A Method for Measuring Impedance Parameters of Three-Phase Asymmetrical Lines Based on Different Frequency Increments

Abstract

This invention discloses a method for measuring the impedance parameters of a three-phase asymmetrical line based on inter-frequency increments. The method includes defining measurement parameters; simultaneously measuring the voltage and current phasors at the beginning and end of the three phases of the line using three measurement methods; processing the phase voltage and current data measured under the three measurement methods to calculate the phase voltage increment and phase current increment; calculating the phase resistance and phase reactance matrices corresponding to the 50Hz power frequency according to the inter-frequency phase impedance measurement equation; and converting the phase resistance and phase reactance into sequence resistance and sequence inductance according to the phase sequence transformation matrix. This method can simultaneously and effectively suppress power frequency and inter-frequency interference on the line under test, and accurately measure the phase impedance parameters and sequence impedance parameters of the three-phase asymmetrical line.

Description

Technical Field

[0001] This invention relates to the field of power system measurement technology, and in particular to a method for measuring the impedance parameters of a three-phase asymmetrical line based on frequency increments. Background Technology

[0002] Transmission and distribution line parameters are important benchmark parameters for various numerical analyses of power systems. Inaccurate parameters will lead to problems in analysis and calculation such as relay protection settings and line fault location.

[0003] With the expansion of power grids, electromagnetic coupling between lines in dense transmission and distribution corridors has become increasingly severe. When measuring the parameters of a newly built or renovated line within a transmission and distribution corridor, the surrounding normally energized lines will induce voltage and current on the line under test due to three-phase imbalance. Because the induced current on the line under test generates an additional voltage drop, the measured voltage and current data no longer conform to the original voltage-current characteristics. Therefore, the induced voltage and current will affect the measurement results of the line under test, significantly increasing the measurement error. In the field of line parameter measurement, such induced voltage and current are called "interference," which can be further divided into power frequency interference and inter-frequency interference depending on whether the frequency is the 50Hz power frequency.

[0004] In actual power line construction, short lines are usually not transposed, and long lines are difficult to transpose completely. Therefore, the parameters of each phase in a three-phase line are usually asymmetrical. When measuring the impedance parameters of an asymmetrical three-phase line in a power transmission and distribution corridor with complex electromagnetic coupling relationships, existing measurement methods can only minimize power frequency interference but cannot simultaneously suppress the influence of inter-frequency interference. Therefore, their measurement accuracy is insufficient and cannot meet engineering requirements. Summary of the Invention

[0005] The purpose of this section is to outline some aspects of the embodiments of the present invention and to briefly introduce some preferred embodiments. Some simplifications or omissions may be made in this section, as well as in the abstract and title of the present application, to avoid obscuring the purpose of this section, the abstract and title of the invention. Such simplifications or omissions shall not be used to limit the scope of the present invention.

[0006] In view of the problems existing in the above and / or prior art, the present invention is proposed.

[0007] Therefore, the technical problem to be solved by the present invention is that existing measurement methods can only avoid the influence of power frequency interference when measuring line impedance parameters in a strong interference environment, but cannot overcome the problem of inter-frequency interference.

[0008] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a method for measuring the impedance parameters of a three-phase asymmetrical line based on frequency-incremental impedance, comprising, Define measurement parameters; The voltage and current phasors at the beginning and end of the three phases of the line are measured simultaneously using three measurement methods. The phase voltage and phase current data measured under the three measurement methods are processed to calculate the phase voltage increment and phase current increment; Calculate the phase resistance and phase reactance matrix corresponding to the power frequency of 50Hz based on the line phase impedance measurement equation; The phase resistance and phase reactance are converted into sequence resistance and sequence inductance according to the phase sequence transformation matrix.

[0009] As a preferred embodiment of the three-phase asymmetrical line impedance parameter measurement method based on frequency increment described in this invention, the defined measurement parameters include: A three-phase unbalanced line is defined as consisting of phases A, B, and C; the current phasors at the beginning of the three-phase lines A, B, and C are defined as follows: , , The current phasor at the end is , , Define the voltage phasors at the beginning of the three-phase lines A, B, and C as follows: , , Define the operating frequency as The amplitudes are respectively and The three-phase symmetrical frequency power supply, and Define the voltage increments of the three phases A, B, and C of line as follows: , , The current increments of phases A, B, and C are , , The length of a three-phase unbalanced line is defined as... .

[0010] As a preferred embodiment of the three-phase asymmetrical line impedance parameter measurement method based on frequency increment described in this invention, the three measurement methods include: First measurement method: Apply a frequency of [frequency value] to the starting ends of phases A, B, and C of the line. Amplitude A symmetrical frequency power supply is used to ground the ends of the three phases A, B, and C of the line, and the parameters are measured. Second measurement method: Apply a frequency of [frequency value] to the starting ends of phases A, B, and C of the line. Amplitude For a symmetrical power supply with different frequencies, disconnect the power supply wiring at the beginning of phase C and measure the parameters. The third measurement method: Apply a frequency of [frequency value missing] to the starting ends of phases A, B, and C of the line. Amplitude For a symmetrical power supply with different frequencies, disconnect the power supply wiring at the beginning of phases A and C, and ground the ends of phases A, B, and C of the line, then measure the parameters.

[0011] As a preferred embodiment of the three-phase asymmetrical line impedance parameter measurement method based on differential frequency increments described in this invention, the calculation of phase voltage increments and phase current increments includes: Define the voltage increments of the three phases A, B, and C of line as follows: , , The current increments of phases A, B, and C are , , The phase voltage and phase current data measured under the three measurement methods are processed to calculate the phase voltage increment and phase current increment.

[0012] As a preferred embodiment of the three-phase asymmetrical line impedance parameter measurement method based on frequency increment described in this invention, the frequency-incremental phase impedance measurement equation is derived from the lumped parameter model of the three-phase asymmetrical line, describing the voltage and current of each phase when the A, B, and C phases of the line are grounded under the action of a frequency power source. in, For different frequencies The corresponding line phase impedance matrix at different frequencies: matrix middle, , , These are phases A, B, and C of the line at different frequencies. The phase impedance below, , , They are respectively in different frequencies The mutual impedance between phases AB, phases AC, and phases BC of the lower line.

[0013] As a preferred embodiment of the three-phase asymmetrical line impedance parameter measurement method based on frequency-increment as described in this invention, wherein: substituting the phase voltage and phase current increments under the three measurement methods into the line frequency-increment phase impedance measurement equation yields: The different frequencies can be solved using the following formula. Corresponding line phase impedance matrix The elements in .

[0014] As a preferred embodiment of the three-phase asymmetrical line impedance parameter measurement method based on frequency increments described in this invention, the phase impedance matrix is ​​divided into real and imaginary parts. Unfold to obtain different frequencies Corresponding phase resistance matrix and different frequencies Corresponding phase reactance matrix ,Right now .

[0015] As a preferred embodiment of the three-phase asymmetrical line impedance parameter measurement method based on frequency increments described in this invention, wherein: according to frequency increments... Phase resistance matrix and phase reactance matrix After conversion, the phase resistance and phase reactance matrices corresponding to the 50Hz power frequency are obtained. The conversion formula is as follows: (4) in, The operating frequency of the differential power supply added at the beginning of the line is between 45 and 55 Hz. and This represents the power frequency phase resistance and phase reactance matrix of the line, where each element is the phase resistance and phase reactance of the line.

[0016] As a preferred embodiment of the three-phase asymmetrical line impedance parameter measurement method based on differential frequency increments described in this invention, wherein: converting the phase resistance and phase reactance into sequence resistance and sequence inductance according to the phase sequence transformation matrix includes: make , This is the power frequency phase impedance matrix of a three-phase asymmetrical line.

[0017] Phase sequence transformation matrix of line parameters for: in, This represents a unit phasor with an argument of 120°. This represents a unit phasor with an argument of 240°.

[0018] As a preferred embodiment of the three-phase asymmetrical line impedance parameter measurement method based on frequency increment described in this invention, the power frequency phase impedance parameters of the line are converted into power frequency sequence resistance and power frequency sequence inductance per unit length according to the following formula: in, Represents the zero-sequence, positive-sequence, and negative-sequence resistance per unit length of a three-phase unbalanced circuit; Represents the zero-sequence, positive-sequence, and negative-sequence inductance per unit length of a three-phase unbalanced circuit; This represents the mutual resistance per unit length between two different sequences in a three-phase unbalanced circuit. It represents the mutual inductance per unit length between two different sequences in a three-phase unbalanced circuit; 0 represents zero sequence, 1 represents positive sequence, and 2 represents negative sequence.

[0019] The beneficial effects of this invention are: the method can simultaneously and effectively suppress power frequency and heterogeneous frequency interference on the line under test, and accurately measure the phase impedance parameters and sequence impedance parameters of a three-phase unbalanced line. Attached Figure Description

[0020] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. 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. Wherein: Figure 1 A simplified wiring diagram for measuring the impedance parameters of a three-phase unbalanced line based on differential frequency incremental measurement, provided in an embodiment of the present invention; Figure 2 A lumped parameter model diagram of a three-phase unbalanced circuit provided in an embodiment of the present invention; Figure 3 A comparison chart of the positive sequence resistance measurement error between the measurement method provided in this embodiment of the invention and existing measurement methods; Figure 4 A comparison chart of the zero-sequence inductance measurement error between the measurement method provided in this embodiment of the invention and existing measurement methods. Detailed Implementation

[0021] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0022] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0023] Secondly, the present invention will be described in detail with reference to the schematic diagrams. When detailing the embodiments of the present invention, for ease of explanation, the cross-sectional views illustrating the device structure will be partially enlarged, not according to the usual scale. Furthermore, the schematic diagrams are merely examples and should not limit the scope of protection of the present invention. In addition, actual fabrication should include three-dimensional spatial dimensions of length, width, and depth.

[0024] Furthermore, the term "an embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places throughout this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that mutually excludes other embodiments.

[0025] Example 1 Reference Figure 1 and 2 This embodiment provides a method for measuring the impedance parameters of a three-phase asymmetrical line based on frequency increments, including: I. Define the measurement parameters. Specifically, this step includes: A three-phase unbalanced line is defined as consisting of phases A, B, and C; the current phasors at the beginning of the three-phase lines A, B, and C are defined as follows: , , The current phasor at the end is , , Define the voltage phasors at the beginning of the three-phase lines A, B, and C as follows: , , Define the operating frequency as The amplitudes are respectively and The three-phase symmetrical frequency power supply, and Define the voltage increments of the three phases A, B, and C of line as follows: , , The current increments of phases A, B, and C are , , The length of a three-phase unbalanced line is defined as... .

[0026] II. Measurement steps include: Step 1: Simultaneously measure the voltage and current phasors at the beginning and end of the three phases of the line. The three measurement methods used are as follows: Measurement Method 1: Apply a frequency of [frequency value] to the starting ends of phases A, B, and C of the line. Amplitude A symmetrical, different-frequency power supply is used, and the ends of phases A, B, and C of the line are grounded. The synchronization and timing function of a satellite navigation system is used to synchronously measure the voltage phasors of the three phases at the beginning of the line. , , The current phasors of the three phases at the beginning of the line , , The current phasors of the three phases at the end of the line , , Using automatic devices to quickly change the frequency to Amplitude The frequency of the power supply is switched to a frequency of Amplitude The power supply operates at a different frequency, with the rest of the wiring remaining unchanged; the synchronization and timing function of the satellite navigation system is used again to synchronously measure the voltage phasors of the three phases at the beginning of the line. , , The current phasors of the three phases at the beginning of the line , , The current phasors of the three phases at the end of the line , , .

[0027] Measurement Method Two: Apply a frequency of [frequency value] to the starting ends of phases A, B, and C of the line. Amplitude With a symmetrical, non-polar power supply, disconnect the power connection at the beginning of phase C, ground the ends of phases A, B, and C of the line, and use the synchronization function of the satellite navigation system to synchronously measure the voltage phasors of the three phases at the beginning of the line. , , The current phasors of the three phases at the beginning of the line , , The current phasors of the three phases at the end of the line , , Using automatic devices to quickly change the frequency to Amplitude The frequency of the power supply is switched to a frequency of Amplitude The power supply operates at a different frequency, with the rest of the wiring remaining unchanged; the synchronization and timing function of the satellite navigation system is used again to synchronously measure the voltage phasors of the three phases at the beginning of the line. , , The current phasors of the three phases at the beginning of the line , , The current phasors of the three phases at the end of the line , , .

[0028] Measurement Method 3: Apply a frequency of [frequency value] to the starting ends of phases A, B, and C of the line. Amplitude With a symmetrical, non-polar power supply, disconnect the power connections at the beginning of phases A and C, ground the ends of phases A, B, and C, and use the synchronization function of the satellite navigation system to synchronously measure the voltage phasors of the three phases at the beginning of the line. , , The current phasors of the three phases at the beginning of the line , , The current phasors of the three phases at the end of the line , , Using automatic devices to quickly change the frequency to Amplitude The frequency of the power supply is switched to a frequency of Amplitude The power supply operates at a different frequency, with the rest of the wiring remaining unchanged; the synchronization and timing function of the satellite navigation system is used again to synchronously measure the voltage phasors of the three phases at the beginning of the line. , , The current phasors of the three phases at the beginning of the line , , The current phasors of the three phases at the end of the line , , .

[0029] Step 2: Process the phase voltage and phase current data obtained from the three measurement methods in Step 1 to calculate the phase voltage increment and phase current increment. The calculation method is as follows: Define the voltage increments of the three phases A, B, and C of line as follows: , , The current increments of phases A, B, and C are , , The phase voltage and phase current data measured under the three measurement methods are processed to calculate the phase voltage increment and phase current increment. The calculation method is as follows: Calculation Step 1: Measurement Method 1 corresponding to the phase voltage increment and phase current increment: The phase voltage increments of phases A, B, and C are as follows: , , The phase current increments of phases A, B, and C are: , , .

[0030] Calculation step 1: Phase voltage increment and phase current increment corresponding to measurement method 2: The phase voltage increments of phases A, B, and C are as follows: , , The phase current increments of phases A, B, and C are: , , .

[0031] Calculation step 1: Measurement mode 3 corresponding to the phase voltage increment and phase current increment: The phase voltage increments of phases A, B, and C are as follows: , , The phase current increments of phases A, B, and C are: , , .

[0032] The calculation of the phase resistance and phase reactance matrix corresponding to the power frequency of 50Hz based on the line phase impedance measurement equation includes: Step 3: Based on the lumped parameter model of the three-phase unbalanced line, write the equations for measuring the phase impedance of the line at different frequencies, describing the voltage and current of each phase when the three phases A, B, and C of the line are grounded under the action of the different frequency power supply, as shown in equation (1): (1) in, For different frequencies The corresponding line phase impedance matrix at different frequencies: matrix middle, , , These are phases A, B, and C of the line at different frequencies. The phase impedance below, , , They are respectively in different frequencies The mutual impedance between phases AB, phases AC, and phases BC of the lower line.

[0033] Step 4: Substitute the phase voltage and current increments obtained in Step 2 under the three measurement methods into Equation (1) to obtain Equation (2), and solve for the different frequencies according to Equation (3). Corresponding line phase impedance matrix The elements in.

[0034] (2) (3) Step 5: Arrange the phase impedance matrix according to its real and imaginary parts. Unfold to obtain different frequencies Corresponding phase resistance matrix and different frequencies Corresponding phase reactance matrix ,Right now .

[0035] Step 6, based on different frequencies Phase resistance matrix and phase reactance matrix After conversion, the phase resistance and phase reactance matrices corresponding to the 50Hz power frequency are obtained. The conversion formula is as follows: (4) in, The operating frequency of the differential power supply added at the beginning of the line is between 45 and 55 Hz. and This represents the power frequency phase resistance and phase reactance matrix of the line, where each element is the phase resistance and phase reactance of the line.

[0036] Step 7: Convert the phase resistance and phase reactance obtained in Step 6 into sequence resistance and sequence inductance according to the phase sequence transformation matrix, as follows: make , This is the power frequency phase impedance matrix of a three-phase asymmetrical line.

[0037] Phase sequence transformation matrix of line parameters for: (5) in, This represents a unit phasor with an argument of 120°. This represents a unit phasor with an argument of 240°.

[0038] Equations (6) and (7) can be used to convert the power frequency phase impedance parameters of the line into power frequency sequence resistance and power frequency sequence inductance per unit length: (6) (7) in, Represents the zero-sequence, positive-sequence, and negative-sequence resistance per unit length of a three-phase unbalanced circuit; Represents the zero-sequence, positive-sequence, and negative-sequence inductance per unit length of a three-phase unbalanced circuit; This represents the mutual resistance per unit length between two different sequences in a three-phase unbalanced circuit. It represents the mutual inductance per unit length between two different sequences in a three-phase unbalanced circuit; 0 represents zero sequence, 1 represents positive sequence, and 2 represents negative sequence.

[0039] The technical solution provided by this invention achieves effective suppression of power frequency interference and heterofrequency interference from surrounding operating lines on the line under test during both the parameter measurement process and the measurement results. This solves the problem that existing parameter measurement methods can only resist power frequency interference but not heterofrequency interference, and further improves the measurement accuracy of impedance parameters of three-phase unbalanced lines under strong interference environments.

[0040] Example 2 This embodiment uses a simulation calculation to demonstrate the beneficial effects of the present invention.

[0041] Step 1: Select a 20km long three-phase unbalanced line as the line to be tested and de-energize it; there is a normally energized 220kV line operating nearby, which is considered an interfering line; according to... Figure 1 The wiring diagram shown illustrates the wiring of the circuit under test. The voltage and current phasors at the beginning and end of the three phases of the circuit are measured simultaneously using the following three measurement methods: Measurement Method 1: Apply a symmetrical power supply with a frequency of 47.5Hz and an amplitude of 800V to the starting ends of phases A, B, and C of the line. Ground the ending ends of phases A, B, and C of the line. Utilize the synchronization and timing function of the satellite navigation system to synchronously measure the voltage phasors of the three phases at the starting ends of the line. , , The current phasors of the three phases at the beginning of the line , , The current phasors of the three phases at the end of the line , , The system uses an automatic device to switch the power supply from 47.5Hz and 800V to 47.5Hz and 850V within a short time, while keeping the rest of the wiring unchanged. Then, the system uses the synchronization function of the satellite navigation system to simultaneously measure the voltage phasors of the three phases at the beginning of the line. , , The current phasors of the three phases at the beginning of the line , , The current phasors of the three phases at the end of the line , , Store measurement data.

[0042] Measurement Method Two: Apply a symmetrical power supply with a frequency of 47.5Hz and an amplitude of 800V to the starting ends of phases A, B, and C of the line. Disconnect the power supply connection at the starting end of phase C, and ground the ending ends of phases A, B, and C of the line. Utilize the synchronization and timing function of the satellite navigation system to synchronously measure the voltage phasors of the three phases at the starting ends of the line. , , The current phasors of the three phases at the beginning of the line , , The current phasors of the three phases at the end of the line , , The system uses an automatic device to switch the power supply from 47.5Hz and 800V to 47.5Hz and 850V within a short time, while keeping the rest of the wiring unchanged. Then, the system uses the synchronization function of the satellite navigation system to simultaneously measure the voltage phasors of the three phases at the beginning of the line. , , The current phasors of the three phases at the beginning of the line , , The current phasors of the three phases at the end of the line , , Store measurement data.

[0043] Measurement Method 3: Apply a symmetrical power supply with a frequency of 47.5Hz and an amplitude of 800V to the starting ends of phases A, B, and C of the line. Disconnect the power supply connections at the starting ends of phases A and C, and ground the ending ends of phases A, B, and C. Utilize the synchronization and timing function of the satellite navigation system to synchronously measure the voltage phasors of the three phases at the starting ends of the line. , , The current phasors of the three phases at the beginning of the line , , The current phasors of the three phases at the end of the line , , The system uses an automatic device to switch the power supply from 47.5Hz and 800V to 47.5Hz and 850V within a short time, while keeping the rest of the wiring unchanged. Then, the system uses the synchronization function of the satellite navigation system to simultaneously measure the voltage phasors of the three phases at the beginning of the line. , , The current phasors of the three phases at the beginning of the line , , The current phasors of the three phases at the end of the line , , Store measurement data.

[0044] Step 2: Process the phase voltage and phase current measurement data of the line under test obtained in Step 1 under the three measurement methods, and calculate the phase voltage increment and phase current increment. The calculation method is as follows: Calculation Step 1: Measurement Method 1 corresponding to the phase voltage increment and phase current increment: The phase voltage increments of phases A, B, and C are as follows: , , The phase current increments of phases A, B, and C are: , , .

[0045] Calculation step 1: Phase voltage increment and phase current increment corresponding to measurement method 2: The phase voltage increments of phases A, B, and C are as follows: , , The phase current increments of phases A, B, and C are: , , .

[0046] Calculation step 1: Measurement mode 3 corresponding to the phase voltage increment and phase current increment: The phase voltage increments of phases A, B, and C are as follows: , , The phase current increments of phases A, B, and C are: , , .

[0047] Step 3, according to Figure 2 Given the lumped parameter model of the three-phase unbalanced line shown, write the phase impedance measurement equations describing the phase voltages and currents of each phase when the three phases A, B, and C of the line under test are grounded under the action of a 47.5Hz power supply, as shown in equation (A1): (A1) in, The line phase impedance matrix corresponding to a frequency of 47.5Hz is as follows: matrix middle, , , These are the phase impedances of phases A, B, and C of the line under test at a different frequency of 47.5Hz. , , These are the mutual impedances between phases AB, phases AC, and phases BC of the circuit under test at a different frequency of 47.5Hz.

[0048] Step 4: Substitute the phase voltage and current increments obtained in Step 2 under the three measurement methods into equation (A1) to obtain equation (A2). Solve for the line phase impedance matrix corresponding to the 47.5Hz frequency using equation (A3). The elements in.

[0049] (A2) (A3) Step 5: Arrange the phase impedance matrix according to its real and imaginary parts. Expanding, we obtain the phase resistance matrix corresponding to the 47.5Hz frequency. and phase reactance matrix ,Right now .

[0050] Step 6, based on the phase resistance matrix of the 47.5Hz different frequency. and phase reactance matrix After conversion, the phase resistance and phase reactance matrices corresponding to the 50Hz power frequency are obtained. The conversion formula is as follows: (A4) in, and This represents the power frequency phase resistance and phase reactance matrix of the line, where each element is the power frequency phase resistance and phase reactance of the line.

[0051] Step 7: Convert the phase resistance and phase reactance obtained in Step 6 into sequence resistance and sequence inductance according to the phase sequence transformation matrix, as follows: make , This is the power frequency phase impedance matrix of the circuit under test.

[0052] Phase sequence transformation matrix of line parameters for: (A5) in, This represents a unit phasor with an argument of 120°. This represents a unit phasor with an argument of 240°.

[0053] Equations (A6) and (A7) convert the power frequency phase impedance parameters of the circuit under test into power frequency sequence resistance and power frequency sequence inductance per unit length: (A6) (A7) in, In this embodiment, the length of the line to be measured is indicated. ; This represents the zero-sequence, positive-sequence, and negative-sequence resistance per unit length of the three-phase unbalanced circuit under test. Represents zero-sequence, positive-sequence, and negative-sequence inductance per unit length; This represents the mutual resistance per unit length between two different sequences in the three-phase unbalanced circuit under test. It represents the mutual inductance per unit length between two different sequences; 0 represents zero sequence, 1 represents positive sequence, and 2 represents negative sequence.

[0054] To illustrate the effectiveness of the embodiments of the present invention, the theoretical values ​​of the impedance parameters per unit length of the three-phase unbalanced line under test in PSCAD / EMTDC simulation and the measurement results of the impedance parameters obtained using the measurement method of the present invention are given below.

[0055] The theoretical values ​​of the positive-sequence and zero-sequence impedance per unit length of the three-phase unbalanced line under test are as follows: The theoretical values ​​for positive-sequence resistance are 0.3380 Ω / km and positive-sequence inductance are 1.0893 mH / km; the theoretical values ​​for zero-sequence resistance are 0.2395 Ω / km and zero-sequence inductance are 3.0415 mH / km.

[0056] The measurement results of the line impedance parameters obtained using the measurement method of the present invention (referred to as the differential frequency incremental method in this embodiment) are as follows: The positive-sequence resistance was measured to be 0.3402 Ω / km, and the positive-sequence inductance was measured to be 1.0921 mH / km; the zero-sequence resistance was measured to be 0.2416 Ω / km, and the zero-sequence inductance was measured to be 3.0500 mH / km. The relative errors for the positive-sequence resistance and positive-sequence inductance measurements were 0.65% and 0.26%, respectively; the relative errors for the zero-sequence resistance and zero-sequence inductance measurements were 0.88% and 0.28%, respectively.

[0057] To further illustrate the effects of the embodiments of the present invention, the measurement results of the impedance parameters of the three-phase unbalanced line using existing measurement methods are given below.

[0058] Existing measurement methods include the traditional differential frequency method and the incremental method. The traditional differential frequency method applies a differential frequency power supply to the line under test and calculates the impedance parameters by measuring the differential frequency signal of the line, thereby avoiding the influence of power frequency interference. The incremental method applies a power frequency power supply to the line under test and artificially generates a set of voltage and current increments on the line under test for a short time. It uses these increments to calculate the line impedance parameters, thereby reducing the influence of power frequency interference on the measurement results.

[0059] Table 1 shows a comparison of the measurement errors of the three-phase unbalanced line impedance measured using the traditional differential frequency method and incremental method with the measurement error of the measurement method of the present invention (different frequency incremental method).

[0060] Table 1. Comparison of measurement results of the traditional heterogeneous frequency method, the incremental method, and the heterogeneous frequency incremental method.

[0061] Here, the level 1 interference intensity on the three-phase unbalanced line under test is defined as: the interference voltage on the 50km test line is 5% of the amplitude of the test power supply. Similarly, level 2 interference intensity is 10%, and level 5 interference intensity is 25%. Taking positive-sequence resistance and zero-sequence inductance as examples, a comparison of the parameter measurement errors of the traditional differential frequency method, incremental method, and the measurement method of this invention (different-frequency incremental method) under different interference intensities is shown below. Figure 3 and Figure 4 As shown.

[0062] From Table 1, Figure 3 and Figure 4 As can be seen, compared with existing measurement methods (traditional differential frequency method and incremental method), the measurement accuracy of the measurement method of the present invention (different frequency incremental method) is further improved. Moreover, as the interference intensity increases, the measurement error of the measurement method of the present invention remains very small and is basically unaffected by changes in interference intensity. This is because the traditional differential frequency method can only resist power frequency interference and cannot eliminate differential frequency interference caused by the differential frequency test source itself. However, the measurement method of the present invention can effectively suppress both power frequency and differential frequency interference present in the line. Usually, the incremental method generates power frequency increments under the power frequency test source. However, since both the increment and the interference are at the power frequency, the interference signal that is not completely eliminated may be mixed into the increment, thus affecting the measurement accuracy. The measurement method of the present invention generates differential frequency increments of voltage and current in the line under the differential frequency test source. At this time, the power frequency interference that has the main influence can be easily separated by filtering algorithms.

[0063] It is important to note that the constructions and arrangements of this application shown in several different exemplary embodiments are merely illustrative. Although only a few embodiments are described in detail in this disclosure, those who consult this disclosure will readily understand that many modifications are possible (e.g., changes in the size, dimensions, structure, shape, and proportions of various elements, as well as parameter values ​​(e.g., temperature, pressure, etc.), mounting arrangements, use of materials, color, orientation, etc.) without substantially departing from the novel teachings and advantages of the subject matter described in this application). For example, an element shown as integrally formed may be composed of multiple parts or elements, the position of elements may be inverted or otherwise altered, and the nature or number or position of discrete elements may be changed or altered. Therefore, all such modifications are intended to be included within the scope of the invention. The order or sequence of any process or method steps may be changed or rearranged according to alternative embodiments. In the claims, any "device plus function" clause is intended to cover the structure described herein that performs the function, and not only structurally equivalent but also equivalent in structure. Other substitutions, modifications, alterations, and omissions may be made in the design, operation, and arrangement of the exemplary embodiments without departing from the scope of the invention. Therefore, the present invention is not limited to the specific embodiments, but extends to various modifications that still fall within the scope of the appended claims.

[0064] Furthermore, in order to provide a concise description of exemplary embodiments, not all features of actual embodiments (i.e., those features that are not relevant to the currently considered best mode for carrying out the invention, or those features that are not relevant to implementing the invention) may be omitted.

[0065] It should be understood that numerous specific implementation decisions can be made during the development of any practical implementation, such as in any engineering or design project. Such development efforts may be complex and time-consuming, but for those skilled in the art who benefit from this disclosure, the development effort will be a routine work of design, manufacturing, and production without requiring much experimentation.

[0066] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for measuring impedance parameters of a three-phase unbalanced line based on differential frequency increments, characterized in that: include, Define measurement parameters; The defined measurement parameters include: A three-phase unbalanced line is defined as consisting of phases A, B, and C; the current phasors at the beginning of the three-phase lines A, B, and C are defined as follows: , , The current phasor at the end is , , Define the voltage phasors at the beginning of the three-phase lines A, B, and C as follows: , , Define the operating frequency as The amplitudes are respectively and The three-phase symmetrical frequency power supply, and Define the voltage increments of the three phases A, B, and C of line as follows: , , The current increments of phases A, B, and C are , , The length of a three-phase unbalanced line is defined as... ; The voltage and current phasors at the beginning and end of the three phases of the line are measured simultaneously using three measurement methods. The three measurement methods include: First measurement method: Apply a frequency of [frequency value] to the starting ends of phases A, B, and C of the line. Amplitude A symmetrical frequency power supply is used to ground the ends of the three phases A, B, and C of the line, and the parameters are measured. Second measurement method: Apply a frequency of [frequency value] to the starting ends of phases A, B, and C of the line. Amplitude For a symmetrical power supply with different frequencies, disconnect the power supply wiring at the beginning of phase C and measure the parameters. The third measurement method: Apply a frequency of [frequency value missing] to the starting ends of phases A, B, and C of the line. Amplitude For a symmetrical power supply with different frequencies, disconnect the power supply wiring at the beginning of phases A and C, and ground the ends of phases A, B, and C of the line, and measure the parameters. The phase voltage and phase current data measured under the three measurement methods are processed to calculate the phase voltage increment and phase current increment; Calculate the phase resistance and phase reactance matrix corresponding to the power frequency of 50Hz based on the line phase impedance measurement equation; The equation for measuring the phase impedance of the line at different frequencies is based on the lumped parameter model of a three-phase unbalanced line. It describes the phase voltage and current of each phase when the three-phase terminals A, B, and C of the line are grounded under the action of a different frequency power source. in, For different frequencies The corresponding line phase impedance matrix at different frequencies: matrix middle, , , These are phases A, B, and C of the line at different frequencies. The phase impedance below, , , They are respectively in different frequencies The mutual impedance between phases AB, phases AC, and phases BC of the lower line. Substituting the phase voltage and phase current increments under the three measurement methods into the line cross-frequency phase impedance measurement equation, we get: The different frequencies can be solved using the following formula. Corresponding line phase impedance matrix The elements in ； The phase impedance matrix is ​​divided into real and imaginary parts. Unfold to obtain different frequencies Corresponding phase resistance matrix and different frequencies Corresponding phase reactance matrix ,Right now ; According to different frequencies Phase resistance matrix and phase reactance matrix After conversion, the phase resistance and phase reactance matrices corresponding to the 50Hz power frequency are obtained. The conversion formula is as follows: (4) in, The operating frequency of the differential power supply added at the beginning of the line is between 45 and 55 Hz. and This represents the power frequency phase resistance and phase reactance matrix of the line, where each element is the phase resistance and phase reactance of the line. The phase resistance and phase reactance are converted into sequence resistance and sequence inductance according to the phase sequence transformation matrix.

2. The method for measuring the impedance parameters of a three-phase asymmetrical line based on differential frequency increments according to claim 1, characterized in that: The calculation of phase voltage increment and phase current increment includes: Define the voltage increments of the three phases A, B, and C of line as follows: , , The current increments of phases A, B, and C are , , The phase voltage and phase current data measured under the three measurement methods are processed to calculate the phase voltage increment and phase current increment.

3. The method for measuring the impedance parameters of a three-phase asymmetrical line based on differential frequency increments according to claim 2, characterized in that: The phase resistance and phase reactance are converted into sequence resistance and sequence inductance according to the phase sequence transformation matrix, including: make , This is the power frequency phase impedance matrix of a three-phase unbalanced line; Phase sequence transformation matrix of line parameters for: in, This represents a unit phasor with an argument of 120°. This represents a unit phasor with an argument of 240°.

4. The method for measuring the impedance parameters of a three-phase asymmetrical line based on differential frequency increments according to claim 3, characterized in that: The power frequency phase impedance parameters of the line can be converted into power frequency sequence resistance and power frequency sequence inductance per unit length using the following formula: in, Represents the zero-sequence, positive-sequence, and negative-sequence resistance per unit length of a three-phase unbalanced circuit; Represents the zero-sequence, positive-sequence, and negative-sequence inductance per unit length of a three-phase unbalanced circuit; This represents the mutual resistance per unit length between two different sequences in a three-phase unbalanced circuit. It represents the mutual inductance per unit length between two different sequences in a three-phase unbalanced circuit; 0 represents zero sequence, 1 represents positive sequence, and 2 represents negative sequence.

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