A method for arranging ultra-high frequency sensors in an oil-immersed distribution transformer

Abstract

This invention discloses a method for arranging ultra-high frequency (UHF) sensors in an oil-immersed distribution transformer. The method includes the following steps: constructing a simulation model of the oil-immersed distribution transformer based on the finite-time integral method; setting the location of partial discharge sources; performing UHF electromagnetic wave analysis within the oil-immersed distribution transformer; calculating the coordinates of candidate sensor placement locations using boundary conditions, amplitude superposition effect parameters, and geometric diffraction conditions as constraints; normalizing the peak-to-peak values ​​of all output voltages, using the ratio of the number of normalized amplitudes within a preset range to the total number as the coverage rate, and using the average signal amplitude as the detection mean; using the coverage rate and detection mean as optimization objectives, optimizing the UHF sensor placement location based on the Grey Wolf optimization algorithm to obtain the acquisition point with the largest coverage rate and detection mean, thus obtaining the optimal UHF sensor placement location. This invention improves detection efficiency and accuracy, and enhances the safety and stability of partial discharge detection.

Description

Technical Field

[0001] This invention relates to the field of ultra-high frequency partial discharge detection technology, specifically to a method for arranging ultra-high frequency sensors in an oil-immersed distribution transformer. Background Technology

[0002] Distribution transformers are a crucial component essential for the normal operation of power distribution systems. Their operational status and equipment quality directly affect the safety and stability of the entire power distribution system. Simultaneously, the insulation condition of distribution transformers directly impacts their overall operation, determining their lifespan. Partial discharge generates numerous physical and chemical effects, including electrical, optical, acoustic, and thermal properties, which are the primary cause of transformer insulation aging and deformation. This can potentially lead to varying degrees of power accidents. Identifying partial discharge phenomena in transformers and providing accurate early warnings of insulation faults can effectively improve the safety and stability of transformer operation.

[0003] Because the sensitivity of UHF partial discharge detection is closely related not only to sensor performance but also to its proper installation and arrangement on the transformer, current installation schemes for UHF sensors on oil-immersed transformers mostly employ drain valve-type sensors, installed on the transformer's drain valve. This placement is limited, and most transformers equipped with drain valves are large power transformers, while distribution transformers rarely have drain valves. Furthermore, distribution transformers are smaller than large power transformers, resulting in differences in the propagation characteristics of UHF electromagnetic waves within them. Therefore, the installation location of built-in disc-type UHF sensors with dielectric windows requires further analysis based on practical considerations. Moreover, currently used built-in disc sensors suffer from low sensitivity due to poor matching with metal flange holes, unoptimized performance, and unreasonable placement, severely hindering the development and application of UHF (Ultra High Frequency) detection technology.

[0004] Because the UHF electromagnetic waves generated by partial discharge are shielded by the oil tank due to the skin effect, they mainly propagate within the oil tank. The internal core of the transformer causes the UHF electromagnetic waves to undergo diffusion, diffraction, and reflection when propagating inside the transformer. This makes the propagation process of UHF electromagnetic waves very complex, and the attenuation of the UHF signal is difficult to estimate. Under these circumstances, blindly assembling UHF sensors often results in low detection sensitivity, small coverage area, or redundant installation, which increases the detection cost.

[0005] Therefore, the propagation patterns, paths, and losses of ultra-high frequency electromagnetic waves generated at different locations in oil-immersed distribution transformers by different types of partial discharge are complex, variable, and difficult to estimate. How to obtain the optimal arrangement of ultra-high frequency sensors is a key issue in realizing online monitoring of oil-immersed distribution transformers. Summary of the Invention

[0006] To overcome the defects and shortcomings of existing technologies, this invention provides a method for arranging ultra-high frequency (UHF) sensors in oil-immersed distribution transformers. Based on the propagation characteristics of UHF electromagnetic waves, this invention determines the location of local sources and the basic arrangement direction of the sensors. Peak values ​​and average detection values ​​are obtained through simulation modeling using the finite-time integral method. The coverage rate and average detection value of sensors installed at different locations on the transformer are calculated. Finally, the peak normalization calculation model and the average value calculation model are imported into the multi-objective optimization gray wolf algorithm for comparison to obtain the coordinate points with the highest coverage and detection sensitivity. Combined with the inherent structural design of the transformer, a UHF sensor arrangement scheme with the highest acquisition sensitivity is obtained. This method detects partial discharge within the entire oil-immersed distribution transformer, improving detection efficiency and accuracy, and enhancing the safety and stability of the overall detection process.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] This invention provides a method for arranging ultra-high frequency sensors in an oil-immersed distribution transformer, comprising the following steps:

[0009] A simulation model of an oil-immersed distribution transformer is constructed based on the finite-integral time-domain method. The integral form of Maxwell's equations is discretized into a grid equation system. Under the truncation boundary condition of the response, the spatial electromagnetic field of the grid equation system is solved sequentially on the spatial grid in time order. The time-domain and frequency-domain results are obtained by fast Fourier transform.

[0010] Set the location for the local power supply;

[0011] UHF electromagnetic wave analysis was performed inside an oil-immersed distribution transformer to obtain boundary conditions, amplitude superposition effect parameters, and geometric diffraction conditions. The UHF electromagnetic wave analysis included skin effect analysis, boundary electromagnetic wave reflection and refraction analysis, and UHF electromagnetic wave geometric diffraction and attenuation analysis.

[0012] Using boundary conditions, amplitude superposition effect parameters, and geometric diffraction conditions as constraints, the coordinates of the candidate sensor placement positions are calculated.

[0013] The peak-to-peak values ​​of all output voltages are normalized, and the ratio of the number of normalized amplitudes within the preset range to the total number is used as the coverage rate, and the average value of the signal amplitude is used as the detection mean.

[0014] Using coverage and average detection value as optimization objectives, the optimal placement of UHF sensors is determined based on the Grey Wolf optimization algorithm. The collection point with the highest coverage and average detection value is obtained, and its corresponding coordinate position is acquired, which is the optimal placement of the UHF sensors.

[0015] As a preferred technical solution, the specific steps of discretizing the integral form of Maxwell's equations into a grid system of equations include:

[0016] Solving Maxwell's equations in integral form in the time domain:

[0017]

[0018]

[0019] Where H is the magnetic field; E is the electric field; D is the electric displacement; B is the magnetic induction intensity; J ei J mi J represents the injection terms of the electric and magnetic fields at this node; eL J mL This represents the loss terms for the electric and magnetic fields at this node; A and r are represented by the surface integral and line integral of the magnetic field and electric field, respectively.

[0020] After converting to matrix form, the parameters D = εE, B = μH, and J, which characterize the effect of the medium on the electromagnetic field, are used. e,l =σE,J m,l Substituting the four constitutive relations of κH into the system of equations, we discretize it into a grid system of equations;

[0021] Where ε is the relative permittivity, μ is the permeability, σ is the conductivity, and κ is the magnetic loss.

[0022] As a preferred technical solution, the truncation boundary condition of the response is expressed as follows:

[0023]

[0024] Where c represents the ultra-high frequency electromagnetic wave velocity, Δt represents the time step, and δ b Indicates the spatial step size.

[0025] As a preferred technical solution, the partial discharge power supply uses a dipole antenna as an electromagnetic wave source, and a discharge power supply is added to the gap between the top surfaces of the two cylinders, with the gap size satisfying 1 / 4 of the electromagnetic wave wavelength.

[0026] As a preferred technical solution, skin effect analysis yields the following:

[0027]

[0028] Where δ is the skin penetration depth, α is the transmission attenuation coefficient, ω is the electromagnetic wave angular frequency, μ is the magnetic permeability, and γ is the electrical conductivity.

[0029] As a preferred technical solution, the boundary conditions are expressed as follows:

[0030]

[0031] Where c represents the ultra-high frequency electromagnetic wave velocity, Δt represents the time step, and δ represents the skin penetration depth.

[0032] As a preferred technical solution, the amplitude superposition effect parameter is expressed as follows:

[0033] Ge=be∑ / be=p(α s ) / p(α n )

[0034] Where Ge represents the amplitude effect, be∑ represents the signal-to-noise ratio after superposition, be represents the signal-to-noise ratio before superposition, and p(α) represents the signal-to-noise ratio before superposition. s p(α) represents the intensity of the electromagnetic diffraction peak. n The intensity of the background is ).

[0035] As a preferred technical solution, the geometric diffraction condition is expressed as follows:

[0036] kφ>1

[0037] Where k represents the phase constant of the UHF signal and φ represents the winding radius. The geometric diffraction condition is used to determine whether geometric diffraction exists in the propagation of UHF electromagnetic waves in oil-immersed distribution transformers.

[0038] As a preferred technical solution, the peak-to-peak value of all output voltages is normalized to U. S0 As a baseline value, it is specifically expressed as:

[0039] U S0 =max(U Si ), i = 1, 2, 3, 4... U

[0040] The number N of normalized magnitudes falling within the interval [a, 1] a The ratio of the coverage percentage to the total number of data points N is used as the coverage ratio, specifically expressed as:

[0041] Cover = N a / N

[0042] Where Cover represents coverage, U represents the number of collection points set, and a represents the preset interval boundary constant;

[0043] The average value of the signal amplitude is used as the detection mean, specifically expressed as follows:

[0044]

[0045] Where S represents the detection mean, A Pn Indicates local release source P n The normalized amplitude.

[0046] As a preferred technical solution, the optimal placement of UHF sensors is achieved based on the Grey Wolf optimization algorithm, and the specific steps include:

[0047] Set the gray wolf population size and iteration number thresholds, store the size of the non-dominated solution unit, the wavelength of the ultra-high frequency electromagnetic wave, the superposition effect parameters of the constraint variables, as well as the geometric diffraction conditions, the coverage of decision variables, and the detection mean;

[0048] Parameters are randomly initialized, including the initial coefficient factor and convergence factor. An initial gray wolf population is randomly generated within the search space.

[0049] Calculate the values ​​of individuals in the initial gray wolf population according to the corresponding objective function and constraint function, find the non-dominant solution, initialize the storage unit, and select dominant individuals and record their positions;

[0050] The convergence factor and coefficient factor are updated iteratively, the fitness of individuals in the population is calculated and sorted, the storage unit is updated, dominant individuals are selected and their positions are updated, until the iteration number threshold is reached and the non-dominated solution is output. The collection point with the largest coverage and detection mean is obtained and the corresponding coordinate position is obtained, that is, the optimized UHF sensor layout position is output.

[0051] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0052] This invention, based on the propagation characteristics of ultra-high frequency electromagnetic waves, determines the location of local sources and the basic arrangement direction of sensors. Peak values ​​and average detection values ​​are obtained through simulation modeling using the finite-time integral method. The coverage rate and average detection value of sensors installed at different locations on the transformer are calculated. Finally, the peak value normalization calculation model and the average value calculation model are imported into the multi-objective optimization grey wolf algorithm for comparison, yielding the coordinate points with the highest coverage and detection sensitivity. Combined with the inherent structural design of the transformer, a UHF sensor arrangement scheme with the highest acquisition sensitivity is obtained, enabling the detection of partial discharge within the entire oil-immersed distribution transformer, thus improving safety and reliability. Attached Figure Description

[0053] Figure 1 This is a flowchart illustrating the method for arranging ultra-high frequency sensors in an oil-immersed distribution transformer according to the present invention.

[0054] Figure 2 This is a schematic diagram of the simulation model of the oil-immersed distribution transformer of the present invention;

[0055] Figure 3 This is a schematic diagram of the simulation model of the partial discharge source of the present invention;

[0056] Figure 4 This is a schematic diagram of the Gaussian pulse waveform of the present invention;

[0057] Figure 5(a) is a schematic diagram of the position arrangement of the partial discharge power source under the XY observation view of the present invention;

[0058] Figure 5(b) is a schematic diagram of the position arrangement of the partial discharge power source under the XZ observation view of the present invention;

[0059] Figure 6 (a) is a schematic diagram of the propagation path of the electromagnetic wave of the present invention after being reflected by the tank wall;

[0060] Figure 6 (b) is a schematic diagram of the propagation path of the electromagnetic wave of the present invention after diffraction by the winding;

[0061] Figure 6 (c) is a schematic diagram of the propagation path of the electromagnetic wave of the present invention after refraction and reflection through the oil paper layer;

[0062] Figure 6 (d) is a schematic diagram of the propagation path of the electromagnetic wave of the present invention after refraction and reflection through multiple dielectric layers;

[0063] Figure 7 A schematic diagram of reflections at the corners of the transformer housing of this invention;

[0064] Figure 8 This is a schematic diagram of the diffraction process of the electromagnetic wave through the transformer windings of the present invention;

[0065] Figure 9(a) is a schematic diagram of the probe arrangement position under the XYZ observation view of the present invention;

[0066] Figure 9(b) is a schematic diagram of the probe arrangement position under the XY observation view of the present invention;

[0067] Figure 9(c) is a schematic diagram of the probe arrangement position under the XZ observation view of the present invention;

[0068] Figure 10(a) is a schematic diagram of the time-frequency domain waveform of the ultra-high frequency electromagnetic wave collected by the sensor acquisition point of the present invention;

[0069] Figure 10(b) is a schematic diagram of the frequency domain waveform of ultra-high frequency electromagnetic waves collected by the sensor acquisition points of the present invention;

[0070] Figure 11 This is a schematic diagram showing the optimal arrangement position of the ultra-high frequency sensor of the present invention. Detailed Implementation

[0071] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0072] Example

[0073] like Figure 1 As shown, this embodiment provides a method for arranging ultra-high frequency sensors in an oil-immersed distribution transformer, including the following steps:

[0074] S1: A simulation model of an oil-immersed distribution transformer is constructed based on the Finite-in-Time (FITD) method. The integral form of Maxwell's equations with time variables is discretized into a grid equation system. Under the truncation boundary conditions of the response, the spatial electromagnetic field of the grid equation system is solved sequentially on the spatial grid in time order. Various effective frequency responses contained in the pulse can be obtained by Fast Fourier Transform (FFT), thus obtaining the time-domain and frequency-domain results of the system. The specific steps include:

[0075] (1) Solving Maxwell's equations in integral form in the time domain:

[0076]

[0077]

[0078] Where H is the magnetic field; E is the electric field; D is the electric displacement; B is the magnetic flux density, J ei J mi J represents the injection terms of the electric and magnetic fields at this node; eL J mL This represents the loss terms for the electric and magnetic fields at that node. A and r are represented by the surface integral and line integral of the magnetic field and electric field, respectively.

[0079] (2) After converting to matrix form, the parameters D = εE, B = μH, and J, which characterize the effect of the medium on the electromagnetic field, are transformed into matrix form. e,l =σE,J m,l Substituting the four constitutive relations =κH into the equation, we discretize it into a system of grid equations:

[0080] The constitutive relation is introduced into the integral:

[0081]

[0082]

[0083]

[0084]

[0085] Where ε is the relative permittivity, μ is the permeability, σ is the conductivity, and κ is the magnetic loss. i The expression for the constitutive relation of electric displacement D under finite-time integration; M κ This is an expression for the constitutive relation of magnetic induction intensity B under finite-time integrals; M σ J is the electric field loss term under finite-time integration.eL Expression of constitutive relations; M μ J is the loss term of the magnetic field under finite-time integral. mL Expression of constitutive relations.

[0086] The discretized grid equations, i.e., the iterative formulas for electromagnetic quantities in the finite-domain integral algorithm:

[0087]

[0088]

[0089] in, The electric field quantity in the target space; Let C be the magnetic field quantity in the target space; and C be the matrix. The curl operator is defined on the primary and dual meshes; For the surface integral of the electric field plane under the spatial grid; This is the surface integral of the magnetic field plane under the spatial grid.

[0090] (3) Truncation boundary conditions of the response:

[0091] In FITD, the spatial grid is mostly composed of cubic cells, and the spatial step size in the discrete grid is Δx = Δy = Δz = δ. b Given that the velocity is the electromagnetic wave speed c, and based on the Courant-Friedrichs-Levy stability condition that should be satisfied between the spatial and temporal discrete intervals, the truncation boundary condition of the response is as follows:

[0092]

[0093] Where, δ b Δt represents the spatial step size in the discrete grid, c represents the electromagnetic wave speed, and Δt represents the time step.

[0094] (4) Solve the spatial electromagnetic field sequentially on the spatial grid in chronological order:

[0095] (5) Obtain the various effective frequency responses contained in the pulse through FFT transformation, and obtain the time domain and frequency domain results;

[0096] In this embodiment, a simulation model is established based on a 630kVA oil-immersed distribution transformer as an example. Its external dimensions are 1418×780.202×1634mm, and the tank dimensions are 1058×488×1215mm. The main structure consists of high and low voltage windings, the core and its support, high and low voltage bushings, and a base. Because UHF signals mainly propagate within the tank, such as... Figure 2As shown in the figure, this embodiment establishes a simulation model covering the oil tank, iron core and windings. The parameter settings are shown in Table 1 below. The transformer oil has a very small loss on the propagation of UHF electromagnetic waves in the transformer, so its parameter settings are not considered.

[0097] Table 1 Material parameters of 630kVA transformer

[0098]

[0099] S2: Set the location of the local power supply;

[0100] The discharge channel formed by the PD discharge path caused by insulation defects in the oil-immersed distribution transformer is extremely thin, and the current passing through it is uniformly distributed. Its discharge current can be equivalent to the element current. A dipole antenna is used as the electromagnetic wave source. The discharge power supply is added to the gap between the top surfaces of the double cylinders, and the gap size meets 1 / 4 of the electromagnetic wave wavelength.

[0101] Because dipole antennas can generate more stable electromagnetic waves compared to discharge sources, and are easier to model and verify results in simulations. Furthermore, according to antenna theory, antenna radiation is strongest when the antenna size is comparable to one-quarter of the electromagnetic wave wavelength. Figure 3 As shown, the simulated structure of the dipole antenna is obtained. In the simulation, a Gaussian pulse can be used as the excitation source, which can radiate relatively stable electromagnetic waves at the dipole antenna, such as... Figure 4 As shown, the Gaussian pulse waveform is obtained.

[0102] In this embodiment, considering that the parts of the oil-immersed distribution transformer most prone to insulation faults are the coil winding insulation and parts with inherent defects such as air bubbles and suspended particles, they can be summarized into the following categories of parts and structures: ① coil winding ② suspended impurities in oil ③ internal steel frame structure (yoke), etc. Based on the above summary, as shown in Figures 5(a) and 5(b), the specific location arrangement of the partial discharge source is obtained. The specific location arrangement information of the partial discharge source is shown in Table 2 below:

[0103] Table 2 PD Source Location Layout

[0104]

[0105] S3: Perform ultra-high frequency (UHF) electromagnetic wave analysis inside an oil-immersed distribution transformer;

[0106] In this embodiment, the propagation modes of UHF electromagnetic waves can be mainly divided into three types: transverse electromagnetic mode (TEM), transverse electric mode (TE), and transverse magnetic mode (TM). In transformer oil, the main propagation mode of electromagnetic waves is TEM, such as... Figure 6 (a)- Figure 6As shown in (d), the propagation path can also be altered by composite insulating media and air gaps. The ultra-high frequency electromagnetic waves generated by partial discharge propagate almost without attenuation in transformer oil or cardboard; the main factors to consider are the effects of reflection and refraction by metallic conductors and diffraction by curved windings on the electromagnetic wave propagation characteristics.

[0107] The steps for analyzing ultra-high frequency (UHF) electromagnetic waves include:

[0108] (1) Skin effect analysis

[0109]

[0110] Based on the above calculation, if the frequency of UHF electromagnetic waves is 1GHz, then the skin depth of the enclosure is approximately 0.119μm. Therefore, most electromagnetic waves will not be able to pass through the tank. To detect UHF signals with greater sensitivity, an internal sensor should be used.

[0111] (2) Boundary electromagnetic refraction and reflection analysis

[0112] A point source signal at any location in space can be regarded as an integral superposition of two plane spectra (TE type and TM type).

[0113] According to the reflection coefficient R of electromagnetic waves TE R TM With refractive index T TE T TM The formula, and considering that all metal conductors in an oil-immersed distribution transformer can be regarded as ideal conductor boundaries, yields:

[0114] R TE =-1

[0115] R M =1

[0116] T TE =T TM =0

[0117] Simultaneously, electromagnetic waves satisfying the coherence condition exhibit interference, forming a superposition phenomenon of stable distributions of vibration intensity. For ultra-high frequency electromagnetic waves moving to the corner of the fuel tank, total internal reflection occurs upon impact with the tank wall. The confined boundary environment at the corner increases the number of reflections, resulting in a superposition of numerous reflections and thus an enhanced radiation intensity of the ultra-high frequency electromagnetic waves. Figure 7 As shown, the electromagnetic field intensity reflection and superposition are strongest at the corners.

[0118] According to the formula for calculating the superposition amplitude effect:

[0119] Ge=be∑ / be=p(α s ) / p(α n )

[0120] Where Ge represents the amplitude effect; be∑ represents the signal-to-noise ratio after superposition; be represents the signal-to-noise ratio before superposition; p(α) s p(α) represents the intensity of the electromagnetic diffraction peak; n The intensity of the background is ).

[0121] By analyzing the reflection and refraction of electromagnetic waves at the boundary, we can determine the general direction of the electromagnetic waves that are more concentrated and have a higher electromagnetic field intensity in the closed oil tank.

[0122] (3) Geometric diffraction and attenuation analysis of ultra-high frequency electromagnetic waves

[0123] The propagation speed of ultra-high frequency electromagnetic waves in oil is v = 203.1 mm / ns, and the wavelength is λ = 67.7–677 mm. The phase constant of the ultra-high frequency signal can be calculated as k ≈ 0.928–9.28. For the winding radius φ, based on the condition kφ > 1, it can be determined that geometric diffraction exists in the propagation of ultra-high frequency electromagnetic waves in oil-immersed distribution transformers. For example... Figure 8 As shown, the diffracted surface rays continuously emit diffracted rays tangentially as they propagate along the curved surface, thus their energy decays rapidly. Theoretically, UHF diffracted through the winding attenuates by 6 dB; in reality, when part of the electromagnetic wave comes into contact with the winding, the UHF attenuation is only 3 dB.

[0124] Geometric diffraction analysis of ultra-high frequency electromagnetic waves can reveal the influence of the winding surface on the electromagnetic field strength generated by the diffraction of ultra-high frequency electromagnetic waves.

[0125] Among them, the parameters obtained from the two types of analysis, refraction and diffraction, can be used as constraints for determining the arrangement position.

[0126] S5: Calculate the ultra-high frequency electromagnetic wave velocity c according to the formula... Establish boundary conditions, using the amplitude superposition effect parameter Ge and the geometric diffraction condition kφ>1 as constraints, and determine the coordinates of the candidate sensor placement positions.

[0127] In this embodiment, the location of the UHF sensor acquisition point is set, and each acquisition point acquires the ultra-high frequency electromagnetic wave data emitted by the partial discharge source propagating in the oil tank, that is, the signal strength in V / m.

[0128] Based on the conclusions drawn from the propagation analysis of UHF electromagnetic waves, such as the fact that electromagnetic waves cannot pass through the corners of oil tanks and transformer enclosures where reflection and superposition are strongest, etc., Figures 9(a)-9(b) As shown, the probe points are arranged, i.e., the multi-point sensor positions are arranged. The coordinates of the probe positions are shown in Table 3 below:

[0129] Table 3 Probe Location Arrangement

[0130]

[0131]

[0132] In this embodiment, based on the location coordinates of the candidate sensor at point U and the arrangement of the partial discharge source at point P, combined with the establishment of a simulation model, U*(P*2) ultra-high frequency signal strength data are obtained.

[0133] S6: The mathematical model of coverage and detection mean S in the data processing method of normalized classification analysis is used as the optimization model in the objective optimization algorithm. The Grey Wolf Optimization Algorithm (GWO) is applied to optimize the placement of UHF sensors. Coverage and detection mean S are used as decision variables of the Grey Wolf Optimization Algorithm.

[0134] Taking sensor N1 as an example, as shown in Figures 10(a) and 10(b), the analysis of the collected time and frequency domain waveforms shows that the UHF electromagnetic wave is superimposed by reflection and refraction between the core and the tank wall, which increases the amplitude of the signal between 15ns and 40ns. Since the simulation is set as an ideal conductor and there are no metal parts such as leads or clamps between the core and the tank wall, the signal continues to oscillate within the 50ns simulation time. At 17ns, the signal is enhanced due to the superposition of reflection and refraction.

[0135] Taking the partial discharge source PD1 as an example, the peak-to-peak values ​​of the waveforms at each sensor acquisition point are shown in Table 4 below, from which the sensor signal gain is obtained:

[0136] Table 4 Sensor Signal Gain

[0137]

[0138] As shown in the table above: when PD1 is set between the B and C phase windings, sensors N1 and N2 are located at 1 / 2 the height of the transformer, and their overall gain is basically the same; N3 is located in the middle of the transformer, slightly above the B phase winding, and N5 is located near the top corner of the C phase winding, with higher overall gain; N8 and N9 are located in the middle and upper part of the side respectively, and N6 is located at the lower left corner of the A phase winding, with lower signal gain.

[0139] However, the above data is only from one partial discharge source, and the amount of data to be processed is enormous. The data processing method of normalization classification analysis is adopted to quantify all data to a unified level of analysis, thereby reducing the difficulty of data processing.

[0140] (1) Normalize the peak-to-peak values ​​of all output voltages, using U S0 As a benchmark value.

[0141] U S0 =max(U Si ), i = 1, 2, 3, 4... U

[0142] The normalized value is: U Si / U S0

[0143] (2) The number N of normalized magnitudes falling within the interval [a, 1] a The ratio of the coverage rate to the total number of data points N is used as the coverage rate.

[0144] Cover = N a / N

[0145] Where 'a' represents a preset interval boundary constant, preferably 0.4-0.5.

[0146] (3) The average value of the signal amplitude is used as the detection mean S.

[0147] Among them, A Pn It is the source P of the bureau n The normalized amplitude;

[0148] After processing the data through the above steps, the coverage rate and the average detection value can be used as the evaluation criteria for sensor sensitivity.

[0149] In this embodiment, the Gray Wolf Optimization Algorithm (GWO) divides the wolf pack into four hierarchical classes: α, β, δ, and ω. α, β, and δ represent the leadership level, decreasing sequentially, while ω represents the lowest level of the pack, obeying the instructions of the leadership. During hunting, α, β, and δ guide ω to search for and surround prey, thereby obtaining the globally optimal solution. The wolf pack's hunt for prey can be described as follows:

[0150] D = |C·X p (t)-X(t)|

[0151] X(t+1)=X p (t)-A·D

[0152] A = 2ar² - a

[0153] C = 2r1

[0154] In the formula, D represents the distance between an individual wolf and its prey; A and C are coefficient factors; X p X(t) and X(t) represent the positions of the individual gray wolf and the prey, respectively; r1 and r2 are random numbers between [0,1], and a is a convergence factor that decays linearly from 2, negatively correlated with the number of iterations, and eventually decays to 0. The update description of the position during a wolf pack hunt is as follows:

[0155] X1 = X α -A1D α

[0156] X2 = X β -A2Dβ

[0157] X3 = X δ -A3D δ

[0158]

[0159] Among them, X α X β X δ D represents the current positions of α, β, and δ, respectively. α D β D δ Let α, β, δ, and ω represent the distances between wolves. A global search is performed when |A| > 1, and a local search is performed when |A| < 1. The iteration is complete when |A| decreases to 0, and the prey position is output as the optimal solution.

[0160] The specific implementation steps of the Grey Wolf Algorithm are as follows:

[0161] The main steps of the Grey Wolf Optimization Algorithm (GWO) for optimizing the objective optimization model of UHF sensor deployment scheme are as follows:

[0162] Step (1): Input parameter settings. Set the gray wolf population size N = U * (P * 2), and the number of iterations T. max The storage includes the size of the non-dominated solution unit, the wavelength λ of the ultra-high frequency electromagnetic wave, the superposition effect parameter Ge of the constraint variables, the geometric diffraction condition kφ>1, the coverage rate C of the decision variables, and the detection mean S. Ge is determined based on the reflection coefficient R of the electromagnetic wave. TE R TM With refractive index T TE T TM The phase constant k of the ultra-high frequency signal is determined by the wavelength; data obtained from each partial discharge source can yield a type of U... S0 As a benchmark, U S0 =max(U Si Returns 1 when ) U S0 ≠max(U Si Returns 0 when ).

[0163] Step (2): Random parameter initialization. Initialize a, A, and C, and randomly generate an initial gray wolf population within the search space.

[0164] Step (3): Calculate the values ​​of individuals in the initial gray wolf population according to the corresponding objective function and constraint function, find the non-dominant solution, initialize the storage unit, and select dominant individuals α, β, δ and record their positions.

[0165] Step (4): Determine if the iteration number t is greater than T. maxIf so, output a non-dominated solution, that is, an optimized UHF sensor arrangement; otherwise, proceed to the next step.

[0166] Step (5): Update convergence factor a, coefficient factors A and C, calculate and sort the fitness of individuals in the population, update the storage unit, select dominant individuals α, β, δ and update their positions.

[0167] Step (6): Let t = t + 1, then return to step (4).

[0168] S7: Apply the Grey Wolf Optimization Algorithm (GWO) to perform big data processing and optimization, obtain the collection point with the highest coverage and average detection value (sensitivity), and obtain the corresponding coordinate position, which is the optimal placement position of the UHF sensor.

[0169] In summary, analysis shows that sensor N3 has the highest coverage, N5 has both high coverage and sensitivity, and N7 has the highest sensitivity. Their installation coordinates are (0, 264.5, 243), (329, 407.5, 243), and (400, 500, 243). Considering the design of the transformer's external structure and dimensions, as well as the sensor's structure and dimensions, the long side of the actual transformer is usually the high-voltage or low-voltage side, which will be equipped with electrical or magnetic shielding. Placing sensors there might disrupt the electromagnetic shielding, and the sensor's own structural dimensions also need to be considered. Therefore, to ensure the detection coverage of partial discharges outside the core of the entire transformer tank by a single sensor, the UHF sensor should be placed in the middle of the transformer, slightly above the B-phase winding; to ensure high detection coverage and maximum sensitivity of partial discharges outside the core of the entire transformer tank by a single sensor, the UHF sensor should be placed at the front or back corner near the top. Figure 11 As shown, taking a 630KVA enclosure as an example, the tank dimensions are 1058×488×1215mm, and the optimal placement position of the UHF sensor is obtained.

[0170] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. An oil-immersed distribution transformer ultra-high frequency sensor arrangement method, characterized by, The method comprises the following steps: Discretize the integral form of Maxwell's equations into a grid equation set based on the finite integration method in time domain, sequentially solve the grid equation set in time sequence on the spatial grid under the response truncation boundary condition to obtain the spatial electromagnetic field, and obtain the time domain and frequency domain results through fast Fourier transform; Set the partial discharge source position; Perform ultra-high frequency electromagnetic wave analysis in the oil-immersed distribution transformer to obtain boundary conditions, amplitude superposition effect parameters and geometric diffraction conditions, and the ultra-high frequency electromagnetic wave analysis comprises skin effect analysis, boundary electromagnetic wave reflection analysis, ultra-high frequency electromagnetic wave geometric diffraction and attenuation analysis; Take the boundary conditions, amplitude superposition effect parameters and geometric diffraction conditions as constraint conditions to calculate the candidate sensor arrangement position coordinates; Normalize all output voltage peak values, take the ratio of the number of normalized amplitude values in a preset interval to the total number as the coverage rate, and take the average value of the signal amplitude as the detection mean value; Take the coverage rate and the detection mean value as optimization objectives, perform optimization on the ultra-high frequency sensor arrangement position based on the grey wolf optimization algorithm, obtain the acquisition point with the maximum coverage rate and detection mean value, obtain the corresponding coordinate position, and obtain the optimal arrangement position of the ultra-high frequency sensor.

2. The oil-immersed distribution transformer ultra-high frequency sensor arrangement method according to claim 1, characterized in that, The discretization of the integral form of Maxwell's equations into a grid equation set comprises the following steps: Solve the integral form of Maxwell's equations in time domain: where H is the magnetic field, E is the electric field, D is the electric displacement, B is the magnetic induction, J e,i , J m,i are the injection terms of the electric and magnetic fields at the node; J e,L , J m,L are the loss terms of the electric and magnetic fields at the node, and A, r are the area and line integral representations of the magnetic and electric fields, respectively; After converting into matrix form, the four types of constitutive relations D = εE, B = μH, J e,l = σE, J m,l = κH representing the effect of the medium on the electromagnetic field are substituted into the equation set, which is discretized into a grid equation set; Wherein, ε is the relative permittivity, μ is the magnetic permeability, σ is the conductivity, and κ is the magnetic loss.

3. The oil-immersed distribution transformer ultra-high frequency sensor arrangement method according to claim 1, characterized in that, The response truncation boundary condition is expressed as: where c represents the speed of the ultra-high frequency electromagnetic wave, Δt represents the time step, and δ b represents the spatial step.

4. The oil-immersed distribution transformer ultra-high frequency sensor arrangement method according to claim 1, characterized in that, The partial discharge source uses a dipole antenna as an electromagnetic wave source, and a discharge power supply is added to the gap between the top surfaces of the double cylinders, and the gap size meets the 1 / 4 electromagnetic wave wavelength.

5. The oil-immersed distribution transformer ultra-high frequency sensor arrangement method according to claim 1, characterized in that, The skin effect analysis obtains: Wherein, δ is the skin penetration depth, α is the transmission attenuation coefficient, ω is the electromagnetic wave angular frequency, μ is the magnetic permeability, and γ is the conductivity.

6. The oil-immersed distribution transformer ultra-high frequency sensor arrangement method according to claim 1, characterized in that, The boundary condition is expressed as: Wherein, c represents the ultra-high frequency electromagnetic wave velocity, Δt represents the time step, and δ is the skin penetration depth.

7. The oil-immersed distribution transformer ultra-high frequency sensor arrangement method according to claim 1, characterized in that, The amplitude superposition effect parameter is expressed as: Ge = be∑ / be = p(a s ) / p(a n ) Where Ge represents the amplitude effect, be∑ represents the signal-to-noise ratio after superposition, be represents the signal-to-noise ratio before superposition, and p(α) represents the signal-to-noise ratio before superposition. s p(α) represents the intensity of the electromagnetic diffraction peak. n The intensity of the background is ).

8. The oil-immersed distribution transformer ultra-high frequency sensor arrangement method according to claim 1, characterized in that, The geometric diffraction condition is expressed as: kφ>1 Wherein, k represents the ultra-high frequency signal phase constant, and φ represents the winding radius. According to the geometric diffraction condition, it is judged whether there is geometric diffraction in the propagation of the ultra-high frequency electromagnetic wave in the oil-immersed distribution transformer.

9. The oil-immersed distribution transformer ultra-high frequency sensor arrangement method according to claim 1, characterized in that, The peak-to-peak value of all output voltages is normalized to U S0 As a reference value, it is expressed as: U S0 = max(U Si ), i = 1, 2, 3, 4... U the number N of normalized amplitudes falling in the interval [a, 1] a the ratio of the number N of data points to the total number of data points N as coverage, specifically expressed as: Cover = N a / N Wherein, Cover represents the coverage rate, U represents the number of set acquisition points, and a represents the preset interval boundary constant. The average value of the signal amplitude is taken as the detection mean value, and is specifically expressed as: where S denotes the detection mean value, A Pn represents the normalized amplitude of the partial discharge source P n .

10. The oil-immersed distribution transformer ultra-high frequency sensor arrangement method according to claim 1, characterized in that, The optimization on the ultra-high frequency sensor arrangement position based on the grey wolf optimization algorithm comprises the following steps: Set the grey wolf population size, iteration number threshold, store the size of the non-dominated solution unit, the ultra-high frequency electromagnetic wave wavelength, the constraint variable superposition effect parameter and the geometric diffraction condition, and the decision variable coverage rate and detection mean value; Randomly initialize the parameters, initialize the coefficient factor and the convergence factor, and randomly generate the initial grey wolf population in the search space; Calculate the corresponding target function and constraint function values of the individuals in the initial grey wolf population, find the non-dominated solution, initialize the storage unit, and select the dominant individuals and record the positions. The circulating iteration updates a convergence factor and a coefficient factor, calculates population individual fitness and sorts, updates a storage unit, selects a superior individual and updates a position, until a threshold value of iteration times is reached, non-dominated solutions are output, the maximum coverage rate and detection mean of the collection point are obtained, the corresponding coordinate position is acquired, and the optimized ultra-high frequency sensor arrangement position is output.

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