Power network oscillation analysis method and system considering line distribution characteristics

Abstract

The invention discloses a power network oscillation analysis method and system considering line distribution characteristics, and the method comprises the steps: building a generalized state space model based on a matrix pencil based on the related parameters of lumped parameter transmission equipment, and building a time-delay algebraic equation set based on the obtained related parameters of a distribution parameter line; converting the time-delay algebraic equation set into a finite-dimensional differential equation set by adopting a spectral discretization method; forming a free oscillation model of the passive power network by using the Kirchhoff's law, and determining a forced oscillation model of the passive power network under the ideal excitation source; performing generalized eigenvalue decomposition, identifying a key resonance mode, solving a forced oscillation model of the passive power network under an ideal excitation source, and obtaining right and left eigenvectors corresponding to dynamic characteristics of the power network; and analyzing the obtained right and left feature vectors corresponding to the dynamic characteristics of the power network, determining harmonic voltage distribution of each bus of the power network and a weak area susceptible to harmonic waves, drawing a harmonic distribution diagram, and outputting an identified key resonance mode.

Description

Background Art

[0002] Large-scale new energy power systems are increasingly showing the technical characteristics of a high proportion of renewable energy and a high proportion of power electronic devices. The stability characteristics of power systems are undergoing profound changes. According to the latest IEEE working group's definition and classification of power system stability, new categories such as resonance and converter-driven stability have been introduced. These new problems involve faster dynamic processes and smaller time scales, posing higher requirements for the theoretical analysis of electromagnetic transients (EMT) in power systems, and even the wave propagation process. Using electromagnetic transient simulations at the microsecond level can accurately depict the oscillation and instability phenomena after the power system is disturbed, but it cannot provide more information on control means and oscillation suppression. A direct theoretical method for analyzing oscillation problems is to perform small-signal stability analysis (SSSA) at the electromagnetic transient time scale. By performing eigenvalue analysis on the linearized state-space model of the system, the purpose of discriminating the system stability and identifying the oscillation characteristics of the system can be achieved. In addition, the eigenvectors obtained by SSSA provide relevant information on controllability and observability, which can be used in fields such as designing power system control strategies and parameter optimization.

[0003] The key to establishing the electromagnetic transient time scale is to establish the linear state-space model of the system. To solve problems such as the selection of state variable space and the elimination of algebraic variables, a method called generalized state-space modeling has been widely used in recent years. Compared with conventional state-space modeling methods, this type of method retains the redundancy of variables, making the leading matrix before the derivative term of the state variable singular. For large and complex power networks, this type of modeling method faces at least two problems:

[0004] 1) Existing generalized state-space modeling methods do not adopt a general framework to model diverse transmission equipment in the power network;

[0005] 2) For long transmission lines, the distributed parameter characteristics must be considered, rather than the lumped parameter Π-type cascade representation.

[0006] The latter simplifies the transmission line into a conventional RLC circuit and cannot consider the time delay introduced by the wave propagation process. Considering the above, a large power network will be represented as a set of high-dimensional delay differential-algebraic equations (DDAEs), and conventional eigenvalue analysis methods cannot be directly applied. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to provide a power network oscillation analysis method and system considering line distribution characteristics in view of the deficiencies in the above-mentioned prior art, to model a passive power network with lumped parameters and distributed parameters at the electromagnetic transient time scale, and to analyze the stability of the power network at the electromagnetic transient time scale by accurately and efficiently performing eigenvalue analysis, and to analyze electromagnetic oscillation problems through free oscillation and forced oscillation theories, so as to solve the technical problem of electromagnetic oscillation of a power network with lumped parameter components and distributed parameter transmission lines.

[0008] The present invention adopts the following technical solutions:

[0009] A power network oscillation analysis method considering line distribution characteristics, characterized by comprising the following steps:

[0010] S1. Obtain the relevant parameters of lumped parameter transmission equipment and distributed parameter lines, and separately perform parameter preprocessing on the distributed parameter lines;

[0011] S2. Based on the relevant parameters of the lumped parameter transmission equipment obtained in step S1, establish a generalized state space model based on the matrix pencil, and based on the relevant parameters of the distributed parameter lines obtained in step S1, establish a time-delay algebraic equation set, and use the spectral discretization method to transform the time-delay algebraic equation set into a finite-dimensional differential equation set;

[0012] S3. Based on the generalized state space model and the finite-dimensional differential equation set obtained in step S2, use Kirchhoff's law to form a free oscillation model of the passive power network, and determine the forced oscillation model of the passive power network under an ideal excitation source;

[0013] S4. Perform generalized eigenvalue decomposition on the free oscillation model of the passive power network obtained in step S3, identify key resonance modes, solve the forced oscillation model of the passive power network under an ideal excitation source, and obtain the right and left eigenvectors corresponding to the dynamic characteristics of the power network;

[0014] S5. Analyze the right and left eigenvectors corresponding to the dynamic characteristics of the power network obtained in step S4, determine the harmonic voltage distribution of each bus of the power network and the weak areas vulnerable to harmonics, draw a harmonic distribution map and output the identified key resonance modes.

[0015] Preferably, step S2 is specifically as follows:

[0016] S201. For lumped parameter transmission equipment, clarify the number of ports, regard the bus voltage corresponding to the port as the input variable, and the current flowing through the port as the output variable, write differential-algebraic equations according to Kirchhoff's law and the dynamic relationship of LC components, retain algebraic variables, and establish a generalized state space model;

[0017] S202. Establish the time-delay algebraic equation of the distributed parameter transmission line based on the Bergeron model; use the sparse low-order solution operator discretization method to transform the time-delay algebraic equation set into a finite-dimensional differential equation set, and then dynamically couple it with the generalized state space model obtained in step S201.

[0018] Preferably, write the differential-algebraic equations according to Kirchhoff's law and the dynamic relationship of LC components as follows:

[0019]

[0020] Among them, u m represents the voltage at the T-junction; u p , u q represent the port voltages on both sides of the transformer; i p , i q and i m respectively represent the currents flowing through the primary winding, secondary winding and exciting winding; T k1 / T k2 represents the turns ratio of the ideal transformers on both sides; R 1σ (R 2σ ) and L 1σ (L 2σ ) represent the resistance and leakage inductance of the primary (secondary) winding of the transformer; R m and L m represent the resistance and leakage inductance of the exciting winding of the transformer.

[0021] Preferably, use the sparse low-order solution operator discretization method to transform the time-delay algebraic equation set into a finite-dimensional differential equation set as follows:

[0022]

[0023] Among them, i p (t), i q (t) and u p (t), u q (t) respectively represent the instantaneous currents flowing through the sending and receiving sides and the instantaneous voltages at the sending and receiving ends; τ is the propagation time of the line; Z represents the modified wave impedance, γ is defined as the adjustment coefficient, and k1 to k4 are the characteristic coefficients of the distributed parameter transmission line.

[0024] Preferably, step S3 is specifically:

[0025] Construct the generalized model of the branch element, establish Kirchhoff's current law for the bus, and form the free oscillation model of the passive power network; establish the power network model excited by current sources and the power network model excited by voltage sources based on the free oscillation model of the passive power network.

[0026] Preferably, the free oscillation model of the passive power network is:

[0027]

[0028] where x is the variable of all branches and buses, and (J, T) is the matrix pencil, is the derivative of the generalized variable x.

[0029] Preferably, the power network model excited by a current source is:

[0030]

[0031] where b s is the selection vector related to the position of the current source, and I s (t) is the injection current source excitation existing on bus s;

[0032] The power network model excited by a voltage source is:

[0033]

[0034] where b s ′ is the selection vector related to the position of the voltage source; is the corresponding matrix pencil, and U s (t) is the voltage source excitation existing on bus s.

[0035] Preferably, step S4 is specifically:

[0036] Obtain the matrix pencil (J, T) corresponding to the generalized state space equation, obtain the orthogonal matrix through the generalized Schur decomposition, transform the matrix pencil into an upper triangular matrix based on the orthogonal transformation, and further extract the generalized eigenvalues from the diagonal elements; obtain the input vector and output vector corresponding to the forced oscillation, and determine the harmonic voltage distribution and the additional gain from the excitation source to the corresponding mode through the right and left eigenvectors.

[0037] Preferably, all the eigenvalues of the matrix pencil (J, T) are:

[0038] λ(J, T) = {A ii / B ii , i = 1, …, n}

[0039] where A ii and B ii are the diagonal elements of matrices A and B respectively, and λ is the eigenvalue;

[0040] By solving the eigenvectors of A and B, and then transforming them into the eigenvectors ξ of the original problem through the unitary matrices Q and Z.

[0041] Second aspect, an embodiment of the present invention provides a power network oscillation analysis system considering line distribution characteristics, including:

[0042] A data module, which acquires relevant parameters of lumped-parameter transmission devices and distributed-parameter lines, and separately performs parameter preprocessing on the distributed-parameter lines;

[0043] A construction module, which establishes a generalized state space model based on matrix pencil based on the relevant parameters of the lumped-parameter transmission devices obtained by the data module, establishes a time-delay algebraic equation set based on the relevant parameters of the distributed-parameter lines obtained by the data module, and uses the spectral discretization method to transform the time-delay algebraic equation set into a finite-dimensional differential equation set;

[0044] An oscillation module, which forms a free oscillation model of a passive power network based on the generalized state space model and the finite-dimensional differential equation set obtained by the construction module, and determines a forced oscillation model of the passive power network under an ideal excitation source;

[0045] An identification module, which performs a generalized eigenvalue decomposition on the free oscillation model of the passive power network obtained by the oscillation module, identifies key resonance modes, solves the forced oscillation model of the passive power network under an ideal excitation source, and obtains the right and left eigenvectors corresponding to the dynamic characteristics of the power network;

[0046] An analysis module, which analyzes the right and left eigenvectors corresponding to the dynamic characteristics of the power network obtained by the identification module, determines the harmonic voltage distribution of each bus of the power network and the weak areas vulnerable to harmonics, draws a harmonic distribution map, and outputs the identified key resonance modes.

[0047] Third aspect, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the above-mentioned power network oscillation analysis method considering line distribution characteristics are implemented.

[0048] Fourth aspect, an embodiment of the present invention provides a computer-readable storage medium, including a computer program, and when the computer program is executed by a processor, the steps of the above-mentioned power network oscillation analysis method considering line distribution characteristics are implemented.

[0049] Fifth aspect, a chip includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the above-mentioned power network oscillation analysis method considering line distribution characteristics are implemented.

[0050] Sixth aspect, an embodiment of the present invention provides an electronic device, including a computer program, and when the computer program is executed by the electronic device, the steps of the above-mentioned power network oscillation analysis method considering line distribution characteristics are implemented.

[0051] Compared with the prior art, the present invention has at least the following beneficial effects:

[0052] A power network oscillation analysis method considering line distribution characteristics reveals the key influencing factors in the harmonic resonance phenomenon of a dynamic power network under the electromagnetic transient time scale, making it a valuable tool for analyzing electromagnetic oscillation modes. Compared with the traditional state-space modeling method, the generalized modeling framework proposed in the present invention is applicable to various complex multi-port power transmission devices, expanding the flexibility and generality of modeling; the sparse low-order discretization model proposed in the present invention for distributed parameter transmission lines takes into account the time-delay effect generated by the propagation of electromagnetic waves and can be used to analyze electromagnetic oscillation behaviors under high-frequency bandwidths; the generalized eigenvalue calculation and right- and left-eigenvector analysis methods proposed in the present invention accurately characterize the sensitivity of different buses to specific modes and indicate the weak areas prone to resonance in the power network.

[0053] Furthermore, constructing generalized differential-algebraic equations for lumped parameter elements is the basic model for the electromagnetic transient oscillation analysis of the present invention. Compared with the conventional state-space modeling method, this model is more flexible and can be compatible with different types of multi-input multi-output power network transmission devices; by retaining variable redundancy and introducing a singular leading matrix, a series of problems such as the difficulty in selecting state variables and eliminating algebraic equations are overcome, greatly reducing the workload of modeling.

[0054] Furthermore, establishing a time-delay algebraic equation set for long transmission lines considering distributed parameter characteristics and transforming it into a finite-dimensional differential-algebraic equation set through spectral discretization is the key step for the electromagnetic oscillation analysis of the power network in the present invention. Under the electromagnetic time scale, the propagation of electromagnetic waves in transmission lines has a time-delay effect, and conventional eigenvalue analysis cannot handle such infinite-dimensional systems. Therefore, based on the proposed unified generalized modeling framework, using the low-order sparse discretization technology of time-delay characteristic equations helps to realize the general modeling and eigenvalue analysis workflow.

[0055] Furthermore, formulating a forced oscillation model of a passive power network excited by an ideal perturbation source is a necessary step for analyzing the resonance occurrence conditions under the electromagnetic transient time scale and provides a mathematical model for detailed electromagnetic oscillation analysis.

[0056] Furthermore, using the generalized Schur decomposition method to solve the generalized eigenvalues of a given matrix pencil is the core algorithm of the present invention. By reducing the matrix pencil to a Hessenberg-upper triangular form through unitary equivalence transformation, the efficiency of eigenvalue calculation is greatly improved; in addition, compared with the conventional eigenvalue calculation that cannot handle singular matrix pencils, this method expands the application boundary.

[0057] Further, using the right and left eigenvectors to describe the distribution of harmonic voltages of each bus and ideal periodic harmonic sources in the power network is the key step for the present invention to determine the influencing factors of oscillation modes. Based on the obtained generalized eigenvalues and right and left eigenvectors, using the input vector and output vector, indicators for the response degree of different buses to a specific mode and the weakness degree of the bus where the forcing source is placed are constructed. This measure reveals the reasons for the occurrence of electromagnetic oscillations in the power network and lays a foundation for using controllers for parameter stabilization and strategy design.

[0058] It can be understood that the beneficial effects of the above second aspect to the sixth aspect can be referred to the relevant descriptions in the above first aspect, and will not be elaborated here.

[0059] In summary, the present invention is used for the analysis of power system resonance or sub-synchronous oscillation at the electromagnetic transient scale. Compared with the algebraic equations at a single frequency of the original phasor method, it focuses on considering the distributed parameters and time-delay characteristics of long transmission lines, can accurately derive the harmonic distribution in the power network and determine the weak areas, and provides a theoretical basis for filter location selection and harmonic elimination.

[0060] The technical solutions of the present invention will be further described in detail below through the drawings and embodiments. Brief Description of the Drawings

[0061] To more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required to be used in the embodiments of the present application will be briefly introduced below. Obviously, the following described drawings are only some embodiments of the present application, and those of ordinary skill in the art can also obtain other drawings based on these drawings without creative efforts.

[0062] Figure 1 It is a schematic flow chart of the analysis method of the present invention;

[0063] Figure 2 It is a circuit diagram of multi-branch resistance-inductance coupling;

[0064] Figure 3 It is a distribution parameter transmission line diagram described by the Bergeron model considering resistance loss;

[0065] Figure 4 It is a topology diagram of a calculation example;

[0066] Figure 5 It is a distribution diagram of the characteristic roots calculated by the matrix pencil;

[0067] Figure 6 It is a comparison diagram of the right eigenvector amplitude and the 18th harmonic voltage distribution;

[0068] Figure 7Schematic diagram of a computer device provided by an embodiment of the present invention;

[0069] Figure 8 Block diagram of an electronic device provided by the present invention according to an embodiment.

[0070] Among them, 60. Computer device; 61. Processor; 62. Memory; 63. Computer program; 600. Electronic device; 610. Processing unit; 620. Storage unit; 6201. Random access storage unit; 6202. Cache storage unit; 6203. Read-only storage unit; 6204. Program / utilities; 6205. Program module; 630. Bus; 640. Display unit; 650. Input / output interface; 660. Network adapter; 700. External device. Detailed implementation manners

[0071] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0072] In the description of the present invention, it should be understood that the terms "include" and "comprise" indicate the presence of the described features, wholes, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or their combinations.

[0073] It should also be understood that the terms used in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. As used in the specification of the present invention and the appended claims, unless the context clearly indicates otherwise, the singular forms "a", "an" and "the" are intended to include the plural forms.

[0074] It should be further understood that the term " / and" used in the specification of the present invention and the appended claims refers to any combination and all possible combinations of one or more of the related listed items, and includes these combinations. For example, A and / or B can represent: A exists alone, A and B exist simultaneously, and B exists alone. In addition, the character " / " in the present invention generally represents an "or" relationship between the preceding and following related objects.

[0075] It should be understood that although terms such as first, second, third, etc. may be used in the embodiments of the present invention to describe preset ranges and the like, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from each other. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0076] Depending on the context, the word "if" as used herein can be interpreted as "when" or "while" or "in response to determining" or "in response to detecting". Similarly, depending on the context, the phrase "if determined" or "if detected (stated condition or event)" can be interpreted as "when determined" or "in response to determining" or "when detected (stated condition or event)" or "in response to detecting (stated condition or event)".

[0077] Various structural schematic diagrams according to the disclosed embodiments of the present invention are shown in the drawings. These figures are not drawn to scale, where for the purpose of clear expression, some details are enlarged and some details may be omitted. The shapes of various regions and layers shown in the figures and their relative sizes and positional relationships are only exemplary, and may actually deviate due to manufacturing tolerances or technical limitations, and those skilled in the art can additionally design regions / layers with different shapes, sizes, and relative positions according to actual needs.

[0078] The present invention provides a power network oscillation analysis method considering line distribution characteristics, revealing the key influencing factors in the harmonic resonance phenomenon of a dynamic power network at the electromagnetic transient time scale, making it a valuable tool for analyzing electromagnetic oscillation modes. Compared with the traditional state space modeling method, the generalized modeling framework proposed by the present invention is applicable to various complex multi-port power transmission devices, expanding the flexibility and generality of modeling; the sparse low-order discretization model proposed by the present invention for distributed parameter transmission lines takes into account the time delay effect generated by the propagation of electromagnetic waves and can be used to analyze electromagnetic oscillation behavior at high frequency bandwidths; the generalized eigenvalue calculation and right and left eigenvector analysis methods proposed by the present invention accurately characterize the sensitivity of different buses to specific modes and indicate the weak areas prone to resonance in the power network. In summary, the method proposed by the present invention is very suitable for the electromagnetic oscillation analysis of industrial-level large interconnected networks, can be used to obtain the key factors affecting oscillation modes, guide the tuning of controller parameters and the design of control strategies, and provide a theoretical basis for effectively suppressing electromagnetic oscillations.

[0079] Embodiment 1

[0080] Please refer to Figure 1, a method for power network oscillation analysis considering line distribution characteristics, based on the matrix pencil modeling framework, studies the free oscillation, forced oscillation, and node impedance calculation method in the power network; considering the basic assumptions of power network modeling, a unified dynamic modeling framework is proposed, which is applicable to lumped parameter branches and distributed parameter transmission lines. The specific steps are as follows:

[0081] S1. Obtain the relevant parameters of lumped parameter components such as transformers and filters, and distributed parameter components such as long transmission lines, and perform parameter preprocessing on the transmission lines separately;

[0082] The key data of power transmission equipment includes: line topology; short-circuit resistance, short-circuit reactance, exciting resistance, exciting reactance, and primary and secondary turns ratios of transformers; shunt conductance and shunt susceptance of single-tuned filters; resistance and reactance of the load equivalent impedance-inductance series branch; concentrated resistance, concentrated reactance, and ground admittance of long transmission lines.

[0083] For long transmission lines, calculate distributed parameters such as wave impedance, propagation time, and phase constant according to lumped parameters.

[0084] S2. Establish a generalized state-space model based on matrix pencil for lumped parameter transmission equipment and distributed parameter lines respectively. When using the spectral discretization method to process the time-delay term for distributed parameter lines, convert it into a finite-dimensional differential equation system, including the following steps:

[0085] S201. For lumped parameter transmission equipment, clarify the number of its ports, regard the bus voltage corresponding to the ports as the input, and the current flowing through the ports as the output. Write differential-algebraic equations according to Kirchhoff's laws and the dynamic relationship of LC components, and note that state variables and algebraic variables are no longer distinguished during the modeling process.

[0086] The general generalized state-space model is expressed as: where x represents the generalized variable, (J, T) is the matrix pencil, represents the derivative of the generalized variable.

[0087] In this modeling method, J and T may be singular. When T is diagonal or has a special block structure, the model can be reduced to a general state-space model.

[0088] Please refer to Figure 2 , taking a relatively complex type of transmission equipment, namely a two-winding transformer, as an example to illustrate the modeling process of the generalized state-space model. When not considering core saturation, the two-winding transformer is regarded as a multi-branch impedance-inductance coupling circuit, where the branch to the ground corresponds to the exciting winding, and the connecting branches correspond to the primary winding and secondary winding of the transformer respectively. The differential-algebraic equations describing the voltage-current relationship of this two-winding transformer are as follows:

[0089]

[0090] Among them, u m represents the voltage at the T-junction; u p , u q represents the port voltages on both sides of the transformer; i p , i q and i m respectively represent the currents flowing through the primary winding, secondary winding, and exciting winding; T k1 / T k2 represents the turns ratio of the ideal transformers on both sides; R 1σ (R 2σ ) and L 1σ (L 2σ ) represent the resistance and leakage inductance of the primary (secondary) winding of the transformer; R m and L m represent the resistance and leakage inductance of the exciting winding of the transformer.

[0091] S202. Considering the propagation delay generated by electromagnetic waves in long-distance transmission lines, establish the time-delay algebraic equations of the distributed-parameter transmission line based on the Bergeron model; use the method of discretization with a sparse low-order solution operator to transform the time-delay algebraic equations into a finite-dimensional differential equation system to conform to the generalized modeling framework.

[0092] S2021. Establish the time-delay algebraic equations for the distributed-parameter transmission line

[0093] Please refer to Figure 3 , in actual engineering, the Bergeron model is used to describe the distributed-parameter transmission line considering resistance loss, that is: divide the transmission line into two lossless lines on average, and then connect the lumped resistance of the whole line at three places: connect a quarter at each end in series, and connect a half in the middle. Its specific form can be expressed as:

[0094]

[0095] Among them, i p (t), i q (t) and u p (t), u q (t) respectively represent the instantaneous currents flowing through the sending and receiving sides and the instantaneous voltages at the sending and receiving ends; τ is the propagation time of the line; Z represents the modified wave impedance, and γ is defined as the adjustment coefficient.

[0096] The adjustment coefficient γ is:

[0097] γ = (Z0 - r / 4) / (Z0 + r / 4)(3)

[0098] Among them, Z0 represents the wave impedance of the lossless line; r represents the lumped resistance of the line.

[0099] Equation (2) is a set of time-delay algebraic equations, belonging to a typical infinite-dimensional system. Its characteristic equation contains exponential terms and has an infinite number of eigenvalues, making it impossible to use a conventional eigenvalue calculation module.

[0100] S2022. Transform it into a finite-dimensional differential-algebraic equation system by using the sparse low-order solution operator discretization method

[0101] The basic idea for dealing with the above time-delay system is to transform it into a time-delay-free finite-dimensional differential equation system, and then use the existing eigenvalue analysis method to analyze the small-signal stability of the time-delay system. Let's assume that N is the number of discrete points or sampling points, that is, the discrete order of a single time-delay variable. Then, for the time-delay term x(t - τ) in Equation (2), after discretization by Chebyshev polynomials, there is the following linear system approximation model:

[0102]

[0103] where, represents an implicit auxiliary variable; matrices Π and vectors l1 and

[0104] matrices and vectors have the following forms:

[0105]

[0106] Γ = [0|I N (6)

[0107] l1 = [1, 1, …, 1]; l2 = [(-1) 0 , (-1) 1 , …, (-1) N (7)

[0108] where, I N represents the N-order identity matrix.

[0109] For the time-delay variables u p (t - τ), u q (t - τ), i p (t - τ) and i p (t - τ) in Equation (2), apply (4) for discretization respectively, then the discrete model of the distributed parameter transmission line is established as follows:

[0110]

[0111] where, k1 to k4 are determined by the following formulas respectively:

[0112]

[0113] The adjustment coefficient γ is determined by equation (3).

[0114] It can be seen that after adopting the sparse low-order spectral discretization technology for the distributed transmission line, a model structure similar to that of the lumped parameter element is obtained.

[0115] S3. Establish a forced model of the passive power network under the excitation of current sources and voltage sources respectively, and establish the relationship between the harmonic periodic disturbance source and the natural oscillation mode of the passive power network through the steady-state phasor method of sinusoidal excitation;

[0116] Establish a well-posed forced model of the passive power network, and determine the conditions for the occurrence of this system under forced oscillation by analyzing the relationship between the free oscillation of the passive power network and the excitation source.

[0117] S301. Use Kirchhoff's current law to form a free oscillation model of the passive power network;

[0118] S3011. Construct a generalized model of the branch element

[0119] Based on the lumped parameter element model in step S2 and the discretized distributed parameter transmission line model, a generalized state space model based on the matrix pencil is refined:

[0120]

[0121] Among them, x represents the generalized state variable; u and i represent the node voltage vector and the branch port current vector respectively; J, T, B, and C are coefficient matrices respectively. Note that J and T are allowed to be singular matrices, and when T is invertible or has a special block structure, the above formula can be equivalently transformed into a standard state space model.

[0122] For the k-th branch in the network, it is uniformly expressed as:

[0123]

[0124] Among them, (J k , T k ) is the corresponding matrix pencil; x k represents the generalized state variable of the dynamic process of branch k; n k > 0 is the number of ports of branch k; (u j , i j ) represents the bus voltage where the corresponding port is located and the current flowing through; (b j , c j ) are the relevant coefficient vectors; m represents the number of buses in a general power network.

[0125] S3012. Construct Kirchhoff's current law for the bus

[0126] For any bus k in the entire network, the voltage of the corresponding variable bus has a corresponding relationship with Kirchhoff's current law (KCL). Let's assume that the current directions in the set of branch currents I k connected to bus k are all flowing out of the bus. Then KCL states that the algebraic sum of all currents flowing out of the bus is zero, that is:

[0127]

[0128] S3013. Form the free oscillation model of the passive power network

[0129] For branches, without considering external input variables, that is, the bus voltages at the ports, the number of variables and equations in model (11) is well - defined; for buses, the variables are bus voltages, and the equations are algebraic relationships (12), and the current comes from the output variables of the connected branches (i.e., the output variables of equation (11)).

[0130] In summary, since the number of equations and variables is well - defined, the passive power network model is expressed as:

[0131]

[0132] where the set x contains all branch and bus variables.

[0133] S302. Form the forced oscillation model of the passive power network under an ideal excitation source.

[0134] S3021. Establish the power network model excited by a current source

[0135] Based on the formed free oscillation model of the passive power network, assume that there is an injected current source excitation on bus s, denoted as I s (t). Note that I s is not a branch current, that is:

[0136]

[0137] The KCL equation for bus s in equation (12) is modified to:

[0138]

[0139] while the remaining equations remain unchanged. Thus, the passive power network model excited by a current source is established as:

[0140]

[0141] where b s is a selection vector related to the position of the current source, that is, the position of the current source is - 1, and the other elements are 0.

[0142] S3022. Establish a power network model excited by a voltage source

[0143] Based on the free oscillation model of the passive power network formed in step S301, assume that there is a voltage source excitation on bus s, denoted as U s (t). At this time, the current I s (t) flowing through the voltage source is unknown. Therefore, the KCL equation of this bus in equation (12) is replaced with a voltage constraint model:

[0144] u s -U s (t) = 0 (17)

[0145] Thus, the passive power network model excited by a voltage source is established as:

[0146]

[0147] where b s ′ is a selection vector related to the position of the voltage source; is the corresponding matrix pencil.

[0148] S4. Use the QZ method to solve the generalized state - space model represented by equation (13), and solve to obtain the generalized eigenvalues and the corresponding right and left eigenvectors characterizing the dynamic characteristics of the power network, including the following steps:

[0149] S401. Obtain the matrix pencil corresponding to the generalized state - space equation, obtain an orthogonal matrix through generalized Schur decomposition, transform the matrix pencil into an upper - triangular matrix based on the orthogonal transformation, and further extract the generalized eigenvalues from the diagonal elements;

[0150] S402. Obtain the input vector and output vector corresponding to the forced oscillation, and determine the harmonic voltage distribution and the additional gain from the excitation source to the corresponding mode through the right and left eigenvectors.

[0151] Based on the matrix pencil (J, T) obtained in step S301, its eigenvalue problem is expressed as:

[0152] Tξ = λJξ (19)

[0153] where λ and ξ correspond to the eigenvalue and the eigenvector respectively.

[0154] For equation (19), when T is singular, the degree of the polynomial on the left - hand side of this equation is lower than its order, which indicates that there are infinite eigenvalues in this equation. To handle this situation, perform a unitary equivalence transformation on the matrix pencil (J, T) to make it into the simplest form. Let's assume J, According to the generalized Schur decomposition theorem, there exist n - order unitary matrices Q and Z such that:

[0155] QH TZ = A, Q H JZ = B(20)

[0156] where A and B are both upper triangular matrices. At this time, all the eigenvalues of the matrix pencil (J, T) are:

[0157] λ(J, T) = {A ii / B ii , i = 1, …, n}(21)

[0158] where A ii and B ii are the diagonal elements of matrices A and B respectively.

[0159] If the eigenvectors need to be solved, solve the eigenvectors of A and B, and then transform them into the eigenvectors of the original problem through the unitary matrices Q and Z.

[0160] S5. Analyze the right and left eigenvectors corresponding to the dynamic characteristics of the power network obtained in step S4, determine the harmonic voltage distribution of each bus of the power network and the weak areas vulnerable to harmonics, draw the harmonic distribution map and output the identified key resonance modes.

[0161] S501. Identify the key resonance modes

[0162] Let the normalized right eigenvectors of the matrix pencil (J, T) form a matrix V by columns, and the normalized left eigenvectors form a matrix W by columns, which have the following form:

[0163] V = [v1 … v Q , W = [w1 … w Q (22)

[0164] Since the left and right eigenvectors corresponding to different eigenvalues are orthogonal, then:

[0165]

[0166] where the superscript H represents the conjugate transpose of the matrix; is a general matrix; Λ J and Λ T ∈ C P ×P are diagonal matrices, which have the following form:

[0167] Λ J = diag{μ J,1 , …, μ J,P}, Λ T = diag{μ T,1 , …, μ T,P} (24)

[0168] Among them, diag{·} represents a diagonal matrix.

[0169] Equation (24) indicates that the matrix pencil (J, T) includes P generalized eigenvalues and Q - P infinite eigenvalues, where the generalized eigenvalues have the following form:

[0170]

[0171] If the distance between λ JT,1 ~λ JT,P and the imaginary axis is less than one-thousandth, it can be determined as a potential resonance mode.

[0172] S502. Determine the harmonic voltage distribution and weak areas of each bus in the power network

[0173] For the forced oscillation caused by a periodic excitation source with an angular frequency of ω S , the coefficient vector r corresponding to its steady-state solution is determined by the following formula:

[0174]

[0175] Among them, A represents the amplitude of the resonance excitation source.

[0176] The above formula indicates that the analytical solution contains two parts, one part is related to the frequency ω S of the external excitation, and the other part is not. In resonance analysis, the impact of the first part on the steady-state solution is mainly concerned.

[0177] Equation (26) also shows that when jω S is close to a certain eigenvalue λ JT,i , a resonance phenomenon will occur between the external excitation source and the power network, and the related coefficient vector r is dominated by the right eigenvector v i . Therefore, v i determines the response of each component and the main dynamic process after forced oscillation in this mode. Once the parameter structure of the power network and the form of the external excitation source are determined, determines the additional gain from the excitation source to mode i. Connecting the excitation source at different bus positions in the power network will result in different coefficient vectors b. This means that for mode i, there are relatively weak positions in the power network, making the amplitude relatively large and more serious resonance will occur.

[0178] The above analysis shows that through the relative magnitudes of the amplitudes of each component of the right eigenvector v i , the harmonic voltage distribution of each bus in the power network can be determined; through the conjugate product of the left eigenvector w i and the coefficient vector b By the relative magnitude, the weak areas of the power network can be determined. The larger the magnitude, the higher the weakness degree of the area.

[0179] Those skilled in the art to which the present invention pertains can understand that various aspects of the present invention can be implemented as a system, a method, or a program product. Therefore, various aspects of the present invention can be specifically implemented in the following forms, namely: a complete hardware implementation, a complete software implementation (including firmware, microcode, etc.), or an implementation combining hardware and software aspects, which can be collectively referred to herein as "circuit", "module", or "platform".

[0180] Embodiment 2

[0181] The present invention provides a power network oscillation analysis system considering line distribution characteristics, which can be used to implement the power network oscillation analysis method considering line distribution characteristics. Specifically, the power network oscillation analysis system considering line distribution characteristics includes a data module, a construction module, an oscillation module, an identification module, and an analysis module.

[0182] Among them, the data module obtains the relevant parameters of the lumped parameter transmission equipment and the distributed parameter line, and separately performs parameter preprocessing on the distributed parameter line;

[0183] The construction module establishes a generalized state space model based on matrix pencil based on the relevant parameters of the lumped parameter transmission equipment obtained by the data module, establishes a time-delay algebraic equation set based on the relevant parameters of the distributed parameter line obtained by the data module, and uses the spectral discretization method to transform the time-delay algebraic equation set into a finite-dimensional differential equation set;

[0184] The oscillation module forms a free oscillation model of the passive power network based on the generalized state space model and the finite-dimensional differential equation set obtained by the construction module, and determines the forced oscillation model of the passive power network under an ideal excitation source;

[0185] The identification module performs a generalized eigenvalue decomposition on the free oscillation model of the passive power network obtained by the oscillation module, identifies the key resonance modes, solves the forced oscillation model of the passive power network under an ideal excitation source, and obtains the right and left eigenvectors corresponding to the dynamic characteristics of the power network;

[0186] The analysis module analyzes the right and left eigenvectors corresponding to the dynamic characteristics of the power network obtained by the identification module, determines the harmonic voltage distribution of each bus of the power network and the weak areas vulnerable to harmonics, draws a harmonic distribution map, and outputs the identified key resonance modes.

[0187] Embodiment 3

[0188] The present invention provides a terminal device, which includes a processor and a memory. The memory is used to store a computer program, and the computer program includes program instructions. The processor is used to execute the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or may also be other general-purpose processors, Graphics Processing Unit (GPU), Tensor Processing Unit (TPU), Digital Signal Processor (DSP), Application Specific Integrated Circuit (ASIC), Field-Programmable Gate Array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, and is suitable for implementing one or more instructions. Specifically, it is suitable for loading and executing one or more instructions to implement the corresponding method flow or corresponding function; the processor described in the embodiments of the present invention can be used for the operation of a power network oscillation analysis method considering line distribution characteristics, including:

[0189] Obtain the relevant parameters of the lumped-parameter transmission device and the distributed-parameter line, and separately perform parameter preprocessing on the distributed-parameter line; establish a generalized state-space model based on the matrix pencil based on the obtained relevant parameters of the lumped-parameter transmission device, establish a time-delay algebraic equation set based on the obtained relevant parameters of the distributed-parameter line, and use the spectral discretization method to transform the time-delay algebraic equation set into a finite-dimensional differential equation set; based on the obtained generalized state-space model and finite-dimensional differential equation set, use Kirchhoff's law to form a free oscillation model of the passive power network, and determine the forced oscillation model of the passive power network under an ideal excitation source; perform a generalized eigenvalue decomposition on the obtained free oscillation model of the passive power network to identify the key resonance modes, solve the forced oscillation model of the passive power network under an ideal excitation source, and obtain the right and left eigenvectors corresponding to the dynamic characteristics of the power network; analyze the obtained right and left eigenvectors corresponding to the dynamic characteristics of the power network, determine the harmonic voltage distribution of each bus of the power network and the weak areas vulnerable to harmonics, draw a harmonic distribution map and output the identified key resonance modes.

[0190] Please refer to Figure 7, the terminal device is a computer device. The computer device 60 in this embodiment includes: a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When the computer program 63 is executed by the processor 61, it implements the power network oscillation analysis method considering line distribution characteristics in the embodiment. To avoid repetition, it will not be elaborated here one by one. Alternatively, when the computer program 63 is executed by the processor 61, it implements the functions of each model / unit in the power network oscillation analysis system considering line distribution characteristics in the embodiment. To avoid repetition, it will not be elaborated here one by one.

[0191] The computer device 60 can be a computing device such as a desktop computer, a notebook, a palm computer, and a cloud server. The computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art can understand that Figure 7 This is only an example of the computer device 60 and does not constitute a limitation on the computer device 60. It may include more or fewer components than shown in the figure, or combine some components, or different components. For example, the computer device may also include input / output devices, network access devices, a bus, etc.

[0192] The so-called processor 61 may be a central processing unit (CPU), or may also be other general-purpose processors, a graphics processing unit (GPU), a tensor processing unit (TPU), a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc.

[0193] The memory 62 may be an internal storage unit of the computer device 60, such as the hard disk or memory of the computer device 60. The memory 62 may also be an external storage device of the computer device 60, such as a plug-in hard disk equipped on the computer device 60, a smart media card (SMC), a secure digital (SD) card, a flash card, etc.

[0194] Further, the memory 62 may also include both the internal storage unit of the computer device 60 and an external storage device. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 may also be used to temporarily store data that has been output or is to be output.

[0195] Please refer to Figure 8 , the terminal device is an electronic device 600, and the electronic device 600 is presented in the form of a general-purpose computing device. The components of the electronic device may include but are not limited to: at least one processing unit 610, at least one storage unit 620, a bus 630 connecting different platform components (including the storage unit 620 and the processing unit 610), a display unit 640, etc.

[0196] Among them, the storage unit stores program code, and the program code can be executed by the processing unit 610, so that the processing unit 610 executes the steps according to various exemplary embodiments of the present invention described in the method part of this specification. For example, the processing unit 610 can execute the steps shown in the figure.

[0197] The storage unit 620 may include a readable medium in the form of a volatile storage unit, such as a random access storage unit (RAM) 6201 and / or a cache storage unit 6202, and may further include a read-only storage unit (ROM) 6203.

[0198] The storage unit 620 may also include a program / utilities 6204 having a set (at least one) of program modules 6205. Such program modules 6205 include but are not limited to: an operating system, one or more application programs, other program modules, and program data. The implementation of a network environment may be included in each or some combination of these examples.

[0199] The bus 630 may represent one or more of several types of bus structures, including a memory bus or a memory controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of the multiple bus structures.

[0200] The electronic device 600 can also communicate with one or more external devices 700 (such as a keyboard, a pointing device, a Bluetooth device, etc.), and can also communicate with one or more devices that enable a user to interact with the electronic device 600, and / or communicate with any device (such as a router, a modem) that enables the electronic device 600 to communicate with one or more other computing devices. Such communication can be carried out through the input / output interface 650. Moreover, the electronic device 600 can also communicate with one or more networks (such as a local area network, a wide area network, and / or a public network, such as the Internet) through the network adapter 660. The network adapter 660 can communicate with other modules of the electronic device 600 through the bus 630. It should be understood that, although not shown in the figure, other hardware and / or software modules can be used in combination with the electronic device 600, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage platforms, etc.

[0201] Embodiment 4

[0202] The present invention also provides a storage medium, specifically a computer-readable storage medium, which is a memory device in a terminal device and is used for storing programs and data. It can be understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and, of course, the extended storage medium supported by the terminal device. It can be any tangible medium that contains or stores a program, and this program can be used by or in combination with an instruction execution system, apparatus, or device. The computer-readable storage medium provides a storage space, and the operating system of the terminal is stored in this storage space. Moreover, one or more instructions suitable for being loaded and executed by a processor are stored in this storage space, and these instructions can be one or more computer programs (including program codes). It should be noted that more specific examples of the computer-readable storage medium here include: an electrical connection having one or more wires, a portable disk, a hard disk, a random access memory, a read-only memory, an erasable programmable read-only memory, an optical fiber, a portable compact disk read-only memory, an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0203] The computer-readable storage medium also includes a data signal propagated in a baseband or as part of a carrier wave, which carries the readable program code. Such a propagated data signal can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. The readable storage medium can also be any readable medium other than the readable storage medium, which can send, propagate, or transmit a program for use by or in conjunction with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium can be transmitted using any appropriate medium, including but not limited to wireless, wired, optical fiber cable, radio frequency, etc., or any suitable combination of the above.

[0204] The program code for performing the operations of the present invention can be written in any combination of one or more programming languages, including object-oriented programming languages such as Java, C++, etc., and also including conventional procedural programming languages such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computing device, partially on the user's device, executed as a stand-alone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In the case of a remote computing device, the remote computing device can be connected to the user's computing device through any type of network, including a local area network or a wide area network, or can be connected to an external computing device (e.g., by using an Internet service provider to connect through the Internet).

[0205] One or more instructions stored in the computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the power network oscillation analysis method considering line distribution characteristics in the above embodiments; the one or more instructions in the computer-readable storage medium are loaded and executed by the processor to perform the following steps:

[0206] Obtain the relevant parameters of the lumped-parameter transmission device and the distributed-parameter line, and separately perform parameter preprocessing on the distributed-parameter line; establish a generalized state-space model based on the matrix pencil based on the obtained relevant parameters of the lumped-parameter transmission device, establish a time-delay algebraic equation set based on the obtained relevant parameters of the distributed-parameter line, and use the spectral discretization method to transform the time-delay algebraic equation set into a finite-dimensional differential equation set; based on the obtained generalized state-space model and finite-dimensional differential equation set, use Kirchhoff's law to form a free oscillation model of the passive power network, and determine the forced oscillation model of the passive power network under an ideal excitation source; perform a generalized eigenvalue decomposition on the obtained free oscillation model of the passive power network, identify the key resonance modes, solve the forced oscillation model of the passive power network under an ideal excitation source, and obtain the right and left eigenvectors corresponding to the dynamic characteristics of the power network; analyze the obtained right and left eigenvectors corresponding to the dynamic characteristics of the power network, determine the harmonic voltage distribution of each bus of the power network and the weak areas vulnerable to harmonics, draw a harmonic distribution map and output the identified key resonance modes.

[0207] In each of the embodiments provided in the present application, the databases involved may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., and is not limited thereto. In each of the embodiments provided in the present application, the processors involved may be general-purpose processors, central processors, graphics processors, digital signal processors, programmable logics, data processing logics based on quantum computing, etc., and are not limited thereto.

[0208] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Usually, the components described and shown in the accompanying drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed present invention, but merely represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0209] Case analysis

[0210] To verify the effectiveness of the method proposed in the present invention, a IEEE standard case, namely the New England 39-bus system, will be used for modeling and resonance analysis in this case analysis. All transmission lines adopt the distributed-parameter model. The case topology diagram is as Figure 4 shown.

[0211] The eigenvalue distribution diagram calculated by the matrix pencil is shown byFigure 5 As shown. Under per-unit values (with 60 Hz as the reference), the damping of the vast majority of oscillation modes lies within the interval of [-1.5, 0), and the oscillation frequencies are all much greater than 1. This indicates that, with the network structure and parameters unchanged, the system will not resonate under the power frequency excitation source and can operate normally. Below 3 kHz (i.e., the region where the imaginary part is less than 50), there are a total of 36 key characteristic roots in the system, and the oscillation frequencies of some characteristic roots are listed in Table 1.

[0212] Table 1 Correspondence between Oscillation Frequencies of Some Modes and Peak Values of Sweep Frequency Curves

[0213]

[0214] The above results give the key modes where resonance may potentially occur. Continuously applying a periodic forcing source at the corresponding positions is very likely to activate these modes and cause voltage amplification or even resonance in the system. As mentioned in Step 4.2, the right eigenvector v i represents the sensitivity of different buses to mode i and can be regarded as a measure to evaluate the response degree of each bus to mode i; the left eigenvector w i determines the weakness degree of the bus where the forcing source is placed. To verify this conclusion, this section will conduct a characteristic analysis on the 16th key mode, that is, λ = -0.2255 ± j18.00.

[0215] Table 2 lists the amplitudes of the components corresponding to the bus voltages in the left and right eigenvectors. By comparing the amplitudes of the left eigenvectors, it can be seen that the voltage component corresponding to bus 14 is the largest, which is the weakest position in the power grid. Injecting a current source with the corresponding oscillation frequency at this bus position will cause the most severe harmonic amplification phenomenon.

[0216] To observe the harmonic amplification phenomenon, in this paper, sinusoidal current forcing sources with a unit amplitude are respectively applied 18 times at relatively strong and weak bus positions, namely bus 8 and bus 9 (which are at both ends of a certain transmission line). An electromagnetic transient simulation is performed on this system, and the Prony method is used to analyze the instantaneous voltages of each bus. The rightmost two columns of Table 4 show the amplitudes of the 18th harmonic voltage responses in the instantaneous voltage waveforms during the two electromagnetic transient simulations. In addition, the comparison of the amplitudes of the right eigenvectors and the distribution of the 18th harmonic voltages is as Figure 6 shown.

[0217] Table 2 Components in the Left and Right Eigenvectors Corresponding to Bus Voltages

[0218]

[0219] In summary, the power network oscillation analysis method and system considering line distribution characteristics of the present invention are suitable for the electromagnetic oscillation analysis of large-scale interconnected networks at the industrial level, can be used to obtain the key factors affecting oscillation modes, guide the tuning of controller parameters and the design of control strategies, and provide a theoretical basis for effectively suppressing electromagnetic oscillations.

[0220] The above content is only to illustrate the technical idea of the present invention, and the protection scope of the present invention cannot be limited thereby. Any changes made on the basis of the technical solution according to the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A power network oscillation analysis method considering line distribution characteristics, characterized in that It includes the following steps: S1. Obtain the relevant parameters of the lumped-parameter transmission device and the distributed-parameter line, and separately perform parameter preprocessing on the distributed-parameter line; S2. Based on the relevant parameters of the lumped-parameter transmission device obtained in step S1, establish a generalized state-space model based on the matrix pencil, and based on the relevant parameters of the distributed-parameter line obtained in step S1, establish a time-delay algebraic equation set. Use the spectral discretization method to transform the time-delay algebraic equation set into a finite-dimensional differential equation set; S3. Based on the generalized state-space model and the finite-dimensional differential equation set obtained in step S2, use Kirchhoff's law to form a free-oscillation model of the passive power network, and determine the forced-oscillation model of the passive power network under an ideal excitation source; S4. Perform a generalized eigenvalue decomposition on the free-oscillation model of the passive power network obtained in step S3, identify the key resonance modes, solve the forced-oscillation model of the passive power network under an ideal excitation source, and obtain the right and left eigenvectors corresponding to the dynamic characteristics of the power network; S5. Analyze the right and left eigenvectors corresponding to the dynamic characteristics of the power network obtained in step S4, determine the harmonic voltage distribution of each bus of the power network and the vulnerable areas susceptible to harmonics, draw a harmonic distribution map and output the identified key resonance modes.

2. The power network oscillation analysis method considering line distribution characteristics according to claim 1, characterized in that, Step S2 is specifically as follows: S201. For the lumped-parameter transmission device, clarify the number of ports. Regard the bus voltage corresponding to the port as the input variable and the current flowing through the port as the output variable. Write differential-algebraic equations according to Kirchhoff's law and the dynamic relationship of LC elements, retain the algebraic variables, and establish a generalized state-space model; S202. Establish a time-delay algebraic equation of the distributed-parameter transmission line based on the Bergeron model; Use the method of sparse low-order solution operator discretization to transform the time-delay algebraic equation set into a finite-dimensional differential equation set, and then perform dynamic coupling with the generalized state-space model obtained in step S201.

3. The power network oscillation analysis method considering line distribution characteristics according to claim 2, characterized in that Write the differential-algebraic equations according to Kirchhoff's law and the dynamic relationship of LC elements as follows: Among them, u m represents the voltage at the T-junction; u p , u q represent the port voltages on both sides of the transformer; i p , i q and i m respectively represent the currents flowing through the primary winding, secondary winding and exciting winding; T k1 / T k2 represents the turns ratio of the ideal transformers on both sides; R 1σ (R 2σ ) and L 1σ (L 2σ ) represent the resistance and leakage inductance of the primary (secondary) winding of the transformer; R m and L m represent the resistance and leakage inductance of the exciting winding of the transformer.

4. The power grid oscillation analysis method considering line distribution characteristics according to claim 2, characterized in that, Use the method of sparse low-order solution operator discretization to transform the time-delay algebraic equation set into a finite-dimensional differential equation set as follows: where, i p (t), i q (t) and u p (t), u q (t) respectively represent the instantaneous current flowing through both the sending and receiving sides and the instantaneous voltage at both ends of the sending and receiving; τ is the propagation time of the line; Z represents the modified wave impedance, γ is defined as the adjustment coefficient, and k1 to k4 are respectively the characteristic coefficients of the distributed parameter transmission line.

5. The power network oscillation analysis method considering line distribution characteristics according to claim 1, characterized in that Step S3 is specifically as follows: Construct a generalized model of the branch element, establish Kirchhoff's current law for the bus, and form a free-oscillation model of the passive power network; respectively establish a power network model excited by a current source and a power network model excited by a voltage source based on the free-oscillation model of the passive power network.

6. The power network oscillation analysis method considering line distribution characteristics according to claim 5, characterized in that, The free-oscillation model of the passive power network is: where x is the variable of all branches and buses in the set, (J, T) is a matrix pencil, is the derivative of the generalized variable x.

7. The power grid oscillation analysis method considering line distribution characteristics according to claim 5, characterized in that The power network model excited by a current source is: where b s is a selection vector related to the position of the current source, and I s (t) is the injection current source excitation existing on bus s; The power network model excited by a voltage source is: where b s ′ is a selection vector related to the location of the voltage source; is the corresponding matrix pencil, and U s (t) is the voltage source excitation existing on bus s.

8. The power network oscillation analysis method considering line distribution characteristics according to claim 1, characterized in that, Step S4 is specifically as follows: Obtain the matrix pencil (J, T) corresponding to the generalized state-space equation, obtain an orthogonal matrix through the generalized Schur decomposition, transform the matrix pencil into an upper triangular matrix based on the orthogonal transformation, and further extract the generalized eigenvalues from the diagonal elements; obtain the input vector and output vector corresponding to the forced oscillation, and determine the harmonic voltage distribution and the additional gain from the excitation source to the corresponding mode through the right and left eigenvectors.

9. The power grid oscillation analysis method considering line distribution characteristics according to claim 8, characterized in that, All the eigenvalues of the matrix pencil (J, T) are: λ(J,T) = {A ii / B ii , i = 1, …, n} where A ii and B ii are the diagonal elements of matrices A and B respectively, and λ is the eigenvalue; Solve the eigenvectors for A and B, and then transform them into the eigenvectors ξ of the original problem through the unitary matrices Q and Z.

10. A power network oscillation analysis system considering line distribution characteristics, characterized in that, Including: A data module that obtains relevant parameters of a lumped-parameter transmission device and a distributed-parameter line, and separately performs parameter preprocessing on the distributed-parameter line; A construction module that establishes a generalized state-space model based on matrix pencil using the relevant parameters of the lumped-parameter transmission device obtained by the data module, establishes a time-delay algebraic equation set using the relevant parameters of the distributed-parameter line obtained by the data module, and transforms the time-delay algebraic equation set into a finite-dimensional differential equation set using the spectral discretization method; An oscillation module that forms a free oscillation model of a passive power network based on the generalized state-space model and the finite-dimensional differential equation set obtained by the construction module, and determines a forced oscillation model of the passive power network under an ideal excitation source; An identification module that performs a generalized eigenvalue decomposition on the free oscillation model of the passive power network obtained by the oscillation module, identifies key resonance modes, solves the forced oscillation model of the passive power network under an ideal excitation source, and obtains the right and left eigenvectors corresponding to the dynamic characteristics of the power network; An analysis module that analyzes the right and left eigenvectors corresponding to the dynamic characteristics of the power network obtained by the identification module, determines the harmonic voltage distribution of each bus of the power network and the vulnerable areas susceptible to harmonics, draws a harmonic distribution map, and outputs the identified key resonance modes.

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