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

Abstract

The invention provides a transient oscillation characteristic analysis method and system for a single-loop PI control direct current power flow controller. The method comprises the following steps: constructing a transfer function matrix of a two-line common inductance type direct current power flow controller; dynamically dividing the direct current power flow controller into a full-control system and a semi-autonomous system based on the transfer function matrix; solving the maximum singular value of the semi-autonomous system by using the singular value decomposition technology, and researching the transient oscillation characteristic of the direct current power flow controller; the singular value decomposition result of the direct-current power flow controller semi-autonomous system is analyzed through frequency sweeping, the line resistance and the control reference value are comprehensively considered, and the influence rule of the key parameters of the direct-current power flow controller on the transient oscillation of the system is analyzed. According to the method, the active response characteristic of the direct current power flow controller to direct current micro-grid disturbance is fully utilized, reference is provided for transient oscillation suppression of the direct current micro-grid based on system dynamic, and direct current power flow control adapting to a direct current power grid complex scene can be achieved.

Description

Technical Field

[0001] This invention relates to the technical field of electrical engineering, specifically to a method and system for analyzing the transient oscillation characteristics of a single-loop PI-controlled DC power flow controller, and more particularly to a method for analyzing the transient oscillation characteristics of a single-loop PI-controlled DC power flow controller based on dynamic system segmentation. Background Technology

[0002] With the integration of renewable energy into the power system considered an irreversible path to carbon neutrality, the gradual replacement of traditional non-renewable energy with clean energy and the further increase in the utilization of solar, wind, and nuclear power have become an inevitable trend. Currently, the power distribution system is undergoing significant changes, with increasingly diversified energy demands, a growing variety of energy sources, and a rising proportion of renewable energy connected to the grid. However, the high penetration rate of renewable energy brings significant challenges to the power grid due to its randomness and volatility. Flexible DC transmission technology can mitigate the uncertainties brought about by large-scale renewable energy grid integration, improving the flexibility, stability, and economy of the new power system.

[0003] By employing flexible DC transmission technology based on multi-terminal DC transmission, large-scale grid integration and consumption of new energy sources in the new power system can be achieved, along with an improvement in overall energy efficiency. However, multi-terminal DC transmission technology suffers from a mesh topology, leading to problems such as incomplete control of DC power flow, cross-sectional blockage, and line overload. Introducing a DC power flow controller into the multi-terminal DC transmission system enables active regulation of the power flow on each line, ensuring the stable operation of the flexible DC grid. Furthermore, by employing a transient oscillation characteristic analysis method based on system dynamic segmentation using a single-loop PI control DC power flow controller, targeted transient oscillation suppression can be achieved in DC grids containing DC power flow controllers.

[0004] In the literature "Inter-line DC Power Flow Controller with Fault Current Limiting Function and Its Control Method," high-voltage flexible DC grids, as an effective means to solve the problem of large-scale integration and consumption of renewable energy, have become one of the important development directions of future power systems. However, this has also made the problems of power flow control and fault protection more prominent. To overcome these problems and improve system stability, an inductor-coupled composite device with dual functions of DC power flow control and fault current limiting is proposed. First, the topology of the composite device is proposed, which adds a current limiting branch that can share the coupling inductor on the basis of the traditional DC power flow controller. Second, the working principle, theoretical derivation, and control strategy of the DC power flow function are analyzed in detail. Then, based on the current limiting action sequence proposed under fault conditions, the effect of the coupling inductor under four different time periods—steady state, current limiting, fault clearing, and energy discharge—is further analyzed, and the calculation of DC fault current in each time period is studied. Finally, a four-terminal DC grid model is built on MATLAB / SIMULINK simulation software. Simulation results show that the proposed topology achieves good power flow control and short-circuit current suppression functions by sharing the coupling inductor, shortening the fault current clearing time under short-circuit fault conditions, and improving system stability while ensuring economy. This paper proposes a DC power flow controller with current limiting function to suppress transient fault currents and proposes a timing sequence for the current limiting switch operation during fault transients. However, it does not address the transient study during the switching process of the DC power flow controller under normal operating conditions. In contrast, this paper proposes an analysis method based on dynamic system segmentation that covers the transient oscillation characteristics under normal operating conditions. Furthermore, this paper does not address the factors influencing the magnitude of transient oscillations.

[0005] The method for analyzing transient oscillation characteristics of a single-loop PI-controlled DC power flow controller based on system dynamic segmentation mainly includes four parts: construction of the transfer function matrix of the two-line shared inductor type DC power flow controller, system dynamic segmentation based on the transfer function matrix, singular value analysis of the semi-autonomous system of the DC power flow controller, and the influence of DC controller parameters on transient oscillation characteristics. Regarding the construction of the transfer function matrix of the two-line shared inductor type DC power flow controller, most existing studies only focus on linearizing the state-space equation modeling of the dynamics in the DC power flow controller, and there is no research on DC power flow controllers based on the transfer function matrix. In terms of transient characteristic analysis of the two-line shared inductor type DC power flow controller, there is currently no literature that studies the transient oscillation characteristics of the DC power flow controller based on methods such as system dynamic segmentation and singular value analysis. This scheme proposes a method for analyzing the transient oscillation characteristics of a DC power flow controller based on the transfer function matrix and system dynamic segmentation, based on a single-loop PI-controlled two-line shared inductor type DC power flow controller, providing a good reference for targeted transient oscillation suppression in DC power grids containing DC power flow controllers.

[0006] Therefore, a new technical solution is needed to improve the above-mentioned technical problems. 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 characteristics of a single-loop PI-controlled DC power flow controller.

[0008] A method for analyzing transient oscillation characteristics of a single-loop PI-controlled DC power flow controller according to the present invention includes the following steps:

[0009] Step S1: Construct the transfer function matrix of the two-line shared inductor DC power flow controller. This matrix is ​​based on the equivalent state-space model of the two-line shared inductor DC power flow controller with single-loop PI control.

[0010] Step S2: Based on the transfer function matrix, dynamically divide the DC power flow controller into two parts: a fully controlled system and a semi-autonomous system;

[0011] Step S3: Use singular value decomposition (SVD) to solve for the maximum singular value of the semi-autonomous system and study the transient oscillation characteristics of the DC power flow controller.

[0012] Step S4: By analyzing the singular value decomposition results of the DC power flow controller semi-autonomous system through frequency sweep analysis, and taking into account the line resistance and control reference value, analyze the influence of the key parameters of the DC power flow controller on the transient oscillation of the system.

[0013] Preferably, the process of constructing the transfer function matrix in step S1 includes the following steps:

[0014] Step S1.1: Write out the state-space equations of the two-line shared inductance type DC power flow controller:

[0015]

[0016] Where D represents a small-signal perturbation of the variable. and They represent lines respectively. 13 Differential of current, differential term of PI current loop, differential of common inductor current, line 12 Differential of current, line 23 The differential of the voltage across capacitor C1, the differential of the voltage across capacitor C2, the differential of the voltage at port VSC1 of the voltage source converter, and the differential of the voltage at port VSC2 of the voltage source converter; d is the dynamic duty cycle of switch Q1; U C1 U C2 and I L All are steady-state values, while u C1 u C2 and iL All values ​​are dynamic; A represents the system matrix of the two-line shared inductor type DC power flow controller, 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;

[0017] Step S1.2: Based on whether it is completely controlled by a PI single loop, dynamically divide the state variables, assign the state variables controlled by the PI single loop to the controllable system, and assign the other state variables to the autonomous system;

[0018] Step S1.3: Based on the input and output variables of the autonomous system, construct the small-signal model of the autonomous system and obtain the transfer function matrix.

[0019] Preferably, the process of dynamically dividing the system into a fully autonomous system and a semi-autonomous system in step S2 includes the following steps:

[0020] Step S2.1: Determine the state variables under PI single-loop control and classify them into the controllable system;

[0021] Step S2.2: Determine the state variables that are not controlled by the PI single loop and include them in the autonomous system;

[0022] Step S2.3: Establish the state-space equations for the controllable system and the autonomous system respectively.

[0023] Preferably, the process of solving for the maximum singular value using singular value decomposition in step S3 includes the following steps:

[0024] Step S3.1: Perform singular value decomposition on the transfer function matrix at a preset frequency;

[0025] Step S3.2: Determine the maximum singular value corresponding to each frequency point to characterize the peak response of the autonomous system state variables that the system input variables can excite.

[0026] Preferably, the frequency sweep analysis process in step S4 includes the following steps:

[0027] Step S4.1: Change the frequency of the input signal and calculate the maximum singular value corresponding to each frequency point;

[0028] Step S4.2: Taking into account the changes in line resistance and control reference value, analyze the influence of key parameters of DC power flow controller on system transient oscillation.

[0029] Preferably, the method further includes:

[0030] Step S5: Verify the effectiveness of the transient oscillation characteristic analysis method in a three-terminal ring network DC transmission system by changing the line resistance and the reference value of the line current and observing the changes in the transient oscillation characteristics of the system.

[0031] Preferably, the verification process in step S6 includes the following steps:

[0032] Step S6.1: Place the two-line DC power flow controller with single-loop PI control into the three-terminal ring network DC transmission system;

[0033] Step S6.2: Set the line current reference value and actively regulate the power flow of the preset line;

[0034] Step S6.3: Change the reference values ​​of line resistance and line current, and observe and record the changes in the transient oscillation characteristics of the system.

[0035] Preferably, the topology of the two-line shared inductor type DC power flow controller includes two voltage source converters and a shared inductor.

[0036] Preferably, the single-loop PI control includes a current loop and a voltage loop, wherein the current loop is used to control the current in the common inductor, and the voltage loop is used to control the output voltage of the voltage source converter.

[0037] This invention also provides a transient oscillation characteristic analysis system for a single-loop PI-controlled DC power flow controller, comprising the following modules:

[0038] Module M1: Constructs the transfer function matrix of the two-line shared inductance DC power flow controller, which is based on the equivalent state-space model of the single-loop PI-controlled two-line shared inductance DC power flow controller;

[0039] Module M2: Based on the aforementioned transfer function matrix, the DC power flow controller is dynamically divided into two parts: a fully controlled system and a semi-autonomous system.

[0040] Module M3: Using singular value decomposition (SVD) to solve for the maximum singular value of a semi-autonomous system and to study the transient oscillation characteristics of a DC power flow controller;

[0041] Module M4: By analyzing the singular value decomposition results of the DC power flow controller semi-autonomous system through frequency sweep analysis, and taking into account the line resistance and control reference value, the influence of key parameters of the DC power flow controller on the transient oscillation of the system is analyzed.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] 1. This invention fully utilizes the active response characteristics of DC power flow controller to DC microgrid disturbances, providing a reference for the dynamic suppression of transient oscillations in DC microgrids based on system dynamics, and can realize DC power flow control adapted to complex DC grid scenarios;

[0044] 2. This invention innovatively introduces a system dynamic partitioning method into a two-line shared inductor type DC power flow controller. By dividing the system into a controllable part and an autonomous part, it is beneficial to establish a targeted DC power flow controller control strategy.

[0045] 3. This invention transforms the small-signal model of a single-loop PI-controlled two-line DC power flow controller into a transfer function matrix, performs singular value decomposition on the transfer function matrix, and effectively characterizes the oscillation amplitude of different state variables during transient processes.

[0046] 4. This invention performs frequency sweep analysis on the singular value decomposition results of the autonomous system of the DC controller within the operating frequency range, and reveals the influence of changes in key system parameters on transient oscillation characteristics at different frequencies by changing the line resistance and the reference line current. Attached Figure Description

[0047] 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:

[0048] Figure 1 This is a schematic diagram of the topology of the DC power flow controller with shared inductor between two lines according to the present invention;

[0049] Figure 2 This is a schematic diagram of the working sub-mode 1 of the two-line shared inductor type DC power flow controller of the present invention;

[0050] Figure 3 This is a schematic diagram of the working sub-mode 2 of the two-line shared inductor type DC power flow controller of the present invention;

[0051] Figure 4 This is a schematic diagram of the dynamic partitioning of the DC power flow controller with shared inductance between two lines according to the present invention.

[0052] Figure 5 This is a schematic diagram showing the maximum singular values ​​corresponding to each frequency point of the transfer function of the present invention;

[0053] Figure 6 This is a schematic diagram showing the maximum singular value of the transfer function at each frequency point under different line resistances R according to the present invention.

[0054] Figure 7 The reference values ​​i for different line currents in this invention 13ref Below is a schematic diagram of the maximum singular values ​​corresponding to each frequency point of the transfer function;

[0055] Figure 8This is a schematic diagram of the three-terminal ring network DC transmission system of the present invention;

[0056] Figure 9 The common inductor current i under different line resistances in this invention L Transient waveform diagram;

[0057] Figure 10 The voltage u of capacitor C2 under different line resistances in this invention C2 Transient waveform diagram;

[0058] Figure 11 The common inductor current i under different line current reference values ​​of the present invention L Transient waveform diagram;

[0059] Figure 12 This is a schematic diagram of the transient waveform of VSC2 voltage u2 under different line current reference values ​​according to the present invention. Detailed Implementation

[0060] 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.

[0061] Example 1

[0062] Reference Figure 1 and Figure 2 The present invention provides a method for analyzing the transient oscillation characteristics of a single-loop PI-controlled DC power flow controller, comprising the following steps:

[0063] Step S1: Construct the transfer function matrix of the two-line shared inductor DC power flow controller. This matrix is ​​based on the equivalent state-space model of the two-line shared inductor DC power flow controller with single-loop PI control.

[0064] The process of constructing the transfer function matrix includes the following steps:

[0065] Step S1.1: Write out the state-space equations of the two-line shared inductance type DC power flow controller:

[0066]

[0067] Where D represents a small-signal perturbation of the variable. and They represent lines respectively. 13 Differential of current, differential term of PI current loop, differential of common inductor current, line 12Differential of current, line 23 The differential of the voltage across capacitor C1, the differential of the voltage across capacitor C2, the differential of the voltage at port VSC1 of the voltage source converter, and the differential of the voltage at port VSC2 of the voltage source converter; d is the dynamic duty cycle of switch Q1; U C1 U C2 and I L All are steady-state values, while u C1 u C2 and i L All values ​​are dynamic; A represents the system matrix of the two-line shared inductor type DC power flow controller, B represents the system input matrix, C represents the system output matrix, and X represents the system output matrix.

[0068] Represents the system's state variables. Let represent the derivative of the system state variable, u represent the system input variable, and Y represent the system output variable;

[0069] Step S1.2: Based on whether it is completely controlled by a PI single loop, dynamically divide the state variables, assign the state variables controlled by the PI single loop to the controllable system, and assign the other state variables to the autonomous system;

[0070] Step S1.3: Based on the input and output variables of the autonomous system, construct the small-signal model of the autonomous system and obtain the transfer function matrix.

[0071] Step S2: Based on the transfer function matrix, dynamically divide the DC power flow controller into two parts: a fully controlled system and a semi-autonomous system;

[0072] The process of dynamically dividing a system into a fully autonomous system and a semi-autonomous system includes the following steps:

[0073] Step S2.1: Determine the state variables under PI single-loop control and classify them into the controllable system;

[0074] Step S2.2: Determine the state variables that are not controlled by the PI single loop and include them in the autonomous system;

[0075] Step S2.3: Establish the state-space equations for the controllable system and the autonomous system respectively.

[0076] Step S3: Use singular value decomposition (SVD) to solve for the maximum singular value of the semi-autonomous system and study the transient oscillation characteristics of the DC power flow controller.

[0077] The process of finding the maximum singular value using singular value decomposition includes the following steps:

[0078] Step S3.1: Perform singular value decomposition on the transfer function matrix at a preset frequency;

[0079] Step S3.2: Determine the maximum singular value corresponding to each frequency point to characterize the peak response of the autonomous system state variables that the system input variables can excite.

[0080] Step S4: By analyzing the singular value decomposition results of the DC power flow controller semi-autonomous system through frequency sweep analysis, and taking into account the line resistance and control reference value, analyze the influence of the key parameters of the DC power flow controller on the transient oscillation of the system.

[0081] The process of frequency sweep analysis includes the following steps:

[0082] Step S4.1: Change the frequency of the input signal and calculate the maximum singular value corresponding to each frequency point;

[0083] Step S4.2: Taking into account the changes in line resistance and control reference value, analyze the influence of key parameters of DC power flow controller on system transient oscillation.

[0084] Step S5: Verify the effectiveness of the transient oscillation characteristic analysis method in a three-terminal ring network DC transmission system by changing the line resistance and the reference value of the line current and observing the changes in the transient oscillation characteristics of the system.

[0085] The verification process includes the following steps:

[0086] Step S5.1: Place the two-line DC power flow controller with single-loop PI control into the three-terminal ring network DC transmission system;

[0087] Step S5.2: Set the line current reference value and actively regulate the power flow of the preset line;

[0088] Step S5.3: Change the reference values ​​of line resistance and line current, and observe and record the changes in the transient oscillation characteristics of the system.

[0089] The topology of the two-line common inductor type DC power flow controller includes two voltage source converters and a common inductor; the single-loop PI control includes a current loop and a voltage loop, wherein the current loop is used to control the current in the common inductor and the voltage loop is used to control the output voltage of the voltage source converter.

[0090] The present invention also provides a transient oscillation characteristic analysis system for a single-loop PI-controlled DC power flow controller. The transient oscillation characteristic analysis system for a single-loop PI-controlled DC power flow controller can be implemented by executing the process steps of the transient oscillation characteristic analysis method for a single-loop PI-controlled DC power flow controller. That is, those skilled in the art can understand the transient oscillation characteristic analysis method for a single-loop PI-controlled DC power flow controller as a preferred embodiment of the transient oscillation characteristic analysis system for a single-loop PI-controlled DC power flow controller.

[0091] Example 2

[0092] This invention also provides a transient oscillation characteristic analysis system for a single-loop PI-controlled DC power flow controller, comprising the following modules:

[0093] Module M1: Constructs the transfer function matrix of the two-line shared inductance DC power flow controller, which is based on the equivalent state-space model of the single-loop PI-controlled two-line shared inductance DC power flow controller;

[0094] Module M2: Based on the aforementioned transfer function matrix, the DC power flow controller is dynamically divided into two parts: a fully controlled system and a semi-autonomous system.

[0095] Module M3: Using singular value decomposition (SVD) to solve for the maximum singular value of a semi-autonomous system and to study the transient oscillation characteristics of a DC power flow controller;

[0096] Module M4: By analyzing the singular value decomposition results of the DC power flow controller semi-autonomous system through frequency sweep analysis, and taking into account the line resistance and control reference value, the influence of key parameters of the DC power flow controller on the transient oscillation of the system is analyzed.

[0097] Example 3

[0098] To fill the theoretical gap in the analysis of transient oscillation characteristics of DC power flow controllers, this paper summarizes the influence of DC transmission system parameters on the oscillation characteristics of power flow controllers, aiming to achieve safer and more stable DC power flow controller switching. Combining the dynamic partitioning of the transfer function matrix of a DC power flow controller under single-loop PI control and the study of transient oscillation characteristics based on singular value analysis, a method for analyzing the transient oscillation characteristics of a single-loop PI-controlled DC power flow controller based on system dynamic partitioning is proposed. This method has the following characteristics: considering the equivalent state-space model of a two-line inductance-shared DC power flow controller under single-loop PI control, the transfer function matrix of the two-line DC power flow controller is established, and a dynamic partitioning method for the DC power flow controller is given. Based on singular value decomposition (SFD) technology, the maximum singular value of the semi-autonomous system of the DC power flow controller after dynamic partitioning is calculated, and the transient oscillation characteristics of the DC power flow controller are studied. By performing frequency sweep analysis on the SFD results of the semi-autonomous system of the DC power flow controller, and comprehensively considering line resistance and control reference values, the influence of key parameters of the DC power flow controller on system transient oscillations is analyzed.

[0099] The technical solution proposed in this invention is a method for analyzing the transient oscillation characteristics of a single-loop PI-controlled DC power flow controller based on dynamic system segmentation in a three-terminal ring network DC transmission system. The method mainly includes dynamic segmentation of the inter-line DC controller system, construction of the transfer function matrix of the inter-line DC power flow controller, singular value analysis of the semi-autonomous system of the DC power flow controller, and the influence of key parameters of the DC power flow controller on the system's transient oscillations. Based on the small-signal model of the single-loop PI-controlled DC power flow controller, the transfer function matrix is ​​derived and solved. Based on the transfer function matrix, the DC power flow controller is dynamically segmented into a fully controlled system and a semi-autonomous system. Then, the maximum singular value of the semi-autonomous system is solved using singular value decomposition technology. Finally, considering the changes in line resistance and control reference values, the influence of key parameters of the DC power flow controller on the system's transient oscillations is analyzed.

[0100] The specific implementation methods are as follows:

[0101] A. Dynamic partitioning of a single-loop PI control two-wire shared inductor type DC power flow controller system

[0102] Based on such Figure 1 The working mechanism of the two-line single-loop PI control shared inductor type DC power flow controller shown includes two working sub-modes in a complete power flow regulation cycle, such as... Figure 2 and Figure 3 As shown. Based on the operating principle of each sub-mode, the state-space equations can be written as equations (1) and (2):

[0103]

[0104] Where D represents a small-signal perturbation of the variable. and These represent the differentials of the current in line 13, the differential term of the PI current loop, the differential of the common inductor current, the differential of the current in line 12, the differential of the current in line 23, the differential of the voltage across capacitor C1, the differential of the voltage across capacitor C2, the differential of the voltage at port VSC1 of the voltage source converter, and the differential of the voltage at port VSC2 of the voltage source converter. d is the dynamic duty cycle of switch Q1. UC1, UC2, and IL are steady-state values, while uC1, uC2, and iL are dynamic values. A represents the system matrix of the two-line common inductor DC power flow controller, 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.

[0105] The small-signal model of the DC power flow controller between two lines is dynamically segmented based on whether it is completely controlled by a PI single-loop system, and divided into two parts: a controllable system and an autonomous system. Due to the state variable i... 13 If ξ is completely controlled by a single PI loop, then these two state variables can be classified as controllable systems, while other state variables are classified as autonomous systems.

[0106] The dynamic partitioning process of the DC power flow controller model between the two lines can be represented as follows: Figure 4 As shown. The state variable vectors of the controllable part and the autonomous part of the inter-line DC power flow controller can be represented as shown in equations (3) and (4), respectively:

[0107] ΔX1=[Δi 13 Δu C1 Δξ1 Δξ2] T (3)

[0108] ΔX2=[Δi L Δi 12 Δi 23 Δu C2 Δu1 Δu2] T (4)

[0109] 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:

[0110]

[0111] A1 represents the system matrix of the controllable system, B1 represents the input matrix of the controllable system, and u1 represents the input variable vector of the controllable system. A2 represents the system matrix of the autonomous system, B2 represents the input matrix of the autonomous system, and u2 represents the input variable vector of the autonomous system.

[0112] B. Construction of the transfer function matrix for a single-loop PI control DC power flow controller with shared inductance between two lines.

[0113] Due to the state variable Δi 13 Since neither the input variable Δd nor the input variable can be obtained from within the autonomous system, these two variables are classified as input variables of the autonomous system. That is, the input variable vector of the autonomous system can be represented as shown in equation (7):

[0114] Δu2=[Δi 13 Δd] T (7)

[0115] Therefore, the small-signal model of the autonomous system can be represented as shown in equation (8):

[0116]

[0117] Among them, B2Δu2 can be decomposed as shown in equation (9):

[0118]

[0119] Let any state variable be the output variable of the autonomous system, then the output variable is defined as shown in equation (10):

[0120] ΔY 2_i =C 2_i ΔX2,(i=0,1,2...,7) (10)

[0121] Where ΔY 2_i C represents the output variable of the autonomous system. 2_i Let represent the output matrix of the autonomous system, and be a 1×7 row vector where the i-th element is 1 and the rest are 0. In a two-line shared-inductance DC power flow controller, the input is i 13 The output is Y 2_i The transfer function can be calculated using the formula (11):

[0122] G i1 =C 2_i (sI-A2) -1 B 2_1 (i = 0, 1, 2, ..., 7) (11)

[0123] Among them, G i1 For input i 13 The output is Y 2_i The transfer function is given by I, the identity matrix, and s, the Laplace operator. In a two-line shared-inductance DC power flow controller, the transfer function with input d and output Y2 can be calculated using the formula (12):

[0124] G i2 =C 2_i (sI-A2) -1 B 2_2 (i = 0, 1, 2, ..., 7) (12)

[0125] Among them, G i2 The input is d, and the output is Y. 2_i The transfer function. Therefore, the following seven transfer functions and their input / output variable expressions can be listed as shown in equations (13) to (19):

[0126] Δi L =G 11 Δi 13 +G 12 Δd (13)

[0127] Δi 12 =G 21 Δi 13 +G 22 Δd (14)

[0128] Δi 23 =G 31 Δi 13 +G 32 Δd (15)

[0129] Δu C1 =G 41 Δi 13 +G 42 Δd (16)

[0130] Δu C2 =G 51 Δi 13 +G 52 Δd (17)

[0131] Δu1=G 61 Δi 13 +G 62 Δd (18)

[0132] Δu2=G 71 Δi 13 +G 72 Δd (19)

[0133] Equations (13) to (19) are expressed in matrix form, that is, the transfer function matrix G of the DC power flow controller with shared inductance between two lines under single-loop PI control is established, as shown in equation (20):

[0134]

[0135] C. Singularity Analysis of Semi-Autonomous Systems with Two-Line Shared Inductor DC Power Controller

[0136] The transfer function matrix G has 2 input signals and 7 output signals. At a given frequency ω, it can be decomposed by SVD as shown in equation (21):

[0137] G(jω)=U∑V T (twenty one)

[0138] Where G(jω) is the transfer function matrix at a given frequency ω, U and V are orthogonal matrices of 2×2 and 7×7 respectively, and Σ is a 2×7 diagonal matrix; Σ=[Σ1 0;0 0], where Σ1 is the matrix containing singular values ​​σ1,...,σ n A diagonal matrix. For an input vector v i The system's output response at frequency ω can be calculated as shown in equation (22):

[0139] G(jω)v i =σ i u i (twenty two)

[0140] Where, row vector u i With column vector v i Let σ be the system's output and input vectors. i This is a singular value of the system. When the input signal of a multi-input multi-output system is v... i Direction, output response is u i The direction and the magnitude gain between the input and output vectors are si. Therefore, among all input vectors, the maximum magnitude gain is the maximum singular value.

[0141] Singular value decomposition is performed on the transfer function matrix, and frequency sweeping is used to obtain the maximum singular value corresponding to each frequency point. This characterizes the peak response of the autonomous system's state variables that can be excited by the input variables of the single-loop inter-line DC power flow controller system. The frequency sweep results are as follows: Figure 5 As shown.

[0142] D. The impact of key parameters of a two-line shared-inductance DC power flow controller on system transients

[0143] Key parameters of a single-loop PI-controlled DC power flow controller with a shared inductor between two lines have a significant impact on the system's transient oscillation characteristics. Increasing the line resistance R... 12 R 13 R 23 The variation of the system's maximum singular value is shown in [link to relevant documentation]. Figure 6 Reduce the current reference value i 13ref The variation of the system's maximum singular value is as follows: Figure 7 .Depend on Figure 6 and Figure 7 It can be seen that as the line resistance R... 12 R 13 R 23 As the current reference value i increases, the resonant peak value of the overall state variable of the autonomous system continuously decreases. 13ref As the value decreases, the resonance peak value of the overall state variables of the autonomous system continuously decreases.

[0144] In such Figure 8 The transient oscillation characteristic analysis method of DC power flow controller based on system dynamic segmentation is verified in the three-terminal ring network DC transmission system shown. A two-line DC power flow controller containing single-loop PI control is placed into the line of the three-terminal ring network DC transmission system. 13 and line 23 In this process, by setting a reference value for the line current, the line current can be controlled. 13Active flow control and line management 23 The power flow is passively controlled. By changing the reference values ​​of line resistance and line current, the effectiveness of the transient oscillation analysis method of the DC power flow controller based on system dynamic segmentation in revealing oscillation conditions is verified. The initial parameters of the system are shown in Table 1.

[0145] Table 1: Parameters of a Three-Terminal DC Transmission System Including a Two-Line DC Power Flow Controller with Dual-Loop PI Control

[0146]

[0147]

[0148] Table 2: Experimental parameters for increasing line resistance

[0149]

[0150] Table 3: Experimental Parameters for Increasing Reference Values ​​of Line Current

[0151]

[0152] Set line 13 The reference current is 3.5A. The line resistance is gradually increased, and the line resistance parameters are shown in Table 2. After 1 second, the DC power flow controller between the two lines is connected to the three-terminal ring network DC transmission system. From... Figure 9 and Figure 10 It can be seen that the greater the line resistance, the greater the main state variable i of the autonomous system after the DC power flow controller between the two lines is connected. L with u C2 The smaller the transient oscillation amplitude, the shorter the oscillation time.

[0153] Set the line resistance R 12 R 13 With R 23 Starting with 1W, gradually increase the line size. 13 Reference current and line current reference values ​​are shown in Table 3. At 1 second, the DC power flow controller between the two lines is connected to the three-terminal ring network DC transmission system. From Figure 11 and Figure 12 It can be seen that the larger the reference value of the line current, the higher the main state variable i of the autonomous system after the DC power flow controller between the two lines is connected. L The larger the transient oscillation amplitude of u2, the longer the oscillation time. It can be seen that the proposed transient oscillation characteristic analysis method of DC power flow controller based on system dynamic segmentation can accurately reflect the oscillation of the state variables of the autonomous system.

[0154] Those skilled in the art can understand this embodiment as a more specific description of Embodiment 1 and Embodiment 2.

[0155] 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.

[0156] 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 characteristics of a single-loop PI-controlled DC power flow controller, characterized in that, Includes the following steps: Step S1: Construct the transfer function matrix of the two-line shared inductor DC power flow controller. This matrix is ​​based on the equivalent state-space model of the two-line shared inductor DC power flow controller with single-loop PI control. Step S2: Based on the transfer function matrix, dynamically divide the DC power flow controller into two parts: a fully controlled system and a semi-autonomous system; Step S3: Use singular value decomposition (SVD) to solve for the maximum singular value of the semi-autonomous system and study the transient oscillation characteristics of the DC power flow controller. Step S4: By analyzing the singular value decomposition results of the DC power flow controller semi-autonomous system through frequency sweep analysis, and taking into account the line resistance and control reference value, analyze the influence of the key parameters of the DC power flow controller on the transient oscillation of the system.

2. The method for analyzing transient oscillation characteristics of a single-loop PI-controlled DC power flow controller according to claim 1, characterized in that, The process of constructing the transfer function matrix in step S1 includes the following steps: Step S1.1: Write out the state-space equations of the two-line shared inductance type DC power flow controller: Where D represents a small-signal perturbation of the variable. and They represent lines respectively. 13 Differential of current, differential term of PI current loop, differential of common inductor current, line 12 Differential of current, line 23 The differential of the voltage across capacitor C1, the differential of the voltage across capacitor C2, the differential of the voltage at port VSC1 of the voltage source converter, and the differential of the voltage at port VSC2 of the voltage source converter; d is the dynamic duty cycle of switch Q1; U C1 U C2 and I L All are steady-state values, while u C1 u C2 and i L All values ​​are dynamic; A represents the system matrix of the two-line shared inductor type DC power flow controller, 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; Step S1.2: Based on whether it is completely controlled by a PI single loop, dynamically divide the state variables, assign the state variables controlled by the PI single loop to the controllable system, and assign the other state variables to the autonomous system; Step S1.3: Based on the input and output variables of the autonomous system, construct the small-signal model of the autonomous system and obtain the transfer function matrix.

3. The method for analyzing transient oscillation characteristics of a single-loop PI-controlled DC power flow controller according to claim 1, characterized in that, The process of dynamically dividing the system into a fully autonomous system and a semi-autonomous system in step S2 includes the following steps: Step S2.1: Determine the state variables under PI single-loop control and classify them into the controllable system; Step S2.2: Determine the state variables that are not controlled by the PI single loop and include them in the autonomous system; Step S2.3: Establish the state-space equations for the controllable system and the autonomous system respectively.

4. The method for analyzing transient oscillation characteristics of a single-loop PI-controlled DC power flow controller according to claim 1, characterized in that, The process of solving for the maximum singular value using singular value decomposition in step S3 includes the following steps: Step S3.1: Perform singular value decomposition on the transfer function matrix at a preset frequency; Step S3.2: Determine the maximum singular value corresponding to each frequency point to characterize the peak response of the autonomous system state variables that the system input variables can excite.

5. The method for analyzing transient oscillation characteristics of a single-loop PI-controlled DC power flow controller according to claim 1, characterized in that, The frequency sweep analysis process in step S4 includes the following steps: Step S4.1: Change the frequency of the input signal and calculate the maximum singular value corresponding to each frequency point; Step S4.2: Taking into account the changes in line resistance and control reference value, analyze the influence of key parameters of DC power flow controller on system transient oscillation.

6. The method for analyzing transient oscillation characteristics of a single-loop PI-controlled DC power flow controller according to claim 1, characterized in that, The method further includes: Step S5: Verify the effectiveness of the transient oscillation characteristic analysis method in a three-terminal ring network DC transmission system by changing the line resistance and the reference value of the line current and observing the changes in the transient oscillation characteristics of the system.

7. The method for analyzing transient oscillation characteristics of a single-loop PI-controlled DC power flow controller according to claim 6, characterized in that, The verification process in step S5 includes the following steps: Step S5.1: Place the two-line DC power flow controller with single-loop PI control into the three-terminal ring network DC transmission system; Step S5.2: Set the line current reference value and actively regulate the power flow of the preset line; Step S5.3: Change the reference values ​​of line resistance and line current, and observe and record the changes in the transient oscillation characteristics of the system.

8. The method for analyzing transient oscillation characteristics of a single-loop PI-controlled DC power flow controller according to claim 1, characterized in that, The topology of the two-line shared inductor type DC power flow controller includes two voltage source converters and a shared inductor.

9. The method for analyzing transient oscillation characteristics of a single-loop PI-controlled DC power flow controller according to claim 1, characterized in that, The single-loop PI control includes a current loop and a voltage loop, wherein the current loop is used to control the current in the common inductor, and the voltage loop is used to control the output voltage of the voltage source converter.

10. A transient oscillation characteristic analysis system for a single-loop PI-controlled DC power flow controller, characterized in that, Includes the following modules: Module M1: Constructs the transfer function matrix of the two-line shared inductance DC power flow controller, which is based on the equivalent state-space model of the single-loop PI-controlled two-line shared inductance DC power flow controller; Module M2: Based on the aforementioned transfer function matrix, the DC power flow controller is dynamically divided into two parts: a fully controlled system and a semi-autonomous system. Module M3: Using singular value decomposition (SVD) to solve for the maximum singular value of a semi-autonomous system and to study the transient oscillation characteristics of a DC power flow controller; Module M4: By analyzing the singular value decomposition results of the DC power flow controller semi-autonomous system through frequency sweep analysis, and taking into account the line resistance and control reference value, the influence of key parameters of the DC power flow controller on the transient oscillation of the system is analyzed.

Images