A method for establishing an equivalent model of broadband dielectric response of transformer oil

Abstract

The application provides a transformer oil broadband dielectric response equivalent model establishment method, and belongs to the electrical engineering field.The method comprises the following steps: S1: transformer oil sample preparation;S2: transformer oil frequency domain dielectric spectrum measurement;S3: transformer polarization current measurement;S4: according to the frequency domain dielectric spectrum measurement data, a double-branch extended Debye model of the transformer oil is established;S5: according to the established double-branch extended Debye model, combined with the polarization current measurement data, a three-branch extended Debye model of the transformer oil is established.The application can accurately model the dielectric response of the transformer oil in a wide frequency range, realize the quantitative description of the frequency dielectric characteristics of the transformer oil, and has important significance for more comprehensively understanding the conductivity and polarization characteristics.

Description

Technical Field

[0001] This invention relates to the field of electrical engineering, specifically to a method for establishing an equivalent model of the broadband dielectric response of transformer oil. Background Technology

[0002] Transformer oil is a crucial component of the insulation in oil-immersed power transformers. It both impregnates the insulating paper, increasing its insulating strength, and exists as a separate oil channel, serving functions of insulation, cooling, and arc extinguishing. During long-term operation, transformer oil gradually deteriorates due to the influence of moisture, oxygen, heat, electricity, and mechanical factors, resulting in corresponding changes in its dielectric properties.

[0003] Regarding the dielectric properties of transformer oil, it is generally accepted that transformer oil is a weakly polar dielectric, and its complex permittivity can be simplified to a real part that is constant at 2.2, while the imaginary part is determined by the DC conductivity σ0, which is σ0 / ε0ω. However, this simplified dielectric response model function cannot reflect the relaxation characteristics exhibited by transformer oil in specific frequency bands. Furthermore, when the frequency band is very wide, transformer oil exhibits complex dielectric properties resulting from the superposition of conductivity and polarization processes. Therefore, it is necessary to construct a new dielectric response model function to quantitatively describe the broadband dielectric response of transformer oil. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a method for establishing an equivalent model of the broadband dielectric response of transformer oil. A two-branch extended Debye model is established by measuring the frequency domain dielectric spectrum of the transformer oil, and then a three-branch extended Debye model is established by combining the polarization current.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A method for establishing an equivalent model of the broadband dielectric response of transformer oil includes the following steps:

[0007] S1: Prepare transformer oil samples;

[0008] S2: Measure the frequency domain dielectric spectrum of the transformer oil sample prepared in step S1;

[0009] S3: Measure the transformer oil polarization current of the transformer oil sample prepared in step S1.

[0010] S4: Based on the frequency domain dielectric spectrum of the transformer oil obtained in step S2, establish a two-branch extended Debye model of the transformer oil.

[0011] S5: Based on the dual-branch extended Debye model established in step S4, and combined with the transformer oil polarization current measured in step S3, establish the three-branch extended Debye model of the transformer oil.

[0012] Furthermore, S1 specifically involves: vacuum filtering the transformer oil using a vacuum oil filter machine with a vacuum degree of -0.099 MPa and a heating temperature of 80°C. After vacuum degassing, a certain amount of water is injected into the oil, stirred evenly, sealed, and placed in a constant temperature chamber at 45°C to allow the water to fully dissolve in the oil. Then, the oil is cooled to room temperature for storage.

[0013] Furthermore, S2 specifically involves: taking approximately 25 ml of treated transformer oil and placing it into a liquid electrode, removing air from the oil by vacuuming at room temperature, sealing the liquid electrode and placing it in a constant temperature chamber to measure its frequency domain dielectric spectrum, including the real and imaginary parts of the complex dielectric constant, with a frequency measurement range of 1 mHz-1 kHz.

[0014] Furthermore, S4 specifically includes:

[0015] S41: The double-branch extended Debye model shown in Equation (1) is adopted as the basic model. Based on this model, the model consists of infinite frequency dielectric constant, DC conductance and two Debye relaxation polarization processes.

[0016]

[0017] Where, ε * (ω) is the complex permittivity of the transformer oil and its frequency domain dielectric spectrum, where ω is the angular frequency and ε is the dielectric constant. ∞ ε0 is the optical frequency dielectric constant, σ0 is the vacuum dielectric constant, Δε1 and Δε2 are the dielectric relaxation intensities, and τ1 and τ2 are the relaxation time constants.

[0018] S42: Construct the objective function as shown in Equation (2) for parameter identification of the dual-branch extended Debye model. The purpose of parameter identification is to calculate all dielectric parameters in the model except for the angular frequency, so that the error between the calculated spectrum obtained according to Equation (1) and the measured spectrum is minimized.

[0019]

[0020] Where, ε' 拟合 and ε' 测量 The real parts of the complex permittivity, ε”, are obtained by fitting the model function and by measurement, respectively. 拟合 and ε” 测量 These are the imaginary parts of the complex permittivity obtained by fitting a model function and by actual measurement, respectively.

[0021] S43: Using the least squares method, the frequency domain dielectric spectrum of the transformer oil obtained in S2 is used to solve the above objective function (2) to obtain the parameter values ​​of the double-branch extended Debye model of the transformer oil.

[0022] Furthermore, S5 specifically includes:

[0023] S51: The polarization current of the transformer oil obtained in S3 is fitted using equation (3) using least squares fitting:

[0024]

[0025] The values ​​of parameters τ1 and τ2 are taken from the values ​​of parameters τ1 and τ2 in the two-branch extended Debye model obtained in S4, and the values ​​of A1 and A2 are determined by the parameters Δε1, Δε2, τ1, and τ2 in the two-branch extended Debye model obtained in S4.

[0026]

[0027] Where U0 is the polarization voltage and C0 is the geometric capacitance of the liquid electrode;

[0028] S52: By fitting the parameters A0, A3, and τ3, a three-branch extended Debye model of transformer oil is constructed, the expression of which is as follows:

[0029]

[0030] Where the model parameter ε ∞ The values ​​of Δε1, Δε2, τ1, and τ2 are taken from the corresponding parameters of the two-branch extended Debye model obtained in S4. The parameters σ0 and Δε3 can be calculated using the following formula:

[0031]

[0032] Furthermore, the three-branch extended Debye model in S5 is used to accurately and quantitatively describe the broadband dielectric properties of transformer oil in the 0-1kHz frequency range.

[0033] The beneficial effects of this invention are as follows: Based on the measured frequency domain dielectric spectrum and polarization current, this invention can obtain an equivalent model of the broadband dielectric response of transformer oil. This model can accurately and quantitatively describe the dielectric characteristics of transformer oil in a wide frequency range of 0-1kHz, which is of great significance for a more comprehensive understanding of its conductivity and polarization characteristics. Attached Figure Description

[0034] Figure 1 This is the frequency domain dielectric spectrum of transformer oil obtained by measurement according to an embodiment of the present invention;

[0035] Figure 2 The transformer oil polarization current measured according to the embodiments of the present invention;

[0036] Figure 3 This is the frequency domain dielectric spectrum of the result of broadband dielectric response modeling of transformer oil provided in the embodiments of the present invention;

[0037] Figure 4 The polarization current is the result of broadband dielectric response modeling of transformer oil provided in the embodiments of the present invention. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] This invention provides a method for establishing an equivalent model of the broadband dielectric response of transformer oil, the method comprising the following steps:

[0040] S1: Preparation of transformer oil samples;

[0041] This invention uses No. 25 transformer oil produced in Karamay as the test object. The transformer oil is vacuum filtered using a vacuum oil filter machine at a vacuum degree of -0.099 MPa and a heating temperature of 80℃. After vacuum degassing treatment, its moisture content is measured to be 8.9 ppm.

[0042] S2: Measurement of the frequency domain dielectric spectrum of transformer oil;

[0043] Take about 25ml of the treated transformer oil and put it into the liquid electrode. After removing the air from the oil by vacuuming at room temperature, seal the liquid electrode and place it in a constant temperature chamber at 45℃ for 12 hours. Then measure its frequency domain dielectric spectrum, including the real and imaginary parts of the complex dielectric constant. The effective voltage value is 140V and the frequency measurement range is 1mHz-1kHz. Figure 1 The results of frequency domain dielectric spectrum measurements are shown.

[0044] S3: Measurement of transformer oil polarization current;

[0045] After the frequency domain dielectric spectrum measurement was completed, the high and low voltage electrodes of the liquid were short-circuited to depolarize the transformer oil for 2 hours. Then, the polarization current was measured. The polarization voltage was 140V and the polarization time was 3600s. Figure 2 The results of the polarization current measurement are shown.

[0046] S4: Based on the frequency domain dielectric spectrum measurement data, establish a two-branch extended Debye model for transformer oil;

[0047] The measured frequency domain dielectric spectrum is modeled according to the dual-branch extended Debye model as shown in equation (1), and the model parameters are solved by the least squares method:

[0048]

[0049] Where, ε * (ω) is the complex permittivity of the transformer oil and its frequency domain dielectric spectrum, where ω is the angular frequency and ε is the dielectric constant. ∞ ε is the optical frequency dielectric constant, ε0 is the vacuum dielectric constant, σ0 is the DC conductivity, Δε1 and Δε2 are the dielectric relaxation intensities, and τ1 and τ2 are the relaxation time constants.

[0050] The objective function is:

[0051]

[0052] Where, ε' 拟合 and ε' 测量 The real parts of the complex permittivity, ε”, are obtained by fitting the model function and by measurement, respectively. 拟合 and ε” 测量 These are the imaginary parts of the complex permittivity obtained by fitting a model function and by actual measurement, respectively.

[0053] Table 1 shows the parameters of the dual-branch extended Debye model obtained by modeling the frequency domain dielectric spectrum of transformer oil with a moisture content of 8.9 ppm using the present invention.

[0054] Table 1

[0055] <![CDATA[ε ∞ ]]> <![CDATA[σ0]]> <![CDATA[Δε1]]> <![CDATA[τ1]]> <![CDATA[Δε2]]> <![CDATA[τ2]]> 2.2 0.6pS / m 5.4 2.4 7.5 15.4

[0056] S5: Based on the established double-branch extended Debye model and combined with polarization current measurement data, a three-branch extended Debye model of transformer oil is established.

[0057] S51: The measured polarization current is fitted using equation (3) using least squares fitting:

[0058]

[0059] The values ​​of parameters τ1 and τ2 are taken from the values ​​of parameters τ1 and τ2 in the two-branch extended Debye model obtained in S4, and the values ​​of A1 and A2 are determined by the parameters Δε1, Δε2, τ1, and τ2 in the two-branch extended Debye model obtained in S4.

[0060]

[0061] Where U0 is the polarization voltage and C0 is the geometric capacitance of the liquid electrode.

[0062] S52: By fitting the parameters A0, A3, and τ3, a three-branch extended Debye model of transformer oil is constructed, the expression of which is as follows:

[0063]

[0064] Where the model parameter ε∞ Δε1, Δε2, τ1, and τ2 are the parameters of the two-branch extended Debye model obtained in S4. Parameters σ0 and Δε3 can be calculated using the following formula:

[0065]

[0066] Table 2 shows the parameters of the three-branch extended Debye model obtained by modeling the broadband dielectric response of transformer oil with a moisture content of 8.9 ppm using the present invention.

[0067] Table 2

[0068] <![CDATA[ε ∞ ]]> <![CDATA[σ0]]> <![CDATA[Δε1]]> <![CDATA[τ1]]> <![CDATA[Δε2]]> <![CDATA[τ2]]> <![CDATA[Δε3]]> <![CDATA[τ3]]> 2.2 0.4pS / m 5.4 2.4 7.5 15.4 3.1 102

[0069] The three-branch extended Debye model can accurately and quantitatively describe the broadband dielectric properties of transformer oil in the 0-1kHz frequency range. Figure 3 The frequency domain dielectric spectrum of the results of broadband dielectric response modeling of transformer oil provided by an embodiment of the present invention is shown. Figure 4 The polarization current is shown as the result of broadband dielectric response modeling of transformer oil provided in this embodiment of the invention. The frequency domain dielectric spectrum fitting value and the polarization current fitting value of the model function agree well with the corresponding measured values, verifying the accuracy of the model function.

[0070] 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 variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for establishing an equivalent model of broadband dielectric response of transformer oil, characterized in that, The method comprises the following steps: S1: preparing a transformer oil sample; S2: measuring the frequency domain dielectric spectrum of the transformer oil sample prepared in step S1; S3: measuring the polarization current of the transformer oil sample prepared in step S1; S4: establishing a double-branch extended Debye model of the transformer oil according to the frequency domain dielectric spectrum measured in step S2; S5: establishing a three-branch extended Debye model of the transformer oil according to the double-branch extended Debye model established in step S4 and the polarization current measured in step S3; The S4 specifically comprises: S41: taking the double-branch extended Debye model as shown in formula (1) as a basic model, which is composed of an infinite frequency dielectric constant, a direct current conductance and two Debye relaxation polarization processes; （1）； wherein ɛ * (ω) is the complex permittivity frequency domain dielectric spectroscopy of the transformer oil, ω is the angular frequency, ɛ ∞ is the optical frequency dielectric constant, ε0 is the vacuum permittivity, σ0 is the direct current conductivity, Δε1 and Δε2 are the dielectric relaxation strengths, τ1 and τ2 are the relaxation time constants; S42: constructing a target function as shown in formula (2) for parameter identification of the double-branch extended Debye model, and 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 frequency spectrum and the measured frequency spectrum according to formula (1) is minimized; （2）； wherein, and are the real parts of the complex dielectric constant fitted and measured, respectively, using a model function, and are the imaginary parts of the complex dielectric constant fitted and measured, respectively, using a model function. S43: using the least square method, the frequency domain dielectric spectrum of the transformer oil obtained in S2 is used to solve the above target function (2) to obtain the parameter values of the double-branch extended Debye model of the transformer oil; The S5 specifically comprises: S51: performing least square fitting on the polarization current of the transformer oil obtained in S3 by using formula (3): （3）； Wherein the values of parameters τ1 and τ2 are the values of parameters τ1 and τ2 in the double-branch extended Debye model obtained in S4, and the values of A1 and A2 are determined by the parameters Δε1, Δε2, τ1 and τ2 of the double-branch extended Debye model obtained in S4: 、 ； Wherein U0 is the polarization voltage, and C0 is the liquid electrode geometric capacitance; S52: fitting to obtain parameters A0 and A3 and τ3, thereby constructing a three-branch extended Debye model of the transformer oil, and the expression is as follows: （4）； where the model parameters ɛ ∞ The values of the model parameters ɛ 0, Δɛ1, Δɛ2, τ1, τ2 are taken from the values of the corresponding parameters of the two-branch extended Debye model obtained in S4, and the parameters σ0and Δɛ3are obtained by calculating according to the following formula: 、 。 2. The method of claim 1, wherein the method further comprises: The S1 specifically comprises: vacuum filtering the transformer oil by a vacuum oil filter, the vacuum degree is-0.099 Mpa, the heating temperature is 80 DEG C, after vacuum degassing treatment, a certain amount of water is injected into the oil, stirred uniformly, sealed, and placed in a constant temperature box at 45 DEG C to make the water fully dissolved in the oil, and then cooled to room temperature for preservation.

3. The method of claim 1, wherein the method further comprises: The S2 specifically comprises: taking 25 ml of the treated transformer oil into a liquid electrode, removing the air in the oil after vacuumizing at room temperature, sealing the liquid electrode and placing it in a constant temperature box to measure its frequency domain dielectric spectrum, including the real part and the imaginary part of the complex dielectric constant, and the frequency measurement range is 1 mHz-1 kHz.

4. The method of claim 1, wherein the method further comprises: The three-branch extended Debye model in S5 is used to accurately and quantitatively describe the wide frequency dielectric characteristics of the transformer oil in the frequency range of 0-1 kHz.

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