CN105353218A - Method for calculating split wire AC resistance and self inductance with consideration of proximity effect and skin effect - Google Patents

Abstract

The invention provides a method for calculating split wire AC resistance and self inductance with the consideration of a proximity effect and a skin effect, belonging to the field of AC impedance parameter calculation of split wires. According to the method, the proximity effect and the skin effect of the split wires are converted into a change of an equivalent flow area, an equivalent area function sequence which is changed with the geometric dimension and relative position of the wires is constructed, and the functions of the proximity effect and the skin effect are reflected by the size of a wire equivalent cross section. The calculation formula of conductor equivalent complex impedance with conductor radius and flow frequency changes is provided in the condition of a large scale (a condition that d is much smaller than a is not satisfied, d is current penetration depth, and a is a conductor outer radius). The calculation method and formula of multiple split wires with the consideration of proximity effect and skin effect equivalent areas are given, and thus the calculation method of an equivalent AC resistance is obtained. According to the conductive wire current resistance, an equivalent inner radius is obtained, and thus the conductive wire inner self inductance with the consideration of the proximity effect and the skin effect is calculated.

Description

Consider proximity effect and the split conductor AC resistance of skin effect and the computing method of interior self-induction

Technical field

The AC impedance parameter that the invention belongs to split conductor calculates field.The present invention is converted into the change of equivalent flow area the skin effect of split conductor and proximity effect, construct the equivalent area sequence of function of the physical dimension with wire, relative position change, with the size of wire equivalence cross-sectional area, the effect of reflection skin effect and proximity effect.Propose large scale and (do not meet d < < a, d is the depth of current penetration, a is conductor external radius) time, conductor complex equivalent impedance is with the computing formula of conductor radius, through-flow frequency change, propose the computing formula of common conductors complex equivalent impedance with conductor radius, through-flow frequency change, for power frequency minor radius conductor parameter calculates the foundation providing reference; Give two, three, four, six-multiple conductor considers computing method and the computing formula of skin effect and proximity effect equivalent area, give two, three, four, six-multiple conductor considers the computing method of skin effect and proximity effect equivalent AC resistance.Its equivalent inside radius is drawn according to the AC resistance of wire, and then self-induction in the wire of calculating consideration skin effect and proximity effect.

Background technology

The direct current resistance of conductor is an important parameter of examination conductor performance.But for exchanging the conductor of transmission, due to the existence of skin effect, the current density in conductor is not be uniformly distributed, but reduces gradually to center along conductor is radial on surface, thus the effective resistance of same wire is just greater than its direct current resistance, AC resistance that Here it is.Along with the continuous increase of power transmission capabilities, the electric pressure of power transmission line is more and more higher, and the sectional area of conductor is also increasing.But due to the problem of the AC resistance increase that skin effect causes, people have to be carried out in a different manner by large size conductor splitting the increase reducing AC resistance.When using split conductor, the proximity effect between parallel conductor can have an impact to the AC resistance of conductor and interior self-induction jointly along with heading spacing is different from skin effect.

The skin effect of conductor and proximity effect are the key factors affecting AC resistance.When wire is in alternating electromagnetic field, due to electromagnetic induction, make electric current or magnetic flux skewness in the conductor, the closer to surface its current density or magnetic flux density larger, this phenomenon is called as skin effect.Skin effect can cause AC resistance increase along with frequency and increase, and causes wire transmission current efficiency to lower, and expends metals resources.Skin effect is a complicated problem, when the aluminium lamination of wire is thicker, calculates the impact that AC resistance must take into account skin effect.Experiment and research show, single material twisted wire is with same diameter, have identical AC resistance with the solid cylindrical wire of direct current resistance, and the aluminium lamination of the steel-cored aluminium strand skin that becomes also can be similar to tubular cylinder shape wire.The existing computing method to wire AC resistance mainly contain kelvin effect algorithm and Japanese JCS0374 algorithm etc. based on Bessel function.These algorithms generally do not consider that the different proximity effect of the difference generation of split conductor heading spacing is on the impact of conductor AC resistance.Meanwhile, when conductor close to each other is by exchange current, different when the distribution of current in each conductor and its individualism, can be subject to the impact of proximity conductor, this calls " proximity effect ".The existing transmission line proximity effect analytical approach that damages mainly contains: magnetic vector method, impedance circuit method, Symbolic analysis and finite element method etc.Above method is to be considered separately skin effect or considers proximity effect separately, considers not enough on the impact produced split conductor when skin effect and proximity effect acting in conjunction.

Summary of the invention

The present invention is converted into the change of equivalent flow area the skin effect of split conductor and proximity effect, construct the equivalent area sequence of function of the physical dimension with wire, relative position change, with the size of wire equivalence cross-sectional area, the effect of concentrated expression skin effect and proximity effect.Propose large scale and (do not meet d < < a, d is the depth of current penetration, a is conductor external radius) wire complex equivalent impedance with the computing formula of conductor radius, through-flow frequency change, propose the computing formula of common conductors complex equivalent impedance with conductor radius, through-flow frequency change; Give two, three, four, six-multiple conductor considers computing method and the computing formula of skin effect and proximity effect equivalent area, give two, three, four, six-multiple conductor considers the computing method of skin effect and proximity effect equivalent AC resistance.Its equivalent inside radius is drawn according to the AC resistance of wire, and then self-induction in the wire of calculating consideration skin effect and proximity effect.

Inventor to two, the magnetic field of conductors on quad bundled and distribution of current emulate, as accompanying drawing 1-6, as can be seen from simulation result, the AC current density of split conductor is very uneven, magnetic field and current density are concentrated all laterally, the joint effect being subject to proximity effect and skin effect is presented the uneven distribution as figure by proof distribution of current wherein, and along with the change of wire heading spacing, proximity effect and skin effect acting in conjunction also can produce different impacts to the impact of distribution of current in wire.This impact will cause the change of split conductor AC resistance, and namely wire AC resistance not only receives the impact of skin effect, but with the heading spacing joint effect that be subject to proximity effect and skin effect different from division number.

The present invention constructs an equivalent area sequence, and this area changes with the spacing of split conductor, and when wire almost abuts against together, having the greatest impact of proximity effect, equivalent area is minimum.When separation becomes large, proximity effect weakens, and equivalent area increases gradually, and when separation is infinitely great, do not have proximity effect, only have skin effect, equivalent area is maximum.

Binary fission wire shown in accompanying drawing 7, when by alternating current, the outside to two wires is concentrated by electric current.If C1 point is current versus action center (line current, equivalent current axle) in accompanying drawing 7.With C1 point for the center of circle, wire external radius is that radius does a circle, and the area of the public part of this circle and wire diameter circle is defined as equivalent area S _e1.The symmetric points C place of C1 point in circle, does the circle that take wire diameter as radius, and this figure and wire diameter justify the area equation that the area of public part and C1 place obtain, as shown in Figure 8.

The present invention is taken as the inverse point (C point and true origin are about external diameter circle symmetry) of wire diameter circle C point.Then there is d=2h, R ₂ ²=h ²-b ².When two wires are almost close together, h=R ₂, b=0, C point is in true origin position, and the public area of two circles is minimum, and now proximity effect has the greatest impact; When two wire infinity from time, b ≈ h, C point overlaps with the wire diameter center of circle, two circle public areas maximum, now there is no proximity effect, only have skin effect; When two separations are finite value, the public area of two circles changes between minimum and maximum value, now proximity effect and skin effect acting in conjunction.Thus define an equivalent area sequence with two wire relative position changes.

Order (wire diameter radius of circle), two circles are respectively (x+h) ²+ y ²=a ², (x+b) ²+ y ²=a ², then dash area is equivalent area.As shown in Figure 8, definite integral is got to hatched area in figure:

$S_{E1}=\underset{shadow}{\&Integral;\&Integral;}dS$

$S_{E1}=2a^{2}arccos\frac{H-B}{2a}-a^{2}sin\left(2arccos\frac{H-B}{2a}\right)---\left(1\right)$

To the binary fission wire shown in accompanying drawing 8, H=h, B=b in above formula, the equivalent area sequence of this structure is consistent with the variation tendency of binary fission proximity effect.In like manner can obtain three, four, the equivalent area computing formula of six-multiple conductor, the computing formula through derivation equivalent area is identical with formula 1, and just the value of H and B is different.To the tripartition wire shown in accompanying drawing 9, $H=\frac{2}{3}\sqrt{3}h,B=\frac{\sqrt{3}}{6}h+\frac{\sqrt{3}}{2}b.$ To 4 split conductors,

$H=\sqrt{2}h$

$B=\frac{1}{2}\sqrt{2h^2-a^2}+\frac{\sqrt{2}}{4}(h+b)$

To 6 split conductors,

H＝2h

$B=\frac{7h+b+\sqrt{9h^2-3a^2}+4\sqrt{4h^2-3a^2}}{8}$

Above several formula is brought into S _e1expression formula, can obtain three respectively, four, equivalent area that six-multiple conductor is corresponding.

The present invention proposes and propose the computing formula of large scale wire complex equivalent impedance with wire radius, through-flow frequency change.To the uniform plane wave in conducting medium, if ripple is propagated along the y-axis direction, as accompanying drawing 10, then have:

${\stackrel{\&CenterDot;}{E}}_z=\stackrel{\&CenterDot;}{E_z^{+}}{e}^{-\mathrm{\&Gamma;}y}$

${\stackrel{\&CenterDot;}{H}}_x=\stackrel{\&CenterDot;}{H_x^{+}}{e}^{-\mathrm{\&Gamma;}y}$

${\stackrel{\&CenterDot;}{J}}_Z=\mathrm{\&gamma;}\stackrel{\&CenterDot;}{E_z^{+}}{e}^{-\mathrm{\&Gamma;}y}$

${\stackrel{\&CenterDot;}{H}}_x=\frac{{\stackrel{\&CenterDot;}{E}}_z}{Z_c}$

${\stackrel{*}{H}}_x=\frac{{\stackrel{*}{E}}_z}{{\stackrel{*}{Z}}_c}$

Wherein, be respectively the z component of electric field intensity phasor, the x component of magnetic field intensity phasor and the z component of current density phasor.

$\mathrm{\&Gamma;}=\mathrm{\&alpha;}+j\mathrm{\&beta;}=\mathrm{\&omega;}\sqrt{\frac{\mathrm{\&mu;}\mathrm{\&epsiv;}}{2}(\sqrt{1+\frac{{\mathrm{\&gamma;}}^2}{{\mathrm{\&omega;}}^2{\mathrm{\&epsiv;}}^2}}-1)}+j\mathrm{\&omega;}\sqrt{\frac{\mathrm{\&mu;}\mathrm{\&epsiv;}}{2}(\sqrt{1+\frac{{\mathrm{\&gamma;}}^2}{{\mathrm{\&omega;}}^2{\mathrm{\&epsiv;}}^2}}+1)}$

$\mathrm{\&alpha;}=\mathrm{\&omega;}\sqrt{\frac{\mathrm{\&mu;}\mathrm{\&epsiv;}}{2}(\sqrt{1+\frac{{\mathrm{\&gamma;}}^2}{{\mathrm{\&omega;}}^2{\mathrm{\&epsiv;}}^2}}-1)}$

$\mathrm{\&beta;}=\mathrm{\&omega;}\sqrt{\frac{\mathrm{\&mu;}\mathrm{\&epsiv;}}{2}(\sqrt{1+\frac{{\mathrm{\&gamma;}}^2}{{\mathrm{\&omega;}}^2{\mathrm{\&epsiv;}}^2}}+1)}$

$Z_c=\frac{{\stackrel{\&CenterDot;}{E}}_z}{{\stackrel{\&CenterDot;}{H}}_x}=\sqrt{\frac{\mathrm{\&mu;}}{\mathrm{\&epsiv;}(1-j\frac{\mathrm{\&gamma;}}{\mathrm{\&omega;}\mathrm{\&epsiv;}})}}$

The depth of penetration $d=\frac{1}{\mathrm{\&alpha;}}=\frac{1}{\mathrm{\&omega;}\sqrt{\frac{\mathrm{\&mu;}\mathrm{\&epsiv;}}{2}(\sqrt{1+\frac{{\mathrm{\&gamma;}}^2}{{\mathrm{\&omega;}}^2{\mathrm{\&epsiv;}}^2}}-1)}}$

When meeting time,

$\mathrm{\&Gamma;}=(1+j)\sqrt{\frac{\mathrm{\&omega;}\mathrm{\&mu;}\mathrm{\&gamma;}}{2}}=\mathrm{\&alpha;}+j\mathrm{\&beta;}$

$Z_c=\sqrt{\frac{j\mathrm{\&omega;}\mathrm{\&mu;}}{\mathrm{\&gamma;}}}=\frac{\sqrt{2}}{2}(1+j)\sqrt{\frac{\mathrm{\&omega;}\mathrm{\&mu;}}{\mathrm{\&gamma;}}}$

$d=\sqrt{\frac{2}{\mathrm{\&omega;}\mathrm{\&mu;}\mathrm{\&gamma;}}}$

Corresponding multiple Poynting vector:

$\tilde{S}={\stackrel{\&CenterDot;}{E}}_z{\stackrel{*}{H}}_x\left(\stackrel{\&RightArrow;}{e_y}\right)$

Bring into :

$\tilde{S}=\frac{|E_z^{+}{|}^2{e}^{-2\mathrm{\&alpha;}y}\frac{\sqrt{2}}{2}(1+j)}{\sqrt{\frac{\mathrm{\&omega;}\mathrm{\&mu;}}{\mathrm{\&gamma;}}}}\left(\stackrel{\&RightArrow;}{e_y}\right)$

By cylindrical conductor circumferentially often some consistance to the center of circle, get encirclement cylindrical conductor and get a cylindric closed surface S of unit length, can be obtained by Poynting theorem:

Wherein:

$\begin{array}{c}I=\mathrm{\&gamma;}\stackrel{\&CenterDot;}{E_z^{+}}{e}^{-\mathrm{\&Gamma;}a}{\&Integral;}_0^a{e}^{\mathrm{\&Gamma;}r}\&CenterDot;2\mathrm{\&pi;}rdr\\ =\frac{2\mathrm{\&pi;}\mathrm{\&gamma;}{\stackrel{\&CenterDot;}{E}}_z}{{\mathrm{\&Gamma;}}^2}\&lsqb;a\mathrm{\&Gamma;}-\left(1-e^{-\mathrm{\&Gamma;}a}\right)\&rsqb;\end{array}$

I is brought into and can try to achieve:

$R+jX=\frac{\frac{\sqrt{2}}{2}(1+j)a}{2{\mathrm{\&pi;\&gamma;}}^2{\left|\frac{a\mathrm{\&Gamma;}-(1-e^{-\mathrm{\&Gamma;}a})}{{\mathrm{\&Gamma;}}^2}\right|}^2\sqrt{\frac{\mathrm{\&omega;}\mathrm{\&mu;}}{\mathrm{\&gamma;}}}}---\left(2\right)$

When frequency is very high,

$R+jX=\frac{a}{2{\mathrm{\&pi;\&gamma;}}^2\stackrel{*}{Z_c}|\frac{a\mathrm{\&Gamma;}-(1-e^{-\mathrm{\&Gamma;}a})}{{\mathrm{\&Gamma;}}^2}{|}^2}---\left(3\right)$

Wherein a is external radius, for the depth of penetration, to power frequency good conductor, get ω=2 π f=100 π rad/s, π × 10, μ=4 ^-7h/m, γ _al=4 × 10 ⁷s/m (Al: aluminium).Then depth of penetration d ≈ 0.0113m.

The condition that formula (2) (3) set up is d < < a, and general wire and split conductor all can not meet this condition.To power frequency good conductor, the depth of penetration, than an external radius also large order of magnitude of general wire, therefore needs to find new computing method.But (2) (3) formula is set up actual or imaginary Large cylinder and hollow cylindrical wire, can demarcate and verify by (2) (3) formula to other formula.

The present invention proposes the computing formula of common conductors complex equivalent impedance with conductor radius, through-flow frequency change, namely this formula is applicable to the large wire of cross sectional radius and is also applicable to the little wire of cross sectional radius.The circular wire in single cross section as shown in Figure 11.On excircle, each point is completely the same to the center of circle, and it is similar that any one crosses distribution of current in electric current on the profile of axis and conductive plate.If the electric current of cylindric wire is along the z-axis direction, then have:

${\stackrel{\&CenterDot;}{J}}_z=-{\stackrel{\&CenterDot;}{H}}_0\frac{\mathrm{\&Gamma;}sh\mathrm{\&Gamma;}(r-R_1)}{ch\mathrm{\&Gamma;}(R_2-R_1)}$

${\stackrel{\&CenterDot;}{H}}_a=\frac{{\stackrel{\&CenterDot;}{H}}_{0}ch\mathrm{\&Gamma;}\left(r-R_1\right)}{ch\mathrm{\&Gamma;}\left(R_2-R_1\right)}$

The electromagnetic power transmitted vertically if do not consider, electric field intensity only has z component, then

${\stackrel{\&CenterDot;}{E}}_z=-\frac{{\stackrel{\&CenterDot;}{H}}_0\mathrm{\&Gamma;}sh\mathrm{\&Gamma;}\left(r-R_1\right)}{\mathrm{\&gamma;}ch\mathrm{\&Gamma;}\left(R_2-R_1\right)}$

Then Poynting vector (Poyntingvector) is again:

$\tilde{S}={\stackrel{\&CenterDot;}{E}}_z{\stackrel{*}{H}}_a{\stackrel{\&RightArrow;}{e}}_r$

R in various is the distance of any point to axis (z-axis), for the unit vector in r direction, R ₁, R ₂be respectively the interior external radius of conductor.

$\tilde{S}=-\frac{H_0^2\mathrm{\&Gamma;}sh\mathrm{\&Gamma;}\left(r-R_1\right)ch\stackrel{*}{\mathrm{\&Gamma;}}\left(r-R_1\right)}{\mathrm{\&gamma;}ch\mathrm{\&Gamma;}(R_2-R_1)ch\stackrel{*}{\mathrm{\&Gamma;}}(R_2-R_1)}\stackrel{\&RightArrow;}{e_r}---\left(4\right)$

Get the cylindric closed surface that axial unit length hard-pressed bale encloses outer conductor, then:

$\stackrel{\&CenterDot;}{I}={\&Integral;}_{R_1}^{R_2}{\stackrel{\&CenterDot;}{J}}_z\left(2\mathrm{\&pi;}rdr\right)$

$\stackrel{\&CenterDot;}{I}=-\frac{2\mathrm{\&pi;}{\stackrel{\&CenterDot;}{H}}_0}{ch\mathrm{\&Gamma;}\left(R_2-R_1\right)}\&lsqb;R_{2}ch\mathrm{\&Gamma;}(R_2-R_1)-R_1-\frac{1}{\mathrm{\&Gamma;}}sh\mathrm{\&Gamma;}(R_2-R_1)\&rsqb;---\left(6\right)$

By Poynting theorem (Poyntingtheorem)

$R+jX=\frac{2{\mathrm{\&pi;R}}_2{H}_0^2\mathrm{\&Gamma;}sh\mathrm{\&Gamma;}(R_2-R_1)}{I^{2}ch\mathrm{\&Gamma;}(R_2-R_1)\mathrm{\&gamma;}}---\left(8\right)$

Wherein: ω is frequency angular velocity, and μ is magnetic permeability, and γ is conductivity.

In (2) formula, get a=10m, then meet the condition of d < < a, obtain corresponding industrial frequency electric resistance.R is made in (8) formula ₂=10m, R ₁=0, obtain R, contrast with the result of calculation of formula (2), (3), obtain the correction coefficient K of (8) _c.The then industrial frequency electric resistance of the consideration skin effect of unit length

R _C＝RK _C(9)

The direct current resistance of the circular conductor in cross section is:

$R_{DC}=\frac{1}{\mathrm{\&gamma;}}\frac{1}{\mathrm{\&pi;}(R_2^2-R_1^2)}---\left(10\right)$

In order to consider proximity effect and the skin effect of split conductor with equivalent area sequence synthesis, the AC resistance of available formula 10 correspondence obtains its equivalent area.Order then the corresponding equivalent area only considering skin effect.

The division radical physical dimension of split conductor, relative position are brought into 1 formula, the equivalent area S considering proximity effect and skin effect can be obtained _e1, then actual equivalent area is order the equivalent inside radius R considering proximity effect and skin effect can be tried to achieve _12new.R _12newbring following formula into, AC resistance and interior self-induction can be obtained.

$\begin{array}{c}{R}_A=\frac{1}{\mathrm{\&gamma;}\mathrm{\&pi;}(R_2^2-R_{12new}^2)}\\ L_i=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\&lsqb;\frac{R_{12new}^4\ln \frac{R_2}{R_{12new}}}{{\left(R_2^2-R_{12new}^2\right)}^2}+\frac{R_2^2-3R_{12new}^2}{4\left(R_2^2-R_{12new}^2\right)}\&rsqb;\end{array}---\left(11\right)$

Skin effect and proximity effect can consider by the computing method that the present invention proposes, and draw the AC resistance suiting engineering reality.Site test results confirms accuracy and the reliability of divided conductor AC resistance computing method of the present invention indirectly.The computing method that the present invention proposes; consider the impact of skin effect and proximity effect; more accurately can calculate the AC resistance of the split conductor of different frequency and heading spacing and interior self-induction, contribute to transmission line of electricity line losses management, protection seting, condition monitoring and fault diagnosis etc. more accurately.

Embodiment

The formula (1) that the present invention draws by deriving above single conductor, (2) are demarcated formula (7), and carried out ATP (EMTP) simulation calculation, respectively S.C., binary fission, conductors on quad bundled are verified.For the ease of comparing, the solid conductor of employing is solid aluminum steel and the internal diameter 0.41cm of external diameter 1.341cm, and the hollow aluminum steel of external diameter 1.341cm, in order to get rid of the impact of lightning conducter, eliminates whole lightning conducter, and line length is 100km.System wiring figure as shown in Figure 12.

Get d < < a, can be verified under power frequency and higher-frequency condition and calibration-type (8) solving simple solid conductor resistance by formula (2), (3) simple solid wire, be 7m to getting conductor radius under power frequency condition, at higher frequencies, getting conductor radius by the middle hyperbolic function codomain impact of formula (8) is 1m.Calibration value can be obtained as table 1:

The demarcation of table 1. pair resistance calculations formula

As can be seen from Table 1, through the demarcation of formula (2), (3), the computational accuracy being applied to the formula (8) of engineering actual computation is very high, meet the actual conditions of wire and split conductor resistance, the resistance calculations of split conductor under different frequency in engineering reality, different heading spacing can be applied to further.

To binary fission solid aluminum wire, in different h values, namely under different heading spacing, ATP (EMTP) is utilized to ask for line parameter circuit value to accompanying drawing 6 wiring diagram system, extract line resistance value, and the line resistance after utilizing formula (11) to consider skin effect and proximity effect carries out calculating contrast.

To conductors on quad bundled, with binary fission wire, in different h values, namely under different heading spacing, utilize ATP (EMTP) to ask for line parameter circuit value to such as Fig. 6 wiring diagram system, extract line resistance value, and the line resistance after utilizing formula (11) to consider skin effect and proximity effect calculates, respectively under the frequency of 50Hz and 1000Hz, the result of the two is compared.

For solid conductor, binary fission, quadripartion solid conductor ATP in the different heading spacing situation of different frequency emulates the alternating current resistance and variation tendency thereof that draw as accompanying drawing 13, shown in accompanying drawing 16.

To hollow core conductor, binary fission, quadripartion hollow core conductor emulate the alternating current resistance and variation tendency thereof that draw as accompanying drawing 14, shown in accompanying drawing 17 by ATP in the different heading spacing situation of different frequency.

The resistance value that method proposed by the invention calculates and variation tendency thereof as accompanying drawing 15, accompanying drawing 18.

By accompanying drawing 13 ~ accompanying drawing 14, the comparison of accompanying drawing 16 ~ accompanying drawing 17 can be found out, when through-flow frequency significantly increases, ATP increases the skin effect caused reflection to frequency is obvious not, alternating current resistance emulation acquired results difference under different frequency is not obvious, and also cannot clearly reflect with the increase AC resistance respective change of heading spacing.

The comparing as shown shown in 2-table 5 of the split conductor resistance calculations value of computing method of the present invention and the concrete numerical value of ATP simulation result (adopt wire gauge to be solid aluminum steel external diameter 1.341cm, hollow aluminum steel is external diameter 1.341cm, internal diameter 0.41cm's).

The binary fission solid conductor resistance calculations value that table 2. considers skin effect and proximity effect compares with simulation value

The binary fission hollow core conductor resistance calculations value that table 3. considers skin effect and proximity effect compares with simulation value

The quadripartion solid conductor resistance calculations value that table 4. considers skin effect and proximity effect compares with simulation value

The quadripartion hollow core conductor resistance calculations value that table 5. considers skin effect and proximity effect compares with simulation value

Formula (11) can be found out the calculating contrast accompanying drawing 15,18 under the different heading spacing of different frequency: 1, when through-flow frequency increases, due to the impact of skin effect, the AC resistance of wire obviously increases.2, along with the increase of heading spacing, wire alternating current resistance is tending towards a more stable value gradually.3, owing to having considered the impact of skin effect and proximity effect, when frequency change, can obviously find out skin effect and proximity effect to current equivalence circulation area in wire to AC resistance play a part different, when frequency raises, AC resistance increases; When heading spacing diminishes, because the effect wire AC resistance of proximity effect significantly raises.

The AC resistance computing method of cylindric wire that the present invention proposes and ATP emulate compared with the result that draws, when frequency upgrading, the method that the present invention proposes can reflect the impact of skin effect on AC resistance better, and conductor AC resistance obviously increases when frequency raises.When heading spacing changes, skin effect and proximity effect can be considered the AC resistance drawing and gear to actual circumstances by the computing method that the present invention proposes.

The method that the present invention proposes and electric pressure are that the transmission line power frequency parameter test value of 550kV contrasts.The transmission line of electricity that Henan DianKeYuan is 550kV to electric pressure in 2011 has carried out the test of power frequency parameter.Wherein 550kV circuit is double back quadripartion (loop I, II), and line length is 51.68km, test result and as shown in table 6 according to the line resistance of trying to achieve of line parameter circuit value.

Table 6: loop power frequency parameter test result

Adopting on-the-spot actual wire model, shown that the AC resistance of the 500kV circuit that the inventive method is tried to achieve is as table 7, for ease of analyzing contrast, also the result of calculation of ATP (EMTP) being listed in table 7.

Table 7: circuit power frequency resistance test value and calculated value contrast

As shown in Table 7, the result of calculation of ATP/EMTP and field measurement data error are very large, and the AC resistance maximum relative error of 4 divisions is respectively 13.6% and 13.7%, and this illustrates that ATP/EMTP is like the proximity effect not considering split conductor; And computing method and measured data error that the present invention proposes are very little, all about 1%, can be identical with site test gained test result preferably.Site test results confirms the accuracy considering the divided conductor AC resistance computing method of proximity effect and skin effect that the present invention proposes and reliability indirectly.

Accompanying drawing explanation

During accompanying drawing 1.50Hz, spacing 5cm, 2 split conductor magnetic flux densities (T)

During accompanying drawing 2.50Hz, spacing 5cm, 2 split conductors (right side wire) distribution of current (A/m2)

During accompanying drawing 3.50Hz, spacing 50cm, 2 split conductors (right side wire) distribution of current (A/m2)

During accompanying drawing 4.50Hz, spacing 5cm, 4 split conductor magnetic flux densities (T)

During accompanying drawing 5.50Hz, spacing 5cm, 4 split conductors (upper right side) distribution of current (A/m2)

During accompanying drawing 6.50Hz, spacing 50cm, 4 split conductors (upper right side) distribution of current (A/m2)

Accompanying drawing 7. binary fission wire equivalent area building method.

Accompanying drawing 8. binary fission wire considers that skin effect and proximity effect after-current flow through wire equivalent cross-section schematic diagram.

Accompanying drawing 9. tripartition wire considers that skin effect and proximity effect after-current flow through wire equivalent cross-section schematic diagram.

The uniform plane wave signal that accompanying drawing 10. is propagated along the y-axis direction.

The circular conductor cross-section in the single cross section of accompanying drawing 11..

Accompanying drawing 12. line resistance parameters simulation wiring diagram.

Accompanying drawing 13 binary fission solid conductor different frequency resistance value ATP simulation result.

Accompanying drawing 14 binary fission hollow core conductor different frequency resistance value ATP simulation result.

Accompanying drawing 15 binary fission wire different frequency resistance value formula (11) result of calculation.

Accompanying drawing 16 quadripartion solid conductor different frequency resistance value ATP simulation result.

Accompanying drawing 17 quadripartion hollow core conductor different frequency resistance value ATP simulation result.

Accompanying drawing 18 conductors on quad bundled different frequency resistance value formula (11) result of calculation.

Claims (6)

1. computing method for divided conductor AC resistance and interior self-induction, is characterized in that: give the method determining the equivalent flow area dividing (binary fission and more than) wire.The skin effect of split conductor and proximity effect are converted into the change of equivalent flow area, construct the sequence of function of the physical dimension with conductor, relative position change, propose large scale and (do not meet d < < a, d is the depth of current penetration, a is under conductor external radius condition), the computing formula of conductor complex equivalent impedance, propose the computing formula of common conductors complex equivalent impedance with conductor radius, through-flow frequency change, namely this formula is applicable to the large wire of cross sectional radius and is also applicable to the little wire of cross sectional radius.Propose two, three, four, six-multiple conductor considers the AC resistance of skin effect and proximity effect impact and the circular of interior self-induction and formula.

2. method according to claim 1, it is characterized in that: analogy thin flat plate Eddy Distribution formula, propose the cross section magnetic Electromagnetic field calculation formula considering skin effect, the AC resistance of consideration skin effect of having derived and reactance formula, this formula by the restriction of Inside and Outside of Conductor radius physical dimension, does not have versatility.

3. method according to claim 1, is characterized in that: conductor in alternating current situation, to different Inside and Outside of Conductor radius (R ₁, R ₂), different through-flow frequencies, consider that the conductor AC resistance (R) of skin effect calculates with the following formula that the present invention proposes: $\stackrel{\&CenterDot;}{I}=-\frac{2\mathrm{\&pi;}{\stackrel{\&CenterDot;}{H}}_0}{ch\mathrm{\&Gamma;}(R_2-R_1)}\&lsqb;R_{2}ch\mathrm{\&Gamma;}(R_2-R_1)-R_1-\frac{1}{\mathrm{\&Gamma;}}sh\mathrm{\&Gamma;}(R_2-R_1)\&rsqb;,$ $R+jX=\frac{2{\mathrm{\&pi;R}}_2{H}_0^2\mathrm{\&Gamma;}sh\mathrm{\&Gamma;}(R_2-R_1)}{I^{2}ch\mathrm{\&Gamma;}(R_2-R_1)\mathrm{\&gamma;}},$ Wherein: $\mathrm{\&Gamma;}=\mathrm{\&alpha;}+j\mathrm{\&beta;}=\mathrm{\&omega;}\sqrt{\frac{\mathrm{\&mu;}\mathrm{\&epsiv;}}{2}(\sqrt{1+\frac{{\mathrm{\&gamma;}}^2}{{\mathrm{\&omega;}}^2{\mathrm{\&epsiv;}}^2}}-1)}+j\mathrm{\&omega;}\sqrt{\frac{\mathrm{\&mu;}\mathrm{\&epsiv;}}{2}(\sqrt{1+\frac{{\mathrm{\&gamma;}}^2}{{\mathrm{\&omega;}}^2{\mathrm{\&epsiv;}}^2}}+1)},$ When meeting $\frac{\mathrm{\&gamma;}}{\mathrm{\&omega;}\mathrm{\&epsiv;}}>>1$ Time, ω is frequency angular velocity, and μ is magnetic permeability, and γ is conductivity.

4. method according to claim 1, is characterized in that: conductor is considered to the calculated value of the AC resistance of skin effect carries out demarcation under large scale condition and verification in order to lower formula, and obtain COEFFICIENT K, verification resistance when frequency is lower is: $R+jX=\frac{\frac{\sqrt{2}}{2}(1+j)a}{2{\mathrm{\&pi;\&gamma;}}^2|\frac{a\mathrm{\&Gamma;}-(1-e^{-\mathrm{\&Gamma;}a})}{{\mathrm{\&Gamma;}}^2}{|}^2\sqrt{\frac{\mathrm{\&omega;}\mathrm{\&mu;}}{\mathrm{\&gamma;}}}},$ Verification resistance when frequency is higher is: $R+jX=\frac{a}{2{\mathrm{\&pi;\&gamma;}}^2{\stackrel{*}{Z}}_c|\frac{a\mathrm{\&Gamma;}-(1-e^{-\mathrm{\&Gamma;}a})}{{\mathrm{\&Gamma;}}^2}{|}^2}$ (Γ is identical with claim 3, ).

5. method according to claim 1, is characterized in that: to split conductor, and the sequence of function area formula of equivalent flow area is: $S=2a^{2}arccos\frac{H-B}{2a}-a^{2}sin\left(2arccos\frac{H-B}{2a}\right),$ Wherein, for binary fission wire parameter be: H=h, B=b.Can be expressed as tripartition wire parameter: for conductors on quad bundled, area function sequential parameter is: for six-multiple conductor, area function sequential parameter is: $H=2h,B=\frac{7h+b+\sqrt{9h^2-3a^2}+4\sqrt{4h^2-3a^2}}{8},$ In like manner can release the computing formula of 8 divisions and even n division, no longer go to live in the household of one's in-laws on getting married here and chat.Equivalent inside radius (the R in 3 is asked for according to the equivalent flow area of trying to achieve ₁), equivalent inside radius is substituted into the alternating current resistance that formula obtains split conductor.

6. the method according to claim 3 and 5, is characterized in that: when trying to achieve the industrial frequency electric resistance R of consideration skin effect of split conductor equivalence flow area S and unit length _c=RK _cafter, the direct current resistance of the circular conductor in cross section is: $R_{DC}=\frac{1}{\mathrm{\&gamma;}}\frac{1}{\mathrm{\&pi;}(R_2^2-R_1^2)}.$ Order $R_C\stackrel{\mathrm{\&Delta;}}{=}\frac{1}{\mathrm{\&gamma;}}\frac{1}{\mathrm{\&pi;}(R_2^2-R_{11new}^2)},$ Then the corresponding equivalent area only considering skin effect.Actual equivalent area is order the equivalent inside radius R12new considering proximity effect and skin effect can be tried to achieve.R12new is brought into following formula, AC resistance and interior self-induction (R can be obtained ₂the external radius of=a conductive wire cross-section).

$R_A=\frac{1}{\mathrm{\&gamma;}\mathrm{\&pi;}(R_2^2-R_{12new}^2)}$

$L_i=\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}\&lsqb;\frac{R_1^4\ln \frac{R_2}{R_{12new}}}{{(R_2^2-R_{12new}^2)}^2}+\frac{R_2^2-3R_{12new}^2}{4(R_2^2-R_{12new}^2)}\&rsqb;$