Method and system for frequency-dependent parameter identification of flexible dc lines

Abstract

The application provides a flexible direct current line frequency variable parameter identification method and system, belongs to the parameter identification technical field of power grid transmission lines, and changes the number and state of equivalent redundant sub-modules input by each bridge arm; according to the number and state of the input half-bridge sub-modules, a voltage characteristic signal of a direct current line is injected; according to the injected voltage characteristic signal, in combination with a mathematical model of a distributed parameter transmission line, characteristic impedance, propagation constant and attenuation constant corresponding to the frequency of the injected voltage characteristic signal are calculated; and according to the characteristic impedance at different frequencies calculated by injecting voltage characteristic signals at different frequencies for multiple times, the characteristic impedance in the full frequency domain is fitted. The application solves the problem that parameters are difficult to obtain due to the absence of a stable fundamental frequency in a direct current system, and improves the frequency variable parameter identification precision of the flexible direct current line.

Description

Technical Field

[0001] This invention relates to the field of power grid transmission line parameter identification technology, specifically to a method and system for identifying frequency-varying parameters of flexible DC lines based on half-bridge MMC characteristic signal injection. Background Technology

[0002] Flexible DC transmission technology based on modular multilevel converters has advantages such as flexible control, no commutation failure, and controllable power flow. It is applicable to many scenarios such as DC grids, new energy grid connection and transmission, and is an important supporting technology for building new current systems. However, the fault current of flexible DC grids rises rapidly, the overcurrent capacity of power electronics is weak, and improper handling of a single fault may lead to the shutdown of the entire DC system. Therefore, relay protection is the key to its safe operation.

[0003] Currently, flexible DC power grid engineering line protection configurations include traveling wave protection, voltage surge protection, undervoltage protection, and longitudinal differential protection. However, the coordination problem of the "four properties" (traveling wave protection, voltage surge protection, and voltage differential protection) of the existing four protection principles remains unresolved. To improve protection performance, traveling wave differential protection has been proposed, considering the attenuation constant of the traveling wave to address the problems caused by the distributed capacitance of the line. However, the accurate attenuation constant of the line has a significant impact on protection performance. Based on the flexible DC line protection principle of digital twins, the concept of digital twins is introduced into relay protection research, providing a new approach to resolving the contradictions among the current protection "four properties." However, obtaining the parameters of the digital twin model is quite difficult. Therefore, obtaining accurate parameters of flexible DC transmission lines is crucial for improving the performance of relay protection.

[0004] Currently, line parameter identification can be divided into offline measurement methods and online measurement and calculation methods. Offline measurement methods involve appropriately connecting the line under test and applying power based on the parameters to be measured, then calculating the line parameters by measuring basic quantities such as voltage and current. It is practical and easy to operate, but requires setting up an independent measurement circuit or adding an extra power supply at the test site, involves more steps, and has more significant error deviations. The main disadvantage of offline measurement is that the line needs to be switched to a power-off maintenance state, affecting the normal operation of the system.

[0005] Online measurement and calculation methods, based on the classic Carson formula, calculate line parameters using geometric structures such as towers, conductors, and ground wires. However, these calculations rely on various approximations and simplifications, which are no longer sufficient to meet the accuracy requirements of engineering projects due to the increasing complexity of power grid structures. To effectively and quickly identify line parameters, online measurement methods utilizing SCADA data and PMU measured data have become a research focus in recent years. Currently, parameter identification for transmission lines mainly focuses on AC lines, with very little research on DC lines. The main reason is the lack of a stable fundamental frequency in DC systems, making parameter identification difficult under steady-state operating conditions.

[0006] The principle of determining the nature of DC faults based on MMC-injected characteristic signals is to utilize the controllable characteristics of MMCs. By changing the control strategy, the number of sub-modules in operation is adjusted to generate pulse signals of a specific frequency. The nature of the fault is then determined based on the traveling wave reflection theory. Research based on MMC-injected characteristic signals also provides a new approach to parameter identification of flexible DC lines.

[0007] In summary, the main problems with current transmission line parameter identification methods are: 1) The main drawback of offline measurement is that the line needs to be switched to a power outage maintenance state, which affects the normal operation of the system; 2) The lack of a stable fundamental frequency in DC systems makes parameter identification difficult under steady-state operation. Summary of the Invention

[0008] The purpose of this invention is to provide a flexible DC line parameter identification method and system based on MMC feature signal injection that can measure line frequency-varying parameters, is more economical, and has higher parameter identification accuracy, so as to solve at least one of the technical problems existing in the background art.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] On one hand, the present invention provides a method for identifying frequency-varying parameters of flexible DC lines, comprising:

[0011] Control the maximum number of sub-modules that each bridge arm needs to deploy, and change the number and status of redundant sub-modules that the bridge arm can deploy externally in an equivalent manner;

[0012] Based on the number and status of the half-bridge sub-modules, the voltage characteristic signal of the DC line is injected;

[0013] Based on the injected voltage characteristic signal and combined with the mathematical model of the distributed parameter transmission line, the characteristic impedance, propagation constant and attenuation constant corresponding to the frequency of the injected voltage characteristic signal are calculated.

[0014] Based on the characteristic impedances at different frequencies calculated from multiple injections of voltage characteristic signals at different frequencies, the characteristic impedance in the full frequency domain is fitted.

[0015] The preferred mathematical model for distributed parameter transmission lines is:

[0016]

[0017] Where U(0,s) represents the line starting voltage, I(0,s) represents the line starting current, U(l,s) represents the line ending voltage, I(l,s) represents the line ending current, s represents the complex frequency domain, l represents the line length, γ represents the line propagation constant, and Z... c This represents the characteristic impedance of the line.

[0018] Preferably, the characteristic impedance Z corresponding to the frequency of the injected voltage characteristic signal is calculated. c The propagation constant γ(s) and the attenuation constant A(s) are:

[0019]

[0020]

[0021] A(s) = e -γl ;

[0022] Where U1(s) represents the voltage at the beginning of the line, U2(s) represents the voltage at the end of the line, I1(s) represents the current at the beginning of the line, and I2(s) represents the current at the end of the line.

[0023] Preferably, the selection of the frequency of the injected voltage characteristic signal includes: the period of the injected voltage characteristic signal is an integer multiple of the sampling period, the frequency of the injected voltage characteristic signal reflects the changing law of the line characteristic impedance and attenuation coefficient; and the frequency of the square wave generated by the switching of the control redundancy submodule is less than the sampling frequency of the protection.

[0024] Preferably, the amplitude and phase of the characteristic signal are extracted from the measurement data on both sides of the line using the FFT algorithm. If the sampling frequency is f... s Sampling interval t s =1 / f s If the FFT algorithm requires N sampling points, then N×t s The window length of the windowed Fourier transform is given by frequency resolution Δf = f. s / N.

[0025] Preferably, the DC voltage reference value is defined as U. dcref Then, the number of real-time submodules that need to be deployed in the upper and lower bridge arms at time t. for:

[0026]

[0027] Where, N op U represents the maximum number of submodules required for each bridge arm. cN Indicates the rated capacitor voltage. This represents the reference sinusoidal modulation voltage of each phase upper bridge arm. This represents the reference sinusoidal modulation voltage for each lower bridge arm of phase.

[0028] Secondly, a flexible DC line frequency conversion parameter identification system, characterized in that it includes:

[0029] The control module is used to control the maximum number of sub-modules that each bridge arm needs to deploy, and to change the number and status of redundant sub-modules that the bridge arm can deploy externally in an equivalent manner.

[0030] The injection module is used to inject the voltage characteristic signal of the DC line according to the number and status of the half-bridge sub-modules that are engaged.

[0031] The calculation module is used to calculate the characteristic impedance, propagation constant, and attenuation constant corresponding to the frequency of the injected voltage characteristic signal, based on the injected voltage characteristic signal and combined with the mathematical model of the distributed parameter transmission line.

[0032] The fitting module is used to fit the characteristic impedance in the full frequency domain based on the characteristic impedance calculated at different frequencies from multiple injections of voltage characteristic signals at different frequencies.

[0033] Thirdly, the present invention provides a non-transitory computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the method for identifying frequency-varying parameters of flexible DC lines based on half-bridge MMC feature signal injection as described above.

[0034] Fourthly, the present invention provides a computer program product, including a computer program that, when run on one or more processors, is used to implement the method for identifying frequency-varying parameters of flexible DC lines based on half-bridge MMC feature signal injection as described above.

[0035] Fifthly, the present invention provides an electronic device, comprising: a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions for implementing the flexible DC line frequency-varying parameter identification method based on half-bridge MMC characteristic signal injection as described above.

[0036] The beneficial effects of this invention are as follows: It provides a flexible DC line parameter identification method based on MMC feature signal injection, which can measure line frequency-varying parameters, is more economical, and has higher parameter identification accuracy; it utilizes a half-bridge MMC redundant submodule for active feature signal injection, which is more economical than full-bridge and hybrid MMC methods; the use of a half-bridge MMC redundant submodule for active feature signal injection solves the problem of difficulty in parameter acquisition due to the lack of a stable fundamental frequency in the DC system; and it improves the frequency-varying parameter identification accuracy of flexible DC lines.

[0037] The advantages of additional aspects of the invention will be set forth more clearly in the following description or will be learned by practice of the invention. Attached Figure Description

[0038] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0039] Figure 1 This is a schematic diagram of the HB-MMC topology according to an embodiment of the present invention.

[0040] Figure 2 This is a schematic diagram of the traditional HB-MMC control strategy described in an embodiment of the present invention.

[0041] Figure 3 This is a schematic diagram illustrating the deployment status of the sub-modules described in an embodiment of the present invention.

[0042] Figure 4 This is a schematic diagram of the additional control strategy for feature signal injection according to an embodiment of the present invention.

[0043] Figure 5 This is a schematic diagram illustrating the characteristic signal and its spectrum analysis according to an embodiment of the present invention, wherein, Figure 5 (a) is a schematic diagram of the line voltage waveform after the characteristic signal is injected. Figure 5 (b) is a line voltage spectrum analysis diagram after the characteristic signal is injected.

[0044] Figure 6 This is a schematic diagram of a uniform transmission line circuit model according to an embodiment of the present invention.

[0045] Figure 7 This is the characteristic impedance equivalent network diagram described in the embodiment of the present invention.

[0046] Figure 8 This is a flowchart illustrating the parameter identification process for flexible DC lines based on active injection, as described in an embodiment of the present invention.

[0047] Figure 9 This is a simulation diagram of the two-terminal true bipolar flexible DC transmission system described in an embodiment of the present invention.

[0048] Figure 10 This is a schematic diagram of the identification results of the characteristic impedance parameters of the line mode according to an embodiment of the present invention.

[0049] Figure 11 This is a schematic diagram of the identification results of the characteristic impedance parameters of the ground model according to an embodiment of the present invention.

[0050] Figure 12 This is a schematic diagram of the identification results of the linear mode attenuation constant parameter according to an embodiment of the present invention.

[0051] Figure 13This is a schematic diagram of the identification results of the linear mode attenuation constant parameter according to an embodiment of the present invention. Detailed Implementation

[0052] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0053] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0054] It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as here.

[0055] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, and / or groups thereof.

[0056] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0057] To facilitate understanding of the present invention, the present invention will be further explained and described below with reference to the accompanying drawings and specific embodiments. However, the specific embodiments do not constitute a limitation on the embodiments of the present invention.

[0058] Those skilled in the art should understand that the accompanying drawings are merely schematic diagrams of embodiments, and the components in the drawings are not necessarily essential for implementing the present invention.

[0059] Example 1

[0060] This embodiment 1 provides a flexible DC line frequency conversion parameter identification system, including:

[0061] The control module is used to control the maximum number of sub-modules that each bridge arm needs to deploy, and to change the number and status of redundant sub-modules that the bridge arm can deploy externally in an equivalent manner.

[0062] The injection module is used to inject the voltage characteristic signal of the DC line according to the number and status of the half-bridge sub-modules that are engaged.

[0063] The calculation module is used to calculate the characteristic impedance, propagation constant, and attenuation constant corresponding to the frequency of the injected voltage characteristic signal, based on the injected voltage characteristic signal and combined with the mathematical model of the distributed parameter transmission line.

[0064] The fitting module is used to fit the characteristic impedance in the full frequency domain based on the characteristic impedance calculated at different frequencies from multiple injections of voltage characteristic signals at different frequencies.

[0065] In this embodiment 1, the above-described system is used to implement a method for identifying frequency-varying parameters of flexible DC lines, including:

[0066] The control module controls the maximum number of sub-modules that each bridge arm needs to deploy, thus changing the number and status of redundant sub-modules that the bridge arm can deploy externally in an equivalent manner.

[0067] Using the injection module, the voltage characteristic signal of the DC line is injected according to the number and status of the injected half-bridge sub-modules;

[0068] Using the calculation module, based on the injected voltage characteristic signal and combined with the mathematical model of the distributed parameter transmission line, the characteristic impedance, propagation constant, and attenuation constant corresponding to the frequency of the injected voltage characteristic signal are calculated.

[0069] Using the fitting module, the characteristic impedance in the full frequency domain is fitted based on the characteristic impedance at different frequencies of the voltage characteristic signals injected multiple times at different frequencies calculated by the calculation module.

[0070] The mathematical model for distributed parameter transmission lines is as follows:

[0071]

[0072] Where U(0,s) represents the line starting voltage, I(0,s) represents the line starting current, U(l,s) represents the line ending voltage, I(l,s) represents the line ending current, s represents the complex frequency domain, l represents the line length, γ represents the line propagation constant, and Z... c This represents the characteristic impedance of the line.

[0073] The characteristic impedance Z corresponding to the frequency of the injected voltage characteristic signal is calculated.c The propagation constant γ(s) and the attenuation constant A(s) are:

[0074]

[0075]

[0076] A(s) = e -γl ;

[0077] Where U1(s) represents the voltage at the beginning of the line, U2(s) represents the voltage at the end of the line, I1(s) represents the current at the beginning of the line, and I2(s) represents the current at the end of the line.

[0078] The selection of the frequency of the injected voltage characteristic signal includes: the period of the injected voltage characteristic signal is an integer multiple of the sampling period; the frequency of the injected voltage characteristic signal reflects the changing law of the line characteristic impedance and attenuation coefficient; and the frequency of the square wave generated by the switching of the control redundancy submodule is less than the sampling frequency of the protection.

[0079] The amplitude and phase of characteristic signals are extracted from measurement data from both sides of the line using the FFT algorithm. If the sampling frequency is f... s Sampling interval t s =1 / f s If the FFT algorithm requires N sampling points, then N×t s The window length of the windowed Fourier transform is given by frequency resolution Δf = f. s / N.

[0080] Define the DC voltage reference value as U dcref Then, the number of real-time submodules that need to be deployed in the upper and lower bridge arms at time t. for:

[0081]

[0082] Where, N op U represents the maximum number of submodules required for each bridge arm. cN Indicates the rated capacitor voltage. This represents the reference sinusoidal modulation voltage of each phase upper bridge arm. This represents the reference sinusoidal modulation voltage for each lower bridge arm of phase.

[0083] Example 2

[0084] In this second embodiment, a flexible DC line parameter identification method based on MMC feature signal injection is proposed, which is more economical, has higher parameter identification accuracy, and can measure line frequency-varying parameters. The idea of ​​actively injecting MMC feature signals is incorporated into the research on DC line parameter identification to obtain accurate DC line frequency-varying parameters and improve the performance of relay protection.

[0085] In this second embodiment, the HB-MMC topology and control principle are described as follows:

[0086] HB-MMC structure as follows Figure 1 As shown, it consists of six bridge arms, with the upper and lower bridge arms combined to form a phase unit. Each bridge arm contains N structurally identical half-bridge sub-modules (HBSMs) and a bridge arm inductor L. arm It is connected in series. The HBSM consists of two IGBTs (T1-T2), a capacitor C0, and two anti-parallel diodes (D1-D2).

[0087] HBSM has three working states: locked, engaged, and disengaged, and can output U. c There are two voltages: 0 and 0. Figure 1 in,i dc For direct current, U dc DC voltage and Three-phase current in the upper and lower bridge arms and For the three-phase voltage and current on the AC side of the converter

[0088] Classic HB-MMC control strategies, such as Figure 2 As shown. When the system is in normal operation, the MMC adopts a traditional dual-loop control strategy. The outer loop uses constant active power and constant reactive power control, while the inner loop uses constant current control. The DC-side voltage is maintained by using half of the submodule capacitors.

[0089] The principle behind the generation of voltage characteristic signals is explained below:

[0090] Without considering the redundant submodules of the converter station, the number of bridge arm submodules in series N and the DC voltage U dc and rated capacitor voltage U cN The relationship is:

[0091] N = U dc / U cN (1)

[0092] When designing an MMC, the operating condition with a modulation ratio m=1 must be considered. In this case, the voltage variation range of the upper and lower bridge arms output is 0 to U. dc Accordingly, the number of submodules deployed in each bridge arm is 0 to N. The additional submodules connected in series outside of these N submodules are the redundant submodules considered in the design, and their number is denoted as N. de However, in actual MMC operation, the modulation ratio m < 1 in most cases, and the maximum number of submodules N that each bridge arm needs to be deployed can be calculated. op for:

[0093]

[0094] The above analysis shows that, under the modulation ratio m < 1 operating mode, the bridge arm submodules will not be fully utilized, and at any given time, at least NN submodules will be used. op Each submodule is in an idle state; these are referred to as redundant submodules ΔN. op Therefore, the submodule deployment status diagram during normal MMC operation is as follows: Figure 3 As shown, the total number of redundant submodules N re for:

[0095] N re =N de +ΔN op (3)

[0096] In engineering, the most common MMC modulation strategy is Nearest Level Approximation Modulation (NLM). Theoretically, NLM controls the voltage difference between the MMC output voltage and the modulated wave voltage within (±U) / 2. dc Within / 2). Define the DC voltage reference value as U. dcref Then, the number of real-time sub-modules that need to be deployed in the upper and lower arms at time t can be expressed as:

[0097]

[0098] Where, round(x) represents taking the integer closest to x. and This represents the reference sinusoidal modulation voltage for each phase upper and lower bridge arm.

[0099] In this embodiment 2, the active injection of feature signals is achieved by controlling the on / off state of the redundant submodule, that is, controlling N... op The quantity changes the number and status of the equivalent HBSMs connected to the bridge arm. When the number of submodules connected to the upper and lower bridge arms of each phase is increased or decreased simultaneously, the AC side voltage reference potential will not change, and the AC side of the MMC will not be affected. First, all submodules in the bridge arm are charged, discharged, and voltage-equalized using a dynamic redundancy voltage equalization strategy. If N op A sudden increase in the input quantity ΔN will cause a sharp increase in the DC voltage at the converter output; if N op A sudden reduction in the input quantity ΔN results in a sharp drop in DC voltage at the converter output. Therefore, by controlling N... op Increasing or decreasing the quantity allows for the injection of voltage characteristic signals into the DC line. Specific additional control strategies include... Figure 4 As shown, when a rectangular wave characteristic signal is superimposed on the normal operation of the line, the DC line voltage becomes a rectangular wave. A rectangular wave is one type of characteristic signal, and other types of characteristic signals can also be injected.

[0100] In this embodiment 2, the selection of the injected feature signal, including the selection of frequency, amplitude, and signal recognition, is described as follows:

[0101] Regarding the selection of the characteristic signal frequency: The selection of the characteristic signal frequency needs to consider the limitations of the sampling device, the switching control cycle of the converter submodule, and the actual conditions of the engineering site. Specifically: First, to reduce the error in signal extraction, spectral leakage needs to be minimized. Therefore, the period of the injected characteristic signal must be an integer multiple of the sampling period, and the frequency of the injected characteristic signal must be able to reflect the changing patterns of the line's characteristic impedance and attenuation coefficient. Second, the square wave frequency generated by controlling the switching of redundant submodules should be lower than the sampling frequency of the protection system and is limited by the switching speed of the submodules. In actual DC engineering, the sampling frequency of the protection system is 10-50kHz, and the common switching control cycle of the MMC submodule is usually 100μs. Taking a 10kHz sampling frequency as an example, according to Shannon's sampling theorem, the highest frequency that the protection device can correctly distinguish is 5000Hz.

[0102] Regarding the selection of the characteristic signal amplitude: The magnitude of the injected characteristic signal amplitude is limited by the proportion of redundant submodules and should take into account the requirements of the detection device, power system impact, and the withstand capability of power electronic devices in the converter station. Therefore, there are strict limitations on the magnitude of the characteristic signal amplitude. Simultaneously, to meet the accuracy requirements of parameter identification later, a relatively larger amplitude of the injected characteristic signal is more conducive to the detection, extraction, and spectrum analysis of the characteristic signal. Considering that the number of redundant submodules in the bridge arm of the converter is typically 10%-20% of the number of ordinary submodules, this embodiment sets the amplitude of the injected characteristic signal to 5% of the rated DC voltage in subsequent simulations.

[0103] For feature signal identification: To extract the amplitude and phase of feature signals, there are currently various signal extraction methods, including wavelet transform, Prony algorithm, discrete Fourier transform, and fast Fourier transform. Among them, wavelet transform can reflect the time-varying characteristics of a signal, but it cannot provide phase information; the Prony algorithm can describe the transient characteristics of a signal, including amplitude and phase, but it is significantly affected by noise interference and the determination of the accurate model order; the discrete Fourier transform (DFT) transforms the sampling of the time-domain signal into sampling in the frequency domain of the discrete-time Fourier transform, which can accurately describe the amplitude and phase of the signal, but it has a large computational load and consumes a lot of computing resources; the fast Fourier transform (FFT) improves upon the odd, even, imaginary, and real characteristics of the DFT, reducing the number of multiplications and additions in digital systems, and has the advantages of fast computation speed and low complexity.

[0104] In this embodiment, the FFT algorithm is used to extract the amplitude and phase of characteristic signals from the measurement data on both sides of the line for subsequent line parameter identification. If the sampling frequency f...s Sampling interval t s =1 / f s If the FFT algorithm requires N sampling points, then N·t s The window length of the windowed Fourier transform is given by frequency resolution Δf = f. s / N. If the window length is short enough, the influence of submodule capacitor charging and discharging can be ignored, and the amplitude of the characteristic frequency signal can be assumed to be constant and undiminished; if the window length is long enough, the frequency resolution is more accurate. To suppress spectral leakage, the characteristic signal frequency must be an integer multiple of the frequency resolution, i.e., the window length is variable. Taking a 1000Hz characteristic signal injection as an example, the obtained spectral analysis information of the measurements on both sides of the line is as follows: Figure 5 As shown.

[0105] In this second embodiment, based on the above description, the method for identifying parameters of flexible DC lines includes the following:

[0106] For establishing a uniform transmission line distributed parameter model:

[0107] A uniform transmission line is one in which the geometric dimensions and electromagnetic properties of the medium are uniform, and the circuit parameters reflecting the electromagnetic processes of the transmission line are uniformly distributed along the entire line. A circuit model on a micro-element is as follows: Figure 6 As shown. Where U(0,t), U(l,t), I(0,t), and I(l,t) are the voltage and current at both ends of the line, U(x,t), U(x+Δx,t), I(x,t), and I(x+Δx,t) are the voltage and current on both sides of a infinitesimal length of the line, and R0, L0, G0, and C0 are the resistance, inductance, conductance, and capacitance per unit length of the line. The expressions for the traveling waves of voltage and current on the transmission line can be represented by the telegraph equations:

[0108]

[0109] Depending on the different initial and boundary conditions, a unique voltage and current can be determined using equation (5). However, solving this equation in the time domain is quite difficult. Therefore, the Laplace transform is used to convert equation (5) from the time domain to the frequency domain for solution.

[0110]

[0111] Taking the second derivative of equation (6) with respect to x and eliminating variables, we obtain a second-order differential equation containing only voltage and current:

[0112]

[0113] Solving equation (7), we can obtain the general solutions for U(x,s) and I(x,s):

[0114] U(x,s)=D1(s)e-γ(s)x +D2(s)e γ(s)x (8)

[0115] I(x,s)=(D1(s)e -γ(s)x +D2(s)e γ(s)x ) / Z c (9)

[0116] Where D1(s) and D2(s) are coefficients determined by the line boundary conditions; Z c γ(s) is the characteristic impedance of the line, and γ(s) is the propagation constant of the line. Their respective values ​​are:

[0117]

[0118]

[0119] Substituting the boundary conditions at the beginning of the line (x=0, U(x,s)=U(0,s), I(x,s)=I(0,s)) into equations (8) and (9), we get:

[0120]

[0121]

[0122] Substituting the coefficients D1(s) and D2(s) into equations (8) and (9) yields...

[0123]

[0124] Equation (14) allows us to calculate the voltage and current at any point along the line given the voltage and current at the beginning of the line. Substituting x = l into equation (14) yields the mathematical model of a distributed parameter transmission line:

[0125]

[0126] Methods for identifying frequency-varying parameters of flexible DC lines:

[0127] By transforming equation (15), we can obtain

[0128]

[0129] Combining equations (15) and (16), we get:

[0130] U1(s)-U2(s)=(U2(s)-U1(s))cosh(γl)

[0131] +Z c sinh(γl)(I2(s)+I1(s)) (17)

[0132]

[0133]

[0134] Eliminating variables from equations (17), (18), and (19), we can obtain the characteristic impedance, propagation constant, and attenuation constant at a specific frequency as follows:

[0135]

[0136]

[0137] A(s) = e -γl (twenty two)

[0138] The voltage and current signals at both ends of the line at a specific frequency are measured and extracted. The precise characteristic impedance, propagation constant, and attenuation constant can be calculated using equations (20) and (21). Due to the high-frequency skin effect generated by the transmission line and the ground under the action of alternating electromagnetic fields, the distributed parameters of the transmission line will change with frequency. The characteristic impedance and propagation constant become frequency-dependent parameters.

[0139] Choose a linear network that has Z c The frequency characteristics of (s) belong to network synthesis problems. The characteristic impedance can be expressed using a partial fractional sum, and Z can be expressed using RLC elements. c (s). Choose a function in the complex frequency domain:

[0140]

[0141] in, Given the characteristic impedance at infinity, equation (32) can be rewritten as a partial fraction sum:

[0142]

[0143] Among them, the constant term The numerators of other fractional terms The constant term k0 directly corresponds to a resistor R. s0 All other terms are complex frequency domain functions of parallel RC circuits, so the i-th circuit can be expressed as:

[0144]

[0145] Among them, R s0 R si and C si These are the resistive and capacitive elements in each term of the fractional equation, and their meanings are expressed as follows:

[0146]

[0147] The characteristic impedance can be expressed using resistance and capacitance as follows: Figure 7 The equivalent network shown satisfies the boundary conditions for the characteristic impedance: at low frequencies, the capacitors approximate as open circuits, and the characteristic impedance is represented by the series connection of all capacitors; at high frequencies, the capacitors approximate as short circuits, and the characteristic impedance is approximately equal to R. s0 .

[0148]

[0149] The above analysis shows that the characteristic impedance value decreases monotonically with increasing frequency. Therefore, by injecting characteristic signals of different frequencies multiple times, the characteristic impedance at different frequencies is calculated, and the characteristic impedance in the full frequency domain is fitted using linear interpolation. The analysis method for the propagation constant is the same as that for the characteristic impedance. The flowchart of the frequency-varying parameter identification method for flexible DC lines is shown below. Figure 8 As shown.

[0150] In this embodiment 2, a line frequency-varying parameter identification and verification experiment based on half-bridge MMC characteristic signal injection is provided:

[0151] Build such a simulation in PSCAD software Figure 9 The dual-end true bipolar flexible DC transmission system shown uses HB-MMC models for the converters and frequency-varying parameter models for the DC lines, with a sampling frequency of 10kHz. Each bridge arm has a total of 200 submodules. System parameters are shown in Table 1.

[0152] Table 1 Main parameters of flexible DC transmission system

[0153]

[0154] For the analysis of characteristic impedance identification accuracy:

[0155] By adjusting the control strategies of MMC1_p and MMC1_n, a characteristic signal of a specific frequency is injected into line KM, and the characteristic impedance value at different frequencies is calculated according to the flexible DC line parameter identification strategy proposed in this embodiment.

[0156] Table 2 shows a comparison between the identification results and actual values ​​of some characteristic impedances at different frequencies. Table 2 demonstrates that the parameter identification method proposed in this embodiment has good accuracy in calculating characteristic impedances from low to high frequencies. The relative error for both line-mode and ground-mode characteristic impedance calculations can be controlled within 1.5%.

[0157] Table 2. Identification results of characteristic impedance at different frequencies

[0158]

[0159] The full-frequency characteristic signal fitting results for the linear mode and the ground mode are as follows: Figure 10 , 11 As shown in the figure, it can be seen that, whether it is the characteristic impedance fitting of the line mode or the characteristic impedance fitting of the ground mode, the characteristic impedance amplitude-frequency characteristic curve obtained by the parameter identification method proposed in this embodiment is basically consistent with the actual value of the line, the curve trend is the same, the relative error of the parameters in each frequency band is less than 1.5%, and the fitting accuracy is good.

[0160] For the analysis of the accuracy of attenuation constant identification:

[0161] By adjusting the control strategies of MMC1_p and MMC1_n, a characteristic signal of a specific frequency is injected into line KM, and the attenuation constant value at different frequencies is calculated according to the flexible DC line parameter identification strategy proposed in this embodiment.

[0162] Table 3 shows a comparison between the identification results and actual values ​​of some attenuation constants at different frequencies. Table 3 demonstrates that the parameter identification method proposed in this embodiment has good accuracy in calculating attenuation constants from low to high frequencies. The relative error in calculating both the linear mode attenuation constant and the ground mode attenuation constant can be controlled within 0.5%.

[0163] Table 3. Identification results of attenuation constants at different frequencies

[0164]

[0165]

[0166] The full-frequency attenuation constant fitting results for the linear mode and the ground mode are as follows: Figure 12 , 13 As shown, it can be seen that, whether it is the fitting of the linear mode attenuation constant or the fitting of the ground mode attenuation constant, the amplitude-frequency characteristic curve of the attenuation constant obtained by the parameter identification method proposed in this embodiment is basically consistent with the actual value of the line, the curve trend is the same, the relative error of the parameters in each frequency band is less than 1.5%, and the fitting accuracy is good.

[0167] Example 3

[0168] Embodiment 3 of the present invention provides a non-transitory computer-readable storage medium for storing computer instructions. When executed by a processor, the computer instructions implement a method for identifying frequency-varying parameters of flexible DC lines based on half-bridge MMC feature signal injection. The method includes:

[0169] Control the maximum number of sub-modules that each bridge arm needs to deploy, and change the number and status of redundant sub-modules that the bridge arm can deploy externally in an equivalent manner;

[0170] Based on the number and status of the half-bridge sub-modules, the voltage characteristic signal of the DC line is injected;

[0171] Based on the injected voltage characteristic signal and combined with the mathematical model of the distributed parameter transmission line, the characteristic impedance, propagation constant and attenuation constant corresponding to the frequency of the injected voltage characteristic signal are calculated.

[0172] Based on the characteristic impedances at different frequencies calculated from multiple injections of voltage characteristic signals at different frequencies, the characteristic impedance in the full frequency domain is fitted.

[0173] Example 4

[0174] Embodiment 4 of the present invention provides a computer program (product), including a computer program that, when run on one or more processors, is used to implement a method for identifying frequency-varying parameters of flexible DC lines based on half-bridge MMC characteristic signal injection. The method includes:

[0175] Control the maximum number of sub-modules that each bridge arm needs to deploy, and change the number and status of redundant sub-modules that the bridge arm can deploy externally in an equivalent manner;

[0176] Based on the number and status of the half-bridge sub-modules, the voltage characteristic signal of the DC line is injected;

[0177] Based on the injected voltage characteristic signal and combined with the mathematical model of the distributed parameter transmission line, the characteristic impedance, propagation constant and attenuation constant corresponding to the frequency of the injected voltage characteristic signal are calculated.

[0178] Based on the characteristic impedances at different frequencies calculated from multiple injections of voltage characteristic signals at different frequencies, the characteristic impedance in the full frequency domain is fitted.

[0179] Example 5

[0180] Embodiment 5 of the present invention provides an electronic device, including: a processor, a memory, and a computer program; wherein, the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions for implementing a method for identifying frequency-varying parameters of flexible DC lines based on half-bridge MMC characteristic signal injection. The method includes:

[0181] Control the maximum number of sub-modules that each bridge arm needs to deploy, and change the number and status of redundant sub-modules that the bridge arm can deploy externally in an equivalent manner;

[0182] Based on the number and status of the half-bridge sub-modules, the voltage characteristic signal of the DC line is injected;

[0183] Based on the injected voltage characteristic signal and combined with the mathematical model of the distributed parameter transmission line, the characteristic impedance, propagation constant and attenuation constant corresponding to the frequency of the injected voltage characteristic signal are calculated.

[0184] Based on the characteristic impedances at different frequencies calculated from multiple injections of voltage characteristic signals at different frequencies, the characteristic impedance in the full frequency domain is fitted.

[0185] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0186] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0187] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0188] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment, whereby a series of operational steps are performed to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0189] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that, based on the technical solutions disclosed in the present invention, various modifications or variations that can be made by those skilled in the art without creative effort should be included within the scope of protection of the present invention.

Claims

1. A method for identifying frequency-varying parameters of a flexible DC line, characterized in that, include: Control the maximum number of submodules that need to be deployed in each bridge arm, and change the number and status of redundant submodules that are equivalently deployed to the outside of the bridge arm; wherein, the DC voltage reference value is defined as ,but The number of real-time sub-modules that need to be deployed in the upper and lower bridge arms at any given time. , for: ； in, This indicates the maximum number of submodules that need to be deployed in each bridge arm. Indicates the rated capacitor voltage. This represents the reference sinusoidal modulation voltage of each phase upper bridge arm. This represents the reference sinusoidal modulation voltage for each lower bridge arm; round(*) indicates taking the integer closest to *. Based on the number and status of the half-bridge sub-modules, the voltage characteristic signal of the DC line is injected; Based on the injected voltage characteristic signal and combined with the mathematical model of the distributed parameter transmission line, the characteristic impedance, propagation constant and attenuation constant corresponding to the frequency of the injected voltage characteristic signal are calculated. Based on the characteristic impedances at different frequencies calculated from multiple injections of voltage characteristic signals at different frequencies, the characteristic impedance in the full frequency domain is fitted.

2. The method for identifying frequency-varying parameters of flexible DC lines according to claim 1, characterized in that, The mathematical model for a distributed parameter transmission line is: ； in, Indicates the voltage at the beginning of the line. Indicates the current at the beginning of the line. Indicates the voltage at the end of the line. Indicates the current at the end of the line. Represents the complex frequency domain. Indicates the length of the line. Represents the line propagation constant. This represents the characteristic impedance of the line.

3. The method for identifying frequency-varying parameters of flexible DC lines according to claim 2, characterized in that, The characteristic impedance corresponding to the frequency of the injected voltage characteristic signal is calculated. Propagation constant and attenuation constant for: ； ； ； in, Indicates the voltage at the beginning of the line. Indicates the voltage at the end of the line. Indicates the current at the beginning of the line. This indicates the current at the end of the line.

4. The method for identifying frequency-varying parameters of flexible DC lines according to claim 1, characterized in that, The selection of the frequency of the injected voltage characteristic signal includes: the period of the injected voltage characteristic signal is an integer multiple of the sampling period; the frequency of the injected voltage characteristic signal reflects the changing law of the line characteristic impedance and attenuation coefficient; and the frequency of the square wave generated by the switching of the control redundancy submodule is less than the sampling frequency of the protection.

5. The method for identifying frequency-varying parameters of flexible DC lines according to claim 4, characterized in that, The amplitude and phase of characteristic signals are extracted from measurement data from both sides of the line using the FFT algorithm. If the sampling frequency is... Sampling interval The FFT algorithm requires the following number of sampling points: ,but To adjust the window length and frequency resolution of the Fourier transform, .

6. A flexible DC line frequency conversion parameter identification system, characterized in that, include: The control module is used to control the maximum number of submodules that need to be deployed in each bridge arm, changing the number and status of redundant submodules that the bridge arm can effectively deploy externally; among them, the DC voltage reference value is defined as ,but The number of real-time sub-modules that need to be deployed in the upper and lower bridge arms at any given time. , for: ； in, This indicates the maximum number of submodules that need to be deployed in each bridge arm. Indicates the rated capacitor voltage. This represents the reference sinusoidal modulation voltage of each phase upper bridge arm. This represents the reference sinusoidal modulation voltage for each lower bridge arm; round(*) indicates taking the integer closest to *. The injection module is used to inject the voltage characteristic signal of the DC line according to the number and status of the redundant sub-modules. The calculation module is used to calculate the characteristic impedance, propagation constant, and attenuation constant corresponding to the frequency of the injected voltage characteristic signal, based on the injected voltage characteristic signal and combined with the mathematical model of the distributed parameter transmission line. The fitting module is used to fit the characteristic impedance in the full frequency domain based on the characteristic impedance calculated at different frequencies from multiple injections of voltage characteristic signals at different frequencies.

7. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium is used to store computer instructions, which, when executed by a processor, implement the flexible DC line frequency conversion parameter identification method as described in any one of claims 1-5.

8. A computer program product, characterized in that, Includes a computer program, which, when run on one or more processors, is used to implement the method for identifying frequency-varying parameters of flexible DC lines as described in any one of claims 1-5.

9. An electronic device, characterized in that, include: The device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions for implementing the flexible DC line frequency conversion parameter identification method as described in any one of claims 1-5.

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