations embed the converter impedance into the synchronous machine's external admittance matrix, achieving an equivalent mapping of the converter's dynamic characteristics to the synchronous machine side; finally, the damped torque method is used to identify the oscillation source, transforming the complex problem of tracing the source of multi-machine oscillations into a series of single-machine damped torque analyses. These techniques are not simply superimposed but rather generate a synergistic effect through in-depth exploration of the "network-device" interaction mechanism: even without access to the converter's internal information, the oscillation source can be accurately identified in a large-scale multi-machine system, achieving a unification of bidirectional information shielding and precise oscillation tracing, resulting in unexpected technical effects. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating a power system oscillation tracing method including a converter and a synchronous machine according to an exemplary embodiment; Figure 2This is a schematic diagram of the structure of a power system oscillation tracing device including a converter and a synchronous machine, according to an exemplary embodiment; Figure 3 This is a schematic diagram of a power system topology containing two converters and four synchronous machines, according to an exemplary embodiment. Figure 4 It is aimed at Figure 3 The diagram shows a flowchart of a method for tracing the source of medium- and low-frequency oscillations in a power system. Figure 5 To change the integral constant of the voltage control loop of the grid converter 2 T U The calculated torque coefficients of synchronizer 1 and synchronizer 2 M T ( s The amplitude-frequency and phase-frequency characteristic curves of ( ); Figure 6 To change the integral constant of the voltage control loop of the grid converter 2 T U The calculated torque coefficients of synchronizer 3 and synchronizer 4 M T ( s The amplitude-frequency and phase-frequency characteristic curves of ( ); Figure 7 In order to be in t =10 s and t At 16 s, the integral constant of the voltage control loop is changed respectively. T U The rotor angular frequencies of the four synchronous machines G1-G4 ω 1- ω 4. Time-domain simulation waveform. Detailed Implementation

[0020] To more clearly illustrate the technical features of this application, the following detailed description is provided through specific embodiments and in conjunction with the accompanying drawings.

[0021] like Figure 1 As shown in the embodiment of this application, a power system oscillation source tracing method including a converter and a synchronous machine includes the following steps: Step S1: Reduce the order of the power network and establish the linearized admittance matrix of the reduced-order power network with small perturbations. Y s .

[0022] Specifically, step S1 includes the following steps: All power nodes are retained, and all tie nodes are eliminated to obtain a reduced-order network containing only power nodes; the power nodes include synchronous machine nodes and converter nodes. At the steady-state operating point, the differential-algebraic equations describing the dynamic characteristics of the network are linearized, and the time-domain linearized model is transformed into a frequency-domain linearized model through the Laplace operator to obtain the node admittance matrix. The differential-algebraic equations are established based on Kirchhoff's voltage law and current law.

[0023] For any node in the reduced-order network i With nodes j The linearized admittance matrix of the line between them Y ij Based on line resistance R ,inductance L and the system's rated angular frequency ω 0 is confirmed; the specific expression is: , when i = j hour, Y ij For nodes i Self-admittance matrix Y ii , , N This represents the total number of power supply devices.

[0024] The linearized admittance matrix of the reduced-order power network Y s 2 N ×2 N The square array, in which N The total number of power supply devices is determined by the number of synchronizers. n and number of converters m Decide, N = n + m .

[0025] Step S2: Establish the port admittance matrix of the power supply device under small disturbances. Y d The power supply equipment includes a converter and a synchronous machine.

[0026] Specifically, step S2 includes the following steps: To the i Taiwan converter port injection current increment Δ i vi Measure the corresponding port voltage increment Δ u vi The port impedance of the converter is obtained. Thus, the port admittance is obtained. Y vpi = Z vpi 1 ; The first impedance modeling analytical method is used to obtain the... i Internal impedance of the port of the synchronous machine Z gpi Thus, the port admittance is obtained. Y gpi = Z gpi 1 ; The port admittances of all devices are arranged diagonally to form a device port admittance matrix. Y d :

[0027] in, Y dgp and Y dvp These are the device port admittance sub-matrices for the synchronous machine and the converter, respectively, where diag represents the diagonal matrix. n For the number of synchronizing machines, m This represents the number of converters. The current increment Δ i v Injecting current into small signal nodes, the voltage increment Δ u v This represents the voltage of the corresponding small-signal node.

[0028] The impedance modeling analytical method is based on a detailed mathematical model of the synchronous machine, including the Park equation and the rotor motion equation. dq Derive the frequency domain impedance model in the coordinate system.

[0029] Step S3, based on the port admittance matrix of the power supply device Y d The linearized admittance matrix of the power network Y s Establish a synchronous machine port external admittance matrix that takes into account converter impedance embedding. Y vg .

[0030] Specifically, step S3 includes the following steps: Linearized admittance matrix of reduced-order power network Y s Divide into blocks according to synchronous machine nodes and converter nodes: To obtain the submatrix Y ss , Y cc , Y cs , Y sc,in, Y ss Let be the self-admittance matrix of the synchronous machine node. Y cc Let be the self-admittance matrix of the converter node. Y cs and Y sc This is the mutual admittance matrix between the synchronous machine node and the converter node; Calculate the synchronous machine port external admittance matrix, which includes the impedance embedding of the converter, using the following formula. Y vg : , in, Y dvp For device port admittance matrix Y d The converter port admittance submatrix extracted from it.

[0031] The port admittance submatrix of the converter Y dvp This refers to the converter port admittance matrix constructed in step S2. Y vp .

[0032] The Y vg The dimension is 2 n ×2 n ,in n This represents the number of synchronizers.

[0033] The calculation maps the dynamic characteristics of the converter to the synchronous machine port through network equations, forming the synchronous machine port external admittance that takes into account the influence of the converter.

[0034] Step S4, based on the synchronous machine port external admittance matrix Y vg Calculate the port impedance of each synchronizer. Z gop And based on port impedance Z gop Establish a damping torque model for the synchronous machine. M T .

[0035] Specifically, step S4 includes the following steps: For the i One synchronizer, treating the remaining synchronizers as the remaining units, Y vg Re-divided into blocks as follows: , in, Yg0 For the first i The self-admittance sub-matrix of the synchronous machine node, Y grsd For the self-admittance submatrix of the remaining unit nodes, Y gr and Y rg For the first i The mutual admittance submatrix between the synchronous machine node and the remaining unit nodes; Define the equipment port admittance submatrix for the remaining units. Y dgpr : , Y dgpr It is a diagonal matrix formed by the port admittances of each synchronous machine in the remaining units; The first is calculated using the following formula. i Port impedance of the synchronous machine Z gopi : ; Repeat the above steps for each synchronizer to obtain the port impedance of each synchronizer. Z gopi And according to the port impedance of the synchronizer Z gop The mathematical models of the synchronous machine's electrical and control systems are derived. M T =Δ P g / Δ δ g Thus, the damping torque model of each synchronizer is obtained. M Ti , where Δ P g For the increase in active power of the synchronous machine, Δ δ g This is the increment of the work angle.

[0036] The damping torque model M T Let be a complex frequency domain function, and its amplitude be | M T | Characterizes the synchronous torque component, phase φ T Characterizes the damping torque component.

[0037] Step S5, based on the damping torque model M T The phase characteristics are used to identify synchronous machines that provide negative damping torque as the oscillation source of the power system.

[0038] Specifically, step S5 includes the following steps: For each synchronous machine, according to its damping torque model M T phase φ T Make a judgment, if φ T If the value is less than 0, then the synchronous machine provides negative damping torque, which is the oscillation source.

[0039] Traverse all synchronizers and all φ T Synchronous machines with a value of <0 serve as a set of low-frequency oscillation sources for the system; Based on the identified oscillation source, output its corresponding oscillation frequency and damping characteristic information.

[0040] The phase φ T The evaluation is conducted at a specific oscillation frequency, which is determined through analysis. M T The frequency corresponding to the peak value of the amplitude-frequency characteristic is determined.

[0041] like Figure 2 As shown in the figure, an embodiment of this application provides a power system oscillation tracing device including a converter and a synchronous machine, comprising: The network order reduction module is used to reduce the order of power networks and establish the linearized admittance matrix of the power network with small disturbances. Y s ; The device admittance construction module is used to establish the port admittance matrix of power supply devices under small disturbances. Y d The power supply equipment includes a converter and a synchronous machine; External admittance building module, used to construct external admittance based on the port admittance matrix of the power supply device. Y d The linearized admittance matrix of the power network Y s Establish a synchronous machine port external admittance matrix that takes into account converter impedance embedding. Y vg ; Impedance torque calculation module, used for calculating the external admittance matrix of the synchronous machine port. Y vg Calculate the port impedance of each synchronizer. Z gop And based on port impedance Z gop Establish a damping torque model for the synchronous machine. M T ; The oscillation source identification module is used to identify the oscillation source based on the damping torque model.M T The phase characteristics are used to identify synchronous machines that provide negative damping torque as the oscillation source of the power system.

[0042] The network reduction module is specifically used to: retain all power nodes, eliminate interconnection nodes, and obtain a reduced-order network containing only power nodes; and linearize the differential-algebraic equations describing the network dynamics at the steady-state operating point, transforming them to the frequency domain to obtain the node admittance matrix.

[0043] The equipment admittance construction module includes a converter admittance submodule and a synchronous machine admittance submodule. The converter admittance submodule obtains the port internal impedance by injecting current increments into the converter port and measuring voltage increments, thereby obtaining the port admittance. The synchronous machine admittance submodule obtains the port admittance through analytical impedance modeling.

[0044] The external admittance construction module is specifically used to construct the network admittance matrix. Y s The system is divided into blocks based on synchronous machine nodes and converter nodes, and then matrix operations are performed. The external admittance matrix of the synchronous machine port is obtained.

[0045] The impedance torque calculation module is specifically used for: for the first i One synchronizer, treating the remaining synchronizers as the remaining units, Y vg Re-divide into blocks, using the formula Calculate the port impedance; and derive the damping torque model based on the port impedance of the synchronous machine and the mathematical model of the electrical control system of the synchronous machine. M T .

[0046] The oscillation source identification module is specifically used to determine the damping torque model. M T phase φ T If the value is less than 0, then the synchronizer is determined to be an oscillation source; and all synchronizers are traversed to output the set of oscillation sources.

[0047] The following is based on Figure 3 Taking a power system containing two converters and four synchronous machines as an example, this paper will explain in detail the specific process of oscillation source tracing in a power system containing converters and synchronous machines.

[0048] like Figure 3 As shown, this system is a two-zone interconnected system, with synchronous machines G1 and G2 in zone 1 and synchronous machines G3 and G4 in zone 2. Two converters are connected to the grid at nodes 12 and 13 respectively. Converter 1 uses grid-connected control, and converter 2 uses grid-following control. The main system parameters are shown in Table 1.

[0049] Table 1 Main System Parameters

[0050] like Figure 4 As shown, the specific process of oscillation source tracing in a power system containing converters and synchronous machines in this application is as follows.

[0051] (1) For power systems containing converters and synchronous machines, the power network is reduced in order, and a linearized admittance matrix of the reduced-order power network with small disturbances is established. Y s .

[0052] Consider a containing N Table of equipment k Node power systems, including n Taiwan Synchronous Machine m Taiwan converter ( N = n + m and k > N First, the network order is reduced according to Kirchhoff's voltage law, retaining the power nodes and eliminating the remaining interconnected nodes. The number of nodes in the system then becomes... N After order reduction, at the steady-state operating point x Linearizing the system of differential-algebraic equations describing the dynamic characteristics of the system at position 0 yields a linearized model of the entire system, which can then be used to apply the Laplace operator. s =d / d t Transform the time-domain linearized model into a frequency-domain linearized model.

[0053] For the reduced-order power network, nodes i With nodes j Linearized admittance matrix of the line Y ij for: , in R , L Indicates line resistance and inductance; ω 0 represents the system's rated angular frequency; the subscript "-1" indicates matrix inversion. i = j Time as a node i Self-admittance matrix Y ii .

[0054] Furthermore, the linearized admittance matrix of the reduced-order power network is obtained. Y s : , in, Y s 2 N ×2 N A square formation.

[0055] (2) For power systems containing converters and synchronous machines, establish the port admittance matrix of power supply equipment under small disturbances. Y d Including the port admittance of the converter Y v and the port admittance of the synchronous machine Y g .

[0056] In the i Taiwan (1≤ i ≤ m Incremental current injected into the converter port Δ i v Measure the voltage increment Δ at the converter port at this time. u v Then the first i Port impedance model of Taiwan converter Z vpi for: , No. i Taiwan (1≤ i ≤ n Synchronous machine port impedance model Z gpi The impedance modeling method is used to obtain the impedance admittance matrix. The detailed derivation can be found in the reference [Xue Yicheng, Zhang Zheren, Xu Zheng, et al. Analysis of the influence of grid-type converters on low-frequency oscillations in AC systems and damping control [J]. Automation of Electric Power Systems, 2023, 47(16): 103-113.], or it can be obtained through port frequency scanning. After obtaining the port internal impedances of all devices, the port admittance matrix of the entire system is generated. Y d : , Wherein, submatrix Y dgp and Y dvp These are the device port admittance sub-matrices for the synchronous machine and the converter, respectively, with diag representing a diagonal matrix.

[0057] (3) Based on the port admittance model of power supply equipment and power network, establish the synchronous machine port external admittance matrix considering the impedance embedding of converter. Y vg .

[0058] Will Ys The blocks are as follows: , Wherein, submatrix Y ss Let be the self-admittance matrix of the synchronous machine node. Y cc Let be the self-admittance matrix of the converter node. Y cs and Y sc This is the mutual admittance matrix between the synchronous machine node and the converter node. The synchronous machine port external admittance matrix embedded with the converter impedance is calculated using the following formula: Y vg : .

[0059] (4) For a power system containing converters and synchronous machines, the port impedance of each synchronous machine is calculated sequentially. Z gop And establish a damping torque model for the synchronous machine. M T .according to M T Identify the synchronizer that provides negative damping torque, which is the dominant factor inducing low-frequency oscillations in the system, i.e., the source of low-frequency oscillations.

[0060] In establishing the first i Taiwan (1≤ i ≤ n When modeling the damping torque of a synchronous machine, define the following except for the first... i The set of all synchronizers except for the first synchronizer is the th synchronizer. i The remaining units of the synchronous machine. Then the equipment port admittance submatrix of the remaining units. Y dgpr for: , Based on this Y vg The blocks are reorganized as follows: , Wherein, submatrix Y g0 For the first i The self-admittance matrix of the synchronous machine node, Y grsd The self-admittance matrix of the remaining unit nodes. Y gr and Y rg For the first i The mutual admittance matrix between the synchronous machine node and the remaining unit nodes. According to the following formula... iPort impedance of the synchronous machine Z gopi : , according to Z gopi Based on the mathematical models of the synchronous machine's electrical and control systems, a synchronous machine damping torque model considering the embedded impedance of the converter is derived. M T : , in, P g , δ g These represent the active power and power angle of the synchronous machine, respectively. M T | and φ T They are respectively M T The amplitude and phase, Δ T s Δ T d These are the synchronous torque and damping torque components, respectively. When φ T When <0, Δ T d If the value is negative, the system is at risk of low-frequency oscillation.

[0061] In this implementation, the power system containing converters and synchronous machines is a two-zone interconnected system. Synchronous machines 1 (G1) and 2 (G2) are in zone 1, and synchronous machines 3 (G3) and 4 (G4) are in zone 2. The two converters are connected to the grid at nodes 12 and 13 respectively. Converter 1 uses grid-connected control, and converter 2 uses grid-following control. The converter model uses a modular multilevel converter (MMC). Under steady-state operation, the converters operate as inverter stations. Assume the DC voltage of the converters... U dc It is controlled by the converter on the opposite side and is a given value. Under steady state, the converter outputs 200MW of active power and 0MW of reactive power.

[0062] Specifically, let the dominant frequency be... f d Substitute s =j2π f d The reduced-order network is calculated according to step (1). Y s The transfer function can be obtained by using steps (2) and (3). Y d andY vg The analytical solution of each element is obtained, and then the solution is obtained according to step (4). Z gop Then, the torque coefficient of the synchronous machine can be calculated. M T The analytical solution. According to step (5), after traversing all the synchronizers, find the solution. φ T All synchronizers with a value less than 0 act as low-frequency oscillation sources for the system. Since there are four synchronizers in this example, the above calculation process needs to be executed four times.

[0063] For converter 1 using network control, a frequency range of 0.1 Hz or less is selected in the low-frequency band. f d ≤10 Hz, change the integral constant of the voltage control loop. T U Synchronizers G1 and G2 M T ( s The amplitude-frequency and phase-frequency characteristic curves of () are shown in the figure. Figure 5 As shown. Synchronizers G3 and G4 M T ( s The amplitude-frequency and phase-frequency characteristic curves of () are shown in the figure. Figure 6 As shown. The physical quantities with subscripts 1-4 represent the corresponding physical quantities G1-G4, respectively. For example... Figure 5 As shown, the peak torque coefficient of synchronous machine 1 is | M T1 It appears around 0.9Hz. With f d The increase, φ T1 The increased lag indicates that M T1 The accompanying negative damping phenomenon intensifies, increasing the risk of low-frequency oscillations in the system. With... T U The increase, | M T1 The peak value of | decreases, and | M T1 |Peak corresponding f d Decrease. Analysis results for synchronizer 1 show that, as... T U With the increase of , the damping in the low-frequency band near 0.9Hz is enhanced and the oscillation frequency is reduced.

[0064] Figure 5 This indicates that, unlike synchronous machine 1, the peak torque coefficient of synchronous machine 2 is | M T2The peak value appeared around 0.5 Hz, but no peak value was observed in the amplitude-frequency curve around 0.9 Hz. Furthermore, a peak value appeared around 0.5 Hz. φ T2 The condition is <0. This phenomenon indicates that the converter 1 parameter is... T U Under the changed conditions, both Synchronous Machine 1 and Synchronous Machine 2 may cause low-frequency oscillations, but the low-frequency oscillation frequencies caused by the two are different. Therefore, Synchronous Machine 1 and Synchronous Machine 2 are not the oscillation sources corresponding to the same low-frequency oscillation mode.

[0065] exist t =10 s time T U Increased from 0.02 to 0.05, and in t At 17.5 s, the frequency decreases again to 0.02, and the angular frequency of synchronizers G1-G4... ω 1- ω The simulation results of 4 are as follows Figure 7 As shown. ω For example, 1 Figure 7 As shown, when T U When the value is increased to 0.05, the system exhibits oscillation and instability. Furthermore, the oscillation frequency is extracted from the simulation results, and the results show that when... T U When increased to 0.05, the oscillation frequency... f d =0.9Hz. Based on theoretical analysis and simulation results, the low-frequency oscillation source in the system is synchronous machine 1, because it provides a negative damping torque component at 0.9Hz. Although theoretical analysis results show that synchronous machines 2, 3, and 4 have positive damping torques near 0.9Hz, Figure 7 Simulation results show that ω 2- ω A 0.9 Hz oscillation component will also be observed in 4. This is because the low-frequency oscillation is caused by the synchronous machine 1, and the oscillation will eventually propagate to all electrical quantities in the entire system.

[0066] In summary, the above analysis results demonstrate the accuracy of the results obtained by the proposed method for tracing the source of low-frequency oscillations in power systems containing converters and synchronous machines. It can effectively identify the synchronous machine causing the oscillation based on the characteristic oscillation frequency, and thereby determine the source of low-frequency oscillations in the system.

[0067] This application does not require internal converter information, can achieve information shielding, is applicable to converters with different control strategies, has clear physical meaning, can provide theoretical guidance for oscillation suppression in multi-machine systems, can be embedded in power system analysis software, and has significant engineering significance.

[0068] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application and not to limit them. Although this application has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation methods of this application. Any modifications or equivalent substitutions that do not depart from the spirit and scope of this application should be covered within the protection scope of the claims of this application.

Claims

1. A method for tracing the source of power system oscillations, comprising a converter and a synchronous machine, characterized in that, Includes the following steps: Step S1: Reduce the order of the power network and establish the linearized admittance matrix of the power network with reduced order under small disturbances; Step S2: Establish the port admittance matrix of the power supply equipment under small disturbances, wherein the power supply equipment includes a converter and a synchronous machine; Step S3: Based on the port admittance matrix of the power supply equipment and the linearized admittance matrix of the power network, establish the synchronous machine port external admittance matrix taking into account the impedance embedding of the converter. Step S4: Based on the port admittance matrix of the synchronous machine, calculate the port impedance of each synchronous machine, and establish the damping torque model of the synchronous machine based on the port impedance. Step S5: Based on the phase characteristics of the damping torque model, identify the synchronous machine that provides negative damping torque as the oscillation source of the power system.

2. The power system oscillation source tracing method including converter and synchronous machine according to claim 1, characterized in that, Step S1 includes the following steps: All power nodes are retained, and all tie nodes are eliminated to obtain a reduced-order network containing only power nodes; the power nodes include synchronous machine nodes and converter nodes. At the steady-state operating point, the system of differential-algebraic equations describing the dynamic characteristics of the network is linearized, and the time-domain linearized model is transformed into a frequency-domain linearized model using the Laplace operator to obtain the node admittance matrix.

3. The power system oscillation source tracing method including converter and synchronous machine according to claim 2, characterized in that, The differential-algebraic equations are based on Kirchhoff's voltage law and current law.

4. The power system oscillation source tracing method including converter and synchronous machine according to claim 1, characterized in that, Step S2 includes the following steps: To the i Taiwan converter port injection current increment Δ i vi Measure the corresponding port voltage increment Δ u vi The port impedance of the converter is obtained. Thus, the port admittance is obtained. Y vpi = Z vpi 1 The superscript "-1" indicates matrix inversion. The first impedance modeling analytical method is used to obtain the... i Internal impedance of the port of the synchronous machine Z gpi Thus, the port admittance is obtained. Y gpi = Z gpi 1 ; The port admittances of all devices are arranged diagonally to form a device port admittance matrix. Y d : in, Y dgp and Y dvp These are the device port admittance sub-matrices for the synchronous machine and the converter, respectively, where diag represents the diagonal matrix. n This refers to the number of synchronizing machines. m This represents the number of converters.

5. The power system oscillation source tracing method including converter and synchronous machine according to claim 4, characterized in that, The impedance modeling analytical method is based on a detailed mathematical model of the synchronous machine, including the Park equation and the rotor motion equation. dq Derive the frequency domain impedance model in the coordinate system.

6. The power system oscillation source tracing method including converter and synchronous machine according to claim 1, characterized in that, Step S3 includes the following steps: Linearized admittance matrix of reduced-order power network Y s Divide into blocks according to synchronous machine nodes and converter nodes: To obtain the submatrix Y ss , Y cc , Y cs , Y sc ,in, Y ss Let be the self-admittance matrix of the synchronous machine node. Y cc Let be the self-admittance matrix of the converter node. Y cs and Y sc This is the mutual admittance matrix between the synchronous machine node and the converter node; Calculate the synchronous machine port external admittance matrix, which includes the impedance embedding of the converter, using the following formula. Y vg : ， in, Y dvp For device port admittance matrix Y d The converter port admittance submatrix extracted from it.

7. The power system oscillation source tracing method including converter and synchronous machine according to claim 1, characterized in that, Step S4 includes the following steps: For the i One synchronizer, treating the remaining synchronizers as the remaining units, Y vg Re-divided into blocks as follows: ， in, Y g0 For the first i The self-admittance sub-matrix of the synchronous machine node, Y grsd For the self-admittance submatrix of the remaining unit nodes, Y gr and Y rg For the first i The mutual admittance submatrix between the synchronous machine node and the remaining unit nodes; Define the equipment port admittance submatrix for the remaining units. Y dgpr : ， Y dgpr It is a diagonal matrix formed by the port admittances of each synchronous machine in the remaining units; The first is calculated using the following formula. i Port impedance of the synchronous machine Z gopi : ； Repeat the above steps for each synchronizer to obtain the port impedance of each synchronizer. Z gopi And according to the port impedance of the synchronizer Z gop The mathematical models of the synchronous machine's electrical and control systems are derived. M T =Δ P g / Δ δ g Thus, the damping torque model of each synchronizer is obtained. M Ti , where Δ P g Δ represents the increase in active power of the synchronous machine. δ g This is the increment of the work angle.

8. The power system oscillation source tracing method including converter and synchronous machine according to any one of claims 1-7, characterized in that, Step S5 includes the following steps: For each synchronous machine, according to its damping torque model M T phase φ T Make a judgment, if φ T If the value is less than 0, the synchronous machine provides negative damping torque and serves as an oscillation source. Traverse all synchronizers and all φ T Synchronous machines with a value of <0 serve as a set of low-frequency oscillation sources for the system; Based on the identified oscillation source, output its corresponding oscillation frequency and damping characteristic information.

9. The power system oscillation source tracing method including converter and synchronous machine according to claim 8, characterized in that, The phase φ T The evaluation is conducted at a specific oscillation frequency, which is determined through analysis. M T The frequency corresponding to the peak value of the amplitude-frequency characteristic is determined.

10. A power system oscillation tracing device comprising a converter and a synchronous machine, characterized in that, include: The network order reduction module is used to reduce the order of the power network and establish the frequency domain linearized admittance matrix of the power network with small disturbances. The equipment admittance construction module is used to establish the port admittance matrix of the power supply equipment under small disturbances, wherein the power supply equipment includes converters and synchronous machines; The external admittance construction module is used to establish a synchronous machine port external admittance matrix that takes into account the converter impedance embedding, based on the port admittance matrix of the power supply equipment and the linearized admittance matrix of the power network. The impedance torque calculation module is used to calculate the port impedance of each synchronous machine based on the port admittance matrix of the synchronous machine, and to establish the damping torque model of the synchronous machine based on the port impedance. The oscillation source identification module is used to identify the synchronous machine that provides negative damping torque as the oscillation source of the power system based on the phase characteristics of the damping torque model.

Images