Bezier curve-based main insulation frequency domain dielectric response calculation method for oil-immersed inverted current transformer

Abstract

The invention discloses an oil-immersed inverted current transformer main insulation frequency domain dielectric response calculation method based on a Bezier curve. The method comprises the following steps: firstly, reading design parameters of a main insulation structure of the oil-immersed inverted current transformer, wherein the design parameters comprise the length of an inner cylinder of head insulation, the radius of a cylinder at a corner, the length of each layer of insulation of a linear section and the radius of a shielding tube; and fitting the side curve of the main insulation triangular area of the mutual inductor by adopting a Bezier curve. And measuring the thickness and the total thickness of the insulating paper layer of the main insulation of the current transformer before oil immersion and after oil immersion, calculating an oil-paper insulation X model, and determining the quantitative relation of the complex relative dielectric constants among the insulating paper, the insulating oil and the composite insulation system. And obtaining the FDS calculation model of the main insulation of the mutual inductor based on the X model and the Bezier fitting curve. And carrying out complex capacitance measurement on the oil-immersed inverted current transformer prototype by using a dielectric response analysis tester. And finally, comparing a calculation result with actually measured data, and verifying the accuracy of the calculation model. According to the method, the limitation of a traditional test method is effectively overcome, and the accuracy of a mutual inductor FDS calculation model is improved.

Description

Technical Field

[0001] The present invention belongs to the field of electrical equipment insulation fault diagnosis, and more specifically, relates to a calculation method for the frequency-domain dielectric response of the main insulation of an oil-immersed inverted current transformer based on Bessel curves. Background Art

[0002] As an important electrical equipment in the high-voltage power grid, the oil-immersed current transformer shoulders the important tasks of providing metering and relay protection for the power system in the substation. As the main insulation form in the current transformer, the oil-paper insulation will gradually degrade its insulation performance under the influence of factors such as long-term aging and moisture. Therefore, the evaluation of its insulation performance is crucial for ensuring the safe operation of the power system. The frequency-domain dielectric spectroscopy (FDS) method has been widely used in insulation condition assessment due to its advantages such as low test voltage, wide test frequency range, and strong anti-interference ability. The geometric model of capacitive insulation is particularly important for the construction of the complex capacitance calculation model and the mechanism interpretation of FDS. For single coaxial cylindrical insulation structures such as transformers and bushings, the traditional XY model or X model is often used as the calculation model for diagnosing the insulation system, which can not only reflect the dielectric response characteristics of the oil-paper insulation but also be related to the main insulation structure.

[0003] However, the triangular geometry of the oil-immersed inverted current transformer poses a challenge to the accurate modeling of the main insulation geometry. As a mathematical tool, Bessel curves show excellent adaptability for depicting the side profiles of the main insulation triangle due to their flexibility and accuracy in geometric modeling. In addition, the main insulation of the current transformer also adopts a cylindrical insulation with less oil structure, which also makes the X model applicable to the analysis of the main insulation of the current transformer and determines the quantitative relationship between the complex relative permittivities of the insulating paper, insulating oil, and composite insulation system. In view of the deficiencies of the prior art, the present invention proposes a method for constructing a calculation model for the frequency-domain dielectric response of the main insulation of an oil-immersed current transformer based on Bessel curves. This method reads the design parameters of the main insulation structure of the current transformer, fits the side curves of the triangle with Bessel curves, and combines the X model to derive the complex capacitance calculation model of the main insulation. The complex capacitance of the prototype is measured by a dielectric response analyzer, and the calculation results are compared with the measured data to verify the accuracy of the calculation model. This method not only improves the accuracy of the FDS calculation model of the current transformer but also effectively overcomes the limitations of traditional test methods, providing a more reliable means for evaluating the insulation condition of current transformers in the power system. Summary of the Invention

[0004] The purpose of this method is to propose a calculation method for the frequency-domain dielectric response of the main insulation of an oil-immersed inverted current transformer based on Bessel curves, providing a simulation strategy for evaluating the oil-paper insulation condition of oil-immersed current transformers.

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

[0006] S1. Read the design parameters of the main insulation structure of the oil-immersed inverted current transformer, and obtain the inner cylinder length H of the head insulation, the cylinder radius R0 at the turning point, the insulation length L of each layer in the straight section, and the radius r of the shielding tube. z ;

[0007] S2. Measure the thickness dp of the insulation paper layer when the main insulation of the current transformer is not immersed in oil, and the total thickness D of the insulation system after immersion in oil. Calculate the X model of the oil-paper insulation and obtain the quantitative relationship of the complex relative permittivity among the insulation paper, insulation oil, and composite insulation system.

[0008] S3. Use a Bessel curve to fit the side curve profile of the insulation triangle area of the oil-immersed inverted current transformer, determine the coordinates of the three control points of the quadratic Bessel curve, and obtain the parametric equation of the fitted curve.

[0009] S4. Determine the complex capacitance of the triangle area according to the fitted curve in S3, and obtain the ring part complex capacitance and the straight section complex capacitance in the main insulation complex capacitance. The ring part complex capacitance is further divided into the inner cylinder complex capacitance, the outer cylinder complex capacitance, and the turning point complex capacitance. Subtract the capacitance of the overlapping part of the straight section from the complex capacitance of the triangle area.

[0010] S5. Use a dielectric response analyzer to measure the frequency-domain dielectric spectrum of the oil-paper insulation system of the actual machine of the oil-immersed inverted current transformer to obtain the measured complex capacitance data of the whole composite oil-paper insulation part of the transformer.

[0011] S6. Compare the complex capacitance curve obtained by the complex capacitance calculation model based on the Bessel curve with the measured complex capacitance curve in S5 to verify the feasibility of the calculation model.

[0012] Preferably, in step S1, the insulation structure of the current transformer is simplified into a two-dimensional model and approximately equivalent to an axisymmetric structure. Considering the uniformity of its materials, it is assumed that the oil-paper insulation material is uniform at the micro scale.

[0013] Preferably, in step S2, the X model of the oil-paper insulation is described by formula (1):

[0014]

[0015] In the formula: dp is the thickness of the insulation paper layer, and D is the total thickness of the insulation system after immersion in oil.

[0016] Furthermore, the quantitative relationship of the complex relative permittivity among the insulation paper, insulation oil, and oil-paper composite system is described by formulas (2) and (3):

[0017]

[0018] Wherein: is the complex dielectric constant of the oil-paper composite insulation, is the complex dielectric constant of the insulating paper, is the complex dielectric constant of the insulating oil, σ oil represents the direct current conductivity of the insulating oil, and ε0 represents the vacuum permittivity.

[0019] Preferably, in step S3, a Bessel curve is used to fit the side curve profile of the insulating triangular region of the oil-immersed inverted current transformer. The quadratic Bessel curve expression is described by Equation (4):

[0020]

[0021] Wherein: P0 is the starting point; P2 is the ending point; P1 is the control point; t is the curve parameter variable, and its value range is between 0 and 1.

[0022] Preferably, in step S4, both the complex capacitance of the ring part and the complex capacitance of the straight line segment are obtained by connecting I-layer hollow cylindrical complex capacitances in series. The calculation formula for the complex capacitance of each layer of hollow cylindrical capacitor is illustrated by formula (5), and the series relationship of the I-layer complex capacitances in a certain region is illustrated by formula (6);

[0023]

[0024] Wherein: L i represents the height of each layer of coaxial hollow cylinders, r i is the outer diameter of the coaxial hollow cylinder, r i-1 is the inner diameter of the coaxial hollow cylinder, is the complex capacitance of each layer of hollow cylinders in each region, C * is the complex capacitance of each region.

[0025] Preferably, the complex capacitances of the inner cylinder, outer cylinder, turning point, straight line segment, triangular region, and overlapping region in step S4 can be illustrated by formulas (7), (8), (9), (10), and (11) respectively:

[0026]

[0027]

[0028] Furthermore, the overall complex capacitance formula of the main insulation is described by Equation (12):

[0029]

[0030] Wherein: represents the overall complex capacitance of the main insulation, represents the complex capacitance at the head turning point, represents the complex capacitance of the inner cylinder at the head, Represents the complex capacitance of the outer cylinder of the head Represents the complex capacitance at the bend of the head Is the complex capacitance of the triangular area Is the complex capacitance of the straight section

[0031] Compare the measured complex capacitance value of the current transformer in S1 with the complex capacitance value of the calculation model. Finally, the measured complex capacitance value of the current transformer and the complex capacitance value of the calculation model basically coincide, which proves the feasibility and accuracy of a calculation method for the main insulation frequency-domain dielectric response of oil-immersed inverted current transformers based on Bessel curves proposed by the present invention.

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] The present invention combines Bessel curve fitting technology and the X model to construct a calculation model for the main insulation complex capacitance of oil-immersed current transformers used to evaluate the insulation state of oil-paper insulation. By comparing the calculated complex capacitance value with the measured complex capacitance value of the current transformer, the feasibility of this geometric fitting method and calculation model is proved, effectively overcoming the limitations of inaccurate treatment of the insulation triangular area and unclear internal mechanism of the FDS of the current transformer in traditional methods. The constructed calculation model for the main insulation complex capacitance of the current transformer fills the blank of the analytical method for calculating the complex capacitance of oil-paper insulation of oil-immersed current transformers. Description of the Drawings

[0034] Figure 1 Is the flow chart of the present invention

[0035] Figure 2 Is the design parameter diagram of the main insulation structure of the current transformer of the present invention

[0036] Figure 3 Is the X model diagram of the oil-paper insulation of the present invention

[0037] Figure 4 Is the schematic diagram of the key control points for using Bessel fitting for the insulation triangular area of the present invention

[0038] Figure 5 Is the measured connection diagram of the frequency-domain dielectric spectrum of the real machine of the oil-immersed current transformer of the present invention

[0039] Figure 6 is a comparison diagram of the complex capacitance curve obtained from the calculation model provided by the present invention and the measured complex capacitance curve Detailed Embodiment

[0040] Combined with the accompanying drawings in the embodiments of the present invention, the technical solutions in the present invention are clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all embodiments. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope of protection of the present invention.

[0041] Embodiment 1

[0042] This embodiment proposes a calculation method for the frequency-domain dielectric response of the main insulation of an oil-immersed inverted current transformer based on Bessel curves, including the following steps:

[0043] S1. Read the main insulation structure design parameters of the oil-immersed inverted current transformer, and obtain the inner cylinder length H of the head insulation, the cylinder radius R0 at the turning point, the insulation length L of each layer in the straight section, and the shield tube radius r z , and the main insulation structure design parameters of the transformer are as Figure 2 shown;

[0044] S2. Measure the thickness dp of the insulating paper layer when the main insulation of the current transformer is not immersed in oil and the total thickness D of the insulation system after immersion in oil respectively. Calculate the X model of the oil-paper insulation and obtain the quantitative relationship of the complex relative permittivity between the insulating paper, insulating oil, and composite insulation system. The schematic diagram of the X model of the oil-paper insulation is as Figure 3 shown, and the X model of the oil-paper insulation is described by formula (1):

[0045]

[0046] In the formula: dp is the thickness of the insulating paper layer, and D is the total thickness of the insulation system after immersion in oil;

[0047] Furthermore, the quantitative relationship of the complex relative permittivity between the insulating paper, insulating oil, and oil-paper composite system is described by formulas (2) and (3):

[0048]

[0049] In the formula: is the complex permittivity of the oil-paper composite insulation, is the complex permittivity of the insulating paper, is the complex permittivity of the insulating oil, and σ oil represents the direct current conductivity of the insulating oil, and ε0 represents the vacuum permittivity;

[0050] S3. Use Bessel curves to fit the side curve contour of the insulation triangular area of the oil-immersed inverted current transformer, and determine the coordinates of the three control points of the quadratic Bessel curve. The schematic diagram of the control points is as Figure 4As shown in the figure; obtain the parametric equation of the fitting curve. The parametric equation of the quadratic Bézier curve is expressed in matrix form and is described by Equation (4):

[0051]

[0052] The matrix expressions of the components in the X and Y directions on the two-dimensional plane are described by Equations (5) and (6):

[0053]

[0054] The parametric expression of the fitting curve of the outer contour of the side of the triangle is obtained from the coordinates of the three control points of the insulation triangle area of a certain brand of transformer and is described by Equation (7):

[0055]

[0056] S4. Determine the complex capacitance of the triangle area according to the fitting curve in S3, and obtain the ring complex capacitance and the straight-line segment complex capacitance in the main insulation complex capacitance. The ring complex capacitance is further divided into the inner cylinder complex capacitance, the outer cylinder complex capacitance, and the bend complex capacitance. Subtract the capacitance of the overlapping part of the straight-line segment from the triangle area complex capacitance. Both the ring complex capacitance and the straight-line segment complex capacitance are obtained by connecting the I-layer hollow cylinder complex capacitances in series. The calculation formula for the I-layer hollow cylinder complex capacitance of each layer is illustrated by Formula (8), and the series connection relationship of the I-layer complex capacitance of a certain area is illustrated by Formula (9):

[0057]

[0058] In the formula: L i represents the height of each layer of coaxial hollow cylinders, r i is the outer diameter of the coaxial hollow cylinder, r i-1 is the inner diameter of the coaxial hollow cylinder, is the complex capacitance of each layer of hollow cylinders in each area, C * is the complex capacitance of each area;

[0059] The inner cylinder complex capacitance, the outer cylinder complex capacitance, the bend complex capacitance, the straight-line segment complex capacitance, the triangle area complex capacitance, and the overlapping area complex capacitance can be illustrated by Formulas (7), (8), (9), (10), and (11) respectively:

[0060]

[0061] Furthermore, the formula for the overall complex capacitance of the main insulation is described by Equation (12):

[0062]

[0063] In the formula: represents the overall complex capacitance of the main insulation, represents the bend complex capacitance at the head, Denote the complex capacitance of the inner cylinder in the head, Denote the complex capacitance of the outer cylinder in the head, Denote the complex capacitance at the bend in the head, Is the complex capacitance of the triangular region, Is the complex capacitance of the straight segment;

[0064] S5. Use a dielectric response analyzer to measure the frequency-domain dielectric spectrum of the oil-paper insulation system of the real oil-immersed inverted current transformer to obtain the measured complex capacitance data of the overall composite oil-paper insulation part of the transformer. The measured connection diagram of the frequency-domain dielectric spectrum of the real oil-immersed current transformer is as shown in Figure 5 shown;

[0065] S6. Compare the complex capacitance curve obtained by the complex capacitance calculation model based on the Bessel curve with the measured complex capacitance curve in S5 to verify the feasibility of the calculation model. As shown in Figure 6, the trend of the measured FDS curve of the final prototype is consistent with that of the FDS curve of the simulation model, which proves the feasibility and accuracy of the frequency-domain dielectric spectrum calculation method for the main insulation of the oil-immersed inverted current transformer proposed in the present invention.

[0066] The above content is only an explanation of the structure of the present invention. Those skilled in the art of this technology can make various modifications or supplements to the described specific structure. As long as they do not deviate from the structure of the invention or exceed the scope defined by this claim book, they shall fall within the protection scope of the present invention.

Claims

1. A method for calculating the frequency domain dielectric response of the main insulation of an oil-immersed inverted current transformer based on a Bezier curve, characterized in that The following steps are involved: S1, read the main insulation structure design parameters of the oil-immersed inverted current transformer, obtain the inner cylinder length H of the head insulation, the cylinder radius R0 at the bend, the insulation length L of each layer of the straight section, and the shielding tube radius r z ; S2, respectively measure the thickness dp of the insulation paper layer of the current transformer main insulation before oil immersion and the total thickness D of the insulation system after oil immersion. Calculate the oil-paper insulation X model and obtain the quantitative relationship between the complex relative dielectric constant of the insulation paper, insulating oil and composite insulation system; S3, using Bezier curve to fit the side curve profile of the insulating triangle area of ​​the oil-immersed inverted current transformer, determining the coordinates of the three control points of the quadratic Bezier curve, and obtaining the parameter equation of the fitting curve; S4, determining the complex capacitance of the triangular area according to the fitting curve in S3, and obtaining the complex capacitance of the ring part and the complex capacitance of the straight line segment in the main insulation complex capacitance. The complex capacitance of the ring part is further divided into the complex capacitance of the inner cylinder, the complex capacitance of the outer cylinder and the complex capacitance of the bend. The capacitance of the overlapping part of the straight line segment is subtracted from the complex capacitance of the triangular area; S5, using a dielectric response analysis tester to measure the frequency domain dielectric spectrum of the oil-paper insulation system of the real oil-immersed inverted current transformer, so as to obtain the measured complex capacitance data of the composite oil-paper insulation part of the transformer as a whole; S6, comparing the complex capacitance curve obtained by the complex capacitance calculation model based on the Bezier curve with the complex capacitance curve measured in S5 to verify the feasibility of the calculation model.

2. According to the method for calculating the frequency domain dielectric response of the main insulation of an oil-immersed inverted current transformer based on a Bezier curve as described in claim 1, it is characterized by: The oil-paper insulation X model in step S2 is described by formula (1): Where: dp is the thickness of the insulation paper layer, D is the total thickness of the insulation system after oil immersion; The quantitative relationship between the complex relative dielectric constant of insulating paper, insulating oil and oil-paper composite system is described by formulas (2) and (3): Where: is the complex dielectric constant of oil-paper composite insulation, is the complex dielectric constant of the insulating paper, is the complex dielectric constant of insulating oil, σ oil It represents the DC conductivity of insulating oil, and ε0 represents the dielectric constant of vacuum.

3. According to the method for calculating the frequency domain dielectric response of the main insulation of an oil-immersed inverted current transformer based on a Bezier curve as described in claim 1, it is characterized by: In the step S3, a Bezier curve is used to fit the side curve contour of the insulating triangle area of ​​the oil-immersed inverted current transformer. The quadratic Bezier curve expression is described by formula (4). The starting point P0 and the end point P2 are determined in the data point cloud of the edge curve of the triangle area. P1 is the intersection point of the tangents of the Bezier curve at P0 and P2 respectively. Where: P0 is the starting point, P2 is the ending point, P1 is the control point, and t is the curve parameter variable, which ranges from 0 to 1.

4. According to the method for calculating the frequency domain dielectric response of the main insulation of an oil-immersed inverted current transformer based on a Bezier curve as described in claim 1, it is characterized by: In step S4, the complex capacitance of the loop and the complex capacitance of the straight segment are obtained by connecting the complex capacitance of I layers of hollow cylinders in series. The calculation formula of the complex capacitance of each layer of hollow cylinders is described by formula (5). The series relationship of the complex capacitance of I layers in a certain area is described by formula (6). Where: L i Represents the height of each layer of coaxial hollow cylinders, r i is the outer diameter of the coaxial hollow cylinder, r i-1 is the inner diameter of the coaxial hollow cylinder, is the complex capacitance of each layer of hollow cylinder in each region, C * is the complex capacitance of each region.

5. The method for calculating the frequency domain dielectric response of the main insulation of an oil-immersed inverted current transformer based on a Bezier curve according to claim 1, characterized in that: The complex capacitance of each part of the main insulation in step S4 can be calculated or derived by the coaxial cylindrical capacitor formula, wherein the complex capacitance of the triangular area obtained by Bessel curve fitting is described by formula (7): Where: r1(t) represents the height of each layer of coaxial hollow cylinders, ri is the outer diameter of the coaxial hollow cylinders, r i-1 is the inner diameter of the coaxial hollow cylinder, is the complex capacitance of each layer of hollow cylinder in each region, C * is the complex capacitance of each region.

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