CN105241498A - DC overhead transmission line sag and stress monitoring method based on weak magnetic detection - Google Patents

Abstract

The invention discloses a DC overhead transmission line sag and stress monitoring method based on weak magnetic detection. Multiple detection points are selected on a tower rod, magnetic sensors are placed, and by use of the distribution feature of a transmission line space magnetic field, in a corresponding coordinate system, a fitting linear equation formula between a magnetic field component generated by each transmission line at each detection point and a sag of each transmission line is obtained; and based on this, through coordinate conversion and a magnetic field superposition principle, a system of non-homogeneous linear equations is constructed by use of a differential method, sags of the transmission lines at the two sides of a pole and horizontal stress of the transmission lines can be solved, and finally, the size of stress at any point of the transmission lines is solved so that the sags and the stress of the transmission lines are monitored in real time. According to the invention, through a weak magnetic detection technology, through combination with a wireless communication technology, magnetic signals acquired by the magnetic sensors are uploaded to a monitoring terminal and then the sags and the stress of the lines are calculated in real time through a computer, such that faults can be simply and quickly discovered and eliminated.

Description

A kind of direct-current overhead power transmission line sag based on weak magnetic detection and stress monitoring method

Technical field

The present invention is a kind of direct-current overhead power transmission line sag based on weak magnetic detection and stress monitoring method, relates to transmission line of electricity monitoring field.

Background technology

China's transmission line of electricity becomes network-like structure to distribute, and branch is many, and most regional terrain environment numerous and complicated, be easily subject to the impact of weather environment, line failure rate is higher, and more double physical features is on the way changeable, is difficult to search.Therefore carrying out Real-Time Monitoring to the state of transmission line of electricity is the important guarantee realizing power system stability operation, but owing to being subject to the restriction of some technical conditions, does not also have high-precision line status real-time monitoring device at present.Therefore once circuit breaks down, need manually to search along the line, add difficulty and the time of malfunction elimination, and utilize distribution automation system can realize the automatic location of fault, but cost is too large, be difficult to promote.Therefore Real-Time Monitoring and analysis are carried out to the sag of transmission line of electricity, stress, can Timeliness coverage line defct and hidden danger, transmission line of electricity reliability of operation can be improved.

Summary of the invention

The invention provides a kind of direct-current overhead power transmission line sag based on weak magnetic detection and stress monitoring method, by weak magnetic detection technology, combined with radio communication technology, the magnetic signal collected by Magnetic Sensor uploads to monitor terminal, by computer programming, line-sag and stress are calculated in real time again, thus realize simple and fast discovery fault, fix a breakdown, for whole Operation of Electric Systems provides safe and reliable electric power transfer.

The technical solution adopted in the present invention is:

A kind of direct-current overhead power transmission line sag based on weak magnetic detection and stress monitoring method, shaft tower is selected multiple sensing point and settles Magnetic Sensor, utilize the characteristic distributions of power transmission line space magnetic field, in corresponding coordinate system, obtain the fitting linear equation of magnetic-field component that each root power transmission line produces at each sensing point place and power transmission line sag; On this basis by coordinate transform and magnetic field superposition principle, and build a Linear Equations by the method for difference, the sag of tower both sides power transmission line and the horizontal stress of power transmission line can be solved, and finally solve the stress intensity of any point on power transmission line, thus the Real-Time Monitoring realized power transmission line sag and stress, improve transmission line of electricity reliability of operation.

Based on direct-current overhead power transmission line sag and the stress monitoring method of weak magnetic detection, comprise the following steps:

Choose arbitrarily three shaft towers of adjacent position, be labeled as No. 0 tower, No. 1 tower and No. 2 towers respectively.

Step one: set up X ' Y ' Z ' coordinate system to the power transmission line between No. 0 tower and No. 1 tower, wherein X ' Z ' plane is parallel to the plane at power transmission line place, and X ' direction of principal axis is parallel to the vertical join line direction of two shaft towers; XYZ coordinate system is set up for the power transmission line between No. 1 tower and No. 2 towers, and measurement obtains the coordinate of the left hitch point of corresponding power transmission line in respective coordinate system, and the correlation parameter of three shaft towers;

Step 2: select sensing point near the place of hitch point on No. 1 shaft tower, the quantity of sensing point is greater than the power transmission line quantity of shaft tower side, utilize the computing formula of power transmission line space magnetic field, in corresponding coordinate system, calculate that each root power transmission line produces at each sensing point place X ' (or X) magnetic-field component and the fitting linear equation of Y ' (or Y) magnetic-field component and power transmission line sag; By coordinate transform and magnetic field superposition principle, obtain each sensing point X-direction and the linear equation between Y-direction magnetic induction density component and No. 1 shaft tower both sides power transmission line sag in XYZ coordinate system, then to all linear equations difference between two, a Linear Equations containing power transmission line sag is set up;

Step 3: settle Magnetic Sensor at sensing point position place, is the magnetic signal at sensing point place, and all Magnetic Sensor vector directional bearings and XYZ coordinate system is consistent by calibrating the magnetic signal making Magnetic Sensor measure;

Step 4: the X-direction detect Magnetic Sensor on shaft tower and the magnetic induction density component of Y-direction read in real time, substitutes in the Linear Equations obtained in step 2, finally obtains the sag of the power transmission line of No. 1 shaft tower side-by-side mounting;

Step 5: the sag calculated is substituted into the condition that power transmission line equation is set up, stretched wire coefficient and the intercept of power transmission line is obtained by computer programming, the ratio solving power transmission line under different meteorological conditions carries, utilize the relational expression of stretched wire coefficient and horizontal stress, solve the horizontal stress of power transmission line, then utilize the stress formula of any point on power transmission line finally to calculate the stress intensity of every bit on power transmission line.

Due to need on the signal of Magnetic Sensor carry out between two difference to eliminate the impact of terrestrial magnetic field, and each Magnetic Sensor can set up X-direction and the linear equation between Y-direction magnetic induction density component and shaft tower both sides power transmission line sag, in order to ensure that the quantity of equation in the Linear Equations that finally obtains is greater than the number of required power transmission line sag, therefore described Magnetic Sensor quantity should be greater than the power transmission line quantity of shaft tower side.

Described Magnetic Sensor is twin shaft Magnetic Sensor or magnetic sensor, because the coordinate system set up power transmission line is relatively fixing, in order to the magnetic signal that can be detected by Magnetic Sensor, the X ' (or X) of different sensing point and the magnetic-field component in Y ' (or Y) direction under obtaining coordinate system, therefore require the dimensional orientation of the Magnetic Sensor that same shaft tower is installed to be consistent or in quantitative geometric relationship.

In order to eliminate the impact of terrestrial magnetic field, the quantity of Magnetic Sensor can be increased, utilize differential principle, the equidirectional signal that Magnetic Sensor exports is subtracted each other between two.The quantity of Magnetic Sensor is greater than shaft tower both sides power transmission line quantity.

The present invention is a kind of direct-current overhead power transmission line sag based on weak magnetic detection and stress monitoring method, and technique effect is as follows:

1), the present invention is by weak magnetic detection technology, combined with radio communication technology, the magnetic signal collected by Magnetic Sensor uploads to monitor terminal, by computer technology, line-sag and stress are calculated in real time again, thus realize simple and fast discovery fault, fix a breakdown, for whole Operation of Electric Systems provides safe and reliable electric power transfer.

2), this invention adopts weak magnetic detection method, realize the Real-Time Monitoring to direct-current overhead power transmission line sag and stress, there is the measurement data directly remarkable advantage such as reliable, high sensitivity, antijamming capability are strong, measuring accuracy is higher, accurate positioning and real-time remote monitoring.

3), the present invention provides first to defend by for current just under arms and by the high pressure built, superhigh voltage DC power transmission and transformation system; prevention occurrence of large-area electrical network paralysis ahead of time; the protection person, device security, for socio-economic development provides powerful guarantee, its social benefit is huge.

Accompanying drawing explanation

Fig. 1 is when in the present invention, hitch point is not contour, each parameter schematic diagram of power transmission line equation.

Fig. 2 is the matched curve schematic diagram (sag change interval 0.1m) of power transmission line sag and sensing point magnetic-field component in the present invention.

Wherein Fig. 2 (1) represents the matched curve of sensing point X-direction magnetic-field component and power transmission line sag.

Wherein Fig. 2 (2) represents the matched curve of sensing point Y-direction magnetic-field component and power transmission line sag.

Wherein Fig. 2 (3) represents the matched curve of sensing point Z-direction magnetic-field component and power transmission line sag.

Wherein Fig. 2 (4) represents the matched curve of the magnetic field size that sensing point is total and power transmission line sag.

Fig. 3 is the matched curve schematic diagram (sag change interval 0.01m) of power transmission line sag and sensing point magnetic-field component in the present invention.

Wherein Fig. 3 (1) represents the matched curve of sensing point X-direction magnetic-field component and power transmission line sag.

Wherein Fig. 3 (2) represents the matched curve of sensing point Y-direction magnetic-field component and power transmission line sag.

Wherein Fig. 3 (3) represents the matched curve of sensing point Z-direction magnetic-field component and power transmission line sag.

Wherein Fig. 3 (4) represents the matched curve of the magnetic field size that sensing point is total and power transmission line sag.

Fig. 4 is that in the present invention, single loop three line direct-current overhead power transmission line sag solves schematic diagram.

Fig. 5 is that in the present invention, corner power transmission line magnetic-field component in XYZ coordinate system solves schematic diagram.

Embodiment

A kind of direct-current overhead power transmission line sag based on weak magnetic detection and stress monitoring method, shaft tower is selected multiple sensing point and settles Magnetic Sensor, utilize the characteristic distributions of power transmission line space magnetic field, in corresponding coordinate system, obtain the fitting linear equation of magnetic-field component that each root power transmission line produces at each sensing point place and power transmission line sag; On this basis by coordinate transform and magnetic field superposition principle, and build a Linear Equations by the method for difference, the sag of all power transmission lines and the horizontal stress of power transmission line can be solved, and finally solve the stress intensity of power transmission line any point, thus the Real-Time Monitoring realized power transmission line sag and stress, improve transmission line of electricity reliability of operation.

Based on direct-current overhead power transmission line sag and the stress monitoring method of weak magnetic detection, embodiment is shown in Fig. 4, is divided into five steps and completes.

Choose arbitrarily three shaft towers of adjacent position, be labeled as No. 0 tower, No. 1 tower and No. 2 towers respectively.

Step one: X ' Y ' Z ' coordinate system is set up to the power transmission line between No. 0 tower and No. 1 tower, wherein X ' Z ' plane is parallel to the plane at power transmission line place, X ' direction of principal axis is parallel to the vertical join line direction of two shaft towers, in the same way, XYZ coordinate system is set up for the power transmission line between No. 1 tower and No. 2 towers, and measurement obtains the coordinate of the left hitch point of corresponding power transmission line in respective coordinate system, and the correlation parameter of 3 shaft towers is as the discrepancy in elevation and corner in span, span.

Step 2: select sensing point near the place of hitch point on No. 1 shaft tower, the quantity of sensing point is greater than the power transmission line quantity of shaft tower side.Utilize the computing formula of power transmission line space magnetic field, in corresponding coordinate system, obtained the fitting linear equation of X ' (or X) component that each root power transmission line produces at each sensing point place and Y ' (or Y) component magnetic field and power transmission line sag by MATLAB program calculation.By coordinate transform and magnetic field superposition principle, obtain each sensing point X-direction and the linear equation between Y-direction magnetic induction density component and all power transmission line sags, then to all linear equations difference between two, a Linear Equations containing power transmission line sag is set up.

Step 3: settle High-precision Vector Magnetic Sensor at sensing point position place, by calibration make sensor measurement to magnetic signal be the magnetic signal at sensing point place, and all Magnetic Sensor vector directional bearings and XYZ coordinate system are consistent.

Step 4: the X-direction detect all Magnetic Sensors on No. 1 shaft tower and the magnetic induction density component of Y-direction read in real time, substitutes in the Linear Equations obtained in step 2, finally obtains the sag of No. 1 shaft tower both sides power transmission line.

Step 5: the sag calculated is substituted into the condition that power transmission line equation is set up, stretched wire coefficient and the intercept of power transmission line is obtained by computer programming, the ratio solving power transmission line under different meteorological conditions carries, utilize the relational expression of stretched wire coefficient and horizontal stress, solve the horizontal stress of power transmission line, then utilize the stress formula of any point on power transmission line finally to calculate the stress intensity of every bit on power transmission line.

Embodiment:

1, the mathematical model of overhead transmission line:

Transmission line of electricity is in fact a kind of catenary, and it has different sag characteristics under different weather conditions.Usual any material comprises power transmission line, all has certain rigidity, but due to the power transmission line be suspended on shaft tower relatively long, therefore the rigidity of power transmission line material is very little on the impact of its geometric configuration.In addition in engineering reality, owing to being limited by the many factors such as landform, the two ends hitch point great majority of overhead transmission line are not contour, this situation in mountain area, hilly country is commonplace.

In the XYZ coordinate system shown in Fig. 1 (XZ plane is parallel with power transmission line place plane, and X-direction is parallel to the tangential direction of power transmission line minimum point), if the coordinate of the left hitch point A of power transmission line under this coordinate system is (x _a, y _a, z _a).The method of utilizing works mechanics can derive side-by-side mounting point not contour time overhead transmission line equation be:

$\left\{\begin{array}{c}z=a(ch\frac{x-x_A-d}{a}-1)+z_A-c\\ y=y_A\\ a(ch\frac{d}{a}-1)-c=0\\ ach\frac{l-d}{a}-ach\frac{d}{a}-h=0\end{array}\right.---\left(1\right)$

In formula, l is vertical range between two shaft towers and span, c is the minimum sag of power transmission line (being called for short sag in literary composition), d is that namely A point and power transmission line minimum point cut square at the projector distance of X-direction, h is the discrepancy in elevation in the difference in height of power transmission line two ends hitch point and span, and regulation hitch point left low right high time h>0, and h<0 during right low left high, a are the stretched wire coefficient of power transmission line, and

$a=\frac{{\mathrm{\&sigma;}}_0}{\mathrm{\&gamma;}}---\left(2\right)$

Wherein γ is that power transmission line ratio carries, σ ₀for power transmission line minimum point stress and horizontal stress.

2, the calculating of direct-current overhead power transmission line space magnetic field:

If power transmission line current-carrying is I, in (1) formula, make x=t, can obtain power transmission line parametric equation is:

$\left\{\begin{array}{c}x=t\\ y=y_A\\ z=a(ch\frac{t-x_A-d}{a}-1)+z_A-c\end{array}\right.---\left(3\right)$

Ask space any point P (x ₀, y ₀, z ₀) magnetic field.On power transmission line, a current element is got at arbitrary coordinate points (x, y, z) place p point to the position vector of current element is by BiotSavart's law, the magnetic field that this current element produces at a P is

$d\stackrel{\&RightArrow;}{B}=\frac{{\mathrm{\&mu;}}_0}{4\mathrm{\&pi;}}\frac{Id\stackrel{\&RightArrow;}{l}\&times;\stackrel{\&RightArrow;}{r}}{r^3}---\left(4\right)$

Following geometric relationship is substituted in above formula:

$d\stackrel{\&RightArrow;}{l}=dx\stackrel{\&RightArrow;}{i}+dy\stackrel{\&RightArrow;}{j}+dz\stackrel{\&RightArrow;}{k}$

$\stackrel{\&RightArrow;}{r}=(x_0-x)\stackrel{\&RightArrow;}{i}+(y_0-y)\stackrel{\&RightArrow;}{j}+(z_0-z)\stackrel{\&RightArrow;}{k}$

$r=\sqrt{{(x_0-x)}^2+{(y_0-y)}^2+{(z_0-z)}^2}$

Then component type can be written as:

$\left\{\begin{array}{c}{\mathrm{dB}}_x=\frac{{\mathrm{\&mu;}}_0}{4{\mathrm{\&pi;r}}^3}\&lsqb;(z_0-z)dy-(y_0-y)dz\&rsqb;\\ {\mathrm{dB}}_y=\frac{{\mathrm{\&mu;}}_0}{4{\mathrm{\&pi;r}}^3}\&lsqb;(x_0-x)dy-(z_0-z)dx\&rsqb;\\ {\mathrm{dB}}_z=\frac{{\mathrm{\&mu;}}_0}{4{\mathrm{\&pi;r}}^3}\&lsqb;(y_0-y)dy-(x_0-x)dy\&rsqb;\end{array}\right.---\left(5\right)$

Utilize magnetic field superposition principle, the magnetic field that power transmission line produces at P point is:

$\left\{\begin{array}{c}{B}_x=\frac{{\mathrm{\&mu;}}_{0}I}{4\mathrm{\&pi;}}\&Integral;\frac{\left(z_0-z\right)y^{\&prime;}-\left(y_0-y\right)z^{\&prime;}}{r^3}dt\\ B_y=\frac{{\mathrm{\&mu;}}_{0}I}{4\mathrm{\&pi;}}\&Integral;\frac{\left(x_0-x\right)z^{\&prime;}-\left(z_0-z\right)x^{\&prime;}}{r^3}dt\\ B_z=\frac{{\mathrm{\&mu;}}_{0}I}{4\mathrm{\&pi;}}\&Integral;\frac{\left(y_0-y\right)x^{\&prime;}-\left(x_0-x\right)y^{\&prime;}}{r^3}dt\end{array}\right.---\left(6\right)$

X ', y in formula ', z ' is respectively x, and y, z are to the derivative of parametric t, and the direction of a curve that integration specifies along equation carries out.(3) formula is substituted in (6) formula, power transmission line space arbitrary sensing point P (x can be obtained ₀, y ₀, z ₀) magnetic-field component be:

$\left\{\begin{array}{c}{B}_x=\frac{{\mathrm{\&mu;}}_{0}I}{4\mathrm{\&pi;}}{\&Integral;}_{x_A}^{x_A+l}\frac{-\left(y_0-y\right)sh\left(\frac{t-x_A-d}{a}\right)}{r^3}dt\\ B_y=\frac{{\mathrm{\&mu;}}_{0}I}{4\mathrm{\&pi;}}{\&Integral;}_{x_A}^{x_A+l}\frac{\left(x_0-x\right)sh\left(\frac{t-x_A-d}{a}\right)-\left(z_0-z\right)}{r^3}dt\\ B_z=\frac{{\mathrm{\&mu;}}_{0}I}{4\mathrm{\&pi;}}{\&Integral;}_{x_A}^{x_A+l}\frac{y_0-y}{r^3}dt\end{array}\right.---\left(7\right)$

Wherein in integration type, the integral domain of t is for being x _a→ x _a+ l.According to above-mentioned same method, utilize magnetic field superposition principle and coordinate transform can calculate more than single grade, the magnetic-field component of power transmission line space any point in folk art term many and corner situation.

3, the relation of sensing point magnetic field and power transmission line sag:

Programmed by MATLAB, utilize formula obtained above, the magnetic field of the arbitrary sensing point in power transmission line space can be calculated.Be 500 meters with two shaft tower spans below, in span, the discrepancy in elevation is 5 meters, and power transmission line electrical current is 200A, and sensing point is done in any position choosing near left hitch point on shaft tower, analyzes the relation of sensing point magnetic field and power transmission line sag.

When power transmission line because when variation of ambient temperature or icing affect, sag will change.First 50 different sag sizes are chosen with 0.1m interval, calculate sensing point place magnetic-field component value, with origin software, linear least square fitting is carried out to the result calculated again, Fig. 2 is the coordinate of the relatively left hitch point of sensing point is (-0.2m,-1m ,-1m) time the result that obtains.As can be seen from Figure 2, when sag change interval is 0.1m, B _x, B _y, B _zand B all with sag c linearly variation relation substantially.Wherein B _x, B _ymaximum with the linear fit degree of c, related coefficient is all greater than 0.999, and the standard deviation of matching is at about 2nT.

In order to the variation relation of the magnetic-field component and sag of analyzing sensing point further, then be that 50 sags are chosen at interval with 0.01m, the magnetic-field component that calculates same sensing point of using the same method also carries out linear fit with sag, obtains the result shown in Fig. 3.As can be seen from Figure 3, when sag change interval is 0.01m, B _x, B _yhigh linear fit degree (related coefficient >0.99) is still kept with sag c.And B _zobvious discretize characteristic distributions is then presented with sag c.

Comprehensive above analysis, by B in engineering practice _x, B _ymeasurement can obtain the sag size of power transmission line more in real time.Table 1 is the solving precision of sag c in different Magnetic Sensor detection accuracy situations obtained by Fig. 3, the solving precision of sag depends on the detection accuracy of Magnetic Sensor and the sensing point how far from hitch point obviously, when Magnetic Sensor detection accuracy is higher, sensing point from hitch point more close to, the solving precision of sag is higher.

The solving precision complete list of power transmission line sag under the Magnetic Sensor precise manner that table 1 is different

4, the Real-Time Monitoring of power transmission line sag and stress:

Due to the sag of power transmission line and the B of sensing point _xand B _ythe linear changing relation very high in fitting degree, therefore Real-Time Monitoring can be carried out by the Magnetic Sensor installing some on shaft tower to the sag of transmission line of electricity and stress.

Owing to shaft tower being hung with many power transmission lines, and also there is corner between shaft tower, below for single loop three line direct-current overhead power transmission line, introduce the concrete grammar of sag and stress monitoring, extend to the transmission line of electricity of other any framework on this basis.

4.1, the monitoring of power transmission line sag:

Fig. 4 is the schematic diagram of single loop three line direct-current overhead power transmission line, generally, also there is rotational angle theta between two planes that three towers are formed.The coordinate that 1-3 power transmission line is corresponding is XYZ system, and the coordinate that 4-6 power transmission line is corresponding is X ' Y ' Z ' is that the sag of 6 power transmission lines is respectively c ₁, c ₂, c ₃, c ₄, c ₅, c ₆.At No. 1 tower, 3 sensing point P are set near the place of hitch point ₁, P ₂, P ₃, obviously, the magnetic field of each sensing point is that 6 power transmission lines are separately in the superposition in this generation magnetic field, some place.

By analysis above, in XYZ system, 1-3 power transmission line is respectively at the X component of sensing point generation and the sag linearly variation relation of Y-component field signal and this power transmission line.And in X ' Y ' Z ' is, the X ' component that 4-6 power transmission line produces at sensing point and Y ' component magnetic field signal is same and the sag linearly variation relation of this power transmission line.By certain coordinate transform, utilize magnetic field superposition principle, finally in XYZ system, obtain the sag of 6 power transmission lines by the X component of 3 sensing points and the magnetic induction density of Y-component, thus realize the Real-Time Monitoring to power transmission line sag.

(1), in XYZ system 1-3 power transmission line in the magnetic-field component of 3 sensing points

$\left\{\begin{array}{c}{B}_{ijx}=a_{ij}+b_{ij}{c}_i\\ B_{ijy}=e_{ij}+f_{ij}{c}_i\end{array}\right.---\left(8\right)$

I=1 in formula, 2,3, be the sequence number of power transmission line; J=1,2,3, be the sequence number of sensing point; a _ij, b _ijand e _ij, f _ijfor the linear fit coefficient obtained respectively by previous methods.

(2), in XYZ system 4-6 line in the magnetic-field component of 3 sensing points

First in X ' Y ' Z ' is 4-6 line in the magnetic-field component of 3 sensing points

$\left\{\begin{array}{c}{B}_{{\mathrm{kjx}}^{\&prime;}}=a_{kj}+b_{kj}{c}_k\\ B_{{\mathrm{kjy}}^{\&prime;}}=e_{kj}+f_{kj}{c}_k\end{array}\right.---\left(9\right)$

K=4 in formula, 5,6, be the sequence number of power transmission line; a _kj, b _kjand e _kj, f _kjfor linear fit coefficient.Next the magnetic-field component of 4-6 power transmission line in XYZ system can be calculated by the coordinate transform shown in Fig. 5 again.

$\left\{\begin{array}{c}{B}_{kjx}=B_{{\mathrm{kjx}}^{\&prime;}}\cos \mathrm{\&theta;}+B_{{\mathrm{kjy}}^{\&prime;}}\sin \mathrm{\&theta;}=\left(a_{kj}+b_{kj}{c}_k\right)\cos \mathrm{\&theta;}+\left(e_{kj}+f_{kj}{c}_k\right)\sin \mathrm{\&theta;}\\ B_{kjy}=B_{{\mathrm{kjy}}^{\&prime;}}\cos \mathrm{\&theta;}-B_{{\mathrm{kjx}}^{\&prime;}}\sin \mathrm{\&theta;}=\left(e_{kj}+f_{kj}{c}_k\right)\cos \mathrm{\&theta;}-\left(a_{kj}+b_{kj}{c}_k\right)\sin \mathrm{\&theta;}\end{array}\right.---\left(10\right)$

Therefore the magnetic-field component that 6 power transmission lines produce at 3 sensing points is respectively:

$\left\{\begin{array}{c}{B}_{jx}=\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{B}_{ijx}+\underset{k=4}{\overset{6}{\mathrm{\&Sigma;}}}{B}_{kjx}=\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}\left(a_{ij}+b_{ij}{c}_i\right)+\underset{k=4}{\overset{6}{\mathrm{\&Sigma;}}}\&lsqb;\left(a_{kj}+b_{kj}{c}_k\right)\cos \mathrm{\&theta;}+\left(e_{kj}+f_{kj}{c}_k\right)\sin \mathrm{\&theta;}\&rsqb;\\ =\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{a}_{ij}+\underset{k=4}{\overset{6}{\mathrm{\&Sigma;}}}\left(a_{kj}\cos \mathrm{\&theta;}+e_{kj}\sin \mathrm{\&theta;}\right)+\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{b}_{ij}{c}_i+\underset{k=4}{\overset{6}{\mathrm{\&Sigma;}}}\left(b_{kj}\cos \mathrm{\&theta;}+f_{kj}\sin \mathrm{\&theta;}\right)c_k\\ B_{jy}=\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{B}_{ijy}+\underset{k=4}{\overset{6}{\mathrm{\&Sigma;}}}{B}_{kjy}=\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}\left(e_{ij}+f_{ij}{c}_i\right)+\underset{k=4}{\overset{6}{\mathrm{\&Sigma;}}}\&lsqb;\left(e_{kj}+f_{kj}{c}_k\right)\cos \mathrm{\&theta;}-\left(a_{kj}+b_{kj}{c}_k\right)\sin \mathrm{\&theta;}\&rsqb;\\ =\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{e}_{ij}+\underset{k=4}{\overset{6}{\mathrm{\&Sigma;}}}\left(e_{kj}\cos \mathrm{\&theta;}-a_{kj}\sin \mathrm{\&theta;}\right)+\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{f}_{ij}{c}_i+\underset{k=4}{\overset{6}{\mathrm{\&Sigma;}}}\left(f_{kj}\cos \mathrm{\&theta;}-b_{kj}\sin \mathrm{\&theta;}\right)c_k\end{array}\right.---\left(11\right)$

(11) formula is a Linear Equations be made up of 6 equations obviously, by solving this system of equations, can obtain the sag of 6 power transmission lines.

4.2, the monitoring of power transmission line stress:

In the condition that 4.1 power transmission line sag c substitution (1) formulas obtained and power transmission line equation are set up above, namely

$\left\{\begin{array}{c}a\left(ch\frac{d}{a}-1\right)-c=0\\ ach\frac{l-d}{a}-ach\frac{d}{a}-h=0\end{array}\right.---\left(12\right)$

The stretched wire coefficient a of power transmission line can be obtained by computer programming and cut square d.In the ordinary course of things, the ratio of power transmission line carries and is carrying from anharmonic ratio of it.Namely

$\mathrm{\&gamma;}=\frac{9.8G_0}{A}\&times;{10}^{-3}---\left(13\right)$

G in formula ₀for the quality of power transmission line unit length, A is the sectional area of power transmission line.According to (2) Shi Ke get, now the stress of power transmission line minimum point and horizontal stress are

${\mathrm{\&sigma;}}_0=\frac{9.8{\mathrm{aG}}_0}{A}\&times;{10}^{-3}---\left(14\right)$

By the relation between power transmission line stress and horizontal stress, the stress that can obtain any point on power transmission line is:

${\mathrm{\&sigma;}}_x=\&lsqb;{\mathrm{\&sigma;}}_0+\frac{{\mathrm{\&gamma;}}^2{(l-2(x-x_A-d\left)\right)}^2}{8{\mathrm{\&sigma;}}_0}\&rsqb;\sqrt{1+{\left(\frac{h}{l}\right)}^2}-\frac{\mathrm{\&gamma;}(l-2(x-x_A-d))h}{2l}---\left(15\right)$

And the stress of side-by-side mounting point is respectively:

$\left\{\begin{array}{c}{\mathrm{\&sigma;}}_A={\mathrm{\&sigma;}}_0\&lsqb;\left(\sqrt{1+{\left(\frac{h}{\frac{2{\mathrm{\&sigma;}}_0}{\mathrm{\&gamma;}}sh\frac{\mathrm{\&gamma;}l}{2{\mathrm{\&sigma;}}_0}}\right)}^2}\right)ch\frac{\mathrm{\&gamma;}l}{2{\mathrm{\&sigma;}}_0}-\frac{\mathrm{\&gamma;}h}{2{\mathrm{\&sigma;}}_0}\&rsqb;\\ {\mathrm{\&sigma;}}_B={\mathrm{\&sigma;}}_0\&lsqb;\left(\sqrt{1+{\left(\frac{h}{\frac{2{\mathrm{\&sigma;}}_0}{\mathrm{\&gamma;}}sh\frac{\mathrm{\&gamma;}l}{2{\mathrm{\&sigma;}}_0}}\right)}^2}\right)ch\frac{\mathrm{\&gamma;}l}{2{\mathrm{\&sigma;}}_0}-\frac{\mathrm{\&gamma;}h}{2{\mathrm{\&sigma;}}_0}\&rsqb;\end{array}\right.---\left(16\right)$

4.3, other factors is on the impact in sensing point magnetic field and disposal route:

Sensing point magnetic field in fact should be power line current magnetic field, magnetic field of the earth and corona current magnetic field three vector superposed, therefore also should eliminate the impact of these two kinds of factors.

(1), the impact in magnetic field of the earth: the earth is a large magnet, around it, form magnetic field, and terrestrial magnetic field is more weak and more stable, with place or the change of time very little, namely the terrestrial magnetic field interference that is subject at one time of multiple Magnetic Sensor is substantially identical.Therefore the quantity of Magnetic Sensor can be increased, utilize differential principle, the equidirectional signal that Magnetic Sensor exports is subtracted each other between two, just can eliminate static and quasistatic undesired signal, thus improve detection accuracy.

(2), the impact of corona: because corona current is a desultory high-frequency pulse current, its generation has randomness and uncertainty, and power line current magnetic field is relatively stable, therefore phaselock technique process can be carried out to the magnetic signal detected, corona current magnetic field is effectively got rid of.

Claims (6)

1. the direct-current overhead power transmission line sag based on weak magnetic detection and stress monitoring method, it is characterized in that, shaft tower is selected multiple sensing point and settles Magnetic Sensor, utilize the characteristic distributions of power transmission line space magnetic field, in corresponding coordinate system, obtain the fitting linear equation of magnetic-field component that each root power transmission line produces at each sensing point place and power transmission line sag; On this basis by coordinate transform and magnetic field superposition principle, and build a Linear Equations by the method for difference, the sag of shaft tower both sides power transmission line can be solved, the horizontal stress of power transmission line is solved again by sag, and finally solve the stress intensity of any point on power transmission line, thus realize the Real-Time Monitoring to power transmission line sag and stress.

2. a kind of direct-current overhead power transmission line sag based on weak magnetic detection and stress monitoring method according to claim 1, is characterized in that comprising the following steps:

Choose arbitrarily three shaft towers of adjacent position, be labeled as No. 0 tower, No. 1 tower and No. 2 towers respectively.

Step one: set up X ' Y ' Z ' coordinate system to the power transmission line between No. 0 tower and No. 1 tower, wherein X ' Z ' plane is parallel to the plane at power transmission line place, and X ' direction of principal axis is parallel to the vertical join line direction of two shaft towers; XYZ coordinate system is set up for the power transmission line between No. 1 tower and No. 2 towers, and measurement obtains the coordinate of the left hitch point of corresponding power transmission line in respective coordinate system, and the correlation parameter of three shaft towers;

Step 2: select sensing point near the place of hitch point on No. 1 shaft tower, the quantity of sensing point is greater than the power transmission line quantity of shaft tower side, utilize the computing formula of power transmission line space magnetic field, in corresponding coordinate system, calculate that each root power transmission line produces at each sensing point place X ' (or X) magnetic-field component and the fitting linear equation of Y ' (or Y) magnetic-field component and power transmission line sag; By coordinate transform and magnetic field superposition principle, obtain each sensing point X-direction and the linear equation between Y-direction magnetic induction density component and No. 1 shaft tower both sides power transmission line sag in XYZ coordinate system, then to all linear equations difference between two, a Linear Equations containing all power transmission line sags is set up;

Step 3: settle Magnetic Sensor at sensing point position place, is the magnetic signal at sensing point place, and all Magnetic Sensor vector directional bearings and XYZ coordinate system is consistent by calibrating the magnetic signal making Magnetic Sensor measure;

Step 4: the X-direction detect Magnetic Sensor on shaft tower and the magnetic induction density component of Y-direction read in real time, substitutes in the Linear Equations obtained in step 2, finally obtains the sag of the power transmission line of No. 1 shaft tower side-by-side mounting;

Step 5: the sag calculated is substituted into the condition that power transmission line equation is set up, stretched wire coefficient and the intercept of power transmission line is obtained by computer programming, the ratio solving power transmission line under different meteorological conditions carries, utilize the relational expression of stretched wire coefficient and horizontal stress, solve the horizontal stress of power transmission line, then utilize the stress formula of any point on power transmission line finally to calculate the stress intensity of every bit on power transmission line.

3. a kind of direct-current overhead power transmission line sag based on weak magnetic detection and stress monitoring method according to claim 1 or 2, it is characterized in that, Magnetic Sensor quantity is greater than the power transmission line quantity of shaft tower side.

4. a kind of direct-current overhead power transmission line sag based on weak magnetic detection and stress monitoring method according to claim 1 or 2, it is characterized in that, Magnetic Sensor is twin shaft Magnetic Sensor or magnetic sensor, and the dimensional orientation of same shaft tower Magnetic Sensor is consistent or is quantitative geometric relationship.

5. a kind of direct-current overhead power transmission line sag based on weak magnetic detection and stress monitoring method according to claim 1 or 2, is characterized in that, in order to eliminate the impact in corona current magnetic field, can carry out phaselock technique process to the magnetic signal detected.

6. a kind of direct-current overhead power transmission line sag based on weak magnetic detection and stress monitoring method according to claim 1 or 2, it is characterized in that, in order to eliminate the impact of terrestrial magnetic field, the quantity of Magnetic Sensor can be increased, utilize differential principle, the equidirectional signal that Magnetic Sensor exports is subtracted each other between two.