A method for establishing a model function for broadband dielectric response of oil-paper insulation

Abstract

The present invention provides a method for establishing a model function for the broadband dielectric response of oil-paper insulation, belonging to the field of electrical engineering. The method comprises: preparing oil-paper insulation samples; measuring the dielectric response in frequency domains at different temperatures; obtaining the broadband dielectric response; establishing a model function; and verifying the model function. The present invention can measure the broadband dielectric response of oil-paper insulation and establish an equivalent model function thereof, providing a digital and quantitative analysis method for the broadband dielectric characteristics of oil-paper insulation. Compared with the currently available dielectric response equivalent model method, the model function can reflect the dielectric characteristics of oil-paper insulation in a wider frequency domain and provide characteristic parameters with more physical meaning, providing a preliminary foundation for further quantitative evaluation of the oil-paper insulation status based on dielectric response.

Description

Technical Field

[0001] The present invention relates to the field of electrical engineering, and in particular to a method for establishing a model function of a broadband dielectric response of oil-paper insulation. Background Art

[0002] Oil-paper insulation, a mature and reliable insulating material with excellent heat dissipation, stable insulation properties, and low cost, is widely used in the insulation of oil-immersed electrical equipment such as transformers. The condition of oil-paper insulation is a key factor affecting the safe and stable operation of electrical equipment and the entire power grid. Accurate and effective assessment of its insulation condition is of great significance to ensuring the safety and economic viability of the power grid. Frequency domain spectroscopy (FDS), based on dielectric response, is widely used in oil-paper insulation condition monitoring due to its rich information, strong anti-interference capabilities, and non-destructive testing capabilities.

[0003] The frequency-domain dielectric response of oil-paper insulation is affected by factors such as moisture content, degree of aging, and temperature. By establishing a relationship between dielectric characteristics and insulation status, the insulation status of oil-paper can be evaluated. Dielectric models are an effective means of quantitatively describing the frequency-domain dielectric properties of insulation, and their corresponding model parameters are also widely used for quantitative evaluation of the insulation status of oil-paper. However, oil-paper insulation is a non-uniform phase composite material, and its frequency-domain dielectric properties are composed of the superposition of multiple dielectric response processes. The wider the frequency band, the more complex the dielectric properties exhibited, and a single model function is difficult to describe its complete dielectric properties. Therefore, it is necessary to construct a new dielectric model function to quantitatively describe the dielectric response of oil-paper insulation in a wider frequency domain. Summary of the Invention

[0004] In light of this, the present invention aims to provide a method for establishing a model function for the broadband dielectric response of oil-paper insulation. This method measures the frequency-domain dielectric response data of the oil-paper insulation under test at different temperatures. Based on the temperature-shift characteristics of the spectrum, the broadband dielectric properties of the oil-paper insulation are derived. A corresponding dielectric model function is then established, and the model function parameters are calculated, thereby achieving a quantitative description of the broadband dielectric response of the oil-paper insulation.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A method for establishing a model function of a broadband dielectric response of oil-paper insulation comprises the following steps:

[0007] S1: Preparation of oil-paper insulation samples;

[0008] S2: measuring the frequency domain dielectric response of the oil-paper insulation sample prepared in step S1 at different temperatures;

[0009] S3: Obtaining a broadband dielectric response based on the frequency domain dielectric responses at different temperatures obtained in step S2;

[0010] S4: constructing a dielectric model function, constructing an objective function to perform parameter identification on the dielectric model function parameters, and solving the objective function using the broadband dielectric response data obtained in step S3 to obtain dielectric model parameter values ​​of oil-paper insulation;

[0011] S5: Verify the dielectric model function obtained in S4.

[0012] Furthermore, the S1 is specifically:

[0013] S11: Place the insulating paper in a vacuum drying oven at a temperature of 90° C. and a vacuum degree of 50 Pa for drying and degassing for 48 hours;

[0014] S12: The insulating oil is vacuum filtered using a vacuum oil filter with a vacuum degree of -0.099 MPa and a heating temperature of 80° C.

[0015] S13: Immerse the insulating paper in oil in a vacuum drying oven at a temperature of 45° C. and a vacuum degree of 50 Pa for 48 hours;

[0016] S14: Place the prepared dry sample on a precision electronic balance to absorb moisture naturally, and control the moisture content by monitoring the change in sample mass.

[0017] Furthermore, the S2 is specifically:

[0018] S21: Place the prepared oil-paper insulation sample into a sealed three-electrode device and place it in a constant temperature box to measure the frequency domain dielectric response. The frequency measurement range is 1mHz-10kHz.

[0019] S22: Measure the frequency domain dielectric response of oil-paper insulation at temperatures of 45°C, 15°C, -15°C, and -45°C in sequence.

[0020] Furthermore, S3 is specifically as follows: taking the frequency domain dielectric response curve of oil-paper insulation at a temperature of -45°C as a reference, the spectrum curves at other temperatures are shifted as a whole toward the low frequency direction until they overlap with each other. The obtained overlapping curve is the broadband dielectric response of oil-paper insulation. The basis for this is that the frequency domain dielectric response of oil-paper insulation has a temperature frequency shift characteristic and satisfies the following formula:

[0021]

[0022] Among them, f0 corresponds to the frequency at temperature T0, f1 corresponds to the frequency at temperature T1, k is the Boltzmann constant, E a is the activation energy of oil-paper insulation.

[0023] Furthermore, the S4 is specifically:

[0024] Based on the existing single dielectric process model, the dielectric model function shown in formula (1) is constructed. The model function is composed of the optical frequency dielectric constant, the hopping conductance and the two relaxation polarization processes. The model function expression is:

[0025]

[0026] Among them, ε * (ω) is the frequency domain dielectric response of oil-paper insulation, ω is the angular frequency, ε ∞ is the optical frequency dielectric constant, σ ho is the jump conductivity, s is the shape parameter of the jump conductivity process, Δε1 and Δε2 are the dielectric relaxation strengths, τ1 and τ2 are the relaxation time constants, and α and β are the relaxation time distribution parameters;

[0027] The objective function shown in formula (2) is constructed for parameter identification of the dielectric model function. The purpose of parameter identification is to calculate all dielectric parameters in the model except the angular frequency so that the error between the calculated spectrum obtained according to formula (1) and the measured spectrum is minimized. The objective function is:

[0028]

[0029] Among them, ε' 拟合 and ε' 测量 are the real part of the complex dielectric constant fitted by the model function and measured, ε” 拟合 and ε” 测量 are the imaginary parts of the complex dielectric constant fitted by the model function and measured respectively;

[0030] The least squares method is used to solve the objective function (2) using the broadband dielectric response data obtained in S3 to obtain the dielectric model parameter values ​​of oil-paper insulation.

[0031] Furthermore, the S5 specifically includes: reconstructing the broadband dielectric response of the oil-paper insulation using the model function, and comparing it with the measured results to verify the accuracy of the model function.

[0032] The beneficial effects of the present invention are that the present invention can obtain the broadband dielectric properties of oil-paper insulation, and use a new dielectric model function to decouple and analyze its complex dielectric process, thereby achieving a quantitative description of the broadband dielectric response of oil-paper insulation. Compared with the currently available dielectric response equivalent model method, the model function can reflect the dielectric properties of oil-paper insulation in a wider frequency domain and provide characteristic parameters with more physical meaning, providing a preliminary foundation for further realizing the quantitative evaluation of the oil-paper insulation status based on dielectric response. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1The real part and imaginary part of the complex dielectric constant are obtained by measuring an oil-paper insulation sample with a moisture content of 4.6% at different temperatures according to an embodiment of the present invention;

[0034] Figure 2 The broadband dielectric response spectrum of an oil-paper insulation sample with a moisture content of 4.6% obtained by temperature frequency shift according to an embodiment of the present invention;

[0035] Figure 3 These are the real and imaginary parts of the complex dielectric constant used to model the broadband dielectric response of an oil-paper insulation sample with a moisture content of 4.6%, provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0036] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0037] An embodiment of the present invention provides a method for establishing a model function of a broadband dielectric response of oil-paper insulation, comprising the following steps:

[0038] S1: Preparation of oil-paper insulation samples;

[0039] The present invention uses 1mm thick ordinary kraft wood pulp kraft insulation paperboard and 25# mineral oil as test materials. The paperboard is dried and degassed in a vacuum drying oven at 90°C and a vacuum level of 50 Pa for 48 hours. The mineral oil is then filtered using a vacuum oil filter at a vacuum level of -0.099 MPa and a heating temperature of 80°C. After drying and degassed, the paperboard is immersed in the mineral oil in a vacuum drying oven at 45°C and a vacuum level of 50 Pa for 48 hours. After oil immersion, it is placed indoors to naturally absorb moisture, resulting in an oil-paper insulation sample with a moisture content of 4.6%.

[0040] S2: Measurement of frequency domain dielectric response at different temperatures;

[0041] The prepared oil-paper insulation sample was placed in a sealed three-electrode apparatus in a constant temperature chamber, and the frequency domain dielectric response was measured over a frequency range of 1mHz-10kHz. The frequency domain dielectric response of the oil-paper insulation sample was measured at temperatures of 45°C, 15°C, -15°C, and -45°C. Temperature equilibrium was confirmed by measuring the frequency domain dielectric response at one-hour intervals until the frequency domain dielectric response remained stable. Figure 1The real and imaginary parts of the complex dielectric constant of the oil-paper insulation sample with a moisture content of 4.6% measured at different temperatures are shown.

[0042] S3: Acquisition of broadband dielectric response;

[0043] Taking the frequency domain dielectric response curve of oil-paper insulation at -45℃ as the benchmark, the spectrum curves at other temperatures are moved toward the low frequency direction until they overlap with each other. The overlapping curves obtained are the broadband dielectric response of oil-paper insulation, such as Figure 2 shown.

[0044] S4: establishment of model function;

[0045] Based on the existing single dielectric process model, the dielectric model function shown in formula (1) is constructed. The model function is composed of the optical frequency dielectric constant, the hopping conductance and the two relaxation polarization processes. The model function expression is:

[0046]

[0047] Among them, ε * (ω) is the frequency domain dielectric response of oil-paper insulation, ω is the angular frequency, ε ∞ is the optical frequency dielectric constant, σ ho is the jump conductivity, s is the shape parameter of the jump conductivity process, Δε1 and Δε2 are the dielectric relaxation strengths, τ1 and τ2 are the relaxation time constants, and α and β are the relaxation time distribution parameters;

[0048] The objective function shown in formula (2) is constructed for parameter identification of the dielectric model function. The purpose of parameter identification is to calculate all dielectric parameters in the model except the angular frequency so that the error between the calculated spectrum obtained according to formula (1) and the measured spectrum is minimized. The objective function is shown in formula (2):

[0049]

[0050] Among them, ε' 拟合 and ε' 测量 are the real part of the complex dielectric constant fitted by the model function and measured, ε″ 拟合 and ε″ 测量 are the imaginary parts of the complex dielectric constant fitted by the model function and measured respectively.

[0051] The least squares method is used to solve the objective function (2) using the broadband dielectric response data obtained in S3 to obtain the dielectric model parameter values ​​of oil-paper insulation.

[0052] Table 1 shows the parameter values ​​of the model function for modeling the broadband dielectric response data of the oil-paper insulation sample with a moisture content of 4.6% using the present invention:

[0053] Table 1

[0054] <![CDATA[ε ∞ ]]> 3.351076384 <![CDATA[σ ho (S / m)]]> <![CDATA[10 -14.523743103 ]]> s 0.852155144 <![CDATA[Δε1]]> 60.002593475 <![CDATA[τ1(s)]]> <![CDATA[10 5.347057149 ]]> <![CDATA[α1]]> 0.735610322 <![CDATA[β1]]> 0.835656937 <![CDATA[Δε2]]> 1.754150804 <![CDATA[τ2(s)]]> <![CDATA[10 -4.442454696 ]]> <![CDATA[α2]]> 0.340313542 <![CDATA[β2]]> 0.851096472

[0055] The model function includes the optical frequency dielectric constant, the hopping conductivity process and two relaxation polarization processes. Figure 3 The model function fitting values ​​of the broadband dielectric response of the oil-paper insulation sample with a moisture content of 4.6% are shown, as well as the real and imaginary components of the complex dielectric constant of each dielectric process.

[0056] S5: verification of model function;

[0057] The established model function is used to reconstruct the broadband dielectric response of oil-paper insulation and compared with the measured results. Figure 3 The comparison between the model function fitting value and the measured value of the broadband dielectric response of the oil-paper insulation sample with a moisture content of 4.6% is shown. The model function fitting value is in good agreement with the measured value, which verifies the accuracy of the model function.

[0058] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A method for establishing a model function for the broadband dielectric response of oil-paper insulation, characterized in that: The following steps are involved: S1: Preparation of oil-paper insulation samples; S2: measuring the frequency domain dielectric response of the oil-paper insulation sample prepared in step S1 at different temperatures; S3: Obtaining a broadband dielectric response based on the frequency-domain dielectric responses at different temperatures obtained in step S2; the different temperatures include 45° C., 15° C., -15° C., and -45° C.; S4: constructing a dielectric model function, constructing an objective function to perform parameter identification on the dielectric model function parameters, and solving the objective function using the broadband dielectric response data obtained in step S3 to obtain dielectric model parameter values ​​of oil-paper insulation; S5: verify the dielectric model function obtained in S4; Specifically, S3 is as follows: taking the frequency domain dielectric response curve of oil-paper insulation at a temperature of -45°C as a reference, the spectrum curves at other temperatures are shifted toward the low frequency direction until they overlap with each other. The overlapping curves obtained are the broadband dielectric response of oil-paper insulation; The S4 is specifically: Based on the existing single dielectric process model, the dielectric model function shown in formula (1) is constructed. The model function is composed of the optical frequency dielectric constant, the hopping conductance and the two relaxation polarization processes. The model function expression is: （1）； Among them, ε * (ω) is the frequency domain dielectric response of oil-paper insulation, ω is the angular frequency, ε ∞ is the optical frequency dielectric constant, σ ho is the jump conductivity, s is the shape parameter of the jump conductivity process, Δε1 and Δε2 are the dielectric relaxation strengths, τ1 and τ2 are the relaxation time constants, and α and β are the relaxation time distribution parameters; The objective function shown in formula (2) is constructed for parameter identification of the dielectric model function. The purpose of parameter identification is to calculate all dielectric parameters in the model except the angular frequency so that the error between the calculated spectrum obtained according to formula (1) and the measured spectrum is minimized. The objective function is: （2）； Among them, ε' 拟合 and ε' 测量 are the real part of the complex dielectric constant fitted by the model function and measured, ε'' 拟合 and ε'' 测量 are the imaginary parts of the complex dielectric constant fitted by the model function and measured respectively; The least squares method is used to solve the objective function (2) using the broadband dielectric response data obtained in S3 to obtain the dielectric model parameter values ​​of oil-paper insulation.

2. The method for establishing a model function for the broadband dielectric response of oil-paper insulation according to claim 1, characterized in that: The S1 is specifically: S11: Place the insulating paper in a vacuum drying oven at a temperature of 90° C. and a vacuum degree of 50 Pa for drying and degassing for 48 hours; S12: The insulating oil is vacuum filtered using a vacuum oil filter with a vacuum degree of -0.099 MPa and a heating temperature of 80° C. S13: Immerse the insulating paper in oil in a vacuum drying oven at a temperature of 45° C. and a vacuum degree of 50 Pa for 48 hours; S14: Place the prepared dry sample on a precision electronic balance to absorb moisture naturally, and control the moisture content by monitoring the change in sample mass.

3. The method for establishing a model function for the broadband dielectric response of oil-paper insulation according to claim 1, characterized in that: The S2 is specifically: S21: Place the prepared oil-paper insulation sample into a sealed three-electrode device and place it in a constant temperature box to measure the frequency domain dielectric response. The frequency measurement range is 1mHz-10kHz. S22: Measure the frequency domain dielectric response of oil-paper insulation at temperatures of 45°C, 15°C, -15°C, and -45°C in sequence.

4. The method for establishing a model function for the broadband dielectric response of oil-paper insulation according to claim 1, wherein: The obtained overlapping curve is the broadband dielectric response of oil-paper insulation. The basis is that the frequency domain dielectric response of oil-paper insulation has a temperature frequency shift characteristic and satisfies the following formula: ； Among them, f0 corresponds to the frequency at temperature T0, f1 corresponds to the frequency at temperature T1, k is the Boltzmann constant, E a is the activation energy of oil-paper insulation.

5. The method for establishing a model function for the broadband dielectric response of oil-paper insulation according to claim 1, characterized in that: The S5 specifically includes: reconstructing the broadband dielectric response of oil-paper insulation using the model function, and comparing it with the measured results to verify the accuracy of the model function.

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