CN111553089B - Multilevel optimal design method for GIS/GIL basin-type insulator with high power resistance - Google Patents

Multilevel optimal design method for GIS/GIL basin-type insulator with high power resistance Download PDF

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CN111553089B
CN111553089B CN202010379116.6A CN202010379116A CN111553089B CN 111553089 B CN111553089 B CN 111553089B CN 202010379116 A CN202010379116 A CN 202010379116A CN 111553089 B CN111553089 B CN 111553089B
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张冠军
王超
李文栋
江智慧
杨雄
薛建议
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Abstract

The invention discloses a multilevel optimal design method of a GIS/GIL basin-type insulator with high electrical resistance, which comprises an initial design stage and a detailed design stage, wherein in the initial design stage, profile shape optimization is adopted to construct the basic appearance of the GIS/GIL basin-type insulator, a two-dimensional profile function is utilized to describe the shapes of a convex surface and a concave surface of a basin body, the introduction of dielectric function gradient material distribution is considered, the topological optimization is utilized to adjust the dielectric characteristic space distribution to actively regulate and control the electric field distribution, and the surface electric field is further deeply homogenized; in a detailed design stage, according to a result of dielectric distribution topology optimization, the optimized gradient insulation region is converted into a high-dielectric region with constant dielectric constant, the sizes of the high-voltage side metal accessory and the high-dielectric region are finely adjusted, an optimal size parameter is found out by adopting a genetic algorithm or an ant colony algorithm, and the design of the GIS/GIL basin-type insulator is completed. The invention can fully expand the design space, realize the depth inhibition of the surface electric field and achieve the purpose of improving the breakdown voltage of the basin-type insulator.

Description

Multi-level optimization design method for GIS/GIL basin-type insulator with high power-resisting performance
Technical Field
The invention belongs to the technical field of high-voltage power equipment design and manufacture, and particularly relates to a multi-level optimization design method for a GIS/GIL basin-type insulator with high electrical resistance.
Background
Gas Insulated Switchgear (GIS) is widely applied to ultra-high and extra-high voltage transformer substations due to the advantages of small occupied area, stable operation environment and the like. Gas Insulated Transmission Line (GIL) is a novel advanced power Transmission mode, has the advantages of large Transmission capacity, small Transmission loss, high safety and the like, and is often used as a replacement scheme of an overhead Line and applied to special power Transmission environments.
The basin-type insulator is used as an important component in GIS/GIL equipment, and has the functions of supporting a metal guide rod, isolating electric potential, sealing an air chamber, isolating air and the like. On one hand, the surface electric field is not uniformly distributed, equipment runs under high field intensity for a long time, and the phenomenon of flashover/breakdown damage is easy to occur on the surface of the insulator under the condition of external overvoltage, so that the reliability of the equipment is reduced, and the operation and maintenance difficulty is increased. On the other hand, the size of the basin-type insulator directly determines basic dimensions such as the insulation distance of the equipment, the inner diameter of the cylinder and the like, and further determines the floor area and SF (sulfur hexafluoride) of the equipment 6 The amount of gas used. Therefore, miniaturization of the basin insulator is also an urgent development requirement in view of economic efficiency and environmental protection. The well-designed basin-type insulator is an important guarantee for ensuring the high reliability of the GIS/GIL equipment and even the safety of the whole power system.
The visualization of the physical process and the accurate quantification of the physical quantity can be realized through a numerical simulation means, the insulation matching and the electrical design are optimized, the geometric shape can only be adjusted in a limited size range by the traditional structural parameter optimization design method, the electric field optimization effect is limited, and in addition, due to the fact that the design variables are numerous, the finite element model needs to be called for many times, the calculation amount is large, and the optimization efficiency is low. How to realize the efficient optimization design of the insulation structure through numerical simulation is the key point for manufacturing the high-performance basin-type insulator.
Disclosure of Invention
The invention aims to solve the technical problem of providing a multi-level optimization design method of a GIS/GIL basin-type insulator with high electrical resistance aiming at the defects in the prior art. In the detailed design stage, the further regulation and control of the electric field are realized by optimizing and selecting specific size parameters and dielectric parameter values of the central insert, the shielding case and the like; the staged and multilevel optimization strategy combines the advantages of structure optimization and material distribution optimization, and is beneficial to avoiding premature trapping into partial optimal solutions; the fully expanded design space can realize the optimization effect of' 1+1> < 2 >, thereby laying a theoretical foundation for the design and manufacture of the novel basin-type insulator with high electric resistance.
The invention adopts the following technical scheme:
a multilevel optimal design method for a GIS/GIL basin-type insulator with high power resistance comprises an initial design stage and a detailed design stage, wherein in the initial design stage, outline shape optimization is adopted to construct the basic appearance of the GIS/GIL basin-type insulator, two-dimensional outline functions are used to describe the shapes of a convex surface and a concave surface of a basin body, the introduction of dielectric function gradient material distribution is considered, topological optimization is used to adjust dielectric characteristics so as to actively regulate and control electric field distribution, and the surface electric field is further deeply homogenized on the basis of the outline optimization; in a detailed design stage, according to a result of topological optimization of dielectric distribution, the optimized gradient insulation region is converted into a high-dielectric region with constant dielectric constant so as to meet the constraint of the existing manufacturing conditions, the sizes of the high-voltage side metal accessory and the high-dielectric region are finely adjusted, an optimal size parameter is found out by adopting a genetic algorithm or an ant colony algorithm, and the design of the GIS/GIL basin-type insulator is completed.
Specifically, the preliminary design stage specifically includes:
s101, describing the shapes of the convex surface and the concave surface of the pot body by using a two-dimensional profile function, wherein the maximum deformation of the starting point of a profile curve is set as T 0 The deformation at the end point of the contour is zero, and the derivatives at the start point and the end point of the function are set to be zero; adding constraint to the derivative of the curve, and finding out the optimal contour control parameter according to an optimization algorithm;
s102, on the basis of shape contour optimization, discretely dividing the basin body into a plurality of sub-areas, wherein the dielectric constant in each sub-area is the same, searching for optimal dielectric constant distribution in the insulating basin body to enable the convex and concave electric fields to be uniformly distributed, and giving a function independent variable value range in each iteration process by introducing a moving asymptote method so as to find optimal dielectric spatial distribution.
Further, in step S101, the mathematical optimization problem is:
min：E＝max{E_convex,E_concave}
＝f(C 12 ,C 13 ,C 22 ,C 23 )
Figure BDA0002481339780000031
wherein E _ covex and E _ con are respectively the maximum value of the electric field of the convex surface and the concave surface of the pot body, C 12 ，C 13 ，C 22 And C 23 Is a profile control parameter, f is a function of the profile control parameter at the maximum electric field, T min And T max The thinnest and thickest thickness, T, of the basin-type insulator 1 (r) and T 2 (r) is a profile function of the convex and concave surfaces.
Further, in step S102, a solid isotropic material penalty density interpolation function is applied to each discrete unit to find an optimal density distribution, where a mathematical optimization model is:
find ρ＝{ρ 1 ,ρ 2 ,,ρ n }
Figure BDA0002481339780000032
s.t.ε r ＝ε 0 ((ε rmax -ε rmin )ρ i p +ε rmin ),
0＜ρ min ≤ρ i ≤1,i＝1,2,...,n
p＞0,q＞0,0≤w≤1
where ρ is the density vector of each grid, f Eopt As a function of the degree of homogeneity of the in-plane electric field, f grad Q is the proportionality coefficient of the gradient penalty term, E _ covex and E _ covave are the convex electric field distribution, E mean W is the equilibrium coefficient between the degrees of uniformity of the convex and concave electric fields, l 1 And l 2 Respectively convex and concave edge regions, C ref1 And C ref2 Is an initial reference value, h mesh Is the area of the grid, omega is the integral calculation domain, A is the integratorArea of the computation space, p min For the minimum density of the grid, p is a variable parameter of the SIMP interpolation function.
Specifically, the detailed design stage specifically includes:
s201, converting the optimized gradient insulation region into a high dielectric region with constant dielectric constant according to the result of dielectric distribution topology optimization, and finding out the optimal dielectric constant value of the high dielectric region by adopting a parameter scanning mode or a traditional gradient descent algorithm;
s202, establishing a size parameter optimization model to finely adjust the sizes of the high-voltage side metal accessories and the high-dielectric region.
Further, in step S201, a mathematical model is established, and the optimization objective is to limit the maximum electric field of the convex surface and the concave surface, specifically:
min：E＝max{E_convex,E_concave}
＝f(ε i )
s.t.ε min ＜ε i ≤ε max
wherein epsilon min And ε max Is the upper and lower limits of the variation of the dielectric constant, epsilon i For high dielectric zone dielectric constants, E _ covex and E _ covave represent the electric field maximum for the convex and concave basins, respectively.
Further, in step S202, the dimensional variation ranges of the high-side metal attachment and the high-dielectric region are as follows:
min：E＝max{E_convex,E_concave}
＝f(R 1 ,R 2 ,d 1 ,d 2 ,…)
Figure BDA0002481339780000041
wherein R is 1 And R 2 Radius of the convex and concave central inserts, d 1 Is the height of the connecting member, d 2 Is the length of the high dielectric region, R 1_min 、R 2_min 、d 1_min 、d 2_min And R 1_max 、R 2_max 、d 1_max 、d 2_max Are respectively provided withFor the upper and lower bounds of the corresponding parameters, E _ covex and E _ covave represent the maximum electric field values for the convex and concave surfaces of the basin, respectively.
Compared with the prior art, the invention has at least the following beneficial effects:
the invention relates to a multi-level optimization design method of a GIS/GIL basin-type insulator with high electric resistance, which designs the basin-type insulator with high electric resistance by utilizing a multi-level parallel numerical simulation strategy of shape optimization and dielectric distribution optimization. Compared with the traditional size optimization method, the method can fully expand the design space, realize the depth regulation and control of the surface electric field, and achieve the purposes of reducing the size of GIS equipment and improving the breakdown voltage of the basin-type insulator.
Furthermore, in step S101, a shape profile optimization algorithm is firstly adopted, a structural curve is described through a shape function, the design of the overall structure can be controlled by using fewer variables, and compared with the traditional size optimization, the basin body overall profile optimization method has the characteristics of large deformation and small calculation amount, and can realize the basin body overall profile optimization. Meanwhile, constraint conditions can be conveniently adjusted according to design requirements, for example, the thinnest and thickest thicknesses of the pot body can be adjusted according to requirements of different voltage grades, so that the requirements of mechanical performance are met, the processing difficulty in actual manufacturing engineering is reduced by converting the gradient dielectric region into the high dielectric region, and the manufacturing of the gradient insulating structure can be realized on the basis of the existing process. Meanwhile, the most significant value of the high dielectric region can be found out in a parameter scanning mode, so that guidance of designing a formula is provided for specific manufacturing.
Further, in step S102, the adopted dielectric distribution optimization can find out the optimal dielectric property spatial distribution inside the tub body, thereby realizing further depth homogenization of the electric field on the basis of the contour optimization. The combination of the two can realize the optimization effect of ' 1+1> ' 2 '. The surface electric field of the insulating structure can be obviously homogenized, and the maximum field intensity can be greatly reduced. The specifically adopted variable density topological optimization algorithm can realize the design of two-dimensional approximate continuous gradient, and can well solve the problems of numerous design variables and high nonlinearity of optimization problem.
Furthermore, the gradient dielectric region is converted into the homogeneous high dielectric region, so that the manufacturing difficulty can be reduced on the basis of ensuring the electric field homogenization effect, the homogeneous high dielectric region can be quickly, simply and conveniently manufactured by utilizing the photocuring 3D printing technology or the traditional mould resin pouring mode, and then the manufacturing of the whole basin-type insulator is realized by the assembling mode.
Further, in step S202, each size parameter is optimized by using a genetic algorithm, details of the structure can be designed and optimized, and a final manufacturing drawing can be given while electric field regulation is realized.
In conclusion, the multilevel optimization design method for the GIS/GIL basin-type insulator with high power resistance, which is provided by the invention, can combine the advantages of shape optimization and dielectric distribution optimization, greatly reduce the surface electric field intensity of the basin-type insulator and homogenize the electric field distribution. The multi-layer sub-optimization strategy can fully utilize the design space and search the global optimal value of the design. Meanwhile, the design method described by the invention can realize the insulation design with high electricity resistance performance without increasing the difficulty of the existing manufacturing process, the designed insulation structure has high electricity resistance performance, and the mechanical and thermal properties can still be maintained at the same time, so that the actual industrial application requirements can be met, the reliability of the insulation structure is improved, the floor area of electric power equipment is reduced, and the greenhouse gas SF is reduced 6 The amount of (2) used.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a graph of the results of the optimization steps of the method of the present invention, wherein (a) is the pre-optimization insulation system, (b) is the profile-optimized insulation profile shape, (c) is the topologically optimized dielectric constant spatial distribution, and (d) is the size/dielectric parameter optimized insulation system;
FIG. 2 is a work flow chart of the multilayer optimal design method of the GIS/GIL basin-type insulator with high electrical resistance.
Detailed Description
The invention relates to a multilevel optimal design method of a GIS/GIL basin-type insulator with high electrical resistance, which comprises an initial design stage and a detailed design stage, wherein in the initial design stage, the overall contour of a concave surface and a convex surface of a basin body is obtained by the contour optimization of a geometric shape, and on the basis, the dielectric constant spatial distribution in the insulator is adjusted by the topological optimization of dielectric distribution to realize the regulation and control of an electric field along the surface, so that the overall optimal design of an insulating structure is realized; in a detailed design stage, based on a result of geometric shape and dielectric distribution topological optimization, searching an optimal dielectric constant and optimal size parameters of local key structures such as the height of a connecting piece through parameter optimization; the proposed multi-level comprehensive optimization strategy can utilize the design space to the maximum extent, and realize the optimization effect of the geometric shape and the dielectric distribution of 1+1 >. Compared with the original basin-type insulator before optimization, the maximum electric field reduction amplitude of the convex surface and the concave surface of the optimized basin body can reach 25 percent respectively, so that the overall electric field distribution of the basin-type insulator is greatly improved, and the development requirements of miniaturization, environmental protection and higher voltage level of GIS/GIL power equipment are met. The method specifically comprises the following steps:
s1, preliminary design stage
The outline and the shape of the pot body are optimized by adopting a shape optimization means. Because the basin-type insulator is of an axisymmetric structure, a three-dimensional modeling is not needed, and the complete structure of the basin-type insulator can be described through a two-dimensional axisymmetric model (comprising an r axis and a z axis).
S101, describing the shapes of the convex surface and the concave surface of the pot body by using a two-dimensional contour function. A Bernstein polynomial of the fourth order or more of the contour function, or a Fourier polynomial.
Taking the bernstein polynomial as an example, the shape function is shown in equation (1), where the r-axis has been represented by a normalized size and the function has been scaled down such that the polynomial coefficient is close to 1 in order of magnitude. At the same time, due to practical manufacturing process considerations, some reasonable constraints are imposed on the basin shape. The amount of deformation at the starting point of the profile curve, i.e. at the high voltage electrode, should be maximal, set to T 0 (maximum deflection) and zero deflection at the end of the profile. In order to ensure smooth curve transition and avoid electric field distortion points in the optimization process, the starting point of the function isAnd the derivative at the end point is also set to zero.
In addition, in order to prevent the pot body from being thin and thick, the design space is further limited, constraints are added to the derivative of the curve, the outline of the optimization process is guaranteed to be kept monotonously and gradually reduced, and the constraint conditions are summarized in the formula (1).
Figure BDA0002481339780000081
Wherein, C 0 、C 1 、C 2 、C 3 、C 4 、C 5 For adjusting the parameters, T, for the shape 0 For maximum thickness, T (r) is the derivative of the profile function.
According to the constraint condition, the Bernstein polynomial can be reduced to the formula (2), and at the moment, the unknown variable only has C with a limited value range 2 And C 3 In other words, the contour shape of the insulator can be adjusted by changing 2 variables, which is one of the advantages of shape optimization compared with the conventional size optimization.
Figure BDA0002481339780000082
According to the starting point and the end point of the pot body, after the normalized curve is expanded to the actual proportion, the curve function T respectively describing the convex surface and the concave surface outline can be obtained 1 (r) and T 2 (r)。
The decision variable is C describing the change of the contour 12 ，C 13 ，C 22 And C 23 . Usually in view of limiting the maximum electric field, the optimization goal is the maximum of the convex and concave electric fields.
The mathematical model can be extracted as formula (3):
Figure BDA0002481339780000083
wherein E _ covex and E _ covave respectively represent the maximum electric field of the convex surface and the concave surface of the pot body, and T min And T max The thinnest and thickest thicknesses of the basin insulator respectively. And the optimal shape parameters can be found by utilizing an optimization algorithm. The optimization algorithm can be an intelligent optimization algorithm genetic algorithm or a particle swarm algorithm, and can also be an algorithm based on gradient descent, such as moving asymptote emission.
S102, optimizing the dielectric distribution on the basis of optimizing the shape profile. The electric field distribution can be actively regulated and controlled by adjusting the dielectric property space distribution, and the first problem is how to find the optimal dielectric distribution.
To this end, through discrete division of the basin, several sub-regions are formed, the permittivity in each sub-region being the same. The optimization problem can be described as: and searching the optimal dielectric constant distribution in the insulating pot body so that the convex and concave electric fields are distributed most uniformly. The mathematical model is shown as formula (4), f a And f b Describing the uniformity of the concave and convex electric field distributions, w is the balance coefficient between the two, initially set to 0.5 mean Is the average electric field strength, ∈ min And epsilon max The upper and lower dielectric constants. l. the 1 And l 2 Respectively convex and concave edge surface regions, it can be seen that if 1 And l 2 The closer the electric field intensity at each point in the region is to the average field intensity, the smaller the integral value in equation (4), and when E is equal to E at each position in the region mean When the integral value reaches 0, the electric field distribution becomes uniform. Further, an integrated value in an initial condition is introduced as a reference value C ref Realization of f a And f b The normalization of (3) eliminates the influence of the geometrical structure and the size on the design optimization process.
Figure BDA0002481339780000091
In the optimization solving process of the above problems, due to the high nonlinearity of the optimization problem and the complexity of the structure to be optimized, some numerical instability phenomena often occur, wherein the most typical instability phenomena include two types of checkerboard and grid dependency, and topological nodes when the grid density is largeThe appearance of fine branched structures in the structure. The convergence of the numerical calculation process is seriously affected by the occurrence of such numerical instability phenomena. In order to suppress the instability, the sub-target function f a And f b On the basis, a numerical instability phenomenon suppression method based on global gradient penalty is provided, and a gradient penalty term f is introduced into an objective function grad The optimization problem can be further derived as equation (5):
Figure BDA0002481339780000101
a gradient penalty term f grad In q is the proportionality coefficient of the gradient penalty term, h mesh Is the area of the grid, Ω 1 For the design area (bowl), A is the area of the design area.
In the optimization design model of the point-by-point functional gradient insulating part, the design variable dimension is higher, and the difficulty of processing by using a conventional optimization algorithm is higher. Therefore, the design optimization of the point-by-point functional gradient insulator is carried out by utilizing a topological optimization technology. And (3) performing point-by-point functional gradient insulation piece optimization design by adopting a variable density method. On each discrete unit, a Solid Isotropic Material with pealization (SIMP) density interpolation function is applied to find the optimal density distribution, so equation (5) can be further derived as equation (6), where ρ is the density of each grid and p is the variable parameter of the SIMP interpolation function.
Figure BDA0002481339780000102
Compared with a size and shape optimization method, the topological optimization design method has more variables and larger calculation scale, and is difficult to solve by using a general numerical optimization algorithm. The mobile approximation algorithm (MMA) is one of the most widely used algorithms in the field of topology optimization today. But also can be widely applied to the multi-constraint situation. The method constructs an approximate function according to a function value and a first derivative value of an original function at a current design point, and provides a function independent variable value range in each iteration process by introducing a moving asymptote, so that the optimal dielectric space distribution is found.
S2, detailed design stage
S201, after the primary design of the insulation structure is completed, specific variable parameters need to be adjusted, and therefore the surface electric field is further reduced. In the detailed design stage, firstly, according to the result of topological optimization of dielectric distribution, in order to coordinate the contradiction between the manufacturing process and the design, the optimized gradient insulation region is converted into a high-dielectric region with invariable dielectric constant, so that the manufacturing difficulty of the actual insulation structure is reduced. To find the dielectric constant ε of the high dielectric region i The influence of the dielectric constant change on the distribution of the electric field along the surface is researched. The mathematical model can be described as equation (7), with the optimization goal still being to limit the maximum electric field of the convex and concave surfaces, with the upper and lower bounds of the permittivity variation being ε min And ε max 。
Figure BDA0002481339780000111
The optimal dielectric constant value can be found by adopting a parameter scanning mode or a traditional gradient descent algorithm.
S202, the insulator surface electric field distribution after the optimization of the contour shape and the optimization of the dielectric distribution is remarkably improved. The size parameter optimization is that on the basis, the sizes and the like of the high-voltage side metal accessories and the high-dielectric region are finely adjusted, and the electric field intensity along the surface is further reduced.
The optimization model can be extracted as equation (8), and the optimization variable is the fillet radius R of the convex and concave central inserts 1 And R 2 Height d of the connecting piece 1 And a high dielectric region length d 2 And (4) sizing parameters are equal, and corresponding variation ranges are given.
Figure BDA0002481339780000112
The multivariable multi-target optimization problem can be used for finding out the optimal size parameters by adopting a common genetic algorithm, an ant colony algorithm and the like. Thus, the design of the basin-type insulator for the GIS/GIL is completed.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Taking 550kVGIS basin-type insulator as an example, the steps of the design method of the invention are explained in detail.
Referring to fig. 1, fig. 1 (a) shows a simplified simulation model of a 550kV basin-type insulator, in which a basin body is connected to a central guide rod through a connector, and the other end extends to a flange of a box body, so as to realize isolation between two electrodes at high and low potentials. The original structure has serious potential distortion at the high-voltage side, and particularly, a proper electric field regulation strategy needs to be adopted in a concave electric field urgently. By T 1 (r) and T 2 (r) respectively represents the contour shapes of the convex surface and the concave surface, and the goal of shape optimization is to find an optimal contour curve to relieve the local electric stress concentration phenomenon, so that the electric field distribution along the surface is more uniform.
Referring to fig. 2, according to the optimization design strategy shown in fig. 2, in the preliminary design stage i, the basin body profile is described by using a bernstein polynomial of 5 th order, and the optimization problem can be described as formula (9), which defines the thickest thickness of the basin body to be 50mm, and adjusts the thinnest thickness to realize the optimization design of structures with different thicknesses.
Figure BDA0002481339780000131
The multi-objective optimization problem is solved by using a Levenberg-Marquardt optimization algorithm, and different thickness variable parameters are obtained according to different constraint conditions, and the result is shown in Table 1. It can be seen that the maximum electric field of the convex and concave surfaces can be significantly reduced with profile optimization, and the thinner the minimum thickness, the better the optimization. However, since thinner basins lead to a deterioration of the mechanical properties, in the subsequent optimization process, the T is aimed at min A structure of 40mm was developed (the structure is shown in fig. 1 (b)).
TABLE 1 contour shape optimized numerical simulation results
Figure BDA0002481339780000132
In the initial design stage II, the dielectric parameters in the basin body are optimally designed, the spatial distribution of the dielectric constant in the insulation is optimized by referring to the basin-type insulator under the action of alternating voltage, the optimization problem is as shown in formula (10), the upper bound of the dielectric constant is 20, and the lower bound is epoxy/Al 2 O 3 The dielectric constant of the composite material (5.8).
Figure BDA0002481339780000141
And solving the optimization problem by using a moving asymptote optimization algorithm. The optimized dielectric distribution is shown in fig. 1 (c), a gradient region with the dielectric constant of about 8 is grown on the high-voltage side, and the maximum value of the convex and concave electric fields can be further reduced to 9.12 and 9.08kV/mm, so that the electric field is further reduced on the basis of profile optimization.
In step S201, firstly, in order to reduce the difficulty of the manufacturing process, the gradient dielectric region of the tub head is replaced by a homogeneous high dielectric region according to the geometric profile, and an optimization algorithm is used to find an optimal dielectric constant value, where the optimization problem can be described as formula (11), the lower limit of the dielectric constant variation is 5.8, and the upper limit is 30, and the convex and concave electric fields are optimized.
Figure BDA0002481339780000142
The optimal dielectric constant is searched by adopting a parameter scanning mode, and the optimization result shows that when epsilon is i And when the electric field is 8.5, the optimization effect is optimal, and the maximum values of the convex and concave electric fields are respectively 9.34 kV/mm and 9.28kV/mm.
In step S202, fillet radii R for convex and concave center inserts 1 And R 2 Height d of the connecting piece 1 And a high dielectric region length d 2 The optimal parameter selection is developed, and the optimization problem is extracted as the formula (12).
Figure BDA0002481339780000151
And (3) finding out the optimal parameters by adopting a multi-target multi-parameter genetic algorithm. The numerical calculation result is shown in fig. 1 (d), and the optimal parameter of the height of the connecting piece is 70mm; the optimal parameter of the radius of the central insert at the concave side is 120mm; the optimal value of the convex central insert is 110mm; the optimal length parameter of the high dielectric region is 32mm. At this time, the maximum values of the convex and concave electric fields can be reduced to 8.94 and 9.03kV/mm.
In summary, the multilevel optimal design method for the GIS/GIL basin-type insulator with high electrical resistance, provided by the invention, divides the optimal design process of the basin-type insulator into two stages of preliminary design and detailed design, adopts a method combining shape optimization and dielectric distribution optimization, widens the design space, searches for a global optimal value, enables the maximum electric field reduction amplitude to reach more than 30%, and realizes the deep homogenization of the electric field distribution of the basin-type insulator.
The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.

Claims (7)

1. A multilevel optimization design method for a GIS/GIL basin-type insulator with high power-resisting performance is characterized by comprising a preliminary design stage and a detailed design stage, wherein in the preliminary design stage, outline shape optimization is adopted to construct the basic appearance of the GIS/GIL basin-type insulator, a two-dimensional outline function is used for describing the shapes of a convex surface and a concave surface of a basin body, the introduction of dielectric function gradient material distribution is considered, the topological optimization is used for adjusting the dielectric property so as to actively regulate and control the electric field distribution, and the surface electric field is further deeply homogenized on the basis of the outline optimization; in a detailed design stage, according to a result of topological optimization of dielectric distribution, the optimized gradient insulation region is converted into a high-dielectric region with constant dielectric constant so as to meet the constraint of the existing manufacturing conditions, the sizes of the high-voltage side metal accessory and the high-dielectric region are finely adjusted, an optimal size parameter is found out by adopting a genetic algorithm or an ant colony algorithm, and the design of the basin-type insulator for the GIS/GIL is completed.
2. The multi-level optimized design method of the GIS/GIL basin-type insulator with high electrical endurance performance according to claim 1, wherein the preliminary design stage specifically comprises:
s101, describing the shapes of the convex surface and the concave surface of the pot body by using a two-dimensional profile function, wherein the maximum deformation of the starting point of a profile curve is set as T 0 The deformation at the end point of the profile is zero, and the derivatives at the start point and the end point of the function are set to be zero; adding constraint to the derivative of the curve, and finding out the optimal contour control parameter according to an optimization algorithm;
s102, on the basis of shape contour optimization, discretely dividing the basin body into a plurality of sub-areas, wherein the dielectric constant in each sub-area is the same, searching for optimal dielectric constant distribution in the insulating basin body to enable the convex and concave electric fields to be uniformly distributed, and giving a function independent variable value range in each iteration process by introducing a moving asymptote method so as to find optimal dielectric spatial distribution.
3. The multi-level optimization design method of the GIS/GIL basin-type insulator with high electrical endurance performance according to claim 2, wherein in step S101, the mathematical optimization problem is as follows:
min：E＝max{E_convex,E_concave}
＝f(C 12 ,C 13 ,C 22 ,C 23 )
Figure FDA0002481339770000021
wherein E _ covex and E _ covave respectively represent the maximum electric field of the convex surface and the concave surface of the pot body, and C 12 ，C 13 ，C 22 And C 23 Is a profile control parameter, f is a function of the profile control parameter at the maximum electric field, T min And T max The thinnest and thickest thickness, T, of the basin-type insulator 1 (r) and T 2 (r) is a profile function of the convex and concave surfaces.
4. The multi-level optimization design method for the GIS/GIL basin insulator with high electrical endurance performance according to claim 2, wherein in step S102, a solid isotropic material punishment density interpolation function is applied to each discrete unit to find an optimal density distribution, and a mathematical optimization model is as follows:
findρ＝{ρ 1 ,ρ 2 ,…,ρ n }
Figure FDA0002481339770000022
Figure FDA0002481339770000023
/>
0＜ρ min ≤ρ i ≤1,i＝1,2,...,n
p＞0,q＞0,0≤w≤1
where ρ is the density vector of each grid, f Eopt As a function of the degree of homogeneity of the electric field along the surface, f grad Q is the proportionality coefficient of the gradient penalty term, E _ covex and E _ covave are the convex electric field distribution, E mean W is the equilibrium coefficient between the degrees of homogeneity of the convex and concave electric fields, l 1 And l 2 Respectively convex and concave edge regions, C ref1 And C ref2 Is an initial reference value, h mesh Is the area of the grid, omega is the integral calculation domain, A is the area of the integral calculation domain, ρ min For the minimum density of the grid, p is a variable parameter of the SIMP interpolation function.
5. The multi-level optimal design method of the GIS/GIL basin-type insulator with high electrical resistance performance according to claim 1, wherein the detailed design stage specifically comprises the following steps:
s201, converting the optimized gradient insulation region into a high dielectric region with constant dielectric constant according to the result of dielectric distribution topology optimization, and finding out the optimal dielectric constant value of the high dielectric region by adopting a parameter scanning mode or a traditional gradient descent algorithm;
s202, establishing a size parameter optimization model to finely adjust the sizes and the like of the high-voltage side metal accessories and the high-dielectric region.
6. The multi-level optimization design method of the GIS/GIL basin insulator with high electrical endurance performance according to claim 5, wherein in step S201, a mathematical model is established, and the optimization objective is to limit the maximum electric fields of the convex surface and the concave surface, specifically:
min：E＝max{E_convex,E_concave}
＝f(ε i )
s.t.ε min ＜ε i ≤ε max
wherein epsilon min And ε max Upper and lower limits of variation of dielectric constant, epsilon i For high dielectric zone dielectric constants, E _ covex and E _ covave represent the electric field maximum for the convex and concave basins, respectively.
7. The multi-level optimized design method for GIS/GIL basin insulator with high electrical resistance as claimed in claim 5, wherein in step S202, the dimensional variation ranges of the high-voltage side metal accessories and the high-dielectric region are as follows:
min：E＝max{E_convex,E_concave}
＝f(R 1 ,R 2 ,d 1 ,d 2 ,…)
Figure FDA0002481339770000031
wherein R is 1 And R 2 Radius of the convex and concave central inserts, d 1 Is the height of the connecting member, d 2 Is the length of the high dielectric region, R 1_min 、R 2_min 、d 1_min 、d 2_min And R 1_max 、R 2_max 、d 1_max 、d 2_max The upper and lower limits of the corresponding parameters are respectively, and E _ covex and E _ con are respectively used for representing the maximum values of the electric field of the convex surface and the concave surface of the pot body.
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