CN102680856A - Method for measuring zero sequence current of power transmission line based on magnetic sensor array - Google Patents

Abstract

The invention relates to a method for measuring zero sequence current of a power transmission line based on a magnetic sensor array. The method comprises the following steps of: (1) placing the magnetic sensor array below an overhead transmission line to acquire output signals of the magnetic sensor array; (2) transmitting the output signals to a data processor sequentially through a filter circuit and an amplification circuit; and (3) processing the received signals by the data processor to obtain magnetic flux density information of a current-carrying conductor, and obtaining the zero sequence current of the current-carrying conductor by analyzing the characteristics of the magnetic flux density. Compared with the prior art, the method for measuring the zero sequence current of the power transmission line based on the magnetic sensor array, disclosed by the invention, has the advantages of simpleness, low cost, low loss and the like.

Description

Measuring method based on the transmission line of electricity zero-sequence current of array of magnetic sensors

Technical field

The present invention relates to a kind of measuring method of transmission line of electricity zero-sequence current, especially relate to a kind of measuring method of the transmission line of electricity zero-sequence current based on array of magnetic sensors.

Background technology

Zero-sequence current information in the overhead distribution is for getting rid of as the center line broken string, and the earth fault that imperfect earth etc. are relevant is very important.Because zero-sequence current protection has structure and principle of work is simple, performance factor is high; Under the condition of zero-sequence network basicly stable (number and the position that are neutral grounded transformer are constant basically), protection domain is more stable, and the characteristic of continuous action is arranged; Capable of carrying out quick action to close-in fault; Receive the influence of the excessive resistance of fault less; The protection definite value does not receive the influence of load current, does not receive the characteristics such as influence of other isolated neutral short circuit malfunction basically, and zero-sequence current protection is applied in small current neutral grounding system or the heavy current grounding system widely.Zero-sequence current is applied in the transformer Zero sequence current differential protection, the sensitivity in the time of can improving transformer inside single-phase fault greatly.

Traditional zero sequence current measurement is through realizing with the similar zero sequence current mutual inductor of common current mutual inductor (CTs).In the zero sequence current measurement of overhead transmission line, generally all be to adopt three current transformers to be connected into the zero-sequence current pass filter, therefore traditional zero sequence current mutual inductor has traditional shortcoming that current transformer had, and is saturated like mutual inductor; Measurement range is narrow; Ferromagnetic resonance, hysteresis effect; Accuracy of measurement is low; There is potential danger.Electromagnetic current transducer first and second between lean on the electromagnetism transform principle to realize energy delivery, therefore always exist electromagnetic connection between first and second.If open circuit has appearred in second siding ring for a certain reason, the big electric current of primary side becomes exciting current fully, will induce high voltage in the secondary coil side, jeopardizes the safety of the person, equipment; Equipment is installed, maintenance is inconvenient, and maintenance workload is big, wiring complicacy during installation, easy error.Therefore, a kind of novel ZSC measuring technique with actual application value is necessary.

Summary of the invention

The object of the invention is exactly the measuring method that a kind of transmission line of electricity zero-sequence current based on array of magnetic sensors is provided in order to overcome the defective that above-mentioned prior art exists.

The object of the invention can be realized through following technical scheme:

A kind of measuring method of the transmission line of electricity zero-sequence current based on array of magnetic sensors is characterized in that, may further comprise the steps:

1) array of magnetic sensors is placed the below of overhead transmission line, gather the current carrying conductor signal;

2) with signal successively through being transferred to data acquisition equipment behind RC filtering circuit and the three rank amplifying circuits;

3) data acquisition equipment is handled to the received signal, obtains the magnetic flux density information of current carrying conductor, and obtains the zero-sequence current of current carrying conductor through the linear feature of analyzing this magnetic flux density.

If transmission line of electricity is the phase three-wire three overhead transmission line, described array of magnetic sensors is that two Magnetic Sensors are formed array of magnetic sensors.

The calculating of zero-sequence current is specific as follows:

1) two Magnetic Sensor S ₁And S ₂Magnetic flux be respectively B ₁And B ₂, B ₁, B ₂In space coordinates, be decomposed into x, y, three components of z are respectively as follows

$\left\{\begin{array}{c}{B}_{1x}=0\\ B_{1y}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\&CenterDot;(\frac{I_a}{l_1}\&CenterDot;\cos {\mathrm{\&theta;}}_1^2+\frac{I_b}{l_1+{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">l</figure-callout>}}_2}+\frac{I_c}{l_1}\&CenterDot;\cos {\mathrm{\&theta;}}_1^2)\\ B_{1z}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\&CenterDot;(\frac{I_a}{l_1}\&CenterDot;\sin {\mathrm{\&theta;}}_1\&CenterDot;\cos {\mathrm{\&theta;}}_1+\frac{I_c}{l_1}\&CenterDot;\sin {\mathrm{\&theta;}}_1\&CenterDot;\cos {\mathrm{\&theta;}}_1)\end{array}\right.---\left(a1\right)$

$\left\{\begin{array}{c}{B}_{2x}=0\\ B_{2y}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\&CenterDot;(\frac{I_a}{l_1+d}\&CenterDot;\cos {\mathrm{\&theta;}}_2^2+\frac{I_b}{l_1+{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">l</figure-callout>}}_2+d}+\frac{I_c}{l_1+d}\&CenterDot;\cos {\mathrm{\&theta;}}_2^2)\\ B_{2z}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\&CenterDot;(\frac{I_a}{l_1+d}\&CenterDot;\sin {\mathrm{\&theta;}}_1\&CenterDot;\cos {\mathrm{\&theta;}}_1+\frac{I_c}{l_1+d}\&CenterDot;\sin {\mathrm{\&theta;}}_1\&CenterDot;\cos {\mathrm{\&theta;}}_1)\end{array}\right.---\left(a2\right)$

I in last two formulas _a, I _b, I _cBe respectively three-phase current, μ ₀Be air permeability, w is the horizontal range between a phase and the b phase, and d is Magnetic Sensor S ₁And the vertical range between the S2, l ₁Be Magnetic Sensor S ₁With the vertical range of c between mutually, l ₂Be the vertical range between b phase and the c phase, θ ₁Be a phase and S ₁Between line and b mutually and S ₁Between the angle of line, θ ₂Be a phase and S ₂Between line and b mutually and S ₂Between the angle of line;

2) suppose that distance between line of electric force and the magnetic field sensor is greater than the distance between the line of electric force, i.e. l ₁＞＞l ₂, then the magnetic field effect of three line of electric force can be by the equivalent current I that is positioned at the sensor top _vExpression, wherein, I _vAnd S ₁Between the distance be h _v, I _vAt measurement point S ₁, S ₂The place produces the x of magnetic flux density, y, and z axle component is suc as formula (a3) and (a4) expression.

$\left\{\begin{array}{c}{B}_{1\mathrm{vx}}=0\\ B_{1\mathrm{vy}}=\frac{{\mathrm{\&mu;}}_0\&CenterDot;I_v}{2\mathrm{\&pi;}{h}_v}\\ B_{1\mathrm{vz}}=0\end{array}\right.---\left(a3\right)$

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">B</figure-callout>}}_{2\mathrm{vx}}=0\\ {\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">B</figure-callout>}}_{2\mathrm{vy}}=\frac{{\mathrm{\&mu;}}_0\&CenterDot;I_v}{2\mathrm{\&pi;}(h_v+d)}\\ {\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">B</figure-callout>}}_{2\mathrm{vz}}=0\end{array}\right.---\left(a4\right)$

Can know by (a3), (a4) formula, by I _vThe magnetic flux density that produces only comprises y axle component, in zero sequence current measurement, can assert virtual current I _vWith I _a, I _b, I _cAt S ₁, S ₂The y axle component that the place produces magnetic flux density is identical, i.e. B _1y=B _1vy, B _2y=B _2vy, the y axle component in (a1), (a2) formula is substituted into (a3), (a4) formula, can obtain I _vWith I _a, I _b, I _cBetween relational expression (a5);

Suppose l ₁＞＞l ₂, in addition, because l ₁＞＞w and l ₁+ d＞＞w, then cos θ ₁≈ cos θ ₂Therefore, virtual current I _vCan be reduced to (a6) formula;

I _v＝f(I _a，I _b，I _c)＝(I _a+I _b+I _c)＝3I ₀ (a6)

(a6) formula shows, as long as obtain virtual current I _vJust can try to achieve zero-sequence current I ₀, virtual current I _vCan be calculated by (a7) formula, (a7) formula draws on the basis of formula (a3), (a4), wherein B _1vyAnd B _2vyCan pass through magnetic field sensor S respectively ₁, S ₂Measurement is come out,

$I_v=\frac{2\mathrm{\&pi;d}\&CenterDot;B_{1\mathrm{vy}}\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">B</figure-callout>}}_{2\mathrm{vy}}}{{\mathrm{\&mu;}}_0(B_{1\mathrm{vy}}-{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">B</figure-callout>}}_{2\mathrm{vy}})}---\left(a7\right)$

。

If transmission line of electricity is the three-phase and four-line overhead transmission line, described array of magnetic sensors is formed array of magnetic sensors for two or three Magnetic Sensors.

If adopt two Magnetic Sensors, the calculating of zero-sequence current is following:

Article four, line of electric force is equivalently represented by a virtual wires, and equivalent current can be represented as follows:

I _v＝I _a+I _b+I _c+I _n＝3I ₀+I _n＝I _r (a8)

Wherein, I _vBe virtual current, I _a, I _b, I _cBe respectively three-phase current, I ₀Be zero-sequence current, I _nBe current in middle wire, I _rBe aftercurrent;

I _vOr I _rBy magnetic field sensor S ₁, S ₂The magnetic flux density that records is calculated, B ₁, B ₂Y axle component be shown below:

$\left\{\begin{array}{c}{B}_{1y}=\frac{{\mathrm{\&mu;}}_0{\mathrm{<figure-callout\; id="2"\; label="I\; a"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">I</figure-callout>}}_a}{2\mathrm{\&pi;}{l}_1}{\left(\cos {\mathrm{\&theta;}}_1\right)}^2+\frac{{\mathrm{\&mu;}}_0{\mathrm{<figure-callout\; id="2"\; label="I\; b"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">I</figure-callout>}}_b}{2\mathrm{\&pi;}(l_1+l_2)}+\frac{{\mathrm{\&mu;}}_0{\mathrm{<figure-callout\; id="2"\; label="I\; c"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">I</figure-callout>}}_c}{2\mathrm{\&pi;}{l}_1}{\left(\cos {\mathrm{\&theta;}}_1\right)}^2+\frac{{\mathrm{\&mu;}}_0{I}_{\mathrm{<figure-callout\; id="2"\; label="n"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">n</figure-callout>}}}{2\mathrm{\&pi;}{l}_3}\\ B_{2y}=\frac{{\mathrm{\&mu;}}_0{I}_a}{2\mathrm{\&pi;}(l_1+d)}{\left(\cos {\mathrm{\&theta;}}_2\right)}^2+\frac{{\mathrm{\&mu;}}_0{\mathrm{<figure-callout\; id="2"\; label="I\; b"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">I</figure-callout>}}_b}{2\mathrm{\&pi;}(l_1+{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">l</figure-callout>}}_2+d)}\\ +\frac{{\mathrm{\&mu;}}_0{\mathrm{<figure-callout\; id="2"\; label="I\; c"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">I</figure-callout>}}_c}{2\mathrm{\&pi;}(l_1+d)}{\left(\cos {\mathrm{\&theta;}}_2\right)}^2+\frac{{\mathrm{\&mu;}}_0{\mathrm{<figure-callout\; id="2"\; label="I\; n"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">I</figure-callout>}}_n}{2\mathrm{\&pi;}({\mathrm{<figure-callout\; id="3"\; label="I"\; filenames="HDA00001647097700022.png,HDA00001647097700053.png"\; state="\{\{state\}\}">I</figure-callout>}}_3+d)}\end{array}\right.---\left(a9\right)$

Following formula, wherein μ ₀Be air permeability, w is the horizontal range between a phase and the b phase, and d is Magnetic Sensor S ₁And S ₂Between vertical range, l ₁Be Magnetic Sensor S ₁With the vertical range of c between mutually, l ₂Be the vertical range between b phase and the c phase, l ₃Be Magnetic Sensor S ₁With the vertical range of n between mutually, θ ₁Be a phase and S ₁Between line and b mutually and S ₁Between the angle of line, θ ₂Be a phase and S ₂Between line and b mutually and S ₂Between the angle of line;

I _vUtilize equality (a7) to calculate,, utilize the pairing I of each line construction again according to equality (a8) _n/ I ₀Ratio can calculate zero-sequence current.

If adopt three Magnetic Sensors, the calculating of zero-sequence current is following:

See three-phase power line as a virtual wires, center line is positioned at virtual wires below, three magnetic field sensor S ₁, S ₂, S ₃Vertically be positioned at the below of B phase conductor, see three-phase power line as a virtual wires, center line is positioned at the virtual wires below, and equivalent current can be represented as follows:

I _v＝I _a+I _b+I _c＝3I ₀+I _n (a10)

S ₁, S ₂, S ₃The magnetic flux density at place is by formula (a11) expression, I _vWith B _1vy, B _2vy, B _3vyBetween relation suc as formula shown in (a12);

$\left\{\begin{array}{c}{B}_{1y}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\&CenterDot;(\frac{I_1}{l_1}\&CenterDot;\cos {\mathrm{\&theta;}}_1^2+\frac{I_2}{l_1+{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">l</figure-callout>}}_2}+\frac{I_3}{l_1}\&CenterDot;\cos {\mathrm{\&theta;}}_1^2+\frac{I_n}{l_3})\\ B_{2y}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\&CenterDot;(\frac{I_1}{l_1+d_1}\&CenterDot;\cos {\mathrm{\&theta;}}_2^2+\frac{I_2}{l_1+{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">l</figure-callout>}}_2+d_1}\\ +\frac{I_3}{l_1+d_1}\&CenterDot;\cos {\mathrm{\&theta;}}_2^2+\frac{{\mathrm{<figure-callout\; id="3"\; label="I\; n\; l"\; filenames="HDA00001647097700022.png,HDA00001647097700053.png"\; state="\{\{state\}\}">I</figure-callout>}}_n}{l_{}})\\ B_{3y}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\&CenterDot;(\frac{I_1}{l_1+d_1+{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}\&CenterDot;\cos {\mathrm{\&theta;}}_3^2+\frac{I_2}{l_1+{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">l</figure-callout>}}_2+d_1+{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}\\ +\frac{I_3}{l_1+d_1+{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}\&CenterDot;\cos {\mathrm{\&theta;}}_3^2+\frac{{\mathrm{<figure-callout\; id="3"\; label="I\; n\; l"\; filenames="HDA00001647097700022.png,HDA00001647097700053.png"\; state="\{\{state\}\}">I</figure-callout>}}_n}{l_{}})\end{array}\right.---\left(a11\right)$

$\left\{\begin{array}{c}{B}_{1\mathrm{vy}}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}[\frac{1}{h_v}{I}_v+\frac{1}{l_3}{I}_w]\\ {\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">B</figure-callout>}}_{2\mathrm{vy}}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}[\frac{1}{(h_v+d_1)}{I}_v+\frac{1}{({\mathrm{<figure-callout\; id="3"\; label="l"\; filenames="HDA00001647097700022.png,HDA00001647097700053.png"\; state="\{\{state\}\}">l</figure-callout>}}_3+d_1)}{I}_n]\\ {\mathrm{<figure-callout\; id="3"\; label="B"\; filenames="HDA00001647097700022.png,HDA00001647097700053.png"\; state="\{\{state\}\}">B</figure-callout>}}_{3\mathrm{vy}}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}[\frac{1}{(h_v+d_1+d_2)}{I}_v+\frac{1}{({\mathrm{<figure-callout\; id="3"\; label="l"\; filenames="HDA00001647097700022.png,HDA00001647097700053.png"\; state="\{\{state\}\}">l</figure-callout>}}_3+d_1+d_2)}{I}_n]\end{array}\right.---\left(a12\right)$

B _1y, B _2y, B _3yMeasure by magnetic field sensor, in zero sequence current measurement, can assert virtual current I _v, I _nWith I _a, I _b, I _c, I _nAt S ₁, S ₂, S ₃The y axle component that the place produces magnetic flux density is identical, i.e. B _1y=B _1vy, B _2y=B _2vy, B _3y=B _3vy, the variable I in the formula (a12) _v, h _v, I _nBe unknown, can obtain that final, (a10) solves zero-sequence current according to equality through finding the solution formula (a12).

Compared with prior art, the present invention has simply, cost is low, loss is low; Can avoid the conventional current mutual inductor saturated, measurement range is narrow and ferromagnetic resonance magnetic, residual effect should wait shortcoming; The on-the-spot use need not the contact electrification circuit, need not to constitute the zero-sequence current pass filter by the polarity wiring, do not have the danger that causes as conventional current mutual inductor secondary coil open circuit, and be safe.

Description of drawings

Fig. 1 is that phase three-wire three formula aerial condutor distribution plan and the ZSC in the distribution system measures isoboles, and wherein (a) is distribution plan, (b) is isoboles;

Fig. 2 is B _z, B _yWith l ₁Relation curve (w=1.5m, l ₂=0.36m, d=1.0m, I _a=I _b=I _c=200A);

Fig. 3 is B _z, B _yWith l ₁Relation curve (w=1.5m, l ₂=0.36m, d=1.0m, I _a=220A, I _b=200A, I _c=170A);

Fig. 4 is comparative result (w=1.5m, d=1.0m, the I between zero-sequence current estimated value and the actual value in the three-phase three wire system _a=220A, I _b=200A, I _c=190A);

Fig. 5 is comparative result (w=1.5m, the l between zero-sequence current estimated value and the actual value in the three-phase three wire system ₁=9m, I _a=240A, I _b=220A, I _c=190A);

Fig. 6 is the comparative result (three-phase current produces at random) between zero-sequence current estimated value in the three-phase three wire system and the actual value;

Fig. 7 is that the ZSC of three-phase and four-line formula aerial condutor distribution plan and two Magnetic Sensors in the distribution system measures isoboles, and wherein (a) is distribution plan, (b) is isoboles;

Fig. 8 is that the ZSC of three-phase and four-line formula aerial condutor distribution plan and three Magnetic Sensors in the distribution system measures isoboles, and wherein (a) is distribution plan, (b) is isoboles;

Fig. 9 is the comparative result (adopting two magnetic field sensors) between aftercurrent estimated value and the actual value in the three-phase four wire system;

Figure 10 is the comparative result (adopting three magnetic field sensors) between zero-sequence current estimated value and actual value in the three-phase four wire system;

Figure 11 is test platform schematic diagram (w=0.032m, l ₁=0.4m, l ₂=0m, l ₃=0.285m, d ₁=0.065m, d ₂=0.065m);

Figure 12 is the comparative result that sensor measurement zero-sequence current value and CTS measure the zero-sequence current value in the three-phase three wire system;

Figure 13 is the comparative result that sensor measurement zero-sequence current value and CTS measure the zero-sequence current value in the three-phase four wire system.

Embodiment

Below in conjunction with accompanying drawing and specific embodiment the present invention is elaborated.

Embodiment

For the phase three-wire three overhead power transmission line, the measuring principle and the simulating, verifying of its zero-sequence current are described below.Phase three-wire three formula pole line in the distribution system is as shown in Figure 1, and in Fig. 1, three-phase current is respectively I _a, I _b, I _c, magnetic field sensor S ₁, S ₂Vertically be positioned at the below of B phase conductor.The zero-sequence current of line of electric force is following:

$I_0=\frac{I_a+I_b+I_c}{3}---\left(1\right)$

Ignore the transfer current (near low frequency) in the Maxwell equation group, can prove that the magnetic field in the free space is linear with the total current of the overhead transmission line of flowing through.According to than Austria-savart law, magnetic field sensor position (S among Fig. 1 (a) ₁, S ₂) magnetic flux density (B that locates ₁, B ₂) can express through (2) and (3) formula.In (2), (3) formula system of equations, B1, B2 are decomposed into x in space coordinates, y, three components of z.

$\left\{\begin{array}{c}{B}_{1x}=0\\ B_{1y}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\&CenterDot;(\frac{I_a}{l_1}\&CenterDot;\cos {\mathrm{\&theta;}}_1^2+\frac{I_b}{l_1+{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">l</figure-callout>}}_2}+\frac{I_c}{l_1}\&CenterDot;\cos {\mathrm{\&theta;}}_1^2)\\ B_{1z}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\&CenterDot;(\frac{I_a}{l_1}\&CenterDot;\sin {\mathrm{\&theta;}}_1\&CenterDot;\cos {\mathrm{\&theta;}}_1+\frac{I_c}{l_1}\&CenterDot;\sin {\mathrm{\&theta;}}_1\&CenterDot;\cos {\mathrm{\&theta;}}_1)\end{array}\right.---\left(2\right)$

$\left\{\begin{array}{c}{B}_{2x}=0\\ B_{2y}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\&CenterDot;(\frac{I_a}{l_1+d}\&CenterDot;\cos {\mathrm{\&theta;}}_2^2+\frac{I_b}{l_1+{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">l</figure-callout>}}_2+d}+\frac{I_c}{l_1+d}\&CenterDot;\cos {\mathrm{\&theta;}}_2^2)\\ B_{2z}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\&CenterDot;(\frac{I_a}{l_1+d}\&CenterDot;\sin {\mathrm{\&theta;}}_1\&CenterDot;\cos {\mathrm{\&theta;}}_1+\frac{I_c}{l_1+d}\&CenterDot;\sin {\mathrm{\&theta;}}_1\&CenterDot;\cos {\mathrm{\&theta;}}_1)\end{array}\right.---\left(3\right)$

μ in the following formula ₀Be air permeability, w, d, l ₁, l ₂, θ ₁, θ ₂Implication with reference to Fig. 1 (a).Can know by (2), (3) formula, at S ₁, S ₂The x axle component of place's magnetic flux density is zero.

Suppose that distance between line of electric force and the magnetic field sensor is greater than the distance between the line of electric force, i.e. l ₁＞＞l ₂, then the magnetic field effect of three line of electric force can be by the equivalent current I that is positioned at the sensor top _vExpression.Be loaded with virtual current I _vEquivalent lead shown in Fig. 1 (b), wherein, I _vAnd S ₁Between the distance be h _vI _vAt measurement point S ₁, S ₂The place produces the x of magnetic flux density, y, and z axle component is represented suc as formula (4) and (5).

$\left\{\begin{array}{c}{B}_{1\mathrm{vx}}=0\\ B_{1\mathrm{vy}}=\frac{{\mathrm{\&mu;}}_0\&CenterDot;I_v}{2\mathrm{\&pi;}{h}_v}\\ B_{1\mathrm{vz}}=0\end{array}\right.---\left(4\right)$

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">B</figure-callout>}}_{2\mathrm{vx}}=0\\ {\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">B</figure-callout>}}_{2\mathrm{vy}}=\frac{{\mathrm{\&mu;}}_0\&CenterDot;I_v}{2\mathrm{\&pi;}(h_v+d)}\\ {\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">B</figure-callout>}}_{2\mathrm{vz}}=0\end{array}\right.---\left(5\right)$

Can know by (4), (5) formula, by I _vThe magnetic flux density that produces only comprises y axle component.In zero-sequence current ZSC measures, can think virtual current I _vWith I _a, I _b, I _cAt S ₁, S ₂The y axle component that the place produces magnetic flux density is identical, i.e. B _1y=B _1vy, B ₂=B _2vyTherefore, can the y axle component in (2), (3) formula be substituted into (4), (5) formula.So, can obtain I _vWith I _a, I _b, I _cBetween relational expression (6).

For fear of the expression formula (6) of complicacy, can do several rational supposition and simplify I _vExpression formula.We suppose l before ₁＞＞l ₂, in addition, because l ₁＞＞w and l ₁+ d＞＞w, then cos θ ₁≈ cos θ ₂Therefore, virtual current I _vCan be reduced to (7) formula.

I _v＝f(I _a，I _b，I _c)＝(I _a+I _b+I _c)＝3I ₀ (7)

(7) formula shows, as long as obtain virtual current I _vJust can be in the hope of zero-sequence current I ₀Virtual current I _vCan be calculated by (8) formula, (8) formula draws on the basis of formula (4), (5), wherein B _1vyAnd B _2vyCan pass through magnetic field sensor S respectively ₁, S ₂Measurement is come out.

$I_v=\frac{2\mathrm{\&pi;d}\&CenterDot;B_{1\mathrm{vy}}\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">B</figure-callout>}}_{2\mathrm{vy}}}{{\mathrm{\&mu;}}_0(B_{1\mathrm{vy}}-{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">B</figure-callout>}}_{2\mathrm{vy}})}---\left(8\right)$

Adopt virtual equivalent current I _vReplace three-phase current I _a, I _b, I _c, measure virtual current I _vThe y axle component of the magnetic flux density that produces calculates ZSC.

Verify the accuracy of the phase three-wire three overhead power transmission line ZSC measuring method that is proposed with following emulation case.

On the basis of formula (2)-(5), magnetic flux density y, the root-mean-square value (RMS) of z axle component with apart from l ₁Between relation shown in Fig. 2 and 3.Three-phase balance (I among Fig. 2 _a=I _b=I _c=200A), and three-phase current unbalance (I among Fig. 3 _a=220A, I _b=200A, I _c=170A).Usually the magnetic field intensity around the overhead distribution line very a little less than, so magnetic flux density generally to adopt mG be unit.

At l ₁＞＞l ₂Condition under, make h _v=l ₁B among Fig. 2 and Fig. 3 _1yAnd B _2ySolve by formula (2), (3), be exact value; B _1vy, B _2vySolve through (4), (5) formula, i.e. B _1vy, B _2vyBe estimated value.Fig. 2 shows, under the situation of three-phase balance, and l ₁During greater than 8m, approach zero.Simultaneously, in this case because I _a+ I _b+ I _c=0, zero-sequence current is zero, and can know that according to formula (6) virtual equivalent current is zero, so B _1vy, B _2vyAll equal zero.Therefore, suppose B _1y=B _1vy, B _2y=B _2vyBe rational.Fig. 3 shows, is satisfying l ₁Under the condition greater than 8m, this hypothesis is equally applicable to the situation of three-phase current unbalance.

Fig. 4 has shown at w=1.5m, d=1.0m, I _a=220A, I _b=200A, I _cUnder the condition of=190A, l ₁The comparative result of zero-sequence current estimated value and actual value when changing from 4 to 15m.Can find out, if l ₁Greater than 10m, zero-sequence current estimated value and actual value are very approaching, at l ₁Two difference between currents and l during=10m ₁Compare variation and little during=20m, i.e. l ₁Get the distance of 10m and just can enough estimate zero-sequence current exactly.

Shown in Figure 5 is at w=1.5m, l ₁=9m, I _a=240A, I _b=220A, I _cThe estimated value curve and the actual value curve of the zero-sequence current when d changes under the condition of=190A.As can beappreciated from fig. 5, transducer spacing is very little to the influence of zero-sequence current estimation error from d.In fact, distribution wire to the distance between the ground usually less than 11.7m, in order to ensure l ₁Greater than 9m, recommend d to get about 1.0m and realize that with the interference that abates the noise zero-sequence current calculates more accurately.

Fig. 6 represented at the comparative result between zero-sequence current estimated value and the actual value under 50 kinds of situation, in these cases, and three-phase current (I _a, I _b, I _c) produce at random between from 180A to 260A.This simulation result shows, at w=1.5m, and l ₁=10.0m, l ₂=0.36m, under the condition of d=1.0m, the estimated value of zero-sequence current and actual value are very approaching in the three-phase three wire system.When the zero-sequence current value when 2A is in the scope of 16A, the absolute error between its estimated value and actual value is between ± 1A.

For the three-phase and four-line overhead power transmission line, the measuring principle of its zero-sequence current is described below.

Three-phase and four-line formula pole line in the distribution system is as shown in Figure 7.Current in middle wire is I _nArticle four, line of electric force is equivalently represented by a virtual wires, and equivalent current can be represented as follows:

I _v＝I _a+I _b+I _c+I _n＝3I ₀+I _n＝I _r (9)

Wherein, I _rBe aftercurrent.Similar with three-phase three wire system, the zero-sequence current I in the three-phase four wire system ₀Can be by I _vOr I _rEstimation obtains, I _vOr I _rAgain can be by magnetic field sensor S ₁, S ₂The magnetic flux density that records is calculated.

B ₁, B ₂Y axle component be shown below:

$\left\{\begin{array}{c}{B}_{1y}=\frac{{\mathrm{\&mu;}}_0{I}_a}{2\mathrm{\&pi;}{l}_1}{\left(\cos {\mathrm{\&theta;}}_1\right)}^2+\frac{{\mathrm{\&mu;}}_0{\mathrm{<figure-callout\; id="2"\; label="I\; b"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">I</figure-callout>}}_b}{2\mathrm{\&pi;}(l_1+l_2)}+\frac{{\mathrm{\&mu;}}_0{I}_c}{2\mathrm{\&pi;}{l}_1}{\left(\cos {\mathrm{\&theta;}}_1\right)}^2+\frac{{\mathrm{\&mu;}}_0{\mathrm{<figure-callout\; id="2"\; label="I\; n"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">I</figure-callout>}}_n}{2\mathrm{\&pi;}{l}_3}\\ B_{2y}=\frac{{\mathrm{\&mu;}}_0{I}_a}{2\mathrm{\&pi;}(l_1+d)}{\left(\cos {\mathrm{\&theta;}}_2\right)}^2+\frac{{\mathrm{\&mu;}}_0{\mathrm{<figure-callout\; id="2"\; label="I\; b"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">I</figure-callout>}}_b}{2\mathrm{\&pi;}(l_1+{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">l</figure-callout>}}_2+d)}\\ +\frac{{\mathrm{\&mu;}}_0{I}_c}{2\mathrm{\&pi;}(l_1+d)}{\left(\cos {\mathrm{\&theta;}}_2\right)}^2+\frac{{\mathrm{\&mu;}}_0{\mathrm{<figure-callout\; id="2"\; label="I\; n"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">I</figure-callout>}}_n}{2\mathrm{\&pi;}(I_3+d)}\end{array}\right.---\left(10\right)$

I _vCan also utilize equality (8) to calculate.So, according to equality (9), utilize the corresponding I of each line construction _n/ I ₀Radiometer is calculated zero-sequence current.

In Fig. 7, utilize the estimation relation between zero-sequence current and the current in middle wire only to use two magnetic field sensors just can obtain zero-sequence current.In order to obtain result more accurately, can see three-phase power line as a virtual wires, center line is positioned at the virtual wires below, and is as shown in Figure 8, and this situation must need three magnetic field sensors.Three-phase current is respectively I _a, I _b, I _c, current in middle wire is I _nMagnetic field sensor (S ₁, S ₂, S ₃) vertically be positioned at the below of B phase conductor.See three-phase power line as a virtual wires, center line is positioned at the virtual wires below, and equivalent current can be represented as follows:

I _v＝I _a+I _b+I _c＝3I ₀+I _n (11)

S among Fig. 8 ₁, S ₂, S ₃The magnetic flux density at place is represented by formula (12).I _vWith B _1vy, B _2vy, B _3vyBetween relation suc as formula shown in (13).

$\left\{\begin{array}{c}{B}_{1y}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\&CenterDot;(\frac{I_1}{l_1}\&CenterDot;\cos {\mathrm{\&theta;}}_1^2+\frac{I_2}{l_1+{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">l</figure-callout>}}_2}+\frac{I_3}{l_1}\&CenterDot;\cos {\mathrm{\&theta;}}_1^2+\frac{I_n}{l_3})\\ B_{2y}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\&CenterDot;(\frac{I_1}{l_1+d_1}\&CenterDot;\cos {\mathrm{\&theta;}}_2^2+\frac{I_2}{l_1+{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">l</figure-callout>}}_2+d_1}\\ +\frac{I_3}{l_1+d_1}\&CenterDot;\cos {\mathrm{\&theta;}}_2^2+\frac{I_n}{l_3+d_1})\\ B_{3y}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\&CenterDot;(\frac{I_1}{l_1+d_1+{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}\&CenterDot;\cos {\mathrm{\&theta;}}_3^2+\frac{I_2}{l_1+{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">l</figure-callout>}}_2+d_1+{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}\\ +\frac{I_3}{l_1+d_1+{\mathrm{<figure-callout\; id="2"\; label="d"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">d</figure-callout>}}_2}\&CenterDot;\cos {\mathrm{\&theta;}}_3^2+\frac{I_n}{l_3+d_1+d_2})\end{array}\right.---\left(12\right)$

$\left\{\begin{array}{c}{B}_{1\mathrm{vy}}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}[\frac{1}{h_v}{I}_v+\frac{1}{l_3}{I}_w]\\ {\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="HDA00001647097700031.png,HDA00001647097700041.png"\; state="\{\{state\}\}">B</figure-callout>}}_{2\mathrm{vy}}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}[\frac{1}{(h_v+d_1)}{I}_v+\frac{1}{({\mathrm{<figure-callout\; id="3"\; label="l"\; filenames="HDA00001647097700022.png,HDA00001647097700053.png"\; state="\{\{state\}\}">l</figure-callout>}}_3+d_1)}{I}_n]\\ {\mathrm{<figure-callout\; id="3"\; label="B"\; filenames="HDA00001647097700022.png,HDA00001647097700053.png"\; state="\{\{state\}\}">B</figure-callout>}}_{3\mathrm{vy}}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}[\frac{1}{(h_v+d_1+d_2)}{I}_v+\frac{1}{({\mathrm{<figure-callout\; id="3"\; label="l"\; filenames="HDA00001647097700022.png,HDA00001647097700053.png"\; state="\{\{state\}\}">l</figure-callout>}}_3+d_1+d_2)}{I}_n]\end{array}\right.---\left(13\right)$

B _1y, B _2y, B _3yMeasure by magnetic field sensor, in ZSC measures, can think virtual current I _v, I _nWith I _a, I _b, I _c, I _nAt S ₁, S ₂, S ₃The y axle component that the place produces magnetic flux density is identical, i.e. B _1y=B _1vy, B _2y=B _2vy, B _3y=B _3vyVariable I in the formula (13) _v, h _v, I _nBe unknown, can obtain through finding the solution formula (13).Finally, solve zero-sequence current according to equality (11).

Verify the accuracy of the three-phase and four-line overhead power transmission line ZSC measuring method that is proposed with following emulation case.

For the three-phase four wire system that adopts two sensors, the measuring method that aftercurrent can be passed through to be proposed is directly obtained, and then, according to formula (9), utilizes I _n/ I ₀Ratio can calculate zero-sequence current.This ratio is influenced by power line structures mainly, in many earthed distribution systems, and I _n/ I ₀Ratio can be taken as 3.9.

Fig. 9 has compared aftercurrent estimated value and the actual value when adopting two magnetic field sensors.At w=1.22m, l ₁=10.0m, l ₂=0.36m, l ₃=9.0m has carried out emulation to 50 kinds of different situations under the condition of d=1.0m.Electric current I in emulation _a, I _b, I _cRandom variation between 180A and 260A, current in middle wire I _nAmplitude and phase angle random variation in 0-20A and 0-180 ° of scope respectively.

As can be seen from Figure 9, the aftercurrent estimated value approaches its actual value.When aftercurrent when 1A is in the 25A scope, the absolute error between aftercurrent estimated value and the actual value is also in ± 1A scope.

The comparative result of zero-sequence current estimated value and actual value is shown in figure 10 under the situation of three magnetic field sensors of employing, and simulated conditions is identical with Fig. 9 with the electric current variation among Figure 10, and this result shows by the zero-sequence current value and the actual value of this method estimation very approaching.Error ratio three-phase three wire system in the three-phase four wire system between zero-sequence current estimated value and actual value error between the two wants big.When zero-sequence current when 5A is in the 24A scope, the absolute error between zero-sequence current estimated value and actual value is in ± 2A scope.

Measuring method the present invention based on above-mentioned transmission line of electricity zero-sequence current has built a cover measuring table with accuracy and feasibility through the measuring method that experimental verification was proposed.The schematic diagram of test macro is shown in figure 11.

This test macro is by three-phase voltage source, magnetic field sensor, and parallel wire, current transformer (CTs) and load are formed.Power frequency is 50HZ in the test macro, uses two variable Burden box to regulate the amplitude of zero-sequence current, adopts current transformer to obtain reference current and verifies.Experimental data collects through the data acquisition system (DAS) (shown in Figure 11) based on Lab-View.Because the restriction of lab space, in the test platform shown in Figure 11 apart from l ₁, l ₃, w has compared proportional reducing with the value in the actual field.

Magnetic field sensor is a kind of inductive coil sensor of single shaft, and inductance is 0.15H, and the bandwidth up to 80KHz is arranged.The diameter of this coil pickoff is 8mm.Compare with the distance between lead and the magnetic field sensor, the size of sensor can be ignored.The output of each magnetic field sensor is all amplified through one three rank amplifying circuit.The full gain of amplifying circuit is approximately 2000.Before amplifying circuit, RC filtering circuit, its cutoff frequency being arranged is 1.2KHz.The output of each road amplifying circuit is sampled by NI DAQ data acquisition equipment.Magnetic field sensor circuit plate by coil pickoff and electronic devices and components constitute has been accomplished calibration in the laboratory, its error is approximately 1%.Voltage is 3.3 * 10 for the factor of magnetic flux density ⁵(V/G).In order to eliminate the edge effect of limited lead, magnetic field sensor is installed on the plank perpendicular to parallel wire, and this plank is positioned at the centre position of lead, recommends to adopt the laser vertical surveying instrument of portable can conveniently install to guarantee sensor.In test, the zero-sequence current estimated value calculates through the magnetic flux density of being measured by magnetic field sensor, and reference value is 100mV/A by sensitivity, and degree of accuracy is that 0.5% Fluke current sensor measurement obtains.Each signal is carried out fast Fourier transform (FFT) can get access to some fundametal components.

Figure 12 and 13 has represented this paper proposed in phase three-wire three and the three-phase four wire system the measuring method and the comparing result of CTs measuring method respectively.In test process, change from 0 to 6A through regulating Burden box impedance zero-sequence current.For the situation of three-phase three wire system shown in Figure 12, neutral conductor breaks off and has only adopted two magnetic field sensors to measure.For the situation of three-phase four wire system shown in Figure 13, adopted three magnetic field sensors to measure.

Can find out that from Figure 12 and 13 measuring relative errors of phase three-wire three and three-phase four wire system is lower than 5% and 7% respectively.Experimental result shows that in phase three-wire three and three-phase four wire system, the measuring method that this paper proposed can calculate zero-sequence current more exactly.

Adopting two magnetic field sensors to measure under the situation of three-phase four wire systems, measuring to such an extent that the accuracy of zero-sequence current mainly receives I _n/ I ₀The influence of this ratio.A main uncertain factor that causes measuring error is exactly the distribution wire below in the middle of sensor vertically is not placed on.In actual field, the deviation of 1.0m will cause about 5% error.0.5m deviation can cause about 1% error.The scene can adopt easily the laser vertical surveying instrument to place sensor array.Like this,, actual field can avoid this main measuring uncertainty factor in measuring.

Measuring method based on the ZSC of array of magnetic sensors is simple, cost is low, loss is low; Can avoid the conventional current mutual inductor saturated, measurement range is narrow and ferromagnetic resonance magnetic, residual effect should wait shortcoming; The on-the-spot use need not the contact electrification circuit, need not to constitute the zero-sequence current pass filter by the polarity wiring, do not have the danger that causes as conventional current mutual inductor secondary coil open circuit, and be safe.

Claims (6)

1. the measuring method based on the transmission line of electricity zero-sequence current of array of magnetic sensors is characterized in that, may further comprise the steps:

1) array of magnetic sensors is placed the below of overhead transmission line, gather array of magnetic field output signal;

2) with signal successively through being transferred to data processing equipment behind filtering circuit and the amplifying circuit;

3) data processing equipment is handled to the received signal, obtains the magnetic flux density information of current carrying conductor, and obtains the zero-sequence current of current carrying conductor through the characteristic of analyzing this magnetic flux density.

2. the measuring method of a kind of transmission line of electricity zero-sequence current based on array of magnetic sensors according to claim 1; It is characterized in that; If transmission line of electricity is the phase three-wire three overhead transmission line, described array of magnetic sensors is that two Magnetic Sensors are formed array of magnetic sensors.

3. the measuring method of a kind of transmission line of electricity zero-sequence current based on array of magnetic sensors according to claim 2 is characterized in that the calculating of zero-sequence current is specific as follows:

1) two Magnetic Sensor S ₁And S ₂Magnetic flux be respectively B ₁And B ₂, B ₁, B ₂In space coordinates, be decomposed into x, y, three components of z are respectively as follows

$\left\{\begin{array}{c}{B}_{1x}=0\\ B_{1y}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\&CenterDot;(\frac{I_a}{l_1}\&CenterDot;\cos {\mathrm{\&theta;}}_1^2+\frac{I_b}{l_1+l_2}+\frac{I_c}{l_1}\&CenterDot;\cos {\mathrm{\&theta;}}_1^2)\\ B_{1z}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\&CenterDot;(\frac{I_a}{l_1}\&CenterDot;\sin {\mathrm{\&theta;}}_1\&CenterDot;\cos {\mathrm{\&theta;}}_1+\frac{I_c}{l_1}\&CenterDot;\sin {\mathrm{\&theta;}}_1\&CenterDot;\cos {\mathrm{\&theta;}}_1)\end{array}\right.---\left(1\right)$

$\left\{\begin{array}{c}{B}_{2x}=0\\ B_{2y}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\&CenterDot;(\frac{I_a}{l_1+d}\&CenterDot;\cos {\mathrm{\&theta;}}_2^2+\frac{I_b}{l_1+l_2+d}+\frac{I_c}{l_1+d}\&CenterDot;\cos {\mathrm{\&theta;}}_2^2)\\ B_{2z}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\&CenterDot;(\frac{I_a}{l_1+d}\&CenterDot;\sin {\mathrm{\&theta;}}_1\&CenterDot;\cos {\mathrm{\&theta;}}_1+\frac{I_c}{l_1+d}\&CenterDot;\sin {\mathrm{\&theta;}}_1\&CenterDot;\cos {\mathrm{\&theta;}}_1)\end{array}\right.---\left(2\right)$

I in last two formulas _a, I _b, I _cBe respectively three-phase current, μ ₀Be air permeability, w is the horizontal range between a phase and the b phase, and d is Magnetic Sensor S ₁And S ₂Between vertical range, l ₁Be Magnetic Sensor S ₁With the vertical range of c between mutually, l ₂Be the vertical range between b phase and the c phase, θ ₁Be a phase and S ₁Between line and b mutually and S ₁Between the angle of line, θ ₂Be a phase and S ₂Between line and b mutually and S ₂Between the angle of line;

2) suppose that distance between line of electric force and the magnetic field sensor is greater than the distance between the line of electric force, i.e. l ₁＞＞l ₂, then the magnetic field effect of three line of electric force can be by the equivalent current I that is positioned at the sensor top _vExpression, wherein, I _vAnd S ₁Between the distance be h _v, I _vAt measurement point S ₁, S ₂The place produces the x of magnetic flux density, y, and z axle component is represented suc as formula (3) and (4).

$\left\{\begin{array}{c}{B}_{1\mathrm{vx}}=0\\ B_{1\mathrm{vy}}=\frac{{\mathrm{\&mu;}}_0\&CenterDot;I_v}{2\mathrm{\&pi;}{h}_v}\\ B_{1\mathrm{vz}}=0\end{array}\right.---\left(3\right)$

$\left\{\begin{array}{c}{B}_{2\mathrm{vx}}=0\\ B_{2\mathrm{vy}}=\frac{{\mathrm{\&mu;}}_0\&CenterDot;I_v}{2\mathrm{\&pi;}(h_v+d)}\\ B_{2\mathrm{vz}}=0\end{array}\right.---\left(4\right)$

Can know by (3), (4) formula, by I _vThe magnetic flux density that produces only comprises y axle component, in zero sequence current measurement, can assert virtual current I _vWith I _a, I _b, I _cAt S ₁, S ₂The y axle component that the place produces magnetic flux density is identical, i.e. B _1y=B _1vy, B _2y=B _2vy, the y axle component in (1), (2) formula is substituted into (3), (4) formula, can obtain I _vWith I _a, I _b, I _cBetween relational expression (5);

Suppose l ₁＞＞l ₂, in addition, because l ₁＞＞w and l ₁+ d＞＞w, then cos θ ₁≈ cos θ ₂Therefore, virtual current I _vCan be reduced to (6) formula;

I _v＝f(I _a，I _b，I _c)＝(I _a+I _b+I _c)＝3I ₀ (6)

(6) formula shows, as long as obtain virtual current I _vJust can try to achieve zero-sequence current I ₀, virtual current I _vCan be calculated by (7) formula, (7) formula draws on the basis of formula (3), (4), wherein B _1vyAnd B _2vyCan pass through magnetic field sensor S respectively ₁, S ₂Measurement is come out.

$I_v=\frac{2\mathrm{\&pi;d}\&CenterDot;B_{1\mathrm{vy}}\&CenterDot;B_{2\mathrm{vy}}}{{\mathrm{\&mu;}}_0(B_{1\mathrm{vy}}-B_{2\mathrm{vy}})}---\left(7\right)$

4. the measuring method of a kind of transmission line of electricity zero-sequence current based on array of magnetic sensors according to claim 1; It is characterized in that; If transmission line of electricity is the three-phase and four-line overhead transmission line, described array of magnetic sensors is two or three Magnetic Sensors composition array of magnetic sensors.

5. the measuring method of a kind of transmission line of electricity zero-sequence current based on array of magnetic sensors according to claim 4 is characterized in that, if adopt two Magnetic Sensors, the calculating of zero-sequence current is following:

Article four, line of electric force is equivalently represented by a virtual wires, and equivalent current can be represented as follows:

I _v＝I _a+I _b+I _c+I _n＝3I ₀+I _n＝I _r (8)

Wherein, I _vBe virtual current, I _a, I _b, I _cBe respectively three-phase current, I ₀Be zero-sequence current, I _nBe current in middle wire, I _rBe aftercurrent;

I _vOr I _rBy magnetic field sensor S ₁, S ₂The magnetic flux density that records is calculated, B ₁, B ₂Y axle component be shown below:

$\left\{\begin{array}{c}{B}_{1y}=\frac{{\mathrm{\&mu;}}_0{I}_a}{2\mathrm{\&pi;}{l}_1}{\left(\cos {\mathrm{\&theta;}}_1\right)}^2+\frac{{\mathrm{\&mu;}}_0{I}_b}{2\mathrm{\&pi;}(l_1+l_2)}+\frac{{\mathrm{\&mu;}}_0{I}_c}{2\mathrm{\&pi;}{l}_1}{\left(\cos {\mathrm{\&theta;}}_1\right)}^2+\frac{{\mathrm{\&mu;}}_0{I}_n}{2\mathrm{\&pi;}{l}_3}\\ B_{2y}=\frac{{\mathrm{\&mu;}}_0{I}_a}{2\mathrm{\&pi;}(l_1+d)}{\left(\cos {\mathrm{\&theta;}}_2\right)}^2+\frac{{\mathrm{\&mu;}}_0{I}_b}{2\mathrm{\&pi;}(l_1+l_2+d)}\\ +\frac{{\mathrm{\&mu;}}_0{I}_c}{2\mathrm{\&pi;}(l_1+d)}{\left(\cos {\mathrm{\&theta;}}_2\right)}^2+\frac{{\mathrm{\&mu;}}_0{I}_n}{2\mathrm{\&pi;}(I_3+d)}\end{array}\right.---\left(9\right)$

Following formula, wherein μ ₀Be air permeability, w is the horizontal range between a phase and the b phase, and d is Magnetic Sensor S ₁And S ₂Between vertical range, l ₁Be Magnetic Sensor S ₁With the vertical range of c between mutually, l ₂Be the vertical range between b phase and the c phase, l ₃Be Magnetic Sensor S ₁With the vertical range of n between mutually, θ ₁Be a phase and S ₁Between line and b mutually and S ₁Between the angle of line, θ ₂Be a phase and S ₂Between line and b mutually and S ₂Between the angle of line;

I _vUtilize equality (7) to calculate,, utilize the pairing I of each line construction again according to equality (8) _n/ I ₀Ratio can calculate zero-sequence current.

6. the measuring method of a kind of transmission line of electricity zero-sequence current based on array of magnetic sensors according to claim 5 is characterized in that, if adopt three Magnetic Sensors, the calculating of zero-sequence current is following:

See three-phase power line as a virtual wires, center line is positioned at virtual wires below, three magnetic field sensor S ₁, S ₂, S ₃Vertically be positioned at the below of B phase conductor, see three-phase power line as a virtual wires, center line is positioned at the virtual wires below, and equivalent current can be represented as follows:

I _v＝I _a+I _b+I _c＝3I ₀+I _n (10)

S ₁, S ₂, S ₃The magnetic flux density at place is by formula (11) expression, I _vWith B _1vy, B _2vy, B _3vyBetween relation suc as formula shown in (12);

$\left\{\begin{array}{c}{B}_{1y}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\&CenterDot;(\frac{I_1}{l_1}\&CenterDot;\cos {\mathrm{\&theta;}}_1^2+\frac{I_2}{l_1+l_2}+\frac{I_3}{l_1}\&CenterDot;\cos {\mathrm{\&theta;}}_1^2+\frac{I_n}{l_3})\\ B_{2y}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\&CenterDot;(\frac{I_1}{l_1+d_1}\&CenterDot;\cos {\mathrm{\&theta;}}_2^2+\frac{I_2}{l_1+l_2+d_1}\\ +\frac{I_3}{l_1+d_1}\&CenterDot;\cos {\mathrm{\&theta;}}_2^2+\frac{I_n}{l_3+d_1})\\ B_{3y}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\&CenterDot;(\frac{I_1}{l_1+d_1+d_2}\&CenterDot;\cos {\mathrm{\&theta;}}_3^2+\frac{I_2}{l_1+l_2+d_1+d_2}\\ +\frac{I_3}{l_1+d_1+d_2}\&CenterDot;\cos {\mathrm{\&theta;}}_3^2+\frac{I_n}{l_3+d_1+d_2})\end{array}\right.---\left(11\right)$

$\left\{\begin{array}{c}{B}_{1\mathrm{vy}}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}[\frac{1}{h_v}{I}_v+\frac{1}{l_3}{I}_w]\\ B_{2\mathrm{vy}}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}[\frac{1}{(h_v+d_1)}{I}_v+\frac{1}{(l_3+d_1)}{I}_n]\\ B_{3\mathrm{vy}}=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}[\frac{1}{(h_v+d_1+d_2)}{I}_v+\frac{1}{(l_3+d_1+d_2)}{I}_n]\end{array}\right.---\left(12\right)$

B _1y, B _2y, B _3yMeasure by magnetic field sensor, in zero sequence current measurement, can assert virtual current I _v, I _nWith I _a, I _b, I _c, I _nAt S ₁, S ₂, S ₃The y axle component that the place produces magnetic flux density is identical, i.e. B _1y=B _1vy, B _2y=B _2vy, B _3y=B _3vy, the variable I in the formula (12) _v, h _v, I _nBe unknown, can obtain through finding the solution formula (12), final, solve zero-sequence current according to equality (10).

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