Long-distance ac submarine cable impedance equivalent modeling method and system

Abstract

The application provides a long-distance alternating current submarine cable impedance equivalent modeling method and system, wherein the method comprises the following steps: calculating parameters of a submarine cable distributed parameter circuit model according to submarine cable circuit parameters and a circuit segmentation number, obtaining a unit segmentation resistance value, a unit segmentation inductance value and a unit segmentation capacitance value, establishing an alternating current submarine cable impedance model according to the circuit segmentation number, the unit segmentation resistance value, the unit segmentation inductance value and the unit segmentation capacitance value, performing frequency sweep analysis on the alternating current submarine cable impedance model, and calculating a submarine cable open loop oscillation mode. The application can directly substitute the expression form of the alternating current submarine cable distributed parameter circuit model, establish the impedance model, and is simple to apply.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of submarine cable impedance modeling, in particular to a long-distance AC submarine cable impedance equivalent modeling method and system. BACKGROUND

[0002] In recent years, with the progress of technology, offshore wind power has been vigorously developed and widely used around the world. However, as the scale of offshore wind power grid connection continues to grow, its impact on the stability of the power system has gradually emerged, of which the current more serious is the oscillation stability problem. At present, the commonly used grid connection methods for offshore wind power are high-voltage alternating current transmission and flexible direct current transmission. The power industry and academia generally recognize that the alternating current transmission scheme is generally suitable for offshore wind power transmission due to the limitations of transmission distance and capacity, while the flexible direct current transmission scheme has obvious advantages in the transmission of large-capacity offshore wind power in the open sea. At present, most of the offshore wind power projects under construction or completed in China adopt the high-voltage alternating current transmission method for grid connection. In addition, due to the simple principle and mature technology of high-voltage alternating current transmission, and the ability to improve system transmission capacity through reactive power compensation, there are also cases of using high-voltage alternating current transmission for grid connection for large-capacity long-distance offshore wind power projects in practice, such as the Hornsea one offshore wind power project in the United Kingdom.

[0003] The existing submarine cable impedance modeling methods are mostly direct methods, that is, based on the structure of the circuit principle and the submarine cable distributed parameter circuit, the submarine cable impedance model is derived and established. This method is only suitable for cases where the number of segments in the submarine cable distributed parameter circuit model is small. When the number of segments is increased to improve the accuracy of the submarine cable impedance model, the order of the submarine cable impedance model will also increase. Therefore, when a detailed modeling of the submarine cable is required, the order of the submarine cable impedance model will greatly increase, thereby increasing the workload of the submarine cable impedance frequency characteristic scanning and system stability analysis, especially when considering different lengths, different types or different numbers of parallel circuits, which will cause the system stability analysis to be inefficient. In solving the frequency points of the submarine cable impedance amplitude-frequency characteristic peak and phase-frequency characteristic jump based on the submarine cable impedance model established by the direct method, or in the open-loop oscillation mode of the alternating current submarine cable, a high-order equation is established by setting the determinant of the impedance matrix equal to 0, and the result obtained by solving the equation is the angle frequency corresponding to the peak or jump. However, the above method also faces the problems of large calculation amount and low efficiency when detailed modeling is required. SUMMARY

[0004] To solve the above technical problems, the present application provides a long-distance AC submarine cable impedance equivalent modeling method and system, which represents the AC submarine cable impedance model as a weighted sum of several τ-type circuit impedance models, and can directly substitute the representation form of the AC submarine cable distributed parameter circuit model to establish its impedance model, which is simple to apply.

[0005] The first aspect of the present application provides a long-distance AC submarine cable impedance equivalent modeling method, comprising:

[0006] According to the submarine cable circuit parameters and the circuit segment number, the parameters of the submarine cable distributed parameter circuit model are calculated to obtain the resistance value of a unit segment, the inductance value of a unit segment and the capacitance value of a unit segment,

[0007] According to the circuit segment number, the resistance value of a unit segment, the inductance value of a unit segment and the capacitance value of a unit segment, an AC submarine cable impedance model is established.

[0008] The AC submarine cable impedance model is subjected to frequency sweep analysis, and the open-loop oscillation mode of the submarine cable is calculated.

[0009] Further, the AC submarine cable impedance model is represented by the following formula:

[0010] ΔV N =Z TA (s)ΔI w ;

[0011] Wherein, ΔV N represents the port voltage of the Nth impedance circuit, ΔI w is the input current of the AC power grid, and Z TA (s) is the equivalent impedance model of the circuit.

[0012] Further, the weighted sum of the impedance of the circuit is calculated by the following formula:

[0013]

[0014] Wherein, Z TA (s) is the weighted sum of the impedance of the circuit, N is the total number of circuit segments, i represents the ith circuit, d i is the weight of the circuit segment of the ith circuit, and Z Ai (s) is the equivalent impedance model of the circuit.

[0015] Further, the impedance model of the circuit is calculated by the following formula:

[0016] Z Ai (s)=[Z L0 -1 (s)+λ i c0(s)] -1 ;

[0017] Wherein, Z Ai (s) is the impedance model of the circuit, Z L0 (s) is the resistance-inductance model, λ i c0(s) is the capacitance of the ith segment.

[0018] The second aspect of the present application provides a long-distance AC submarine cable impedance equivalent modeling system, comprising:

[0019] A parameter calculation module is configured to calculate parameters of a submarine cable distributed parameter circuit model according to submarine cable circuit parameters and a circuit segment number, to obtain a resistance value of a unit segment, an inductance value of a unit segment, and a capacitance value of a unit segment,

[0020] A model establishment module is configured to establish an AC submarine cable impedance model according to the circuit segment number, the resistance value of a unit segment, the inductance value of a unit segment, and the capacitance value of a unit segment.

[0021] A model analysis module is configured to perform sweep analysis on the AC submarine cable impedance model and calculate an open-loop oscillation mode of the submarine cable.

[0022] Further, the AC submarine cable impedance model is represented by the following formula:

[0023] ΔV N = Z TA (s)ΔI w ;

[0024] wherein ΔV N represents a port voltage of an Nth impedance circuit, ΔI w represents an input current of an AC power grid, and Z TA (s) represents an equivalent impedance model of the circuit.

[0025] Further, the weighted sum of the impedance of the circuit is calculated by the following formula:

[0026]

[0027] wherein Z TA (s) represents the weighted sum of the impedance of the circuit, N represents a total number of circuit segments, i represents an ith circuit, d i represents a weight of a circuit segment of the ith circuit, and Z Ai (s) represents the equivalent impedance model of the circuit.

[0028] Further, the impedance model of the circuit is calculated by the following formula:

[0029] Z Ai (s) = [Z L0 -1 (s) + λ i c0(s)] -1 ;

[0030] wherein Z Ai (s) represents the impedance model of the circuit, and ZL0 (s) is a resistance-inductance model, λ i c0(s) is the capacitance of the i-th section.

[0031] The third aspect of the present application provides an electronic device, comprising a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein the processor implements the long-distance AC submarine cable impedance equivalent modeling method according to any one of the first aspect when executing the computer program.

[0032] The fourth aspect of the present application provides a computer-readable storage medium, comprising a stored computer program, wherein the computer-readable storage medium controls the device where the computer-readable storage medium is located to execute the long-distance AC submarine cable impedance equivalent modeling method according to any one of the first aspect when the computer program is running.

[0033] Compared with the prior art, the beneficial effects of the embodiment of the present application are as follows:

[0034] The present application provides a long-distance AC submarine cable impedance equivalent modeling method and system, wherein the method comprises: calculating the parameters of a submarine cable distributed parameter circuit model according to the submarine cable circuit parameters and the number of circuit sections, obtaining the resistance value of a unit section, the inductance value of a unit section, and the capacitance value of a unit section, establishing an AC submarine cable impedance model according to the number of circuit sections, the resistance value of a unit section, the inductance value of a unit section, and the capacitance value of a unit section, performing frequency sweep analysis on the AC submarine cable impedance model, and calculating the open-loop oscillation mode of the submarine cable. The present application can directly substitute according to the representation form of the AC submarine cable distributed parameter circuit model to establish its impedance model, and is simple to apply. BRIEF DESCRIPTION OF DRAWINGS

[0035] In order to more clearly illustrate the technical solutions of the present application, the following will briefly introduce the drawings required to be used in the embodiments. Obviously, the drawings described in the following are only some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0036] Figure 1 is a flowchart of a long-distance AC submarine cable impedance equivalent modeling method provided by an embodiment of the present application;

[0037] Figure 2 is a schematic diagram of an AC submarine cable distributed parameter circuit model provided by an embodiment of the present application;

[0038] Figure 3 is a schematic diagram of an AC submarine cable distributed parameter circuit model provided by an embodiment of the present application;

[0039] Figure 4 is a schematic diagram of a distributed parameter model of an AC submarine cable (ignoring the difference in ground capacitance) provided by some embodiments of the present application;

[0040] Figure 5 is a schematic diagram of an i-th τ-type circuit provided by some embodiments of the present application;

[0041] Figure 6 is a graph of frequency-sweep results of impedance characteristics of a submarine cable provided by some embodiments of the present application;

[0042] Figure 7 is a flowchart of a method for equivalent modeling of impedance of a long-distance AC submarine cable provided by another embodiment of the present application;

[0043] Figure 8 is a block diagram of a system for equivalent modeling of impedance of a long-distance AC submarine cable provided by some embodiments of the present application;

[0044] Figure 9 is a block diagram of an electronic device provided by some embodiments of the present application. DETAILED DESCRIPTION

[0045] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some, but not all, of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative effort are within the scope of the present application.

[0046] It should be understood that the step numbers used herein are only for the convenience of description, and are not limited to the execution sequence of the steps.

[0047] It should be understood that the terms used in the present application are only for the purpose of describing specific embodiments and are not intended to limit the present application. As used in the present application and the appended claims, unless otherwise clearly indicated by the context, the singular forms "a", "an" and "the" are intended to include the plural forms.

[0048] The terms "comprise" and "include" indicate the presence of described features, integers, steps, operations, elements, and / or components, but do not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0049] The term "and / or" means any combination of one or more of the associated listed items and all possible combinations, and includes these combinations.

[0050] First aspect.

[0051] Referring to Figure 1 , the embodiment of the present application provides a long-distance AC submarine cable impedance equivalent modeling method, comprising:

[0052] S10, according to the submarine cable circuit parameters and the circuit segment number, calculating the parameters of the submarine cable distributed parameter circuit model, obtaining the resistance value of the unit segment, the inductance value of the unit segment and the capacitance value of the unit segment.

[0053] S20, according to the circuit segment number, the resistance value of the unit segment, the inductance value of the unit segment and the capacitance value of the unit segment, establishing an AC submarine cable impedance model.

[0054] S30, performing frequency sweep analysis on the AC submarine cable impedance model, and calculating the open loop oscillation mode of the submarine cable.

[0055] In a specific embodiment of the embodiment, the AC submarine cable impedance model is represented by the following formula:

[0056] ΔV N = Z TA (s)ΔI w ;

[0057] Wherein, ΔV N represents the port voltage of the Nth impedance circuit, ΔI w is the input current of the AC power grid, Z TA (s) is the equivalent impedance model of the circuit.

[0058] The weighted sum of the impedance of the circuit is calculated by the following formula:

[0059]

[0060] Wherein, Z TA (s) is the weighted sum of the impedance of the circuit, N is the total number of circuit segments, i represents the ith circuit, d i is the weight of the circuit segment of the ith circuit, Z Ai (s) is the equivalent impedance model of the circuit.

[0061] The impedance model of the circuit is calculated by the following formula:

[0062] Z Ai (s) = [Z L0 -1 (s) + λ i c0(s)] -1 ;

[0063] Wherein, Z Ai (s) is the impedance model of the circuit, ZL0 (s) is a resistance-inductance model, λ i c0(s) is the capacitance of the i-th section.

[0064] The method provided by the application can be directly substituted according to the expression form of the distributed parameter circuit model of the AC submarine cable, the impedance model is established, and the application is simple.

[0065] In another embodiment of the application, the application provides a long-distance AC submarine cable impedance equivalent modeling method, which can effectively reduce the calculation amount of the frequency sweep analysis and model parameter solving of the submarine cable impedance characteristics.

[0066] 1. Establishment of the submarine cable impedance model (direct method):

[0067] Figure 2 The distributed parameter circuit model of an AC submarine cable is shown, which can be regarded as a series of N π-type circuits (N is any positive integer). Figure 2 It can be further simplified as Figure 3 The form shown, wherein,

[0068]

[0069] In the formula, c is Figure 2 The ground capacitance in each π-type circuit.

[0070] Figure 3 In the formula, the dynamic equation of each ground capacitance is (k=0,1,…,N),

[0071] ΔΙ k =c k (s)ΔV k (2);

[0072] In the formula, Δ represents the small increment of a variable or a variable column vector; V k =[V kx V ky ] T , I k =[I kx I ky ] T , V kx +jV ky , I kx +jI ky respectively represent the voltage of node k in the AC power grid public x-y coordinate system and the current on the ground capacitance at node k; Figure 3

[0073] Figure 3 In the formula, the dynamic equation of each RL circuit is (k=1,2,…,N), ​

[0074] ΔV k -ΔV k-1 =Z L0 (s)ΔI Lk (3);

[0075] In the formula, I Lk =[I Lkx I Lky ] T ;I Lkx +jI Lky This represents the current on line k in the common xy coordinate system of the AC power grid; r0 and l0 are the resistance and inductance of the AC submarine cable distributed parameter circuit, respectively.

[0076] According to Kirchhoff's current law Figure 3 There are (k = 1, 2, ..., N).

[0077]

[0078] In the formula, I w =[I wx I wy ] T I wx +jI wy These represent the output current of the wind farm in the common xy coordinate system of the AC power grid.

[0079] From equation (3),

[0080]

[0081] Substituting equation (4) into equation (5) yields the following:

[0082]

[0083] Writing equation (6) in matrix form, we get:

[0084]

[0085] In the formula, That is, let m ij Let m be the element in the i-th row and j-th column of M. If j ≤ i, m ij =j, if j>i, m ij =i (i,j = 1,2,...,N), Represents the Kronecker product;

[0086]

[0087] From equation (7),

[0088] ΔI=T1(s)ΔI w +T2(s)ΔV0 (8);

[0089] In the formula, T1(s)=[E+C(s)Z T (s)] -1 C(s)Z I (s), where E is a 2N×2N identity matrix; T2(s)=[E+C(s)Z T (s)] -1 C(s)E N E N =[E2 E2 ... E2] T E2 is a 2×2 identity matrix.

[0090] In equation (8), T1(s) and T2(s) have the following representations:

[0091]

[0092] In the formula, t 1i (s) and t 2i (s) are all 2×2 matrices, i=1,2,…,N.

[0093] From equations (8) and (9),

[0094] ΔI i =t 1i (s)ΔI w +t 2i (s)ΔV0 (10);

[0095] Substituting equation (10) into equation (6), we get Figure 3 The impedance model for the AC submarine cable is as follows:

[0096]

[0097] In the formula, This is the impedance model for an AC submarine cable.

[0098] 2. Equivalent values ​​of the submarine cable impedance model:

[0099] for Figure 4 The AC submarine cable distributed parameter circuit model shown below, if c is ignored N With c i The difference between (i = 1, 2, ..., N-1), i.e., considering c N =c i =c0, then the AC submarine cable distributed parameter circuit shown in the figure can be regarded as several identical ground capacitors connected in series through an RL circuit, and the impedance of the connecting lines between adjacent ground capacitors is the same, as shown in the figure.Figure 5

[0100] Let λ i denote the eigenvalues of the matrix M in equation (7) (i = 1, 2,..., N), and u i = [u 1i u 2i ... u iN ] T denote the corresponding eigenvectors. Since M is a real symmetric matrix, U T MU = diag[λ i ] (12).

[0101] where diag[λ i ] denotes a diagonal matrix with λ i on the diagonal,

[0102] Then the following variable transformation can be introduced,

[0103] ΔV = U2ΔV Y ΔI = U2ΔI Y (13).

[0104] where

[0105] According to the property of the Kronecker product,

[0106]

[0107] Substituting equation (13) into equation (7) gives

[0108]

[0109] where C(s) = diag[c0(s)] denotes a block diagonal matrix with c0(s) on the diagonal,

[0110] According to the property of the Kronecker product,

[0111]

[0112]

[0113] where E N is the N x N identity matrix.

[0114] From equations (15) and (16), when the state variables described by equation (13) are used to describe the dynamic characteristics of the AC submarine cable, the submarine cable impedance model can be expressed as follows,

[0115] ​

[0116] where Z TY (s) = diag[-λ i Z L0 (s)] is a block-diagonal matrix with λ i Z L0 (s) on the diagonal elements; i, k = 1, 2,..., N.

[0117] According to equation (17), the AC submarine cable impedance model shown in equation (11) can be decoupled into N independent equivalent subsystems, where the impedance model of the i-th equivalent subsystem is

[0118]

[0119] According to equation (18),

[0120] ΔV Yi = a i F i (s)Z L0 (s)ΔI w +b i F i (s)ΔV0 (19);

[0121] where F i (s) = [E2+ λ i Z L0 (s)c0(s)] -1 .

[0122] According to equation (13),

[0123]

[0124] According to equations (19) and (20), the equivalent representation of the AC submarine cable impedance model is

[0125] ΔV N = Z TA (s)ΔI w (21);

[0126] where d i = u iN a i , Z Ai (s) = [Z L0 -1 (s) + λ i c0(s)] -1 .

[0127] The equivalent impedance model of the AC submarine cable shown in equation (21) can be regarded as N segments with resistance r0, inductance l0, and capacitance λ. i The weighted summation of the impedances of a τ-type circuit with c0, where the weights are d. i (i = 1, 2, ..., N), the structure of the i-th τ-type circuit is as follows: Figure 5 As shown (i.e.) Figure 6 The impedance model of the circuit shown is Z. Ai (s)). Therefore, for a high-order submarine cable impedance model composed of N π-type circuits, it can be simplified to a weighted sum of the impedances of N low-order τ-type circuits using the above method, thereby reducing the computational load during frequency sweep analysis of submarine cable impedance characteristics. Furthermore, by solving for the open-loop oscillation mode of the τ-type circuit, the open-loop oscillation mode of the AC submarine cable can be obtained, thus reducing the order of the AC submarine cable mode calculation.

[0128] 3. Submarine cable impedance equivalent modeling method:

[0129] Based on the impedance equivalent modeling method for submarine cables, when performing refined modeling of submarine cables, the impedance characteristic curve of the submarine cable can be obtained by sweeping the frequency of several low-order τ-type RLC circuits and weighted summing the resulting frequency response curves. The specific implementation process is as follows:

[0130] 1) Based on the submarine cable circuit parameters and the number of π-type circuits to be divided, calculate the parameters of the submarine cable distributed parameter circuit model to obtain r0, l0 and c0;

[0131] 2) Based on the number of π-type circuits in the distributed parameter circuit model of the submarine cable, establish matrix M in equation (7) and calculate the eigenvalues ​​λ of matrix M. i and eigenvector u i (i = 1, 2, ..., N);

[0132] 3) Based on the equivalent impedance model of the submarine cable given in equation (21), for Z Ai (s) Perform frequency sweep and sum the obtained impedance characteristics by weighted summation to obtain the impedance frequency characteristics of the submarine cable.

[0133] Table 1. Parameters of π-type circuit 1

[0134]

[0135] Taking a submarine cable modeled as an example, consisting of a distributed parameter circuit composed of 150 π-type circuit segments, and with the π-type circuit parameters shown in Table 1, the frequency sweep is performed based on equations (11) and (21), respectively, using the direct method and the equivalent modeling method for the submarine cable described above. The impedance-frequency characteristics of the submarine cable are obtained as follows: Figure 6 As shown, the time required for frequency sweeping using the direct method and the equivalent model is 1003.3s and 61.5s, respectively. From...Reduced order model computation It can be seen that the impedance frequency characteristics of submarine cables can be accurately obtained based on the equivalent model, and the time required to sweep the frequency of the impedance characteristics of submarine cables can be effectively reduced. The equivalent model can effectively grasp the frequency points and magnitudes of the amplitude-frequency characteristic peaks and phase-frequency characteristic jumps of the impedance of submarine cables, so that the oscillation stability of offshore wind power grid-connected systems can be analyzed on this basis.

[0136] 4. Method for reducing the order of open-loop oscillation modes in AC submarine cables:

[0137] The open-loop oscillation mode of the submarine cable is crucial information for analyzing the oscillation stability of offshore wind power grid-connected systems. When analyzing the oscillation stability of offshore wind power grid-connected systems based on mode resonance theory, it is necessary to accurately determine the open-loop oscillation mode of the AC submarine cable. The open-loop oscillation mode of the submarine cable can be obtained through a direct method, that is, based on equation (11), the open-loop oscillation mode of the submarine cable can be obtained by solving the equation shown in equation (22).

[0138] det[Z TI [(s)]=0 (22);

[0139] In the formula, det represents the matrix determinant.

[0140] If we use the equivalent representation of the AC submarine cable impedance model shown in equation (21), we can obtain the open-loop oscillation mode of the AC submarine cable by solving the following equation.

[0141] det[Z Ai (s)]=0,i=1,2,...,N (23);

[0142] By comparing equations (22) and (23), it can be seen that for a submarine cable distributed parameter circuit model composed of N segments of π-type circuits, when solving the open-loop oscillation mode of the submarine cable based on equation (22), it is necessary to solve a 4Nth order equation, while when solving the open-loop oscillation mode of the submarine cable based on equation (23), only N fourth order equations need to be solved, thus effectively reducing the order of solving the open-loop oscillation mode of the submarine cable, i.e., the amount of computation.

[0143] In summary, a method for equivalent impedance modeling of long-distance AC submarine cables can be derived as follows (reduced-order mode calculation method):

[0144] 1) Based on the submarine cable circuit parameters and the number of π-type circuits to be divided, calculate the parameters of the submarine cable distributed parameter circuit model to obtain r0, l0 and c0;

[0145] 2) Based on the number of π-type circuits in the distributed parameter circuit model of the submarine cable, establish matrix M in equation (7) and calculate the eigenvalues ​​λ of matrix M. i and eigenvector u i (i = 1, 2, ..., N);

[0146] 3) Based on the equivalent impedance model of the submarine cable given in equation (21), establish and solve the equation det[Z Ai [(s)] = 0, thus obtaining the open-loop oscillation mode of the submarine cable (i = 1, 2, ..., N).

[0147] Taking a submarine cable distributed parameter circuit model divided into 10 π-type circuit segments as an example, the π-type circuit parameters are shown in Table 2. The AC submarine cable oscillation mode is solved using the direct method and the above-mentioned reduced-order mode calculation method, respectively. The results are shown in Table 3. It can be seen that the AC submarine cable open-loop oscillation mode obtained by the proposed reduced-order mode calculation method is basically consistent with the result obtained by the direct method. That is, the proposed reduced-order mode calculation method can accurately obtain the AC submarine cable open-loop oscillation mode. Since the difference between the AC submarine cable capacitances to the ground is ignored when deriving the equivalent expression of the AC submarine cable impedance model shown in Equation (21), while the actual capacitances to the ground at both ends of the AC submarine cable are... The intermediate capacitance to ground is c0. Therefore, the AC submarine cable open-loop oscillation mode obtained based on the reduced-order mode calculation method has a slight difference compared with its actual value, but this difference is very small and can be ignored.

[0148] Table 2 π-type circuit parameters 2

[0149]

[0150] Table 3 Calculation results of AC submarine cable oscillation mode

[0151] Direct method Figure 7 -1.72+j13938.09 -1.72+j14048.99 -1.72+j13184.11 -1.72+j13712.34 -1.72+j13481.98 -1.72+j13295.01 -1.72+j12727.99 -1.72+j13047.33 -1.72+j12733.13 -1.72+j12958.36 -1.72+j11979.15 -1.72+j12293.35 -1.72+j11708.26 -1.72+j12070.33 -1.72+j10954.28 -1.72+j11316.35 -1.72+j10430.27 -1.72+j10805.41 -1.72+j9676.29 -1.72+j10051.43 -1.72+j8927.70 -1.72+j9283.70 -1.72+j8173.72 -1.72+j8529.72 -1.72+j7234.13 -1.72+j7542.68 -1.72+j6480.15 -1.72+j6788.70 -1.72+j5387.38 -1.72+j5625.22 -1.72+j4633.40 -1.72+j4871.24 -1.72+j3428.70 -1.72+j3578.53 -1.72+j2674.72 -1.72+j2824.54 -1.72+j1401.86 -1.72+j1452.99 -1.72+j647.88 -1.72+j699.02

[0152] 5. Equivalent modeling and analysis method for AC submarine cable impedance:

[0153] Based on the above analysis, a method for equivalent impedance modeling of long-distance AC submarine cables can be derived, the specific process of which is as follows: Figure 8 As shown, it is possible to perform reduced-order frequency sweep and open-loop mode calculations on the impedance frequency characteristics of AC submarine cables.

[0154] This invention proposes an equivalent modeling method for the impedance of long-distance AC submarine cables, and based on this, obtains an equivalent representation of the AC submarine cable impedance model. The AC submarine cable impedance model is represented as a weighted sum of several τ-type circuit impedance models, which can be directly substituted into the representation of the distributed parameter circuit model of the AC submarine cable to establish its impedance model, making it simple to apply. Based on the equivalent representation of the submarine cable impedance model, a reduced-order frequency sweep method for the frequency characteristics of AC submarine cable impedance is proposed. By scanning the impedance frequency characteristics of N τ-type RLC circuits, the impedance frequency characteristics of the AC submarine cable composed of N π-type circuits can be obtained, effectively reducing the computational burden of frequency sweep analysis of submarine cable impedance characteristics. Existing direct frequency sweep analysis methods for submarine cable impedance characteristics mostly involve direct frequency sweeping of the high-order impedance model of the submarine cable, resulting in large computational loads and low efficiency. This is especially problematic when performing refined modeling of submarine cables in large-scale offshore AC transmission systems, where the number of π-type circuits is enormous, significantly increasing the computational burden of direct frequency sweeping.

[0155] For a distributed parameter circuit model of an AC submarine cable consisting of N π-type circuits, solving the open-loop oscillation mode of the submarine cable using the existing direct method requires solving a 4Nth-order equation. However, by using the proposed reduced-order mode calculation method, the open-loop oscillation mode of the AC submarine cable can be obtained by solving N four-section equations, thereby effectively reducing the order of the mode calculation and the computational workload of solving the open-loop oscillation mode of the submarine cable.

[0156] Secondly.

[0157] Please see Figure 9 An embodiment of the present invention provides a long-distance AC submarine cable impedance equivalent modeling system, comprising:

[0158] The parameter calculation module 10 is used to calculate the parameters of the submarine cable distributed parameter circuit model based on the submarine cable circuit parameters and the number of circuit segments, and to obtain the resistance value, inductance value and capacitance value per unit segment.

[0159] The model building module 20 is used to build an AC submarine cable impedance model based on the number of circuit segments, the resistance value of the unit segment, the inductance value of the unit segment, and the capacitance value of the unit segment.

[0160] The model analysis module 30 is used to perform frequency sweep analysis on the impedance model of the AC submarine cable and calculate the open-loop oscillation mode of the submarine cable.

[0161] Preferably, the AC submarine cable impedance model is expressed by the following formula:

[0162] ΔV N =Z TA (s)ΔI w ;

[0163] Where, ΔV N Let ΔI represent the port voltage of the Nth impedance circuit. w Z is the input current of the AC power grid. TA (s) represents the equivalent impedance model of the circuit.

[0164] The weighted sum of the impedances of the circuit is calculated using the following formula:

[0165]

[0166] Among them, Z TA (s) represents the weighted sum of the circuit impedances, N is the total number of circuit segments, i represents the i-th circuit segment, and d i Z is the weight of the circuit segment in the i-th segment. Ai (s) represents the equivalent impedance model of the circuit.

[0167] The impedance model of the circuit is calculated using the following formula:

[0168] Z Ai (s)=[Z L0 -1 (s)+λ i c0(s)] -1 ;

[0169] Among them, Z Ai (s) represents the impedance model of the circuit, Z L0 (s) represents the resistance-inductance model, λ i c0(s) is the capacitance of the i-th segment.

[0170] The system provided by this invention can be directly substituted into the representation of the AC submarine cable distributed parameter circuit model to establish its impedance model, which is simple to apply.

[0171] Thirdly.

[0172] This invention provides an electronic device comprising:

[0173] Processor, memory, and bus;

[0174] The bus is used to connect the processor and the memory;

[0175] The memory is used to store operation instructions;

[0176] The processor is configured to execute operations corresponding to the long-distance AC submarine cable impedance equivalent modeling method shown in the first aspect of this application by invoking the operation instructions.

[0177] In one alternative embodiment, an electronic device is provided, such asFigure 9 As shown, Figure 9 The illustrated electronic device 5000 includes a processor 5001 and a memory 5003. The processor 5001 and the memory 5003 are connected, for example, via a bus 5002. Optionally, the electronic device 5000 may also include a transceiver 5004. It should be noted that in practical applications, the transceiver 5004 is not limited to one type, and the structure of this electronic device 5000 does not constitute a limitation on the embodiments of this application.

[0178] Processor 5001 may be a CPU, a general-purpose processor, a DSP, an ASIC, an FPGA, or other programmable logic device, transistor logic device, hardware component, or any combination thereof. It may implement or execute the various exemplary logic blocks, modules, and circuits described in conjunction with the disclosure of this application. Processor 5001 may also be a combination that implements computational functions, such as including one or more microprocessor combinations, a combination of a DSP and a microprocessor, etc.

[0179] Bus 5002 may include a path for transmitting information between the aforementioned components. Bus 5002 may be a PCI bus or an EISA bus, etc. Bus 5002 can be divided into address bus, data bus, control bus, etc. For ease of representation, ​ The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0180] The memory 5003 may be a ROM or other type of static storage device capable of storing static information and instructions, RAM or other type of dynamic storage device capable of storing information and instructions, or it may be an EEPROM, CD-ROM or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.), magnetic disk storage media or other magnetic storage devices, or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and accessible by a computer, but is not limited thereto.

[0181] The memory 5003 is used to store application code that executes the scheme of this application, and its execution is controlled by the processor 5001. The processor 5001 is used to execute the application code stored in the memory 5003 to implement the content shown in any of the foregoing method embodiments.

[0182] Among them, electronic devices include, but are not limited to: mobile terminals such as mobile phones, laptops, digital radio receivers, PDAs (personal digital assistants), PADs (tablet computers), PMPs (portable multimedia players), and in-vehicle terminals (such as in-vehicle navigation terminals), as well as fixed terminals such as digital TVs and desktop computers.

[0183] Fourth aspect.

[0184] The present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements a method for impedance equivalence modeling of long-distance AC submarine cables as shown in the first aspect of this application.

[0185] Another embodiment of this application provides a computer-readable storage medium storing a computer program that, when run on a computer, enables the computer to execute the corresponding content in the aforementioned method embodiments.

Claims

1. A method for impedance equivalent modeling of long-distance AC submarine cables, characterized in that, include: Based on the submarine cable circuit parameters and the number of circuit segments, the parameters of the submarine cable distributed parameter circuit model are calculated to obtain the resistance value, inductance value and capacitance value per unit segment. The submarine cable distributed parameter circuit model is composed of several π-type circuits connected in series. The π-type circuits have the same capacitance to ground and the impedance of the connecting lines between adjacent capacitances to ground is the same. An AC submarine cable impedance model is established based on the number of circuit segments, the resistance value of each segment, the inductance value of each segment, and the capacitance value of each segment; the AC submarine cable impedance model is a weighted sum of several low-order τ-type circuit impedance models. Frequency sweep analysis was performed on the impedance model of the AC submarine cable, and the open-loop oscillation mode of the submarine cable was calculated. The impedance model of the AC submarine cable is expressed by the following formula: ΔV N =Z TA (s)ΔI w ; Where, ΔV N Let ΔI represent the port voltage of the Nth impedance circuit. w Z is the input current of the AC power grid. TA (s) represents the equivalent impedance model of the circuit; The weighted sum of the impedances of the circuit is calculated using the following formula: Among them, Z TA (s) represents the weighted sum of the circuit impedances, N is the total number of circuit segments, i represents the i-th circuit segment, and d i Z is the weight of the i-th circuit segment. Ai (s) represents the equivalent impedance model of the circuit; The calculation method for the impedance characteristic curve of the submarine cable in the AC submarine cable impedance model includes: Based on the submarine cable circuit parameters and the number of π-type circuits to be divided, calculate the parameters of the submarine cable distributed parameter circuit model. Based on the number of π-type circuits in the distributed parameter circuit model of the submarine cable, a matrix is ​​established, and the eigenvalues ​​and eigenvectors of the matrix are calculated. Based on the equivalent impedance model of the submarine cable, the impedance model of the circuit is swept by frequency, and the obtained impedance characteristics are weighted and summed to obtain the impedance frequency characteristics of the submarine cable.

2. The method for equivalent impedance modeling of long-distance AC submarine cables as described in claim 1, characterized in that, The impedance model of the circuit is calculated using the following formula: Z Ai (s)=[Z L0 -1 (s)+λ i c0(s)] -1 ; Among them, Z Ai (s) represents the impedance model of the circuit, Z L0 (s) represents the resistance-inductance model, λ i c0(s) is the capacitance of the i-th segment.

3. A long-distance AC submarine cable impedance equivalent modeling system, characterized in that, include: The parameter calculation module is used to calculate the parameters of the submarine cable distributed parameter circuit model based on the submarine cable circuit parameters and the number of circuit segments, and to obtain the resistance value, inductance value and capacitance value per unit segment. The submarine cable distributed parameter circuit model is composed of several π-type circuits connected in series. The π-type circuits have the same ground capacitance and the connection line impedance between adjacent ground capacitances is the same. The model building module is used to establish an AC submarine cable impedance model based on the number of circuit segments, the resistance value of the unit segment, the inductance value of the unit segment, and the capacitance value of the unit segment; the AC submarine cable impedance model is a weighted sum of several low-order τ-type circuit impedance models. The model analysis module is used to perform frequency sweep analysis on the impedance model of the AC submarine cable and calculate the open-loop oscillation mode of the submarine cable. The impedance model of the AC submarine cable is expressed by the following formula: ΔV N =Z TA (s)ΔI w ; Where, ΔV N Let ΔI represent the port voltage of the Nth impedance circuit. w Z is the input current of the AC power grid. TA (s) represents the equivalent impedance model of the circuit; The weighted sum of the impedances of the circuit is calculated using the following formula: Among them, Z TA (s) represents the weighted sum of the circuit impedances, N is the total number of circuit segments, i represents the i-th circuit segment, and d i Z is the weight of the i-th circuit segment. Ai (s) represents the equivalent impedance model of the circuit; The calculation method for the impedance characteristic curve of the submarine cable in the AC submarine cable impedance model includes: Based on the submarine cable circuit parameters and the number of π-type circuits to be divided, calculate the parameters of the submarine cable distributed parameter circuit model. Based on the number of π-type circuits in the distributed parameter circuit model of the submarine cable, a matrix is ​​established, and the eigenvalues ​​and eigenvectors of the matrix are calculated. Based on the equivalent impedance model of the submarine cable, the impedance model of the circuit is swept by frequency, and the obtained impedance characteristics are weighted and summed to obtain the impedance frequency characteristics of the submarine cable.

4. The long-distance AC submarine cable impedance equivalent modeling system as described in claim 3, characterized in that, The impedance model of the circuit is calculated using the following formula: Z Ai (s)=[Z L0 -1 (s)+λ i c0(s)] -1 ; Among them, Z Ai (s) represents the impedance model of the circuit, Z L0 (s) represents the resistance-inductance model, λ i c0(s) is the capacitance of the i-th segment.

5. An electronic device, characterized in that, It includes a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein the processor, when executing the computer program, implements the long-distance AC submarine cable impedance equivalent modeling method as described in any one of claims 1 to 2.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored computer program, wherein, when the computer program is executed, it controls the device containing the computer-readable storage medium to perform the long-distance AC submarine cable impedance equivalent modeling method as described in any one of claims 1 to 2.

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