A non-contact voltage measurement decoupling method for three-phase line delta configuration

Abstract

The application discloses a kind of non-contact voltage measurement decoupling methods of three-phase line delta type erection working condition, belong to power system voltage measurement technical field, solve the problem that it is difficult to calibrate coefficient under the working condition that distribution network three-phase voltage is close to balance, the present application includes the following steps: step 1: design the voltage sensing mechanism suitable for three-phase line, establish three-phase operation voltage sensing mechanism measurement equivalent circuit;Step 2: according to the geometric relationship between three-phase line and voltage sensing mechanism under actual working condition, deduce the distributed capacitance analytical expression, obtain three-phase line response voltage equation after approximate equivalent capacitance;Step 3: design decoupling matrix, propose three-phase line response voltage decoupling algorithm, decouple three-phase coupling equation to three independent equations, solve the coefficient in equation by using least square method;Calculate whether the relative error is less than 2.5%.The present application realizes the measurement of three-phase line non-contact voltage, and the simulation calculation relative error is less than 2.5%.

Description

Technical Field

[0001] This invention belongs to the field of power system voltage measurement technology, specifically relating to a non-contact voltage measurement decoupling method for a three-phase line in a delta-connected configuration. Background Technology

[0002] In power systems, high-voltage metering plays a crucial role in practical electrical engineering applications. Voltage metering is widely used in current power grids, such as online overvoltage monitoring, relay protection, energy metering, and automated equipment control. The reliability and accuracy of voltage measurement are essential for the safe, reliable, and economical operation of the power grid. Compared to traditional contact-based voltage measurement, non-contact voltage measurement offers advantages such as ease of installation and maintenance, and avoidance of insulation, because there is no direct electrical connection between the device and the line, resulting in no energy exchange or loss. However, complex capacitive coupling exists between the three-phase lines and the sensors. In practical calibration, traditional calibration methods involve a large number of unknowns, leading to a complex calibration process. Furthermore, it is difficult to calibrate coefficients under conditions where the three-phase voltages in the distribution network are nearly balanced, limiting the application scenarios of non-contact three-phase voltage measurement. Summary of the Invention

[0003] The purpose of this invention is:

[0004] To address the challenges of complex calibration processes due to the large number of unknowns in traditional non-contact voltage measurement methods, and the difficulty in calibrating coefficients under conditions where the three-phase voltages in a distribution network are nearly balanced, a non-contact voltage measurement decoupling method is proposed for three-phase lines with delta-connected installations.

[0005] The technical solution adopted in this invention is as follows:

[0006] A non-contact voltage measurement decoupling method for a three-phase line in a delta-connected configuration includes the following steps:

[0007] Step 1: Design a voltage sensing mechanism suitable for three-phase lines and establish the equivalent circuit for voltage sensing mechanism measurement during three-phase operation;

[0008] Step 2: Based on the geometric relationship between the three-phase line and the voltage sensing mechanism under actual working conditions, derive the analytical expression of the distributed capacitance, and obtain the three-phase line response voltage equation after approximating the equivalent capacitance.

[0009] Step 3: Design a decoupling matrix based on the numerical characteristics of the coefficient matrix of the response equation. Based on the characteristics of the decoupling matrix, propose a three-phase line response voltage decoupling algorithm to decouple the three-phase coupled equation into three independent equations. Solve the coefficients in the equations using the least squares method. Calculate whether the relative error of this decoupling method is less than 2.5% under the delta-connected 10kV three-phase line construction condition using Matlab and Comsol simulation software, thereby verifying the effectiveness of this decoupling method.

[0010] Furthermore, step 1 specifically includes the following steps:

[0011] Step 1.1: Design the coupling mechanism installed on the three-phase line;

[0012] The coupling mechanism installed on the three-phase line consists of three independent single-phase coupling mechanisms. Each single coupling mechanism consists of two cylindrical copper poles, an inner and an outer one. The outer copper pole has a radius of 25mm and a length of 48cm, while the inner copper pole has a radius of 22.6mm and a length of 24cm. The space between the inner and outer copper poles is filled with a PVC dielectric with a thickness of 2.4mm.

[0013] The medium between the line and the inner copper electrode is air, and the PVC material is polyvinyl chloride with a relative permittivity of 3; the end cap material is epoxy resin, and a hole is punched in the middle of the end cap for the line to pass through; the coupling mechanism is installed sequentially on the 10kV three-phase line, and the coupling mechanisms are installed facing each other.

[0014] Step 1.2: Establish the equivalent circuit for measuring the coupling mechanism of each phase during three-phase operation;

[0015] Using C A0 C B0 C C0 Indicates the coupling capacitance between the circuit and the inner copper electrode; C As C Bs C Cs Indicates the coupling capacitance between the inner and outer copper layers; C Ax C Bx C Cx This represents the coupling capacitance between the outer copper electrode and ground; C AB1 C BC1 C CA1 Indicates the mutual capacitance between the external copper electrodes; C BC2 C AB2 C AC2 This indicates the mutual capacitance between the external copper electrodes of the line; the capacitances of adjacent phase coupling mechanisms are equal.

[0016] Furthermore, step 2 specifically includes the following steps:

[0017] Step 2.1: Adapt to the 10kV three-phase line and coupling mechanism erection method, derive the expressions for the self-capacitance between the current phase line and the coupling mechanism and the mutual capacitance between the adjacent phase line and the coupling mechanism, and analyze the numerical relationship of each element;

[0018] In the actual environment, the transmission lines are erected in a triangular arrangement, where r represents the radius of the outer copper electrode, h is the erection height of the A-phase and C-phase lines, L is the distance between the three phases; x is the distance by which the B-phase is higher than the A-phase and C-phase; where r<<h, x=50cm, L=57.73cm, the relational expression between the potential and charge of the three-phase line is derived according to the mirror image method and the electric axis method, and the specific expression of the equivalent model is as follows:

[0019]

[0020] where is the potential of the three-phase line, τ A , τ B , τ C are the charges of the three-phase line;

[0021] Let the coefficient matrix of Equation (1) be α, and its inverse matrix be β, that is, α -1 =β, β ij represents the value at the i-th row and j-th column in the β matrix;

[0022] The first row equation can be written as:

[0023]

[0024] Define that:

[0025]

[0026] C AB1 =C BA1 =-β 12 , C AC1 =C CA1 =-β 13 , C CB1 =C BC1 =-β 23

[0027] The expressions of the outer copper electrode-to-ground capacitance of each phase coupling mechanism and the mutual capacitance expression between the outer copper electrodes can be derived. The capacitance value difference rate is defined as |C1-C2| / C1; calculated by Matlab, when the line-to-ground height is 6m to 10m, the value difference rate of the outer copper electrode-to-ground capacitance of each phase and the value difference rate between the capacitance between adjacent phase outer copper electrodes and the capacitance between spaced phase outer copper electrodes are obtained; the smaller the value, the closer the two capacitance values are, and it can finally be obtained that: C Ax ≈C Bx ≈C Cx ≈C x , C AB1 ≈C BC1 ≈C AC1 ≈C1; after analyzing the mutual capacitance value between the adjacent phase line and the coupling mechanism, it can be obtained that: C AB2 ≈C BC2 ≈C AC2≈C2;

[0028] The formula for the self-capacitance of the circuit and coupling mechanism is as follows:

[0029]

[0030]

[0031]

[0032]

[0033] Where φ0, φ1, and φ2 are the diameters of the circuit and the inner and outer copper electrodes, respectively, and L1 and L2 are the lengths of the inner and outer copper electrodes;

[0034] Step 2.2: Based on the equivalent circuit of the line and coupling mechanism, and combined with the numerical characteristics of the coupling capacitor, the coupling model is further simplified, and the equations of the three-phase line voltage and the voltage between the inner and outer copper electrodes are derived.

[0035] Based on the nodal voltage method and the coupling capacitance relationship derived in step 2.1, the equations for the three-phase line voltage and the voltage between the inner and outer copper electrodes are as follows:

[0036]

[0037] in:

[0038]

[0039]

[0040] Let the diagonal elements of the coefficient matrix B in equation (7) be p1 and the off-diagonal elements be m1, and the diagonal elements of the coefficient matrix C be p2 and the off-diagonal elements be m2; then equation (7) can be expressed as:

[0041]

[0042] Furthermore, step 3 specifically includes the following steps:

[0043] Step 3.1: Design the decoupling matrix based on the characteristics of the coefficient matrix;

[0044] Since coefficient matrices B and C are symmetric matrices, they are diagonalized using decoupling matrices A1 and A2. Furthermore, because B and C have the same element distribution structure (i.e., identical diagonal and off-diagonal elements), they possess the same eigenvectors. That is:

[0045] A1 -1 ·B·A1=Λ1 (9)

[0046] A2 -1 ·C·A2=Λ2 (10)

[0047] in:

[0048] A1=A2=A

[0049] Let the decoupling matrix be A = (L1, L2, L3). Analysis shows that L3 = (1, 1, 1). T Let A be an eigenvector of A, and let the other two eigenvectors satisfy the following form:

[0050]

[0051] Where k1 and k2 are constants, and i = 1, 2;

[0052] Let k1 = 0, k2 = 1 to obtain vector L1; let k1 = -2, k2 = 1 to obtain vector L2, then we get:

[0053]

[0054] Therefore, matrices B and C can be diagonalized using constant decoupling matrices. The calculated similar diagonal matrices corresponding to B and C are:

[0055]

[0056]

[0057] Step 3.2: Multiply the decoupling matrix by the response equation on the left, so that the unknown capacitance values ​​of the coefficient matrix are concentrated in the diagonal matrix, and the three-phase decoupling equation is obtained.

[0058] Based on the decoupling matrix given in step 3.1, substituting equations (12), (13), and (14) into equation (7) yields:

[0059]

[0060] Because of A1 -1 A2=E and A1=A2=A,A1 -1 =A2 -1 =A -1 ,Right now:

[0061]

[0062] in:

[0063]

[0064] After analysis, the final expressions for line voltage and response voltage are:

[0065]

[0066] Step 3.3: Use the least squares method to obtain the unknown proportionality coefficients of the three independent equations, and substitute the measured internal and external copper electrode voltages into the equations to deduce the three-phase line voltages.

[0067] In a 10kV distribution network, the voltage amplitudes of the three phases are Q, ... A Q B Q C With a phase difference of 120°, the three-phase voltage equations for A, B, and C are U... A =Q A ·sin(100*π*t-120°), U B =Q B ·sin(100*π*t), U C =Q C ·sin(100*π*t+120°); According to equation (17), the phase difference of the three-phase response voltage is 120°, and the amplitude is denoted as q. A q B q C After simplifying equation (17), we get:

[0068]

[0069] U * u represents the inverse of the decoupling matrix multiplied by the line voltage. * The inverse of the decoupling matrix is ​​multiplied by the response voltage. The diagonal matrix M = diag(M1, M2, M3) is then expressed as:

[0070] U * =M·u * (19)

[0071] in:

[0072]

[0073]

[0074] The coupling devices are installed on the three-phase lines respectively, and multiple sets of line voltage and device response voltage data are recorded. Substituting these data into equation (19), the diagonal matrix elements M1, M2, and M3 are obtained using the least squares method. The method for finding the diagonal matrix M is as follows:

[0075] M = U * (u * ) T [u * (u * ) T ] -1 (20)

[0076] In actual three-phase line operation, after solving the diagonal matrix M, the voltage between the inner and outer copper electrodes of each phase coupling mechanism is measured, and the three-phase line voltage is obtained by substituting it into equation (19).

[0077] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0078] This invention establishes coupling mechanisms sequentially under three-phase delta-connected conditions in a 10kV distribution network. Based on the equivalent circuit between capacitors, it establishes the three-phase line response voltage equations and, after eigenvalue decomposition of the coefficient matrix, establishes the three-phase decoupling equations. Building upon single-phase non-contact voltage measurement, it achieves non-contact measurement of three-phase line voltage. Simulation calculations show that the relative error of this decoupling method is less than 2.5%. It also enables calibration coefficients under near-balanced three-phase voltage conditions in the distribution network, broadening the application scenarios for non-contact three-phase voltage measurement. Attached Figure Description

[0079] Figure 1 This is a flowchart of the method of the present invention;

[0080] Figure 2 This is a diagram showing the actual setup for three-phase voltage measurement.

[0081] Figure 3 This is the equivalent circuit diagram of the coupling capacitor between the three-phase line and the device.

[0082] Figure 4 Equivalent model diagram of the measurement system;

[0083] Figure 5 This is a curve showing the difference in the coupling capacitance between the outer copper layers after equivalent conversion.

[0084] Figure 6 This is a curve showing the difference in the equivalent outer copper layer's coupling capacitance to ground. Detailed Implementation

[0085] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0086] This invention provides a non-contact voltage measurement decoupling method adapted to the delta-connected installation condition of a 10kV three-phase line, comprising the following steps:

[0087] Step 1: Design a voltage sensing mechanism suitable for three-phase lines and establish the equivalent circuit for voltage sensing mechanism measurement during three-phase operation;

[0088] Step 2: Based on the geometric relationship between the three-phase line and the voltage sensing mechanism under actual working conditions, derive the analytical expression of the distributed capacitance, and obtain the three-phase line response voltage equation after approximating the equivalent capacitance.

[0089] Step 3: Design a decoupling matrix based on the numerical characteristics of the coefficient matrix of the response equation. Based on the characteristics of the decoupling matrix, propose a three-phase line response voltage decoupling algorithm to decouple the three-phase coupling equation into three independent equations. Solve the coefficients in the equations using the least squares method. The relative error of this decoupling method is less than 2.5% under the delta-connected 10kV three-phase line construction condition, as calculated by Matlab and Comsol simulation software, thus verifying the effectiveness of this decoupling method.

[0090] Step 1 specifically includes the following steps;

[0091] Step 1.1: Design the coupling mechanism installed on the three-phase line;

[0092] The coupling mechanism installed on the three-phase line consists of three independent single-phase coupling mechanisms, each with two cylindrical copper electrodes as its main components. The outer copper electrode has a radius of 25mm and a length of 48cm, while the inner copper electrode has a radius of 22.6mm and a length of 24cm. A 2.4mm thick PVC dielectric fills the space between the inner and outer copper electrodes. The dielectric between the line and the inner copper electrode is air, and the PVC material is polyvinyl chloride with a relative permittivity of 3. The end caps are made of epoxy resin with good insulation properties, and a hole is drilled in the center to facilitate the line's passage. These coupling mechanisms are sequentially installed on the 10kV three-phase line, with each coupling mechanism installed opposite each other, such as... Figure 2 As shown.

[0093] Step 1.2: Establish a model of the three-phase circuit and measuring mechanism and draw the equivalent circuit;

[0094] After considering edge effects, the coupling capacitance between adjacent phase lines and the outer copper electrode, as well as the coupling capacitance between the outer copper electrodes, are two orders of magnitude higher than other mutual capacitances. Therefore, other types of mutual capacitances are not considered for the time being. In summary, the equivalent circuit diagram of the three-phase line and sensor is as follows: Figure 3 As shown.

[0095] Among them, C A0 C B0 C C0 Indicates the coupling capacitance between the circuit and the inner copper electrode; C As C Bs C Cs Indicates the coupling capacitance between the inner and outer copper layers; C Ax C Bx C Cx This represents the coupling capacitance between the outer copper electrode and ground; C AB1 C BC1 CCA1 denotes the mutual capacitance between outer copper poles; C BC2 , C AB2 , C AC2 denotes the mutual capacitance between the line and the outer copper pole. (The capacitances of adjacent two-phase coupling mechanisms are equal, for example: C AB1 =C BA1 )

[0096] Step 2 specifically includes the following steps:

[0097] Step 2.1: Adapt to the 10kV three-phase line and sensor erection method, derive the expressions of the self-capacitance between the local phase line and the coupling mechanism and the mutual capacitance between the adjacent phase line and the coupling mechanism, and analyze the numerical relationship of each element;

[0098] In the actual environment, the transmission lines are erected in a triangular shape, r represents the radius of the outer copper pole, h is the erection height of the A and C phase lines, L is the distance between the three phases. x is the distance by which the B phase is higher than the A and C phases. Wherein, r<<h, x=50cm, L=57.73cm, the relational expression between the potential and charge of the three-phase line is derived according to the mirror image method and the electric axis method, and the equivalent model is as Figure 3 shown, and the specific expression is as follows:

[0099]

[0100] where is the potential of the three-phase line, τ A , τ B , τ C are the charges of the three-phase line.

[0101] Let the coefficient matrix of Equation (1) be α, and its inverse matrix be β, that is, α -1 =β, β ij denotes the value of the i-th row and j-th column in the β matrix. Since the first row of equations can be written as:

[0102]

[0103] Let:

[0104]

[0105] C AB1 =C BA1 =-β 12 , C AC1 =C CA1 =-β 13 , C CB1 =C BC1 =-β 23

[0106] The above capacitance derivation yields expressions for the capacitance of the outer copper electrode to ground and the mutual capacitance between the outer copper electrodes of each phase. The capacitance difference rate is defined as |C1-C2| / C1. MATLAB calculations show that, at a line height of 6m to 10m above ground, the capacitance difference rate between the outer copper electrodes of each phase to ground is as follows: Figure 4 As shown, the difference rate between the capacitance between adjacent phase external copper electrodes and the capacitance between interphase external copper electrodes is as follows: Figure 5 As shown. The smaller the value, the closer the two capacitance values ​​are. Ultimately, we can obtain: C Ax ≈C Bx ≈C Cx ≈C x C AB1 ≈C BC1 ≈C AC1 ≈C1. Similarly, after numerical analysis of the mutual capacitance between adjacent phase lines and coupling mechanisms, we can obtain: C AB2 ≈C BC2 ≈C AC2 ≈C2.

[0107] For the self-capacitance of the circuit and coupling mechanism, the formula is as follows:

[0108]

[0109]

[0110]

[0111]

[0112] Where φ0, φ1, and φ2 are the diameters of the circuit and the inner and outer copper electrodes, respectively, and L1 and L2 are the lengths of the inner and outer copper electrodes.

[0113] Step 2.2: Based on the equivalent circuit diagram of the capacitor and combined with the numerical characteristics of the coupling capacitor, the coupling model is further simplified, and the equations of the three-phase line voltage and the voltage between the inner and outer copper electrodes are derived.

[0114] Based on the nodal voltage method and the coupling capacitance relationship derived in step 2.1, the equations for the three-phase line voltage and the voltage between the inner and outer copper electrodes are as follows:

[0115]

[0116] in:

[0117]

[0118]

[0119] Let the diagonal elements of coefficient matrix B in equation (7) be p1 and the off-diagonal elements be m1, and the diagonal elements of coefficient matrix C be p2 and the off-diagonal elements be m2. Then equation (7) can be expressed as:

[0120]

[0121] Step 3 specifically includes the following steps:

[0122] Step 3.1: Design the decoupling matrix based on the characteristics of the coefficient matrix;

[0123] Since coefficient matrices B and C are symmetric matrices, they can be diagonalized using decoupling matrices A1 and A2. Furthermore, because B and C have the same element distribution structure (i.e., identical diagonal and off-diagonal elements), they possess the same eigenvectors. That is:

[0124] A1 -1 ·B·A1=Λ1 (9)

[0125] A2 -1 ·C·A2=Λ2 (10)

[0126] in:

[0127] A1=A2=A

[0128] Let the decoupling matrix be A = (L1, L2, L3). Analysis shows that L3 = (1, 1, 1). T Let A be an eigenvector, and let the other two eigenvectors satisfy the following form (k1 and k2 are constants, i = 1, 2), that is:

[0129]

[0130] Let k1 = 0, k2 = 1 to obtain vector L1; let k1 = -2, k2 = 1 to obtain vector L2, then we can obtain:

[0131]

[0132] Therefore, matrices B and C can be diagonalized using constant decoupling matrices. The calculated similar diagonal matrices corresponding to B and C are:

[0133]

[0134]

[0135] Step 3.2: Multiply the decoupling matrix by the response equation on the left, so that the unknown capacitance values ​​of the coefficient matrix are concentrated in the diagonal matrix, and the three-phase decoupling equation is obtained.

[0136] Based on the decoupling matrix given in step 3.1, substituting equations (12), (13), and (14) into equation (7) yields:

[0137]

[0138] Because of A1 -1 A2=E and A1=A2=A,A1 -1 =A2 -1 =A -1 ,Right now:

[0139]

[0140] in:

[0141]

[0142] Analysis reveals that the final expression for the relationship between line voltage and response voltage is:

[0143]

[0144] Step 3.3: Using the least squares method, obtain the unknown proportionality coefficients of the three independent equations. Substitute the measured internal and external copper electrode voltages into the equations to deduce the three-phase line voltage.

[0145] Assuming that in a 10kV distribution network, the three-phase line voltage amplitudes are Q A Q B Q C With a phase difference of 120°, the three-phase voltage equations for A, B, and C are U... A =Q A ·sin(100*π*t-120°), U B =Q B ·sin(100*π*t), U C =Q C ·sin(100*π*t+120°). According to equation (17), the phase difference of the three-phase response voltage is 120°, and the amplitude is denoted as q. A q B q C After simplifying equation (17), we get:

[0146]

[0147] U * This represents the decoupling matrix multiplied by the line voltage, u * Let M = diag(M1, M2, M3) represent the decoupling matrix multiplied by the response voltage, where M1 = M2. Then equation (18) can be expressed as:

[0148] U* =M·u * (19)

[0149] in:

[0150]

[0151]

[0152] First, the coupling devices are installed on the three-phase lines respectively, and multiple sets of line voltage and device response voltage data are recorded. Substituting these data into equation (19), the diagonal matrix elements M1, M2, and M3 can be obtained using the least squares method. The method for finding the diagonal matrix M is as follows:

[0153] M = U * (u * ) T [u * (u * ) T ] -1 (20)

[0154] In actual three-phase line operation, after solving the diagonal matrix M, the voltage between the inner and outer copper electrodes of each phase coupling mechanism is measured, and the three-phase line voltage is obtained by substituting it into equation (19).

[0155] Step 3.4: In COMSOL and MATLAB simulation software, build a three-phase line and coupling mechanism model, write the corresponding algorithm to solve the three-phase line voltage, and calculate the relative error of this method.

[0156] Based on the simulation model of the three-phase line and coupling mechanism built in step 1.2, a boundary probe with a period of 4*pi is added to the component to measure the voltage between the inner and outer copper electrodes in the three-phase lines A, B, and C in sequence. The difference between the inner and outer copper electrodes is then used to obtain the voltage value between them. By changing the voltage amplitude in the three-phase line, the voltage amplitude fluctuation of the three-phase line in the actual 10kV distribution network is simulated (amplitude less than 7%), and the response voltage values ​​of the three-phase line under different voltage amplitudes are recorded.

[0157] Import the data from the COMSOL simulation software into MATLAB and write the relevant algorithm. First, select six sets of line voltage and response voltage values ​​to determine the values ​​in the diagonal matrix M, as shown in Table 2. After calculation, M1 = M2 = 198.64 and M3 = 395.72.

[0158] Secondly, by substituting the measured response voltage value after the three-phase line voltage amplitude fluctuations into the algorithm, the line voltage can be solved in reverse. The actual three-phase voltage value is Q. A Q B Q C The three-phase response voltage value is q A q Bq C The three-phase voltage value derived using this decoupling algorithm is... Specific values ​​are shown in Table 3. The calculated relative error of this decoupling method is less than 2.5%.

[0159] Table 1 shows the relative errors considering different mutual capacitance types.

[0160]

[0161] Table 2 Solving for the diagonal matrix M

[0162]

[0163] Table 3 Accuracy Test

[0164]

[0165] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A non-contact voltage measurement decoupling method for a three-phase line in a delta-connected configuration, characterized in that, Includes the following steps: Step 1: Design a voltage sensing mechanism suitable for three-phase lines and establish the equivalent circuit for voltage sensing mechanism measurement during three-phase operation; Step 2: Based on the geometric relationship between the three-phase line and the voltage sensing mechanism under actual working conditions, derive the analytical expression of the distributed capacitance, and obtain the three-phase line response voltage equation after approximating the equivalent capacitance. Step 3: Design a decoupling matrix based on the numerical characteristics of the coefficient matrix of the response equation. Based on the characteristics of the decoupling matrix, propose a three-phase line response voltage decoupling algorithm to decouple the three-phase coupled equations into three independent equations. Solve the coefficients in the equations using the least squares method. Calculate the relative error of this decoupling method under the delta-connected 10kV three-phase line construction condition using Matlab and Comsol simulation software to verify the effectiveness of this decoupling method. Step 1 specifically includes the following steps: Step 1.1: Design the coupling mechanism installed on the three-phase line; The coupling mechanism installed on the three-phase line consists of three independent single-phase coupling mechanisms. Each single coupling mechanism consists of two cylindrical copper poles, an inner and an outer one. The outer copper pole has a radius of 25mm and a length of 48cm, while the inner copper pole has a radius of 22.6mm and a length of 24cm. The space between the inner and outer copper poles is filled with a PVC dielectric with a thickness of 2.4mm. The medium between the line and the inner copper electrode is air, and the PVC material is polyvinyl chloride with a relative permittivity of 3; the end cap material is epoxy resin, and a hole is punched in the middle of the end cap for the line to pass through; the coupling mechanism is installed sequentially on the 10kV three-phase line, and the coupling mechanisms are installed facing each other. Step 1.2: Establish the equivalent circuit for measuring the coupling mechanism of each phase during three-phase operation; use This indicates the coupling capacitance between the circuit and the inner copper electrode; This indicates the coupling capacitance between the inner and outer copper electrodes; This indicates the coupling capacitance between the outer copper electrode and ground. Indicates the mutual capacitance between the external copper electrodes; This indicates the mutual capacitance between the external copper electrodes of the line; the capacitances of adjacent phase coupling mechanisms are equal; Step 2 specifically includes the following steps: Step 2.1: Adapt to the 10kV three-phase line and coupling mechanism erection method, derive the expressions for the self-capacitance between the current phase line and the coupling mechanism and the mutual capacitance between the adjacent phase line and the coupling mechanism, and analyze the numerical relationship of each element; In real-world environments, power transmission lines are typically installed in a triangular configuration. r This indicates the radius of the outer copper electrode. h The installation height of phases A and C is specified. L The distance between the three phases; x Phase B is higher than A, C The distance between phases; where, r<<h , x =50cm, L =57.73cm. Based on the image method and the electric axis method, the relationship between the potential and charge of the three-phase line is derived. The specific expression of the equivalent model is as follows: （2）； in This is the three-phase line potential. For three-phase line charge; Let the coefficient matrix of equation (1) be... Its reverse formation is ,Right now , express The value in the i-th row and j-th column of the matrix; The first line of equations can be written as: （3）； make: ； ； The expressions for the capacitance to ground of the outer copper electrode and the mutual capacitance between the outer copper electrodes of each phase coupling mechanism can be derived, and the capacitance difference rate is defined as follows: ; Calculations using MATLAB were performed to obtain the numerical difference rate of the capacitance to ground of each phase's external copper electrode and the numerical difference rate of the capacitance between adjacent phase external copper electrodes and between the external copper electrodes of the separated phases when the line height to ground is 6m~10m. The smaller the value, the closer the two capacitance values ​​are. Finally, the following can be obtained: , Numerical analysis of the mutual capacitance between adjacent phase lines and coupling mechanisms yields the following results: ; The formula for the self-capacitance of the circuit and coupling mechanism is as follows: （4）； （5）； （6）； （7）； in, These are the diameters of the circuit and the inner and outer copper electrodes, respectively. The length of the inner and outer copper electrodes; Step 2.2: Based on the equivalent circuit of the line and coupling mechanism, and combined with the numerical characteristics of the coupling capacitor, the coupling model is further simplified, and the equations of the three-phase line voltage and the voltage between the inner and outer copper electrodes are derived. Based on the nodal voltage method and the coupling capacitance relationship derived in step 2.1, the equations for the three-phase line voltage and the voltage between the inner and outer copper electrodes are as follows: （8）； in: ； ； Let the coefficient matrix of equation (7) B The diagonal elements are Off-diagonal elements are coefficient matrix C The diagonal elements are Off-diagonal elements are Then equation (7) can be expressed as: （9）； Step 3 specifically includes the following steps: Step 3.1: Design the decoupling matrix based on the characteristics of the coefficient matrix; Since coefficient matrices B and C are symmetric matrices, they are diagonalized using decoupling matrices A1 and A2. Furthermore, because B and C have the same element distribution structure (i.e., identical diagonal and off-diagonal elements), they possess the same eigenvectors. That is: （10）； （11）； in: ； Let the decoupling matrix be... After analysis for A One eigenvector of , the other two eigenvectors satisfy the following form, i.e.: （12）； in, All are constants. i =1,2; make Obtain vector ;make Obtain vector Then we get: （13）； thus B, C The matrix can be diagonalized by a constant decoupling matrix, as calculated. B, C The corresponding similar diagonal matrix is: （14）； （15）； Step 3.2: Multiply the decoupling matrix by the response equation on the left, so that the unknown capacitance values ​​of the coefficient matrix are concentrated in the diagonal matrix, and the three-phase decoupling equation is obtained. Based on the decoupling matrix given in step 3.1, substituting equations (12), (13), and (14) into equation (7) yields: （16）； because and , ,Right now: （17）； in: ； After analysis, the final expressions for line voltage and response voltage are: （18）； Step 3.3: Use the least squares method to obtain the unknown proportionality coefficients of the three independent equations, and substitute the measured internal and external copper electrode voltages into the equations to deduce the three-phase line voltages. Assume that in a 10kV distribution network, the voltage amplitudes of the three phases are respectively Phase difference The three-phase voltage equations for A, B, and C are as follows: , , According to equation (17), the phase difference of the three-phase response voltage is: The amplitude is denoted as After simplifying equation (17), we get: （19）； This represents the inverse of the decoupling matrix multiplied by the line voltage. The inverse of the decoupling matrix is ​​multiplied by the response voltage, a diagonal matrix. Then equation (18) can be expressed as: （20）； in: ； ； The coupling devices were installed on the three-phase lines respectively, and multiple sets of line voltage and device response voltage data were recorded. Substituting these data into equation (19), the diagonal matrix elements were obtained using the least squares method. The method for finding the diagonal matrix M is as follows: （20）； In actual three-phase line operation, after solving the diagonal matrix M, the voltage between the inner and outer copper electrodes of each phase coupling mechanism is measured, and the three-phase line voltage is obtained by substituting it into equation (19).

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