Key Feature Extraction Method for Electro-Electrical Coupled Systems Based on Modal Synthesis

Abstract

This invention relates to the field of dynamic characteristic analysis technology for complex integrated energy systems, and particularly to a method for extracting key features of an electro-gas coupled system based on modal synthesis. The method includes: acquiring the dynamic nonlinear models of components in the electro-gas coupled system; obtaining a unified nonlinear equation set in the electro-gas coupled system based on the dynamic nonlinear models of the components, and then obtaining a unified linear equation set through linearization, thereby obtaining the system state matrix; obtaining the system's full-order eigenvalues ​​using the eigenvalue decomposition method based on the obtained system state matrix, analyzing the system's full-order modes, and then using modal synthesis to analyze the full-order eigenvalues ​​to obtain the system's key dominant modes; analyzing the dynamic process of the system based on the obtained key dominant modes, and performing simulation. This invention reduces the difficulty of dynamic simulation by reducing the system's high-order dynamics to low-order dynamics, effectively solving the problem of inaccurate time scale division in previous methods.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of dynamic characteristic analysis of complex integrated energy systems, and particularly relates to a key feature extraction method for an electricity-gas coupled system based on modal synthesis. BACKGROUND

[0002] In the past few decades, the green and low-carbon transformation trend of China's power industry is obvious. The energy system dominated by fossil fuels will be transformed into an energy system dominated by renewable energy. The energy system dominated by renewable energy implements multi-energy complementation, which can give full play to the characteristics of various power sources, complement each other's advantages, promote better grid connection and consumption of wind power and photovoltaic power, expand the market space of new energy development, increase the proportion of renewable energy, achieve the goal of energy saving and emission reduction, improve power supply quality, and better guarantee the safe, stable and economic operation of the power grid.

[0003] The integrated energy system has a large number of coupled elements, resulting in high-order modal coupling dynamic processes, and the dynamic process analysis of high-order nonlinear dynamic systems is very difficult. In the current dynamic process analysis of integrated energy systems, the dynamic time scales of different sub-energy systems are usually used for modal division, and the differences in dynamic characteristics of various elements in the system and the consistency of dynamic characteristics of similar elements in different sub-energy systems have not been reasonably considered. Therefore, how to map the original high-order modal to a low-dimensional space to simplify the calculation under the premise of minimizing the error is one of the difficulties to be studied. SUMMARY

[0004] The purpose of the present application is to propose a key feature extraction method for an electricity-gas coupled system based on modal synthesis, to perform modal analysis on a high-order nonlinear dynamic system by using eigenvalue decomposition and modal synthesis, to extract key dominant modes of the system, and to analyze the participation degree of different variables in each dominant mode according to the modal participation factor, so as to solve the problem of how to map the original high-order modal to a low-dimensional space to simplify the calculation under the premise of minimizing the error proposed in the background technology. The present application has significant engineering practical value and wide application prospect.

[0005] To achieve this purpose, the present application adopts the following technical solutions:

[0006] The key feature extraction method for an electricity-gas coupled system based on modal synthesis comprises the following steps:

[0007] S1, obtaining a dynamic nonlinear model of an element in the electricity-gas coupled system;

[0008] S2, obtaining a unified nonlinear equation set in the electricity-gas coupled system according to the dynamic nonlinear model of the element, and then obtaining a unified linear equation set by linearization to obtain a system state matrix;

[0009] S3, according to the obtained system state matrix, eigenvalue decomposition method is used to obtain system full order eigenvalue, analyze system full order modal, and then the full order eigenvalue analysis is carried out by using modal synthesis method, so as to obtain the key dominant modal of the system;

[0010] S4, according to the obtained system key dominant modal, the dynamic process of the system is analyzed, and simulation is carried out.

[0011] Preferably, the dynamic nonlinear model of the element in the electro-gas coupling system comprises an electric power subsystem model, a natural gas subsystem model and an electrical subsystem model.

[0012] Preferably, the electric power subsystem model comprises the following mathematical functions:

[0013] (1) the differential equation of the electric power subsystem is represented as:

[0014]

[0015] F e =[F e (1) (x e ,y e ,x eg );F e (2) (x e ,y e ,x eg )]

[0016] In the formula, x e represents the differential variable of the electric power subsystem, including the excitation potential E f , the d-axis and q-axis sub-transient potential E′ d , E′ q , the power angle δ, the speed ω and the performance parameters x1, x2 of the exciter, i.e. x e =[E f ,E′ d ,δ,ω,x1,x2];

[0017] y e represents the algebraic variable of the electric power subsystem, including the stator voltage V x , V y , the mechanical power P m of the generator, i.e. y e =[V x ,V y ,P m ];

[0018] x eg represents the differential variable of the electrical coupling element, including the coupling unit speed ω, the reactance x gt , i.e. xeg = [ω, x gt ];

[0019] where the generator's nonlinear equations are represented as:

[0020]

[0021]

[0022] where the exciter's nonlinear equations are represented as:

[0023]

[0024]

[0025] where T' do and T' qo represent the generator transient time constant, X d represents the generator d-axis reactance, X' d represents the generator d-axis transient reactance, X q represents the generator q-axis reactance, X' q represents the generator q-axis transient reactance, D represents the generator field current; T A , T b , T c all represent the exciter time constant, K A represents the controller parameters;

[0026] (2) The power subsystem's representative equations are represented as:

[0027] 0 = G e (x e , y e , x eg )

[0028] G(e) = [G e (1) (x e , y e , x eg ); G e (2) (x e , y e , x eg ); G e (3) (x e , y e , x eg )]

[0029] where the generator's terminal voltages and currents G e (1) (x ey e x eg The mathematical expression of (x

[0030]

[0031] The mathematical expression of (x e (2) (x e y e x eg ) is:

[0032] The mathematical expression of (x e (2) (x e y e x eg ) = YV = I

[0033]

[0034] The mathematical expression of (x e (3) (x e y e x eg ) is:

[0035]

[0036]

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043]

[0044] In the formula, I and V represent column vectors composed of bus injection current and node voltage; Y represents node admittance matrix, G represents electric conductance, and B represents electric inductance.

[0045] Preferably, the differential equation of the natural gas subsystem model is represented as:

[0046]

[0047]

[0048] where pr represents the node pressure pa, M represents the gas flow rate kg / s, A represents the pipe cross-sectional area m 3 , L represents the pipe length m, and the subscripts "in" and "out" represent the start and end points of the pipe, respectively.

[0049] Preferably, the differential algebraic equation of the electrical subsystem model is represented as:

[0050]

[0051]

[0052] where η gt represents the gas turbine efficiency, and K gas represents the coal gas heat value.

[0053] Preferably, in S2, the unified nonlinear equations of the electrical-gas coupling system are obtained according to the dynamic nonlinear model of the element, and the unified linear equations are obtained by linearization, so as to obtain the system state matrix, and the specific steps include the following steps.

[0054] S201. Unified nonlinear equations of the electrical-gas coupling system are obtained according to the dynamic nonlinear model of the element, and are represented as:

[0055]

[0056] S202. Unified linear equations of the electrical-gas coupling system are obtained by linearization at the equilibrium point (x0, y0) according to the unified nonlinear equations, and are represented as:

[0057]

[0058] where x = [x e T x g T x eg T ] T represents the differential variables of the electrical-gas coupling system, y = [y e T y g T ] T represents the algebraic variables of the electrical-gas coupling system; x = x0, y = y0 represents the equilibrium point of the electrical-gas coupling system.

[0059] S203. Unified linear equations of the electrical-gas coupling system are obtained by linearization at the equilibrium point (x0, y0) according to the unified linear equations, and are represented as:

[0060]

[0061]

[0062] In the formula, A represents a system state matrix, containing all information of the source-to-load of the electro-aero coupled comprehensive energy system.

[0063] Preferably, in S3, the system full-order characteristic roots are obtained by using eigenvalue decomposition method according to the obtained system state matrix, the system full-order modes are analyzed, and then the key dominant modes are obtained by using modal synthesis method to analyze the full-order characteristic roots, specifically including the following steps:

[0064] S301, solving the characteristic equation of the system state matrix A according to the unified linear equation group, expressed as:

[0065] det(λI i -A)=0

[0066] In the formula, the system full-order characteristic roots λ i (i=1,···,N);

[0067] wherein the system dynamic order is N order, λ i characterizes the mode;

[0068] S302, using modal synthesis method to synthesize the modes under the same time scale of the system, obtaining the real part Re(λ i ) of the characteristic root λ i of the mode, Re(λ i ) reflects the mode attenuation performance, and the mode attenuation speed is judged according to the first judgment condition:

[0069] Re(λ i )<0

[0070] Wherein |Re(λ i )| is larger, indicating that the mode attenuation speed is faster;

[0071] Then, whether the characteristic roots of the two modes are the same time scale is judged according to the second judgment condition:

[0072]

[0073] Wherein when the characteristic roots of the two modes satisfy the second judgment condition, it means that the characteristic roots of the two modes are the same time scale; when the characteristic roots of the two modes do not satisfy the second judgment condition, it means that the characteristic roots of the two modes are not the same time scale;

[0074] S303, according to step S302, the modes of the same time scale of the system are synthesized, and m different modes μ1, μ2,…, μ mm<N, then m modes represent the key feature mode group of the system;

[0075] Thus, the key feature mode m order of the N order complex system can be extracted, and the dynamic equation of the key mode of the system is represented as:

[0076]

[0077] In the formula, x μ1 represents the variable related to the feature mode μ1, f μ1 represents the equation on the time scale represented by the μ1 mode.

[0078] One of the technical solutions in the above technical solution has the following beneficial effects:

[0079] 1. The application overcomes the problem of inaccurate time scale division caused by traditional division of time scale of sub-energy systems, and according to the system eigenvalue, the time scale of the system is divided by using the time scale division principle, so that the scientificity of time scale division is ensured.

[0080] 2. The application overcomes the problem of large dynamic simulation calculation amount of traditional high-order comprehensive energy system, and by reducing the high-order dynamic of the system to low-order dynamic, the difficulty of dynamic simulation is reduced.

[0081] 3. Compared with the equal step method and the traditional subsystem multi-step method, the calculation time of the method is short, the calculation result error is small, and the method is more stable and has more advantages.

[0082] 4. The application has strong applicability, can be applied to the modeling, analysis and optimization field of large-scale heat-electricity coupled system, and has significant engineering practical value and wide application prospect. BRIEF DESCRIPTION OF DRAWINGS

[0083] Figure 1 The flowchart of the method of the application is shown in the figure.

[0084] Figure 2 The model diagram of the HIES model is shown in the figure.

[0085] Figure 3 The specific simulation results of node 2 flow within 5s of the three methods are shown in the figure.

[0086] Figure 4 The specific simulation results of the power generator 1 power angle within 5s of the three methods are shown in the figure.

[0087] Figure 5 The specific simulation results of the coupling link variable within 5s of the three methods are shown in the figure.

[0088] Figure 6is a schematic diagram of the comparison of the node pressure simulation results of the three methods within 5s. DETAILED DESCRIPTION

[0089] The application will be further described in connection with the embodiments and drawings, but the embodiments of the application are not limited thereto.

[0090] The application provides a key feature extraction method of an electro-gas coupling system based on modal synthesis, comprising the following steps:

[0091] S1, acquiring a dynamic nonlinear model of an element in the electro-gas coupling system, including a power subsystem model, a natural gas subsystem model and an electrical subsystem model;

[0092] The power subsystem model comprises the following mathematical functions:

[0093] (1) the differential equation of the power subsystem is represented as:

[0094]

[0095] F e =[F e (1) (x e ,y e ,x eg );F e (2) (x e ,y e ,x eg )]

[0096] In the formula, x e represents differential variables of the power subsystem, including excitation potential E f , d-axis and q-axis sub-transient potential E′ d of the generator, E′ q , power angle δ, rotating speed ω and performance parameters x1 and x2 of the exciter, i.e., x e =[E f ,E′ d ,δ,ω,x1,x2];

[0097] y e represents algebraic variables of the power subsystem, including stator voltage V x , V y and mechanical power P m of the generator, i.e., y e =[V x ,V y ,P m ];

[0098] x egThe differential variable representing the electrical coupling element, including the coupling machine speed ω, the reactance x gt i.e. x eg = [ω, x gt ];

[0099] wherein the non-linear equation of the generator is represented as:

[0100]

[0101]

[0102] The non-linear equation of the exciter is represented as:

[0103]

[0104]

[0105] wherein T' do and T' qo represent the generator transient time constant, X d represents the reactance of the generator d-axis, X' d represents the generator d-axis transient reactance, X q represents the reactance of the generator q-axis, X' q represents the generator q-axis transient reactance, D represents the generator excitation current; T A , T b , T c all represent the exciter time constant, K A represents the controller parameter;

[0106] (2) The representative equation of the power subsystem is represented as:

[0107] 0 = G e (x e , y e , x eg )

[0108] G(e) = [G e (1) (x e , y e , x eg ); G e (2) (x e , y e , x eg ); G e (3) (x e , y e , x eg )]

[0109] where the terminal voltage and current of the generator G e (1) (x e ,y e ,x eg ) is given by:

[0110]

[0111] The mathematical expression of the electrical network model G e (2) (x e ,y e ,x eg ) is given by:

[0112] The mathematical expression of the coupling between the generator and the electrical network G e (2) (x e ,y e ,x eg ) = YV = I

[0113]

[0114] The mathematical expression of the coupling between the generator and the electrical network G e (3) (x e ,y e ,x eg ) is given by:

[0115]

[0116]

[0117]

[0118]

[0119]

[0120]

[0121]

[0122]

[0123]

[0124] In the formula, I and V represent the column vector composed of the grid bus injection current and the node voltage; Y represents the node admittance matrix, G represents the conductance, and B represents the susceptance.

[0125] The differential equation of the natural gas subsystem model is represented as:

[0126]

[0127]

[0128] where pr represents the node pressure pa, M represents the gas flow rate kg / s, A represents the pipe cross-sectional area m 3 , L represents the pipe length m, and the subscripts "in" and "out" represent the start and end points of the pipe, respectively.

[0129] The differential algebraic equation representation of the electrical subsystem model is as follows:

[0130]

[0131]

[0132] where η gt represents the gas turbine efficiency, and K gas represents the coal gas heat value.

[0133] S2, obtaining a unified nonlinear equation set in the electro-gas coupling system according to the dynamic nonlinear model of the element, and then obtaining a unified linear equation set through linearization to obtain a system state matrix; specifically including the following steps:

[0134] S201, obtaining a unified nonlinear equation set in the electro-gas coupling system according to the dynamic nonlinear model of the element, and represented as:

[0135]

[0136] S202, linearizing at the equilibrium point (x0, y0) according to the unified nonlinear equation set to obtain a unified linear equation set of the electro-gas coupling system, and represented as:

[0137]

[0138] where x = [x e T x g T x eg T ] T represents the differential variable of the electro-gas coupling system, y = [y e T y g T ] T represents the algebraic variable of the electro-gas coupling system; x = x0, y = y0 represents the equilibrium point of the electro-gas coupling system;

[0139] S203, eliminating the algebraic variable of the unified linear equation set to obtain:

[0140]

[0141]

[0142] In the formula, A represents a system state matrix, containing all information of the source-to-load of the electro-gas coupling comprehensive energy system.

[0143] S3, according to the obtained system state matrix, the eigenvalue decomposition method is used to obtain the system full-order eigenvalue, the system full-order modal is analyzed, and then the key dominant modal is obtained by using the modal synthesis method for the full-order eigenvalue analysis; specifically including the following steps:

[0144] S301, according to the unified linear equation set, the characteristic equation of the system state matrix A is solved, which is expressed as:

[0145] det(λI i -A)=0

[0146] In the formula, the system full-order eigenvalue λ i (i=1,···,N);

[0147] Wherein, the system dynamic order is N order, λ i characteristic modal;

[0148] S302, using the modal synthesis method, the modal at the same time scale of the system is synthesized to obtain the real part Re(λ i ) of the characteristic root λ i of the modal, Re(λ i ) reflects the modal damping performance, and the first judgment condition is used to judge the modal damping speed:

[0149] Re(λ i )<0

[0150] Wherein, the larger |Re(λ i )| indicates the faster the modal damping speed;

[0151] Then, the second judgment condition is used to judge whether the characteristic roots of the two modes are the same time scale:

[0152]

[0153] Wherein, when the characteristic roots of the two modes satisfy the second judgment condition, it indicates that the characteristic roots of the two modes are the same time scale; when the characteristic roots of the two modes do not satisfy the second judgment condition, it indicates that the characteristic roots of the two modes are not the same time scale;

[0154] S303、According to step S302, the modes of the same time scale of the system are synthesized, and m different modes μ1, μ2, …, μm of the system can be obtained. m , m < N, then the m modes represent the key characteristic mode group of the system;

[0155] Thus, the key characteristic mode m order of the N order complex system can be extracted, and the dynamic equation of the key mode of the system is represented as:

[0156]

[0157] In the formula, x μ1 represents the variable related to the characteristic mode μ1, f μ1 represents the equation on the time scale represented by the mode μ1.

[0158] S4, according to the obtained key dominant mode of the system, the dynamic process of the system is analyzed and simulated.

[0159] In order to further illustrate the purpose of the present application, the present application proposes the following embodiments, which specifically study the heterogeneous integrated energy system HIES model of IEEE 9-node power system EPS and 4-node natural gas system NGS coupling, as shown in Figure 2 And the dynamic process of the system is analyzed by using equal step method, conventional multi-step method and high-order modal reduction method respectively, and the accuracy and calculation time of different methods are compared. In addition, the dynamic characteristics of the system on different time scales are discussed by using the reduction method proposed in this paper.

[0160] Table 1 describes the modal synthesis results of the multi-step method based on reduction (ORBMS). There are 47 equations in the system, including 20-dimensional algebraic equations and 27-dimensional differential equations. The numbers in the brackets represent the nodes of the power system (EPS) or the natural gas system (NGS). Through the ORBMS method, the 27 order dynamic process is simplified to 6 order, and the main influence variables are as shown in the following table.

[0161] Table 1: Modal synthesis results of ORBMS

[0162]

[0163]

[0164] As can be seen from Table 1, there can be great differences between similar variables of different individuals. For example, the E dThe fast mode, i.e. mode 1. In contrast, the modes of generators 2 and 3 are slow modes, i.e. mode 3. It is worth noting that the power angle dynamic characteristic of generator 3 is the slowest mode, i.e. mode 6, which is different from the power angle dynamic characteristics of the other generators, modes 4 for generators 1 and 2. This is mainly because generator 3 is the coupling unit between the EPS and the NGS.

[0165] In this example, the EPS is simulated to have a three-phase short circuit at 3 s and is cleared in 0.2 s. The simulation step sizes for the two methods are listed in Table 2.

[0166] Table 2: Simulation step size settings for different methods

[0167]

[0168] In this example, three methods are used to calculate the dynamic process of HIES, and the corresponding simulation step sizes for each method are shown in Table 3.

[0169] The first method uses the equal step (ES) method, which selects a small simulation step size ΔT EPS for all individuals to accurately understand the dynamic process of the fast mode system.

[0170] The second method uses the traditional subsystem multi-step method (CSMS), which uses two different simulation step sizes, ΔT EPS and ΔT NGS for the EPS and NGS, respectively.

[0171] The third method uses the order-reduction-based multi-step (ORBMS) method, which also uses the same simulation step sizes ΔT EPS and ΔT NGS for the fast and slow systems, respectively. However, this method obtains the partition results of the system sub-modes through order reduction, rather than simply dividing the two simulation step sizes by physical subsystems. Modes 1-4 of the system are considered as the fast subsystem, while modes 5-6 are considered as the slow subsystem.

[0172] Table 3: Simulation average error for three methods

[0173]

[0174] The simulation results of the three methods are compared as shown in Figures 3-6 , and the average error is calculated as shown in Table 3. In summary, it can be seen that the simulation accuracy of the ORBMS method is the highest, with a maximum error of 0.88. The average error of the ES method is 1.55, while the average error of the CSMS method is the highest (1.88). The error of the proposed ORBMS method is only 47% of the CSMS method. In addition, all three methods perform well in simulating the slow mode of the system, for example, prgt and M in_gt while the error is larger when simulating the faster mode. For the slow mode pr gt the simulation error is 3.15 x 10 -4 the simulation error is 0.88 for the fast mode delta.

[0175] In terms of calculation time, the performance of the three methods in simulating dynamic processes in three different time windows is compared in Table 4. Compared with the ES method, both MS methods can significantly save calculation time, especially when simulating a long time window, the advantage is more obvious. When the simulation window is 0-10s, the calculation time of the three methods is almost the same. In contrast, when the simulation window is 0-100s, the time cost of the ES method is 203.28s, which is much higher than the 85.41s of the ORBMS method, and nearly 60% of the calculation time can be saved by using the method. It can be seen that the calculation error of the method of the present application is lower and the calculation time is shorter.

[0176] Table 4: Simulation calculation time of three methods

[0177] Simulation window (s) ES method CSMS method ORBMS method [0,10] 8.26s 8.53s 8.50s [0,30] 34.56s 25.96s 24.26s [0,100] 203.28s 88.57s 85.41s

[0178] The technical principles of the present application are described above in combination with specific embodiments. These descriptions are only to explain the principles of the present application, and cannot be interpreted in any way as a limitation on the scope of protection of the present application. Based on the explanations here, those skilled in the art can think of other specific embodiments of the present application without creative labor, and these equivalent variations or replacements are all included in the scope defined by the claims of the present application.

Claims

1. A method for extracting key features of an electro-aero coupled system based on modal synthesis, characterized in that, The method comprises the following steps: S1, obtaining a dynamic nonlinear model of an element in an electro-pneumatic coupling system; S2, obtaining a unified nonlinear equation set in the electro-pneumatic coupling system according to the dynamic nonlinear model of the element, and then obtaining a unified linear equation set through linearization to obtain a system state matrix; S3, obtaining system full-order characteristic roots by using a characteristic root decomposition method according to the obtained system state matrix, analyzing system full-order modes, and then obtaining key dominant modes of the system by using a modal synthesis method to analyze the full-order characteristic roots; S4, analyzing a dynamic process of the system according to the obtained key dominant modes of the system and performing simulation; The dynamic nonlinear model of the element in the electro-pneumatic coupling system comprises an electric power subsystem model, a natural gas subsystem model and an electrical subsystem model; The electric power subsystem model comprises the following mathematical functions: (1) a differential equation of the electric power subsystem is expressed as: wherein differential variable representing the electric power subsystem, including the field voltage , the generator shaft and shaft sub-transient voltage , the power angle , the rotational speed and the performance parameters of the exciter i.e. ; Algebraic variables representing the electrical power subsystem, including stator voltage , , generator mechanical power , i.e. ; The differential variable representing the electrical coupling element, including the coupling machine speed , the electrical reactance , i.e. ; wherein a nonlinear equation of a generator is expressed as: a nonlinear equation of an exciter is expressed as: wherein and represents the generator transient time constant, represents the generator reactance of the shaft, represents the generator transient reactance of the shaft, represents the generator reactance of the shaft, represents the generator transient reactance of the shaft, represents the generator excitation current; , , all represent the exciter time constant, represents the controller parameter; (2) a representative equation of the electric power subsystem is expressed as: wherein the terminal voltage and current of the generator The mathematical expression for the terminal voltage and current of the generator is: Electrical network model The mathematical expression is: Generator coupling to an electrical network The mathematical expression is: wherein , represents a column vector consisting of the grid bus injection currents and the node voltages; represents the node admittance matrix, represents the conductance, represents the susceptance; a differential equation of the natural gas subsystem model is expressed as: ： wherein representing the node pressure , representing the gas flow , representing the pipe cross-sectional area , representing the pipe length , the subscripts ” and ” represent the start and end points of the pipe, respectively; a differential algebraic equation of the electrical subsystem model is expressed as: ： wherein represents the efficiency of the gas turbine, represents the calorific value of the coal gas; In S2, the unified nonlinear equation set in the electro-pneumatic coupling system is obtained according to the dynamic nonlinear model of the element, and then the unified linear equation set is obtained through linearization to obtain the system state matrix, and the specific steps comprise the following steps: S201, obtaining the unified nonlinear equation set in the electro-pneumatic coupling system according to the dynamic nonlinear model of the element, which is expressed as: S202. According to the unified nonlinear equation system, at the equilibrium point ( Linearization at point ) yields the unified linear equations for the electro-pneumatic coupled system, expressed as: wherein denotes a differential variable of the electro-pneumatic coupling system, denotes an algebraic variable of the electro-pneumatic coupling system; denotes an equilibrium point of the electro-pneumatic coupling system; S203, according to the unified linear equation set, the algebraic variables are eliminated to obtain: In the formula, represents the system state matrix, containing all information of the source-to-load of the electro-mechanical integrated energy system; In S3, the system full-order characteristic roots are obtained by using the characteristic root decomposition method according to the obtained system state matrix, the system full-order modes are analyzed, and then the key dominant modes of the system are obtained by using the modal synthesis method to analyze the full-order characteristic roots, and the specific steps comprise the following steps: S301, solve the system state matrix according to the unified linear equation group whose characteristic equation is expressed as: where the system all-order characteristic roots ; wherein the system dynamic order is order, characterizing mode; S302, using modal synthesis method, synthesizing the modes of the system at the same time scale to obtain the characteristic roots of the modes of the real part of the characteristic roots , reflecting the mode attenuation performance, and determining the mode attenuation speed according to the first determination condition wherein The greater the value, the faster the modal decay rate. Then, it is judged whether the characteristic roots of the two modes are of the same time scale according to a second judgment condition: wherein when the characteristic roots of the two modes satisfy the second judgment condition, it is indicated that the characteristic roots of the two modes are of the same time scale; when the characteristic roots of the two modes do not satisfy the second judgment condition, it is indicated that the characteristic roots of the two modes are not of the same time scale; S303、According to step S302, the modes of the system in the same time scale are synthesized, and the system different modes , , The mode represents the key characteristic mode group of the system. Thus, the following can be extracted Key feature modes of complex systems The order, the dynamic equation representation of the key modes of the system is obtained as wherein representative feature modalities related variables, representative equations on the time scale represented by the modalities.

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