Construction method and system of temperature-frequency domain dielectric spectrum of insulation paper, and storage medium

Abstract

The invention belongs to the related technical field of electrical equipment insulation state monitoring, and discloses a construction method and system of a temperature-frequency domain dielectric spectrum of insulation paper and a storage medium. The method comprises the following steps: inputting sample parameters into an insulation paper complex dielectric response prediction model; the complex dielectric response of the insulation paper represented by the model at least comprises an optical frequency dielectric constant, a jump conductance process and complex dielectric responses of three relaxation polarization processes; the relationship between the jump conductivity and the temperature and the relationship between the relaxation time coefficient and the temperature meet the Arrhenius equation, and the relationship between the relaxation polarization intensity and the temperature and the relationship between the shape parameter and the temperature meet the condition that the former is enhanced along with the temperature rise and gradually tends to be saturated; and by taking the deviation between the minimum prediction and actual measurement complex dielectric response as an optimization target, optimizing model parameters to obtain a temperature-frequency domain dielectric spectrum of the insulation paper. According to the invention, the temperature-frequency domain dielectric spectrum of the insulation paper can be accurately constructed, and the dielectric spectrum of the insulation paper at any different temperatures can be rapidly and accurately obtained.

Description

Technical Field

[0001] The present invention belongs to the technical field related to insulation status monitoring of electrical equipment, and more specifically, relates to a method for constructing a temperature-frequency domain dielectric spectrum of insulating paper, a system thereof, and a storage medium. Background Art

[0002] Frequency Domain Dielectric Spectroscopy (FDS) is widely used to assess the condition of transformer insulation paper for condition-based maintenance of power transformers due to its non-destructive nature, strong anti-interference capabilities, and rich information. However, transformers experience complex and variable temperature environments during actual operation, and temperature significantly affects the dielectric properties of transformer insulation paper, resulting in significant differences in FDS spectra at different temperatures.

[0003] To effectively apply FDS evaluation models established in laboratory environments to field equipment, the current approach is to temperature-normalize the measured FDS curves to eliminate interference caused by temperature variations and ensure the accuracy of the evaluation results. The "master curve" method is a common means of achieving temperature normalization. Its core concept is to translate FDS curves at different temperatures to a "master curve" at a reference temperature using the Arrhenius equation.

[0004] However, this method assumes that all relaxation processes have the same activation energy, while the activation energies of different relaxation processes in actual insulating paper materials are not consistent, resulting in errors in the "master curve" method when dealing with the dielectric response of insulating paper, especially in a wide temperature range. Summary of the Invention

[0005] In response to the above-mentioned defects or improvement needs of the prior art, the present invention provides a method for constructing a temperature-frequency domain dielectric spectrum of insulating paper, a system thereof, and a storage medium thereof. The purpose is to construct an accurate temperature-frequency domain dielectric spectrum of insulating paper, so as to accurately obtain the dielectric properties of insulating paper at any temperature.

[0006] To achieve the above objectives, according to a first aspect of the present invention, a method for constructing a temperature-frequency domain dielectric spectrum of insulating paper is provided, comprising:

[0007] Obtaining sample parameters of multiple groups of insulating paper samples and the measured complex dielectric response under each group of sample parameters, wherein the sample parameters include the temperature of the sample and the frequency of the external electric field when the complex dielectric response of the sample is measured;

[0008] Inputting each set of sample parameters into a complex dielectric response prediction model for insulating paper; the complex dielectric response prediction model characterizes the complex dielectric response of the insulating paper by at least including the optical frequency dielectric constant, the complex dielectric response of the jump conductance process, and the superposition of the complex dielectric responses of three relaxation polarization processes; wherein the relationship between the jump conductivity and temperature in the jump conductance process and the relationship between the relaxation time coefficient and temperature in each relaxation polarization process all satisfy the Arrhenius equation, the relationship between the relaxation polarization intensity and temperature in each relaxation polarization process and the relationship between the shape parameter of the jump conductance process and each relaxation polarization process and temperature all satisfy that the former increases with increasing temperature and gradually approaches saturation;

[0009] With the optimization goal of minimizing the deviation between the complex dielectric response predicted by the prediction model and the measured complex dielectric response under the same sample parameters, the model parameters in the complex dielectric response prediction model are optimized, and the relationship between the complex dielectric response of the insulating paper and the temperature and frequency is obtained as the temperature-frequency domain dielectric spectrum of the insulating paper.

[0010] Alternatively, the complex dielectric response of the insulating paper can be expressed as:

[0011]

[0012] Where, ε * paper (ω,T) is the complex dielectric response of the insulating paper with ω and T as variables, ε ∞ is the optical frequency dielectric constant, ε * hop (ω,T) is the complex dielectric response of the jump conductance process with ω and T as variables, σ hop (T) is the temperature function of the jump conductivity, ε0 ​​is the vacuum dielectric constant, s(T) is the temperature function of the shape parameter of the jump conductivity process, ε * pi (ω,T) is the complex dielectric response of the ith relaxation polarization process with ω and T as variables, Δε i (T), τ i (T) are the temperature functions of the relaxation polarization intensity and the relaxation time coefficient in the i-th relaxation polarization process, respectively. i (T), β i (T) are the temperature functions of the low-frequency slope shape parameters and high-frequency slope shape parameters in the i-th relaxation polarization process, respectively.

[0013] Optionally, the relationship between the jump conductivity and temperature during the jump conductivity process satisfies the Arrhenius equation, which is expressed as follows:

[0014]

[0015] Where T is temperature, σ hop (T) is the temperature function of the jump conductivity, σ inf is the jump conductivity when T approaches infinity, W hop is the activation energy of the jump conductivity process, k B is the Boltzmann constant, and σ in the above relationship inf and W hop are the model parameters to be optimized.

[0016] Optionally, the relationship between the relaxation time coefficient and temperature in each relaxation polarization process satisfies the Arrhenius equation, which is:

[0017]

[0018] Where T is temperature, τ i (T) is the temperature function of the relaxation time coefficient in the i-th relaxation polarization process, i = 1, 2, 3, τ inf_i is the relaxation time when T approaches infinity in the ith relaxation polarization process, W pi is the activation energy of the ith relaxation polarization process, k B is the Boltzmann constant, and τ in the above relationship inf_i and W pi are the model parameters to be optimized.

[0019] Optionally, the relationship between the relaxation polarization intensity of each relaxation polarization process and the shape parameter in the jump conductivity process and each relaxation polarization process and the temperature is:

[0020]

[0021] Where T is temperature, Δε i (T) is the temperature function of the relaxation polarization intensity in the i-th relaxation polarization process, Δε inf_i is the relaxation polarization intensity when T approaches infinity in the ith relaxation polarization process, b i is the temperature function Δε i The unknown coefficient in (T); s(T) is the temperature function of the shape parameter of the jump conductivity process, s inf is the shape parameter when T approaches infinity during the jump conductance process, a is the undetermined coefficient in the temperature function s(T); i (T), β i (T) are the temperature functions of the low-frequency slope shape parameters and high-frequency slope shape parameters in the i-th relaxation polarization process, α inf_i , β inf_i are the low-frequency slope shape parameter and high-frequency slope shape parameter when T approaches infinity in the ith relaxation polarization process, c id i is the unknown coefficient, Δε in the above relationship inf_i 、b i 、s inf ,a,α inf_i , β inf_i and c i d i are the model parameters to be optimized.

[0022] Optionally, the optimization objective is expressed as:

[0023]

[0024] Where Φ is the deviation between the predicted complex dielectric response and the measured complex dielectric response, ε′ model (ω,T) and ε” model (ω,T) are the real and imaginary parts of the complex dielectric response of the insulating paper at the angular frequency ω predicted by the prediction model, respectively. mea (ω,T) and ε” mea (ω,T) are the real and imaginary parts of the complex dielectric response of the insulating paper at the measured temperature T at the angular frequency ω.

[0025] Optionally, the optimization algorithm used to optimize the model parameters in the complex dielectric response prediction model is any one of a simulated annealing algorithm, a genetic algorithm, a particle swarm optimization algorithm, and the like.

[0026] Optionally, among the sample parameters of all insulating paper samples, the temperature of the samples is uniformly sampled within the range of -75°C to 135°C.

[0027] According to a second aspect of the present invention, a system for constructing a temperature-frequency domain dielectric spectrum of insulating paper is provided, comprising a memory and a processor, wherein the memory stores a computer program, wherein the processor implements the steps of any of the above methods when executing the computer program.

[0028] According to a third aspect of the present invention, a computer-readable storage medium is provided, on which a computer program is stored, wherein when the computer program is executed by a processor, the steps of any of the above methods are implemented.

[0029] In general, the above technical solutions conceived by the present invention have the following beneficial effects compared with the prior art:

[0030] The present invention constructs a prediction model for the complex dielectric response of insulating paper, which characterizes the complex dielectric response of the insulating paper by at least including the optical frequency dielectric constant, the complex dielectric response of the jump conductance process, and the superposition of the complex dielectric responses of three relaxation polarization processes. The relationship between the jump conductivity and temperature in the jump conductance process and the relationship between the relaxation time coefficient and temperature in each relaxation polarization process all satisfy the Arrhenius equation. The relationship between the relaxation polarization intensity and temperature in each relaxation polarization process and the relationship between the shape parameter of the jump conductance process and each relaxation polarization process and the temperature all satisfy that the former increases with increasing temperature and gradually tends to saturation. Based on this model, a small amount of experimental data can be used to determine the variation law of the physical parameters corresponding to the frequency domain dielectric response of the insulating paper with temperature, and then the temperature-frequency domain dielectric spectrum of the insulating paper can be reconstructed to quickly and accurately obtain the dielectric spectrum of the insulating paper at any different temperature. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 is a flowchart of the steps of a method for constructing a temperature-frequency domain dielectric spectrum of insulating paper in one embodiment of the present invention;

[0032] Figure 2 This is a schematic diagram of the dielectric spectrum measurement device for insulating paper in the laboratory;

[0033] Figure 3 The measured dielectric spectrum data of 1 mm thick insulating paper with a moisture content of 1.1% at different temperatures in one embodiment of the present invention are shown in Figure 1, where (a) is the real part of the dielectric spectrum at different temperatures, and (b) is the imaginary part of the dielectric spectrum at different temperatures.

[0034] Figure 4 : is the temperature-frequency domain dielectric spectrum of the insulating paper in one embodiment of the present invention, wherein (a) is the real part variation surface of the dielectric spectrum, and (b) is the imaginary part variation surface of the dielectric spectrum;

[0035] Figure 5 The figures are comparison results of the dielectric spectrum of insulating paper measured at 60°C with a moisture content of 1.1% and the broadband dielectric spectrum of insulating paper at 60°C obtained by the present invention, wherein (a) is the comparison result of the real part of the complex dielectric constant, and (b) is the comparison result of the imaginary part of the complex dielectric constant. DETAILED DESCRIPTION

[0036] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is 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 for the purpose of explaining the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.

[0037] Example 1

[0038] The present invention provides a method for constructing the temperature-frequency domain dielectric spectrum of insulating paper, such as Figure 1 The figure shows a flowchart of the steps of a method for constructing a temperature-frequency domain dielectric spectrum of insulating paper in one embodiment of the present invention, and the steps are described in detail below.

[0039] S1. Obtain sample parameters of multiple groups of insulating paper samples and the measured complex dielectric response under each group of sample parameters. The sample parameters include the temperature of the sample and the frequency of the external electric field when the complex dielectric response of the sample is measured.

[0040] Before building the model, it is necessary to obtain the sample parameters of different insulating paper samples and the measured complex dielectric response under the corresponding sample parameters. The method is as follows.

[0041] S11. Prepare insulating paper samples.

[0042] S111: Place the insulating paper sample in a vacuum drying oven at 90°C and 50 Pa for 24 hours to remove moisture.

[0043] S112: Place the dried insulating paper sample in a room temperature environment to absorb moisture, and use a high-precision balance to monitor the sample mass change in real time until the expected moisture content is reached;

[0044] S113: Place the sample into the three-electrode test device and seal the container to ensure that the moisture content of the sample remains unchanged during the test.

[0045] S12. Measure the frequency domain dielectric spectrum of the insulating paper sample.

[0046] S121, placing the sealed container containing the insulating paper sample in step S113 in a constant temperature box, setting a temperature and maintaining it for 12 hours for temperature equilibrium;

[0047] S122. Use frequency domain dielectric spectrometer to measure the complex dielectric response ε of insulating paper * mea (ω), the real part ε' is obtained according to the following formula mea (ω) and the imaginary part ε” mea (ω) Data:

[0048] ε * mea (ω)=ε′ mea (ω)-jε” mea (ω);

[0049] Where ω is the angular frequency used in frequency domain dielectric testing.

[0050] S123. Change the temperature of the constant temperature box, repeat S121-S122, and measure and record the complex dielectric response of the insulating paper at multiple uniform sampling points between -75℃ and 135℃ (such as 135℃, 105℃, 75℃, 45℃, 15℃, -15℃, -45℃, and -75℃), which is the measured complex dielectric response under different sample parameters.

[0051] Based on the above operations, multiple data sets can be collected. Each data set includes the sample parameters (temperature and measurement frequency) and the measured complex dielectric response under these sample parameters. Based on these data sets, model optimization can be achieved.

[0052] S2. Input each group of sample parameters into the complex dielectric response prediction model of the insulating paper respectively; the complex dielectric response prediction model characterizes the complex dielectric response of the insulating paper, including at least the optical frequency dielectric constant, the complex dielectric response of the jumping conductivity process, and the superposition of the complex dielectric responses of the three relaxation polarization processes; among them, the relationship between the jump conductivity and temperature in the jumping conductivity process and the relationship between the relaxation time coefficient and temperature in each relaxation polarization process all satisfy the Arrhenius equation, the relationship between the relaxation polarization intensity and temperature in each relaxation polarization process and the relationship between the shape parameters of the jumping conductivity process and each relaxation polarization process and the temperature all satisfy that the former increases with increasing temperature and gradually tends to saturation.

[0053] The core of this invention lies in constructing a function that accurately reflects the changes in the complex dielectric response of insulating paper as it changes with temperature and frequency, thereby constructing an accurate prediction model for the complex dielectric response of insulating paper. Based on the frequency distribution characteristics and response trend analysis of multi-temperature complex dielectric spectrum measured data, this invention establishes a complex dielectric response prediction model with temperature and frequency as variables. This model accurately describes the dielectric response of insulating paper over a wide frequency and temperature range. This model is described below.

[0054] The present invention analyzes the temperature-dielectric spectrum data covering a frequency domain range of about 15 orders of magnitude. The measured data show significant low-frequency jump conductivity characteristics and multiple relaxation behaviors, indicating that the dielectric response of insulating paper includes at least one jump conductivity process and three relaxation polarization processes at different time scales.

[0055] Based on this, the present invention constructs a complex dielectric response prediction model, which characterizes the complex dielectric response of insulating paper by at least including the superposition of the complex dielectric response of the optical frequency dielectric constant, the complex dielectric response of the jump conductivity process, and the complex dielectric response of three relaxation polarization processes. The three relaxation polarization processes are the first relaxation polarization process, the second relaxation polarization process, and the third relaxation polarization process, which can be considered to correspond to low frequency, medium frequency, and high frequency, respectively. In other words, the complex dielectric response includes five main physical process components: the optical frequency dielectric constant, the jump conductivity process, and three typical relaxation polarization processes of low frequency, medium frequency, and high frequency. This can fully express the real change process of the dielectric response of insulating paper with frequency and temperature, and achieve high-precision modeling.

[0056] It should be noted that the low frequency, medium frequency and high frequency here are relative, which is intended to illustrate that the relaxation polarization process of the insulating paper will undergo relaxation polarization in three different frequency bands, and there is no absolute range of values.

[0057] Among them, the hopping conductance process describes the transition behavior of carriers between localized states in the insulating paper. Generally, different relaxation polarization processes correspond to interface polarization or dipole polarization behavior at different scales and mechanisms, and can be described by the generalized Havriliak–Negami model to characterize the polarization relaxation dielectric response at different time scales. Without considering the influence of temperature, the complex dielectric response of the hopping conductance process and the complex dielectric response of the relaxation polarization process are both dielectric processes with angular frequency ω as a single variable. In this case, the expressions of the complex dielectric response of the hopping conductance process and the complex dielectric response of the relaxation polarization process are as follows:

[0058]

[0059] Where, ε * hop (ω) is the complex dielectric response of the jump conductivity process with ω as the variable, σ hop is the jump conductivity, ε0 ​​is the vacuum dielectric constant, s is the shape parameter of the jump conductivity process, ε * pi (ω) is the complex dielectric response of the ith relaxation polarization process with ω as the variable, Δε i , τ i are the relaxation polarization intensity and relaxation time in the ith relaxation polarization process, α i , β i are the shape parameters of the i-th relaxation polarization process.

[0060] If only the effect of frequency is considered, the σ in the above complex dielectric response hop ,s,Δε i , τ i , α i , β iIn this invention, due to the introduction of the temperature dimension, by analyzing the measured data, it is found that σ hop ,s,Δε i , τ i , α i , β i All of them change with temperature, so it is necessary to hop ,s,Δε i , τ i , α i , β i Constructed into a temperature function about temperature T, namely σ hop (T), s(T), Δε i (T), τ i (T), α i (T), β i (T).

[0061] Therefore, if the influence of temperature is considered, the complex dielectric response of the jump conductance process and the complex dielectric response of the relaxation polarization process are both dielectric processes with angular frequency ω and temperature T as dual variables. At this time, the expressions of the complex dielectric response of the jump conductance process and the complex dielectric response of the relaxation polarization process are as follows:

[0062]

[0063] Where, ε * hop (ω,T) is the complex dielectric response of the jump conductance process with ω and T as variables, σ hop (T) is the temperature function of the jump conductivity, and ε0 is the vacuum dielectric constant, which is 8.854×10 -12 F / m,s(T) is the temperature function of the shape parameter of the jump conductivity process; ε * pi (ω, T) is the complex dielectric response of the ith relaxation polarization process with ω and T as variables, Δε i (T), τ i (T) are the temperature functions of the relaxation polarization intensity and the relaxation time coefficient in the i-th relaxation polarization process, respectively. i (T), β i (T) are the temperature functions of the low-frequency slope shape parameters and high-frequency slope shape parameters in the i-th relaxation polarization process, respectively.

[0064] At this point, the complex dielectric response of the insulating paper can be written as follows:

[0065]

[0066] Where, ε * paper(ω,T) is the complex dielectric response of the insulating paper with ω and T as variables, ε ∞ is the optical frequency dielectric constant.

[0067] Therefore, after analyzing the basic process of the dielectric response of insulating paper, it is also necessary to analyze the temperature functions of the relevant parameters in the jumping conductivity process and relaxation polarization process with respect to temperature.

[0068] Specifically, the hopping conductivity represents the ability of carriers to jump between local potential wells. Studies have found that its value increases significantly with increasing temperature, showing typical temperature-activated behavior. Therefore, the present invention uses the Arrhenius equation (Arrhenius-type equation) to express the relationship between hopping conductivity and temperature, which can be specifically expressed as the following relationship:

[0069]

[0070] Where T is temperature, σ hop (T) is the temperature function of the jump conductivity, σ inf is the jump conductivity when T approaches infinity, W hop is the activation energy of the jump conductivity process, k B is the Boltzmann constant, which is 8.617×10 -5 eV / K, σ in the above relationship inf and W hop are the model parameters to be optimized.

[0071] For the relaxation time coefficients of the three relaxation polarization processes, the study found that their values ​​also show a trend of shortening with increasing temperature, indicating that the polarization process accelerates with increasing temperature. Therefore, the present invention uses the Arrhenius equation (Arrhenius type equation) to express the relationship between the relaxation time coefficient and temperature, which can be specifically written as the following relationship:

[0072]

[0073] Where T is temperature, τ i (T) are the temperature functions of the relaxation time coefficient in the ith relaxation polarization process, τ inf_i is the relaxation time when T approaches infinity in the ith relaxation polarization process, W pi is the activation energy of the ith relaxation polarization process, k B is the Boltzmann constant, which is 8.617×10 -5 eV / K, τ in the above relationship inf_i and W pi are the model parameters to be optimized.

[0074] For the relaxation polarization intensity of each relaxation polarization process, as well as the jump conductivity process and the shape parameters in each relaxation polarization process, it is found that they all increase with increasing temperature and gradually tend to saturation. Therefore, they can be expressed as a linear function of the inverse of temperature and have a linear relationship with the inverse of temperature, for example, written as the following relationship:

[0075]

[0076] Where T is temperature, Δε i (T) is the temperature function of the relaxation polarization intensity in the i-th relaxation polarization process, Δε inf_i is the relaxation polarization intensity when T approaches infinity in the ith relaxation polarization process, b i is the temperature function Δε i The unknown coefficient in (T); s(T) is the temperature function of the shape parameter of the jump conductivity process, s inf is the shape parameter when T approaches infinity during the jump conductance process, a is the undetermined coefficient in the temperature function s(T); i (T), β i (T) are the temperature functions of the low-frequency slope shape parameters and high-frequency slope shape parameters in the i-th relaxation polarization process, α inf_i , β inf_i are the high-frequency slope shape parameter and low-frequency slope shape parameter when T approaches infinity in the ith relaxation polarization process, c i d i is the unknown coefficient, Δε in the above relationship inf_i 、b i 、s inf ,a,α inf_i , β inf_i and c i d i are the model parameters to be optimized.

[0077] It should be noted that fine-tuning can be performed on the basis of the above expression, such as adding a slight correction factor, as long as the main structure is still proportional to 1 / T as above.

[0078] In a specific embodiment, the insulation paper complex dielectric response prediction model can be expressed as follows:

[0079]

[0080] S3. With the optimization goal of minimizing the deviation between the complex dielectric response predicted by the prediction model and the measured complex dielectric response under the same sample parameters, the model parameters in the complex dielectric response prediction model are optimized, and the relationship between the complex dielectric response of the insulating paper and the temperature and frequency is obtained as the temperature-frequency domain dielectric spectrum of the insulating paper.

[0081] In the present invention, the model optimization goal is to minimize the deviation between the complex dielectric response predicted by the prediction model and the measured complex dielectric response under the same sample parameters. Specifically, the parameter optimization algorithm is executed according to the optimization goal to obtain the optimized model parameters. The obtained parameters are substituted into the complex dielectric response function of the insulating paper to obtain the trend of the complex dielectric response of the insulating paper with temperature and frequency, that is, the temperature-frequency domain dielectric spectrum of the insulating paper is formed.

[0082] In one embodiment, the deviation between the measured complex dielectric response and the complex dielectric response calculated by the model can be directly calculated, and then a parameter optimization algorithm is executed to minimize the deviation and output the optimized parameters.

[0083] In another embodiment, the dielectric response may be logarithmically processed before the deviation is calculated. The specific expression of the optimization objective is as follows:

[0084]

[0085] Where Φ is the deviation between the predicted complex dielectric response and the measured complex dielectric response, ε′ model (ω,T) and ε” model (ω,T) are the real and imaginary parts of the complex dielectric response of the insulating paper at the angular frequency ω predicted by the prediction model, respectively. mea (ω,T) and ε” mea (ω,T) are the real and imaginary parts of the complex dielectric response of the insulating paper at the measured temperature T at the angular frequency ω.

[0086] In one embodiment, the optimization algorithm used to optimize the model parameters in the complex dielectric response prediction model may be a simulated annealing algorithm, a genetic algorithm, a particle swarm optimization algorithm, or the like.

[0087] Take particle swarm optimization and other algorithms as examples to illustrate.

[0088] S331: Set the particle swarm size N. Each particle represents a set of possible model parameters. There are 29 model parameters in total, including the optical frequency dielectric constant ε. ∞ , σ of the jump conductance process inf 、W hop 、s inf and a, Δε of the relaxation polarization process inf_i 、b i , τ inf_i 、W p_i , α inf_i , β inf_i 、c i d i , (i=1,2,3);

[0089] S332: Randomly generate the initial position X of each particle n and initial velocity V n , n is the particle number, n = 1, 2, 3, ..., N, and the algorithm's inertia weight w, cognitive factor k1 and social factor k2 are set.

[0090] S333: For each particle, according to its current position X n , calculate the objective function value (fitness value), the objective function is the deviation between the complex dielectric response predicted by the prediction model and the measured complex dielectric response under the same sample parameters;

[0091] S334: For each particle, compare the current fitness value with its historical optimal fitness value. If the current fitness value is better, update the individual optimal position P of the particle. n is the current position X n , find the particle with the best fitness value among all particles, and update the global optimal position P g is the position of the particle;

[0092] S335: According to the improved particle swarm algorithm update rule, adjust the speed V of each particle n and position X n , and introduce the dynamic adjustment of the inertia weight w as shown below:

[0093]

[0094] Among them, j is the current iteration number, r1 and r2 are random numbers in the interval [0,1], and w max and w min are the maximum and minimum values ​​of the inertia weight, j max is the maximum number of iterations;

[0095] S335: Determine whether the algorithm satisfies the fitness value less than the preset threshold or the global optimal position P g The change of is less than a certain range. If it is satisfied, the iteration is stopped and the global optimal position P is output. g As the recognition result of the model parameters, otherwise, return to step S333 to continue iteration.

[0096] By obtaining the optimal parameters through the above optimization algorithm and inputting them into the prediction model, the temperature-frequency domain dielectric spectrum of the insulating paper can be obtained, and the corresponding insulating paper spectrum can be determined according to the temperature of the insulating paper.

[0097] Example 2

[0098] The present invention also relates to a system for constructing a temperature-frequency domain dielectric spectrum of insulating paper, comprising a memory and a processor, wherein the memory stores a computer program, and the processor implements the steps of the above method when executing the computer program.

[0099] The system can be installed on computing devices such as desktop computers, notebooks, PDAs and cloud servers. The processor can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The memory can be used to store computer programs and / or modules, and the processor can run or execute computer programs and / or modules stored in the memory, as well as call data stored in the memory, to realize various functions of the electronic device.

[0100] Example 3

[0101] The present invention also relates to a computer-readable storage medium having a computer program stored thereon, which implements the steps of the above method when the computer program is executed by a processor.

[0102] Specifically, the memory may include a high-speed random access memory, and may also include a non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), at least one disk storage device, a flash memory device, or other volatile solid-state storage device.

[0103] Example 4

[0104] In this embodiment, a 1 mm thick unbleached sulfate wood pulp kraft insulation paper sample is selected, and the insulation paper sample is placed in a vacuum drying oven and dried at 90 ° C and 50 Pa for 24 hours to remove residual moisture. After drying, the sample is placed in a room temperature environment to absorb moisture, and a high-precision balance is used to monitor the mass change in real time until the moisture content reaches 1.1%. The sample after moisture absorption is then placed in a three-electrode test device and the container is sealed to ensure that the moisture content of the sample remains unchanged during the test. Subsequently, the sealed container containing the insulation paper sample is placed in a constant temperature box, a target temperature is set and maintained for 12 hours to allow the sample to fully reach temperature equilibrium. Then, a frequency domain dielectric spectrometer is used to measure the dielectric spectrum ε of the insulation paper. * mea (ω), get its real part ε' mea (ω) and the imaginary part ε” mea(ω) data. After the measurement is completed, change the temperature of the constant temperature box in turn, repeat the above steps, and measure and record the frequency domain dielectric spectrum data of the insulating paper at 135℃, 105℃, 75℃, 45℃, 15℃, -15℃, -45℃, and -75℃ respectively. The schematic diagram of the experimental setup is shown in the figure. Figure 2 As shown in FIG, it includes a sealed container, a constant temperature box, a frequency domain dielectric spectrometer and a three-electrode test device. The dielectric spectrum test results of the insulating paper with a moisture content of 1.1% at different temperatures are shown in FIG. Figure 3 As shown, (a) is the real part data of the dielectric spectrum at different temperatures, and (b) is the imaginary part data of the dielectric spectrum at different temperatures.

[0105] The complex dielectric response prediction model of the insulating paper proposed in the present invention is constructed.

[0106] Then, the particle swarm algorithm is used to solve:

[0107] First, set the particle swarm size N = 50, each particle represents a set of possible model parameters, a total of 29 parameters. Randomly generate the initial position X of each particle n and initial velocity V n , and set the inertia weight w (initial value is 0.9, dynamic adjustment range is 0.4 to 0.9), cognitive factor k1 = 2.0 and social factor k2 = 2.0. For each particle, calculate the objective function value (fitness value) according to its current position and update the individual optimal position P n and the global optimal position P g According to the improved particle swarm optimization update rule, the inertia weight w is dynamically adjusted, and the speed and position of each particle are updated as follows:

[0108]

[0109] Among them, j is the current iteration number, r1 and r2 are random numbers in the interval [0,1], and w max and w min are the maximum and minimum values ​​of the inertia weight, j max is the maximum number of iterations;

[0110] If the fitness value is less than the preset threshold (10 -8 ) or the global optimal position P g Change is less than a certain range (10 -7 ), then stop the iteration and output the global optimal position P g , thus obtaining the optimal parameters of the model, as shown in Table 1;

[0111] By using the optimal parameters shown in Table 1 and substituting them into the prediction model, the dielectric spectrum data that varies with temperature and frequency can be reconstructed, thus obtaining the following: Figure 4The complete temperature-frequency domain dielectric spectrum of the insulating paper is shown, where (a) is the real part change surface of the dielectric spectrum and (b) is the imaginary part change surface of the dielectric spectrum.

[0112] Table 1

[0113]

[0114] Further spectrum measurements were performed at 60°C for verification. The constructed temperature-frequency domain dielectric spectrum was used to reconstruct the broadband dielectric response of the insulating paper at 60°C, and the model calculation values ​​were compared and analyzed with the measured results. Figure 5 Comparisons of the broadband dielectric response curves output by the model for an insulating paper sample at 60°C with measured data are shown, with (a) comparing the real part of the complex permittivity and (b) comparing the imaginary part. The figures show a high degree of agreement between the calculated and measured values ​​across the low- to high-frequency range, and the calculated and measured spectra agree well, validating the accuracy of the constructed temperature-frequency domain dielectric spectrum.

[0115] In general, the present invention provides a method for constructing a temperature-frequency domain dielectric spectrum of an insulating paper, by building an insulating paper complex dielectric response prediction model, it is possible to quickly and accurately obtain the insulating paper dielectric spectrum at any different temperatures based on only relying on a small amount of experimental data. The prediction model constructed by the present invention can more comprehensively reflect the dielectric properties of insulating paper at different temperatures, reduce the error of insulating paper temperature normalization, provide the analytical ability of a better insulating paper relaxation process, provide a reliable theoretical basis for the performance evaluation of subsequent insulating paper, and have a wide range of engineering application value. The temperature-frequency domain dielectric spectrum of the present invention not only provides efficient data acquisition path for laboratory research, but also provides a data basis for further studying the dielectric properties of insulating paper at different temperatures.

[0116] The technical features of the above embodiments can be combined in any manner. To simplify the description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification. It should be noted that the phrases "in one embodiment", "for example", "and another example", etc. of the present invention are intended to illustrate the present invention and are not intended to limit the present invention.

[0117] The above embodiments merely illustrate several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, and all such variations and improvements fall within the scope of protection of the present invention.

Claims

1. A method for constructing a temperature-frequency domain dielectric spectrum of insulating paper, characterized in that: include: Obtaining sample parameters of multiple groups of insulating paper samples and the measured complex dielectric response under each group of sample parameters, wherein the sample parameters include the temperature of the sample and the frequency of the external electric field when the complex dielectric response of the sample is measured; Inputting each set of sample parameters into a complex dielectric response prediction model for insulating paper; the complex dielectric response prediction model characterizes the complex dielectric response of the insulating paper by at least including the optical frequency dielectric constant, the complex dielectric response of the jump conductance process, and the superposition of the complex dielectric responses of three relaxation polarization processes; wherein the relationship between the jump conductivity and temperature in the jump conductance process and the relationship between the relaxation time coefficient and temperature in each relaxation polarization process all satisfy the Arrhenius equation, the relationship between the relaxation polarization intensity and temperature in each relaxation polarization process and the relationship between the shape parameter of the jump conductance process and each relaxation polarization process and temperature all satisfy that the former increases with increasing temperature and gradually approaches saturation; With the optimization goal of minimizing the deviation between the complex dielectric response predicted by the prediction model and the measured complex dielectric response under the same sample parameters, the model parameters in the complex dielectric response prediction model are optimized, and the relationship between the complex dielectric response of the insulating paper and the temperature and frequency is obtained as the temperature-frequency domain dielectric spectrum of the insulating paper.

2. The construction method according to claim 1, wherein The expression of the complex dielectric response of insulating paper is: Where, ε * paper (ω,T) is the complex dielectric response of the insulating paper with ω and T as variables, ε ∞ is the optical frequency dielectric constant, ε * hop (ω,T) is the complex dielectric response of the jump conductance process with ω and T as variables, σ hop (T) is the temperature function of the jump conductivity, ε0 ​​is the vacuum dielectric constant, s(T) is the temperature function of the shape parameter of the jump conductivity process, ε * pi (ω,T) is the complex dielectric response of the ith relaxation polarization process with ω and T as variables, Δε i (T), τ i (T) are the temperature functions of the relaxation polarization intensity and the relaxation time coefficient in the i-th relaxation polarization process, respectively. i (T), β i (T) are the temperature functions of the low-frequency slope shape parameters and high-frequency slope shape parameters in the i-th relaxation polarization process, respectively.

3. The construction method according to claim 1, wherein The relationship between the jump conductivity and temperature in the jump conductivity process satisfies the Arrhenius equation, and the relationship is: Where T is temperature, σ hop (T) is the temperature function of the jump conductivity, σ inf is the jump conductivity when T approaches infinity, W hop is the activation energy of the jump conductivity process, k B is the Boltzmann constant, and σ in the above relationship inf and W hop are the model parameters to be optimized.

4. The construction method according to claim 1, wherein The relationship between the relaxation time coefficient and temperature in each relaxation polarization process satisfies the Arrhenius equation, which is: Where T is temperature, τ i (T) is the temperature function of the relaxation time coefficient in the i-th relaxation polarization process, i = 1, 2, 3, τ inf_i is the relaxation time when T approaches infinity in the ith relaxation polarization process, W pi is the activation energy of the ith relaxation polarization process, k B is the Boltzmann constant, and τ in the above relationship inf_i and W pi are the model parameters to be optimized.

5. The construction method according to claim 1, wherein: The relationship between the relaxation polarization intensity of each relaxation polarization process and the shape parameters of the jump conductivity process and each relaxation polarization process and temperature is as follows: Where T is temperature, Δε i (T) is the temperature function of the relaxation polarization intensity in the i-th relaxation polarization process, Δε inf_i is the relaxation polarization intensity when T approaches infinity in the ith relaxation polarization process, b i is the temperature function Δε i The unknown coefficient in (T); s(T) is the temperature function of the shape parameter of the jump conductivity process, s inf is the shape parameter when T approaches infinity during the jump conductance process, a is the undetermined coefficient in the temperature function s(T); i (T), β i (T) are the temperature functions of the low-frequency slope shape parameters and high-frequency slope shape parameters in the i-th relaxation polarization process, α inf_i , β inf_i are the low-frequency slope shape parameter and high-frequency slope shape parameter when T approaches infinity in the ith relaxation polarization process, c i d i is the unknown coefficient, Δε in the above relationship inf_i 、b i 、s inf ,a,α inf_i , β inf_i and c i d i are the model parameters to be optimized.

6. The construction method according to claim 1, wherein: The expression of the optimization objective is: Where Φ is the deviation between the predicted complex dielectric response and the measured complex dielectric response, ε' model (ω,T) and ε” model (ω,T) are the real and imaginary parts of the complex dielectric response of the insulating paper at the angular frequency ω predicted by the prediction model, respectively. ε' mea (ω,T) and ε” mea (ω,T) are the real and imaginary parts of the complex dielectric response of the insulating paper at the measured temperature T at the angular frequency ω.

7. The construction method according to claim 1, wherein: The optimization algorithm used to optimize the model parameters in the complex dielectric response prediction model is any one of the algorithms such as simulated annealing algorithm, genetic algorithm, particle swarm optimization, etc.

8. The construction method according to claim 1, wherein: Among the sample parameters of all insulating paper samples, the temperature of the samples was uniformly sampled in the range of -75°C to 135°C.

9. A system for constructing a temperature-frequency domain dielectric spectrum of insulating paper, comprising a memory and a processor, wherein the memory stores a computer program, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 8 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

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