Rapid calculation system and method for electric-magnetic circuit coupling model of oil-immersed transformer

Abstract

The invention discloses a rapid calculation system and method for an electric-magnetic circuit coupling model of an oil-immersed transformer. The system comprises a magnetic circuit model construction module, a circuit model construction module and a coupling calculation module, the magnetic circuit model building module is used for determining physical parameters of the transformer and building a magnetic circuit model of the oil-immersed transformer based on the physical parameters; the circuit model construction module is used for constructing a simplified circuit model of the transformer and calculating a real-time current based on the circuit model; and the coupling calculation module is used for inputting the real-time current into the magnetic circuit model to construct an electric-magnetic circuit coupling nonlinear equation set, and solving the nonlinear equation set through a Newton-Raphson method.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of transformer simulation, and particularly relates to a fast calculation system and method for an oil-immersed transformer electro-magnetic coupling model. BACKGROUND

[0002] The duality principle proves the duality relationship between electricity and magnetism in the magnetic circuit. Scholars use the duality principle to model the transformer, but the focus is on the calculation of parameters such as leakage inductance, and the structure of the transformer and saturation phenomena are not considered in detail. Subsequently, scholars determine the parameter values by calculating the magnetic core segment reluctance based on finite element simulation, then convert the magnetic circuit into an electric circuit to obtain circuit parameters, compare the current and magnetic flux based on the correlation of electromagnetic force of the transformer, and establish a nonlinear magnetic circuit model. The coupling relationship among the oil-immersed transformer circuit, magnetic circuit and thermal circuit is complex, and the current finite element calculation method takes a long time, which is difficult to meet the real-time requirements of transformer monitoring. The research on the electro-magnetic coupling model of the transformer mostly does not consider and divide the structure of the transformer in detail, resulting in a large error in the results and the calculation results cannot effectively replace the calculation results of the finite element simulation software. SUMMARY

[0003] The application aims to solve the problems in the prior art and provides the following scheme:

[0004] A fast calculation system for an oil-immersed transformer electro-magnetic coupling model, comprising a magnetic circuit model construction module, an electric circuit model construction module and a coupling calculation module.

[0005] The magnetic circuit model construction module is configured to determine the physical parameters of the transformer and construct a magnetic circuit model of the oil-immersed transformer based on the physical parameters.

[0006] The electric circuit model construction module is configured to construct a simplified electric circuit model of the transformer and calculate a real-time current based on the electric circuit model.

[0007] The coupling calculation module is configured to input the real-time current into the magnetic circuit model to construct an electro-magnetic coupling nonlinear equation set, and solve the nonlinear equation set by the Newton-Raphson method.

[0008] Preferably, the working process of the magnetic circuit model construction module comprises:

[0009] Obtaining various physical parameters of the transformer to construct a transformer model, dividing the transformer model into three types of regions, the first type being a corner region, the second type being a T-shaped region, and the third type being a uniform magnetic circuit segment.

[0010] According to the local magnetic flux distribution, a local equivalent magnetic circuit topology model is constructed based on the divided transformer model.

[0011] An oil magnetic resistance is added around the local equivalent magnetic circuit topology model to represent the leakage magnetic condition of the core, and the magnetic circuit model is obtained.

[0012] Preferably, the process of constructing the local equivalent magnetic circuit topology model comprises:

[0013] Each corner region is refined into three parallel magnetic resistances, and the magnetic resistance area is 1 / 3 of the original magnetic resistance area.

[0014] Preferably, for any magnetic circuit in the magnetic circuit model, the following conditions are met:

[0015] Hl = NI

[0016] Where H represents the magnetic field strength, l represents the magnetic circuit length, N represents the number of turns, and I represents the excitation current.

[0017] Preferably, the working process of the circuit model construction module comprises:

[0018] A simplified circuit model of the transformer is constructed, which includes an alternating voltage source, a resistance of the alternating voltage source and the line, an inductance of the alternating voltage source and the line, a load resistance, a self-inductance of the left column alternating coil of the transformer, and a self-inductance of the right column alternating coil of the transformer.

[0019] Based on the simplified circuit model, a differential equation of the current is constructed:

[0020]

[0021] Where u S represents the voltage of the alternating voltage source, R S represents the resistance of the alternating voltage source and the line, L S represents the inductance of the alternating voltage source and the line, R l represents the load resistance, L 11 represents the self-inductance of the left column alternating coil of the transformer, L 22 represents the self-inductance of the right column alternating coil of the transformer, M 12 represents the mutual inductance of the left column alternating coil and the right column alternating coil.

[0022] The differential equation of the current is solved using an improved Euler method, and the iterative formula of the real-time current is obtained as:

[0023]

[0024] Where, represents the instantaneous current iterative result at the previous moment, i n represents the instantaneous current iterative result at the previous moment, t nt-1 n+1 t+1 t+1

[0025] Preferably, the workflow of the coupling calculation module comprises:

[0026] The real-time current is substituted into the magnetic circuit model, and a nonlinear equation set of the transformer equivalent model is written by using a loop.

[0027] The magnetic flux density in the nonlinear equation set is iteratively solved by using the Newton-Raphson method.

[0028] The application further provides a fast calculation method of an oil-immersed transformer electro-magnetic circuit coupling model, and the method is applied to the system according to any one of claims 1-6, and characterized in that the method comprises the following steps:

[0029] The physical parameters of the transformer are determined, and a magnetic circuit model of the oil-immersed transformer is constructed based on the physical parameters;

[0030] A simplified circuit model of the transformer is constructed, and real-time current is calculated based on the circuit model;

[0031] The real-time current is input into the magnetic circuit model to construct an electro-magnetic circuit coupling nonlinear equation set, and the nonlinear equation set is solved by using the Newton-Raphson method.

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

[0033] The application uses a computer with an AMD R74800U processor to perform corresponding simulation and calculation, and in the same running environment, the finite element simulation takes 20 minutes, while the transformer equivalent magnetic circuit method calculation takes only 25 seconds, accounting for 2.08% of the time required for the finite element simulation. In the uniform zone magnetic circuit section, the results calculated by the magnetic circuit model are very close to the finite element simulation results. In the corner zone magnetic circuit section, due to the leakage magnetic field in the actual transformer and the influence of multiple physical fields, there are some errors between the transformer model considering only the electromagnetic field and the multiple physical field simulation results, but generally, the core equivalent magnetic circuit model established by the application and the solving method used are effective. The solving results are within the allowable error range, and the time only accounts for 2.08% of the time required for the finite element algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0034] In order to more clearly illustrate the technical solutions of the application, the following briefly introduces the drawings needed in the embodiments. Obviously, the drawings in the following description only constitute some embodiments of the application, and for those skilled in the art, other drawings can also be obtained from these drawings without creative labor.

[0035] Figure 1 A system structure schematic diagram of an embodiment of the present application;

[0036] Figure 2 A transformer path section area schematic diagram of an embodiment of the present application;

[0037] Figure 3 A magnetic circuit model schematic diagram of a transformer of an embodiment of the present application;

[0038] Figure 4 A circuit model schematic diagram of a transformer of an embodiment of the present application. DETAILED DESCRIPTION

[0039] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0040] In order to make the above objectives, characteristics and advantages of the present application more obvious and easy to understand, the present application will be further described in detail below with reference to the drawings and specific embodiments.

[0041] Embodiment One

[0042] In this embodiment, as shown in the figure, a fast calculation system of an oil-immersed transformer electro-magnetic circuit coupling model includes a magnetic circuit model construction module, a circuit model construction module and a coupling calculation module. Figure 1 The magnetic circuit model construction module is used to determine the physical parameters of the transformer, and to construct the magnetic circuit model of the oil-immersed transformer based on the physical parameters.

[0043] The working process of the magnetic circuit model construction module includes: obtaining each physical parameter of the transformer to construct the transformer model, dividing the transformer model into three types of areas, as shown in the figure.

[0044] Figure 2 ​As shown, the first type is the corner region A1, A3, A4, A6, the second type is the T-shaped region A2, A5, and the third is the uniform magnetic path segment B1, B2, B3, B4, B5, B6, B7; considering the uneven distribution of local magnetic flux of each magnetic path segment of the transformer, these magnetic path segments need to be further divided into multiple magnetic path segments according to the local magnetic flux distribution, so as to establish a local equivalent magnetic path topology: each corner region is refined into 3 parallel magnetic resistances, and the magnetic resistance area is 1 / 3 of the original magnetic resistance area, and the equivalent magnetic path length of other regions is respectively taken as the length of the respective geometric center line. According to the local magnetic flux distribution, on the basis of the divided transformer model, a local equivalent magnetic path topology model is constructed; the oil magnetic resistance around the local equivalent magnetic path topology model is increased to represent the leakage magnetic condition of the core, and a magnetic path model is obtained, as shown in Figure 3 , wherein only the refinement of one corner region is taken as an example, and the other corner regions are the same as the refined region.

[0045] In this embodiment, for the oil-immersed transformer magnetic path model in Figure 3 , the corresponding parameter calculation is needed for each magnetic resistance. The calculation method is similar to the circuit calculation method, and the Ohm's law expression in the magnetic path is as shown in the following formula:

[0046] F=R m φ

[0047] , wherein Rm represents the magnetic resistance in the magnetic path, l represents the magnetic path length, Φ represents the magnetic flux, μ represents the magnetic permeability, and s represents the magnetic resistance cross-sectional area; the permeance of the magnetic path is:

[0048]

[0049] The calculation of the magnetic path parameters refers to the transformer size parameters in Figure 2 , the length of the oil magnetic resistance corresponds to the length of the corresponding core magnetic resistance magnetic path, and the calculation formula of the geometric center line length of each magnetic resistance is:

[0050]

[0051] , wherein l a represents the corner region outside magnetic resistance length, l oa represents the radius of the equivalent arc length of the corner region outside magnetic resistance length, l b represents the corner region middle magnetic resistance length, l ob represents the radius of the equivalent arc length of the corner region middle magnetic resistance length, l c represents the corner region inside magnetic resistance length, and l oc represents the radius of the equivalent arc length of the corner region inside magnetic resistance length.

[0052] According to Stokes theorem, the electromagnetic induction law in the Maxwell equation group is integrated on the surface S on both sides, and the definition of conduction current is combined, to obtain:

[0053]

[0054] For any magnetic circuit in the magnetic circuit model, when the total current contained by the closed curve L is NI, and the direction of the magnetic field is along the tangential direction of the curve L and the size is the same everywhere, the above formula can be written in the form of the following formula: and

[0055] Hl=NI

[0056] Where H represents the magnetic field strength, N represents the number of turns of the coil, and I represents the excitation current.

[0057] The circuit model construction module is configured to construct a simplified circuit model of the transformer and calculate real-time current based on the circuit model.

[0058] The working process of the circuit model construction module includes: constructing a simplified circuit model of the transformer, as shown in Figure 4 The simplified circuit model includes: an alternating voltage source U S , a resistance R S of the alternating voltage source and the line, an inductance L S of the alternating voltage source and the line, a load resistance R l , a self-inductance L 11 of the left column alternating coil of the transformer, and a self-inductance L 22 of the right column alternating coil of the transformer; based on the simplified circuit model, a differential equation of the current is constructed:

[0059]

[0060] Where u S represents the voltage of the alternating voltage source, R S represents the resistance of the alternating voltage source and the line, L S represents the inductance of the alternating voltage source and the line, R l represents the load resistance, L 11 represents the self-inductance of the left column alternating coil of the transformer, L 22 represents the self-inductance of the right column alternating coil of the transformer, and M 12 ​Mutual inductance of left column AC coil and right column AC coil; since the working point of the core is related to the magnetic flux density inside the core, and the magnetic flux density inside the core is related to the material of the core and the magnetic motive force of the permanent magnet and the two AC coils. When the structure of the transformer, the material of the core, the parameters of the permanent magnet, and the number of turns of the AC coil are determined, the working point of the core only changes with the change of the current in the AC coil. The self-inductance parameter and the mutual inductance parameter also change with the change of the current in the AC coil. The self-inductance parameter and the mutual inductance parameter are functions of the alternating current i, and the flux linkage equations of the two AC coils are:

[0061]

[0062] Ψ1 represents the flux linkage equation of the left column AC coil, Ψ2 represents the flux linkage equation of the right column AC coil, i1 represents the current of the left column AC coil, and i2 represents the current of the right column AC coil; the circuit in which the AC coil is located is written as a voltage equation and a flux linkage equation of the coil:

[0063]

[0064] Ψ1 and Ψ2 are substituted into u S

[0065]

[0066] The differential equation of the current i is written as:

[0067]

[0068] The differential equation of the current i is solved using the improved Euler method, and the iterative formula of the real-time current is obtained as:

[0069]

[0070] represents the instantaneous current iterative result at the previous time, i n represents the instantaneous current iterative result at the previous time, i n represents the instantaneous current iterative result at the previous time, i n+1 represents the instantaneous current iterative result at the previous time, i represents the instantaneous current iterative result at the previous time, i

[0071] The coupling calculation module is used to input the real-time current into the magnetic circuit model to construct the electric-magnetic circuit coupling nonlinear equation set, and solve the nonlinear equation set by Newton-Raphson method.

[0072] ​​The workflow of the coupling calculation module includes: substituting the real-time current into the magnetic circuit model, using the loop sting to write the nonlinear equations of the transformer equivalent model; and using the Newton-Raphson method to iteratively solve the magnetic flux density in the nonlinear equations.

[0073] In this embodiment, the transformer magnetic circuit model includes multiple nonlinear magnetic resistances of the core. During the solution, a magnetic pressure source is used to equivalently replace the nonlinear magnetic resistance in the magnetic circuit. Due to the nonlinear characteristics of the magnetic resistance, the BH curve of the core needs to be interpolated to obtain the magnetic voltage drop on each magnetic resistance when solving the equations. In the process of solving the model, the loop flux method is used. This method is similar to the loop current method in circuit principles. It is based on the dual relationship between the magnetic circuit and the electric circuit, and uses the circuit network solution method to simulate and equivalent the calculated magnetic circuit. The magnetic resistance in the magnetic circuit is the dual resistance in the circuit, the magnetic pressure source is the dual voltage source, and the magnetic flux is the dual current.

[0074] Write a set of nonlinear equations consisting of independent loop equations. For the parallel magnetic resistance in the corner area or uniform area, simply make their magnetic potentials equal. Taking the corner area as an example, the equation is as follows:

[0075] F C4 =F C5 =F C6

[0076] for Figure 3 The total loop in the left half of the region is as follows:

[0077]

[0078] Among them, FA represents the equivalent magnetic potential of the coil, F ck represents the magnetic voltage drop of the nonlinear magnetic resistance of the iron core labeled k, Represents the magnetic flux of the circuit. Due to the nonlinear characteristics of the magnetic resistance, when expressing the magnetic voltage drop on the magnetic resistance, it is necessary to divide the actual magnetic flux passing through the magnetic resistance by the cross-sectional area of ​​the magnetic resistance to obtain the actual magnetic flux density of the magnetic resistance, and then use the BH curve of the iron core to interpolate the magnetic voltage drop on each magnetic resistance.

[0079] For the nonlinear equations, the present invention adopts the Newton-Raphson method to solve them, and when the equation is obtained:

[0080]

[0081] set up is the solution of the equation, let:

[0082]

[0083] Among them, then Use Taylor's formula to expand the original formula and omit the higher-order terms greater than or equal to the second order to obtain:

[0084]

[0085] Because is the solution of the equation, then:

[0086]

[0087] Substitute into the equation, get:

[0088]

[0089] That is:

[0090]

[0091] Thus the iterative equation of the original equation group is obtained:

[0092]

[0093] When is less than the given accuracy, the iteration converges, thereby obtaining the solution of the original equation group, the method of the present application converges to the second order, and the required accuracy can be quickly reached to obtain the result.

[0094] Example two

[0095] In the embodiment, a fast calculation method of an oil-immersed transformer electric-magnetic circuit coupling model comprises the following steps:

[0096] Determine the physical parameters of the transformer, and construct a magnetic circuit model of the oil-immersed transformer based on the physical parameters; construct a simplified circuit model of the transformer, and calculate real-time current based on the circuit model; input the real-time current into the magnetic circuit model to construct an electric-magnetic circuit coupling nonlinear equation group, and solve the nonlinear equation group by the Newton-Raphson method.

[0097] The above-described embodiments are merely descriptions of the preferred modes of the present application, and are not intended to limit the scope of the present application, and various modifications and improvements to the technical solutions of the present application made by those of ordinary skill in the art without departing from the design spirit of the present application shall fall within the protection scope of the present application as defined by the claims.

Claims

1. A fast calculation system for the electric-magnetic circuit coupling model of an oil-immersed transformer, characterized in that: include: Magnetic circuit model building module, circuit model building module and coupling calculation module; The magnetic circuit model building module is used to determine the physical parameters of the transformer and build a magnetic circuit model of the oil-immersed transformer based on the physical parameters; The circuit model building module is used to build a simplified circuit model of the transformer and calculate the real-time current based on the circuit model; The coupling calculation module is used to input the real-time current into the magnetic circuit model to construct an electric-magnetic circuit coupling nonlinear equation group, and solve the nonlinear equation group by the Newton-Raphson method.

2. The fast calculation system for the electric-magnetic circuit coupling model of an oil-immersed transformer according to claim 1, characterized in that: The workflow of the magnetic circuit model building module includes: Obtaining various physical parameters of the transformer to construct a transformer model, and dividing the transformer model into three types of areas, the first type is a corner area, the second type is a T-shaped area, and the third type is a uniform magnetic circuit section; According to the local magnetic flux distribution, a local equivalent magnetic circuit topology model is constructed on the basis of the divided transformer model; The magnetic circuit model is obtained by adding oil magnetic resistance around the local equivalent magnetic circuit topology model to represent the magnetic leakage of the iron core.

3. The fast calculation system for the electric-magnetic circuit coupling model of an oil-immersed transformer according to claim 2, characterized in that: The process of constructing the local equivalent magnetic circuit topology model is as follows: Each of the corner regions is subdivided into three parallel magnetic resistors, and the magnetic resistor area is 1 / 3 of the original magnetic resistor area. The equivalent magnetic circuit lengths of the other regions are taken as the lengths of their respective geometric center lines.

4. The fast calculation system for the electric-magnetic circuit coupling model of an oil-immersed transformer according to claim 2, characterized in that: For any magnetic circuit in the magnetic circuit model, we have: Hl=NI, where H represents the magnetic field strength, l represents the magnetic path length, N represents the number of coil turns, and I represents the excitation current.

5. The fast calculation system for the electric-magnetic circuit coupling model of an oil-immersed transformer according to claim 1, characterized in that: The workflow of the circuit model building module includes: Constructing a simplified circuit model of the transformer, wherein the simplified circuit model includes: an AC voltage source, resistance of the AC voltage source and the circuit, inductance of the AC voltage source and the circuit, a load resistance, a self-inductance of the AC coil of the left leg of the transformer, and a self-inductance of the AC coil of the right leg of the transformer; The differential equation of the current is constructed based on the simplified circuit model: Among them, u S represents the voltage of the AC voltage source, R S Represents the resistance of the AC voltage source and line, L S represents the inductance of the AC voltage source and the line, R l Indicates the load resistance, L 11 Indicates the self-inductance of the left-hand AC coil of the transformer, L 22 Indicates the self-inductance of the transformer's right-hand AC coil, M 12 It represents the mutual inductance of the left column AC coil and the right column AC coil; The improved Euler method is used to solve the differential equation of the current, and the iterative formula of the real-time current is obtained as follows: in, Indicates the instantaneous current iteration result of the previous moment, i n Indicates the previous level iteration result of the instantaneous current at the previous moment, t n represents the previous moment, t n+1 Indicates the next moment, represents the instantaneous current iteration result at the next moment, and ξ represents the Cauchy formula.

6. The fast calculation system for the electric-magnetic circuit coupling model of an oil-immersed transformer according to claim 1, characterized in that: The workflow of the coupling calculation module includes: Substituting the real-time current into the magnetic circuit model, and using loop current to write a nonlinear equation group of the transformer equivalent model; The magnetic flux density in the nonlinear equations is iteratively solved using the Newton-Raphson method.

7. A method for quickly calculating an electric-magnetic circuit coupling model of an oil-immersed transformer, the method being applied to the system according to any one of claims 1 to 6, characterized in that: The following steps are involved: Determining physical parameters of the transformer, and constructing a magnetic circuit model of the oil-immersed transformer based on the physical parameters; constructing a simplified circuit model of the transformer and calculating real-time current based on the circuit model; The real-time current is input into the magnetic circuit model to construct an electric-magnetic circuit coupling nonlinear equation group, and the nonlinear equation group is solved by the Newton-Raphson method.

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