A method for optimizing the number of series-connected insulating rings in a high-voltage insulation stack

Abstract

The present invention provides a method for optimizing and determining the number of insulating rings in series in a high-voltage insulation stack, used to address the technical challenge of optimizing the number of insulating rings in series in a large Z-pinch device. The method includes: given the insulating ring circumference, the total height of the insulation stack, the thickness of a single grading ring, the operating voltage of the insulation stack, and the statistical flashover constant of the insulation material; establishing a model for calculating the flashover probability of the entire insulation stack based on a simplified statistical model; calculating the flashover probability of the insulation stack for different values of the number of insulating rings in series, n, using the formula for calculating the flashover probability of the entire insulation stack based on the simplified statistical model, and then obtaining a curve of the flashover probability as a function of the average electric field strength; calculating the average electric field strength of the insulation stack for different numbers of insulating rings in series, and combining the obtained curve of the flashover probability of the entire insulation stack as a function of the average electric field strength for different values of the number of insulating rings in series, n, to determine the number of insulating rings in series that minimizes the flashover probability of the insulation stack.

Description

Technical Field

[0001] The invention relates to a high-voltage insulation stack, and in particular to a method for optimizing and determining the number of series-connected insulation rings in a high-voltage insulation stack. Background Art

[0002] The high-voltage insulation stack is a crucial component of a large-scale Z-pinch device, providing mechanical support and physical isolation between different types of insulating media. Requirements for this stack include large size (2-5m diameter), high withstand voltage (several MV), high average electric field strength (80-200kV / cm), and low inductance (several nanowatts). Furthermore, it must possess excellent mechanical strength, structural stability, and resistance to X-ray radiation. The insulation stack is often the weakest link in the Z-pinch device's insulation, constituting a bottleneck hindering the construction of next-generation, 100-terawatt Z-pinch devices.

[0003] Factors such as the effective duration of the pulse voltage, the type of insulating ring material, the size and surface condition of the insulating ring structure, the uniformity of the electric field distribution along the surface, and the number of insulating ring series connections all influence the vacuum surface flashover characteristics of a high-voltage insulation stack. Given the insulating ring material and surface condition, the dimensions of the insulation stack, and the operating voltage of the insulation stack, the vacuum surface characteristics of the insulation stack are closely related to the number of insulating ring series connections, n. An optimal value exists for the number of insulating ring series connections that minimizes the flashover probability of the entire insulation stack. However, determining this optimal value for the number of insulating ring series connections that minimizes the flashover probability of the entire insulation stack remains a pressing challenge. Summary of the Invention

[0004] Aiming at the problem of optimizing the number of series-connected insulating rings in an insulating stack of a large Z pinch device, the present invention provides a method for optimizing and determining the number of series-connected insulating rings in a high-voltage insulating stack.

[0005] In order to achieve the above objectives, the technical solutions of the present invention are as follows:

[0006] A method for optimizing and determining the number of series-connected insulating rings in a high-voltage insulating stack, wherein the insulating stack is composed of insulating rings and metal grading rings stacked in series in sequence, and the method specifically comprises the following steps:

[0007] 1] Given the structural parameters and working voltage U of the insulation stack stack The structural parameters include the circumference of the single-piece insulation ring L, the total height of the insulation stack H, the thickness of the single-piece metal grading ring h GR And the statistical flashover constant γ of the insulating material SM ;

[0008] 2] Ignoring the influence of the circumferential transit time of the large-sized insulation stack and the non-uniform distribution of the insulation stack voltage on the flashover probability of the entire insulation stack, a calculation formula for the flashover probability of the entire insulation stack based on a simplified statistical model is established. The flashover probability F(t) of the entire insulation stack based on the simplified statistical model is:

[0009]

[0010] Among them, n is the number of insulation rings in series; R represents the size of the insulation ring structure and the average electric field strength E p Constants related to material properties; g j Indicates the overvoltage factor of the insulation ring; β is the power index, 8≤β≤12; a j represents the coefficient related to the overvoltage factor matrix, j represents the jth column of the matrix, 1≤j≤n;

[0011] 3] According to the calculation formula of the full stack flashover probability of the insulation stack of the simplified statistical model, the full stack flashover probability of the insulation stack is calculated when the number of series insulation rings n is different, and then the full stack flashover probability of the insulation stack with the average electric field strength E is obtained when the number of series insulation rings n is different. p (n) change curve;

[0012] 4] Calculate the average electric field strength E of the insulation stack when the number of insulation ring series n is different p (n), combined with the obtained step 3], the flashover probability of the entire insulation stack changes with the average electric field strength E when the number of insulation rings in series n is different p The variation curve of (n) is used to obtain the corresponding breakdown probability, thereby determining the series number of insulating rings that minimizes the flashover probability of the insulation stack.

[0013] Furthermore, the average electric field strength E of the insulation stack when the number of series-connected insulation rings n is different is: p (n) is calculated by the following formula:

[0014]

[0015] Furthermore, in step 2], the insulating ring structure size, average electric field strength E p The constant R related to material properties is determined by the following formula:

[0016]

[0017] Among them, E p is the average peak electric field strength of the insulation stack; L is the circumference of the single-piece insulation ring; d is the thickness of the single-piece insulation ring; λ is a constant, 0.15≤λ≤0.33; t eff is the effective action time of the applied voltage; γ SMis the statistical flashover constant of the insulating material.

[0018] Furthermore, in step 2], the insulating ring overvoltage factor g j Determined by the following formula:

[0019]

[0020] Furthermore, in step 2], the coefficient a related to the insulation ring overvoltage factor matrix j Determined by the following formula:

[0021]

[0022] Where G represents the overvoltage factor matrix; G ij Represents the value of the element in the i-th row and j-th column of the matrix G; 1≤i≤n, 1≤j≤n.

[0023] The beneficial effects of the present invention are:

[0024] 1. In order to solve the technical difficulties in optimizing the number of series-connected insulating rings in an insulating stack in a large Z-pinch device, the present invention innovatively proposes a method for optimizing the number of series-connected insulating rings in a high-voltage insulating stack. This method is based on a simplified statistical model for calculating the flashover probability of an insulating stack. It assumes that the effects of the circumferential transit time and the non-uniform distribution of the insulating stack voltage on the flashover probability offset each other. This not only simplifies the prediction process of the insulating stack flashover probability, but also maintains good calculation accuracy.

[0025] 2. The present invention provides a method for optimizing and determining the number of series-connected insulating rings in a high-voltage insulating stack, which optimizes the number of series-connected insulating rings in the insulating stack, provides support for the design of insulating stacks in large-scale pulse power devices, and has significant application value in large-scale Z-pinch devices. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 For the A-layer insulation stack of the 15MA Z pinch device in the embodiment of the present invention, the flashover probability curve of the entire insulation stack changes with the average electric field strength E when the number of insulation rings in series is different. p The change curve diagram of

[0027] Figure 2 This is a comparison diagram of the flashover probability of a 15MA device obtained by using a simplified statistical model in an embodiment of the method of the present invention and a complete statistical flashover probability model. DETAILED DESCRIPTION

[0028] In order to make the advantages and features of the present invention more clear, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0029] An insulation stack consisting of insulating rings and metal grading rings stacked in series, comprising two coaxially arranged support electrodes, multiple insulating rings, and multiple metal grading rings. A metal grading ring is disposed between each pair of insulating rings, such that the insulating rings and metal grading rings are stacked in a cross-stack arrangement. The metal grading rings extend from the inner and outer sidewalls of the insulating rings on either side, respectively, so that the inner portions of the metal grading rings are immersed in a vacuum and the outer portions are immersed in a liquid insulating medium. The flashover probability of this insulation stack is closely related not only to the performance of the individual insulating rings but also to the overvoltage factor matrix of the insulation stack. This overvoltage factor matrix is closely related to the number of insulating rings in series and is influenced by the voltage distribution uniformity of the insulation stack and the transit time of electromagnetic waves along the circumference of the insulation stack. The voltage distribution uniformity and the transit time of electromagnetic waves along the circumference of the insulation stack have opposite effects on the flashover probability of the insulation stack. Ignoring the voltage distribution uniformity of the insulation stack will underestimate the flashover probability of the insulation stack; ignoring the transit time of electromagnetic waves along the circumference of the insulation stack will overestimate the flashover probability of the insulation stack. Assuming that the effects of the insulation stack voltage distribution uniformity and the circumferential transit time on the insulation stack flashover probability cancel each other out, the present invention simultaneously ignores the effects of the insulation stack circumferential transit time and the non-uniform distribution of the insulation stack voltage, and adopts a simplified statistical model to calculate the flashover probability of the insulation stack, thereby simplifying the calculation process of the insulation stack flashover probability and making it possible to obtain the optimized value of the insulation ring series series series with the goal of minimizing the flashover probability of the entire stack.

[0030] The present invention provides a method for optimizing and determining the number of insulating ring series stages in a high-voltage insulating stack composed of insulating rings and metal grading rings stacked in series, specifically comprising the following steps:

[0031] 1] Given the structural parameters and working voltage U of the insulation stack stack The structural parameters include the circumference of the single-piece insulation ring L, the total height of the insulation stack H, the thickness of the single-piece metal grading ring h GR And the statistical flashover constant γ of the insulating material SM .

[0032] In this embodiment, the 15MA Z pinch device has an insulation stack consisting of four layers, which are marked as A, B, C, and D from top to bottom. Taking the optimization of the series number of insulation stacks in layer A as an example, the input conditions are: the circumference of a single insulation ring L = 1037 cm, the total height of the insulation stack H = 28.2 cm, and the thickness of a single metal grading ring h GR =0.8cm, insulation stack working voltage U stack =3MV; In addition, the insulating material in this embodiment is cross-linked polystyrene, and the statistical flashover constant γ of the material SM =250.

[0033] 2] Ignoring the influence of the circumferential transit time of the large-size insulation stack and the non-uniform distribution of the insulation stack voltage on the flashover probability of the entire insulation stack, based on the structural parameters of the insulation stack and the working voltage U stack , a calculation model for the flashover probability of the entire insulation stack is established based on a simplified statistical model. Specifically, the flashover probability F(t) of the entire insulation stack is:

[0034]

[0035] In formula (1), n is the number of series-connected insulating rings; R represents the structure size of the insulating ring (the circumference L of a single insulating ring and the thickness d of a single insulating ring), the average electric field strength E p Constants related to material properties; g j represents the overvoltage factor of the insulating ring; β is the power exponent, 8≤β≤12, in this embodiment, β=4, a j Represents the coefficient associated with the overvoltage factor matrix, j represents the j-th column of the matrix, and 1≤j≤n.

[0036] Among them, the flashover probability F(t) of the insulation stack based on the simplified statistical model is determined by the following formulas, that is, the formula (1) is related to the insulation ring structure size, the average electric field strength E p Constant R and overvoltage factor g related to material properties j and the coefficient a associated with the overvoltage factor matrix j Parameter value.

[0037] The structure size of the insulating ring and the average electric field strength E p The constant R related to material properties is determined by the following formula:

[0038]

[0039] In formula (2), E p is the average peak electric field strength of the insulation stack, in kV / cm; L is the circumference of the single-piece insulation ring, in cm; d is the thickness of the single-piece insulation ring, in cm; λ is a constant, 0.15≤λ≤0.33, in this embodiment λ=0.24; t eff is the effective action time of voltage, in μs; γ SM is the statistical flashover constant of the insulating material.

[0040] Without considering the voltage non-uniformity of the insulation stack and the transit time of the electric pulse along the circumference of the insulation stack, the insulation ring overvoltage factor g j Determined by the following formula:

[0041]

[0042] Coefficient a related to the overvoltage factor matrix jDetermined by the following formula:

[0043]

[0044] In formula (4), G represents the overvoltage factor matrix; G ij Represents the value of the element in the i-th row and j-th column of the matrix G; 1≤i≤n, 1≤j≤n.

[0045] 3] Input different numbers of insulating ring series series n into the insulation stack full stack flashover probability calculation model of the simplified statistical model in step 2], and calculate the insulation stack full stack flashover probability F(t) when the insulating ring series series series n is different values, and then obtain the insulation stack full stack flashover probability F(t) when the insulating ring series series series n is different values with the average electric field strength E p 's change curve.

[0046] 4] Calculate the average electric field strength E of the insulation stack under different series levels using formula (5) p (n);

[0047]

[0048] According to the average electric field strength E of the insulating stack obtained under different series series p (n), combined with step 3, the flashover probability F(t) of the insulation stack with different series series n varies with the average electric field strength E p The change curve of Figure 1 As shown, the corresponding breakdown probability is obtained according to the curve, so as to determine the number n of insulating ring series connections that minimizes the flashover probability of the insulating stack.

[0049] In this embodiment, the total height of the insulation stack is H = 28.2 cm, and the working voltage of the insulation stack is U stack =3MV, different numbers of insulating rings in series n correspond to different average electric field strengths E of the insulating stack p Specifically, when the number of insulating rings in series is 4, the average electric field strength E p is 116.28kV / cm; when the number of insulating rings in series is 5, the average electric field strength E p is 120.00kV / cm; when the number of insulating rings in series is 6, the average electric field strength E p is 123.97kV / cm; when the number of insulating rings in series is 7, the average electric field strength E pThe flashover probability of the entire A-layer insulation stack is 128.21 kV / cm. Combined with the flashover probability of the entire A-layer insulation stack when the number of insulating rings in series, n, is 4, 5, 6, and 7, the average electric field strength and flashover probability of the A-layer insulation stack of the 15MAZ pinch device vary with the number of insulating rings in series. Specific data are shown in Table 1. The flashover probability of the entire A-layer insulation stack is 6.51%, 5.76%, 7.73%, and 10.83% when the number of insulating rings in series, n, is 4, 5, 6, and 7, respectively. It can be seen that for the given operating conditions, the flashover probability of the A-layer insulation stack is lowest when the number of insulating rings in series, n, is 5.

[0050] Table 1

[0051]

[0052] In order to further verify the reliability of the method for optimizing the number of series-connected insulating rings in a high-voltage insulating stack provided by the present invention, the present invention compares the flashover probability curve of the insulating stack obtained by the simplified statistical model in the above embodiment with the flashover probability curve of the insulating stack obtained by the strict statistical model taking into account the uneven distribution of insulating stack voltage and the circumferential transit time. Figure 2 As shown, when the number of series-connected insulating rings in the A-layer insulating stack is n=5, the flashover probability curve of the entire insulating stack varies with the operating field strength. P1 in the figure is the flashover probability curve of the entire insulating stack obtained by adopting the simplified statistical model of the present invention, and P is the flashover probability curve of the entire insulating stack obtained by adopting the strict statistical model taking into account the uneven distribution of the insulating stack voltage and the circumferential transit time. Figure 2 It can be seen from the comparison curve that the simplified statistical model can obtain the insulation stack flashover probability close to that of the strict statistical model.

[0053] The present invention is directed to an insulation stack composed of an insulation ring and a metal grading ring stacked in series. stack , total height of insulation stack H, thickness of single grading ring h GR Under the condition of given parameters, a flashover probability calculation model for insulation stacks based on a simplified statistical model was established. It was assumed that the effects of the circumferential transit time and the non-uniform distribution of insulation stack voltage on the flashover probability offset each other. This not only simplifies the insulation stack flashover probability prediction process, but also maintains good calculation accuracy. It provides an optimal determination method for the number of insulation ring series to minimize the flashover probability of the insulation stack, provides support for the design of vacuum insulation stacks for large-scale pulse power devices, and has significant application value in large-scale Z-pinch devices.

[0054] The above description is only used to illustrate the technical solution of the present invention, rather than to limit it. For ordinary professional and technical personnel in this field, the specific technical solutions recorded in the above embodiments can be modified, or some of the technical features therein can be replaced by equivalents. These modifications or replacements do not cause the essence of the corresponding technical solution to deviate from the scope of the technical solution protected by the present invention.

Claims

1. A method for optimizing and determining the number of series-connected insulating rings in a high-voltage insulating stack, wherein the insulating stack is composed of insulating rings and metal grading rings stacked in series, characterized in that: The following steps are involved: 1] Given the structural parameters and working voltage U of the insulation stack stack The structural parameters include the circumference of the single-piece insulation ring L, the total height of the insulation stack H, the thickness of the single-piece metal grading ring h GR And the statistical flashover constant γ of the insulating material SM ; 2] Ignoring the influence of the circumferential transit time of the large-sized insulation stack and the non-uniform distribution of the insulation stack voltage on the flashover probability of the entire insulation stack, a calculation formula for the flashover probability of the entire insulation stack based on a simplified statistical model is established. The flashover probability F(t) of the entire insulation stack based on the simplified statistical model is: Among them, n is the number of insulation rings in series; R represents the size of the insulation ring structure and the average electric field strength E p Constants related to material properties; g j Indicates the overvoltage factor of the insulation ring; β is the power index, 8≤β≤12; a j represents the coefficient related to the overvoltage factor matrix, j represents the jth column of the matrix, 1≤j≤n; 3] According to the calculation formula of the full stack flashover probability of the insulation stack of the simplified statistical model, the full stack flashover probability of the insulation stack is calculated when the number of series insulation rings n is different, and then the full stack flashover probability of the insulation stack with the average electric field strength E is obtained when the number of series insulation rings n is different. p (n) change curve; 4] Calculate the average electric field strength E of the insulation stack when the number of insulation ring series n is different p (n), combined with the obtained step 3], the flashover probability of the entire insulation stack changes with the average electric field strength E when the number of insulation rings in series n is different p (n) variation curve, obtain the corresponding breakdown probability, and thus determine the series number of insulating rings that minimizes the flashover probability of the insulation stack; The average electric field strength E of the insulation stack when the number of insulation ring series series n is different p (n) is calculated by the following formula:

2. The method for optimizing and determining the number of series-connected insulating rings in a high-voltage insulating stack according to claim 1, wherein: In step 2], the insulating ring structure size and average electric field strength E p The constant R related to material properties is determined by the following formula: Where L is the circumference of the single-piece insulating ring; d is the thickness of the single-piece insulating ring; λ is a constant, 0.15≤λ≤0.33; t eff is the effective action time of the applied voltage; γ SM is the statistical flashover constant of the insulating material.

3. The method for optimizing and determining the number of series-connected insulating rings in a high-voltage insulating stack according to claim 2, wherein: In step 2], the insulation ring overvoltage factor g j Determined by the following formula:

4. The method for optimizing and determining the number of series-connected insulating rings in a high-voltage insulating stack according to claim 3, wherein: In step 2, the coefficient a related to the insulation ring overvoltage factor matrix j Determined by the following formula: Where G represents the overvoltage factor matrix; G ij Represents the value of the element in the i-th row and j-th column of the matrix G; 1≤i≤n, 1≤j≤n.

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