CN103605836A - Parallel computing method for three-dimensional electromagnetic fields of high-voltage transformer substation - Google Patents

Abstract

The invention relates to a parallel computing method for three-dimensional electromagnetic fields of a high-voltage transformer substation. The parallel computing method is characterized in that an electromagnetic field model is established by using a three-dimensional finite element and a boundary element and can be solved; and the distribution condition of the electromagnetic fields of electromagnetic equipment of the high-voltage transformer substation can be sufficiently reflected by researching applicability of the finite element and applicability of the boundary element on computation of the electromagnetic fields of the transformer substation, and particularly, the distribution condition of the electromagnetic fields of the electromagnetic equipment such as a transformer comprising high-magnetic-permeability materials and the distribution condition of the electromagnetic fields of high-voltage electrical equipment such as an electric reactor can be reflected. The parallel computing method is quick and accurate in computation, is well-adapted, and has high engineering value.

Description

A kind of high voltage substation 3 D electromagnetic field parallel calculating method

Technical field

The present invention is a kind of high voltage substation 3 D electromagnetic field parallel calculating method, is applied to the research of electromagnetic-field simulation method and the field analysis of high voltage substation and electromagnetic equipment.

Background technology

Along with greatly developing of China's high voltage power transmission engineering, electric pressure and the electric current of electrical network improve constantly, and the magnetic field that system and equipment produce also becomes and becomes increasingly complex.For reaching the indices of electromagnetic environment and guaranteeing the normal operation of system, the electromagnetic environment of research substation equipment seems particularly important.The electric charge of the power supply of the various electromagnetic equipments of transformer station and framework induction produces power frequency magnetic field at the near space in transformation device district, because transformer station's Charging system position is complicated and varied, except there being high-low voltage leads, also have the miscellaneous equipments such as transformer, high-voltage shunt reactor, grounding switch, capacitance type potential transformer and GIS, therefore, in transformer station, the power frequency magnetic field of electromagnetic equipment is that a complicated three dimensional field distributes.Research method about transformer station's electromagnetic environment has field measurement, simulation test and numerical evaluation both at home and abroad, comprises transmission line simulation corridor electric field, and computing equipment space electromagnetism distributes, and simplified model improves counting yield etc.Classic method is too single, calculated amount is huge, and the matrix of coefficients symmetry that coupling generates and orthotropicity are difficult to meet, when processing the tangential continuous problem of coupled field, there is defect, when device structure more complicated, especially, in the situation that equipment magnetic conduction medium consists of multiple material, with this class methods calculating magnetic field, can bring very large error.Ideal model is the complex apparatus of simulated field really, and versatility is not high, and following research need to reduce difficulty in computation meeting under the prerequisite of requirement of engineering precision.

Summary of the invention

The object of the invention is to overcome the deficiencies in the prior art, provide a kind of calculating fast, accurately, strong adaptability, has the high voltage substation electromagnetic field simulation method of higher actual application value.

The object of the invention is to be realized by following technical scheme:

A high voltage substation 3 D electromagnetic field parallel calculating method, is characterized in that, it comprises the following steps:

1) space electric field based on boundary element calculates

Put r then and there on the surface of conductor time, boundary integral equation can be expressed as

In formula, r is field point position vector; R ' is source point position vector;

for field point current potential; σ is source point surface charge density; R is the distance between a point and source point, for solving variable, border is discrete with σ, and adopts the golden weighted residual method of gal the Liao Dynasty, and formula (1) is write as:

In formula, e represents the numbering of a unit; E ' represents the numbering of source unit; I, j represents discrete nodes numbering; S _ethe integral domain that represents a unit, S _{e '}the integral domain that represents source unit;

represent node potential; σ _irepresent node surface charge density; N _i, N _jfor interpolating function; ε ₀for the specific inductive capacity of vacuum, discrete by interpolation, formula (2) is converted into algebraic equation, then tries to achieve Electric Field Distribution;

2) space magnetic field based on finite element calculates

Vector magnetic potential finite element method adopts vector magnetic potential A, ignores hysteresis effect and eddy effect, according to Maxwell equation, obtains magnetic field equation:

$\▿\×\frac{1}{\mathrm{\μ}}\▿\×A=J---\left(3\right)$

In formula, ▽ * be curl operator, the magnetic permeability that μ is medium, J is current density,

Take seamed edge finite element as example, and the whole interpolating function that solves field domain is

$A=\underset{n=1}{\overset{n_l}{\mathrm{\Σ}}}{M}_n(x,y,z)A_n---\left(4\right)$

According to formula (1), to formula (2) application Green's theorem, obtain the golden Weighted Residual equation of gal the Liao Dynasty:

In formula, be vector dot product computing, disregard border item, equation arranges and is:

$\underset{\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="121102150249.png"\; state="\{\{state\}\}">V</figure-callout>}}{\&Integral;\&Integral;\&Integral;}\frac{1}{\mathrm{\&mu;}}(\&dtri;\&times;M_m)\&CenterDot;(\&dtri;\&times;M_n)A_n\mathrm{dV}=\underset{V}{\&Integral;\&Integral;\&Integral;}{M}_m\&CenterDot;\mathrm{JdV}---\left(6\right)$

By formula (6) substitution formula (4), for whole weight functions, by the discrete formation Algebraic Equation set of Weighted Residual equation, solve the scalar magnetic potential A that obtains whole seamed edges,

Draw after the vector magnetic potential function of model, directly utilize the differential formulas in magnetic field, field, the magnetic field amount of computer memory any point, as magnetic flux density vector B and magnetic field intensity H, is shown in following formula,

$\left\{\begin{array}{c}\&dtri;\&times;A=\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="121102150249.png"\; state="\{\{state\}\}">B</figure-callout>}\\ \frac{1}{\mathrm{\&mu;}}\&dtri;\&times;A=H\end{array}\right.$

Utilize the parallel computation of finite element-Element BEM to simulate high voltage substation 3 D electromagnetic field, and contrast with actual conditions, conclude efficiency and the error of finite element-Element BEM when simulation calculation electromagnetic equipment power frequency magnetic field, the calculating applicability of research finite element-Element BEM, for the calculating of high voltage substation complex apparatus periphery electromagnetic environment provides feasibility.

The present invention is a kind of high voltage substation 3 D electromagnetic field parallel calculating method, compare with existing computing method, the present invention utilizes three-dimensional finite element-boundary element set up electromagnetic field model and solve, the applicability when calculating transformer station's electromagnetic field by research finite element and boundary element, the electromagnetic field distribution situation that can fully reflect high voltage substation electromagnetic equipment, it is quick, accurate that the method is calculated, and strong adaptability, has higher actual application value.

Accompanying drawing explanation

Fig. 1 substation equipment schematic diagram;

Fig. 2 substation equipment model schematic diagram;

Fig. 3 substation equipment mirror image model schematic diagram;

Near field intensity maximal value cloud atlas Fig. 4 transformer station;

Fig. 5 electric field intensity is along the distribution plan of straight line L;

Fig. 6 core limb axon is to magnetic flux density vector distribution plan;

Fig. 7 cylinder unshakable in one's determination is magnetic flux density vector distribution plan radially.

embodiment

Below in conjunction with the drawings and specific embodiments, computing method of the present invention are further described:

As shown in Figure 1, substation equipment is the wire 8 on high-voltage shunt reactor 1, the first support insulator 2, lightning arrester 3, the second support insulator 4, capacitance type potential transformer 5, grounding switch 6, steel tower 7 and steel tower from right to left successively.By the electric field intensity near 1.5 meters, ground of distance plane boundary Element high-voltage shunt reactor 1, establish this plane and represent with P, as shown in Figure 2, set up the three-dimensional finite element magnetic field model of substation transformer.

1) space electric field based on boundary element calculates

Put r then and there on the surface of conductor time, boundary integral equation can be expressed as

In formula, r is field point position vector; R ' is source point position vector;

for field point current potential; σ is source point surface charge density; R is the distance between a point and source point, for solving variable, border is discrete with σ, and adopts the golden weighted residual method of gal the Liao Dynasty, and formula (1) is write as:

In formula, e represents the numbering of a unit; E ' represents the numbering of source unit; I, j represents discrete nodes numbering; S _ethe integral domain that represents a unit, S _{e '}the integral domain that represents source unit;

represent node potential; σ _irepresent node surface charge density; N _i, N _jfor interpolating function; ε ₀for the specific inductive capacity of vacuum, discrete by interpolation, formula (2) is converted into algebraic equation, then tries to achieve Electric Field Distribution;

2) space magnetic field based on finite element calculates

Vector magnetic potential finite element method adopts vector magnetic potential A, ignores hysteresis effect and eddy effect, according to Maxwell equation, obtains magnetic field equation:

$\&dtri;\&times;\frac{1}{\mathrm{\&mu;}}\&dtri;\&times;A=J---\left(3\right)$

In formula, ▽ * be curl operator, the magnetic permeability that μ is medium, J is current density,

Take seamed edge finite element as example, and the whole interpolating function that solves field domain is

$A=\underset{n=1}{\overset{n_l}{\mathrm{\&Sigma;}}}{M}_n(x,y,z)A_n---\left(4\right)$

According to formula (1), to formula (2) application Green's theorem, obtain the golden Weighted Residual equation of gal the Liao Dynasty:

In formula, be vector dot product computing, disregard border item, equation arranges and is:

$\underset{\mathrm{<figure-callout\; id="1"\; label="V"\; filenames="121102150249.png"\; state="\{\{state\}\}">V</figure-callout>}}{\&Integral;\&Integral;\&Integral;}\frac{1}{\mathrm{\&mu;}}(\&dtri;\&times;M_m)\&CenterDot;(\&dtri;\&times;M_n)A_n\mathrm{dV}=\underset{V}{\&Integral;\&Integral;\&Integral;}{M}_m\&CenterDot;\mathrm{JdV}---\left(6\right)$

By formula (6) substitution formula (4), for whole weight functions, by the discrete formation Algebraic Equation set of Weighted Residual equation, solve the scalar magnetic potential A that obtains whole seamed edges,

Draw after the vector magnetic potential function of model, directly utilize the differential formulas in magnetic field, field, the magnetic field amount of computer memory any point, as magnetic flux density vector B and magnetic field intensity H, is shown in following formula,

$\left\{\begin{array}{c}\&dtri;\&times;A=\mathrm{<figure-callout\; id="1"\; label="B"\; filenames="121102150249.png"\; state="\{\{state\}\}">B</figure-callout>}\\ \frac{1}{\mathrm{\&mu;}}\&dtri;\&times;A=H\end{array}\right.$

Utilize the parallel computation of finite element-Element BEM to simulate high voltage substation 3 D electromagnetic field, and contrast with actual conditions, conclude efficiency and the error of finite element-Element BEM when simulation calculation electromagnetic equipment power frequency magnetic field, the calculating applicability of research finite element-Element BEM, for the calculating of high voltage substation complex apparatus periphery electromagnetic environment provides feasibility.

Adopt the device structures such as finite element and boundary element model difference analog bus, transformer and grading ring, with other equipment such as surface model emulating reactance device grounding shells, the subdivision model of ABC three-phase equipment as shown in Figure 2.In actual computation process, be to keep the zero potential on ground, using ground as the plane of symmetry, to have set up the mirror image model of all devices, as shown in Figure 3.

In plane P, electric field intensity maximal value distributes as shown in Figure 4, can find out, in the symmetrical position of A, C, be on the phase position of limit, to have occurred the region that field intensity is larger, the conclusion of this and classic method is consistent, and A, 2 meters of left and right of C phase reactor axis are departed from respectively in this region.The maximal value of electric field intensity appears at the lower zone of C capacitance type potential transformer, and maximal value is 9.178kV/m.

On the straight line L apart from high resistance Ontology 20m place, carry out in-site measurement, on this straight line, the peaked measurement curve of electric field intensity and calculated curve are as shown in Figure 5, as seen from Figure 5, A, corresponding two crests in two limits of C, the corresponding middle trough of B, measures curve and simulation curve basically identical, and it is better that limit partly coincide mutually, this region that transformer station's power frequency electric field maximal value occurs is just the position of primary study.B mediates mutually, and surrounding devices is more, and the impact being subject to during measurement is larger, and therefore, curve is in trough part some deviation a little.

Set up simple iron core-coil former, the long 3m of cylinder unshakable in one's determination, radius 0.5m, adopts respectively two-dimensional axial symmetric face unit (PFEM), node finite element (NFEM), seamed edge finite element (EFEM), calculates different relative permeability μ _rthe distribution of Shi Tiexin axis z and radial line r magnetic field B.With reference to Fig. 6, core limb axon is to magnetic flux density vector distribution plan, the magnetic field result of wherein calculating based on two-dimensional axial symmetric face element method conforms to actual conditions, has higher accuracy, and the result of calculation of nodal element and Edge Finite Element Method is compared.With reference to Fig. 7, cylinder unshakable in one's determination is magnetic flux density vector distribution plan radially, and three kinds of computing method are constant.Under linear conditions, when iron core is identical with air permeability, the error of NFEM, EFEM and PFEM is very little; Along with μ _rincrease, EFEM is consistent with the result of PFEM, but the increase of NFEM error, while showing higher magnetic permcability, there is larger error in the result of calculation of NFEM.

The present invention is a kind of high voltage substation 3 D electromagnetic field parallel calculating method, and algorithm principle is clear and definite, and model is simple.By Example Verification near the method electromagnetic intensity calculation of complex equipment more accurately, for the calculating of high voltage substation complex apparatus periphery electromagnetic environment provides a kind of feasible method, realized the object of the invention, reached described effect.

Claims (1)

1. a high voltage substation 3 D electromagnetic field parallel calculating method, is characterized in that, it comprises the following steps:

1) space electric field based on boundary element calculates

Put r then and there on the surface of conductor time, boundary integral equation can be expressed as

In formula, r is field point position vector; R ' is source point position vector;

for field point current potential; σ is source point surface charge density; R is the distance between field point and source point.For solving variable, border is discrete with σ, and adopt the golden weighted residual method of gal the Liao Dynasty, formula (1) is write as:

In formula, e represents the numbering of a unit; E ' represents the numbering of source unit; I, j represents discrete nodes numbering; S _ethe integral domain that represents a unit, S _{e '}the integral domain that represents source unit;

represent node potential; σ _irepresent node surface charge density; N _i, N _jfor interpolating function; ε ₀for the specific inductive capacity of vacuum, discrete by interpolation, formula (2) is converted into algebraic equation, then tries to achieve Electric Field Distribution;

2) space magnetic field based on finite element calculates

Vector magnetic potential finite element method adopts vector magnetic potential A, ignores hysteresis effect and eddy effect, according to Maxwell equation, obtains magnetic field equation:

$\&dtri;\&times;\frac{1}{\mathrm{\&mu;}}\&dtri;\&times;A=J---\left(3\right)$

In formula, ▽ * be curl operator, the magnetic permeability that μ is medium, J is current density,

Take seamed edge finite element as example, and the whole interpolating function that solves field domain is

$A=\underset{n=1}{\overset{n_l}{\mathrm{\&Sigma;}}}{M}_n(x,y,z)A_n---\left(4\right)$

According to formula (1), to formula (2) application Green's theorem, obtain the golden Weighted Residual equation of gal the Liao Dynasty:

In formula, be vector dot product computing, disregard border item, equation arranges and is:

$\underset{V}{\&Integral;\&Integral;\&Integral;}\frac{1}{\mathrm{\&mu;}}(\&dtri;\&times;M_m)\&CenterDot;(\&dtri;\&times;M_n)A_n\mathrm{dV}=\underset{V}{\&Integral;\&Integral;\&Integral;}{M}_m\&CenterDot;\mathrm{JdV}---\left(6\right)$

By formula (6) substitution formula (4), for whole weight functions, by the discrete formation Algebraic Equation set of Weighted Residual equation, solve the scalar magnetic potential A that obtains whole seamed edges,

Draw after the vector magnetic potential function of model, directly utilize the differential formulas in magnetic field, field, the magnetic field amount of computer memory any point, as magnetic flux density vector B and magnetic field intensity H, is shown in following formula,

$\left\{\begin{array}{c}\&dtri;\&times;A=B\\ \frac{1}{\mathrm{\&mu;}}\&dtri;\&times;A=H\end{array}\right.$

Utilize the parallel computation of finite element-Element BEM to simulate high voltage substation 3 D electromagnetic field, and contrast with actual conditions, conclude efficiency and the error of finite element-Element BEM when simulation calculation electromagnetic equipment power frequency magnetic field, the calculating applicability of research finite element-Element BEM, for the calculating of high voltage substation complex apparatus periphery electromagnetic environment provides feasibility.

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