CN106294914A - A kind of converter transformer valve-side three-dimensional electric field emulation mode considering Anisotropic Nonlinear - Google Patents

Abstract

The invention belongs to the field of power system simulation, in particular to a three-dimensional electric field simulation method at the valve side of a converter transformer. This method focuses on the current research on the electric field of converter transformers, most of which focus on two-dimensional electric field modeling and analysis, and there are few three-dimensional modeling and analysis. and anisotropy, methods for the simulation of DC electric fields in valve-side windings of converter transformers. First, use ANSYS finite element analysis software to establish a three-dimensional model of the winding end of the converter transformer, and divide it into mesh; then, use the secondary development APDL module of ANSYS to write a calculation program for nonlinear anisotropic DC electric field; finally, Set the boundary conditions, initial resistivity, loading test voltage, and calculate the three-dimensional electric field. The invention provides a three-dimensional electric field simulation method at the valve side of a converter transformer considering the nonlinear anisotropy, and provides a method for improving the simulation accuracy of the electric field of the converter transformer.

Description

A three-dimensional electric field simulation method on valve side of converter transformer considering nonlinear anisotropy

technical field

The invention belongs to the field of power system simulation, in particular to a three-dimensional electric field simulation method at the valve side of a converter transformer.

Background technique

At present, a number of large-scale DC transmission projects have been built in my country. With the commissioning of these DC transmission projects, the stable operation of DC transmission is becoming more and more important. The main longitudinal insulation design of power transformers is the calculation design of large transformers, especially ultra-high voltage power transformers. It is not only of great significance to the ultimate capacity and operational reliability of power transformers, but also has an extremely important impact on the economic indicators of transformers.

At present, oil and paper composite insulation structures are still generally used inside large-scale converter transformers. Under normal operating conditions, the electric field in the oil-paper composite insulation is a mixed electric field of AC and DC, and the electric field distribution under DC voltage is determined by the conductivity, and the conductivity is nonlinear, and has an exponential relationship with the electric field strength and temperature. , so that the electric field is nonlinear when the converter transformer is subjected to DC voltage. In addition, due to the manufacturing process, there is anisotropy in the resistivity of the cardboard. When solving the DC electric field of the valve side winding of the converter transformer, it needs to be calculated according to the nonlinear field, and at the same time, the anisotropy of the material needs to be considered, which makes the calculation complicated. Therefore, it is necessary to conduct an in-depth study on the electric field distribution of the converter transformer.

Existing research mainly focuses on the study of the two-dimensional electric field of the converter transformer, and there are few studies on the three-dimensional electric field analysis, especially the research that considers the nonlinearity and material anisotropy caused by temperature and field strength at the same time. The document "Electric Field Analysis of Valve Side Winding of Converter Transformer Under the Action of Mixed Electric Field" analyzed the voltage of the valve side winding of the converter transformer, and pointed out that under the action of DC steady-state voltage, the electric field of the insulating material obeys the resistive distribution and is proportional to its resistivity. Proportional, and calculated the distribution of the electric field under different resistivity ratios, and analyzed the necessity of non-linearity for the calculation of the DC electric field on the valve side. The literature "Finite Element Calculation of Anisotropic DC Electric Field of Converter Transformer" uses self-programming to calculate the DC electric field of the valve side winding of the converter transformer, and through the simulation of the finite element software ANSYS, deduces the DC electric field under the condition of anisotropic conductivity The mathematical model of the paper gives a discrete format, analyzes the influence of conductivity on the DC electric field, and calculates a 500kV converter transformer. The calculation results show that the field strength of the cardboard decreases and the field strength of the oil increases after considering the anisotropy of the material, and the magnitude of the change is related to the initial value of the electrical conductivity. In the literature "Nonlinear Anisotropic DC Electric Field Analysis of Converter Transformer Valve Side Winding", the author used ANSYS secondary development technology to calculate the nonlinear DC electric field and nonlinear various Anisotropic DC electric field. The calculation results show that the electric field distribution is very different when taking into account the resistivity nonlinearity and anisotropy of the insulating material than when these conditions are not taken into account. In the literature "Analysis of Three-Dimensional Electric Field at the End of Valve-side Winding of Converter Transformer" in this paper, through modeling and grid division, the three-dimensional DC electric field, AC electric field and polarity reversal of the end of valve-side winding of a ±500kV converter transformer are carried out. The analysis and calculation of the electric field are compared with the traditional two-dimensional calculation method, and the material nonlinearity and anisotropy are not considered in the calculation.

The research on the DC electric field at the valve side of the converter transformer in the above literatures mainly focuses on the distribution of the two-dimensional electric field, and less research on the distribution of the three-dimensional electric field. There is no literature on the analysis and calculation of the three-dimensional electric field considering nonlinearity and anisotropy. As a spatial entity, the converter transformer can only accurately analyze the distribution of its electric field through a three-dimensional model, so it is worth further research on the electric field distribution of the converter transformer.

Description of drawings

Fig. 1 is three-dimensional electric field calculation model diagram of the present invention

Fig. 2 is grid division figure of the present invention

Fig. 3 is conductivity-electric field intensity fitting curve figure of the present invention

Fig. 4 is the non-linear DC electric field calculation block diagram of the present invention

Contents of the invention

Most of the current research on the electric field of converter transformers focuses on two-dimensional electric field modeling and analysis, and as a spatial entity, it is necessary to carry out three-dimensional modeling and analysis on the converter transformer. The patent of the invention uses the three-dimensional model of the main insulation of the converter transformer As the core, a simulation method for the DC electric field of the valve side winding of the converter transformer is proposed considering the nonlinearity and anisotropy of the material. First, use ANSYS finite element analysis software to establish a three-dimensional model of the winding end of the converter transformer, and divide it into mesh; then, use the secondary development APDL module of ANSYS to write a nonlinear anisotropic DC electric field calculation program, through iteration The nonlinear electric field is calculated by the method, and the components in different directions of the electric field intensity are read in the iterative process, and the anisotropy of the material is calculated based on each component; finally, the boundary conditions, initial resistivity, and loading test voltage are set, and the calculated Three-dimensional electric field.

To achieve the above object, the present invention takes the following technical solutions:

1. Modeling and grid division. Taking a 500KV converter transformer as an example, the model is established by solid modeling, mainly for the main insulation modeling of the converter transformer. Considering the symmetry, only the end of the winding can be selected to build the model, and the actual working conditions and model The characteristics of the structure itself mesh the model.

2. Consider the influence of electric field strength on resistivity. Using the APDL parametric design language is an iterative method, based on the field strength obtained from the previous solution, to calculate the resistivity of each finite element unit. Then modify the resistivity of each finite element unit for the next solution. Loop in turn until the iteration precision is met or the specified maximum number of iterations is reached.

3. Consider the influence of temperature on resistivity. Here, the temperature excitation is loaded based on experience, and only the conduction process of heat in the insulating cardboard and transformer oil is considered. By establishing a coupling field, the result of the temperature field is transferred to the electric field, and the resistivity of each finite element element is modified by using the result. To solve the steady state DC electric field.

4. Calculation of anisotropic DC electric field. When modeling, make the plane direction of the insulating cardboard parallel or perpendicular to the z coordinate axis of the system. When calculating the nonlinear anisotropic steady-state DC electric field, it is only necessary to read the x, y, and z components of the electric field intensity during the iterative process, calculate the horizontal and vertical components of the point, and then calculate the corresponding horizontal and vertical resistance rate, and then calculate the resistivity in the x, y, and z directions through coordinate transformation.

The invention considers material nonlinearity and anisotropic three-dimensional electric field calculation, provides a method for calculating the DC electric field of the valve side winding of the converter transformer, and provides a corresponding basic model for simulating the main insulation electric field of the converter transformer through software.

detailed description

The present invention comprises the following steps:

1. Electric field analysis under the action of DC voltage

Due to the working conditions, the converter transformer not only bears the action of AC power frequency voltage, but also bears the action of DC voltage. Under the action of DC voltage, the electric field distribution of the oil-paper composite insulation structure mainly depends on the resistivity of the insulating material, showing a resistive distribution. Therefore, the electric field under the action of AC and DC voltages is completely different and requires different solution methods.

Under the action of DC voltage, the electric field distribution is not only related to the insulating structure, but also related to the resistivity of the insulating medium. The internal insulation medium of the converter transformer mainly includes transformer oil, oil-impregnated paper and cardboard. The resistivity of these media will be affected by many factors such as temperature, humidity, and electric field strength, and the range of variation is also large. At the same time, the manufacturing of insulating cardboard The process leads to its laminated structure, so that the resistivity of the insulating paperboard is also anisotropic. In the actual operating converter transformer, the resistivity of oil generally varies between 10 ¹² and 10 ¹⁴ Ω·m, while that of oil-impregnated paper and cardboard is between 10 ¹² and 10 ¹⁵ Ω·m. According to available data, the ratio of oil to paper resistivity may be between 1:10 and 1:500 at room temperature, and may be between 1:1 and 1:1000 under operating conditions. In addition, the absolute value of the resistivity of the insulating material also has an important influence on the transient DC electric field.

2. Mathematical model of electric field distribution

The differential form of Maxwell's equations is as follows:

$\left\{\begin{array}{c}\mathrm{rot\; H}=J+\frac{\∂\mathrm{D.}}{\∂t}\\ \mathrm{rotE}=-\frac{\∂B}{\∂t}\\ \mathrm{div}\mathrm{D.}=\mathrm{\ρ}\\ \mathrm{div}B=0\end{array}\right.$ (Formula 2.1)

Where H, B, E, D, J and ρ represent magnetic field strength, magnetic induction strength, electric field strength, electric displacement, conduction current density vector and charge density, respectively;

The dielectric material characteristic equation is as follows:

D＝εE (Formula 2.2)

J＝γE (Formula 2.3)

Among them, ε and γ represent the dielectric constant and conductivity of the medium respectively; in the calculation of the AC electric field, ε and γ can be regarded as constants, while in the DC electric field, ε and γ change with the change of the field strength;

The formula for calculating the electric field strength is:

$\mathrm{E.}=-\mathrm{grad}u-\frac{\∂A}{\∂t}$ (Formula 2.4)

Because the length of the electromagnetic wave is much larger than the field domain of the calculation model, it can be ignored have to:

E＝-grad u (Formula 2.5) Assuming that there is no free charge in the insulating cardboard and transformer oil, we get:

$\mathrm{div}(J+\frac{\∂\mathrm{D.}}{\∂t})=0$ (Formula 2.6)

$\mathrm{div}(\mathrm{\γE}+\mathrm{\ϵ}\frac{\∂\mathrm{E.}}{\∂t})=0$ (Formula 2.7)

Put E=-grad u into the above formula to get:

$\mathrm{\γ}\mathrm{div}\mathrm{grad}u+\mathrm{\ϵ}\frac{\∂}{\∂t}\mathrm{div}\mathrm{grad}u=0$ (Formula 2.8)

In vector calculations, swapping the order of derivation with respect to time and derivation with respect to space yields:

$(\mathrm{\γ}+\mathrm{\ϵ}\frac{\∂}{\∂t})\mathrm{div}\mathrm{grad}u=0$ (Formula 2.9)

In the Cartesian coordinate system, the mathematical model for considering both ε and γ in the three-dimensional transient electric field in the composite medium is:

(Formula 2.10)

3. Modeling and meshing

In the ANSYS finite element software, the three-dimensional geometric model of the main insulation of the converter transformer is established by means of solid modeling; the physical parameters of the materials in the three-dimensional geometric model of the main insulation of the converter transformer are determined and the model is meshed.

ANSYS, as a finite element analysis software, can establish various models in the software in a way similar to CAD drawing, and input the material permittivity, initial resistivity, thermal conductivity, specific heat capacity, density of each part, determine the unit type and model Perform mesh division.

The calculation model used here is a single-phase four-column structure. The windings on the two core columns in the middle adopt a parallel structure. Two side yokes are added to guide the magnetic flux and reduce the height of the core. Therefore, the electric field calculation model can choose 1/8 structure, and because of the symmetrical structure of the core column, and the main analysis is the structure of the end, the actual calculation model is less than 1/8. The calculation model is shown in Figure 1.

In the insulation model of the transformer end, the insulating paper tube and the corner ring can be approximated as circular rings, so the surface can be divided first, and then the volume can be divided by volume sweeping. However, the shape of transformer oil is extremely irregular, and it needs to be split into regular shapes, that is, the axisymmetric part filled between the windings and the irregular part outside the winding, and then divided and controlled separately. When performing surface subdivision, by setting the length of the edge or the number of segments, it is ensured that the meshes between the model structures can transition reasonably. When subdividing a rotating body, the accuracy of mesh subdivision is controlled by setting the number of cells generated along the direction of rotation. Since the field strength near the fuel tank is very small, the subdivision accuracy can be controlled by setting the number of units on the boundary line. Through the above series of subdivision control, the smooth transition of the mesh between the model structures is guaranteed, and the finite element model with better quality is obtained. Since both the winding and the iron core should be given a constant potential value, it is not necessary to subdivide it, only the insulating material should be subdivided into a grid. The grid model is shown in Figure 2.

4. Consider the influence of electric field strength on resistivity

4.1 Iterative formula considering the nonlinearity of electric field intensity

In the nonlinear analysis, the conductivity-electric field intensity nonlinear curve of oil in Fig. 3 was re-fitted with an exponential function, as shown in formula 5.1, the conductivity-electric field intensity nonlinear relationship perpendicular to the paper surface is still expressed in the traditional way , as shown in Equation 5.2:

${\mathrm{\γ}}_{\mathrm{the\; oil}}={\mathrm{\γ}}_{0\mathrm{the\; oil}}\exp \left(\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{a}_i{\mathrm{E.}}^{i-1}\right)$ (Formula 4.1)

γ _paper ＝γ _0paper (βE) (Formula 4.2)

In the formula, E is the value of electric field intensity kV/mm; γ _0oil and γ _0paper are room temperature (20°C), and E=0, the estimated value of the conductivity of the oil and the direction perpendicular to the paperboard. Take N=7 in the calculation formula, and the value of coefficient a _i (i=1,2,...7) is obtained by fitting the conductivity-electric field intensity curve in Figure 3, and the nonlinear coefficient β of the cardboard in formula 5.2 is 0.017.

4.2 Calculation method considering the nonlinearity of electric field intensity

The nonlinear calculation adopts the secondary development program APDL of ANSYS software, that is, the ANSYS parametric design language, which can directly use the APDL command to operate the ANSYS main program and pass the DO cycle. The basic idea is to use the *VGET command to save the field strength obtained from the previous solution as an array through an iterative method, and use the array to calculate the resistivity of each finite element element. Then use the EMODIF command to modify the resistivity of each finite element unit for the next solution. Loop in turn until the iteration precision is met or the specified maximum number of iterations is reached. The program block diagram of the nonlinear solution is shown in Figure 4.

4.3 Convergence Criterion

There are several options in the electric field calculation of oil-paper insulation:

From the selection of field quantity (criterion object), the rate of change of potential, field strength, regional conductivity, etc. can be taken; from the algorithm, there are many ways. Here, since the field strength E is the focus of attention, E is taken as the criterion object, and the independence of the criterion is considered, and the maximum change rate of the field strength E of each unit is taken as the basis for the algorithm, namely:

$\max \left\{\frac{{\mathrm{E.}}_{\mathrm{no}+1}^{\′}-{\mathrm{E.}}_{\mathrm{no}}}{{\mathrm{E.}}_{\mathrm{no}}}{|}_{k=1\&Right\; Arrow;N}\right\}\%\≤{\mathrm{E.}}_{\max }$ (Formula 4.3)

In the formula: E _n is the calculation result of the nth field strength of each unit; k is the number of iterations; N is the total number of subdivided units; E _max is the set maximum field strength change rate.

5. Consider the effect of temperature on resistivity.

5.1 Determination of end temperature

When calculating the temperature distribution at the end of the winding in this patent, the method of setting the temperature value according to experience is adopted. Add temperature excitation on the surface of the winding and the static ring, and its value is 30°C. The ambient temperature was set to 20 °C. The winding end temperature is simulated by a separate temperature field calculation. Since the flow rate of transformer oil is almost negligible in the externally applied DC voltage withstand test. Only the conduction process of heat in the insulating cardboard and transformer oil is considered, and the convective heat transfer and heat radiation on the surface of the winding are not considered.

5.2 Coupling method

After completing the solution of the temperature field at the end of the winding, use *VGET to read the temperature value of each unit, and then use the *VWRITE command to save the temperature of each unit to a text file. When calculating the DC steady-state electric field, use the *VREAD command to read the data in the text file and save it in an array, use this array to modify the resistivity of each finite element element, and modify Eq. 4.1 and The values of γ _0oil and γ _0paper in Equation 4.2 are the estimated values of the electrical conductivity of the oil and the direction perpendicular to the paperboard when E=0 at the corresponding temperature, so as to solve the steady-state DC electric field.

6. Calculation of anisotropic DC electric field

The converter transformer uses laminated cardboard and oil-impregnated paper. Their resistivity is anisotropic along the direction parallel to the paper surface and the direction perpendicular to the paper surface. This property can be expressed as:

$\mathrm{\σ}=\left(\begin{array}{cc}{\mathrm{\σ}}_h& 0\\ 0& {\mathrm{\σ}}_t\end{array}\right)$ (Formula 6.1)

σ _h is the resistivity in the horizontal paper direction;

σ _t is the resistivity perpendicular to the direction of the paper.

In the insulation model of the 1/8 end of the transformer in Fig. 1, the insulating paper tube and the corner ring can be approximated as rings. When modeling, the cross-section of the ring is taken as the x, z plane, and the longitudinal axis of the ring is taken as The y-axis, at this time, the angle between the cardboard and the y-axis direction is θ, then the coordinates of any point a on the cardboard are (x _a , y _a , z _a ) and the vertical paper direction is expressed as:

$\stackrel{\&Right\; Arrow;}{a_h}=(x_a,\mathrm{the\; tan}\mathrm{\θ}\sqrt{{x_a}^2+{z_a}^2},z_a)$ (Formula 6.2)

Assuming that the electric field intensity read at point a at this time is expressed as E _a = (E _x , E _y , E _z ), then the component of E _a perpendicular to the paper surface is:

${\mathrm{E.}}_h=\frac{\stackrel{\&Right\; Arrow;}{{\mathrm{E.}}_a}\&Center\; Dot;\stackrel{\&Right\; Arrow;}{a_h}}{\left|\stackrel{\&Right\; Arrow;}{a_h}\right|}=\frac{{\mathrm{E.}}_x{x}_a+{\mathrm{E.}}_{\mathrm{the\; y}}\mathrm{the\; tan}\mathrm{\θ}\sqrt{{x_a}^2+{z_a}^2}+{\mathrm{E.}}_z{z}_a}{\sqrt{{x_a}^2+{\mathrm{the\; tan}}^2\mathrm{\θ}({x_a}^2+{z_a}^2)+{z_a}^2}}$ (Formula 6.3)

The components of E _a horizontal paper surface are:

${\mathrm{E.}}_t=\sqrt{{{\mathrm{E.}}_a}^2-{{\mathrm{E.}}_h}^2}=\sqrt{({{\mathrm{E.}}_x}^2+{{\mathrm{E.}}_{\mathrm{the\; y}}}^2+{{\mathrm{E.}}_z}^2)-\frac{{({\mathrm{E.}}_x{x}_a+{\mathrm{E.}}_{\mathrm{the\; y}}\mathrm{the\; tan}\mathrm{\θ}\sqrt{{x_a}^2+{z_a}^2}+{\mathrm{E.}}_z{z}_a)}^2}{{x_a}^2+{\mathrm{the\; tan}}^2\mathrm{\θ}({x_a}^2+{z_a}^2)+{z_a}^2}}$ (Formula 6.4)

Then, according to E _h and E _t respectively brought into the non-linear fitting formula of cardboard vertical and horizontal resistivity in 4.1, σ _h and σ _t are calculated.

After some corresponding mathematical transformations, it can be concluded that when any point a(x _a , y _a , z _a ) on the cardboard has an angle θ with the coordinate axis y:

$\left(\begin{array}{c}{\mathrm{\σ}}_r\\ {\mathrm{\σ}}_{\mathrm{the\; y}}\end{array}\right)=\left(\begin{array}{cc}{\mathrm{\σ}}_{\mathrm{rr}}& {\mathrm{\σ}}_{\mathrm{ry}}\\ {\mathrm{\σ}}_{\mathrm{yr}}& {\mathrm{\σ}}_{\mathrm{yy}}\end{array}\right)$ (Formula 6.5)

in:

$\left\{\begin{array}{c}{\mathrm{\σ}}_{\mathrm{rr}}={\mathrm{\σ}}_h{\cos }^2\mathrm{\θ}+{\mathrm{\σ}}_t{\sin }^2\mathrm{\θ}\\ {\mathrm{\σ}}_{\mathrm{ry}}={\mathrm{\σ}}_h\cos \mathrm{\θ}\sin \mathrm{\θ}-{\mathrm{\σ}}_t\cos \mathrm{\θ}\sin \mathrm{\θ}\\ {\mathrm{\σ}}_{\mathrm{yr}}={\mathrm{\σ}}_{\mathrm{ry}}\\ {\mathrm{\σ}}_{\mathrm{yy}}={\mathrm{\σ}}_h{\sin }^2\mathrm{\θ}+{\mathrm{\σ}}_t{\cos }^2\mathrm{\θ}\end{array}\right.$ (Formula 6.6)

In the same way:

$\left(\begin{array}{c}{\mathrm{\σ}}_x\\ {\mathrm{\σ}}_z\end{array}\right)=\left(\begin{array}{cc}{\mathrm{\σ}}_{\mathrm{xx}}& {\mathrm{\σ}}_{\mathrm{xz}}\\ {\mathrm{\σ}}_{\mathrm{zx}}& {\mathrm{\σ}}_{\mathrm{zz}}\end{array}\right)$ (Formula 6.7)

in:

(Formula 6.8)

where σ _x , σ _y , σ _z , and σ _r are the resistivity components in x, y, z directions and the radial direction of point a, respectively, is the angle between the y-axis and the plane where a is located and the plane where the x-axis and y-axis are located, and

In summary:

(Formula 6.9)

The obtained σ _x , σ _y , σ _z are the corresponding isotropic resistivity components of the cardboard.

Bring the above calculation formula of cardboard resistivity components into 4.2 iterative calculation of cardboard nonlinear resistivity, calculate the resistance components in each direction according to the obtained field strength values in each direction, and modify the cardboard unit isotropic resistivity through EMODIF command Component, as the parameter of the next iteration operation, the anisotropy can be considered in the simulation at the same time.

Claims (5)

1. consider a converter transformer valve-side three-dimensional electric field emulation mode for Anisotropic Nonlinear, including Following steps:

1), in ANSYS finite element software, the mode of solid modelling is used to set up converter power transformer major insulation three-dimensional several What model, is determined Material Physics parameter in converter power transformer major insulation 3-D geometric model and model is carried out net Lattice divide；2), secondary development program APDL of ANSYS software is used to be programmed, by the method for iteration, profit Carry out computing next time with the front results modification resistivity of material once calculated, until result restrains, calculate electric field with this The intensity impact on resistivity；3), the method that temperature value is empirically set is used to add temperature at winding and electrostatic ring surface Excitation, simulates winding overhang temperature by single Temperature calculating, according to temperature computation result in iterative computation, The calculating parameter of amendment corresponding units, to calculate the temperature field impact on electric field；4), derivation anisotropy computing formula, Obtain electric field all directions component the most respectively, calculate all directions resistive component, and repaiied by EMODIF instruction Change cardboard unit respectively to resistivity component, as the parameter of next iteration computing, with consider the most simultaneously each to The opposite sex.

2. according to the converter transformer valve-side three-dimensional electric field emulation side of the consideration Anisotropic Nonlinear described in claim l Method, it is characterised in that: described step 1) in modeling use computation model be single-phase four-column type structure, model includes Iron core, winding, paper oil insulation, the winding on middle two core limbs uses parallel-connection structure, and increasing by two return yokes is In order to dredge magnetic flux, reduce height unshakable in one's determination；1/8 structure chosen by electric Field Calculation model；

The first split surface of stress and strain model employing, then the subdivision of perfect aspect is scanned by body, first it is split into rule Shape, the irregularities outside the axial symmetry part being i.e. filled between winding and winding, distinguish the most again Carry out subdivision control, carrying out face subdivision when, by arranging length or the segments in sideline, it is ensured that mould Grid between type structure can reasonably transition.

3. according to the converter transformer valve-side three-dimensional electricity of the consideration Anisotropic Nonlinear described in claim l Emulation mode, it is characterised in that: described step 2) in consider that electric field intensity is non-linear；

(1) the nonlinear iterative formula of electric field intensity is considered

Electrical conductivity-electric field intensity nonlinear curve with exponential function matching oil is as follows:

${\mathrm{\γ}}_{\mathrm{oil}}={\mathrm{\γ}}_{0\mathrm{oil}}\exp \left(\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{a}_i{E}^{i-1}\right)$

Electrical conductivity-electric field intensity the non-linear relation of vertical paper is still as follows by traditional mode:

γ_paper=γ_0paper(βE)

In formula, E is electric field intensity value kV/mm；γ_0oilAnd γ_0paperIt is room temperature (20 DEG C) respectively, during E=0 The estimated value of oily and vertical cardboard direction electrical conductivity；Calculate in Chinese style and take N=7, coefficient a_i(i=1,2 ... 7) value Obtain according to electrical conductivity-electric field strength profile matching, nonlinear factor β=0.017 of cardboard；

(2) the nonlinear computational methods of electric field intensity are considered

NONLINEAR CALCULATION uses the secondary exploitation technology of ANSYS software, i.e. ANSYS Parametric designing Language；Basic thought is through the method for iteration, utilizes * VGET order front once solving to be obtained Field intensity saves as array, utilizes this array to calculate the resistivity of each finite element unit, then utilizes The resistivity of each finite element unit is revised in EMODIF order, solves next time, circulates successively, directly To meeting iteration precision or reaching the maximum iteration time of regulation；

(3) convergence criterion

Multiple choices are had in paper oil insulation electric Field Calculation:

With E for criterion object, it is considered to the independence of criterion, algorithm takes the maximum change of each unit field intensity E Rate is foundation, i.e. $\max \left\{\frac{E_{n+1}^{\′}-E_n}{E_n}{|}_{k=1\→N}\right\}\%\≤E_{\max }$

In formula: k is iterations；N is subdivision unit sum；E_maxFor the maximum field strength rate of change set.

4. according to the converter transformer valve-side three-dimensional electric field of the consideration Anisotropic Nonlinear described in claim l Emulation mode, it is characterised in that: described step 3) the middle consideration temperature impact on resistivity, first basis Empirical hypothesis temperature value, then calculate the temperature impact on resistivity by the method for coupling；

(1) determination of end region temperature

Adding Temperature Excitation at winding and electrostatic ring surface, its value is 30 DEG C, and ambient temperature is set to 20 DEG C, Flow velocity is ignored, and only considers heat conductive process in insulating board and transformer oil, do not consider around The heat convection on group surface and heat radiation；

(2) coupling process

After completing winding overhang solution of Temperature, the temperature value reading each unit with * VGET, then utilize * the temperature of each unit is saved in a text by VWRITE order, when calculating DC Steady electricity During field, utilize * VREAD order read the data in text and be saved in array, utilize this array Revise the resistivity of each finite element unit, to carry out solving of steady-state DC electric field.

5. according to the converter transformer valve-side three-dimensional electricity of the consideration Anisotropic Nonlinear described in claim l Emulation mode, it is characterised in that: described step 4) in anisotropy DC electric field calculate:

(1) there is anisotropy in paper direction, and this character can be expressed as:

$\mathrm{\σ}=\left(\begin{array}{cc}{\mathrm{\σ}}_h& 0\\ 0& {\mathrm{\σ}}_t\end{array}\right)$

σ_hResistivity for horizontal paper direction；

σ_tFor being perpendicular to the resistivity in paper direction；

In transformator 1/8 overhang insulation model, insulating paper cylinder and square ring etc. all can be approximately cylindrical ring body, during modeling With cylindrical ring body cross section as x, z-plane, with the cylindrical ring body longitudinal axis as y-axis, now with cardboard with the folder in y-axis direction Angle is θ, then the coordinate of cardboard arbitrfary point a is (x_a,y_a,z_a) vertical paper direction be expressed as:

$\stackrel{\→}{a_h}=(x_a,\tan \mathrm{\θ}\sqrt{{x_a}^2+{z_a}^2},z_a)$

Assume that the electric field intensity that now a point reads is expressed as E_a=(E_x,E_y,E_z), then E_aThe component of vertical paper is:

$E_h=\frac{\stackrel{\→}{E_a}\·\stackrel{\→}{a_h}}{\left|\stackrel{\→}{a_h}\right|}=\frac{E_x{x}_a+E_y\tan \mathrm{\θ}\sqrt{{x_a}^2+{z_a}^2}+E_z{z}_a}{\sqrt{{x_a}^2+{\tan }^2\mathrm{\θ}({x_a}^2+{z_a}^2)+{z_a}^2}}$

E_aThe component of horizontal paper is:

$E_t=\sqrt{{E_a}^2-{E_h}^2}=\sqrt{({E_x}^2+{E_y}^2+{E_z}^2)-\frac{{(E_x{x}_a+E_y\tan \mathrm{\θ}\sqrt{{x_a}^2+{z_a}^2}+E_z{z}_a)}^2}{{x_a}^2+{\tan }^2\mathrm{\θ}({x_a}^2+{z_a}^2)+{z_a}^2}}$

Then according to E_hAnd E_tBring cardboard nonlinear fitting formula vertically and horizontally in 5.1 respectively into and calculate σ_h And σ_t；

Obtain through more corresponding mathematic(al) manipulations:

Obtained σ_x,σ_y,σ_zIt is the cardboard resistivity initial anisotropy component of iteration next time；

Cardboard is respectively brought into resistivity component computing formula the interative computation of cardboard nonlinear resistivity again, and passes through EMODIF instruction modification cardboard unit is respectively to resistivity component, as the parameter of next iteration computing, and can be in emulation Middle consider anisotropy simultaneously.