CN103605894A - Method and device for acquiring unequal section core excitation features - Google Patents

Abstract

The invention provides a method and device for obtaining the excitation characteristics of iron cores with different cross-sections. The method includes: fitting the BH curve fitting function of iron core materials with different cross-sections; B is the magnetic induction intensity, and H is the magnetic field intensity; Decompose the magnetic circuit of the magnetic circuit to obtain the equivalent circuit of the iron core with different cross-sections. The equivalent excitation branch in the equivalent circuit is connected in parallel by multiple excitation branches; each excitation branch corresponds to a section of the magnetic circuit; using the fitting function of the BH curve Obtain the ψ-i curves of each excitation branch separately; ψ is the flux linkage, i is the current; from the ψ-i curves of all the excitation branches, the ψ-i curves of the cores with different cross-sections are obtained. Decompose the magnetic circuit of the iron core with unequal cross-section, decompose it into multiple excitation branches and connect them in parallel, so as to obtain the excitation characteristics of each section, and then obtain the excitation characteristics of the entire iron core with unequal cross-section equivalently from the excitation characteristics of each section.

Description

A kind of method and device that obtains unequal section iron core excitation characteristic

Technical field

The present invention relates to electrical equipment technical field, particularly a kind of method and device that obtains unequal section iron core excitation characteristic.

Background technology

In UHV (ultra-high voltage) and UHV transmission equipment, some power equipment need to be used with device unshakable in one's determination, for example magnet controlled fault current limiter.According to the requirement of power equipment electric property, may use the core construction of unequal section.In the core construction of unequal section, the area of section of each iron leg heart and length are unequal.

In some cases, excitation property unshakable in one's determination is very large to the properties influence of device, therefore has and must obtain excitation property unshakable in one's determination.For example, in magnet controlled fault current limiter, iron core can be operated under state of saturation for a long time, the affect highly significant of its excitation property on fault current limiter impedance operator.Therefore, obtain its excitation property significant.

Two curves that paper is relevant with excitation property;

BH curve:

B is magnetic induction density (unit is T), and H is magnetic field intensity (unit is A/m), and BH curve can characterize excitation property unshakable in one's determination.

ψ-i curve:

ψ is magnetic linkage (unit is Wb), and i is electric current (unit is A), and ψ-i curve also can characterize excitation property unshakable in one's determination.In the simulation calculation such as electro-magnetic transient, excitation property unshakable in one's determination represents with ψ-i curve conventionally.

For prismatic iron core, BH curve and physical dimension unshakable in one's determination by core material, can be easier to obtain curve unshakable in one's determination.But for the iron core of unequal section, its excitation property is unshakable in one's determination complicated more a lot of than uniform cross section, the ψ-i excitation property unshakable in one's determination that therefore how to obtain unequal section is those skilled in the art's technical issues that need to address.

Summary of the invention

The technical problem to be solved in the present invention is to provide a kind of method and device that obtains unequal section iron core excitation characteristic, can accurately obtain the excitation property of unequal section iron core.

The embodiment of the present invention provides a kind of method that obtains unequal section iron core excitation characteristic, comprising:

The fitting function of the BH curve of matching unequal section core material; B is magnetic induction density, and H is magnetic field intensity;

The magnetic circuit of unequal section iron core is decomposed, obtain the equivalent circuit of unequal section iron core, the equivalent field excitation branch line in described equivalent circuit is in parallel by a plurality of field excitation branch lines; The corresponding one section of magnetic circuit of field excitation branch line described in each;

Utilize the fitting function of described BH curve to obtain respectively ψ-i curve of field excitation branch line described in each; ψ is magnetic linkage, and i is electric current;

By ψ-i curve of all described field excitation branch lines, obtained ψ-i curve of unequal section iron core.

Preferably, the fitting function of described BH curve comprises linear term and saturated item;

The slope of described linear term equals air permeability μ ₀, μ ₀=4 π * 10 ^-7h/m;

Described saturated adopts asinh function, arctan function or ambipolar S compression function.

Preferably, when described unequal section iron core is magnet controlled fault current limiter, and magnet controlled fault current limiter adopts two independently magnetic circuits; The corresponding equivalent field excitation branch line of magnetic circuit described in each, described in each, equivalent field excitation branch line is decomposed into three field excitation branch lines and carries out parallel connection, described three field excitation branch lines respectively corresponding direct current post field excitation branch line, exchange post field excitation branch line and yoke field excitation branch line.

Preferably, when described unequal section iron core is magnet controlled fault current limiter, and magnet controlled fault current limiter adopts three pillar type magnetic circuit; Corresponding three the equivalent field excitation branch lines of described three pillar type magnetic circuit, wherein two described equivalent field excitation branch lines carry out parallel connection for exchanging post field excitation branch line and yoke field excitation branch line, and described in another, equivalent field excitation branch line is direct current post field excitation branch line.

Preferably, the described fitting function that utilizes described BH curve obtains respectively ψ-i curve of field excitation branch line described in each, is specially:

By sectional area and the length of segmentation magnetic circuit, obtain reduction to ψ-i curve of AC winding or DC side winding.

The embodiment of the present invention also provides a kind of device that obtains unequal section iron core excitation characteristic, comprising: fitting function acquiring unit, magnetic circuit resolving cell, segmentation magnetic circuit ψ-i curve acquisition unit and unequal section ψ-i curve acquisition unshakable in one's determination unit;

Described fitting function acquiring unit, for the fitting function of the BH curve of matching unequal section core material; B is magnetic induction density, and H is magnetic field intensity;

Described magnetic circuit resolving cell, for obtaining the equivalent circuit of unequal section iron core, the equivalent field excitation branch line in described equivalent circuit is in parallel by a plurality of field excitation branch lines; The corresponding one section of magnetic circuit of field excitation branch line described in each;

Described segmentation magnetic circuit ψ-i curve acquisition unit, for utilizing the fitting function of described BH curve to obtain respectively ψ-i curve of field excitation branch line described in each; ψ is magnetic linkage, and i is electric current;

Described unequal section ψ-i curve acquisition unshakable in one's determination unit, for ψ-i curve of the ψ-i curve acquisition unequal section iron core by all described field excitation branch lines.

Preferably, the fitting function of described BH curve comprises linear term and saturated item;

The slope of described linear term equals air permeability μ ₀, μ ₀=4 π * 10 ^-7h/m;

Described saturated adopts asinh function, arctan function or ambipolar S compression function.

Preferably, when described unequal section iron core is magnet controlled fault current limiter, and magnet controlled fault current limiter adopts two independently magnetic circuits, the corresponding equivalent field excitation branch line of magnetic circuit described in each; Described magnetic circuit resolving cell, is decomposed into three field excitation branch lines for equivalent field excitation branch line described in each and carries out parallel connection, and described three field excitation branch lines are corresponding direct current post field excitation branch line, interchange post field excitation branch line and yoke field excitation branch line respectively.

Preferably,

When described unequal section iron core is magnet controlled fault current limiter, and magnet controlled fault current limiter adopts three pillar type magnetic circuit; Described magnetic circuit resolving cell, be used for corresponding three the equivalent field excitation branch lines of described three pillar type magnetic circuit, wherein two described equivalent field excitation branch lines carry out parallel connection for exchanging post field excitation branch line and yoke field excitation branch line, and described in another, equivalent field excitation branch line is direct current post field excitation branch line.

Compared with prior art, the present invention has the following advantages:

Method provided by the invention and device, carry out magnetic circuit decomposition to the iron core of unequal section, obtains the equivalent circuit of unequal section iron core, and the equivalent field excitation branch line in described equivalent circuit is in parallel by a plurality of field excitation branch lines; The corresponding one section of magnetic circuit of field excitation branch line described in each; Utilize like this fitting function of BH curve of the core material of matching, obtain ψ-i curve of each field excitation branch line; By ψ-i curve of each field excitation branch line, obtained ψ-i curve of whole unequal section iron core, ψ-i curve can represent excitation property unshakable in one's determination again.Method provided by the invention is carried out magnetic circuit decomposition by the iron core of unequal section, is decomposed into a plurality of field excitation branch lines and carries out parallel connection, thereby obtain the excitation property of every section, and then by the excitation property equivalence of every section, gone out the excitation property of whole unequal section iron core.

Accompanying drawing explanation

In order to be illustrated more clearly in the embodiment of the present invention or technical scheme of the prior art, to the accompanying drawing of required use in embodiment or description of the Prior Art be briefly described below, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skills, do not paying under the prerequisite of creative work, can also obtain according to these accompanying drawings other accompanying drawing.

Fig. 1 is embodiment of the method one process flow diagram of acquisition unequal section iron core excitation characteristic provided by the invention;

Fig. 2 is the fitting effect curve map of the BH curve of certain core material provided by the invention;

Fig. 3 is that the iron core of magnet controlled fault current limiter provided by the invention adopts two independently schematic diagram of magnetic circuit;

Fig. 4 is that the iron core of magnet controlled fault current limiter adopts two independently equivalent circuit diagrams of magnetic circuit;

Fig. 5 a is the equivalent circuit schematic diagram of field excitation branch line 1 in Fig. 4;

Fig. 5 b is the equivalent circuit schematic diagram of field excitation branch line 2 in Fig. 4;

Fig. 6 is that magnet controlled fault current limiter is the schematic diagram of three pillar type structure;

Fig. 7 is the equivalent circuit diagram that Fig. 6 is corresponding;

Fig. 8 a be field excitation branch line 1 in Fig. 7 ' equivalent circuit schematic diagram;

Fig. 8 b be field excitation branch line 2 in Fig. 7 ' equivalent circuit schematic diagram;

Fig. 8 c is the equivalent circuit schematic diagram of field excitation branch line 3 in Fig. 7;

Fig. 9 is the comparison schematic diagram of unequal section provided by the invention equivalent rear exciting characteristic curve unshakable in one's determination and each section of exciting characteristic curve;

Figure 10 is device embodiment mono-schematic diagram of the excitation property of acquisition unequal section iron core provided by the invention.

Embodiment

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is clearly and completely described, obviously, described embodiment is only the present invention's part embodiment, rather than whole embodiment.Embodiment based in the present invention, those of ordinary skills, not making the every other embodiment obtaining under creative work prerequisite, belong to the scope of protection of the invention.

For above-mentioned purpose of the present invention, feature and advantage can be become apparent more, below in conjunction with accompanying drawing, the specific embodiment of the present invention is described in detail.

Referring to Fig. 1, this figure is embodiment of the method one process flow diagram of acquisition unequal section iron core excitation characteristic provided by the invention.

The method of the acquisition unequal section iron core excitation characteristic that the present embodiment provides, comprises the following steps:

S101: the fitting function of the BH curve of matching unequal section core material; B is magnetic induction density, and H is magnetic field intensity;

When iron core reach the degree of depth saturated after, owing to there is no rotating magnetic domain, its unit permeance is close to air.Therefore, the limit slope of the core material BH curve degree of depth after saturated is knownly (to equal air permeability μ ₀=4 π * 10 ^-7h/m).

Fitting function can be divided into two parts: linear term and saturated item.The slope of linear term equals air permeability μ ₀.The fitting function of saturated can have multiple, as asinh function, arctan function, ambipolar S compression function etc.Wherein ambipolar S compression function is usually used in error back propagation (BP, Error Back Propagation) algorithm.

S102: the magnetic circuit of unequal section iron core is decomposed, obtain the equivalent circuit of unequal section iron core, the equivalent field excitation branch line in described equivalent circuit is in parallel by a plurality of field excitation branch lines; The corresponding one section of magnetic circuit of field excitation branch line described in each;

For prismatic iron core, by BH curve, can obtain ψ-i curve.The number of turn of supposing coil is N, and average cross-section is A, and the length of center line is l, has following relation:

$\left\{\begin{array}{c}\mathrm{\ψ}=\mathrm{N\Φ}\\ \mathrm{\Φ}=\mathrm{BA}\\ H\·l=N\·i\end{array}\right.---\left(1\right)$

By formula (1), can obtain formula (2):

$\left\{\begin{array}{c}\text{\ψ=NA\·B}\\ i=l/N\·H\end{array}\right.---\left(2\right)$

By formula (1), BH curve can be converted into Ψ-i curve.

But for the iron core of unequal section, first need iron core to be divided into some sections.

By formula (1) and (2), can only obtain Ψ-i curve of every iron leg heart.

By the excitation property of each iron leg heart, how to obtain the excitation property of whole unequal section iron core, be key point of the present invention.

S103: utilize the fitting function of described BH curve to obtain respectively ψ-i curve of field excitation branch line described in each; ψ is magnetic linkage, and i is electric current;

Utilize the fitting function of BH curve and the relation of formula (1) and (2) can obtain ψ-i curve of segmentation magnetic circuit.

S104: the ψ-i curve that is obtained unequal section iron core by ψ-i curve of all described field excitation branch lines.

The iron core of different structure, can adopt the nonlinear field excitation branch line of several parallel connections to represent conventionally.Yet, when employing electromagnetic transient state procedure (EMTP) etc. carries out simulation calculation, if directly a plurality of nonlinear field excitation branch lines are carried out to parallel connection, may produce some problems.For this reason, suggestion is by a plurality of non-linear exciter branch roads of parallel connection equivalent merging in addition.

The method that the present embodiment provides, carries out magnetic circuit decomposition to the iron core of unequal section, obtains the equivalent circuit of unequal section iron core, and the equivalent field excitation branch line in described equivalent circuit is in parallel by a plurality of field excitation branch lines; The corresponding one section of magnetic circuit of field excitation branch line described in each; Utilize like this fitting function of BH curve of the core material of matching, obtain ψ-i curve of each field excitation branch line; By ψ-i curve of each field excitation branch line, obtained ψ-i curve of whole unequal section iron core, ψ-i curve can represent excitation property unshakable in one's determination again.Method provided by the invention is carried out magnetic circuit decomposition by the iron core of unequal section, is decomposed into a plurality of field excitation branch lines and carries out parallel connection, thereby obtain the excitation property of every section, and then by the excitation property equivalence of every section, gone out the excitation property of whole unequal section iron core.

Embodiment bis-:

Introduce the fitting function of the BH curve of the matching unequal section core material that the embodiment of the present invention provides below.

Saturated in the fitting function that the present embodiment provides preferably adopts asinh function.

Consider the problem of fitting precision, saturated in the fitting function in the present invention adopts a plurality of asinh functions.The BH curve of certain core material of take is example, and its fitting function is suc as formula (3), and its raw data and fitting result are as shown in table 1.Fitting effect curve map as shown in Figure 2.

B=μ ₀H-0.6299arsh(0.0280H)+0.6925arsh(0.280H) （3）

The fitting result of certain material B-H curve of table 1

Embodiment tri-:

How the unequal section iron core of take below carries out magnetic circuit decomposition as magnet controlled fault current limiter as example introduction.

Magnet controlled fault current limiter has two kinds of typical structures, is respectively to adopt two independently magnetic circuit and employing three pillar type structures.

Referring to Fig. 3, the iron core that this figure is magnet controlled fault current limiter provided by the invention adopts two independently schematic diagram of magnetic circuit.

According to the positive dirction of each physical quantity of stipulating in Fig. 3, there is following winding voltage equation:

Wherein, u ₁the voltage at the first interchange winding two ends, u ₂the voltage at the second interchange winding two ends, u ₃the voltage at DC excitation winding two ends;

$\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">u</figure-callout>}}_1=r_1{\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">i</figure-callout>}}_1+N_1(\frac{{\mathrm{d\&Phi;}}_1}{\mathrm{dt}}+\frac{{\mathrm{d\&Phi;}}_{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">k</figure-callout>}1}}{\mathrm{dt}})\\ {\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">u</figure-callout>}}_2=r_2{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">i</figure-callout>}}_2+N_2(\frac{{\mathrm{d\&Phi;}}_2}{\mathrm{dt}}+\frac{{\mathrm{d\&Phi;}}_{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">k</figure-callout>}2}}{\mathrm{dt}})\\ u_3=r_3{i}_3+N_3(\frac{{\mathrm{d\&Phi;}}_1}{\mathrm{dt}}-\frac{{\mathrm{d\&Phi;}}_2}{\mathrm{dt}}+\frac{{\mathrm{d\&Phi;}}_{k3}}{\mathrm{dt}})\end{array}---\left(4\right)$

Because two windings are series relationship, so the first current i exchanging in winding ₁exchange the current i of winding with second ₂equate:

i ₁=i ₂ （5）

According to the Kirchhoff's second law of magnetic circuit, for two iron circuits, can obtain:

H ₁₁l ₁+H ₁₂l ₂+H ₁₃l ₃=N ₁i ₁+N ₃i ₃

（6）

H ₂₁l ₁+H ₂₂l ₂+H ₂₃l=N ₂i ₂-N ₃i ₃

Wherein, H ₁₁and H ₂₁be respectively the magnetic field intensity in the first magnetic circuit and AC core limb in the second magnetic circuit (be called for short and exchange post), H ₁₃and H ₂₃be respectively the magnetic field intensity in DC side core limb in the first magnetic circuit and the second magnetic circuit (being called for short direct current post), and H ₁₂and H ₂₂be respectively the magnetic field intensity of yoke part in the first magnetic circuit and the second magnetic circuit; l ₁, l ₂, l ₃be respectively the centerline length that exchanges post, yoke, direct current post.N ₁the number of turn of the first interchange winding, N ₂the number of turn of the second interchange winding, N ₃it is the number of turn of direct current winding; Φ ₁the main flux of the first magnetic circuit, Φ ₂it is the main flux of the second magnetic circuit; ; i ₃it is the electric current in direct current winding.

If arranged:

$\begin{array}{c}{i}_1={\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">i</figure-callout>}}_1^{\&prime;}+{\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">i</figure-callout>}}_1^{\&prime;\&prime;}\\ i_2={\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">i</figure-callout>}}_2^{\&prime;}+{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">i</figure-callout>}}_2^{\&prime;\&prime;}\end{array}---\left(7\right)$

And meet following constraint condition

N ₁i′ ₁+N ₃i ₃＝0

(8)

N ₂i′ ₂-N ₃i ₃＝0

Can obtain the magnetic potential drop expression formula of two iron circuits:

$\begin{array}{c}{H}_{11}{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">l</figure-callout>}}_1+H_{12}{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">l</figure-callout>}}_2+H_{13}{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">l</figure-callout>}}_2=N_1{\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">i</figure-callout>}}_1^{\&prime;\&prime;}\\ H_{21}{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">l</figure-callout>}}_1+H_{22}{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">l</figure-callout>}}_2+H_{23}{l}_3=N_2{i}^{\&prime;\&prime;}\end{array}---\left(9\right)$

According to above-mentioned winding voltage equation, can obtain the equivalent circuit of the magnet controlled fault current limiter of two independent magnetic circuit formulas, the equivalent field excitation branch line in described equivalent circuit is in parallel by a plurality of field excitation branch lines, the corresponding one section of magnetic circuit of field excitation branch line described in each.

As shown in Figure 4.Wherein, r ₁and L _k1for exchanging resistance and the leakage inductance of winding 1, r ₂and L _k2for exchanging resistance and the leakage inductance of winding 2, r ₃and L _k3resistance and leakage inductance for DC excitation winding; " equivalent field excitation branch line 1 " and " equivalent field excitation branch line 2 " represents respectively the excitation property of two iron circuits.

Under the unequal condition of each section of sectional area of magnetic circuit, magnetic circuit can be decomposed.Order

$\begin{array}{c}{i}_1^{\&prime;\&prime;}=i_{11}^{\&prime;\&prime;}+i_{12}^{\&prime;\&prime;}+i_{13}^{\&prime;\&prime;}\\ i_2^{\&prime;\&prime;}=i_{21}^{\&prime;\&prime;}+i_{22}^{\&prime;\&prime;}+i_{23}^{\&prime;\&prime;}\end{array}---\left(10\right)$

And meet following condition:

$\begin{array}{c}{H}_{11}{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">l</figure-callout>}}_1=N_1{i}_{11}^{\&prime;\&prime;}\\ H_{12}{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">l</figure-callout>}}_2=N_1{i}_{12}^{\&prime;\&prime;}\\ H_{13}{l}_3=N_1{i}_{13}^{\&prime;\&prime;}\\ H_{21}{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">l</figure-callout>}}_1=N_2{i}_{21}^{\&prime;\&prime;}\\ H_{22}{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">l</figure-callout>}}_2=N_2{i}_{22}^{\&prime;\&prime;}\\ H_{23}{l}_3=N_2{i}_{23}^{\&prime;\&prime;}\end{array}---\left(11\right)$

Like this, each iron core is broken down into three parts: exchange post, direct current post and yoke.The equivalent circuit of equivalent field excitation branch line 1 and equivalent field excitation branch line 2 is respectively as shown in Fig. 5 a and Fig. 5 b.From circuit, equivalent field excitation branch line 1 and equivalent field excitation branch line 2 form by three field excitation branch lines in parallel.Described three field excitation branch lines in parallel are corresponding direct current post field excitation branch line, interchange post field excitation branch line and yoke field excitation branch line respectively.

Be more than to take the magnetic circuit that magnet controlled fault current limiter is two independent magnetic circuit structures to decompose, the magnetic circuit of introducing magnet controlled fault current limiter below and be three pillar type structure decomposes.

Magnet controlled fault current limiter is three pillar type structure, and each physical quantity and positive dirction as shown in Figure 6, according to the positive dirction shown in Fig. 6, have following winding voltage equation:

$\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="u"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">u</figure-callout>}}_1=r_1{\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">i</figure-callout>}}_1+N_1(\frac{{\mathrm{d\&Phi;}}_1}{\mathrm{dt}}+\frac{{\mathrm{d\&Phi;}}_{\mathrm{<figure-callout\; id="1"\; label="k"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">k</figure-callout>}1}}{\mathrm{dt}})\\ {\mathrm{<figure-callout\; id="2"\; label="u"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">u</figure-callout>}}_2=r_2{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">i</figure-callout>}}_2+N_2(\frac{{\mathrm{d\&Phi;}}_2}{\mathrm{dt}}+\frac{{\mathrm{d\&Phi;}}_{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">k</figure-callout>}2}}{\mathrm{dt}})\\ u_3=r_3{i}_3+N_3(\frac{{\mathrm{d\&Phi;}}_3}{\mathrm{dt}}+\frac{{\mathrm{d\&Phi;}}_{k3}}{\mathrm{dt}})\end{array}---\left(12\right)$

And have:

i ₁=i ₂

（13）

Φ ₃=Φ ₁-Φ ₂

Kirchhoff's second law according to magnetic circuit, has

H ₁₁l ₁+H ₁₂l ₂+H ₃l ₃=N ₁i ₁+N ₃i ₃

（14）

H ₂₁l ₁+H ₂₂l ₂-H ₃l ₃=N ₂i ₂-N ₃i ₃

Wherein, H ₁₁and H ₂₁be respectively the magnetic field intensity in AC core limb in the first magnetic circuit and the second magnetic circuit, H ₃for the magnetic field intensity in DC side core limb, and H ₁₂and H ₂₂be respectively the magnetic field intensity of yoke part in the first magnetic circuit and the second magnetic circuit; l ₁, l ₂, l ₃be respectively the centerline length that exchanges post, yoke, direct current post.N ₁the number of turn of the first interchange winding, N ₂the number of turn of the second interchange winding, N ₃it is the number of turn of direct current winding; Φ ₁that the first magnetic circuit exchanges the main flux in post and yoke, Φ ₂that the second magnetic circuit exchanges the main flux in post and yoke; Φ ₂it is the main flux in direct current post; Φ _k1the leakage flux of the first interchange winding, Φ _k2it is the leakage flux of the second interchange winding; i ₃it is the electric current in DC excitation winding.

By formula (14), can be obtained:

H ₁₁l ₁+H ₁₂l ₂=N ₁i ₁+(N ₃i ₃-H ₃l ₃)

（15）

H ₂₁l ₁+H ₂₂l ₂=N ₂i ₂-(N ₃i ₃-H ₃l ₃)

Magnetic circuit is decomposed:

$\begin{array}{c}{i}_1={\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">i</figure-callout>}}_1^{\&prime;}+{\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">i</figure-callout>}}_1^{\&prime;\&prime;}\\ i_2={\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">i</figure-callout>}}_2^{\&prime;}+{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">i</figure-callout>}}_2^{\&prime;\&prime;}\\ i_3=i_3^{\&prime;}+i_3^{\&prime;\&prime;}\end{array}---\left(16\right)$

And meet following constraint condition:

$\begin{array}{c}{H}_3{l}_3=N_3{i}_3^{\&prime;\&prime;}\\ N_1{\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">i</figure-callout>}}_1^{\&prime;}+N_3{i}_3^{\&prime;}=0\\ N_2{\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">i</figure-callout>}}_1^{\&prime;}-N_3{i}_3^{\&prime;}=0\end{array}----\left(17\right)$

Can obtain the magnetic potential drop expression formula of all the other magnetic circuits:

$\begin{array}{c}{H}_{11}{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">l</figure-callout>}}_1+H_{12}{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">l</figure-callout>}}_2=N_1{\mathrm{<figure-callout\; id="1"\; label="i"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">i</figure-callout>}}_1^{\&prime;\&prime;}\\ H_{21}{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">l</figure-callout>}}_1+H_{22}{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">l</figure-callout>}}_2=N_2{\mathrm{<figure-callout\; id="2"\; label="i"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">i</figure-callout>}}_2^{\&prime;\&prime;}\end{array}---\left(18\right)$

According to above-mentioned winding voltage equation, can obtain the equivalent circuit of this restrictor, as shown in Figure 7.

Wherein, " equivalent field excitation branch line 1' " refers to excitation property corresponding to magnetic circuit that left side core limb (having the first interchange winding on it) and upper magnet yoke, lower yoke form, and " equivalent field excitation branch line 2' " represents excitation property corresponding to magnetic circuit that right side core limb (having the second interchange winding on it) and upper magnet yoke, lower yoke form; " equivalent field excitation branch line 3 " represents the excitation property corresponding to magnetic circuit of middle core limb (having direct current winding on it).

Under the inhomogeneous condition of each section of sectional area of magnetic circuit, also can, on the basis of formula (18), magnetic circuit be decomposed.Order

$\begin{array}{c}{i}_1^{\&prime;\&prime;}=i_{11}^{\&prime;\&prime;}+i_{12}^{\&prime;\&prime;}\\ i_2^{\&prime;\&prime;}=i_{21}^{\&prime;\&prime;}+i_{22}^{\&prime;\&prime;}\end{array}---\left(19\right)$

And meet following condition:

$\begin{array}{c}{H}_{11}{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">l</figure-callout>}}_1=N_1{i}_{11}^{\&prime;\&prime;}\\ H_{12}{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">l</figure-callout>}}_2=N_1{i}_{12}^{\&prime;\&prime;}\\ H_{21}{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">l</figure-callout>}}_1=N_2{i}_{21}^{\&prime;\&prime;}\\ H_{22}{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA0000422721110000022.png"\; state="\{\{state\}\}">l</figure-callout>}}_2=N_2{i}_{22}^{\&prime;\&prime;}\end{array}---\left(20\right)$

Like this, equivalent field excitation branch line 1 ' with equivalent field excitation branch line 2 ' be all broken down into two parts: exchange post field excitation branch line and yoke field excitation branch line.From circuit, be two field excitation branch lines in parallel.Equivalent field excitation branch line 1 ', 2 ' and 3 equivalent magnetic circuit respectively as shown in Fig. 8 a-8c.

From circuit, equivalent field excitation branch line 1 ' and 2 ' by two field excitation branch lines in parallel, forming, correspondence exchanges post field excitation branch line and yoke field excitation branch line respectively.

Certain core material take below as example, introduce ψ-i curve of segmentation magnetic circuit;

ψ-i curvilinear function that can be obtained each section of magnetic circuit by formula (2) and formula (3) is as follows:

$\mathrm{\&psi;}=\frac{{\mathrm{\&mu;}}_0{N}^{2}A}{l}i-0.6299\&CenterDot;\mathrm{NA}\&CenterDot;\mathrm{arsh}\left(0.0280\frac{N}{l}i\right)+0.6925\&CenterDot;\mathrm{NA}\&CenterDot;\mathrm{arsh}\left(0.280\frac{N}{l}i\right)---\left(21\right)$

According to the length of the sectional area of each section of magnetic circuit and center line, can obtain reduction to ψ-i curve of AC winding or DC side winding.

The iron core of magnet controlled fault current limiter of take below adopt two-way independently structure be introduced as example.

The reduction of take is introduced to direct current winding side as example:

Its number of turn N=868; The sectional area that exchanges post, yoke, direct current post is respectively 0.43m ², 0.77m ², 0.86m ², its centerline length is respectively 2.94m, 5.82m, 2.94m.

According to formula (21), can obtain:

ψ-i the curve that exchanges post can be expressed as:

ψ=0.1385i-235.1arsh(8.267i)+258.5arsh(82.67i) （22）

In like manner, ψ-i curve of yoke can be expressed as:

ψ=0.1253i-421.0arsh(4.176i)+462.8arsh(41.76i) （23）

ψ-i curve of direct current post can be expressed as:

ψ=0.2769i-470.2arsh(8.267i)+516.9arsh(82.67i) （24）

Field excitation branch line is carried out to equivalence: by add certain voltage on three shunt excitation branch roads, solve respectively the branch current on each field excitation branch line, three current summations can be obtained to total current; By branch current, by ψ-i curve, can obtain corresponding magnetic linkage value.

The iron core of magnet controlled fault current limiter of take adopt two-way independently structure be example, the ψ-i characteristic after equivalence is as shown in table 2, corresponding curve as shown in Figure 9.

For comparison curves characteristic, in the embodiment of the present invention, provided the ψ-i characteristic that exchanges post, yoke and direct current post.Can find out, the ψ-i curve after equivalence is more approaching with the ψ-i curve that exchanges post.Because it is minimum to exchange the sectional area of post.When magnetic flux one timing, the degree of saturation that exchanges post is higher, therefore exciting current Main Current is crossed the corresponding field excitation branch line of interchange post.Obviously, the magnetic circuit situation of interchange post winding plays conclusive effect to iron core excitation characteristic.

The above embodiment of the present invention carries out segmentation by unequal section iron core, has proposed the matching of multistage iron core excitation characteristic and equivalent method, thereby obtains the excitation property of whole unequal section iron core.

The method of the excitation property of the acquisition unequal section iron core providing based on above embodiment, the present invention also provides a kind of device that obtains the excitation property of unequal section iron core, below in conjunction with accompanying drawing, introduces in detail its principle of work,

Device embodiment mono-:

Referring to Figure 10, this figure is device embodiment mono-schematic diagram of acquisition unequal section iron core excitation characteristic provided by the invention.

The embodiment of the present invention provides a kind of device that obtains unequal section iron core excitation characteristic, comprising: fitting function acquiring unit 1001, magnetic circuit resolving cell 1002, segmentation magnetic circuit ψ-i curve acquisition unit 1003 and unequal section ψ-i curve acquisition unshakable in one's determination unit 1004;

Described fitting function acquiring unit 1001, for the fitting function of the BH curve of matching unequal section core material; B is magnetic induction density, and H is magnetic field intensity;

When iron core reach the degree of depth saturated after, owing to there is no rotating magnetic domain, its unit permeance is close to air.Therefore, the limit slope of the core material BH curve degree of depth after saturated is knownly (to equal air permeability μ ₀=4 π * 10 ^-7h/m).

Fitting function can be divided into two parts: linear term and saturated item.The slope of linear term equals air permeability μ ₀.The fitting function of saturated can have multiple, as asinh function, arctan function, ambipolar S compression function etc.Wherein ambipolar S compression function is usually used in error back propagation (BP, Error Back Propagation) algorithm.

Described magnetic circuit resolving cell 1002, for obtaining the equivalent circuit of unequal section iron core, the equivalent field excitation branch line in described equivalent circuit is in parallel by a plurality of field excitation branch lines; The corresponding one section of magnetic circuit of field excitation branch line described in each;

For prismatic iron core, by BH curve, can obtain ψ-i curve.The number of turn of supposing coil is N, and average cross-section is A, and the length of center line is l, has following relation:

$\left\{\begin{array}{c}\mathrm{\&psi;}=\mathrm{N\&Phi;}\\ \mathrm{\&Phi;}=\mathrm{BA}\\ H\&CenterDot;l=N\&CenterDot;i\end{array}\right.---\left(1\right)$

By formula (1), can obtain formula (2):

$\left\{\begin{array}{c}\text{\&psi;=NA\&CenterDot;B}\\ i=l/N\&CenterDot;H\end{array}\right.---\left(2\right)$

By formula (1), BH curve can be converted into Ψ-i curve.

But for the iron core of unequal section, first need iron core to be divided into some sections.

By formula (1) and (2), can only obtain Ψ-i curve of every section of magnetic circuit.

By the excitation property of each section of magnetic circuit, how to obtain the excitation property of whole unequal section iron core, be key point.

Described segmentation magnetic circuit ψ-i curve acquisition unit 1003, for utilizing the fitting function of described BH curve to obtain respectively ψ-i curve of field excitation branch line described in each; ψ is magnetic linkage, and i is electric current;

Utilize the fitting function of BH curve and the relation of formula (1) and (2) can obtain ψ-i curve of segmentation magnetic circuit.

Described unequal section ψ-i curve acquisition unshakable in one's determination unit 1004, for ψ-i curve of the ψ-i curve acquisition unequal section iron core by all described field excitation branch lines.

The iron core of different structure, can adopt the nonlinear field excitation branch line of several parallel connections to represent conventionally.Yet, when employing electromagnetic transient state procedure (EMTP) etc. carries out simulation calculation, if directly a plurality of nonlinear field excitation branch lines are carried out to parallel connection, may produce some problems.For this reason, suggestion is by a plurality of non-linear exciter branch roads of parallel connection equivalent merging in addition.

The device that the present embodiment provides, carries out magnetic circuit decomposition to the iron core of unequal section, obtains the equivalent circuit of unequal section iron core, and the equivalent field excitation branch line in described equivalent circuit is in parallel by a plurality of field excitation branch lines; The corresponding one section of magnetic circuit of field excitation branch line described in each; Utilize like this fitting function of BH curve of the unequal section core material of matching, obtain ψ-i curve of each field excitation branch line; By ψ-i curve of each field excitation branch line, obtained ψ-i curve of whole unequal section iron core, ψ-i curve can represent excitation property unshakable in one's determination again.Method provided by the invention is carried out magnetic circuit decomposition by the iron core of unequal section, is decomposed into a plurality of field excitation branch lines and carries out parallel connection, thereby obtain the excitation property of every section, and then by the excitation property equivalence of every section, gone out the excitation property of whole unequal section iron core.

Saturated in the fitting function that the present embodiment provides preferably adopts asinh function.

Consider the problem of fitting precision, saturated in the fitting function in the present invention adopts a plurality of asinh functions.

B=μ ₀H-0.6299arsh(0.0280H)+0.6925arsh(0.280H) （3）

Introduce ψ-i curve of segmentation equivalent magnetic circuit below;

ψ-i curvilinear function that can be obtained each section of magnetic circuit by formula (2) and formula (3) is as follows:

$\mathrm{\&psi;}=\frac{{\mathrm{\&mu;}}_0{N}^{2}A}{l}i-0.6299\&CenterDot;\mathrm{NA}\&CenterDot;\mathrm{arsh}\left(0.0280\frac{N}{l}i\right)+0.6925\&CenterDot;\mathrm{NA}\&CenterDot;\mathrm{arsh}\left(0.280\frac{N}{l}i\right)---\left(21\right)$

According to the length of the sectional area of each section of magnetic circuit and center line, can obtain reduction to ψ-i curve of AC winding or DC side winding.

When described unequal section iron core is magnet controlled fault current limiter, and magnet controlled fault current limiter adopts two independently magnetic circuits; The corresponding equivalent field excitation branch line of each magnetic circuit, this field excitation branch line is decomposed into three field excitation branch lines and carries out parallel connection, and described three field excitation branch lines are corresponding direct current post magnetic circuit, interchange post magnetic circuit and yoke magnetic circuit respectively.

When described unequal section iron core is magnet controlled fault current limiter, and magnet controlled fault current limiter adopts three pillar type magnetic circuit; Three pillar type magnetic circuit is decomposed into three equivalent field excitation branch lines, and wherein two equivalent field excitation branch lines are for exchanging field excitation branch line and field excitation branch line parallel connection corresponding to yoke that post is corresponding, and another equivalent field excitation branch line is the field excitation branch line that direct current post is corresponding.

Magnet controlled fault current limiter has structure and two kinds of typical types of three pillar type structure of two independent magnetic circuits, in embodiment of the method, specifically introduced and how for these two types, to have carried out magnetic circuit decomposition, in device embodiment, no longer specifically introduce, can reference method embodiment content partly.

The above, be only preferred embodiment of the present invention, not the present invention done to any pro forma restriction.Although the present invention discloses as above with preferred embodiment, yet not in order to limit the present invention.Any those of ordinary skill in the art, do not departing from technical solution of the present invention scope situation, all can utilize method and the technology contents of above-mentioned announcement to make many possible changes and modification to technical solution of the present invention, or be revised as the equivalent embodiment of equivalent variations.Therefore, every content that does not depart from technical solution of the present invention,, all still belongs in the scope of technical solution of the present invention protection any simple modification made for any of the above embodiments, equivalent variations and modification according to technical spirit of the present invention.

Claims (9)

1. a method that obtains unequal section iron core excitation characteristic, is characterized in that, comprising:

The fitting function of the BH curve of matching unequal section core material; B is magnetic induction density, and H is magnetic field intensity;

The magnetic circuit of unequal section iron core is decomposed, obtain the equivalent circuit of unequal section iron core, the equivalent field excitation branch line in described equivalent circuit is in parallel by a plurality of field excitation branch lines; The corresponding one section of magnetic circuit of field excitation branch line described in each;

Utilize the fitting function of described BH curve to obtain respectively ψ-i curve of field excitation branch line described in each; ψ is magnetic linkage, and i is electric current;

By ψ-i curve of all described field excitation branch lines, obtained ψ-i curve of unequal section iron core.

2. the method for acquisition unequal section iron core excitation characteristic according to claim 1, is characterized in that, the fitting function of described BH curve comprises linear term and saturated item;

The slope of described linear term equals air permeability μ ₀, μ ₀=4 π * 10 ^-7h/m;

Described saturated adopts asinh function, arctan function or ambipolar S compression function.

3. the method for acquisition unequal section iron core excitation characteristic according to claim 1 and 2, is characterized in that, when described unequal section iron core is magnet controlled fault current limiter, and magnet controlled fault current limiter adopts two independently magnetic circuits; The corresponding equivalent field excitation branch line of magnetic circuit described in each, described in each, equivalent field excitation branch line is decomposed into three field excitation branch lines and carries out parallel connection, described three field excitation branch lines respectively corresponding direct current post field excitation branch line, exchange post field excitation branch line and yoke field excitation branch line.

4. the method for acquisition unequal section iron core excitation characteristic according to claim 1 and 2, is characterized in that, when described unequal section iron core is magnet controlled fault current limiter, and magnet controlled fault current limiter adopts three pillar type magnetic circuit; Corresponding three the equivalent field excitation branch lines of described three pillar type magnetic circuit, wherein two described equivalent field excitation branch lines carry out parallel connection for exchanging post field excitation branch line and yoke field excitation branch line, and described in another, equivalent field excitation branch line is direct current post field excitation branch line.

5. the method for acquisition unequal section iron core excitation characteristic according to claim 1, is characterized in that, the described fitting function that utilizes described BH curve obtains respectively ψ-i curve of field excitation branch line described in each, is specially:

By sectional area and the length of segmentation magnetic circuit, obtain reduction to ψ-i curve of AC winding or DC side winding.

6. a device that obtains unequal section iron core excitation characteristic, is characterized in that, comprising: fitting function acquiring unit, magnetic circuit resolving cell, segmentation magnetic circuit ψ-i curve acquisition unit and unequal section ψ-i curve acquisition unshakable in one's determination unit;

Described fitting function acquiring unit, for the fitting function of the BH curve of matching unequal section core material; B is magnetic induction density, and H is magnetic field intensity;

Described magnetic circuit resolving cell, for obtaining the equivalent circuit of unequal section iron core, the equivalent field excitation branch line in described equivalent circuit is in parallel by a plurality of field excitation branch lines; The corresponding one section of magnetic circuit of field excitation branch line described in each;

Described segmentation magnetic circuit ψ-i curve acquisition unit, for utilizing the fitting function of described BH curve to obtain respectively ψ-i curve of field excitation branch line described in each; ψ is magnetic linkage, and i is electric current;

Described unequal section ψ-i curve acquisition unshakable in one's determination unit, for ψ-i curve of the ψ-i curve acquisition unequal section iron core by all described field excitation branch lines.

7. the device of acquisition unequal section iron core excitation characteristic according to claim 6, is characterized in that, the fitting function of described BH curve comprises linear term and saturated item;

The slope of described linear term equals air permeability μ ₀, μ ₀=4 π * 10 ^-7h/m;

Described saturated adopts asinh function, arctan function or ambipolar S compression function.

8. according to the device of the acquisition unequal section iron core excitation characteristic described in claim 6 or 7, it is characterized in that, when described unequal section iron core is magnet controlled fault current limiter, and magnet controlled fault current limiter adopts two independently magnetic circuits, the corresponding equivalent field excitation branch line of magnetic circuit described in each; Described magnetic circuit resolving cell, is decomposed into three field excitation branch lines for equivalent field excitation branch line described in each and carries out parallel connection, and described three field excitation branch lines are corresponding direct current post field excitation branch line, interchange post field excitation branch line and yoke field excitation branch line respectively.

9. according to the device of the acquisition unequal section iron core excitation characteristic described in claim 6 or 7, it is characterized in that,

When described unequal section iron core is magnet controlled fault current limiter, and magnet controlled fault current limiter adopts three pillar type magnetic circuit; Described magnetic circuit resolving cell, be used for corresponding three the equivalent field excitation branch lines of described three pillar type magnetic circuit, wherein two described equivalent field excitation branch lines carry out parallel connection for exchanging post field excitation branch line and yoke field excitation branch line, and described in another, equivalent field excitation branch line is direct current post field excitation branch line.

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