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CN-121981053-A - A-alpha formula-based transient electromagnetic field-circuit coupling high-precision calculation method

CN121981053ACN 121981053 ACN121981053 ACN 121981053ACN-121981053-A

Abstract

The application relates to an A-alpha formula-based transient electromagnetic field-circuit coupling high-precision calculation method, which is characterized in that grid data are divided into a plurality of polyhedron smooth domains centering on corresponding edges according to each edge in grid data of a 1/8 period model of a three-dimensional motor, smooth vector functions of the edges and smooth functions of nodes in the polyhedron smooth domains are calculated, a transient field coupling equation set is constructed based on an A-alpha formula, transient eddy currents and coulomb specifications, and the transient field coupling equation set is rewritten according to the smooth vector functions of each edge, the smooth functions of each node and a Galerkin method to obtain a transient field coupling system equation, the transient field coupling system equation is further rewritten into a Newton iteration linear equation, and the Newton iteration linear equation is solved iteratively by adopting a Newton iteration method until convergence is achieved, so that magnetic vector positions in field coupling are obtained, and high-precision numerical solution of a transient field coupling problem in a complex motor system is realized.

Inventors

  • CUI XIANGYANG
  • DENG HUI
  • ZHENG JINGYU

Assignees

  • 湖南迈曦软件有限责任公司

Dates

Publication Date
20260505
Application Date
20260409

Claims (10)

  1. 1. A transient electromagnetic field-circuit coupling high-precision calculation method based on an A-alpha formula is characterized by comprising the following steps: s1, importing grid data of a 1/8 period model of a three-dimensional motor; S2, dividing the grid data into a plurality of polyhedral smooth domains taking the corresponding edges as the center according to each edge in the grid data, wherein the polyhedral smooth domains are formed by surrounding nodes, body centers and face centers of tetrahedron units in the grid data with the corresponding edges; S3, constructing a transient field path coupling equation set based on an A-alpha formula, transient eddy current and coulomb specification, and rewriting the transient field path coupling equation set according to smooth vector functions of all edges, smooth functions of all nodes and a Galerkin method to obtain a system equation of transient field path coupling; and S4, iteratively solving a Newton iteration linear equation by adopting a Newton iteration method until convergence to obtain a magnetic vector bit in field path coupling.
  2. 2. The method of claim 1, wherein the smooth vector-shaped function of the edge is calculated as: ; Wherein, the A smooth vector-shaped function representing the edge e in the polyhedral smooth field k, Indicating the deviation of the deflection of the beam, Represents the r direction, which includes Direction(s), Direction(s), The direction of the light beam is changed, Representing the smooth field of the kth polyhedron, A vector-shaped function representing the edge e, A smoothing function representing the smooth field of the kth polyhedron, Representing the number of tetrahedral units in the k-th polyhedral smooth field, A vector-shaped function representing the edge e in the nth tetrahedral unit, Representing the volume of the nth tetrahedral unit, Representing differentiation of the integral domain.
  3. 3. The method of claim 1, wherein the smooth function of the node is calculated as: ; Wherein, the Representing a smooth shape function at node i in the polyhedral smooth field k, Indicating the deviation of the deflection of the beam, Represents the r direction, which includes Direction(s), Direction(s), The direction of the light beam is changed, Representing the smooth field of the kth polyhedron, Representing the shape function at node i, A smoothing function representing the smooth field of the kth polyhedron, Representing the number of tetrahedral units in the k-th polyhedral smooth field, Representing the shape function at node i in the nth tetrahedral unit, Representing the volume of the nth tetrahedral unit, Representing differentiation of the integral domain.
  4. 4. A method according to claim 2 or 3, wherein the smoothing function is the inverse of the volume of the corresponding polyhedral smoothing field, and the smoothing function is satisfied as: ; Wherein, the Representing the smooth field of the kth polyhedron, A smoothing function representing the smooth field of the kth polyhedron, Representing differentiation of the integral domain.
  5. 5. The method of claim 1, wherein the expression of the transient field coupling equation set is: ; Wherein, the The rotation is indicated by the rotation of the rotor, The magnetic resistance rate is indicated as a function of the magnetic resistance, The magnetic vector bits are represented as such, Represents the potential of the virtual scalar, Representing the transient induced eddy current term, The time is represented by the time period of the day, Indicating the deviation of the deflection of the beam, Represents the difference in the voltages of the terminals, Representing the source potential of the source, The current is represented by a value representing the current, Representing the voltage applied by the external circuit, Representing the external resistance of the resistor, Representing the external inductance of the inductor, The domain of integration is represented by a representation of the integrated domain, Representing differentiation of the integral domain.
  6. 6. The method of claim 5, wherein deriving the system equation for the transient field coupling comprises: Rewriting a transient field path coupling system equation set according to the smooth vector function of each edge, the smooth function of each node and the Galerkin method to obtain a weak form of the transient field path coupling system equation set; Expanding magnetic vector potential and virtual scalar potential according to the smooth vector function of each edge, the smooth shape function of each node and the difference theorem; And (3) coupling the weak form of the transient field coupling equation set, the expansion of the magnetic vector bit and the expansion of the virtual scalar potential to obtain a transient field coupling system equation.
  7. 7. The method of claim 6, wherein the weak form of the transient field coupling equation set is expressed as: ; Wherein, the A smooth vector-shaped function representing the edge e in the polyhedral smooth field k, Representing a smooth shape function at node i in the polyhedral smooth field k, Representing the smooth field of the kth polyhedron, Representing the smooth regions of the coarse conductor regions in the periodic model, The rotation is indicated by the rotation of the rotor, The magnetic resistance rate is indicated as a function of the magnetic resistance, The magnetic vector bits are represented as such, Represents the potential of the virtual scalar, Representing the transient induced eddy current term, The time is represented by the time period of the day, Indicating the deviation of the deflection of the beam, Represents the difference in the voltages of the terminals, Representing the source potential of the source, The current is represented by a value representing the current, Representing the voltage applied by the external circuit, Representing the external resistance of the resistor, Representing the external inductance of the inductor, Representing differentiation of the integral domain.
  8. 8. The method of claim 6, wherein the expansion of the magnetic vector bits, the expansion of the virtual scalar potentials are respectively: ; ; Wherein, the The magnetic vector bits are represented as such, Represents the potential of the virtual scalar, Representing polyhedral smooth fields The number of the middle edges is equal to the number of the middle edges, Representing polyhedral smooth fields The number of intermediate nodes is determined by the number of intermediate nodes, A smooth vector-shaped function representing the edge e in the polyhedral smooth field k, Representing the tangential magnetic vector value at edge e, Representing a smooth shape function at node i in the polyhedral smooth field k, Representing the virtual scalar potential value at node i.
  9. 9. The method of claim 1, wherein the newton's iterative linear equation is expressed as: ; ; ; Wherein, the Representing a system jacobian matrix; a residual representing magnetic vector bits; Representing the residual of the system equation; a magnetic vector bit representing the h+1 iteration step; A magnetic vector bit representing the h iteration step; Representing a system stiffness matrix; Representing a known external force vector.
  10. 10. The method of claim 9, wherein the iterative solution process of the newton's iterative method comprises: initializing an iteration step; step 2, solving a Newton iteration linear equation under the current iteration step to obtain a magnetic vector bit of the current iteration step; step3, adding the residual error of the magnetic vector bit and the magnetic vector bit of the current iteration step to obtain the magnetic vector bit of the next iteration step; Step 4, updating the iteration step; And 5, repeatedly executing the steps 2-4 until the Newton iterative linear equation converges and the magnetic vector bit in the field path coupling is achieved.

Description

A-alpha formula-based transient electromagnetic field-circuit coupling high-precision calculation method Technical Field The application relates to the technical field of engineering electromagnetic calculation, in particular to a transient electromagnetic field-circuit coupling high-precision calculation method based on an A-alpha formula. Background The problem of coupling of transient electromagnetic fields and external circuits is widely found in engineering applications such as motors, power equipment and power electronic systems, and the numerical calculation of which usually depends on a finite element method. The current mainstream method is a transient field path coupling control equation established by scalar potential alpha (A-alpha for short) in a magnetic vector bit A-circuit, and adopts an edge element and node element method to carry out space dispersion on A and alpha, and combines an improved node element technology in the circuit to realize strong coupling calculation of a transient electromagnetic field and the circuit. However, in the existing a- α transient field path coupling method, in the multi-connected conductor structure, the coil and the thick conductor region, due to insufficient uniqueness of scalar potential inside the conductor, non-object understanding is easily generated or numerical calculation is not converged, so that reliability of a calculation result is affected. Meanwhile, the traditional A-alpha field path coupling method needs to simultaneously couple node finite elements, edge finite elements and improved node analysis algorithms in a circuit, and different algorithms have differences in variable types, degree of freedom definition, discrete forms and the like, so that the coupling realization process is complex, and a unified and universal coupling processing mechanism is lacked. In addition, in numerical modeling of complex electromagnetic equipment (such as a motor system), a calculation region usually includes various structural components such as a stator, a rotor, a winding, a casing and the like, and the geometric shape is complex and the material distribution is uneven, so that the discrete is usually required to be performed by adopting an unstructured grid, and the numerical precision and stability of the traditional node element and edge element method still have certain limitations when the transient field path coupling calculation is performed under the condition. Disclosure of Invention Aiming at the defects of the existing A-alpha transient field coupling method in the aspects of conductor region uniqueness, algorithm coupling compatibility, unstructured grid computing precision and the like, it is necessary to provide a transient field coupling numerical value computing method for realizing high-precision numerical solution of a transient field coupling problem in a complex motor system, in particular to an A-alpha formula-based transient electromagnetic field-circuit coupling high-precision computing method, which comprises the following steps: s1, importing grid data of a 1/8 period model of a three-dimensional motor; S2, dividing the grid data into a plurality of polyhedral smooth domains taking the corresponding edges as the center according to each edge in the grid data, wherein the polyhedral smooth domains are formed by surrounding nodes, body centers and face centers of tetrahedron units in the grid data with the corresponding edges; S3, constructing a transient field path coupling equation set based on an A-alpha formula, transient eddy current and coulomb specification, and rewriting the transient field path coupling equation set according to smooth vector functions of all edges, smooth functions of all nodes and a Galerkin method to obtain a system equation of transient field path coupling; and S4, iteratively solving a Newton iteration linear equation by adopting a Newton iteration method until convergence to obtain a magnetic vector bit in field path coupling. Preferably, the smooth vector function of the edge is calculated as: ; Wherein, the A smooth vector-shaped function representing the edge e in the polyhedral smooth field k,Indicating the deviation of the deflection of the beam,Represents the r direction, which includesDirection(s),Direction(s),The direction of the light beam is changed,Representing the smooth field of the kth polyhedron,A vector-shaped function representing the edge e,A smoothing function representing the smooth field of the kth polyhedron,Representing the number of tetrahedral units in the k-th polyhedral smooth field,A vector-shaped function representing the edge e in the nth tetrahedral unit,Representing the volume of the nth tetrahedral unit,Representing differentiation of the integral domain. Preferably, the smooth function of the node is calculated as: ; Wherein, the Representing a smooth shape function at node i in the polyhedral smooth field k,Indicating the deviation of the deflection of the beam,Repr