Transient oscillation law analysis method and system for double-loop PI control direct current power flow controller

Abstract

The invention provides a transient oscillation rule analysis method for a double-loop PI control direct current power flow controller. The method comprises the following steps: segmenting a small signal model of the double-loop PI direct current power flow controller; carrying out transfer function model construction on the autonomous DC power flow controller system obtained after segmentation; performing singular value decomposition on the autonomous DC power flow controller; natural damping distribution and injection power distribution are defined to quantify the line symmetry degree, and then the influence of the line symmetry degree on transient oscillation of the autonomous system is regularly summarized through the singular value decomposition technology. According to the method, natural damping distribution and injection power distribution are innovatively defined, the application line symmetry degree of the inter-line direct current power flow controller is further quantized, and application line configuration for reducing transient oscillation of the direct current power flow controller is given in combination with singular value analysis.

Description

Technical Field

[0001] The present invention relates to the technical field of electrical engineering. Specifically, it relates to a method and system for analyzing the transient oscillation law of a dual-loop PI-controlled DC power flow controller, and particularly to a method for analyzing the transient oscillation law of a dual-loop PI-controlled DC power flow controller based on singular value decomposition technology. Background Technique

[0002] The new distribution system is accelerating its transformation and upgrading, and is gradually evolving into a new type of regional power system that combines collection, transmission, storage, and trading. At the same time, with the continuous increase in the proportion of new energy generation in the distribution system and the diversification of types of power electronic devices, problems such as low inertia and weak damping in a large number of control links bring new challenges to the power grid. The flexible DC transmission technology can independently adjust active and reactive power, and thus has the ability to reduce the uncertainty problems brought by low inertia and weak damping to the power grid, and has been widely used at home and abroad.

[0003] The flexible DC transmission system can be directly connected to the power grid and effectively participate in power grid support, slowing down the gradual reduction of system strength and inertia caused by the access of a large number of various new energy sources to the main grid. However, the natural distribution of the DC power grid current may cause problems such as line overload, converter station failure, and uncontrollable power flow. Therefore, introducing a DC power flow controller into the flexible DC transmission system can effectively reduce the impact of multi-source power fluctuations on the power grid and is conducive to realizing regional energy mutual assistance. However, the transient oscillation under the non-fault switching of the DC power flow controller will cause DC grid overload and may also damage the voltage source converter. For the problem of transient oscillation under the non-fault switching of the DC power flow controller, the method for analyzing the transient oscillation law of the dual-loop PI-controlled DC power flow controller based on singular value decomposition technology proposed in the present invention can provide a reference for related research on reducing the impact of the switching of the DC power flow controller on the system.

[0004] Currently, in terms of constructing the transfer function matrix of the dual-loop PI-controlled two-line DC power flow controller in the market, there is no literature on constructing and studying the transfer function matrix of the DC power flow controller under the dual-loop PI control of the outer-loop current loop and the inner-loop voltage loop. In terms of analyzing the transient oscillation law of the line-interconnected DC power flow controller under dual-loop PI control, there is no literature on studying the influence of the natural damping distribution and the injected power distribution on the transient oscillation of the DC power flow controller. Based on the dual-loop PI-controlled DC power flow controller, this solution proposes a method for analyzing the transient oscillation law of the DC power flow controller based on singular value decomposition technology, providing a reference for line configuration to reduce the transient oscillation of the DC power flow controller under non-fault conditions.

[0005] The literature Zhu Yuanzhe, Yao Ruotian, Wang Ling, et al. A Sensitivity Analysis Method for Power Grid Resonance Frequency Based on Singular Value Decomposition [J / OL]. Southern Power Grid Technology, 1-8 [2024-10-22] discloses a sensitivity analysis method for power grid resonance frequency based on singular value decomposition, which effectively overcomes the deficiency of modal frequency sensitivity in analyzing branch current resonance characteristics. However, it does not address the analysis of transient oscillation characteristics for DC distributed systems. Our proposed solution, based on singular value decomposition technology, establishes a small-signal model of a DC power flow controller between two lines with dual-loop PI control and performs small-signal segmentation. By changing the line symmetry, it achieves the induction of transient oscillation laws for DC systems. Furthermore, this literature does not consider combining the controllability of different state variables in the transfer function matrix to perform targeted singular value analysis on state variables with high potential resonance probability.

[0006] The literature He Dalu, Liao Jianquan, Wang Qianggang. Unbalanced power flow suppression in a ring bipolar DC distribution network based on a three-active-bridge series-parallel DC power flow controller [J]. Journal of Electrical Engineering, 2022, 37(11):2837-2848, discloses a DC power flow controller with unbalanced power flow suppression function in a ring bipolar DC distribution network, and introduces a decoupling control matrix for the transient process of load switching. However, it does not address the study of transient process suppression caused by the switching of the DC power flow controller itself in the DC system. In contrast, this scheme proposes a transient law analysis method for the switching process of the DC power flow controller between dual-loop PI control lines based on small-signal model segmentation. In addition, this literature does not address the study of the influence of line symmetry on transient oscillation. Summary of the Invention

[0007] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for analyzing the transient oscillation law of a dual-loop PI-controlled DC power flow controller.

[0008] A method for analyzing transient oscillation patterns in a dual-loop PI-controlled DC power flow controller, provided by the present invention, is characterized by comprising:

[0009] Step S1: Small-signal model segmentation of the dual-loop PI DC power flow controller;

[0010] Step S2: Construct the transfer function model of the autonomous DC power flow controller system obtained after the segmentation;

[0011] Step S3: Singular value decomposition of autonomous DC power flow controller;

[0012] Step S4: Define the natural damping distribution and injected power distribution to quantify the line symmetry, and then use singular value decomposition technology to summarize the regularity of the influence of line symmetry on the transient oscillation of the autonomous system.

[0013] Preferably, step S1 includes:

[0014] Step S1.1: Based on the corresponding linearized models of each power flow control mode, merge and summarize to obtain the small-signal model of the common inductor type inter-line dual-loop PI control DC power flow controller;

[0015] Step S1.2: Based on the state variables involved in the PI dual-loop control, the state variables of the small-signal model of the common inductor type inter-line dual-loop PI control DC power flow controller are divided into those fully controlled by PI and those indirectly controlled by PI, thereby obtaining the controllable system and the autonomous system.

[0016] Preferably, the small-signal model of the shared inductor-type inter-line dual-loop PI control DC power flow controller is as follows:

[0017]

[0018] Where Δ represents a small-signal disturbance. Represent the derivative of the common inductor current and the line, respectively. 12 Differential of current, line 13 Differential of current, line 23 Differentials of current, differentials of voltage across capacitor C1, differentials of voltage across capacitor C2, differentials of voltage at port VSC1 of the voltage source converter, differentials of voltage at port VSC2 of the voltage source converter, differential terms of the PI current loop, and differential terms of the PI voltage loop; i 13ref For line 13 The current control reference values ​​are: U1 and U2 are steady-state values; D, P1, and P2 are the steady-state duty cycle of switch Q1, the output power of voltage source converter VSC1, and the output power of voltage source converter VSC2, respectively; while u1 and u2 are dynamic values; A represents the system matrix of the two-line shared inductor DC power flow controller under dual-loop PI control; B represents the system input matrix; C represents the system output matrix; and X represents the system state variables. Let represent the derivative of the system state variable, u represent the system input variable, and Y represent the system output variable.

[0019] Preferably, the state variables of the controllable system include the outer loop current loop state variable i. 13 Inner loop voltage loop state variable u C1 And the duty cycle d of the dual-ring PI output;

[0020] The state variables of the autonomous system include the common inductor current i. L Line 12 Current i 12 Line 23 Current i 23 The voltage u across capacitor C2 C2Voltage u1 at port VSC1 of voltage source converter; voltage u2 at port VSC2 of voltage source converter;

[0021] The state-space equations for the controllable system and the autonomous system are as follows:

[0022]

[0023] Where A1 represents the system matrix of the controllable system, u1 represents the input variable vector of the controllable system, and B1 represents the input matrix corresponding to the input variable vector u1 in the controllable system. 21 B represents the input variable vector of the autonomous system that generates the input controllable system. 21 Represents the input variable vector u 21 The corresponding input matrix; A2 represents the system matrix of the autonomous system, B 12 B1 represents the input matrix corresponding to the input variable vector u1 in the autonomous system, u2 represents the input variable vector of the autonomous system, and B2 represents the input matrix corresponding to the input variable vector u2.

[0024] Preferably, it is assumed that the i-th state variable is the output variable of the autonomous DC power flow controller, and the output variable is as follows:

[0025] ΔY 2_i =C 2_i ΔX2, (i = 0, 1, 2, ..., 6)

[0026] Where, ΔY 2_i C represents the output variable of the autonomous DC power flow controller. 2_i Represents the output matrix of the autonomous DC power flow controller, and is a 1×6 row vector with the i-th element being 1 and the rest being 0;

[0027] In a dual-loop PI-controlled inter-line DC power flow controller, the input is d and the output is Y. 2_i The transfer function is as follows:

[0028] G i1 =C 2_i (sI-A2) -1 B 3_1 (i = 0, 1, 2, ..., 6)

[0029] Among them, G i1 The input is d and the output is Y. 2_i The transfer function, where I is the identity matrix and s is the Laplace operator;

[0030] Similarly, in the autonomous DC power flow controller, the input is i 13 The output is Y 2_i The transfer function is as follows:

[0031] Gi2 =C 2_i (sI-A2) -1 B 3_2 (i = 0, 1, 2, ..., 6)

[0032] Input is u C1 The output is Y 2_i The transfer function is as follows:

[0033] G i3 =C 2_i (sI-A2) -1 B 3_3 (i = 0, 1, 2, ..., 6)

[0034] Among them, G i2 For input i 13 The output is Y 2_i The transfer function, G i3 For input u C1 The output is Y 2_i The transfer function is given; therefore, the transfer function matrix G of the autonomous DC power flow controller is written as follows:

[0035]

[0036] Preferably, step S3 includes:

[0037] Step S3.1: Write out the transfer function model columns corresponding to the key state variables to be studied in the transfer function matrix, as shown in the following formula:

[0038] Δu C2 =G 41 Δd+G 42 Δi 13 +G 43 Δu C1 =G4Δu3

[0039] Δu1=G 51 Δd+G 52 Δi 13 +G 53 Δu C1 =G5Δu3

[0040] Δu3=[ΔdΔi 13 Δu C1 ] T

[0041] Where Δd and Δi 13 and Δu C1 These represent the duty cycle of the dual-loop PI output and the line, respectively. 13 Current and voltage across capacitor C1, Δu C2G2 represents the voltage across capacitor C2, Δu3 represents the input variable vector of the autonomous system, and G4 represents the distance from the input variable vector Δu3 to the output variable Δu. C2 The transfer function. Δu1 represents the voltage at port VSC1 of the voltage source converter, and G5 represents the transfer function from the input variable vector Δu3 to the output variable Δu1 of the autonomous system;

[0042] Step S3.2: Calculate the singular value decomposition results of the transfer function matrix at different frequencies. The maximum singular value at each frequency point represents the maximum response value of the capacitor voltage and VSC1 port voltage that the input variable Δu3 can excite, as shown in the following formula:

[0043]

[0044] Wherein, λ4(ω c )and They represent frequencies w respectively c Maximum and minimum response amplitudes of the capacitor voltage at the point; λ5(ω c )and They represent frequencies w respectively c The maximum and minimum response amplitudes of the VSC1 port voltage can be obtained, similarly, through singular value decomposition to obtain the state variables of other autonomous DC power flow controllers. and At frequency w c The maximum response amplitude at that location.

[0045] Preferably, the natural damping distribution is used to reflect the line impedance of the flexible DC transmission system;

[0046] The injected power distribution is used to reflect the power distribution symmetry of the flexible DC transmission system.

[0047] Preferably, step S4 includes:

[0048] Step S4.1: Adjust the natural damping distribution and injected power distribution, and calculate the maximum response amplitude of the autonomous DC power flow controller corresponding to the transfer function matrix G under different natural damping distribution and injected power distribution conditions. The amplitude Bode plot curve;

[0049] Step S4.2: Select the maximum singular value of the Bode plot curve for each amplitude and plot a 3D graph;

[0050] Step S4.3: Determine the influence of the current line symmetry on the transient oscillation of the autonomous system based on the three-dimensional diagram.

[0051] Preferably, the higher the symmetry of the line impedance and power distribution of the flexible DC transmission system, the smaller the oscillation amplitude of the overall state variable of the autonomous DC power flow controller; the lower the symmetry, the larger the oscillation amplitude of the overall state variable of the autonomous system.

[0052] A transient oscillation law analysis system for a dual-loop PI-controlled DC power flow controller, provided by the present invention, includes:

[0053] Module M1: Small-signal model segmentation for dual-loop PI DC power flow controller;

[0054] Module M2: Constructs the transfer function model of the autonomous DC power flow controller system obtained after the partitioning;

[0055] Module M3: Singular value decomposition of autonomous DC power flow controller;

[0056] Module M4: Defines the natural damping distribution and injected power distribution to quantify line symmetry, and then uses singular value decomposition technology to summarize the regularity of the influence of line symmetry on the transient oscillation of the autonomous system.

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] 1. This invention applies the small-signal model segmentation method to divide the dual-loop PI-controlled DC power flow controller into two parts: a controllable system and an autonomous system, which facilitates the establishment of a more accurate method for damping transient oscillations in the DC power flow controller.

[0059] 2. This invention establishes a transfer function model for the autonomous DC power flow controller after small-signal segmentation, and innovatively applies singular value decomposition technology to the DC power flow controller to accurately characterize the degree of transient oscillation of the autonomous system caused by input variables.

[0060] 3. This invention adjusts the natural damping distribution and injected power distribution, calculates the Bode plot curves of the maximum singular value amplitude of the autonomous system under different line symmetries, and summarizes the influence of different line damping distributions and power distribution symmetries on the transient oscillations of the autonomous DC power flow controller. Attached Figure Description

[0061] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0062] Figure 1 This is a dual-loop PI control two-line DC power flow controller topology;

[0063] Figure 2 This is the first operating mode of the dual-loop PI control inter-line DC power flow controller;

[0064] Figure 3 This is the second operating mode for the dual-loop PI control inter-line DC power flow controller;

[0065] Figure 4A schematic diagram of dynamic segmentation of a DC power flow controller between two lines under dual-loop PI control.

[0066] Figure 5 This is a schematic diagram showing the maximum singular values ​​corresponding to each frequency point of the transfer function matrix G1 to G6.

[0067] Figure 6 The maximum singular value of the state variable under different natural damping distributions and injected power distributions. 3D graph;

[0068] Figure 7 A schematic diagram of a city-wide distributed DC system;

[0069] Figure 8 For different natural damping distributions and injected power distributions, the common inductor current i L Transient waveform diagram;

[0070] Figure 9 Transient waveform of VSC2 port voltage u2 under different natural damping distributions and injected power distributions;

[0071] Figure 10 The voltage u of capacitor C2 under different natural damping distributions and injected power distributions. C2 Transient waveform diagram;

[0072] Figure 11 Lines under different natural damping distributions and injected power distributions 23 Current i 23 Transient waveform diagram

[0073] Figure 12 This is a schematic diagram of the working method of the present invention. Detailed Implementation

[0074] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

[0075] This invention, based on a small-signal model of a dual-loop PI-controlled DC power flow controller, decomposes the fully controllable state variables and autonomous variables of the dual-loop PI controller to obtain a partial transfer function model of the autonomous system of the two-line DC power flow controller. It also constructs a state-space model of a dual-loop PI-controlled two-line shared-inductance DC power flow controller and analyzes the influence of natural damping distribution and injected power distribution on the transient oscillation characteristics of the autonomous DC power flow controller using singular value decomposition (SVD). Furthermore, this invention defines the natural damping distribution and injected power distribution to further quantify the application line symmetry of the inter-line DC power flow controller and, combined with SVD, provides application line configurations to reduce transient oscillations of the DC power flow controller.

[0076] Example 1

[0077] The present invention provides a method for analyzing the transient oscillation law of a dual-loop PI-controlled DC power flow controller, such as... Figure 12 As shown, it includes:

[0078] Step S1: Small-signal model segmentation of the dual-loop PI DC power flow controller. Based on the linearized model of the dual-loop PI control inter-line DC power flow controller, dynamic segmentation of the small-signal model is performed. Step S1 includes:

[0079] Step S1.1: Based on the corresponding linearized models of each power flow control mode, merge and summarize to obtain the small-signal model of the common inductor type inter-line dual-loop PI control DC power flow controller. The working mechanism of the common inductor type inter-line dual-loop PI control DC power flow controller is as follows: Figure 1 As shown, the power flow control in this invention includes two operating modes, namely operating mode one and operating mode two, as follows: Figure 2 and Figure 3 As shown. Based on the linearized models of each working mode, the small-signal models of the common inductor type inter-line dual-loop PI control DC power flow controller can be combined and summarized as shown in equations (1) and (2):

[0080]

[0081] Where Δ represents a small-signal disturbance. Represent the derivative of the common inductor current and the line, respectively. 12 Differential of current, line 13 Differential of current, line 23 Differentials of current, differentials of voltage across capacitor C1, differentials of voltage across capacitor C2, differentials of voltage at port VSC1 of voltage source converter, differentials of voltage at port VSC2 of voltage source converter, differential terms of PI current loop, and differential terms of PI voltage loop. 13ref For line 13Current control reference values. U1 and U2 are steady-state values. D, P1, and P2 are the steady-state duty cycle of switch Q1, the output power of voltage source converter VSC1, and the output power of voltage source converter VSC2, respectively. u1 and u2 are dynamic values. A represents the system matrix of a two-line shared inductor DC power flow controller under dual-loop PI control, B represents the system input matrix, C represents the system output matrix, and X represents the system state variables. Let represent the derivative of the system state variable, u represent the system input variable, and Y represent the system output variable.

[0082] Step S1.2: Based on the state variables involved in the PI dual-loop control, the state variables of the small-signal model of the shared inductor-type inter-line dual-loop PI control DC power flow controller are divided into those fully controlled by the PI and those indirectly controlled by the PI, thus obtaining the controllable system and the autonomous system. The small-signal model segmentation process of the shared inductor-type DC power flow controller is as follows: Figure 4 As shown, based on the state variables involved in the PI dual-loop control, the state variables of the DC power flow controller between two lines can be divided into two parts: one fully controlled by the PI and the other indirectly controlled by the PI. The former can constitute a controllable system, while the latter can be classified as an autonomous system. The outer loop current loop state variable i of the dual-loop PI controller... 13 Inner loop voltage loop state variable u C1 The duty cycle d of the dual-loop PI output is incorporated into the controllable system, while other state variables are incorporated into the autonomous system. The state variable vectors of the controllable and autonomous parts of the dual-loop PI control line DC controller are shown in equations (3) and (4):

[0083] ΔX1=[Δi 13 Δu C1 Δξ1Δξ2] T (3)

[0084] ΔX2=[Δi L Δi 12 Δi 23 Δu C2 Δu1 Δu2] T (4)

[0085] Where ΔX1 represents the state variable vector of the controllable system, and ΔX2 represents the state variable vector of the autonomous system. The state-space equations of the controllable system and the autonomous system can be expressed as shown in equations (5) and (6), respectively:

[0086]

[0087] Where A1 represents the system matrix of the controllable system, u1 represents the input variable vector of the controllable system, and B1 represents the input matrix corresponding to the input variable vector u1 in the controllable system. 21B represents the input variable vector of the autonomous system that generates the input controllable system. 21 Represents the input variable vector u 21 The corresponding input matrix; A2 represents the system matrix of the autonomous system, B 12 Let u1 represent the input matrix corresponding to the input variable vector u1 in the autonomous system, u2 represent the input variable vector of the autonomous system, and B2 represent the input matrix corresponding to the input variable vector u2. The input variable vectors of the dual-loop PI control line DC controller are shown in equations (7) to (9):

[0088] Δu1=Δd (7)

[0089] Δu 21 =[Δi L Δi 12 Δi 23 Δu C2 Δu1 Δu2] T (8)

[0090] Δu2=[Δi 13 Δu C1 Δξ1 Δξ2] T (9)

[0091] Since in an autonomous system, the three main input variables are Δd, Δi 13 and Δu C1 These three variables can be uniformly classified into the input variable vector Δu3 of the autonomous system, as shown in equation (10):

[0092] Δu3=[Δd Δi 13 Δu C1 ] T (10)

[0093] Therefore, the state-space equations of the autonomous system can be rewritten as shown in equations (11) and (12):

[0094]

[0095]

[0096] Where B3 represents the input matrix corresponding to the input variable vector u3, U C1 and U C2 Let B3Δu3 be the steady-state value of the capacitor voltage. B3Δu3 can be re-expressed as shown in equation (13):

[0097]

[0098] Step S2: Construct the transfer function model of the autonomous DC power flow controller. The transfer function model of the segmented autonomous DC power flow controller system is constructed. This invention is based on the small-signal model of a dual-loop PI-controlled DC power flow controller, splitting the fully controllable state variables and autonomous variables of the dual-loop PI controller to obtain a partial transfer function model of the autonomous system of the two-line DC power flow controller.

[0099] Assuming the i-th state variable is the output variable of the autonomous DC power flow controller, then the output variable can be written in the form of equation (14):

[0100] ΔY 2_i =C 2_i ΔX2,(i=0,1,2...,6) (14)

[0101] Where, ΔY 2_i C represents the output variable of the autonomous DC power flow controller. 2_i Let Y represent the output matrix of the autonomous DC power flow controller, and be a 1×6 row vector where the i-th element is 1 and the rest are 0. In a dual-loop PI-controlled inter-line DC power flow controller, the input is d and the output is Y. 2_i The transfer function can be expressed in the form of equation (15):

[0102] G i1 =C 2_i (sI-A2) -1 B 3_1 (i = 0, 1, 2, ..., 6) (15)

[0103] Among them, G i1 The input is d and the output is Y. 2_i The transfer function is given by I, where I is the identity matrix and s is the Laplace operator. Similarly, in the autonomous DC power flow controller, the input is i 13 The output is Y 2_i The transfer function can be expressed in the form of equation (16); the input is u C1 The output is Y 2_i The transfer function can be expressed in the form of equation (17).

[0104] G i2 =C 2_i (sI-A2) -1 B 3_2 (i = 0, 1, 2, ..., 6) (16)

[0105] G i3 =C 2_i (sI-A2) -1 B 3_3 (i = 0, 1, 2, ..., 6) (17)

[0106] Among them, G i2 For input i 13 The output is Y 2_i The transfer function, G i3 For input u C1 The output is Y 2_i The transfer function. Therefore, the transfer function matrix G of the autonomous DC power flow controller can be written as shown in equation (18):

[0107]

[0108] The transfer function matrix G of the autonomous DC power flow controller can be re-expressed as shown in equation (19):

[0109]

[0110] Step S3: Singular value decomposition of the autonomous DC power flow controller. Step S3 includes:

[0111] Step S3.1: Write out the transfer function models corresponding to the key state variables that need to be studied in the transfer function matrix.

[0112] Step S3.2: Calculate the singular value decomposition results of the transfer function matrix at different frequencies.

[0113] In singular value decomposition theory, for a 6×3 transfer function matrix G, there exist 3×3 orthogonal matrices U and 6×6 orthogonal matrices V that satisfy equation (20):

[0114] G = UΛV H (20)

[0115] Among them, V H It is the transpose of the orthogonal matrix V, and Λ is a 3×6 diagonal matrix; Λ=[λ10;00], λ1=diag(λ1,...,λ n The diagonal elements of the vector are the singular values ​​of the transfer function matrix G, arranged in descending order. For an eigenvector v from an orthogonal matrix V... i , will v i As the input variable of the autonomous DC power flow controller, the system response can be obtained as shown in equation (21):

[0116] Gv i =λ i u i (twenty one)

[0117] Among them, u i The eigenvectors are derived from the orthogonal matrix U, and can be considered as v here. i The output response caused by the input semi-autonomous DC power flow controller; λ iLet be the i-th singular value of matrix G, which can be considered as the magnitude gain between the input and output vectors. Let all input variables be unit vectors, then the maximum singular value is shown in equation (22):

[0118]

[0119] Where |||2 is the Euclidean norm, v1 is the input unit vector corresponding to the maximum singular value, and λ1 and It is the largest singular value.

[0120] To study the influence of the input variables of the autonomous DC power flow controller on the transient oscillation of the inter-line DC power flow controller, it is first necessary to write out the transfer function models corresponding to the key state variables to be studied in the transfer function matrix, as shown in equations (23) and (24).

[0121] Δu C2 =G 41 Δd+G 42 Δi 13 +G 43 Δu C1 =G4Δu3 (23)

[0122] Δu1=G 51 Δd+G 52 Δi 13 +G 53 Δu C1 =G5Δu3 (24)

[0123] The singular value decomposition results of the transfer function matrix at different frequencies are calculated respectively. The maximum singular value at each frequency point represents the maximum response of the capacitor voltage and VSC1 port voltage that the input variable Δu3 can excite, as shown in Equation (25).

[0124]

[0125] in, λ 4(ω c )and They represent frequencies w respectively c The maximum and minimum response amplitudes of the capacitor voltage at the location; λ 5(ω c )and They represent frequencies w respectively c The maximum and minimum response amplitudes of the voltage at port VSC1 are obtained. Similarly, the state variables of other autonomous DC power flow controllers can be obtained through singular value decomposition. and At frequency w c The maximum response amplitude at that point. This can be obtained through frequency sweep analysis. The magnitude Bode plot, such as Figure 5As shown.

[0126] Step S4: Determine the influence of line symmetry on the transient oscillations of the autonomous system. Define the natural damping distribution and injected power distribution to quantify the line symmetry, and then summarize the influence of line symmetry on the transient oscillations of the autonomous system using singular value decomposition (SVD) technology. The line impedance and power distribution symmetry of the flexible DC transmission system have a significant impact on the transient oscillation characteristics of the dual-loop PI-controlled shared-inductance type inter-line DC power flow controller. The natural damping distribution is used to reflect the line impedance of the flexible DC transmission system. The injected power distribution is used to reflect the power distribution symmetry of the flexible DC transmission system. Step S4 includes:

[0127] Step S4.1: Adjust the natural damping distribution and injected power distribution, and calculate the maximum response amplitude of the autonomous DC power flow controller corresponding to the transfer function matrix G under different natural damping distribution and injected power distribution conditions. The amplitude Bode plot curve.

[0128] Step S4.2: Select the maximum singular value of each amplitude Bode plot curve to draw a three-dimensional plot.

[0129] Step S4.3: Determine the influence of the current line symmetry on the transient oscillation of the autonomous system based on the three-dimensional diagram. The higher the symmetry of the line impedance and power distribution of the flexible DC transmission system, the smaller the oscillation amplitude of the overall state variable of the autonomous DC power flow controller; the lower the symmetry, the larger the oscillation amplitude of the overall state variable of the autonomous system.

[0130] Line 12 ,line 13 and line 23 The corresponding line resistance R 12 R 13 and R 23 With the total sum constant, the natural damping distribution is defined as R. 13 / R 23 Let the sum of the injected power P1 from VSC1 and P2 from VSC2 remain constant, and define the injected power distribution as P1 / P2. The closer the injected power distribution is to the natural damping distribution (P2), the higher the symmetry of the line impedance and power distribution in the flexible DC transmission system; conversely, the lower the symmetry, the lower the symmetry. Adjusting the natural damping distribution and the injected power distribution, calculate the maximum response amplitude of the autonomous DC power flow controller corresponding to the transfer function matrix G under different natural damping and injected power distribution conditions. The amplitude Bode plot curves are used to select the maximum singular values ​​of each curve to draw a three-dimensional plot, such as... Figure 6 As shown. When P1 / P2 = 1.0376, R 13 / R 23 The maximum singular value of the state variable when = 0.9642. Taking the minimum value indicates that the overall state variable oscillation amplitude is minimized. When P1 / P2 = 0.6, R... 13 / R 23 =1.6667, the maximum singular value of the state variable Taking the maximum value indicates the largest oscillation amplitude of the overall state variable. Relatively speaking, the higher the symmetry of the line impedance and power distribution of the flexible DC transmission system, the smaller the oscillation amplitude of the overall state variable of the autonomous DC power flow controller; the lower the symmetry, the larger the oscillation amplitude of the overall state variable of the autonomous system.

[0131] This invention aims to address the problem of transient oscillation suppression in non-faulty DC power flow controllers by analyzing the influence of the natural damping distribution and injected power distribution of the DC transmission system on the transient oscillations of the DC power flow controller, thereby reducing the impact of DC power flow controller switching on flexible DC systems.

[0132] Furthermore, the transient oscillation law analysis method of the dual-loop PI control DC power flow controller of the present invention is described in detail below with reference to the accompanying drawings:

[0133] In such Figure 7 This paper verifies the transient oscillation law analysis method of a dual-loop PI-controlled DC power flow controller based on singular value decomposition (SVD) technology in the urban distributed DC system shown. A shared-inductance type two-line DC power flow controller is placed between the urban distributed grid UDDG-4 and the adjacent urban distributed grids UDDG-5 and UDDG-7. The connection line between UDDG-4 and UDDG-7 is selected as line... 13 The line connecting UDDG-4 and UDDG-5 is selected as the line. 23 Using a dual-loop PI controller to control line 13 Line current, to achieve line 13 Active regulation of DC power flow and control of line 23 Passive regulation of DC power flow. Three sets of natural damping distribution coefficients and injected power distribution coefficients were set to represent the high, medium, and low line distribution symmetry conditions, respectively. This verifies that the transient oscillation law analysis method of the dual-loop PI control DC power flow controller based on singular value decomposition technology can accurately reflect the influence of different line symmetries on the transient oscillation of the DC power flow controller. System parameters are shown in Table 1.

[0134] Table 1: System Parameters of Dual-Loop PI Control Two-Wire DC Power Flow Controller

[0135]

[0136] Table 2: Experimental parameters for different line symmetries

[0137]

[0138] Set line 13 With a reference current of 3.5A, and keeping the total line resistance and total injected power constant, the natural damping distribution and injected power distribution are adjusted as shown in Table 2. After 1 second, the DC power flow controller between the two lines is connected to the city's distributed DC system. Figure 8 , Figure 9 , Figure 10 and Figure 11 It can be seen that the higher the symmetry of the line impedance and power distribution in the flexible DC transmission system, the higher the main state variable i of the autonomous system after the DC power flow controller between the two lines is connected. L u2, u C2 and i 23 The smaller the transient oscillation amplitude, the shorter the oscillation time.

[0139] Example 2

[0140] The present invention also provides a transient oscillation law analysis system for a dual-loop PI-controlled DC power flow controller. The transient oscillation law analysis system for a dual-loop PI-controlled DC power flow controller can be implemented by executing the process steps of the transient oscillation law analysis method for a dual-loop PI-controlled DC power flow controller. That is, those skilled in the art can understand the transient oscillation law analysis method for a dual-loop PI-controlled DC power flow controller as a preferred embodiment of the transient oscillation law analysis system for a dual-loop PI-controlled DC power flow controller.

[0141] A transient oscillation law analysis system for a dual-loop PI-controlled DC power flow controller, provided by the present invention, includes:

[0142] Module M1: Small-signal model segmentation of the dual-loop PI DC power flow controller. Module M1 includes: Module M1.1: Based on the corresponding linearized models of each power flow control mode, a small-signal model of the common inductor-type inter-line dual-loop PI control DC power flow controller is obtained by merging and summing the models. The formula for the small-signal model of the common inductor-type inter-line dual-loop PI control DC power flow controller is as follows:

[0143]

[0144] Where Δ represents a small-signal disturbance. Represent the derivative of the common inductor current and the line, respectively. 12 Differential of current, line 13 Differential of current, line 23 Differentials of current, differentials of voltage across capacitor C1, differentials of voltage across capacitor C2, differentials of voltage at port VSC1 of voltage source converter, differentials of voltage at port VSC2 of voltage source converter, differential terms of PI current loop, and differential terms of PI voltage loop. 13ref For line13 Current control reference values. U1 and U2 are steady-state values. D, P1, and P2 are the steady-state duty cycle of switch Q1, the output power of voltage source converter VSC1, and the output power of voltage source converter VSC2, respectively. u1 and u2 are dynamic values. A represents the system matrix of a two-line shared inductor DC power flow controller under dual-loop PI control, B represents the system input matrix, C represents the system output matrix, and X represents the system state variables. Let represent the derivative of the system state variable, u represent the system input variable, and Y represent the system output variable.

[0145] Module M1.2: Based on the state variables involved in PI dual-loop control, the state variables of the small-signal model of the shared inductor type inter-line dual-loop PI control DC power flow controller are divided into those fully controlled by PI and those indirectly controlled by PI, thus obtaining a controllable system and an autonomous system. The state variables of the controllable system include the outer loop current loop state variable i. 13 Inner loop voltage loop state variable u C1 And the dual-loop PI output duty cycle d. The state variables of the autonomous system include the common inductor current i. L Line 12 Current i 12 Line 23 Current i 23 The voltage u across capacitor C2 C2 The voltage u1 at port VSC1 of the voltage source converter and the voltage u2 at port VSC2 of the voltage source converter are given. The state-space equations for the controllable system and the autonomous system are as follows:

[0146]

[0147] Where A1 represents the system matrix of the controllable system, u1 represents the input variable vector of the controllable system, and B1 represents the input matrix corresponding to the input variable vector u1 in the controllable system. 21 B represents the input variable vector of the autonomous system that generates the input controllable system. 21 Represents the input variable vector u 21 The corresponding input matrix. A2 represents the system matrix of the autonomous system, B 12 B1 represents the input matrix corresponding to the input variable vector u1 in the autonomous system, u2 represents the input variable vector of the autonomous system, and B2 represents the input matrix corresponding to the input variable vector u2.

[0148] Module M2: Constructs the transfer function model of the resulting autonomous DC power flow controller system after partitioning. Assume the i-th state variable is the output variable of the autonomous DC power flow controller, and the output variables are as follows:

[0149] ΔY2_i =C 2_i ΔX2, (i = 0, 1, 2, ..., 6)

[0150] Where, ΔY 2_i C represents the output variable of the autonomous DC power flow controller. 2_i This represents the output matrix of the autonomous DC power flow controller, and is a 1×6 row vector with the i-th element being 1 and the rest being 0.

[0151] In a dual-loop PI-controlled inter-line DC power flow controller, the input is d and the output is Y. 2_i The transfer function is as follows:

[0152] G i1 =C 2_i (sI-A2) -1 B 3_1 (i = 0, 1, 2, ..., 6)

[0153] Among them, G i1 The input is d and the output is Y. 2_i The transfer function is given by I, where I is the identity matrix and s is the Laplace operator.

[0154] Similarly, in the autonomous DC power flow controller, the input is i 13 The output is Y 2_i The transfer function is as follows:

[0155] G i2 =C 2_i (sI-A2) -1 B 3_2 (i = 0, 1, 2, ..., 6)

[0156] Input is u C1 The output is Y 2_i The transfer function is as follows:

[0157] G i3 =C 2_i (sI-A2) -1 B 3_3 (i = 0, 1, 2, ..., 6)

[0158] Among them, G i2 For input i 13 The output is Y 2_i The transfer function, G i3 For input u C1 The output is Y 2_i The transfer function.

[0159] Therefore, the transfer function matrix G of the autonomous DC power flow controller is listed below:

[0160]

[0161] Module M3: Singular value decomposition for autonomous DC power flow controller. Module M3 includes:

[0162] Module M3.1: Write out the transfer function model columns corresponding to the key state variables to be studied in the transfer function matrix, as shown in the following formula:

[0163] Δu C2 =G 41 Δd+G 42 Δi 13 +G 43 Δu C1 =G4Δu3

[0164] Δu1=G 51 Δd+G 52 Δi 13 +G 53 Δu C1 =G5Δu3

[0165] Δu3=[ΔdΔi 13 Δu C1 ] T

[0166] Where Δd and Δi 13 and Δu C1 These represent the duty cycle of the dual-loop PI output and the line, respectively. 13 Current and voltage across capacitor C1, Δu C2 G2 represents the voltage across capacitor C2, Δu3 represents the input variable vector of the autonomous system, and G4 represents the distance from the input variable vector Δu3 to the output variable Δu. C2 The transfer function is given by G5. Δu1 represents the voltage at port VSC1 of the voltage source converter, and G5 represents the transfer function from the input variable vector Δu3 to the output variable Δu1 of the autonomous system.

[0167] Module M3.2: Calculates the singular value decomposition results of the transfer function matrix at different frequencies. The maximum singular value at each frequency point represents the maximum response value of the capacitor voltage and VSC1 port voltage that the input variable Δu3 can excite, as shown in the following equation:

[0168]

[0169] in, λ 4(ω c )and They represent frequencies w respectively c The maximum and minimum response amplitudes of the capacitor voltage at the location. λ 5(ω c )and They represent frequencies w respectivelyc The maximum and minimum response amplitudes of the VSC1 port voltage can be obtained, similarly, through singular value decomposition to obtain the state variables of other autonomous DC power flow controllers. and At frequency w c The maximum response amplitude at that location.

[0170] Module M4: Defines the natural damping distribution and injected power distribution to quantify line symmetry, and then uses singular value decomposition (SVD) to summarize the regularity of the influence of line symmetry on the transient oscillations of the autonomous system. The natural damping distribution is used to reflect the line impedance of the flexible DC transmission system. The injected power distribution is used to reflect the power distribution symmetry of the flexible DC transmission system. Module M4 includes: Module M4.1: Adjusts the natural damping distribution and injected power distribution, and calculates the maximum response amplitude of the autonomous DC power flow controller corresponding to the transfer function matrix G under different natural damping distribution and injected power distribution conditions. The amplitude Bode plot curves. Module M4.2: Select the maximum singular value of each amplitude Bode plot curve to draw a 3D graph. Module M4.3: Determine the influence of the current line symmetry on the transient oscillation of the autonomous system based on the 3D graph. The higher the symmetry of the line impedance and power distribution of the flexible DC transmission system, the smaller the oscillation amplitude of the overall state variable of the autonomous DC power flow controller; the lower the symmetry, the larger the oscillation amplitude of the overall state variable of the autonomous system.

[0171] Those skilled in the art will understand that, besides implementing the system and its various devices, modules, and units provided by this invention in the form of purely computer-readable program code, the same functions can be achieved entirely through logical programming of the method steps, making the system and its various devices, modules, and units of this invention function in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices, modules, and units provided by this invention can be considered as a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices, modules, and units for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0172] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for analyzing the transient oscillation law of a dual-loop PI-controlled DC power flow controller, characterized in that, include: Step S1: Small-signal model segmentation of the dual-loop PI DC power flow controller; Step S2: Construct the transfer function model of the autonomous DC power flow controller system obtained after the segmentation; Step S3: Singular value decomposition of autonomous DC power flow controller; Step S4: Define the natural damping distribution and injected power distribution to quantify the line symmetry, and then use singular value decomposition technology to summarize the regularity of the influence of line symmetry on the transient oscillation of the autonomous system.

2. The method for analyzing the transient oscillation law of a dual-loop PI-controlled DC power flow controller according to claim 1, characterized in that, Step S1 includes: Step S1.1: Based on the corresponding linearized models of each power flow control mode, merge and summarize to obtain the small-signal model of the common inductor type inter-line dual-loop PI control DC power flow controller; Step S1.2: Based on the state variables involved in the PI dual-loop control, the state variables of the small-signal model of the common inductor type inter-line dual-loop PI control DC power flow controller are divided into those fully controlled by PI and those indirectly controlled by PI, thereby obtaining the controllable system and the autonomous system.

3. The method for analyzing the transient oscillation law of a dual-loop PI-controlled DC power flow controller according to claim 2, characterized in that, The small-signal model of the shared inductor-type inter-line dual-loop PI-controlled DC power flow controller is as follows: Where Δ represents a small-signal disturbance. Represent the derivative of the common inductor current and the line, respectively. 12 Differential of current, line 13 Differential of current, line 23 Differentials of current, differentials of voltage across capacitor C1, differentials of voltage across capacitor C2, differentials of voltage at port VSC1 of the voltage source converter, differentials of voltage at port VSC2 of the voltage source converter, differential terms of the PI current loop, and differential terms of the PI voltage loop; i 13ref For line 13 The current control reference values ​​are: U1 and U2 are steady-state values; D, P1, and P2 are the steady-state duty cycle of switch Q1, the output power of voltage source converter VSC1, and the output power of voltage source converter VSC2, respectively; while u1 and u2 are dynamic values; A represents the system matrix of the two-line shared inductor DC power flow controller under dual-loop PI control; B represents the system input matrix; C represents the system output matrix; and X represents the system state variables. Let represent the derivative of the system state variable, u represent the system input variable, and Y represent the system output variable.

4. The method for analyzing the transient oscillation law of a dual-loop PI-controlled DC power flow controller according to claim 2, characterized in that, The state variables of the controllable system include the outer current loop state variable i. 13 Inner loop voltage loop state variable u C1 And the duty cycle d of the dual-ring PI output; The state variables of the autonomous system include the common inductor current i. L Line 12 Current i 12 Line 23 Current i 23 The voltage u across capacitor C2 C2 Voltage u1 at port VSC1 of voltage source converter; voltage u2 at port VSC2 of voltage source converter; The state-space equations for the controllable system and the autonomous system are as follows: Where A1 represents the system matrix of the controllable system, u1 represents the input variable vector of the controllable system, and B1 represents the input matrix corresponding to the input variable vector u1 in the controllable system. 21 B represents the input variable vector of the autonomous system that generates the input controllable system. 21 Represents the input variable vector u 21 The corresponding input matrix; A2 represents the system matrix of the autonomous system, B 12 B1 represents the input matrix corresponding to the input variable vector u1 in the autonomous system, u2 represents the input variable vector of the autonomous system, and B2 represents the input matrix corresponding to the input variable vector u2.

5. The method for analyzing the transient oscillation law of a dual-loop PI-controlled DC power flow controller according to claim 1, characterized in that, Assume the i-th state variable is the output variable of the autonomous DC power flow controller, and the output variables are as follows: ΔY 2_i =C 2_i ΔX2,(i=0,1,2...,6) Where, ΔY 2_i C represents the output variable of the autonomous DC power flow controller. 2_i Represents the output matrix of the autonomous DC power flow controller, and is a 1×6 row vector with the i-th element being 1 and the rest being 0; In a dual-loop PI-controlled inter-line DC power flow controller, the input is d and the output is Y. 2_i The transfer function is as follows: G i1 =C 2_i (sI-A2) -1 B 3_1 ,(i=0,1,2...,6) Among them, G i1 The input is d and the output is Y. 2_i The transfer function, where I is the identity matrix and s is the Laplace operator; Similarly, in the autonomous DC power flow controller, the input is i 13 The output is Y 2_i The transfer function is as follows: G i2 =C 2_i (sI-A2) -1 B 3_2 ,(i=0,1,2...,6) Input is u C1 The output is Y 2_i The transfer function is as follows: G i3 =C 2_i (sI-A2) -1 B 3_3 ,(i=0,1,2...,6) Among them, G i2 For input i 13 The output is Y 2_i The transfer function, G i3 For input u C1 The output is Y 2_i The transfer function; Therefore, the transfer function matrix G of the autonomous DC power flow controller is listed below:

6. The method for analyzing the transient oscillation law of a dual-loop PI-controlled DC power flow controller according to claim 1, characterized in that, Step S3 includes: Step S3.1: Write out the transfer function model columns corresponding to the key state variables to be studied in the transfer function matrix, as shown in the following formula: Thu C2 =G 41 Δd+G 42 Yes 13 +G 43 Thu C1 =G4Δu3 Δu1=G 51 Δd+G 52 Yes 13 +G 53 Thu C1 =G5Δu3 Δu3=[ΔdΔi 13 Δu C1 ] T Where Δd and Δi 13 and Δu C1 These represent the duty cycle of the dual-loop PI output and the line, respectively. 13 Current and voltage across capacitor C1, Δu C2 G2 represents the voltage across capacitor C2, Δu3 represents the input variable vector of the autonomous system, and G4 represents the distance from the input variable vector Δu3 to the output variable Δu. C2 The transfer function. Δu1 represents the voltage at port VSC1 of the voltage source converter, and G5 represents the transfer function from the input variable vector Δu3 to the output variable Δu1 of the autonomous system; Step S3.2: Calculate the singular value decomposition results of the transfer function matrix at different frequencies. The maximum singular value at each frequency point represents the maximum response value of the capacitor voltage and VSC1 port voltage that the input variable Δu3 can excite, as shown in the following formula: in, λ 4(ω c )and They represent frequencies w respectively c The maximum and minimum response amplitudes of the capacitor voltage at the location; λ 5(ω c )and They represent frequencies w respectively. c The maximum and minimum response amplitudes of the VSC1 port voltage can be obtained, similarly, through singular value decomposition to obtain the state variables of other autonomous DC power flow controllers. and At frequency w c The maximum response amplitude at that location.

7. The method for analyzing the transient oscillation law of a dual-loop PI-controlled DC power flow controller according to claim 1, characterized in that, The natural damping distribution is used to reflect the line impedance of the flexible DC transmission system. The injected power distribution is used to reflect the power distribution symmetry of the flexible DC transmission system.

8. The method for analyzing the transient oscillation law of a dual-loop PI-controlled DC power flow controller according to claim 1, characterized in that, Step S4 includes: Step S4.1: Adjust the natural damping distribution and injected power distribution, and calculate the maximum response amplitude of the autonomous DC power flow controller corresponding to the transfer function matrix G under different natural damping distribution and injected power distribution conditions. The amplitude Bode plot curve; Step S4.2: Select the maximum singular value of the Bode plot curve for each amplitude and plot a 3D graph; Step S4.3: Determine the influence of the current line symmetry on the transient oscillation of the autonomous system based on the three-dimensional diagram.

9. The method for analyzing the transient oscillation law of a dual-loop PI-controlled DC power flow controller according to claim 8, characterized in that, The higher the symmetry of the line impedance and power distribution of the flexible DC transmission system, the smaller the oscillation amplitude of the overall state variable of the autonomous DC power flow controller; the lower the symmetry, the larger the oscillation amplitude of the overall state variable of the autonomous system.

10. A transient oscillation law analysis system for a dual-loop PI-controlled DC power flow controller, characterized in that, include: Module M1: Small-signal model segmentation for dual-loop PI DC power flow controller; Module M2: Constructs the transfer function model of the autonomous DC power flow controller system obtained after the partitioning; Module M3: Singular value decomposition of autonomous DC power flow controller; Module M4: Defines the natural damping distribution and injected power distribution to quantify line symmetry, and then uses singular value decomposition technology to summarize the regularity of the influence of line symmetry on the transient oscillation of the autonomous system.

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