Optimization Method for Maximizing the Structural Stiffness of the Reinforcing Ribs of a Power Transformer and Related Devices

Abstract

The present invention belongs to the technical field of non-electrical quantity protection of power transformers, and discloses an optimization method and related device for maximizing the structural stiffness of the stiffeners of a power transformer. The optimization method includes: establishing a geometric model of an oil-immersed power transformer and the stiffener structure, loading a finite element model, performing a simulation calculation of the internal arc fault of the oil-immersed power transformer to obtain the fault oil pressure load; then performing a stiffness analysis to obtain the control equation of the transformer tank structure; taking the control equation of the transformer tank structure and the volume constraint equation of the stiffeners as constraint conditions, and maximizing the stiffness as the optimization objective function, obtaining the design velocity of the free boundary shape of the stiffeners, updating the shape of the transformer stiffeners, and determining the optimal shape for maximizing the structural stiffness of the stiffeners according to the update result. The present invention improves the scientificity and efficiency of the optimization through simulation calculation and sensitivity analysis, and effectively enhances the explosion-proof performance of the oil-immersed power transformer under the condition of internal arc fault.

Description

Technical Field

[0001] The present invention belongs to the technical field of non-electrical protection of power transformers, and particularly relates to an optimization method for maximizing the structural stiffness of stiffeners of power transformers and related devices. Background Art

[0002] As one of the most critical equipment in the power system, the reliability and stability of extra-high voltage large oil-immersed power transformers directly affect the safe and stable operation of the power grid. When an arc fault occurs inside a large transformer, the surrounding insulating oil quickly vaporizes and decomposes to form high-temperature and high-pressure bubbles. The compression of the surrounding insulating oil by the bubbles correspondingly causes the internal oil pressure of the large transformer to rise. This process poses a great threat to the mechanical structure of the large transformer. If the pressure generated within a short time exceeds the bearing capacity of the oil tank, an explosion accident will occur. In recent years, there have been multiple equipment deflagration accidents caused by high-energy arc faults inside extra-high voltage large transformers, resulting in serious economic losses and adverse social impacts.

[0003] Currently, the method of welding stiffeners on the outer wall of the transformer oil tank is commonly used to improve the structural strength of the transformer oil tank and reduce the probability of deflagration accidents. However, at present, the layout and installation dimensions of the stiffeners on the wall of the oil-immersed power transformer are mostly based on trial-and-error iteration design, which requires researchers to have rich engineering experience and may also lead to the obtained design scheme not being globally optimal, resulting in low safety. Summary of the Invention

[0004] To overcome the problems of unreasonable layout of stiffeners on the transformer tank wall and low safety in the prior art, the purpose of the present invention is to provide an optimization method for maximizing the structural stiffness of stiffeners of power transformers and related devices. This method can achieve the maximum stiffness design under the constraints of the transformer box structure and the volume of the stiffeners, improve the safety of the transformer, and at the same time provide scientific guidance for the design of the oil-immersed power transformer oil tank structure.

[0005] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0006] An optimization method for maximizing the structural stiffness of stiffeners of power transformers includes the following steps:

[0007] Establish a geometric model of the oil-immersed power transformer and the stiffener structure, load the finite element model, and perform simulation calculations on the internal arc fault of the oil-immersed power transformer according to the finite element model to obtain the fault oil pressure load;

[0008] Based on the fault oil pressure load, perform stiffness analysis on the oil-immersed power transformer and the stiffener structure to obtain the control equation of the transformer box structure; perform analysis on the stiffener structure to obtain the volume constraint equation of the stiffeners;

[0009] Taking the control equation of the transformer box structure and the volume constraint equation of the stiffener as the constraint conditions, and the maximization of stiffness as the optimization objective function, the shape gradient function is obtained;

[0010] According to the calculation of the shape gradient function, the design velocity of the free boundary shape of the stiffener is obtained;

[0011] Using the design velocity of the free boundary shape of the stiffener to update the shape of the transformer stiffener, and determining the optimal shape for maximizing the structural stiffness of the stiffener according to the update result.

[0012] Furthermore, the calculation formula for the fault oil pressure load is:

[0013]

[0014] where, is the radius of the bubble, is the bubble expansion velocity, is the bubble expansion acceleration; is the internal pressure of the bubble, is the insulating oil pressure, is the insulating oil domain boundary, is the fluid density, represents the fault oil pressure load.

[0015] Furthermore, the control equation of the transformer box structure is:

[0016]

[0017] where, represents the bilinear form of the stiffness operator, represents the linear form of the load operator, represents the translational displacement component of the transformer box structure, represents the rotational component about the axis of the transformer box structure, represents the local rotational component of the transformer box structure; represents the translational displacement component of the transformer box structure in the virtual displacement, represents the rotational component about the axis of the transformer box structure in the virtual displacement, represents the local rotational component of the transformer box structure in the virtual displacement, represents the allowable displacement space, means the equation holds for all virtual displacement fields belonging to the allowable displacement space of.

[0018] Furthermore, the volume constraint equation of the stiffener is:

[0019]

[0020] Among them, represents the total volume of the rib, represents the volume constraint value of the rib, represents the j th unit volume of the rib, represents the j th unit area domain, h represents the thickness of the rib, N represents the total number of finite elements after the rib is discretized, d A represents the area microelement.

[0021] Furthermore, the shape gradient function is calculated by the following formula:

[0022] (10)

[0023] Among them, represents the elastic tensor of the bending stress, represents the gradient of the actual local rotation field, represents the gradient of the actual local rotation field equivalent to the virtual local rotation field, represents the elastic tensor of the membrane stress, represents the gradient of the actual displacement field, represents the gradient of the actual displacement field equivalent to the virtual local rotation field, represents the shear stiffness coefficient, represents the elastic tensor of the shear stress, represents the component of the actual local rotation field, represents the component of the actual rotation field about the axis, represents the component of the actual local rotation field equivalent to the virtual local rotation field, represents the component of the actual rotation field about the axis equivalent to the virtual rotation field about the axis, represents the Lagrange multiplier of the volume constraint equation of the rib.

[0024] Furthermore, the design velocity of the free boundary shape of the rib is calculated by the following formula:

[0025]

[0026] Among them, is the in-plane unit outer normal vector on the boundary , represents the design velocity of the free boundary shape of the rib and the direction of the shape gradient function is opposite.

[0027] Further, update the shape of the transformer stiffeners using the design speed of the free boundary shape of the stiffeners, and determine the optimal shape that maximizes the structural stiffness of the stiffeners according to the update result, including the following steps:

[0028] After updating the shape of the transformer stiffeners using the design speed of the free boundary shape of the stiffeners, establish a geometric model of the oil-immersed power transformer and the stiffener structure, and perform a loop until the shape of the transformer stiffeners meets the convergence condition. Take the shape of the transformer stiffeners that meets the convergence condition as the optimal shape that maximizes the structural stiffness of the stiffeners.

[0029] In the second aspect of the present invention, there is provided an optimization system for maximizing the structural stiffness of a power transformer stiffener, including:

[0030] An arc fault simulation calculation module for establishing a geometric model of the oil-immersed power transformer and the stiffener structure, loading a finite element model, and performing an internal arc fault simulation calculation of the oil-immersed power transformer according to the finite element model to obtain a fault oil pressure load;

[0031] A control equation and volume constraint equation acquisition module for performing a stiffness analysis on the oil-immersed power transformer and the stiffener structure based on the fault oil pressure load to obtain a control equation for the transformer tank structure; analyzing the stiffener structure to obtain a volume constraint equation for the stiffeners;

[0032] A shape gradient function acquisition module for taking the control equation of the transformer tank structure and the volume constraint equation of the stiffeners as constraint conditions and maximizing the stiffness as the optimization objective function to obtain a shape gradient function;

[0033] A design speed acquisition module for the free boundary shape of the stiffeners for calculating the design speed of the free boundary shape of the stiffeners according to the shape gradient function;

[0034] An update module for updating the shape of the transformer stiffeners using the design speed of the free boundary shape of the stiffeners and determining the optimal shape that maximizes the structural stiffness of the stiffeners according to the update result.

[0035] In the third aspect of the present invention, there is provided an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the optimization method for maximizing the structural stiffness of the power transformer stiffener is implemented.

[0036] In the fourth aspect of the present invention, there is provided a computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, the optimization method for maximizing the structural stiffness of the power transformer stiffener is implemented.

[0037] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0038] In the present invention, by establishing a geometric model of an oil-immersed power transformer and a stiffener structure, loading a finite element model, and performing simulation calculations to obtain the fault oil pressure load, the mechanical response of the oil-immersed power transformer tank wall structure and its stiffeners under internal arc fault conditions can be evaluated. Under the constraints of the control equation of the transformer tank structure and the volume constraint equation of the stiffeners, the stiffness of the oil-immersed power transformer stiffener structure is maximized. The present invention overcomes the limitations of the traditional trial-and-error iterative design method based on engineering experience, combines the finite element calculation method with the sensitivity analysis technology, directly obtains the shape gradient function according to the optimization problem of maximizing the stiffness of the stiffeners, avoids the cumbersome calculation process of the stiffness matrix derivative in the traditional method, meets the rapid iterative requirements for the optimization of the oil-immersed power transformer tank stiffener structure, and the explosion-proof design requirements under severe fault conditions. The present invention provides important technical support for the structural safety design of oil-immersed power transformers under fault conditions and has broad practical application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a geometric model diagram of the oil-immersed power transformer in the present invention;

[0040] Figure 2 It is a mesh division diagram of the oil-immersed power transformer in the present invention;

[0041] Figure 3 It is a flow chart of the method for maximizing the stiffness of the oil-immersed power transformer stiffener structure in the present invention;

[0042] Figure 4 It is an optimized geometric model diagram of the oil-immersed power transformer in the present invention;

[0043] Figure 5 It is a top cover deformation diagram of the oil-immersed power transformer with an unoptimized stiffener structure in the present invention;

[0044] Figure 6 It is a top cover deformation diagram of the oil-immersed power transformer after optimizing the stiffener structure in the present invention;

[0045] Figure 7 It is a schematic diagram of the system for maximizing the stiffness of the oil-immersed power transformer stiffener structure in the present invention;

[0046] In the figure, 1 is the oil conservator of the power transformer, 2 is the oil tank of the power transformer, and 3 is the stiffener. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0047] The present invention will be described in detail below with reference to the accompanying drawings.

[0048] The optimization method for maximizing the structural stiffness of the reinforcing ribs of the power transformer of the present invention can quickly iteratively update and optimize the boundary shape of the reinforcing ribs 3 of the transformer, and achieve the maximization of the stiffness of the reinforcing rib 3 structure added to the power transformer under the constraints of the control equation of the transformer box body structure and the constraint condition of the reinforcing rib volume equation.

[0049] See Figure 3 , the optimization method for maximizing the structural stiffness of the reinforcing ribs of the power transformer of the present invention includes the following steps:

[0050] Step (1): See Figure 1 , there is a conservator 1 and reinforcing ribs 3 on the oil tank 2 of the power transformer. The physical model is reasonably simplified to reduce the computational amount of the geometric model while meeting the simulation accuracy.

[0051] The oil-immersed power transformer and the structure of the reinforcing ribs 3 are simplified, and then a geometric model of the simplified oil-immersed power transformer and the structure of the reinforcing ribs 3 is established through Spacecliam software (a three-dimensional solid direct modeling software).

[0052] Step (2): On the geometric model of the oil-immersed power transformer and the structure of the reinforcing ribs 3, the finite element model of the oil-immersed power transformer and the structure of the reinforcing ribs 3 is loaded by using ANSYS (Analysis of Systems) software. For the mesh division situation in the finite element model, see Figure 2 , and the element quality of the mesh model in the finite element model is checked to ensure that the mesh quality in the subsequent optimization process meets the calculation accuracy requirements.

[0053] Step (3): Using the finite element model of the oil-immersed power transformer and the structure of the reinforcing ribs 3, the internal arc fault simulation calculation of the oil-immersed power transformer is carried out to obtain the fault oil pressure load of the transformer tank wall structure and the reinforcing ribs 3. The fault oil pressure load is determined by the volume change of the arc-induced bubble, and the calculation formula of the fault oil pressure load is:

[0054] (1)

[0055] In the formula, R is the radius of the bubble, is the bubble expansion speed, is the bubble expansion acceleration; is the internal pressure of the bubble, is the insulating oil pressure, is the insulating oil domain boundary, is the fluid density, characterizes the fault oil pressure load.

[0056] Step (4): Define the regional variables of the oil-immersed power transformer and the stiffener 3 structure, and define the forces acting on different regions of the oil-immersed power transformer and the stiffener 3 structure; specifically, the out-of-plane load per unit area on the oil-immersed power transformer tank is q and the in-plane load per unit area on the oil-immersed power transformer tank is , represents the component of the in-plane load on the power transformer tank along different directions, represents different directions of the load, α When, it represents the first two-dimensional in-plane direction of the local coordinate system of the shell (i.e., direction), When, it represents the second two-dimensional in-plane direction of the local coordinate system of the shell (i.e., direction), the shear force per unit length caused by the local shear deformation of the tank wall is Q , and the out-of-plane bending moment per unit area at the connection between the stiffener and the tank wall is is the component of the out-of-plane bending moment per unit area at the connection between the stiffener and the tank wall along different directions, and the bending moment per unit length of the stiffener is , is the component of the bending moment per unit length of the stiffener along different directions, and the in-plane load per unit length of the stiffener is , is the component of the in-plane load per unit length of the stiffener along different directions.

[0057] Step (5): According to the failure oil pressure load of the transformer tank wall structure and the stiffener 3, perform a stiffness analysis on the oil-immersed power transformer and the stiffener 3 structure. The control equation of the transformer box structure can be written as:

[0058] (2)

[0059] In the formula, represents the bilinear form of the stiffness operator, represents the linear form of the load operator, u : 0 represents the translational displacement component of the transformer box structure, which is used to describe the overall translational deformation of the transformer tank and the stiffener 3, represents the rotational component about the axis of the transformer box structure, which is used to describe the bending or torsional deformation of the transformer tank and the stiffener 3, represents the local rotational component of the transformer box structure, which is used to supplement the high-order deformation mode of the transformer tank and the stiffener 3; represents the translational displacement component of the transformer box structure in the virtual displacement, represents the rotational component about the axis of the transformer box structure in the virtual displacement, Represents the local rotation component of the transformer tank structure in the virtual displacement, Represents the allowable displacement space, which contains all displacement fields that satisfy the geometric boundary conditions and continuity, Indicates that the equation holds for all virtual displacement fields belonging to the allowable displacement space of.

[0060] The bilinear form of the stiffness operator and the linear form are defined as follows respectively:

[0061] (3)

[0062] where, Represents the elastic tensor of the membrane stress, Represents the elastic tensor of the bending stress, Represents the elastic tensor of the shear stress, u 0 represents the translational displacement component of the transformer tank structure, Represents the rotational component about the axis of the transformer tank structure, Represents the local rotation component of the transformer tank structure, Represents the translational displacement component of the transformer tank structure in the virtual displacement, Represents the rotational component about the axis of the transformer tank structure in the virtual displacement, Represents the local rotation component of the transformer tank structure in the virtual displacement, j Represents the element number, Represents the j area domain of the th element, Represents the gradient of the actual displacement field, Represents the gradient of the virtual displacement field, Represents the gradient of the actual local rotation field, Represents the shear stiffness coefficient, Represents the actual shear strain component, Represents the virtual shear strain component, Represents the first deformation direction in the actual field, Represents the second deformation direction in the actual field, Represents the first deformation direction in the virtual displacement field, Represents the second deformation direction in the virtual displacement field, = 1, 2, When it is 1, it corresponds to the first direction in the two-dimensional plane of the local coordinate system of the shell, that is, direction, When it is 2, it corresponds to the second direction in the two-dimensional plane of the local coordinate system of the shell, that is, direction, when = 1, = 2, = 2, When = 1, the thin film stress term can be expressed as , represents the gradient of the displacement in the direction along the direction in the actual displacement field. represents the gradient of the displacement in the direction along the direction in the virtual displacement field. The bending stress term can be expressed as , represents the gradient of the bending with respect to the direction in the actual local rotation field around the direction. represents the gradient of the bending with respect to the direction in the virtual local rotation field around the direction. The shear stress term can be expressed as , represents the actual transverse shear strain along the direction. represents the actual transverse shear strain along the direction. d A represents the area element. N represents the total number of finite elements after the stiffeners are discretized.

[0063] (4)

[0064] Among them, represents the translational displacement component of the transformer tank structure in the virtual displacement. represents the rotational component about the axis of the transformer tank structure in the virtual displacement. represents the local rotational component of the transformer tank structure in the virtual displacement. is the component of the in-plane load on the upper edge of the power transformer oil tank in different directions. is the component of the out-of-plane bending moment per unit area at the connection between the stiffeners and the oil tank wall in different directions. is the out-of-plane load per unit area on the oil-immersed power transformer oil tank. represents the component of the in-plane load per unit length of the stiffeners in different directions. represents the component of the bending moment per unit length of the stiffeners in different directions. represents the shear force per unit length in the virtual displacement field. represents the virtual displacement field in the direction of the translational component. represents the virtual displacement field in the direction of the local rotational component. N represents the total number of finite elements after the stiffeners are discretized. Represents the area domain of the j th unit, used to calculate the load contribution inside the unit. Represents the j th unit boundary, used to calculate the load contribution on the boundary. Denoted as d A Represents the area microelement. Represents the boundary area microelement.

[0065] Step (6): Taking the control equation of the transformer tank structure in Equation (2) and the volume constraint equation of the stiffener 3 as the constraint conditions, and maximizing the stiffness as the optimization objective function, the optimization problem of maximizing the stiffness of the stiffener 3 of the oil-immersed power transformer can be written as:

[0066]

[0067] (5)

[0068] Among them, Represents the bilinear form of the stiffness operator. Represents the adjoint variable. Represents the state variable. u 0 represents the translational displacement component of the transformer tank structure. Represents the rotational component about the axis of the transformer tank structure. Represents the local rotational component of the transformer tank structure. Represents the translational displacement component of the transformer tank structure in the virtual displacement. Represents the rotational component about the axis of the transformer tank structure in the virtual displacement. Represents the local rotational component of the transformer tank structure in the virtual displacement. U Represents the allowable displacement space, which contains all displacement fields that satisfy the geometric boundary conditions and continuity. Represents the total volume of the stiffener. Represents the volume constraint value of the stiffener. Represents the of the stiffener j th unit volume. Represents the j th unit area domain. h Represents the thickness of the stiffener, usually a constant or varying with position. N Represents the total number of finite elements after the stiffener is discretized. Denoted as d A Represents the area microelement.

[0069] If represents the Lagrange multiplier of the volume constraint equation of the stiffener, then the Lagrangian function of this optimization problem L can be expressed as:

[0070]

[0071] (6)

[0072] Among them, represents the area domain of the j th unit, u 0 represents the translational displacement component of the transformer tank structure, represents the rotational component about the axis of the transformer tank structure, represents the local rotational component of the transformer tank structure, represents the translational displacement component of the transformer tank structure in the virtual displacement, represents the rotational component about the axis of the transformer tank structure in the virtual displacement, represents the local rotational component of the transformer tank structure in the virtual displacement, is the linear form of the load operator, representing the virtual work contribution of the external load, is the bilinear form of the stiffness operator, describing the stiffness characteristics of the structure, represents the total volume of the stiffeners, represents the volume constraint value of the stiffeners.

[0073] Assume that the sub-boundary under the action of non-zero external forces (bending moment per unit length of the stiffener M , in-plane load per unit length of the stiffener N and shear force per unit length caused by the local shear deformation of the oil tank wall Q ) remains unchanged (i.e., the design speed =0 of the free boundary shape of the stiffener), and the forces acting on the oil-immersed power transformer tank (in-plane load per unit area on the oil-immersed power transformer tank f , out-of-plane bending moment per unit area at the connection of the stiffener 3 and the oil tank wall , out-of-plane load per unit area on the oil-immersed power transformer tank ) do not change with space and time (i.e., , is the derivative of the in-plane load per unit length with respect to space and time, is the derivative of the out-of-plane bending moment per unit area with respect to space and time, is the derivative of the out-of-plane load per unit area with respect to space and time). Furthermore, the derivative of the Lagrangian function of this optimization problem is derived using formula (6):

[0074] (7)

[0075] Among them

[0076]

[0077] (8)

[0079] Among them, represents the translational displacement component of the transformer tank structure, represents the shape derivative of the translational displacement component of the transformer tank structure, represents the rotational component about the axis of the transformer tank structure, represents the shape derivative of the rotational component about the axis of the transformer tank structure, represents the local rotational component of the transformer tank structure, represents the shape derivative of the local rotational component of the transformer tank structure, represents the translational displacement component of the transformer tank structure in the virtual displacement, represents the shape derivative of the translational displacement component of the transformer tank structure in the virtual displacement, represents the rotational component about the axis of the transformer tank structure in the virtual displacement, represents the shape derivative of the rotational component about the axis of the transformer tank structure in the virtual displacement, represents the local rotational component of the transformer tank structure in the virtual displacement, represents the shape derivative of the local rotational component of the transformer tank structure in the virtual displacement, represents the shape gradient function, is the in-plane unit outer normal vector on the boundary represents the design velocity of the free boundary shape of the stiffener, represents the admissible function space of the design velocity, N represents the total number of finite elements after the stiffener is discretized, represents the elastic tensor of the bending stress, represents the elastic tensor of the membrane stress, represents the elastic tensor of the shear stress, represents the gradient of the actual local rotation field, represents the gradient of the virtual local rotation field, represents the gradient of the actual displacement field, represents the gradient of the virtual displacement field, represents the shear stiffness coefficient, represents the component of the actual local rotation field, represents the component of the actual rotational field about the axis, represents the component of the virtual local rotation field, represents the component of the virtual rotational field about the axis, represents the Lagrange multiplier of the volume constraint equation of the stiffener, represents the boundary area element.

[0080] Furthermore, it can be deduced that when the state variable , the adjoint variable and the Lagrange multiplier of the volume constraint equation of the stiffener satisfy the optimality conditions, the derivative of the Lagrangian function can be simplified to:

[0081] (9)

[0082] where represents the shape gradient function, is the in-plane unit outer normal vector on the boundary , represents the design velocity of the free boundary shape of the stiffener, belonging to the admissible function space of the design velocity, represents the inner product.

[0083] The shape gradient function is obtained by substituting the self-adjoint relation into formula (8):

[0084] (10)

[0085] where represents the gradient of the actual local rotation field, represents the gradient of the actual local rotation field equivalent to the virtual local rotation field, represents the gradient of the actual displacement field, represents the gradient of the actual displacement field equivalent to the virtual local rotation field, represents the shear stiffness coefficient, represents the component of the actual local rotation field, represents the component of the actual local rotation field equivalent to the virtual local rotation field, represents the component of the actual rotation field about the axis, represents the component of the actual rotation field about the axis equivalent to the virtual rotation field about the axis.

[0086] Step (7): When the condition of maximizing the stiffness of the stiffener 3 is satisfied, the derivative of the Lagrangian function is equal to 0. Therefore, according to the derivative of the Lagrangian function and the shape gradient function, the design velocity of the free boundary shape of the stiffener 3 is obtained. According to formula (9), it can be known that the design velocity of the free boundary shape of the stiffener 3 is proportional to the shape gradient function , and can be expressed as:

[0087] (11)

[0088] Among them, is the in-plane unit outer normal vector on the boundary , and represents the design velocity of the free boundary shape of the rib is opposite to the direction of the shape gradient function .

[0089] The design velocity of the free boundary shape of rib 3 is divided into in-plane design velocity and out-of-plane design velocity . Then, the analysis control equation of the design velocity of the free boundary shape of rib 3 can be obtained as follows:

[0090] (12)

[0091] Among them, is the in-plane design velocity, is the in-plane design velocity along the direction, is the in-plane design velocity along the direction, is the out-of-plane design velocity, is the bilinear form of the stiffness operator, is the local rotation design velocity, represents the translational displacement component of the transformer tank structure in the virtual displacement, represents the rotational component about the axis of the transformer tank structure in the virtual displacement, represents the local rotational component of the transformer tank structure in the virtual displacement, represents the shape gradient function, is the in-plane unit outer normal vector on the boundary , represents the boundary, represents the allowable displacement space, and the superscript in each variable represents the element number, represents the admissible function space of the design velocity.

[0092] In addition, in order to obtain the optimal free boundary shape of rib 3, the entire region of the transformer tank structure is fixed (i.e., the design velocity V 0 = 0), and it is assumed that there is no change in the out-of-plane direction of rib 3. Therefore, an additional constraint is imposed on the change in the normal direction of the surface of rib 3 (i.e., the out-of-plane design velocity = 0).

[0093] Step (8): Using the design velocity of the free boundary shape of the rib determined in step (7) Iteratively update the shape of the transformer stiffener 3, and continuously repeat steps (1) - (7) until the iterative convergence condition is met (i.e., the increase in the overall stiffness of the stiffener 3 after two adjacent optimizations is less than the preset threshold) or the constraint condition is satisfied (the volume constraint equation of the stiffener 3), to obtain the optimal shape that maximizes the structural stiffness of the oil-immersed power transformer stiffener 3.

[0094] Step (9): Output the optimal shape that maximizes the structural stiffness of the oil-immersed power transformer stiffener 3 obtained in step (8).

[0095] For the oil-immersed power transformer after optimizing the stiffener 3 and its stiffener 3 structure, see Figure 4 , on the power transformer oil tank 2, there is a power transformer conservator 1 and the optimized stiffener 3.

[0096] By comparing and analyzing with the initial shape, compare the deformation amounts of the oil-immersed power transformer box structure under the oil pressure load generated by the same internal arc fault, and verify the improvement effect of the structural stiffness of the optimized oil-immersed power transformer stiffener 3.

[0097] According to the above optimization method, the deformation amounts of the oil-immersed power transformer before and after optimizing the stiffener 3 under the oil pressure load generated by the same internal arc fault are as shown in Figure 5 and Figure 6 . It is set that the total energy released by the arc fault caused by the internal fault of the oil-immersed power transformer before and after optimization is the same, which is 10 MJ. Figure 5 and Figure 6 show the comparison of the deformation degrees of the transformer box structure before and after optimizing the stiffener 3. See Figure 5 and Figure 6 , after optimizing the size parameters of the stiffener 3, the area where the deformation amount of the center area of the oil tank wall exceeds 22 mm is significantly reduced. The calculation results show that this optimization method realizes the maximization of the structural stiffness of the oil-immersed power transformer stiffener 3, enhances the explosion-proof performance of the transformer box, and significantly reduces the risk of transformer explosion accidents.

[0098] See Figure 7 , another embodiment of the present invention provides an optimization system for maximizing the structural stiffness of a power transformer stiffener, including:

[0099] An arc fault simulation calculation module, which is used to establish a geometric model of the oil-immersed power transformer and the stiffener structure, load the finite element model, and perform simulation calculations on the internal arc fault of the oil-immersed power transformer according to the finite element model to obtain the fault oil pressure load;

[0100] A control equation and volume constraint equation acquisition module, which is used to perform stiffness analysis on the oil-immersed power transformer and the stiffener structure based on the fault oil pressure load to obtain the control equation of the transformer tank structure; analyze the stiffener structure to obtain the volume constraint equation of the stiffener.

[0101] A shape gradient function acquisition module, which is used to take the control equation of the transformer tank structure and the volume constraint equation of the stiffener as constraint conditions, and the maximization of stiffness as the optimization objective function to obtain the shape gradient function.

[0102] A design speed acquisition module for the free boundary shape of the stiffener, which is used to calculate according to the shape gradient function to obtain the design speed of the free boundary shape of the stiffener.

[0103] An update module, which is used to update the shape of the transformer stiffener by using the design speed of the free boundary shape of the stiffener, and determine the optimal shape for maximizing the stiffness of the stiffener structure according to the update result.

[0104] Another embodiment of the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the optimization method for maximizing the stiffness of the power transformer stiffener structure is implemented.

[0105] Another embodiment of the present invention provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the optimization method for maximizing the stiffness of the power transformer stiffener structure is implemented.

[0106] The present invention establishes a geometric model and a finite element model of the oil-immersed power transformer and the stiffener 3 structure, and numerically simulates and evaluates the mechanical response of the transformer tank wall structure and its stiffener 3 under internal arc fault conditions. Then, based on the shape gradient function, a sensitivity analysis of the optimization objective is performed on the boundary shape of the stiffener 3. Combining the sensitivity analysis results, the boundary shape of the stiffener 3 is iteratively updated and optimized. Finally, on the premise of meeting the iterative convergence conditions, under the constraint conditions of the control equation of the transformer tank structure and the volume constraint equation of the stiffener, the maximization of the stiffness of the stiffener 3 structure is realized, overcoming the limitations of the traditional trial-and-error iterative design method based on engineering experience, combining the finite element calculation method and the sensitivity analysis technology, meeting the rapid iterative requirements for the optimization of the stiffener 3 structure of the power transformer tank 2, and the explosion-proof design requirements under harsh fault conditions. The present invention improves the mechanical compressive capacity and structural safety of the oil-immersed power transformer under internal arc faults.

[0107] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, optical storage, etc.) that contain computer-usable program code.

[0108] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to the embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as the combination of flows and / or blocks in the flowchart and / or block diagram, can be realized by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices produce means for realizing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0109] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing devices to work in a specific manner, such that the instructions stored in the computer-readable memory produce a manufactured article including instruction means that realizes the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0110] These computer program instructions can also be loaded onto a computer or other programmable data processing devices, such that a series of operation steps are executed on the computer or other programmable devices to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable devices provide steps for realizing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0111] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: still can modify the specific implementation manners of the present invention or make equivalent substitutions, and any modification or equivalent substitution that does not depart from the spirit and scope of the present invention should be covered by the protection scope of the present invention.

Claims

1. Optimization method for maximizing the structural stiffness of the stiffeners of a power transformer, characterized in that, Including the following steps: Establish a geometric model of the oil-immersed power transformer and the stiffener (3) structure, load the finite element model, and perform internal arc fault simulation calculations on the oil-immersed power transformer according to the finite element model to obtain the fault oil pressure load; Based on the fault oil pressure load, perform a stiffness analysis on the oil-immersed power transformer and the stiffener (3) structure to obtain the control equation of the transformer tank structure; Analyze the stiffener (3) structure to obtain the volume constraint equation of the stiffener (3); Taking the control equation of the transformer tank structure and the volume constraint equation of the stiffener (3) as constraint conditions, and maximizing the stiffness as the optimization objective function, obtain the shape gradient function; According to the calculation of the shape gradient function, obtain the design speed of the free boundary shape of the stiffener (3); Use the design speed of the free boundary shape of the stiffener (3) to update the shape of the transformer stiffener (3), and determine the optimal shape that maximizes the stiffness of the stiffener (3) structure according to the update result; The control equation of the transformer tank structure is: In the formula, represents the bilinear form of the stiffness operator, represents the linear form of the load operator, represents the translational displacement component of the transformer tank structure, represents the rotational component about the axis of the transformer tank structure, represents the local rotational component of the transformer tank structure; represents the translational displacement component of the transformer tank structure in the virtual displacement, represents the rotational component about the axis of the transformer tank structure in the virtual displacement, represents the local rotational component of the transformer tank structure in the virtual displacement, represents the allowable displacement space, means that the equation holds for all virtual displacement fields belonging to the allowable displacement space ; The volume constraint equation of the stiffener (3) is: Among them, represents the total volume of the rib, represents the volume constraint value of the rib, represents the j th volume of the rib unit, represents the j th area domain of the unit, h represents the thickness of the rib, N represents the total number of finite elements after the rib is discretized, d A represents the area microelement.

2. The optimization method for maximizing the structural stiffness of the reinforcing ribs of a power transformer according to claim 1, wherein, The calculation formula of the fault oil pressure load is: In the formula, is the radius of the bubble, is the bubble expansion velocity, is the bubble expansion acceleration; is the internal pressure of the bubble, is the insulating oil pressure, is the boundary of the insulating oil region, is the fluid density, represents the fault oil pressure load.

3. The optimization method for maximizing the structural stiffness of the reinforcing ribs of a power transformer according to claim 1, characterized in that The shape gradient function is calculated by the following formula: (10) Among them, denotes the elastic tensor of the bending stress, denotes the gradient of the actual local rotation field, denotes the gradient of the actual local rotation field equivalent to the virtual local rotation field, denotes the elastic tensor of the membrane stress, denotes the gradient of the actual displacement field, denotes the gradient of the actual displacement field equivalent to the virtual local rotation field, denotes the shear stiffness coefficient, denotes the elastic tensor of the shear stress, denotes the component of the actual local rotation field, denotes the component of the actual axis rotation field, denotes the component of the actual local rotation field equivalent to the virtual local rotation field, denotes the component of the actual axis rotation field equivalent to the virtual axis rotation field, denotes the Lagrange multiplier of the volume constraint equation of the stiffener.

4. The optimization method for maximizing the structural stiffness of the reinforcing ribs of a power transformer according to claim 3, characterized in that The design speed of the free boundary shape of the stiffener (3) is calculated by the following formula: Among them, is the unit outer normal vector in the plane on the boundary , and represents the design velocity of the free boundary shape of the rib is opposite to the direction of the shape gradient function .

5. The optimization method for maximizing the structural stiffness of the reinforcing ribs of a power transformer according to claim 1, characterized in that, Using the design speed of the free boundary shape of the stiffener (3) to update the shape of the transformer stiffener (3), and determining the optimal shape that maximizes the stiffness of the stiffener (3) structure according to the update result, including the following steps: After using the design speed of the free boundary shape of the stiffener (3) to update the shape of the transformer stiffener (3), establish a geometric model of the oil-immersed power transformer and the stiffener (3) structure, and perform a loop until the shape of the transformer stiffener (3) meets the convergence condition, and use the shape of the transformer stiffener (3) that meets the convergence condition as the optimal shape that maximizes the stiffness of the stiffener (3) structure.

6. An optimization system for maximizing the structural stiffness of the reinforcing ribs of a power transformer, characterized in that, Including: An arc fault simulation calculation module, which is used to establish a geometric model of the oil-immersed power transformer and the stiffener (3) structure, load the finite element model, and perform internal arc fault simulation calculations on the oil-immersed power transformer according to the finite element model to obtain the fault oil pressure load; A control equation and volume constraint equation acquisition module, which is used to perform a stiffness analysis on the oil-immersed power transformer and the stiffener (3) structure based on the fault oil pressure load to obtain the control equation of the transformer tank structure; Analyze the stiffener (3) structure to obtain the volume constraint equation of the stiffener (3); A shape gradient function acquisition module, which is used to take the control equation of the transformer tank structure and the volume constraint equation of the stiffener (3) as constraint conditions, and maximize the stiffness as the optimization objective function to obtain the shape gradient function; A design speed acquisition module for the free boundary shape of the stiffener (3), which is used to calculate according to the shape gradient function to obtain the design speed of the free boundary shape of the stiffener (3); An update module, which is used to use the design speed of the free boundary shape of the stiffener (3) to update the shape of the transformer stiffener (3), and determine the optimal shape that maximizes the stiffness of the stiffener (3) structure according to the update result; The control equation of the transformer tank structure is: In the formula, represents the bilinear form of the stiffness operator, represents the linear form of the load operator, represents the translational displacement component of the transformer tank structure, represents the rotational component about the axis of the transformer tank structure, represents the local rotational component of the transformer tank structure; represents the translational displacement component of the transformer tank structure in the virtual displacement, represents the rotational component about the axis of the transformer tank structure in the virtual displacement, represents the local rotational component of the transformer tank structure in the virtual displacement, represents the allowable displacement space, means that the equation holds for all virtual displacement fields belonging to the allowable displacement space ; The volume constraint equation of the stiffener (3) is: Among them, represents the total volume of the rib, represents the volume constraint value of the rib, represents the j th volume of the rib unit, represents the j th area domain of the unit, h represents the thickness of the rib, N represents the total number of finite elements after the rib is discretized, d A represents the area microelement.

7. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the described processor executes the described computer program, it implements the optimization method for maximizing the structural stiffness of the power transformer stiffeners as described in any one of claims 1 to 5.

8. A computer-readable storage medium storing a computer program, characterized in that, When the described computer program is executed by the processor, it implements the optimization method for maximizing the structural stiffness of the power transformer stiffeners as described in any one of claims 1 to 5.

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