System frequency response analysis method based on electromechanical wave propagation characteristics

Abstract

The method for analyzing frequency response of system based on electromechanical wave propagation characteristics comprises the following steps: firstly, setting power shortage disturbance point, calculating the turning frequency ω ci and propagation coefficient PC between disturbance source point and generator node, and screening the generator affected by electromechanical disturbance. Then, according to the propagation coefficient, determining whether the generator node is affected by electromechanical disturbance, screening the generator affected by electromechanical disturbance, and calculating the composite electromechanical distance between the disturbance source point and the generator node j affected by disturbance. According to the hierarchical clustering of the system according to the composite electromechanical distance, the power system is divided into research area (affected by electromechanical disturbance, participating in frequency modulation) and external area (not affected by electromechanical disturbance, only for power transmission), the parameters of each generator in the research area are aggregated, the equivalent frequency response model of the system is established, and the frequency response analysis of the research area is carried out. The method provides an effective measure for simplifying the frequency response modeling and analysis of complex power system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of system frequency response analysis, and particularly relates to a system frequency response analysis method based on electromechanical wave propagation characteristics. BACKGROUND

[0002] Modern power system is a highly complex, dynamic interconnected nonlinear power system, whose operation is always affected by multiple random disturbances. Disturbances cause electromechanical dynamic phenomena such as rotor angle deviation and frequency fluctuation of generators, and propagate in the system in the form of approximate electromechanical waves. The propagation characteristics of electromechanical waves have an impact on the frequency safety of the power grid. The disturbance energy decays exponentially with the increase of electrical distance during the propagation process, resulting in a clear localization feature of the spatial distribution of dynamic response. Studies have shown that the influence range of electromechanical waves is usually limited to a limited area centered on the disturbance source, and the energy decay can be described by an exponential function. However, the existing system frequency response (SFR) analysis method has obvious limitations. The traditional SFR model is based on the lumped parameter assumption, which equates the total inertia of the whole network to a single inertia center, and assumes that the frequency dynamics have global consistency. This simplified modeling method cannot accurately reflect the influence of disturbance source location on the frequency propagation path, nor can it accurately evaluate the transmission characteristics of regional frequency support capacity.

[0003] In view of the above limitations, it is technically difficult and practically unnecessary to study the dynamic frequency response characteristics of complete complex modern power systems. Therefore, in modern power systems, the system frequency response analysis method considering the spatial characteristics of electromechanical wave propagation based on the propagation characteristics of electromechanical waves is particularly important in simplifying the complexity of frequency response analysis and reducing the calculation scale. SUMMARY

[0004] To solve the above technical problems, the present application provides a system frequency response analysis method based on electromechanical wave propagation characteristics, which first analyzes the degree of influence of elements in the system on electromechanical wave disturbance and the response speed to the disturbance, then calculates the turning frequency and complex electromechanical distance of each node in the system, and performs hierarchical clustering on the system, thereby dividing the system into a study area and an external area, and then performing system frequency response analysis on the study area. Thus, the complexity of system frequency response analysis is effectively simplified, and the calculation scale is reduced.

[0005] The technical scheme adopted by the present application is as follows:

[0006] The system frequency response analysis method based on electromechanical wave propagation characteristics comprises the following steps:

[0007] Step 1: Set a power shortage disturbance point, calculate the turning frequency ω between the disturbance source point and the generator node ci and the propagation coefficient PC;

[0008] Step 2: Determine whether the generator node is affected by the electromechanical disturbance according to the propagation coefficient PC;

[0009] Step 3: Screen out the generator affected by the electromechanical disturbance, and calculate the composite electromechanical distance between the disturbance source point and the generator node j affected by the disturbance

[0010] Step 4: According to the composite electromechanical distance Hierarchical clustering is performed on the power system, according to which the power system is divided into a research area and an external area, and the parameters of each generator in the research area are aggregated;

[0011] Step 5: Establish a system equivalent frequency response model to calculate the frequency of the research area.

[0012] In step 1, the power system is regarded as a power grid continuum model of unevenly distributed generators, lines and loads, in which the relationship between the electromechanical wave propagation speed and the inertia is:

[0013]

[0014] In formula (1), v is the electromechanical wave propagation speed; ω is the generator angular frequency; U is the voltage amplitude per unit; Δx is the distance between two nodes; z is the line unit impedance per unit; h is the unit length inertia.

[0015] In a discrete power system, the electromechanical wave exists within a limited frequency range, which is related to the generator rotational inertia and system line impedance, and the turning frequency ω c is expressed as:

[0016]

[0017] When the electromechanical wave signal frequency is greater than the turning frequency ω c , the amplitude of the electromechanical wave along the propagation direction will rapidly decay; when the electromechanical wave signal frequency is greater than 3 times the turning frequency ω c , the electromechanical wave amplitude decays to zero, at which time the disturbance energy will not continue to propagate.

[0018] The propagation coefficient PC is set to Δω / ω c , where Δω is the generator rotor angular frequency increment, and the greater the propagation coefficient PC, the less the generator is affected by the electromechanical disturbance. When the propagation coefficient PC is greater than 3, the generator will not be affected by the electromechanical disturbance. In step 3, based on the propagation time of the electromechanical disturbance between any two points, the composite electromechanical distance is defined. The composite electromechanical distance represents the increase in the power angle θ that the generator turns at a constant initial acceleration after the disturbance occursi The required time, i.e.:

[0019]

[0020] In the formula: is the composite electromechanical distance, in seconds; w is the error correction factor; M i is the rotor inertia constant of the generator node i; B is the transfer susceptance; def represents definition, i.e. defining the composite electromechanical distance

[0021] Between the generator node i and the generator node j, Bij = Bji, but generally M i ≠ M j Therefore, it can be seen that the electromechanical distance is directional. For an actual power system, the propagation direction of the electromechanical disturbance is difficult to determine, so the electromechanical distance without direction is set The average electromechanical distance between the generator disturbance source node i and the generator node j is:

[0022]

[0023] In the formula: represents the average electromechanical distance between node i and node j when the disturbance source point is i; represents the average electromechanical distance between node i and node j when the disturbance source point is j; represents the electromechanical distance between node i and node j when the disturbance source point is i; represents the electromechanical distance between node i and node j when the disturbance source point is j; B ij represents the transfer susceptance between node i and node j when the disturbance source point is i; B ji represents the transfer susceptance between node i and node j when the disturbance source point is j.

[0024] Under the action of the same electromechanical wave disturbance, the larger the inertia M i of the generator is, the smaller the rotor acceleration of the generator under the action of the system accelerating power is, the greater the propagation resistance of the electromechanical wave is, and the larger the electromechanical distance is; similarly, the larger the transfer susceptance B ij between the disturbance source point and the generator node is, the greater the accelerating power obtained by the generator is, the greater the rotor acceleration of the generator is, the greater the influence of the electromechanical wave disturbance on the generator is, the smaller the propagation resistance of the electromechanical wave is, and the smaller the electromechanical distance is. When the electromechanical disturbance occurs, the smaller the electromechanical distance is, the faster the response speed of the generator is, and the closer the contact between the two machines is.

[0025] In step 4, the part of the power system in the research area is affected by the electromechanical disturbance and participates in frequency modulation; the part of the power system in the external area is not affected by the electromechanical disturbance and only performs power transmission;

[0026] The power system is hierarchically clustered, and the power system is divided into a research area and an external area according to the hierarchical clustering result, as shown in FIG. 1. Figure 4 Before the division, the generators in the research area and the external area can participate in frequency modulation through the tie line. After the division, the generators in the external area only perform power transmission and do not participate in frequency modulation.

[0027] The parameters of the steam turbine in the research area are aggregated, and the parameter aggregation of the steam turbine in the research area is described by the following equations (5) to (9).

[0028] The mechanical power increment of the steam turbine-governor model is:

[0029]

[0030] In equation (5), ΔP mT (s) is the mechanical power increment; F H is the high-pressure turbine stage power ratio; T R is the reheater time constant; R T is the steam turbine droop coefficient; T C is the gas volume time constant; T G is the gas chamber time constant; s is a complex frequency domain variable in Laplace transform; and Δω s (s) is the angular frequency increment.

[0031] Suppose that the power system has N synchronous machines. Since the steam turbine droop coefficient R T is related to the rated capacity S N , the constant gain of the multi-steam turbine-governor is:

[0032]

[0033] In equation (6), S Ni is the rated power of the synchronous machine i; S sys is the rated power of the entire system; K mi represents the proportion of the rated power of the synchronous machine i to the rated power of the entire system.

[0034] The equivalent droop coefficient R of the power system is:

[0035]

[0036] wherein the equivalent gain is defined as κ i = K mi / R Ti , and R Ti is the droop coefficient of the i-th steam turbine.

[0037] As can be seen from equation (5), the mechanical power increment of the turbine-governor model is affected by T. G T C T R and F H The four parameters have an impact. To simplify the description, equation (7) defines the normalized gain λ. i This represents the combined effect of the turbine-governer in synchronous machine i;

[0038]

[0039] In step 5, according to equations (5) to (8), the transfer functions of multiple synchronous machines are aggregated into a single equivalent machine transfer function:

[0040]

[0041] Based on equation (9), an aggregated equivalent model of the power system frequency response in the study area is established, such as... Figure 5 As shown, i steam turbines ( Figure 5 The parameters in the red box in the upper figure are aggregated and are equivalent to one steam turbine. Figure 5 (See the red box in the lower image).

[0042] This invention provides a system frequency response analysis method based on electromechanical wave propagation characteristics, with the following technical advantages:

[0043] 1) For a complete and complex modern power system, the method proposed in this invention is applied to use a simplified study region to equivalently replace the modern power system, so that the frequency response results of the study region are consistent with the frequency response results of the complex power system. This method provides an effective measure to simplify the frequency response modeling and analysis of complex power systems.

[0044] 2) In step 1 of this invention, the power deficit disturbance point is set, and the corner frequency ω between the disturbance source point and the generator node is calculated. ci By using the propagation coefficient PC, generators affected by electromechanical disturbances are screened out, providing a basis for calculating composite electromechanical distances.

[0045] 3) In step 2 of this invention, it is determined whether the generator node is affected by electromechanical disturbance based on the propagation coefficient. In step 3, generators affected by electromechanical disturbance are screened out, and the composite electromechanical distance between the disturbance source point and the generator node j affected by the disturbance is calculated. This provides the foundation for hierarchical clustering in step 4.

[0046] 4) Step 4 of the present invention is based on the composite electromechanical distance The power system is divided into a research area (affected by the mechanical and electrical disturbance, participating in frequency modulation) and an external area (not affected by the mechanical and electrical disturbance, only performing power transmission) according to the hierarchical clustering of the system, the parameters of each generator in the research area are aggregated, and the system equivalent frequency response model is established in step 5 to provide a basis for frequency response analysis of the research area.

[0047] 5) The step 5 of the present application establishes a system equivalent frequency response model, and the frequency response analysis of the research area can effectively simplify the complexity of system frequency response analysis and reduce the calculation scale. BRIEF DESCRIPTION OF DRAWINGS

[0048] The present application will be further described below in combination with the drawings and examples:

[0049] Figure 1 The flowchart of the embodiment of the present application.

[0050] Figure 2 The simulation system diagram of the embodiment of the present application.

[0051] Figure 3 The hierarchical clustering result diagram.

[0052] Figure 4 The schematic diagram of the division of the research area and the external area.

[0053] Figure 5 The power system frequency response aggregation equivalent model.

[0054] Figure 6 The frequency response curve of the research area. DETAILED DESCRIPTION

[0055] The system frequency response modeling method based on the mechanical and electrical wave propagation characteristics first sets a power shortage disturbance point, calculates the turning frequency ω ci and the propagation coefficient PC between the disturbance source point and the generator node, and screens the generators affected by the mechanical and electrical disturbance. Then, according to the propagation coefficient, it is determined whether the generator node is affected by the mechanical and electrical disturbance, the generators affected by the mechanical and electrical disturbance are screened, and the composite mechanical and electrical distance between the disturbance source point and the generator node j affected by the disturbance is calculated. The system is subjected to hierarchical clustering, according to which the power system is divided into a research area (affected by the mechanical and electrical disturbance, participating in frequency modulation) and an external area (not affected by the mechanical and electrical disturbance, only performing power transmission), the parameters of each generator in the research area are aggregated, the system equivalent frequency response model is established, and the frequency response analysis of the research area is performed. Finally, the effectiveness of the method and the result is verified through an IEEE10 machine 39 node example system.

[0056] The flowchart of the present application is shown in Figure 1 , which includes the following steps:

[0057] Step 1: Set the power deficiency disturbance point, calculate the turning frequency ω between the disturbance source point and the generator node ci and the propagation coefficient PC:

[0058] Due to the uneven distribution of the structure and parameters of the actual power system, considering the propagation characteristics of the electromechanical disturbance load, the geographically widely distributed power system is regarded as a power grid continuum model of unevenly distributed generators, lines and loads, in which the relationship between the electromechanical wave propagation speed and the inertia is:

[0059]

[0060] In formula (1), v is the electromechanical wave propagation speed; ω is the generator angular frequency; U is the voltage amplitude per unit value; Δx is the distance between two nodes; z is the line unit impedance per unit value; h is the unit length inertia.

[0061] However, in a discrete power system, electromechanical waves can only exist within a limited frequency range, which is related to the generator moment of inertia and system line impedance, and is represented by the turning frequency ω c :

[0062]

[0063] When the frequency of the electromechanical wave signal is greater than the turning frequency, the amplitude of the electromechanical wave along the propagation direction will rapidly decay, and when the frequency of the electromechanical wave signal is greater than 3 times the turning frequency, the amplitude of the electromechanical wave will decay to zero, at which time the disturbance energy will not be able to continue to propagate. Set the propagation coefficient PC = Δω / ω c , where Δω is the generator rotor angular frequency increment, and the greater PC, the less the generator node is affected by the electromechanical disturbance. When PC is greater than 3, the generator will not be affected by the electromechanical disturbance.

[0064] Step 2: Determine whether the generator node is affected by the electromechanical disturbance according to the propagation coefficient, screen out the generators affected by the electromechanical disturbance, and calculate the composite electromechanical distance between the disturbance source point and the generator node affected by the disturbance

[0065] Based on the propagation time of the electromechanical disturbance between any two points, the composite electromechanical distance is defined, and the load electromechanical distance represents the power angle increment θ i required by the generator to make uniform acceleration (or deceleration) motion according to the constant initial acceleration after the disturbance occurs, that is:

[0066]

[0067] In the formula, def represents definition, i.e. defining the composite electromechanical distance is the composite electro-mechanical distance, in seconds; w is the error correction factor, generally w = 0.9; M i is the rotor inertia constant of generator node i; B is the transfer admittance.

[0068] Between generator node i and generator node j, Bij = Bji, but generally M i ≠ M j Therefore, it can be seen that the electro-mechanical distance is directional. For the actual power system, the propagation direction of the electro-mechanical disturbance is difficult to determine, so the electro-mechanical distance without direction is set The average electro-mechanical distance between generator node i (the disturbance source node) and j is:

[0069]

[0070] In the formula: represents the average electro-mechanical distance between node i and node j when the disturbance source point is i; represents the average electro-mechanical distance between node i and node j when the disturbance source point is j; represents the electro-mechanical distance between node i and node j when the disturbance source point is i; represents the electro-mechanical distance between node i and node j when the disturbance source point is j; B ij represents the transfer admittance between node i and node j when the disturbance source point is i; B ji represents the transfer admittance between node i and node j when the disturbance source point is j.

[0071] Under the action of the same electro-mechanical wave disturbance, the larger the inertia M i of the generator, the smaller the rotor acceleration of the generator under the action of the system accelerating power, the greater the propagation resistance of the electro-mechanical wave, and the larger the electro-mechanical distance; similarly, the larger the transfer admittance B ij between the disturbance source point and the generator node, the greater the accelerating power obtained by the generator, the greater the rotor acceleration of the generator, the greater the influence of the electro-mechanical wave disturbance on the generator, the smaller the propagation resistance of the electro-mechanical wave, and the smaller the electro-mechanical distance. When an electro-mechanical disturbance occurs, the smaller the electro-mechanical distance, the faster the response speed of the generator, and the closer the contact between the two machines.

[0072] Step three: according to the composite electro-mechanical distance The system is subjected to hierarchical clustering, and accordingly the power system is divided into a research area (affected by the electro-mechanical disturbance and participating in frequency modulation) and an external area (not affected by the electro-mechanical disturbance and only for power transmission), and the parameters of each generator in the research area are aggregated:

[0073] According to hierarchical clustering, the original system is divided into a research area and an external area, and the parameters of the research area are aggregated. For example,Figure 4 Before the division, the generators in both the study area and the external area can participate in frequency modulation through the tie line. After the division, the generators in the external area only perform power transmission and do not participate in frequency modulation. The mechanical power increment of the turbine-governor model is:

[0074]

[0075] In formula (5), ΔP mT (s) is the mechanical power increment; F H is the high-pressure turbine stage power ratio; T R is the reheater time constant; R T is the turbine droop coefficient; T C is the gas volume time constant; T G is the gas chamber time constant; s is a complex frequency domain variable in Laplace transform; Δω s (s) is the angular frequency increment. It is assumed that there are N synchronous machines in the power system. Since the turbine droop coefficient R T is related to the rated capacity S N , the constant gain of the multi-turbine-governor is:

[0076]

[0077] In formula (6), S Ni is the rated power of the synchronous machine i; S sys is the rated power of the entire system. K mi represents the proportion of the rated power of the synchronous machine i to the rated power of the entire system. The equivalent droop coefficient R of the power system is

[0078]

[0079] where the equivalent gain is defined as κ i = K mi / R Ti , and R Ti is the droop coefficient of the i-th turbine. As can be seen from formula (5), the mechanical power increment of the turbine-governor model is affected by four parameters, T G , T C , T R , and F H . To simplify the description, formula (7) defines the normalized gain λ i , which represents the comprehensive effect of the turbine-governor of the synchronous machine i.

[0080]

[0081] Step four: establish a system equivalent frequency response model and perform frequency response analysis on the study system:

[0082] According to formula (5) to formula (8), the transfer functions of multiple synchronous machines are aggregated into a transfer function of an equivalent machine:

[0083]

[0084] The system frequency response aggregation model of the research area is established according to formula (9). As shown in the upper part of the figure, the parameters of i steam turbines (red box in the upper part of the figure) are aggregated, and are equivalent to one steam turbine (red box in the lower part of the figure). Figure 5 Figure 5 Figure 5

[0085] Step five: the system frequency response modeling and characteristic analysis method based on the electromechanical distance established above is verified to be correct through simulation.

[0086] An IEEE 10-machine 39-node system model is built on a MATLAB / Simulink simulation platform as shown in the figure, and the effectiveness of the method is verified. The detailed data of the model and parameters in the example system can be referred to table 1 and table 2. Before executing the example verification, the following settings are made: Figure 2

[0087] (1) At t=100s, a sudden load L3=700MW (10% of the total load) is set to simulate a system frequency disturbance accident.

[0088] (2) The following simulation projects are set:

[0089] 1) The turning frequency and electromechanical distance are calculated according to steps one and two, and the example system is divided into a research area and an external area by hierarchical clustering.

[0090] 2) The system frequency response model is established, the research area frequency is calculated, and the reliability of the classification method is verified by comparing the time domain simulation frequency characteristics of the actual example system.

[0091] Table 1: line parameter values of the example system

[0092]

[0093]

[0094] Table 2: synchronous machine parameter values

[0095]

[0096] The system frequency response modeling method based on the electromechanical wave propagation characteristics is verified:

[0097] ​​​​The sudden load L3 = 700 MW (located at node 39, accounting for 10% of the total load) is set at t = 100 s, simulating a frequency accident and according to Figure 1 the control flow chart is executed.

[0098] Table 3: Turning frequency and propagation coefficient calculation results

[0099]

[0100]

[0101] According to formula (2), the turning frequency ω of each generator node is calculated c , as shown in Table 3. According to step one, since the propagation coefficients PC of G6 and G7 are greater than 3, it indicates that the mechanical and electrical wave disturbance amplitude of G6 and G7 is basically attenuated to zero, at this time G6 and G7 are not affected by the mechanical and electrical wave disturbance and cannot respond to the mechanical and electrical wave disturbance. Therefore, G6 and G7 are divided into the external region and are not the main research object.

[0102] Based on the above turning frequency calculation results, the composite mechanical and electrical distance between the disturbance source point G1 and the generators G2, G3, G4, G5, G8, G9, G10 affected by the mechanical and electrical wave disturbance is calculated , as shown in Table 4:

[0103] Table 4: Composite mechanical and electrical distance calculation results

[0104]

[0105] The hierarchical clustering of the above composite mechanical and electrical distance can clearly observe the connection strength between different generator groups, and the result is shown in Figure 3 . From the Figure 3 hierarchical clustering result, it can be known that the connection between the generators G1, G2, G3, G4, G8 and G9 is very close, forming a relatively concentrated cluster, so G1, G2, G3, G4, G8 and G9 are selected as the research region. The connection between the generator G5 and other generators in the system is weak, so G5 is classified into the external region. From the above results, G1, G2, G3, G4, G8, G9 and G10 are the research region, and G5, G6 and G7 are the external region. For the example system, the time domain simulation method is used to calculate the system frequency characteristics and related indexes.

[0106] The system equivalent inertia constant is calculated by aggregating the research region, and combined with the system synchronous generator model, the research region system frequency response model can be established, as shown in Figure 5 . The system frequency characteristics and related indexes are calculated, and by comparing the consistency of the two frequency dynamic characteristics and related indexes, the research region can be equivalent to replace the system frequency response. The comparison of the simulation frequency response curve and related indexes is shown inFigure 6 and shown in Table 4. At t = 112.68 s, the frequency difference is greatest, with the actual frequency being 49.792 Hz and the study area frequency being 49.776 Hz, for a difference of 0.016 Hz.

Claims

1. A system frequency response analysis method based on electromechanical wave propagation characteristics, characterized in that... Includes the following steps: Step 1: Set the power deficit disturbance point and calculate the corner frequency between the disturbance source point and the generator node. ω ci And the propagation coefficient PC; set the propagation coefficient PC = Δ ω / ω c Where Δω is the increment of the generator rotor angular frequency. ω c The corner frequency; Step 2: Determine whether the generator node is affected by electromechanical disturbances based on the propagation coefficient PC; Step 3: Identify generators affected by electromechanical disturbances and calculate the disturbance source point and the nodes of the affected generators. j Composite electromechanical distance between ; Step 4: Based on the composite electromechanical distance Hierarchical clustering is performed on the power system, which is then divided into the study area and the external area. The parameters of each generator in the study area are then aggregated. In step 4, the power system in the study area is affected by electromechanical disturbances and participates in frequency regulation; the power system in the external area is not affected by electromechanical disturbances and only performs power transmission; before the division, generators in both the study area and the external area participate in frequency regulation through tie lines; after the division, generators in the external area only perform power transmission and do not participate in frequency regulation. Step 5: Establish the system equivalent frequency response model and calculate the frequency of the study area.

2. The system frequency response analysis method based on electromechanical wave propagation characteristics according to claim 1, characterized in that: In step 1, the power system is considered as a grid continuum model with non-uniformly and continuously distributed generators, lines, and loads. In this grid continuum model, the relationship between electromechanical wave propagation speed and inertia is as follows: (1)； In equation (1), v The propagation speed of electromechanical waves; ω The generator's angular frequency; U This is the per-unit value of the voltage amplitude; Δ x The distance between the two nodes; z This is the per-unit impedance value of the line; h The inertia is the unit length.

3. The system frequency response analysis method based on electromechanical wave propagation characteristics according to claim 2, characterized in that: In discrete power systems, electromechanical waves exist within a finite frequency range, which is related to the generator's moment of inertia and the system's line impedance, and is categorized by the corner frequency. ω c express: (2)； When the frequency of the electromechanical signal is greater than the corner frequency ω c When the frequency of the electromechanical wave is greater than three times the corner frequency, the amplitude of the electromechanical wave along the propagation direction will attenuate rapidly. ω c When the amplitude of the electromechanical wave decays to zero, the disturbance energy can no longer propagate.

4. The system frequency response analysis method based on electromechanical wave propagation characteristics according to claim 1, characterized in that: In step 2, the larger the propagation coefficient PC is, the less the generator at that node is affected by electromechanical disturbances. When the propagation coefficient PC is greater than 3, the generator will not be affected by electromechanical disturbances.

5. The system frequency response analysis method based on electromechanical wave propagation characteristics according to claim 1, characterized in that: In step 3, the composite electromechanical distance is defined based on the propagation time of the electromechanical disturbance between any two points. Composite electromechanical distance This represents the increment of the power angle that the generator rotates through when it undergoes uniform acceleration or deceleration with a constant initial acceleration after a disturbance occurs. θ i The required time, i.e.: (3)； In the formula: The distance is a composite electromechanical distance, expressed in seconds. w This is the error correction factor; M i For generator nodes i The rotor inertia constant; B To transfer susceptance; This indicates the definition, specifically the definition of composite electromechanical distance. ; At generator node i and generator node j Between, due to Bij = Bji , M i ≠ M j Therefore, it is evident that electromechanical distance has directionality; however, for actual power systems, the propagation direction of electromechanical disturbances is difficult to determine, hence an average electromechanical distance without direction is assumed. That is, generator disturbance source node i and generator node j The average electromechanical distance between them is: (4) ； In the formula: Indicates the source of the disturbance is i At that time, node i With nodes j The average electromechanical distance between them; Indicates the source of the disturbance is j At that time, node j With nodes i The average electromechanical distance between them; Indicates the source of the disturbance is i At that time, node i With nodes j Electromechanical distance between them; Indicates the source of the disturbance is j At that time, node j With nodes i Electromechanical distance between them; Indicates the source of the disturbance is i At that time, node i With nodes j Transfer susceptance between; Indicates the source of the disturbance is j At that time, node j With nodes i The transfer susceptance between them.

6. The system frequency response analysis method based on electromechanical wave propagation characteristics according to claim 5, characterized in that: Under the same electromechanical disturbance, the generator's inertia M i The larger the value, the smaller the generator rotor acceleration under the action of the system's acceleration power, the greater the resistance to the propagation of electromechanical waves, and the greater the electromechanical distance. Similarly, when the transfer admittance between the disturbance source and the generator node... B ij The larger the value, the greater the acceleration power obtained by the generator, the greater the rotor acceleration of the generator, the greater the influence of electromechanical wave disturbances on the generator, the smaller the resistance to the propagation of electromechanical waves, and the smaller the electromechanical distance. When electromechanical disturbances occur, the smaller the electromechanical distance, the faster the generator response speed, and the closer the connection between the two machines.

7. The system frequency response analysis method based on electromechanical wave propagation characteristics according to claim 1, characterized in that: Parameter aggregation was performed on the steam turbines in the study area. include: The mechanical power increment of the turbine-governor model is: (5)； In equation (5): Δ P mT ( s ) represents the increase in mechanical power; F H This represents the power percentage of the high-pressure turbine. T R The reheater time constant; R T This refers to the turbine droop coefficient; T C The gas volume time constant; T G The time constant of the air chamber; s For the complex frequency domain variables in the Laplace transform; This represents the increment of angular frequency. Assume the power system has a total of synchronous machines N Taiwan; due to the turbine droop coefficient R T With rated capacity S N Regarding the constant gain used in multi-turbine governors: (6)； In equation (6): S Ni Synchronizer i Rated power; S sys This refers to the rated power of the entire system. K mi Indicates a synchronous machine i The proportion of the rated power to the total rated power of the system; Equivalent droop coefficient of power system R for: (7)； Wherein, the equivalent gain is defined as κ i =K mi / R Ti , R Ti For the first i The droop coefficient of the steam turbine; As can be seen from equation (5), the mechanical power increment of the turbine-governor model is affected by... T G , T C , T R and F H The four parameters have an impact; for simplicity, equation (7) defines the normalized gain λ. i Indicates a synchronous machine i The combined effect of the turbine-governor; (8)。 8. The system frequency response analysis method based on electromechanical wave propagation characteristics according to claim 7, characterized in that: In step 5, according to equations (5) to (8), the transfer functions of multiple synchronous machines are aggregated into a single equivalent machine transfer function: (9)； Based on equation (9), establish the system equivalent frequency response model for the study area, and... i The parameters of a steam turbine are aggregated and are equivalent to one steam turbine.

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