A Quantitative Evaluation Method for Water Content in Oil-Impregnated Paper Insulation Based on the Dissado-Hill Model

Abstract

The present invention relates to a method for quantitatively evaluating the moisture content of oil-paper insulation based on the Dissado-Hill model. A broadband equivalent circuit model of oil-paper insulation is constructed, and the complex capacitance expression of the model is deduced. Multiple groups of oil-paper insulation specimens with different moisture contents are prepared, and the complex capacitance test data of the specimens are measured by the frequency-domain dielectric spectroscopy method. An improved grey wolf algorithm is proposed based on the basic grey wolf algorithm and is used to solve the model parameter identification problem. According to the parameter identification results, characteristic parameters that can effectively characterize the moisture content of oil-paper insulation are extracted and a quantitative evaluation formula for the moisture content is constructed. Four groups of oil-paper insulation specimens with different moisture contents are prepared as specimens to be evaluated, and the corresponding complex capacitance test data are collected. The corresponding model parameter values are obtained through parameter identification, and are substituted into the quantitative evaluation formula for the moisture content to obtain the predicted value of the moisture content of the specimens to be evaluated; the relative error is selected as an index to measure the evaluation accuracy, and further the effectiveness of the moisture content quantitative evaluation method is verified.

Description

Technical Field

[0001] The present invention relates to a method for quantitatively evaluating the moisture content of oil-paper insulation based on the Dissado-Hill model. Background Art

[0002] As a core device of a new power system, the safe and stable operation of an oil-immersed transformer is the basis for ensuring the continuous supply of high-quality electric energy. Affected by factors such as moisture, temperature, and aging products, the dielectric properties of the oil-paper insulation system inside the transformer will gradually decline, and moisture is one of the most critical factors among many insulation aging factors. Therefore, studying a method for quantitatively evaluating the moisture content of oil-paper insulation has great practical significance. In the field of evaluating the state of composite insulating media, the dielectric response equivalent circuit model is often used as a medium to analyze the dielectric response process of dielectrics. However, the currently common dielectric response equivalent circuit models such as the extended Debye model, the Cole-Cole model, and the Davidson-Cole model all have obvious deficiencies. Since the modeling processes of the above models are all based on the premise that there is no interaction between the microscopic particles participating in the relaxation process, the premise assumptions are significantly inconsistent with the actual situation, and thus the motion characteristics of the microscopic particles during the polarization process cannot be accurately described. Different from the extended Debye model and a series of empirical models derived therefrom, the Dissado-Hill model fully considers the interaction between microscopic particles during the dielectric polarization process, so this model can better characterize the microscopic polarization process occurring inside the oil-paper insulation system. To better analyze the dielectric response process of the oil-paper insulation composite medium, based on the existing modules of the Dissado-Hill model, the present invention adds a non-dispersive unit to characterize the non-dispersive relaxation process of the dielectric response, and adds a direct current conductance to characterize the energy loss generated during the dielectric polarization process, thereby completing the construction of the wide-frequency dielectric response equivalent circuit model of the oil-paper insulation. In addition, based on the results of model parameter identification, the present invention analyzes the variation law between the model parameters and the moisture content, and then extracts new moisture evaluation characteristic quantities, determines the fitting relationship between each characteristic quantity and the moisture content, constructs a quantitative evaluation formula for the moisture content, and finally proposes a method for quantitatively evaluating the moisture content of oil-paper insulation. Experimental results show that the evaluation method proposed by the present invention can accurately and effectively evaluate the moisture content of oil-paper insulation. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for quantitatively evaluating the moisture content of oil-paper insulation based on the Dissado-Hill model, which can accurately and effectively evaluate the moisture content of oil-paper insulation.

[0004] To achieve the above purpose, the technical solution of the present invention is: A method for quantitatively evaluating the moisture content of oil-paper insulation based on the Dissado-Hill model, comprising the following steps:

[0005] Step 1: Construct an equivalent circuit model for the broadband dielectric response of oil-paper insulation. This equivalent circuit model consists of the Dissado-Hill model, a conductance module, and a frequency-independent capacitance module;

[0006] Step 2: Prepare multiple groups of oil-paper insulation specimens with different moisture contents and conduct FDS tests on them in sequence;

[0007] Step 3: Use the improved grey wolf algorithm to identify the parameters of the equivalent circuit model for the broadband dielectric response of oil-paper insulation;

[0008] Step 4: According to the parameter identification results of the equivalent circuit model for the broadband dielectric response of oil-paper insulation, extract the DC conductance G, the polarization rate amplitude X of the low-frequency dispersion dielectric response module in the Dissado-Hill model QDC(0) and the polarization rate amplitude X of the relaxation peak-type dielectric response module LP(0) as the moisture content quantitative evaluation characteristic quantities, find the fitting relationship between each characteristic quantity and the moisture content, and then construct a moisture content quantitative evaluation formula.

[0009] Step 5: Collect the FDS test data of the oil-paper insulation specimen to be evaluated, solve the corresponding equivalent circuit model parameters, and substitute the numerical values of the model parameters G, X QDC(0) and X LP(0) into the moisture content quantitative evaluation formula to obtain the moisture content of the oil-paper insulation specimen to be evaluated.

[0010] In an embodiment of the present invention, the specific implementation of Step 1 is as follows:

[0011] Introduce the Dissado-Hill model based on many-body theory, i.e., the D-H model, to characterize the dispersion relaxation process of the dielectric response of oil-paper insulation. On the basis of the existing dispersion units in the D-H model, add non-dispersion units to characterize the non-dispersion relaxation process of the dielectric response, and add DC conductance to characterize the energy loss generated during the polarization process of the dielectric, so as to complete the construction of the equivalent circuit model for the broadband dielectric response of oil-paper insulation; the equivalent circuit model for the broadband dielectric response of oil-paper insulation consists of four modules: a conductance module, a relaxation peak-type dielectric response module, a low-frequency dispersion dielectric response module, and a frequency-independent capacitance module;

[0012] In the field of composite insulation medium state evaluation, the complex capacitance is often used to characterize the dielectric response characteristics of the dielectric, and its expression is as shown in Equation (1):

[0013]

[0014] where C′ (ω) is the real part C′ (ω) of the complex capacitance, and C″ (ω)is the imaginary part C″ of the complex capacitance (ω) ;

[0015] According to the topological structure of the equivalent circuit model of the broadband dielectric response of oil-paper insulation, combined with the expressions of each module, the complex capacitance of the equivalent circuit model of the broadband dielectric response of oil-paper insulation is derived from circuit theory and relevant theories of dielectric physics Expression:

[0016]

[0017] In the formula, ω is the angular frequency of the applied electric field; ε0 is the vacuum permittivity; S is the surface area of the measuring electrode; d is the thickness of the insulating paperboard; ε′ (ω) , ε″ (ω) are the real and imaginary parts of the complex permittivity respectively; χ′ (ω) , χ″ (ω) are the real and imaginary parts of the complex polarizability respectively; ε ∞ is the optical-frequency permittivity; δ is the conductivity; are the complex polarizabilities of the relaxation peak-type dielectric response process and the low-frequency dispersion dielectric response process respectively; χ LP(0) , χ QDC(0) are the polarizability amplitudes of the relaxation peak-type dielectric response process and the low-frequency dispersion dielectric response process respectively; F(ω / ω p ), F(ω / ω c ) are the shape functions of the relaxation peak-type dielectric response process and the low-frequency dispersion dielectric response process respectively; ω p , ω c are the characteristic frequencies of the relaxation peak-type dielectric response process and the low-frequency dispersion dielectric response process respectively; m, n1 are the inter-cluster motion correlation coefficients and intra-cluster motion correlation coefficients of the relaxation peak-type dielectric response process respectively; p, n2 are the inter-cluster motion correlation coefficients and intra-cluster motion correlation coefficients of the low-frequency dispersion dielectric response process respectively; C ∞ is the frequency-independent capacitance; G is the DC conductance; Γ(*) is the gamma function; 2F1(a, b; c; z) is the Gaussian hypergeometric function

[0018] In an embodiment of the present invention, the specific implementation of step 2 is as follows:

[0019] First, cut and process insulating cardboard with a thickness of 1 mm to obtain several groups of circular cardboard with a diameter of 80 mm. Secondly, place the circular cardboard and No. 25 insulating oil in a constant temperature vacuum drying oven at 110°C and 100 Pa for 72 hours to remove the initial moisture in the experimental samples. Thirdly, weigh and record the initial weight of the cardboard after drying treatment, and expose it to the air for natural moisture absorption. Weigh the moisture-absorbed cardboard at regular intervals. Stop moisture absorption when the moisture-absorbed cardboard reaches the target moisture content. At the same time, according to the oil-paper mass ratio of 20:1, immerse the cardboard treated by natural moisture absorption in the dried insulating oil and fully impregnate it for 24 hours. Finally, repeat the above operations to prepare multiple groups of oil-paper insulation specimens with different moisture contents, and sequentially perform frequency domain dielectric spectroscopy (FDS) tests to obtain the real part C′ of the complex capacitance corresponding to each oil-paper insulation specimen with different moisture contents. (ω) Spectral line and the imaginary part C″ of the complex capacitance (ω) Spectral line.

[0020] In an embodiment of the present invention, step 3 is specifically implemented as follows:

[0021] First, construct a multivariate nonlinear equation set as shown in Equation (3):

[0022]

[0023] In the formula, C′(ω x ) and C″(ω x ) respectively represent the measured value of the real part of the complex capacitance and the measured value of the imaginary part corresponding to the measurement frequency point ω x ; C j ′(ω x ) and C j ″(ω x ) respectively represent the calculated value of the real part of the complex capacitance and the calculated value of the imaginary part corresponding to the measurement frequency point ω x , x = 1, 2,..., m;

[0024] Secondly, construct an objective function y as shown in Equation (4), and transform the problem of solving the multivariate nonlinear equation set as shown in Equation (3) into an objective function optimization problem:

[0025]

[0026] Finally, use the improved grey wolf algorithm to solve the objective function optimization problem to obtain the equivalent circuit model parameters corresponding to the oil-paper insulation specimens with different moisture contents.

[0027] In an embodiment of the present invention, the steps of the improved grey wolf algorithm are as follows:

[0028] First, set the algorithm parameters, randomly initialize the positions of each individual in the wolf pack, and calculate the individual fitness; according to the fitness values, select the alpha wolf, beta wolf, and delta wolf, and record the positions of the three individuals as X α 、X β 、X δ ;

[0029] Second, calculate the convergence factor a, update coefficient A, and update coefficient C. The non-linear convergence factor used is shown in Equation (5); in each round of iterative optimization process, according to the value of the convergence factor a, update coefficient A and update coefficient C will be updated using Equation (6) and Equation (7), where r is a random number with a value range between 0 and 1;

[0030]

[0031] A = 2ar - a (6)

[0032] C = 2r (7)

[0033] where t is the number of iterations, and t max is the maximum number of iterations;

[0034] Third, according to X α 、X β 、X δ 、update coefficient A, and update coefficient C, perform position update operations on the positions X i of other individuals in the wolf pack except the alpha wolf, beta wolf, and delta wolf; introduce dynamic weights and an adaptive position update strategy, and then construct a position update formula as shown in Equation (8):

[0035]

[0036] where,

[0037]

[0038]

[0039] in the formula, ω1, ω2, and ω3 are all dynamic weights; are the numerical values of the d-th dimensional elements in the position vectors corresponding to the alpha wolf, beta wolf, and delta wolf respectively.

[0040] Then, substitute the updated individual position data into the fitness calculation function to obtain the individual fitness, and compare it with the fitness of the alpha wolf, beta wolf, and delta wolf; if there is a better individual generated in this iteration process, update the alpha wolf, beta wolf, or delta wolf accordingly;

[0041] Finally, repeat the above steps until the maximum number of iterations t max is reached. The position vector X of the alpha wolf finally output α =(x1, x2,..., x m ) The values corresponding to each component are the results of model parameter identification;

[0042] To select the mean agreement degree W av as the accuracy evaluation index for the accuracy of the parameter identification result; The mean agreement degree W av The calculation formula is shown in Equation (11). In the formula, W C′ and W C″ represent the real part agreement degree of the complex capacitance and the imaginary part agreement degree of the complex capacitance respectively; If the value of W av is closer to 1, it indicates that the fitting degree between the measured value and the calculated value of the complex capacitance is higher, and the established equivalent circuit model can more accurately characterize the polarization process of the dielectric;

[0043]

[0044] In an embodiment of the present invention, the specific implementation of step 4 is as follows:

[0045] According to the parameter identification results of the equivalent circuit model, extract the DC conductance G, the polarization rate amplitude X of the low-frequency dispersion dielectric response module in the Dissado-Hill model QDC(0) and the polarization rate amplitude X of the relaxation peak type dielectric response module LP(0) as the moisture content quantitative evaluation features; Obtain the fitting expressions between each feature quantity and the moisture content, as shown in Equations (12), (13), and (14):

[0046]

[0047]

[0048]

[0049] In the formula, A1, A2, A3, B1, B2, B3, C1, and C2 are all fitting coefficients.

[0050] To improve the accuracy of the evaluation results, the present invention comprehensively considers the moisture evaluation prediction values obtained through each feature quantity, constructs an oil-paper insulation moisture content evaluation formula, and the evaluation formula is shown in Equation (15):

[0051]

[0052] In the formula, are respectively obtained from the characteristic parameters G, X QDC(0) and XLP(0) The obtained predicted moisture content value.

[0053] In an embodiment of the present invention, step 5 is specifically implemented as follows:

[0054] First, use a frequency-domain dielectric spectrometer to measure the complex capacitance data of the specimen to be evaluated; secondly, use the improved grey wolf algorithm to obtain the model parameter values corresponding to oil-paper insulation specimens with different moisture contents, and extract the characteristic parameters G, X QDC(0) and X LP(0) ; finally, substitute G, X QDC(0) and X LP(0) into the moisture content quantitative evaluation formula to obtain the predicted value of the moisture content of the oil-paper insulation specimen to be evaluated; thus, the complete process of quantitative evaluation of the moisture content of oil-paper insulation is completed.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] 1. Introduce the Dissado-Hill model and add a non-dispersive unit and a direct current conductance on the basis of the existing modules of the model, and then complete the construction of the equivalent circuit model of the wide-frequency dielectric response of oil-paper insulation. Compared with the extended Debye model and its derivative models, the equivalent circuit model proposed by the present invention can more accurately reflect the microscopic dielectric response process of the oil-paper insulation system.

[0057] 2. Introduce a non-linear convergence factor, a dynamic weight and an adaptive position update strategy on the basis of the basic grey wolf algorithm, further improve the search ability of the algorithm, and provide a more powerful means for solving the problem of parameter identification of the wide-frequency equivalent circuit model of oil-paper insulation.

[0058] 3. Propose new characteristic quantities G, X QDC(0) and X LP(0) for quantitative evaluation of the moisture content of oil-paper insulation. The experimental results show that the goodness of fit R 2 between the above three moisture evaluation characteristic quantities and the moisture content Mc all reaches more than 0.95. Therefore, the moisture evaluation characteristic quantities proposed by the present invention can effectively characterize the moisture content of the oil-paper insulation specimen.

[0059] 4. Use the fitting relationship between each characteristic quantity and the moisture content to construct a quantitative evaluation expression for the moisture content, providing an effective technical basis for the quantitative evaluation of the moisture content of oil-paper insulation. Brief Description of the Drawings

[0060] Figure 1 It is a flow chart of a method for quantitatively evaluating the moisture content of oil-paper insulation based on the Dissado-Hill model according to the present invention.

[0061] Figure 2This is the equivalent circuit model of the wide-frequency dielectric response of oil-paper insulation for the present invention.

[0062] Figure 3 These are the real part test spectra of the complex capacitance of six groups of oil-paper insulation specimens used to construct the quantitative evaluation equation for moisture content.

[0063] Figure 4 These are the imaginary part test spectra of the complex capacitance of six groups of oil-paper insulation specimens used to construct the quantitative evaluation equation for moisture content.

[0064] Figure 5 These are the real part test spectra of the complex capacitance of four groups of oil-paper insulation specimens as samples to be evaluated.

[0065] Figure 6 These are the imaginary part test spectra of the complex capacitance of four groups of oil-paper insulation specimens as samples to be evaluated.

[0066] Figure 7 This is the fitting relationship curve between the DC conductance G and the moisture content Mc.

[0067] Figure 8 This is the fitting relationship curve between the amplitude of the low-frequency dispersion polarization rate and the moisture content Mc.

[0068] Figure 9 This is the fitting relationship curve between the amplitude of the relaxation peak polarization rate and the moisture content Mc. Detailed implementation manner

[0069] The technical solution of the present invention will be specifically described below with reference to the accompanying drawings.

[0070] A method for quantitatively evaluating the moisture content of oil-paper insulation based on the Dissado-Hill model of the present invention is carried out according to the following steps:

[0071] Step 1: Construct an equivalent circuit model of the wide-frequency dielectric response of oil-paper insulation, which is composed of the Dissado-Hill model, a conductance module, and a frequency-independent capacitance module;

[0072] Introduce the Dissado-Hill (D-H) model based on many-body theory to characterize the dispersion relaxation process of the dielectric response of oil-paper insulation. In addition, on the basis of the existing dispersion units in the D-H model, non-dispersion units are added to characterize the non-dispersion relaxation process of the dielectric response, and DC conductance is added to characterize the energy loss generated during the dielectric polarization process, thereby completing the construction of the equivalent circuit model of the wide-frequency dielectric response of oil-paper insulation. This model is composed of four modules: a conductance module G, a relaxation peak type dielectric response module C LP , a low-frequency dispersion dielectric response module C QDC , and a frequency-independent capacitance module C ∞ .

[0073] In the field of the state assessment of composite insulation media, complex capacitance is often used to characterize the dielectric response characteristics of dielectrics, and its expression is as shown in Equation 1.

[0074]

[0075] According to Figure 2 the topological structure of the equivalent circuit model of the wide-frequency dielectric response of oil-paper insulation shown, combined with the expressions of each module, the complex capacitance expression of this equivalent circuit model is deduced from circuit theory and relevant theories of dielectric physics:

[0076]

[0077] In the formula, ω is the angular frequency of the applied electric field; ε0 is the vacuum permittivity; S is the surface area of the measurement electrode; d is the thickness of the insulating cardboard; ε′ (ω) , ε″ (ω) are the real part and the imaginary part of the complex permittivity respectively; χ′ (ω) , χ″ (ω) are the real part and the imaginary part of the complex polarizability respectively; ε ∞ is the optical-frequency permittivity; δ is the conductivity; are the complex polarizabilities of the relaxation-peak-type dielectric response process and the low-frequency dispersion dielectric response process respectively; χ LP(0) , χ QDC(0) are the polarizability amplitudes of the relaxation-peak-type dielectric response process and the low-frequency dispersion dielectric response process respectively; F(ω / ω p ), F(ω / ω c ) are the shape functions of the relaxation-peak-type dielectric response process and the low-frequency dispersion dielectric response process respectively; ω p , ω c are the characteristic frequencies of the relaxation-peak-type dielectric response process and the low-frequency dispersion dielectric response process respectively; m, n1 are the inter-cluster motion correlation coefficients and intra-cluster motion correlation coefficients of the relaxation-peak-type dielectric response process respectively; p, n2 are the inter-cluster motion correlation coefficients and intra-cluster motion correlation coefficients of the low-frequency dispersion dielectric response process respectively; C ∞ is the frequency-independent capacitance; G is the direct current conductance; Γ(*) is the gamma function; 2F1(a, b; c; z) is the Gaussian hypergeometric function.

[0078] Step 2: Prepare multiple groups of oil-paper insulation specimens with different moisture contents and conduct FDS tests in sequence

[0079] First, cut and process insulating cardboard with a thickness of 1 mm to obtain several groups of circular cardboard with a diameter of 80 mm. Second, place the circular cardboard and 25# insulating oil in a constant temperature vacuum drying oven at 110 °C and 100 Pa for 72 hours to remove the initial moisture in the experimental samples. Third, weigh and record the initial weight of the dried cardboard, expose it to the air for natural moisture absorption, weigh the moisture-absorbed cardboard at regular intervals, and stop moisture absorption when the moisture-absorbed cardboard reaches the target moisture content; at the same time, according to the oil-paper mass ratio of 20:1, immerse the naturally moisture-absorbed cardboard in the dried insulating oil and fully impregnate it for 24 hours. Finally, repeat the above operations to prepare multiple groups of oil-paper insulation specimens with different moisture contents, and sequentially perform frequency-domain dielectric spectroscopy (FDS) tests to obtain the real part C′ of the complex capacitance corresponding to each oil-paper insulation specimen with different moisture contents (ω) spectral lines and the imaginary part C″ (ω) of the complex capacitance

[0080] Step 3: Use the improved grey wolf algorithm to identify the parameters of the equivalent circuit model of the broadband dielectric response of oil-paper insulation

[0081] First, construct a system of multivariate nonlinear equations as shown in Equation (3):

[0082]

[0083] where C′(ω x ) and C″(ω x ) respectively represent the measured real part value and imaginary part value of the complex capacitance corresponding to the measurement frequency point ω x ; C j ′(ω x ) and C j ″(ω x ) respectively represent the calculated real part value and imaginary part value of the complex capacitance corresponding to the measurement frequency point ω x .

[0084] Second, construct an objective function y as shown in Equation (4), and then transform the problem of solving the system of multivariate nonlinear equations as shown in Equation (3) into an objective function optimization problem

[0085]

[0086] Finally, use the artificial intelligence optimization algorithm to solve the objective function optimization problem, and then obtain the parameters of the equivalent circuit model corresponding to the oil-paper insulation specimens with different moisture contents

[0087] To improve the accuracy of parameter identification results and shorten the time required for the identification process, the present invention makes improvements based on the basic Grey Wolf Optimization algorithm. When updating the position of each individual in the wolf pack, a non-linear convergence factor is introduced to improve the convergence speed and local search ability of the algorithm; in addition, the present invention further improves the exploration ability of the algorithm by introducing dynamic weights and an adaptive position update strategy. The basic steps of the improved Grey Wolf algorithm proposed by the present invention are as follows:

[0088] First, set the algorithm parameters, randomly initialize the positions of each individual in the wolf pack and calculate the individual fitness; according to the magnitude of the fitness, select the alpha wolf, beta wolf, and delta wolf, and record the positions of the above three individuals as X α 、X β 、X δ 。

[0089] Secondly, calculate the convergence factor a, update coefficient A, and update coefficient C. The non-linear convergence factor adopted by the present invention is shown in Equation (5). In each round of iterative optimization process, the update coefficient A and update coefficient C will be updated using Equations (6) and (7) according to the value of the convergence factor a, where r is a random number with a value range between 0 and 1.

[0090]

[0091] A = 2ar - a (6)

[0092] C = 2r (7)

[0093] Thirdly, according to X α 、X β 、X δ 、update coefficient A, and update coefficient C, perform a position update operation on the positions X i of other individuals in the wolf pack except the alpha wolf, beta wolf, and delta wolf. To further improve the exploration ability of the algorithm, the present invention introduces dynamic weights and an adaptive position update strategy, and then constructs a position update formula as shown in Equation (8).

[0094]

[0095] Among them,

[0096]

[0097]

[0098] In the formula, ω1, ω2, and ω3 are all dynamic weights; are the numerical values of the d-th dimensional elements in the position vectors corresponding to the alpha wolf, beta wolf, and delta wolf respectively.

[0099] Then, substitute the updated individual position data into the fitness calculation function to obtain the individual fitness, and compare it with the fitness of the alpha wolf, beta wolf, and delta wolf; if a better individual is generated during this iteration process, update the alpha wolf, beta wolf, or delta wolf accordingly.

[0100] Finally, repeat the above steps until the maximum number of iterations t max is reached. The position vector X α =(x1, x2,..., x m ) of the final output alpha wolf, and the values corresponding to each component are the results of model parameter identification.

[0101] To verify the accuracy of the parameter identification results, substitute the final identification results of each model parameter into Equation (2) to obtain the calculated real and imaginary parts of the complex capacitance; in addition, select the mean coincidence degree W av as the accuracy evaluation index. The calculation formula of the mean coincidence degree W av is shown in Equation (11). In the formula, W C′ and W C″ represent the real part coincidence degree of the complex capacitance and the imaginary part coincidence degree of the complex capacitance, respectively. If the value of W av is closer to 1, it indicates a higher fitting degree between the measured value and the calculated value of the complex capacitance, and the established equivalent circuit model can more accurately characterize the polarization process of the dielectric.

[0102]

[0103] Step 4: According to the parameter identification results of the equivalent circuit model, extract the DC conductance G, the amplitude of the polarization rate X QDC(0) of the low-frequency dispersion dielectric response module in the Dissado-Hill model, and the amplitude of the polarization rate X LP(0) of the relaxation peak dielectric response module as the moisture content quantitative evaluation features; find the fitting expressions between each feature quantity and the moisture content, as shown in Equations (12), (13), and (14):

[0104]

[0105]

[0106]

[0107] In the formula, A1, A2, A3, B1, B2, B3, C1, and C2 are all fitting coefficients.

[0108] To improve the accuracy of the evaluation results, the present invention comprehensively considers the moisture evaluation prediction values obtained through various characteristic quantities, constructs an evaluation formula for the moisture content of oil-paper insulation, and the evaluation formula is as shown in Equation (15):

[0109]

[0110] In the formula, are the predicted moisture content values obtained from the characteristic parameters G, X QDC(0) and X LP(0) respectively.

[0111] Step 5: Collect the FDS test data of the oil-paper insulation sample to be evaluated, solve the corresponding equivalent circuit model parameters, and substitute the numerical values of the model parameters G, X QDC(0) and X LP(0) into the quantitative evaluation formula for the moisture content, and then obtain the moisture content of the oil-paper insulation sample to be evaluated.

[0112] First, use the frequency domain dielectric spectroscopy tester to measure the complex capacitance data of the sample to be evaluated; secondly, use the improved grey wolf algorithm to obtain the numerical values of the model parameters corresponding to the oil-paper insulation samples with different moisture contents, and extract the characteristic parameters G, X QDC(0) and X LP(0) ; finally, substitute G, X QDC(0) and X LP(0) into the quantitative evaluation formula for the moisture content to obtain the predicted value of the moisture content of the oil-paper insulation sample to be evaluated; thus, the complete quantitative evaluation process of the moisture content of the oil-paper insulation is completed.

[0113] Example of the application of the method of the present invention

[0114] To verify the effectiveness and applicability of the quantitative evaluation method for the moisture content of oil-paper insulation proposed by the present invention. The present invention prepares multiple groups of oil-paper insulation samples with different moisture contents (0.52%, 1.48%, 2.27%, 3.42%, 4.38%, 5.17%) under laboratory conditions to construct a quantitative evaluation formula for the moisture content of oil-paper insulation. In addition, an additional group of samples with a lower moisture content (moisture content of 1.11%), two groups of samples with a medium moisture content (moisture contents of 2.97% and 3.29% respectively), and a group of samples with a higher moisture content (moisture content of 4.8%) are prepared, and the moisture content of the above four groups of oil-paper insulation samples with different moisture contents is evaluated, and the relative error between the measured moisture content of each insulation sample and the predicted moisture content obtained by the evaluation method is calculated, which effectively verifies the effectiveness and applicability of the evaluation method.

[0115] Construct an equivalent circuit model for the broadband dielectric response of oil-paper insulation as Figure 2 shown, and the complex capacitance expression of the equivalent circuit model is as shown in Equation (1):

[0116]

[0117] In the formula, ω is the angular frequency of the applied electric field; ε0 is the vacuum permittivity; S is the surface area of the measuring electrode; d is the thickness of the insulating cardboard; ε′ (ω) , ε″ (ω) are the real part and the imaginary part of the complex permittivity respectively; χ′ (ω) , χ″ (ω) are the real part and the imaginary part of the complex polarizability respectively; ε ∞ is the optical-frequency permittivity; δ is the conductivity; are the complex polarizabilities of the relaxation-peak-type dielectric response process and the low-frequency dispersion dielectric response process respectively; χ LP(0) , χ QDC(0) are the polarizability amplitudes of the relaxation-peak-type dielectric response process and the low-frequency dispersion dielectric response process respectively; F(ω / ω p ), F(ω / ω c ) are the shape functions of the relaxation-peak-type dielectric response process and the low-frequency dispersion dielectric response process respectively; ω p , ω c are the characteristic frequencies of the relaxation-peak-type dielectric response process and the low-frequency dispersion dielectric response process respectively; m, n1 are the inter-cluster motion correlation coefficient and the intra-cluster motion correlation coefficient of the relaxation-peak-type dielectric response process respectively; p, n2 are the inter-cluster motion correlation coefficient and the intra-cluster motion correlation coefficient of the low-frequency dispersion dielectric response process respectively; C ∞ is the frequency-independent capacitance; G is the direct current conductance; Γ(*) is the gamma function; 2F1(a, b; c; z) is the Gaussian hypergeometric function.

[0118] As Figures 3 - 6 shown, six groups of oil-paper insulation specimens with different moisture contents (0.52%, 1.48%, 2.27%, 3.42%, 4.38%, 5.17%) were prepared under laboratory conditions for constructing a quantitative evaluation formula for the moisture content of oil-paper insulation. In addition, an extra group of specimens with a lower moisture level (moisture content of 1.11%), two groups of specimens with a medium moisture level (moisture contents of 2.97% and 3.29% respectively), and a group of specimens with a higher moisture level (moisture content of 4.8%) were prepared. These four groups of oil-paper insulation specimens will be used as samples to be evaluated for verifying the accuracy of the evaluation method. After completing the preparation of all the oil-paper insulation specimens, the complex capacitance data of each oil-paper insulation specimen were measured using an FDS tester.

[0119] The problem of parameter identification of the oil-paper insulation broadband equivalent circuit model is transformed into the optimization problem of the objective function shown in Equation (2), and the improved grey wolf algorithm is used to solve the objective function optimization algorithm. Furthermore, the parameter identification results corresponding to six oil-paper insulation specimens with different moisture contents (0.52%, 1.48%, 2.27%, 3.42%, 4.38%, 5.17%) are obtained. Substitute the parameter identification results into Equation (1) to obtain the calculated value of the complex capacitance. At the same time, substitute the measured value of the complex capacitance and the calculated value of the complex capacitance into Equation (3) to further obtain the corresponding mean degree of coincidence W av 。

[0120]

[0121]

[0122] The parameter identification results and the mean degree of coincidence of the oil-paper insulation specimens with different moisture contents can be seen in Table 1

[0123] Table 1 Parameter identification results and degree of coincidence of oil-paper insulation specimens with different moisture contents

[0124]

[0125]

[0126] As can be seen from Table 1, as the micro-water content in the oil-paper insulation specimen increases, the model parameters G, X QDC(0) and X LP(0) The numerical values also gradually increase. From the microscopic mechanism, the reasons for this numerical change trend can be summarized as follows

[0127] The numerical value of G reflects the concentration of ions participating in the barrier hopping movement inside the dielectric. Since water molecules can promote the dissociation of impurity ions in oil, more solvated ions are generated. Therefore, as the moisture content increases, the concentration of ions participating in the barrier hopping movement increases, the conduction process is strengthened, and the numerical value of G also increases

[0128] X QDC(0) The numerical value of reflects the concentration of carriers participating in the low-frequency dispersion dielectric response process during the polarization process of the dielectric. As a solution of impurity ions, the content of water will directly determine the size of the impurity ion concentration. As the moisture content increases, the concentration of impurity ions dissolved in water molecules will increase significantly; in addition, water molecules themselves will also dissociate into H3O + and OH - ions. Therefore, the concentration of carriers participating in the low-frequency dispersion dielectric response process will gradually increase with the increase of the moisture content, and the numerical value of X QDC(0) increases

[0129] XLP(0) The numerical value of LP(0) reflects the concentration of dipoles participating in the relaxation peak-type dielectric response process during the dielectric polarization process. During the moisture absorption process of the insulating paper, water molecules will combine with the 6-OH groups of glucose units in the form of hydrogen bonds, and then form hydrogen bond polar molecular groups. Under the action of an applied alternating electric field, the dipoles in the hydrogen bond polar molecular groups undergo displacement and interact with other dipoles in adjacent groups, thereby generating a relaxation peak-type dielectric response process. As the moisture content increases, the number of hydrogen bond polar molecular groups increases, the size becomes larger, and the dipole concentration within the groups also increases. Therefore, the dipole concentration participating in the relaxation peak-type dielectric response process becomes larger, and the value of X LP(0) becomes larger.

[0130] To verify the effectiveness of the equivalent circuit model proposed in the present invention, the mean coincidence degree W av is introduced as an accuracy evaluation index. As can be seen from Table 1, the model coincidence degrees of the equivalent circuit models corresponding to the oil-paper insulation specimens with different moisture contents all reach more than 90%, indicating that the model can accurately characterize the polarization characteristics of the oil-paper insulation system.

[0131] According to the numerical analysis of the parameter identification results, there is a close relationship between the model parameters G, X QDC(0) and X LP(0) and the moisture content Mc. Therefore, G, X QDC(0) and X LP(0) are extracted as three new characteristic quantities for quantitatively evaluating the moisture content of oil-paper insulation. To further quantify the relationship between the characteristic quantities and the moisture content Mc, the present invention uses a numerical fitting method to construct a fitting expression, and the obtained fitting curves are as shown in Figure 7 、 Figure 8 、 Figure 9 shown, and the obtained mathematical relationship is shown in Table 2.

[0132] Table 2 Mathematical relationships between various moisture evaluation characteristic quantities and the moisture content Mc

[0133]

[0134] From Figure 7 、 Figure 8 、 Figure 9 and Table 2, it can be seen that the fitting equations constructed in the present invention can well quantify the correlation between various moisture evaluation characteristic quantities and the moisture content Mc, and the goodness of fit R 2 of each fitting curve and the measured moisture content all reach above 0.95. Therefore, the above characteristic quantities can effectively characterize the moisture content of the oil-paper insulation specimens.

[0135] To improve the accuracy of the evaluation results, the present invention comprehensively considers the moisture evaluation prediction values obtained via various characteristic quantities and constructs a quantitative evaluation formula for the moisture content of oil-paper insulation. The evaluation formula is shown in Equation (4):

[0136]

[0137] To verify the effectiveness and applicability of the quantitative evaluation method for the moisture content of oil-paper insulation proposed by the present invention, moisture content evaluations are performed on four groups of specimens to be evaluated with different moisture contents (1.11%, 2.97%, 3.29%, 4.8%). First, the improved Grey Wolf algorithm described above is used for model parameter identification; secondly, the characteristic parameters G, X QDC(0) and X LP(0) are extracted; finally, G, X QDC(0) and X LP(0) are substituted into the quantitative evaluation formula for the moisture content to obtain the corresponding evaluation results; finally, the relative error is introduced to measure the accuracy of the evaluation results. The evaluation results are shown in Table 3.

[0138] Table 3 Moisture content evaluation results

[0139]

[0140] As can be seen from Table 3, in application scenarios with low, medium, or high moisture levels, the relative error of the evaluation results can be controlled within 10%. Therefore, the quantitative evaluation method for the moisture content of oil-paper insulation proposed by the present invention can effectively evaluate the moisture content of oil-paper insulation specimens with different moisture levels and has the characteristics of high evaluation accuracy and strong applicability.

[0141] The above are the preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention in terms of the functions and effects produced belong to the protection scope of the present invention.

Claims

1. A quantitative evaluation method for the moisture content of oil-paper insulation based on the Dissado-Hill model, characterized in that, It includes the following steps: Step 1: Construct an equivalent circuit model for the broadband dielectric response of oil-paper insulation. This equivalent circuit model consists of the Dissado-Hill model, a conductance module, and a frequency-independent capacitance module. The Dissado-Hill model includes a relaxation peak-type dielectric response module and a low-frequency dispersion dielectric response module. In the Dissado-Hill model, a non-dispersive unit is added to characterize the non-dispersive relaxation process of the dielectric response, and a DC conductance is added to characterize the energy loss generated during the dielectric polarization process; Step 2: Prepare multiple groups of oil-paper insulation specimens with different moisture contents and conduct FDS tests in sequence; Step 3: Use the improved grey wolf algorithm for parameter identification of the equivalent circuit model for the broadband dielectric response of oil-paper insulation; The specific implementation is as follows: Construct a system of multivariate non-linear equations shown as follows: C′(ω x ) and C″(ω x ) respectively represent the measured real part and the measured imaginary part of the complex capacitance corresponding to the measurement frequency point ω x ; C j ′(ω x ) and C j ″(ω x ) respectively represent the calculated real part and the calculated imaginary part of the complex capacitance corresponding to the measurement frequency point ω x , where x = 1, 2, …, m; Construct an objective function y shown as follows, and transform the problem of solving the system of multivariate non-linear equations into an objective function optimization problem: Use the improved grey wolf algorithm to solve the objective function optimization problem and obtain the equivalent circuit model parameters corresponding to the oil-paper insulation specimens with different moisture contents; Specifically as follows: Set algorithm parameters, randomly initialize the positions of each individual in the wolf pack and calculate the individual fitness; according to the fitness size, select the alpha wolf, beta wolf and delta wolf, and record the positions of the three individuals as X α 、X β 、X δ ; Calculate the convergence factor a, update coefficient A, and update coefficient C; In each round of iterative optimization process, according to the value of the convergence factor a, update coefficient A and update coefficient C, where r is a random number between 0 and 1; A = 2a*r - a C＝2r t is the number of iterations, where t max is the maximum number of iterations; According to X α , X β , X δ , update coefficient A and update coefficient C, and perform position update operations on the positions X i of other individuals in the wolf pack except alpha wolves, beta wolves, and delta wolves; introduce dynamic weights and an adaptive position update strategy to construct the position update formula shown below: ω1, ω2, and ω3 are all dynamic weights; They are respectively the numerical values of the d-th dimensional elements in the position vectors corresponding to alpha wolf, beta wolf, and delta wolf; Substitute the updated individual position data into the fitness calculation function to obtain the individual fitness, and compare it with the fitness of the alpha wolf, beta wolf, and delta wolf; If a better individual is generated during this iteration process, update the alpha wolf, beta wolf, or delta wolf accordingly; Reach the maximum number of iterations \(t\) max After that, the position vector \(X\) of the alpha wolf output α \(=(x_1,x_2,\cdots,x\) m ) The values corresponding to each component are the results of model parameter identification; Step 4. According to the parameter identification results of the equivalent circuit model, extract the DC conductance G, the polarization rate amplitude X of the low-frequency dispersion dielectric response module QDC(0) and the polarization rate amplitude X of the relaxation peak type dielectric response module LP(0) as the moisture content quantitative evaluation features; obtain the fitting expressions between each feature quantity and the moisture content: A1, A2, A3, B1, B2, B3, C1, C2 are all fitting coefficients; Comprehensively consider the moisture evaluation prediction values obtained through each characteristic quantity, and construct an oil-paper insulation moisture content evaluation formula as shown in the following formula: which are the predicted water content values obtained from the direct current conductance G, X QDC(0) and X LP(0) respectively; Step 5: Collect the FDS test data of the oil-paper insulation specimen to be evaluated, solve the corresponding equivalent circuit model parameters, and substitute the model parameter values of G, X QDC(0) and X LP(0) into the moisture content quantitative evaluation formula, and then obtain the moisture content of the oil-paper insulation specimen to be evaluated.

2. The quantitative evaluation method for moisture content of oil-paper insulation based on the Dissado-Hill model according to claim 1, wherein The specific implementation of Step 1 is as follows: In the field of composite insulation medium state evaluation, complex capacitance is used to characterize the dielectric response characteristics of the dielectric, and its expression is shown as follows: Among them, C ( ′ ω) is the real part C ( ′ ω) of the complex capacitance, and C ( ″ ω) is the imaginary part C ( ″ ω) ; According to the topological structure of the equivalent circuit model of the broadband dielectric response of oil-paper insulation, combined with the expressions of each module, the complex capacitance of the equivalent circuit model of the broadband dielectric response of oil-paper insulation is deduced from circuit theory and relevant theories of dielectric physics Expression: where ω is the angular frequency of the applied electric field; ε0 is the vacuum permittivity; S is the surface area of the measurement electrode; d is the thickness of the insulating cardboard; ε ( ′ ω) and ε ( ″ ω) are the real and imaginary parts of the complex permittivity, respectively; χ ( ′ ω) and χ ( ″ ω) are the real and imaginary parts of the complex polarizability, respectively; ε ∞ is the optical-frequency permittivity; δ is the conductivity; are the complex polarizabilities of the relaxation-peak-type dielectric response process and the low-frequency dispersion dielectric response process, respectively; χ LP(0) and χ QDC(0) are the polarizability amplitudes of the relaxation-peak-type dielectric response process and the low-frequency dispersion dielectric response process, respectively; F(ω / ω p ) and F(ω / ω c ) are the shape functions of the relaxation-peak-type dielectric response process and the low-frequency dispersion dielectric response process, respectively; ω p and ω c are the characteristic frequencies of the relaxation-peak-type dielectric response process and the low-frequency dispersion dielectric response process, respectively; m and n1 are the inter-cluster motion correlation coefficients and intra-cluster motion correlation coefficients of the relaxation-peak-type dielectric response process, respectively; p and n2 are the inter-cluster motion correlation coefficients and intra-cluster motion correlation coefficients of the low-frequency dispersion dielectric response process, respectively; C ∞ is the frequency-independent capacitance; G is the direct current conductance; Γ(*) is the gamma function; 2F1(a, b; c; z) is the Gaussian hypergeometric function.

3. A quantitative evaluation method for the moisture content of oil-paper insulation based on the Dissado-Hill model according to claim 1, characterized in that The specific implementation of Step 2 is as follows: First, cut and process insulating cardboard with a thickness of 1 mm to obtain several groups of circular cardboard with a diameter of 80 mm; secondly, place the circular cardboard and 25# insulating oil in a constant temperature vacuum drying oven at 110°C and 100 Pa for 72 hours to remove the initial moisture in the experimental samples; thirdly, weigh and record the initial weight of the cardboard after drying treatment, and expose it to the air for natural moisture absorption. Weigh the weight of the moisture-absorbed cardboard at regular intervals, and stop moisture absorption when the moisture-absorbed cardboard reaches the target moisture content; at the same time, according to the oil-paper mass ratio of 20:1, immerse the cardboard treated by natural moisture absorption in the dried insulating oil and fully impregnate it for 24 hours; finally, repeat the above operations to prepare multiple groups of oil-paper insulation specimens with different moisture contents, and perform frequency-domain dielectric spectroscopy tests in turn to obtain the real part C ( ′ ω) spectral line and the imaginary part C ( ″ ω) spectral line.

4. A quantitative evaluation method for the moisture content of oil-paper insulation based on the Dissado-Hill model according to claim 2, characterized in that In step 3, to evaluate the accuracy of the parameter identification results, the mean matching degree W av is selected as the accuracy evaluation index; the mean matching degree W av is calculated as shown in the following formula; W C′ and W C″ respectively represent the fitting degree of the real part and the imaginary part of the complex capacitance; if the value of W av is closer to 1, it indicates that the fitting degree between the measured value and the calculated value of the complex capacitance is higher, and the established equivalent circuit model can more accurately characterize the polarization process of the dielectric.

5. A quantitative evaluation method for the moisture content of oil-paper insulation based on the Dissado-Hill model according to claim 1, characterized in that The specific implementation of Step 5 is as follows: First, use a frequency-domain dielectric spectroscopy tester to measure the complex capacitance of the specimen to be evaluated data; secondly, use the improved grey wolf algorithm to obtain the model parameter values corresponding to oil-paper insulation specimens with different moisture contents, and extract G, X QDC(0) and X LP(0) ; finally, substitute G, X QDC(0) and X LP(0) into the moisture content quantitative evaluation formula to obtain the predicted value of the moisture content of the oil-paper insulation specimen to be evaluated; thus, the complete process of quantitative evaluation of the moisture content of oil-paper insulation is completed.

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