WO2013185267A1

WO2013185267A1 - Method for measuring three-dimensional power frequency electric field based on transmission line equivalent surface charge curve integral

Info

Publication number: WO2013185267A1
Application number: PCT/CN2012/001267
Authority: WO
Inventors: 朱轲; 朱军; 刘凡; 吴广宁; 杨琳; 曹晓斌; 苏杰; 吴驰; 熊万亮; 邱璆
Original assignee: 四川电力科学研究院; 国家电网公司
Priority date: 2012-06-15
Filing date: 2012-09-14
Publication date: 2013-12-19
Also published as: CN102721875A

Abstract

A method for measuring a three-dimensional power frequency electric field based on transmission line equivalent surface charge curve integral. First, relevant parameters for calculating three-dimensional power frequency electric field strength of a transmission line are acquired. Next, a three-dimensional model of an unequal-height suspension transmission line is established based on a line catenary equation, the practical line height at the position of any point of the transmission line within the span is determined, the line equivalent surface charge at the position of any point of the transmission line within the span is further acquired by using unequal-height suspension transmission line equivalent surface charge curve integral, and in the end the spatial electric field strength distribution generated by a multi-line system when the lines at the two ends of the span are unequal in height is calculated according to the field strength superposition principle. The method can truthfully reflect the practical spatial erection condition of a high-voltage transmission line, which facilitates accurate calculation of spatial three-dimensional electric field strength of a high-voltage transmission line, so as to provide a reliable reference for evaluating the electromagnetic environment of a transmission line.

Description

Method for measuring three-dimensional power frequency electric field based on integral electric charge curve integral of transmission wire surface

Technical field

The invention relates to a method for measuring a three-dimensional power frequency electric field of a transmission line, in particular to a three-dimensional power frequency electric field measurement method based on the equivalent charge curve integral of a wire surface when the wires at both ends of the overhead transmission line are not equal.

Background technique

With the continuous development of China's economic construction, the demand for electricity and other energy sources has been rising, resulting in the continuous improvement of the voltage level of transmission lines and the increasing transmission power. Running overhead transmission lines generate charge on the wires, and the wires carrying the charge will excite the electric field in the surrounding space. The electric field strength around the transmission line, especially the electric field strength near the ground, is one of the main physical quantities for measuring the electromagnetic pollution level of the transmission line. The core problem of accurate calculation of electric field strength is the calculation of the equivalent charge on the surface of the wire.

For the calculation of the equivalent charge on the surface of overhead conductors, the existing theory mostly uses the average height of the conductor or the minimum height of the conductor as the calculated height. The actual transmission line is simplified to an infinitely long straight line parallel to the earth, and the electric field strength around the transmission line is established. The two-dimensional calculation model ignores the influence of the sag and the span of the overhead conductor on the calculation of the electric field strength. The two-dimensional calculation model of electric field strength is difficult to evaluate the influence of the factors such as the self-weight, wire load, stress and sag of the large-span super/UHV transmission line on the calculation of the spatial electric field strength.

Summary of the invention

The purpose of the invention is to determine the three-dimensional power frequency electric field strength of overhead transmission lines, and to propose a three-dimensional power frequency electric field measurement method based on the equivalent charge curve integral of the conductor surface, aiming at considering the sag and the gear distance of the overhead conductor to the electric field strength result. The effect of the wire surface equivalent charge is used to determine the spatial three-dimensional electric field strength of the overhead transmission line.

The object of the present invention is achieved by a method for determining a three-dimensional power frequency electric field based on the integral charge curve integral of a power transmission line, the calculation method comprising the following steps:

The first step is to obtain parameters for calculating the three-dimensional power frequency electric field strength of the transmission line, including the transmission line span, the transmission line lead erection height, the conductor arrangement parameters, and the wire mechanical parameters; the above-mentioned wire arrangement parameters refer to The relative position of the space between the phase conductors, the number of conductor splits and the splitting distance of the conductors. The mechanical parameters of the conductors are the guiding line radius, the load per unit section of the conductor unit length and the stress at the lowest point of the conductor. The second step is to use The high-suspension wire catenary equation is used to determine the actual height z of the wire at any point X in the transmission line of the unequal suspension, and determine the spatial distance parameter between any point on the high-voltage transmission line and its mirror point;

In the third step, based on the actual height Z of the wire at any point X in the range determined by the above calculation, and the spatial distance parameter between any point and its mirror point, the potential at any point on the wire is obtained, and then the micro-member segments of each transmission wire are obtained. The surface equivalent charge is subjected to curve integration to determine the equivalent charge of the surface of the wire at any point on the transmission line within the span;

The fourth step is to determine the electric field strength generated by the equivalent charge of each conductor surface in the gear space in the surrounding space, and use the field strength superposition technique to obtain the spatial electric field intensity distribution of the multi-conductor system when the conductors at both ends of the gear are not equal.

The above-mentioned wire catenary equation is used to determine the actual height of the wire at any point X in the range τ z ₌ ^ _c _rx _ _{l) + ff >} / _{0A ≤ x ≤} / _m

r ^σ ο

= o

-

Where, J. _A is the horizontal distance between the lowest point of the wire within the gear distance and the suspension point of the wire, Λ _Β is the horizontal distance between the lowest point of the wire within the gear and the suspension point of the other wire, and ^ represents the load on the interface of the unit length of the wire. σ. Indicates the horizontal stress at each point on the wire, that is, the stress at the lowest point of the wire, J indicates the transmission line pitch of the selected segment, Λ indicates the height difference between the suspension points of the two adjacent tower wires, and / indicates the lowest point of the wire. The height of the ground.

The spatial distance parameter between any point on the high-voltage transmission line and its mirror point is determined by the following formula:

4] = ^ ="( - ) ² + + (ch ^-ch 3⁄4] ²

^-\) + 2/

Where, , represents the spatial distance between the point on the wire Α (Α, 7i, A) and the point on the wire 03 03⁄4, y ₂ , z ₂ ), where ₂ represents the point on the wire z and the point on the mirror wire of the wire (. The spatial distance between r ₂ , _Λ , ζ ₂ ), π represents the spatial distance between the point on the mirrored wire of the wire ( (_r;, γ _λ , ζ;) and the point on the wire (x ₂ , Y _V z ₂ ) , ^ denotes the spatial distance between the point on the wire ( , y, z and its mirror point (the spatial distance between _ri, _Ά , ^, indicating the point ₂ , / ₂ , z ₂ on the wire) and its mirror point 03⁄4, _3⁄4, ^ L is the horizontal distance between the wire Λ and the wire ,, which is the X-direction coordinate of the wire Ά> ζ, x ₂ is the X-direction coordinate of the point ₂ , y ₂ , _Z2 on the wire; Point _Ά , ζ) X direction coordinates.

The potential φ at any point on a certain conductor of the above power transmission line is obtained by the following formula: ψ, = Ψυ + <3⁄4, + ··· + ψ,, + φ„ + φ, ', + φ _(Μ)! +■■■ + φ _η , ( ι ) In the formula (1), <^ + (3⁄4+<^ is the self-potential, and the calculation formula is: q. Λ ε ₀ ^_ε ι ,

^4πε ο R £ _0+e , ₂ ) _(ch Zi_ _I)+2y

In the formula (1), φ,, +φ ₂ , + + + φ _ί7+ι + ... + φ _∞ are mutual potentials, and the calculation formula is as follows: 0 CJ υ _{0 /oa} w ₀

In the above formula, φ is the potential at any point on the wire l, <p, which is the mutual charge at any point on the wire 1 at the equivalent charge at any point on the wire j and the equivalent charge at the mirror point, φ„ The self-potential generated by the point charge at any point and its mirror point at the point on the wire surface, φ,,, respectively, is the left and right charges of the wire and the mirror position of the wire within the interface of the calculated point. The self-potential generated by the charge at the wire surface at the calculation point, _£() represents the dielectric constant of air, £ represents the dielectric constant of the soil, ^ represents the point X on the wire j, γ _Ρ the X coordinate axis of the corresponding micro-element ^ Incremental, indicating the corresponding point ( _γ ) of the corresponding line on the mirror wire of the wire j, the increment of the coordinate axis of the corresponding micro-element, "indicating the point on the wire 1, y„ 2-,) any point on the left side C3⁄4L, y, ^ corresponding micro The X coordinate axis increment of the element, ^ represents the point on the mirrored wire of wire 1 03⁄4 γ,, ζ,) any point on the left side ( , _Λ , ζ _ζ ) the X coordinate axis increment of the corresponding micro element, dx _R represents the wire 1 point (, y _lt) to any point on the right side (a, 2R) x coordinate axis corresponding infinitesimal increment of "1 point lead (, y" r right Any point,,) corresponding infinitesimal incremental X coordinate axis 4, showing the point 3) surface of the corresponding conductor of infinitesimal equivalent charge on conductor j, it represents the point (corresponding to the y _f infinitesimal conductors of the lead wires j mirror The surface equivalent charge, which means any point on the left side of the wire 1 , yL, the equivalent charge of the wire surface of the corresponding micro-element, indicating the point on the mirror wire of wire 1 (·3⁄4, γ, any point on the left side ( , ^ ^) The equivalent charge of the wire surface of the corresponding micro-element, indicating any point on the right side of the wire 1 ( , yx, A) 3⁄4, ) the equivalent charge of the corresponding micro-element "3⁄4 wire surface, indicating the point on the mirror wire of wire 1 (·3⁄4;., γ,, ζ,) Any point on the right side, the corresponding surface charge of the corresponding micro-element ^3⁄4.

The surface equivalent charge of each of the above-mentioned electric wire micro-element segments is obtained by the following integral formula:

<1ι ₂

1ι

Where Ιλ is the rated voltage of the line, indicating the point on the wire 1 (A, , ζ θ corresponding micro-element "3⁄4 wire surface equivalent charge, indicating the corresponding point on the mirror wire of wire 1 ( ;, y ;) corresponding micro-element ^ The equivalent charge on the surface of the wire, indicating the equivalent charge on the surface of the wire 2 ( , yi, ) corresponding to the micro-element / ₂ , indicating the corresponding point on the mirror wire of wire 2 ( , , z ₂ ) Surface equivalent charge.

The electric field strength generated by the equivalent charge of each conductor surface in the above-mentioned span is determined by the following steps: the electric field strength generated by the wire ^ and its mirror wire at any point ³ , y, z) in the space to be sought is:

Where , , is a unit vector from ( , > ) pointing to x, y, z) and ( _Ά , ) to y, z), _P , 4> is a point ( _Ά , ) to / ⁵ (ΛΓ, y, And the distance from the point (_η, y ) to ³ y, for the same reason, the electric field strength generated by the wire J ₂ and its mirror wire at the point / ^x, y, _Z ) is -

Where e _p , is a unit vector from (. _1⁄2 y ₂ , z ₂ ) pointing to / ^x, y, z) and (. , γ ₂ , pointing to y, z), 厶-尸, 4 is the point y _v z ₂ ) to ^(χ, y, ζ) and the distance of points ( , γ ₂ , ) to Ρ(χ, y, ζ); using the field strength superposition technique, the synthetic electric field at P, y, z) The strength is:

The invention provides a method for integrating the equivalent charge curve based on the surface of the wire. The invention mainly comprises a transmission line model with unequal height suspension, a curve integral method for equivalent electric charge on the surface of the wire and a three-dimensional power frequency electric field calculation method;

The transmission line model of the unequal height suspension is used to obtain the actual height of the wire at any point within the transmission line distance under different meteorological conditions and line parameters;

The curve integral method of the equivalent electric charge on the surface of the wire is used to integrate the equivalent electric charge on the surface of the overhead wire when the wires at both ends of the gear are not equal, and obtain the equivalent electric charge on the surface of the wire at any point in the span.

The beneficial effects of the invention are:

(1) Establishing a space rectangular coordinate system with a ground point corresponding to the ground point as the coordinate origin in a range of the line, and deducing the catenary equation expression of the unequal suspension transmission line, based on this A three-dimensional model of the unequal suspension transmission line can be used to solve the actual ground height at any point of the conductor within the range.

(2) Based on the principle of mirror image and potential coefficient method to solve the equivalent charge theory of transmission line conductors in two-dimensional space, the method for solving the equivalent charge of the conductor surface on the two-conductor transmission line in three-dimensional space is obtained by stacking and matching the surface potential of the conductor.

(3) The method for solving the equivalent charge on the surface of the conductor on the two-conductor transmission line in the three-dimensional space is generalized, and the method for solving the equivalent charge of the upper surface of each sub-conductor when using the multi-conductor transmission line is obtained. The patented method is more practical.

The method can truly reflect the space erection of the actual high-voltage transmission line, and is beneficial to accurately calculate the spatial three-dimensional electric field strength of the high-voltage transmission line, and provides a reliable basis for evaluating the electromagnetic environment of the transmission line.

DRAWINGS

1 is a schematic view of a unequal suspension power transmission line model of the present invention. 2 is a schematic diagram of solving the surface equivalent electric charge of the micro-segment conductor of the transmission line of the present invention.

3 is a schematic diagram of solving the surface equivalent electric charge of each sub-wire of the multi-conductor system of the present invention.

4 is a schematic diagram of electric field strength calculation at any point in the above-ground space of the multi-conductor system of the present invention.

detailed description

The invention is based on a three-dimensional power frequency electric field measuring method for integrating the equivalent charge curve on the surface of a transmission wire, comprising the following steps:

The first step is to obtain parameters for calculating the three-dimensional power frequency electric field strength of the transmission line, including the transmission line span (refers to the horizontal distance between the suspension points of two adjacent tower wires), and the height of the conductor erection (refers to the erection of the conductors on two adjacent towers) Height), wire arrangement parameters (refer to the relative position of the space between the phase conductors, the number of splits and splitting of the wires), the mechanical parameters of the wire (guide line radius, the unit load of the unit length of the wire and the stress at the lowest point of the wire) ).

In the second step, the wire catenary equation of the unequal height suspension is used to replace the calculation method of the original transmission line wire height, and a three-dimensional model of the unequal height suspension transmission line is established (see Fig. 1), and then the following formula is used to determine the gear distance. The actual height z of the wire at any point xl _OA ≤ x ≤ l _OB ) (see Figure 1):

( 1 )

among them-

In the formula, 3⁄4 indicates the load on the interface of the unit length of the conductor, indicating the horizontal stress at each point on the conductor, that is, the stress at the lowest point of the conductor, / indicates the transmission line distance of the selected section, ^, respectively The height of the wire suspension point Α and Β to the ground (see Figure 1), indicating the height difference between the suspension points of the two adjacent tower wires (see Figure 1), indicating the height of the lowest point of the wire from the ground (ΧΟΥ plane) (see Figure 1) ).

Next, in the schematic diagram of the potential solution on the two overhead conductor microelements shown in FIG. 2, on the conductor 4, / ₂ Take the points ( , yx, ), {χ2, γι, corresponding to the micro-element ^ Λ, dh, which correspond to the mirrored wire micro-components, - corresponding points} ') and (1⁄2 Λ, · 3⁄4), using the above-mentioned range The formula for solving the actual height of the wire at any point in the position can be obtained by the following formula: / ₂ upper point ( , γχ, ΖΧ), (Χ2, yi, ) and its mirror point ( , _{λ λ} ) , (χ ₂ , the spatial distance parameter between γ ₂ and ζ ₂ ) (see Figure 2): , =2^-(ch^-l) + 2^

Υ (2)

{χ -χ ₂ ) ² +Z ² +[^(ch^-ch3⁄4

ϊ σ ₀ σ ₀

(3) =2^(ch^-l) + 2^

Υ σ ₀ (4)

4 = 4 = ( 5 )

Where, , represents the spatial distance between the point on the wire / ι ( , , ) and the point on the wire / ₂ ( , yi, Z2), ₂ represents the point on the wire A ( , , ) and the point on the mirror wire of the wire ( , The spatial distance between y ₂ , ), which represents the spatial distance between the point on the mirrored wire of the wire 4 (y _x , ^ and the point on the wire / ₂ Cr ₂ , .1⁄2, z ₂ ), indicating the point on the wire A ( , , ^ is the spatial distance between its mirror point ( y _v Ζ;), and ₂ is the spatial distance between the point on the wire / ₂ (·3⁄4, , ) and its mirror point ( , y ).

In the third step, based on the actual height z of the wire at any point in the gear distance obtained by the above-mentioned unequal suspension wire catenary equation, the curve integral method of the equivalent electric charge on the surface of the transmission line wire is unequal to any point X. The equivalent charge q of the wire surface is solved, and the functional expression of the equivalent electric charge on the surface of the wire in consideration of the factors such as the self-weight of the transmission line, the load of the wire, the stress and the sag can be obtained. The specific implementation process is as follows.

In the diagram of the potential solution on the two empty conductor micro-segment conductors shown in Figure 2, any point on the conductor (X yi, the power can be obtained by the formula:

4 ^πε ο / L _L , σ _{0 /qa} L _a σ ₀

Where, for the potential at any point on the wire 4, φ ₂₁ is the mutual charge at any point on the wire at the equivalent charge at any point on the wire / ₂ and the equivalent charge at the mirror point, _φι1 is any point on the wire The point charge at the mirror point and the self-potential generated at the point of the wire at the point, <?„, respectively, at the point where the calculated point is the interface, the left and right charges of the wire and their mirror position are at the calculation point. The self-potential generated at the surface of the wire, ε, represents the dielectric constant of air, and £ represents the dielectric constant of the soil, indicating the X-axis increment of the corresponding micro-eq of the point on the wire h ( , γι, ζ ₂ ), άχ _τ represents the X-axis increment of the corresponding pixel (^ γ ₂ , ζ ₂ ) on the mirrored wire of the wire h, indicating the point X on the wire - any point on the left side (.IL, , O, the X coordinate of the corresponding micro-element Axis increment, ^ ^ indicates the point on the mirrored wire of the wire (·3⁄4;, y _x , any point on the left side ( , , ), the coordinate increment of the corresponding micro-element ^3⁄4, d _R flashes the point n on the wire, gamma],) right of any point) corresponding infinitesimal "¾ of the x axis increment ^^ wire /! point _(, γι, a) right Any point corresponding infinitesimal "X axis increment ¾, showing the wire / ₂ points (· ½,, z ₂₎ the corresponding surface of the conductor infinitesimal ^ / ₂ equivalent charge, indicate corresponding lead wires on the mirror / ₂ Point (■3⁄4, _3⁄4, ) corresponds to the equivalent charge of the wire surface of the micro-element ₂ , indicating that the wire surface equivalent of any point (., L, A) on the left side of the wire 4 (., L, A) corresponds to the micro-element The charge, which represents the point on the left side of the point (^, γ, ζ) of the wire A of the wire A (, _3⁄4, ), corresponds to the equivalent charge of the wire of the corresponding micro-element 4, indicating any point on the right side of the wire 0n, VI, ^ ^, VR, 2R) the equivalent charge of the wire surface of the corresponding micro- _eq , k _R represents the point _Ά on the mirror wire of wire k, _Ζ] ) any point on the right side (4, , ) corresponding micro-element "3⁄4 wire surface, etc. Effective charge.

Among them, considering the influence of the self-weight of the transmission line, the load of the conductor, the stress and the sag on the space distance between the conductors in the gear distance, the surface equivalent charge of each conductor micro-element can be obtained by the following integral formula:

q, 9 (11) ε ₀ ^+ε ι

^£ o _ ^ε ι (12)

The invention considers that the conductor potential at any point within the transmission line span is the rated voltage of the line, ie

IA, 1⁄2 is the rated voltage of the line; and the conductor potential at any point consists of two parts: 1 the self-potential generated at the calculation point by the equivalent charge at the position other than the calculation point and its mirror point on the conductor, 2 other The equivalent charge at any point on the wire and the equipotential of the equivalent charge at the corresponding point of the mirrored wire at the calculated point of the wire. As shown in Figure 2, the potential at the point ( , , ) on the wire is equal to: 1 The equivalent charge at the point other than the point ( , yx , ) and its mirror point (·3⁄4, y ) is at the point ( .n, y , the self-potential generated at the point, the equivalent charge at any point ( , yi, z ₂ ) on the 2 wire ^ and its mirror point C3⁄4, Λ, the equivalent charge at the point on the wire /1 ( , The mutual potential generated at 1,), that is, the surface potential of the wire at the point (, γ _λ , ) on the wire 4 is:

ι

. ⁷ ) Solving this equation, you can consider the weight of the transmission line conductor, the conductor load, the stress and the sag The functional expression q _x = Λχ) of the equivalent charge on the upper surface of the wire h in the pitch. In the calculation model of the equivalent charge on the surface of the two wires, the above work is repeated due to the symmetry of the wire Λ and the wire / ₂ . Similarly, the functional expression of the equivalent charge on the upper surface of the wire = = = Λχ,)\ _{Χι =Χι} .

The invention patent can solve the equivalent electric charge on the surface of each wire in the multi-conductor system by establishing a calculation model for the equivalent electric charge of each sub-wire surface of the multi-conductor system (see Fig. 3). As shown in Figure 2, the potential φ of the surface point (" y„) of the wire i is:

Ψ, = Ψυ + φ _2ι +-.. + φ,, + φ,, + ψ,, + ψ _{Μ) , + ··· + <?„, (18) Solve this formula, Considering the self-weight of the transmission line, the load of the conductor, the function of the equivalent charge on the upper surface of the conductor 1 under the factors of stress and sag, etc. = Λχ,) where φ,, +<3⁄4+ is the self-potential, The calculation formula is _:

Ψχ, + <ρ ₂ , +... + φ(, — _Ό , + ψ _{Μ) , +■■■+ φ„„ is a mutual potential, and the formula is as follows: (1≤ ≤/〃 and ≠/) (22 )

In the fourth step, the equivalent electric charge of the wire surface at any point on each wire in the gear distance is obtained, and the electric field intensity generated by the equivalent electric charge of each wire surface in the gear distance at any point in the surrounding space can be obtained, and the field strength superposition technique can be used to obtain The spatial electric field strength distribution of the multi-conductor system when the conductors at both ends of the gear are not equal.

The calculation of the spatial electric field strength considering the unequal height of the wires at both ends of the gear is shown in Fig. 4. In Fig. 4, J\x, y is any point in the space to be solved, which is the wire/[upper point (y 4) Wire micro segment,

^ is the wire segment at its mirror point ( y _x , z), which is a unit vector from 0, _Ά , ζ, ) to ^, , and ( , γ ζ;) to vr, , , Ζ ^ is the distance between points ( , _x , ) to ( , y , and points ( . η , _Ά , ) to ^, ,. Within one gear shown in Figure 4, the wire Λ π The electric field strength 及其 produced by the mirror wire and its mirror wire is:

Similarly, repeat the above work. In a gear width shown in Figure 4, the electric field 4 intensity A produced by the wire / ₂ and its mirror wire at \x, y, z) is: (24)

++

4

Where e _p , is a unit vector from ( , y ₂ , pointing to 7 r, ' and from ( , ' ^:) to ' ζ ), , as a point (·3⁄4, Λ, ) to , and a point (·3⁄4 , Λ, ) to Λ^, y, z).

Using the field strength superposition technique, in the calculation of the spatial electric field strength shown in Figure 4, the combined electric field strength ^ at the point is:

→ → → ^ d → ^/o ? dL → '°fq,dL → '. Fq ₂ dL → ^ _c ,

E _P = E, + E ₂ = J ^yi e _p + J ^y '' + j ^y2 + J ² (25 ) The effects obtained by the method of the present invention are obvious:

2

(1) A 3-space Cartesian coordinate system is established within the range of one gear of the line with the lowest point of the conductor corresponding to the ground position as the coordinate origin, and the equation of the catenary equation of the unequal suspension transmission line is derived. A three-dimensional model of unequal suspension transmission lines is established, which can solve the actual ground height at any point of the conductors in the gear range;

(2) Based on the principle of mirror image and potential coefficient method to solve the equivalent charge theory of transmission line conductors in two-dimensional space, the method for solving the equivalent charge of the conductor surface on the two-conductor transmission line in three-dimensional space is obtained by stacking and matching the surface potential of the conductor;

The three-dimensional power frequency electric field calculation method based on the equivalent charge curve integral of the wire surface proposed by the present invention will be described in detail below with reference to the accompanying drawings and embodiments:

In the first step, parameters for calculating the three-dimensional power frequency electric field strength of the transmission line are obtained. Transmission line tower technology is 2 base, the length of the gear is 450m, the suspension of three-phase wire is high, the height of the suspension point is 24m, the wires are horizontally arranged, the distance between the phases is 14m, the minimum distance of the wire is 16m from the ground, and the wire type is 4xLGJ-300/25, each phase The splitting pitch is 450mm, the wire radius is 11.88mm, the minimum point stress of the wire sag is 100.099N/mm ² , and the wire safety factor is 2.5.

In the second step, a three-dimensional model of the transmission line is established according to the above line parameters and the wire catenary equation of the unequal height suspension proposed by the present invention.

Solve the catenary equation of the three-phase transmission line and its mirror wire according to the above formula (1), and then determine the actual height of the wire at any point on the three-phase transmission line and its mirror wire in the gear range, and then use the above formula (2) ) - (5) The spatial distance parameter between any point on the transmission line and its mirror point can be obtained.

In the third step, using the catenary equation of the three-phase transmission line and its mirror wire obtained in the second step, according to the above formula (6) - (22), the position of the transmission line in the range can be obtained. The equivalent charge of the wire surface.

In the fourth step, using the equivalent electric charge on the surface of the conductor at any point on the conductors in the third step, the three-phase transmission line in the range can be obtained according to the above formula (23)-(25). The distribution of the total electric field strength produced by the surrounding space.

Claims

Claim

A method for determining a three-dimensional power frequency electric field based on an integral charge curve integral of a power transmission line, wherein the calculation method comprises the following steps:

The first step is to obtain parameters for calculating the three-dimensional power frequency electric field strength of the transmission line, including the transmission line spacing, the transmission line conductor erection height, the conductor arrangement parameters, and the wire mechanical parameters; the above-mentioned wire arrangement parameters refer to the spatial relative position between the phase conductors. , the number of wire splits and the splitting distance of the wire. The mechanical parameters of the wire are the guide wire radius, the load per unit section of the wire and the stress at the lowest point of the wire. The second step is to use the wire catenary equation of the suspension with unequal height. Calculate the actual height z of the wire at any point X in the transmission line of the unequal height suspension, and determine the spatial distance parameter between any point on the high-voltage transmission line and its mirror point;

2. The method for determining a three-dimensional power frequency electric field based on an equivalent charge curve integral of a power transmission line according to claim 1, wherein the wire hanging equation is used to determine any point X in the gear range. The actual height of the wire at position z:

₌ ^ _(ch H _i _{) +} ^ /. _A ≤.r≤/ _OB

:

Where, J. _A is the horizontal distance between the lowest point of the wire within the gear and the suspension point of the wire, J. _B is the horizontal distance between the lowest point of the wire within the gear distance and the suspension point of the other wire, indicating that the wire unit length unit is on the interface Load, σ. Indicates the horizontal stress at each point on the conductor, that is, the stress at the lowest point of the conductor, i indicates the transmission line spacing of the selected section, and Λ indicates the height difference between the suspension points of the two adjacent towers, indicating that the lowest point of the conductor is 0 from the ground. the height of.

3. A method for determining a three-dimensional power frequency electric field based on an equivalent charge curve integral of a power transmission line according to claim 2, wherein a spatial distance parameter between any point on the high voltage transmission line and its mirror point is pressed. The following formula determines:

, =2^(ch^-l) + 2^

4=J(3⁄4--3⁄4) ² + ^ ² + (c ^ +ch + 2{H- ^)] In the formula ² , Z ₂₁ represents the point on the wire ( , and the point on the wire 7 7 ₂ ) The spatial distance, 4 ₂ represents the spatial distance between the point 7» on the wire and the point C3⁄4, y ₂ , z ₂ ) on the mirrored wire of the wire, and π represents the point Gr, y _x , ζ on the mirror wire of the wire; The spatial distance between the points on the wire J ₂ ( ₂ , y _v z ₂ ), 4 indicates the spatial distance between the point on the wire (A, YA) and its mirror point ( _Ά , zi), and ^ indicates the point 0f on the wire J ₂ ₂ , y ₂ , ) and its mirror point), the horizontal distance between the wire and the wire, _Xl is the point on the wire (^, Ά, the X-direction coordinate, the point on the wire ₂ , 7 ₂ , ) The direction coordinate is the point on the mirrored wire of the wire ( , y ζ _χ X direction coordinate.

4. A method for measuring a three-dimensional power frequency electric field based on an equivalent charge curve integral of a power transmission line according to claim 3, wherein a potential φ at a position on a certain conductor of the power transmission line is as follows: The formula is: ψ, = ψχ, + <3⁄4, + ··· + φ,, + ψ,, + ψη" + ψ _{Μ) , +...+p _m , α ) In the formula (1), φ„ For the self-potential, the formula is:

In the formula (1), (^υ .-. + φ^ + φ^, +.'Ί is a mutual potential, and the calculation formula is as follows:

In the above formula, φ is the potential at any point on the wire i, φ is the mutual charge at any point on the wire j and the equivalent charge at the mirror point, and the mutual potential generated at any point on the wire 1, φ is the wire The point charge at any point on i and its mirror point at the point where the self-potential generated on the surface of the wire, φ,,, respectively, is the charge at the left and right sides of the wire and the mirror position at the interface of the calculated point. The self-potential, ε, produced at the wire surface at this point of calculation. Indicates the dielectric constant of air, ^ denotes the dielectric constant of the soil, denotes the point X on the wire j, y ^ the increment of the X coordinate axis of the corresponding microelement, ^^ denotes the corresponding point on the mirrored wire of the wire j (y _f ) The increment of the x-axis of the micro-element, "indicates the point on the wire 1 ^, γ „ _Ά ) the X-axis increment of the corresponding micro-element at any point on the left side ( , yL, 2L), indicating the point γ on the mirrored wire of the wire 1 , ζ,) any point on the left side ( , _Λ , ) the X coordinate axis increment of the corresponding micro-element dt _L , dx _R represents the point on the wire 1 r" γ„ ζ,) any point on the right side γκ, 2R) corresponding micro-element The increment of the χ axis, "point 1 on the wire 1, y _lf 2;) any point on the right side, z _R ) the corresponding X-axis increment of the micro-e! _R , representing the wire of the corresponding micro-element on the wire j The surface equivalent charge, which represents the corresponding point on the mirror wire of the wire j (y _f equivalent to the wire surface of the corresponding micro-element, indicating the point on the wire y„ i) any point on the left side ^, y, A) corresponding micro-element ^ I The equivalent charge on the surface of the wire, indicating the point on the mirror wire of wire 1, the point on the left side of z, 任一_Ζ , _Λ , Γ _ζ ) the equivalent charge of the wire surface of the corresponding micro-element, indicating the point on wire 1 ( , Yx, ) any point on the right side, ) the corresponding micro-element wire The equivalent charge on the surface indicates the equivalent charge of the surface of the corresponding micro-element of the corresponding point on the right side of the point ( _Λ , ) on the mirrored wire of the wire i.

5. The method according to claim 4, wherein the surface equivalent electric charge of each of the transmission line micro-element segments is determined by the following integral formula: 2 = =

ε ₀ + ^ε ι

ε _η -ε,

twenty two

Εο— ^ε ι

ε ₀ + ^ε ι ln '22

R

= ι = 2πε. J ch^«3⁄4- ₂

_{_{_{<> Α ι η ι η _}}} 1η 2 (4)

RR Ζ, ₂

Where ΙΑ is the rated voltage of the line, indicating the point on the wire 1 ( , , the equivalent charge of the wire surface of the corresponding micro-element, indicating the corresponding point on the mirror wire of the wire 1 (·τ;, γ corresponding to the wire surface of the micro-component ^ The equivalent charge indicates the equivalent charge of the surface of the corresponding micro-element (3,4) on the wire 2, and ^ represents the equivalent charge of the corresponding surface of the corresponding micro-element on the mirrored wire of the wire 2.

6. A method for determining a three-dimensional power frequency electric field based on an equivalent charge curve integral of a power transmission line according to claim 5, wherein the electric field strength generated by the equivalent charge of each conductor surface in the range is spatially generated. Follow the steps below to determine: The wire Λ and its mirror wire are at any point in the space to be sought, 7-

The electric field strength generated at _Z ) is -

In the formula, y _x (pointing to P(x, y, z) and (, _Ά , ζ) points to POf, γ, unit vector, corpse is point, ζ,) to the corpse (x, y , ζ) and point _Ά , ζ) to / ³ y, z) distance; for the same reason, the electric field strength generated by the wire i ₂ and its mirror wire at the point P f, y, z) is:

Where , , is a unit vector from ( , Λ , ) to ?, z) and from ( , Λ , ) to ζ), Α , > is a point ( , Λ , ) to χ, y, _Z ) and a point ( , y ₂ , ) to ·, y, z); using the field strength superposition technique, the synthetic electric field strength at P, y, z) is: