A frequency response analysis method and system for multi-inertia center power system

Abstract

The present invention discloses a frequency response analysis method and system for a multi-inertia center power system. The method comprises: establishing a generator model, a network model, and a fault disturbance model in a frequency dynamic model of an inertia response phase based on a modal analysis method in vibration dynamics; substituting the network model and the fault disturbance model into the generator model to obtain an overall vibration dynamics model; and solving and obtaining a time domain expression of the frequency dynamic process of the system inertia response phase after a fault at any position based on the overall vibration dynamics model. Thus, a solution method for the dynamic process of the inertia response phase of each rotor after a power disturbance can be obtained, and the frequency dynamic characteristics of all generator rotors in the system can be taken into account. The decomposition relationship of a fault at any position in the modal principal coordinates can be solved, and then the frequency dynamic process of the system inertia response phase after a fault at any position can be solved, which can more accurately reflect the frequency characteristics of different nodes in the system.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems, and more particularly, to a method and system for analyzing frequency response of a multi-inertia center power system. Background Art

[0002] The vigorous development of renewable energy and the integration of a high proportion of renewable energy into the grid present a series of challenges for the power system. Traditional power system operation and control methods utilize the regulation capabilities of conventional synchronous generators to meet random load fluctuations. However, renewable energy generation exhibits significant intermittent, fluctuating, and random characteristics, placing new demands on the power system's balancing capabilities. Furthermore, with the increasing number and scale of UHVDC projects for long-distance power transmission, the magnitude of disturbance power is also increasing, exacerbating the frequency stability issues facing the power system.

[0003] Existing model-based analysis methods are still limited to analyzing a single center of inertia or only provide analysis methods for a few centers of inertia. This results in poor analysis accuracy for the frequency characteristics of the inertia response phase. Measurement-based methods are only suitable for monitoring online operating conditions and cannot guide system planning or advance scheduling of operating modes. It is necessary to develop a model-based analysis method applicable to multiple centers of inertia.

[0004] The frequency dynamics of a power system during the inertia response phase are the result of the mutual vibrations of the rotors of the various generators within the system after a power disturbance. Methods for reflecting the frequency dynamics of multiple inertia centers during this phase are still incomplete. This is essential for assessing the system's effective inertia, specifically the frequency stability of the system during the inertia response phase after large disturbances such as DC blocking. Therefore, it is necessary to propose an analytical method for the frequency response characteristics of a power system with multiple inertia centers. Summary of the Invention

[0005] According to the present invention, a method and system for analyzing the frequency response of a multi-inertia center power system are provided to solve the technical problems that the process of mutual vibration of the rotors of the generators in the power system after being subjected to power disturbances during the inertia response phase is unclear, and the method for reflecting the dynamic process of the frequency of the multi-inertia center of the system during the inertia response phase is still imperfect.

[0006] According to a first aspect of the present invention, a method for analyzing frequency response of a multi-inertia center power system is provided, comprising:

[0007] Based on the modal analysis method in vibration dynamics, the generator model, network model and fault disturbance model in the frequency dynamic model of the inertia response stage are established;

[0008] Substituting the network model and the fault disturbance model into the generator model to obtain an overall vibration dynamics model;

[0009] Based on the overall vibration dynamics model, the time domain expression of the frequency dynamic process of the system inertia response stage after a fault at any position is obtained.

[0010] According to another aspect of the present invention, a multi-inertia center power system frequency response analysis system is provided, comprising:

[0011] Establish a model module for establishing the generator model, network model, and fault disturbance model in the frequency dynamic model of the inertia response stage based on the modal analysis method in vibration dynamics;

[0012] Obtaining an overall vibration dynamics model module, used for substituting the network model and the fault disturbance model into the generator model to obtain an overall vibration dynamics model;

[0013] A frequency dynamic process module is used to obtain a time domain expression of the frequency dynamic process of the system inertia response stage after a fault at any position based on the overall vibration dynamic model.

[0014] This method can be used to determine the dynamic process of the inertia response phase of each rotor after a power disturbance, taking into account the frequency dynamic characteristics of all generator rotors in the system. The decomposition relationship of a fault at any location in the modal principal coordinates can be determined, and the frequency dynamic process of the system inertia response phase after a fault at any location can be determined, which can more accurately reflect the frequency characteristics of different nodes in the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] A more complete understanding of exemplary embodiments of the present invention may be obtained by referring to the following drawings:

[0016] Figure 1 Schematic diagram of a flow chart of a frequency response analysis method for a multi-inertia center power system according to this embodiment;

[0017] Figure 2 Schematic diagram of the frequency dynamic model of the inertia response stage according to this embodiment;

[0018] Figure 3 Schematic diagram of a frequency response analysis system for a multi-inertia center power system according to this embodiment. DETAILED DESCRIPTION

[0019] Exemplary embodiments of the present invention will now be described with reference to the accompanying drawings. However, the present invention may be embodied in many different forms and is not limited to the embodiments described herein. These embodiments are provided to provide a thorough and complete disclosure of the present invention and to fully convey the scope of the present invention to those skilled in the art. The terminology used in the exemplary embodiments shown in the accompanying drawings is not intended to limit the present invention. In the accompanying drawings, identical elements are denoted by the same reference numerals.

[0020] Unless otherwise specified, the terms used herein (including technical terms) have the meanings commonly understood by those skilled in the art. In addition, it is understood that terms defined in commonly used dictionaries should be understood to have the same meanings as those in the context of the relevant fields, and should not be understood as idealized or overly formal meanings.

[0021] According to a first aspect of the present invention, a multi-inertia center power system frequency response analysis method 100 is provided, referring to Figure 1 As shown, the method 100 includes:

[0022] S101: Based on the modal analysis method in vibration dynamics, a generator model, a network model, and a fault disturbance model are established in the frequency dynamic model of the inertia response stage;

[0023] S102: Substituting the network model and the fault disturbance model into the generator model to obtain an overall vibration dynamics model;

[0024] S103: Based on the overall vibration dynamics model, a time domain expression of the frequency dynamic process of the system inertia response phase after a fault at any position is obtained;

[0025] Specifically, the present invention models the frequency dynamics of the inertia response phase based on the modal analysis method in vibration dynamics, obtains the time domain expression solution method of each vibration mode through modal decoupling, and further obtains the time domain expression of each rotor frequency through the modal superposition method, thereby obtaining the solution method of the dynamic process of the inertia response phase of each rotor after power disturbance; further, combined with the concepts of full-step power coefficient, the decomposition relationship of the fault at any position in the modal principal coordinates can be solved, and then the frequency dynamic process of the system inertia response phase after the fault at any position can be solved. Figure 2 As shown, specifically:

[0026] Frequency dynamic modeling of inertia response stage

[0027] The frequency dynamic model of the inertia response stage proposed in the present invention includes four parts: a generator model, a network model, a fault disturbance model and an overall vibration dynamic model.

[0028] A. Generator Model

[0029] The present invention adopts the following assumptions when performing analytical analysis of the frequency characteristics of the large power grid:

[0030] ——The generator adopts the classic second-order model;

[0031] - Ignore the resistance of network components;

[0032] —The load is represented by a constant impedance or admittance;

[0033] ——The disturbance causes a small change in the system state variables, and a linear analysis method near the equilibrium point can be used.

[0034] The frequency characteristics of the power system are modeled under the above assumptions.

[0035] The generator model is described by a set of differential algebraic equations as follows. The differential part represents the rotor motion of the generator, and the algebraic part describes the electrical interaction between the generators:

[0036]

[0037] Among them, Δω, Δδ, ΔP m ,ΔP g ,T J , D represents the column vector composed of the rotor speed, rotor phase angle, mechanical power change, electromagnetic power change, damping coefficient and inertia time constant of each generator set.

[0038] According to the above assumptions, ΔP m =0.

[0039] B. Network Model

[0040] For a power network with n generators and m bus nodes, based on the above assumptions, the DC power flow equation can be written as follows:

[0041]

[0042] where ΔP l , Δθ are column vectors composed of the power change and phase angle change of each load node. gg is a diagonal matrix composed of the d-axis transient reactance xdi" (i = 1, 2, ..., n) of each generator, that is, B gg =diag(xd1”,xd2”,…xdn”).

[0043] Bgl represents the relationship and electrical distance between the generator node and the bus node.

[0044] B gl =Bgg ·A

[0045] Where A is an n*m matrix, and for each element Aij in A, (i=1,2,…,n; j=1,2,…,m), its value is as follows:

[0046]

[0047] B ll is the node admittance matrix that only retains the imaginary part.

[0048] According to the DC power flow equation, the busbar node phase angle change can be expressed as:

[0049] Δθ=B ll -1 ΔP L -B ll -1 B gl T Δδ

[0050] B gl Substituting this expression into the DC power flow equation, the common load nodes can be eliminated, leaving only the generator nodes. At this point, the change in the generator electromagnetic power can be expressed as:

[0051] ΔP g =(B gg -B gl B ll -1 B gl T )Δδ+B gl B ll -1 ΔP L

[0052] make

[0053]

[0054] B K B is the elastic matrix representing the interaction between the generator rotors. F It is the distribution coefficient matrix of the system disturbance power distributed to each generator rotor, that is, the full-step power coefficient.

[0055] C. Fault Disturbance Model

[0056] Assume that the power system involved in this invention transmits power through a DC transmission project (if it is injected power, just negate the sign). Define the step function u(t) and the rectangular pulse function p(t, tC) as follows:

[0057]

[0058] p(t,t C )=u(t)-u(tt C )

[0059] For DC commutation failure fault. During commutation failure, the system injects surplus power disturbance ΔP at node h DC After the commutation failure is restored, the surplus power disappears, and each commutation failure lasts for tC. Therefore, for the DC commutation failure fault disturbance, ΔP L Elements in ΔP Li (i=1,2,…,n) can be described as:

[0060]

[0061] For a DC blocking fault at node h, when the fault occurs, the system is injected with surplus power disturbance ΔP at node h. DC , the system safety control measures take action after the tc delay, cutting off the output of the generator set with the same power. The process is similar to the commutation failure process, except that the generator set cut off by the safety control action after the DC blocking fault is not necessarily located at node h. Assume that the power of the generator set cut off by the safety control system is represented by the vector ΔP C , then ΔP L Elements in ΔP Li (i=1,2,…,n) can be described as:

[0062]

[0063] D. Global Vibration Dynamics Model

[0064] Substituting the network model and fault disturbance model into the generator model, we can obtain:

[0065]

[0066] Through transformation, the above formula can be rewritten as the motion equation with the phase angle of each generator rotor as the state quantity and each rotor performing relative oscillation motion:

[0067]

[0068] Modal principal coordinate decomposition method for faults at arbitrary locations

[0069] Based on the above assumptions, the vibration system is a linear system. Therefore, according to vibration dynamics theory, under external excitation, the oscillation motion of each rotor can be regarded as the superposition of a series of attenuated sinusoidal oscillation processes. The specific oscillation form is related to the system's inherent oscillation mode and the form of excitation.

[0070] The modal analysis method can be used to analyze the oscillation motion process.

[0071] First, solve the natural oscillation frequency Ω, that is, solve the following equation:

[0072] |T J Ω 2 -B|=0

[0073] Where, Ω=[Ω1,Ω2,…,Ω n ], let Ω1,Ω2,…,Ω n Arrange in order from smallest to largest.

[0074] Considering T J is a positive definite matrix, so the above problem can be converted into matrix BT J -1 The eigenvalue solving problem of .

[0075] Further by solving each The eigenvector Φ (i) ,Right now

[0076]

[0077] Its eigenvector Φ (i) It characterizes the vibration mode corresponding to the natural oscillation frequency, that is, the relative ratio of the amplitudes of each rotor phase angle when each rotor phase angle vibrates at the i-th natural frequency.

[0078] Known T J and B are orthogonal, that is:

[0079]

[0080] Using this property, the non-diagonal matrix B can be converted into a diagonal matrix B P , T J and D still maintain their original diagonal matrix form after transformation.

[0081]

[0082] Will Substituting in, we get:

[0083]

[0084] Through coordinate transformation, the rotor motion process can be converted into an n-dimensional space based on n vibration modes. In this space, the motion process of each rotor is the superposition of the vibration processes under each vibration mode. In this way, the decoupling of the rotor oscillation process can be achieved, that is:

[0085]

[0086] Perform Laplace transform on the above equation and convert the above time domain expression into the time domain for analysis and solution.

[0087] M p s 2 x p (s)+D p sx p (s)+K p x p (s)=F P (s)

[0088] The expressions of rotor phase angle and speed corresponding to the principal coordinates are:

[0089]

[0090] Under a given fault disturbance form, the inverse Laplace transform of the above equation can be performed to obtain the principal coordinate time domain expression corresponding to the oscillation mode:

[0091]

[0092] Afterwards, the principal coordinates are transformed back to the original coordinates to obtain the time domain expression of each rotor phase angle and frequency.

[0093]

[0094] This method can be used to determine the dynamic process of the inertia response phase of each rotor after a power disturbance, taking into account the frequency dynamic characteristics of all generator rotors in the system. The decomposition relationship of a fault at any location in the modal principal coordinates can be determined, and the frequency dynamic process of the system inertia response phase after a fault at any location can be determined, which can more accurately reflect the frequency characteristics of different nodes in the system.

[0095] Optionally, a generator model is established based on a modal analysis method in vibration mechanics, including:

[0096] A generator model is established to model the frequency characteristics of the power system. The generator model is represented by a set of differential algebraic equations. The differential part represents the rotor motion process of the generator, and the algebraic part represents the electrical interaction between generators:

[0097]

[0098] Among them, Δω, Δδ, ΔP m ,ΔP g ,T J , D are column vectors composed of the rotor speed, rotor phase angle, mechanical power variation, electromagnetic power variation, damping coefficient and inertia time constant of each generator set, ΔP m =0.

[0099] Optionally, a network model is established based on a modal analysis method in vibration dynamics, including:

[0100] For a power network with n generators and m bus nodes, the DC power flow equation is:

[0101]

[0102] Where ΔP l , Δθ are column vectors composed of power variation and phase angle variation of each load node, B gg is the d-axis transient reactance x of each generator di ″, i = 1, 2, ..., n composed of a diagonal matrix, namely B gg =diag,x d1 ″,x d2 ″,…xdn″;B gl is the relationship and electrical distance between the generator node and the busbar node;

[0103] B gl =B gg ·A

[0104] Where A is an n*m matrix, for each element A ij , i=1,2,…,n;j=1,2,…,m, its value is:

[0105]

[0106] B ll is the node admittance matrix that only retains the imaginary part;

[0107] According to the DC power flow equation, the phase angle change of the busbar node is:

[0108] Δθ=B ll -1 ΔP L -B ll -1 B gl T Δδ

[0109] B gl Substituting the expression into the DC power flow equation, eliminating the common load nodes and retaining only the generator nodes, the change in the generator electromagnetic power is:

[0110] ΔP g =(B gg -B gl B ll -1 B gl T )Δδ+Bgl B ll -1 ΔP L

[0111] make

[0112]

[0113] B K is the elastic matrix of the interaction between the generator rotors, B F It is the distribution coefficient matrix of the system disturbance power distributed to each generator rotor, that is, the full-step power coefficient.

[0114] Optionally, a fault disturbance model is established based on a modal analysis method in vibration dynamics, including:

[0115] Establish a fault disturbance model for the power system that transmits power through a DC transmission project, define the step function u(t), the rectangular pulse function p(t, t C ):

[0116]

[0117] p(t,t C )=u(t)-u(tt C )

[0118] During the commutation failure period of the DC commutation failure fault, the system injects a surplus power disturbance ΔP at node h. DC After the commutation failure is restored, the surplus power disappears. The duration of each commutation failure is t C Therefore, for the DC commutation failure fault disturbance, ΔP L Elements in ΔP Li (i=1,2,…,n) is:

[0119]

[0120] For a DC blocking fault at node h, when the fault occurs, the system is injected with surplus power disturbance ΔP at node h. DC , the system security measures are c After a delay, the generator set with the same power is cut off. The process is similar to the commutation failure process, except that the generator set cut off by the safety control action after the DC blocking fault is not necessarily located at the node h. Assume that the power of the generator set cut off by the safety control system is represented by the vector ΔP C , then ΔP L Elements in ΔP Li (i=1,2,…,n) is:

[0121]

[0122] Optionally, substituting the network model and the fault disturbance model into the generator model to obtain an overall vibration dynamics model includes:

[0123] Substituting the network model and fault disturbance model into the generator model, the overall vibration dynamics model can be obtained:

[0124]

[0125] Through transformation, the above equation can be rewritten as the motion equation with the phase angle of each generator rotor as the state quantity and each rotor performing relative oscillation motion:

[0126]

[0127] Optionally, based on the fault disturbance model, solving and obtaining a frequency dynamic process of the system inertia response phase after a fault at any position includes:

[0128] Under external excitation, the oscillation motion process of each rotor is the superposition of a series of attenuated sinusoidal oscillation processes. The specific oscillation form is related to the system's own inherent oscillation mode and the form of excitation. In the oscillation motion process, the modal analysis method is used for analytical analysis:

[0129] To solve the natural oscillation frequency Ω, we need to solve the following equation:

[0130] |T J Ω 2 -B|=0

[0131] Where, Ω=[Ω1,Ω2,…,Ω n ], let Ω1,Ω2,…,Ω n To arrange in order from smallest to largest;

[0132] Convert to matrix BT J -1 The eigenvalue of is solved by solving each The eigenvector Φ (i) ,Right now

[0133]

[0134] Its eigenvector Φ (i) Characterizes the vibration mode corresponding to the natural oscillation frequency, that is, the relative ratio of the amplitude of each rotor phase angle when each rotor phase angle vibrates at the i-th natural frequency;

[0135] Known T J and B are orthogonal, that is:

[0136]

[0137] Convert the non-diagonal matrix B to a diagonal matrix B P , T J and D remain in their original diagonal matrix form after transformation:

[0138]

[0139] Will Substituting in, we get:

[0140]

[0141] Through coordinate transformation, the rotor motion process is converted into an n-dimensional space based on n vibration modes. In this space, the motion process of each rotor is the superposition of the vibration processes under each vibration mode; the decoupling of the rotor oscillation process is achieved, that is:

[0142]

[0143] Perform Laplace transform on the above equation to convert the above time domain expression into the time domain for analysis and solution;

[0144] M p s 2 x p (s)+D p sx p (s)+K p x p (s)=F P (s)

[0145] The expressions of rotor phase angle and speed corresponding to the principal coordinates are:

[0146]

[0147] Under the given fault disturbance form, the above equation is subjected to inverse Laplace transform to obtain the principal coordinate time domain expression corresponding to the oscillation mode:

[0148]

[0149] By transforming the principal coordinates back to the original coordinates, we can obtain the time domain expression of each rotor phase angle and frequency:

[0150]

[0151] This method can be used to determine the dynamic process of the inertia response phase of each rotor after a power disturbance, taking into account the frequency dynamic characteristics of all generator rotors in the system. The decomposition relationship of a fault at any location in the modal principal coordinates can be determined, and the frequency dynamic process of the system inertia response phase after a fault at any location can be determined, which can more accurately reflect the frequency characteristics of different nodes in the system.

[0152] According to another aspect of the present invention, a multi-inertia center power system frequency response analysis system 300 is provided. Figure 3 As shown, the system 300 includes:

[0153] A model building module 310 is used to build a generator model, a network model, and a fault disturbance model in the frequency dynamic model of the inertia response stage based on a modal analysis method in vibration dynamics;

[0154] Obtaining an overall vibration dynamic model module 320, for substituting the network model and the fault disturbance model into the generator model to obtain an overall vibration dynamic model;

[0155] The frequency dynamic process obtaining module 330 is used to obtain the time domain expression of the frequency dynamic process of the system inertia response stage after a fault at any position based on the overall vibration dynamic model.

[0156] Optionally, a model module is established, including:

[0157] A generator model submodule is established to model the frequency characteristics of the power system. The generator model is represented by a set of differential algebraic equations. The differential part represents the rotor motion process of the generator, and the algebraic part represents the electrical interaction between generators:

[0158]

[0159] Among them, Δω, Δδ, ΔP m ,ΔP g ,T J , D are column vectors composed of the rotor speed, rotor phase angle, mechanical power change, electromagnetic power change, damping coefficient and inertia time constant of each generator set, ΔP m =0.

[0160] Optionally, a model module is established, including:

[0161] A network model submodule is established to write the DC power flow equation for a power network with n generators and m bus nodes as follows:

[0162]

[0163] Where ΔP l , Δθ are column vectors composed of the power variation and phase angle variation of each load node, Bgg is the d-axis transient reactance x of each generator di ″, i = 1, 2, ..., n composed of a diagonal matrix, namely B gg =diag,x d1 ″,x d2″,…xdn″;B gl is the relationship and electrical distance between the generator node and the busbar node;

[0164] B gl =B gg ·A

[0165] Where A is an n*m matrix, for each element Ai in A j , i=1,2,…,n;j=1,2,…,m, its value is:

[0166]

[0167] B ll is the node admittance matrix that only retains the imaginary part;

[0168] According to the DC power flow equation, the phase angle change of the busbar node is:

[0169] Δθ=B ll - 1 ΔP L -B ll - 1 B gl T Δδ

[0170] B gl Substituting the expression into the DC power flow equation, eliminating the common load nodes and retaining only the generator nodes, the change in the generator electromagnetic power is:

[0171] ΔP g =(B gg -B gl B ll -1 B gl T )Δδ+B gl B ll -1 ΔP L

[0172] make

[0173]

[0174] B K is the elastic matrix of the interaction between the generator rotors, B F It is the distribution coefficient matrix of the system disturbance power distributed to each generator rotor, that is, the full-step power coefficient.

[0175] Optionally, a model module is established, including:

[0176] Establish the fault disturbance model submodule, define the step function u(t), rectangular pulse function p(t, tC ):

[0177]

[0178] p(t,t C )=u(t)-u(tt C )

[0179] During the commutation failure period of the DC commutation failure fault, the system injects a surplus power disturbance ΔP at node h. DC After the commutation failure is restored, the surplus power disappears. The duration of each commutation failure is t C Therefore, for the DC commutation failure fault disturbance, ΔP L Elements in ΔP Li (i=1,2,…,n) is:

[0180]

[0181] For a DC blocking fault at node h, when the fault occurs, the system is injected with surplus power disturbance ΔP at node h. DC , the system security measures are c After a delay, the generator set with the same power is cut off. The process is similar to the commutation failure process, except that the generator set cut off by the safety control action after the DC blocking fault is not necessarily located at the node h. Assume that the power of the generator set cut off by the safety control system is represented by the vector ΔP C , then ΔP L Elements in ΔP Li (i=1,2,…,n) is:

[0182]

[0183] Optionally, a global vibration dynamics model module is obtained, including:

[0184] The overall vibration dynamics model submodule is obtained, which is used to substitute the network model and fault disturbance model into the generator model to obtain the overall vibration dynamics model:

[0185]

[0186] Through transformation, the above equation can be rewritten as the motion equation with the phase angle of each generator rotor as the state quantity and each rotor performing relative oscillation motion:

[0187]

[0188] Optionally, deriving a frequency dynamic process module includes:

[0189] The frequency dynamic process submodule is used to analyze the rotor oscillation process using modal analysis, and obtain the time domain expression of the frequency dynamic process of the system inertia response phase after a fault at any position. Under external excitation, the oscillation motion process of each rotor is a superposition of a series of attenuated sinusoidal oscillation processes. The specific oscillation form is related to the system's own natural oscillation mode and the form of excitation:

[0190] To solve the natural oscillation frequency Ω, we need to solve the following equation:

[0191] |T J Ω 2 -B|=0

[0192] Where, Ω=[Ω1,Ω2,…,Ω n ], let Ω1,Ω2,…,Ω n To arrange in order from smallest to largest;

[0193] Convert to matrix BT J -1 The eigenvalue of is solved by solving each The eigenvector Φ (i) ,Right now

[0194]

[0195] Its eigenvector Φ (i) Characterizes the vibration mode corresponding to the natural oscillation frequency, that is, the relative ratio of the amplitude of each rotor phase angle when each rotor phase angle vibrates at the i-th natural frequency;

[0196] Known T J and B are orthogonal, that is:

[0197]

[0198] Convert the non-diagonal matrix B to a diagonal matrix B P , T J and D remain in their original diagonal matrix form after transformation:

[0199]

[0200] Will Substituting in, we get:

[0201]

[0202] Through coordinate transformation, the rotor motion process is converted into an n-dimensional space based on n vibration modes. In this space, the motion process of each rotor is the superposition of the vibration processes under each vibration mode; the decoupling of the rotor oscillation process is achieved, that is:

[0203]

[0204] Perform Laplace transform on the above equation to convert the above time domain expression into the time domain for analysis and solution;

[0205] M p s 2 x p (s)+D p sx p (s)+K p x p (s)=F P (s)

[0206] The expressions of rotor phase angle and speed corresponding to the principal coordinates are:

[0207]

[0208] Under the given fault disturbance form, the above equation is subjected to inverse Laplace transform to obtain the principal coordinate time domain expression corresponding to the oscillation mode:

[0209]

[0210] By transforming the principal coordinates back to the original coordinates, we can obtain the time domain expression of each rotor phase angle and frequency:

[0211]

[0212] A multi-inertia center power system frequency response analysis system 300 according to an embodiment of the present invention corresponds to a multi-inertia center power system frequency response analysis method 100 according to another embodiment of the present invention, and will not be described in detail herein.

[0213] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code. The scheme in the embodiment of the present application can be implemented in various computer languages, for example, object-oriented programming language Java and literal translation scripting language JavaScript, etc.

[0214] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the steps in the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0215] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0216] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0217] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present application.

[0218] Obviously, those skilled in the art may make various changes and modifications to this application without departing from the spirit and scope of this application. Thus, if these modifications and variations of this application fall within the scope of the claims of this application and their equivalents, this application is intended to include these modifications and variations.

Claims

1. A method for analyzing the frequency response of a multi-inertia center power system, characterized in that: include: Based on the modal analysis method in vibration dynamics, the generator model, network model and fault disturbance model in the frequency dynamic model of the inertia response stage are established; Substituting the network model and the fault disturbance model into the generator model to obtain an overall vibration dynamics model; Based on the overall vibration dynamics model, the time domain expression of the frequency dynamic process of the system inertia response stage after a fault at any position is obtained; Substituting the network model and the fault disturbance model into the generator model, an overall vibration dynamics model is obtained, including: Substituting the network model and fault disturbance model into the generator model, the overall vibration dynamics model can be obtained: Through transformation, the above equation can be rewritten as the motion equation with the phase angle of each generator rotor as the state quantity and each rotor performing relative oscillation motion: Among them, Δω, Δδ, and D are the rotor speed, rotor phase angle, and inertia time constant of each generator set, respectively. L is the power change of each load node, B K is the elastic matrix of the interaction between the generator rotors, B F is the distribution coefficient matrix of the system disturbance power distributed to each generator rotor, that is, the full-step power coefficient; Based on the overall vibration dynamics model, the time domain expression of the frequency dynamic process of the system inertia response stage after a fault at any position is obtained, including: The modal analysis method is used to analyze the rotor oscillation process and obtain the time domain expression of the frequency dynamic process of the system inertia response stage after a fault at any position. Under external excitation, the oscillation motion process of each rotor is the superposition of a series of attenuated sinusoidal oscillation processes. The specific oscillation form is related to the system's own inherent oscillation mode and the form of excitation: To solve the natural oscillation frequency Ω, we need to solve the following equation: |T J Oh 2 -B K |=0 Where, Ω=[Ω1,Ω2,...,Ω n ], let Ω1,Ω2,...,Ω n To arrange in order from smallest to largest; Convert to Matrix The eigenvalue of is solved by solving each The eigenvector Φ (i) ,Right now Its eigenvector Φ (i) Characterizes the vibration mode corresponding to the natural oscillation frequency, that is, the relative ratio of the amplitude of each rotor phase angle when each rotor phase angle vibrates at the i-th natural frequency; Known T J and B K With orthogonality, that is: The non-diagonal matrix B K Convert to a diagonal matrix K, T J and D remain in their original diagonal matrix form after transformation: Will Substituting in, we get: Through coordinate transformation, the rotor motion process is converted into an n-dimensional space based on n vibration modes. In this space, the motion process of each rotor is the superposition of the vibration processes under each vibration mode; the decoupling of the rotor oscillation process is achieved, that is: Perform Laplace transform on the above equation to convert the above time domain expression into the time domain for analysis and solution; M p s 2 x p (s)+D p sx p (s)+K p x p (s)=F P (s) The expressions of rotor phase angle and speed corresponding to the principal coordinates are: Under the given fault disturbance form, the above equation is subjected to inverse Laplace transform to obtain the principal coordinate time domain expression corresponding to the oscillation mode: By transforming the principal coordinates back to the original coordinates, we can obtain the time domain expression of each rotor phase angle and frequency:

2. The method according to claim 1, characterized in that The generator model is established based on the modal analysis method in vibration dynamics, including: A generator model is established to model the frequency characteristics of the power system. The generator model is represented by a set of differential algebraic equations. The differential part represents the rotor motion process of the generator, and the algebraic part represents the electrical interaction between generators: Among them, Δω, Δδ, ΔP m ,ΔP g ,T J , D are column vectors composed of the rotor speed, rotor phase angle, mechanical power change, electromagnetic power change, damping coefficient and inertia time constant of each generator set, ΔP m =0.

3. The method according to claim 2, characterized in that The network model is established based on the modal analysis method in vibration dynamics, including: For a power network with n generators and m bus nodes, the DC power flow equation is: Where ΔP L , Δθ are column vectors composed of power variation and phase angle variation of each load node, B gg is the d-axis transient reactance x of each generator di ″, i = 1, 2, ..., n composed of a diagonal matrix, namely B gg =diag,x d1 ″,x d2 ″,…x dn ″;B gl is the relationship and electrical distance between the generator node and the busbar node; B gl =B gg ·A Where A is an n*m matrix, for each element A ij , i=1,2,…,n;j=1,2,…,m, its value is: B ll is the node admittance matrix that only retains the imaginary part; According to the DC power flow equation, the phase angle change of the busbar node is: B gl Substituting the expression into the DC power flow equation, eliminating the common load nodes and retaining only the generator nodes, the change in the generator electromagnetic power is: make B K is the elastic matrix of the interaction between the generator rotors, B F It is the distribution coefficient matrix of the system disturbance power distributed to each generator rotor, that is, the full-step power coefficient.

4. The method according to claim 1, wherein The fault disturbance model is established based on the modal analysis method in vibration dynamics, including: Establish a fault disturbance model for the power system that transmits power through a DC transmission project, define the step function u(t), the rectangular pulse function p(t, t C ): p(t,t C )=u(t)-u(t-t C ) During the commutation failure period of the DC commutation failure fault, the system injects a surplus power disturbance ΔP at node h. DC After the commutation failure is restored, the surplus power disappears. The duration of each commutation failure is t C Therefore, for the DC commutation failure fault disturbance, ΔP L Elements in ΔP Li (i=1,2,…,n) is: For a DC blocking fault at node h, when the fault occurs, the system is injected with surplus power disturbance ΔP at node h. DC , the system security measures are c After a delay, the generator set with the same power is cut off. The process is similar to the commutation failure process, except that the generator set cut off by the safety control action after the DC blocking fault is not necessarily located at the node h. Assume that the power of the generator set cut off by the safety control system is represented by the vector ΔP C , then ΔP L Elements in ΔP Li (i=1,2,…,n) is:

5. A multi-inertia center power system frequency response analysis system, characterized in that: include: Establish a model module for establishing the generator model, network model, and fault disturbance model in the frequency dynamic model of the inertia response stage based on the modal analysis method in vibration dynamics; Obtaining an overall vibration dynamics model module, used for substituting the network model and the fault disturbance model into the generator model to obtain an overall vibration dynamics model; A frequency dynamic process deriving module is used to solve and derive a time domain expression of the frequency dynamic process of the system inertia response phase after a fault at any position based on the overall vibration dynamics model; Get the overall vibration dynamics model module, including: The overall vibration dynamics model submodule is obtained, which is used to substitute the network model and fault disturbance model into the generator model to obtain the overall vibration dynamics model: Through transformation, the above equation can be rewritten as the motion equation with the phase angle of each generator rotor as the state quantity and each rotor performing relative oscillation motion: Among them, Δω, Δδ, and D are the rotor speed, rotor phase angle, and inertia time constant of each generator set, respectively. L is the power change of each load node, B K is the elastic matrix of the interaction between the generator rotors, B F is the distribution coefficient matrix of the system disturbance power distributed to each generator rotor, that is, the full-step power coefficient; The frequency dynamic process module is derived, including: The frequency dynamic process submodule is used to analyze the rotor oscillation process using the modal analysis method, and to obtain the time domain expression of the frequency dynamic process of the system inertia response stage after a fault at any position. Under external excitation, the oscillation motion process of each rotor is the superposition of a series of attenuated sinusoidal oscillation processes. The specific oscillation form is related to the system's own inherent oscillation mode and the form of excitation: To solve the natural oscillation frequency Ω, we need to solve the following equation: |T J Oh 2 -B K |=0 Where, Ω=[Ω1,Ω2,...,Ω n ], let Ω1,Ω2,...,Ω n To arrange in order from smallest to largest; Convert to Matrix The eigenvalue of is solved by solving each The eigenvector Φ (i) ,Right now Its eigenvector Φ (i) Characterizes the vibration mode corresponding to the natural oscillation frequency, that is, the relative ratio of the amplitude of each rotor phase angle when each rotor phase angle vibrates at the i-th natural frequency; Known T J and B K With orthogonality, that is: The non-diagonal matrix B K Convert to a diagonal matrix K, T J and D remain in their original diagonal matrix form after transformation: Will Substituting in, we get: Through coordinate transformation, the rotor motion process is converted into an n-dimensional space based on n vibration modes. In this space, the motion process of each rotor is the superposition of the vibration processes under each vibration mode; the decoupling of the rotor oscillation process is achieved, that is: Perform Laplace transform on the above equation to convert the above time domain expression into the time domain for analysis and solution; M p s 2 x p (s)+D p sx p (s)+K p x p (s)=F P (s) The expressions of rotor phase angle and speed corresponding to the principal coordinates are: Under the given fault disturbance form, the above equation is subjected to inverse Laplace transform to obtain the principal coordinate time domain expression corresponding to the oscillation mode: By transforming the principal coordinates back to the original coordinates, we can obtain the time domain expression of each rotor phase angle and frequency:

6. The system according to claim 5, characterized in that Build model modules, including: A generator model submodule is established to model the frequency characteristics of the power system. The generator model is represented by a set of differential algebraic equations. The differential part represents the rotor motion process of the generator, and the algebraic part represents the electrical interaction between generators: Among them, Δω, Δδ, ΔP m ,ΔP g ,T J , D are column vectors composed of the rotor speed, rotor phase angle, mechanical power change, electromagnetic power change, damping coefficient and inertia time constant of each generator set, ΔP m =0.

7. The system according to claim 6, characterized in that Build model modules, including: A network model submodule is established to write the DC power flow equation for a power network with n generators and m bus nodes as follows: Where ΔP l , Δθ are column vectors composed of the power variation and phase angle variation of each load node, Bgg is the d-axis transient reactance x of each generator di ″, i = 1, 2, ..., n composed of a diagonal matrix, namely B gg =diag,x d1 ″,x d2 ″,…x dn ″;B gl is the relationship and electrical distance between the generator node and the busbar node; B gl =B gg ·A Where A is an n*m matrix, for each element A ij , i=1,2,…,n;j=1,2,…,m, its value is: B ll is the node admittance matrix that only retains the imaginary part; According to the DC power flow equation, the phase angle change of the busbar node is: B gl Substituting the expression into the DC power flow equation, eliminating the common load nodes and retaining only the generator nodes, the change in the generator electromagnetic power is: make B K is the elastic matrix of the interaction between the generator rotors, B F It is the distribution coefficient matrix of the system disturbance power distributed to each generator rotor, that is, the full-step power coefficient.

8. The system according to claim 7, characterized in that Build model modules, including: Establish the fault disturbance model submodule, define the step function u(t), rectangular pulse function p(t, t C ): p(t,t C )=u(t)-u(t-t C ) During the commutation failure period of the DC commutation failure fault, the system injects a surplus power disturbance ΔP at node h. DC After the commutation failure is restored, the surplus power disappears. The duration of each commutation failure is t C Therefore, for the DC commutation failure fault disturbance, ΔP L Elements in ΔP Li (i=1,2,…,n) is: For a DC blocking fault at node h, when the fault occurs, the system is injected with surplus power disturbance ΔP at node h. DC , the system security measures are c After a delay, the generator set with the same power is cut off. The process is similar to the commutation failure process, except that the generator set cut off by the safety control action after the DC blocking fault is not necessarily located at the node h. Assume that the power of the generator set cut off by the safety control system is represented by the vector ΔP C , then ΔP L Elements in ΔP Li (i=1,2,…,n) is:

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