Method for Determining Amplitude and Phase of Stratified Current of Overhead Wire

Abstract

The present invention discloses a method for determining the amplitude and phase of a stratified current of an overhead wire, the method comprising the following steps: S1, determining the specification, the size and main technical parameters of a wire; S2, calculating mutual inductances between conductors within a single-phase wire and the self-inductance thereof; S3, calculating mutual inductance reactance between conductors within the single-phase wire of a three-phase system and the self-inductance reactance thereof; and S4, calculating the distribution of currents in each layer. The method takes into account the magnetic field coupling effect between conductors within a wire, so as to accurately calculate the current flowing through conductors in each layer within the wire, and accurately reflect a phase relationship between conductors in each layer.

Claims

1. A method for determining the amplitude and phase of a stratified current of an overhead wire, characterized in that the method comprises: S1, determining the specification, the size and main technical parameters of a wire, the step specifically being as follows: S101, determining the number of layers of the overhead wire and the number of conductors in each layer and the planned size thereof; and S102, determining the material of the conductors in each layer and the corresponding resistivity and magnetic permeability; S2, calculating mutual inductances between conductors within a single-phase wire and the self-inductance thereof, the step specifically being as follows: S201, calculating the mutual inductance between a conductor layer i and a conductor layer j within the single-phase wire; and S202, calculating the self-inductance of the conductor layer i within the single-phase wire; S3, calculating mutual inductance reactance between conductors within the single-phase wire in a three-phase system and the self-inductance reactance thereof, the step specifically being as follows: S301, calculating the total mutual inductance reactance between the conductor layer i and the conductor layer j within an A-phase wire in a three-phase system; and S302, calculating the self-inductance reactance of the conductor layer i within the A-phase wire in the three-phase system; and S4, calculating the distribution of currents in conductors in each layer within the single-phase wire.

2. The method for determining the amplitude and phase of a stratified current of an overhead wire of claim 1, characterized in that step S101 is specifically as follows: numbering the wires and determining the radius of the overhead wire and the radius of each conductor, wherein each phase of the three-phase wire has m layers, which are numbered, from inside to outside, as 1, 2, . . . m, there are n conductors in each layer within a wire, no distinction is made between conductors in each layer, and the three-phase wires are only distinguished by subscripts a, b and c in derivation; and in terms of current, using .sub.i to indicate the total current of the layer i, and using .sub.i to indicate the current on a conductor in the layer i, that is .sub.i=n.sub.i, where n is the number of conductors in the layer i, and .sub.i appears only in the result analysis to compare effects of a skin effect.

3. The method for determining the amplitude and phase of a stratified current of an overhead wire of claim 1, characterized in that step S102 is specifically as follows: determining the resistivity and magnetic permeability of various conductors based on if the overhead wire is a steel-cored aluminum stranded wire, an aluminum stranded wire or a copper wire.

4. The method for determining the amplitude and phase of a stratified current of an overhead wire of claim 1, characterized in that the calculation formula for the mutual inductance M.sub.aiaj in step S201 is specifically as follows: $M_{\mathrm{aiaj}}=\frac{{}_0}{2.Math.}\left[\mathrm{Ln}\left(\frac{2.Math.l}{D_{\mathrm{ij}}}-1\right)\right],.Math.\mathrm{wherein}.Math..Math.D_{\mathrm{ij}}=\sqrt[\mathrm{mn}]{\underset{k=1}{\overset{m}{.Math.}}.Math.\underset{i=1}{\overset{n}{.Math.}}.Math.\left[r_i^2+r_j^2-2.Math.r_i.Math.r_j.Math.\cos \left({}_{\mathrm{ik}}-{}_{j.Math..Math.1}\right)\right]},$ where m is the number of conductors in the layer i, n is the number of conductors in the layer j, D.sub.ij is a geometric mean of distances between conductors located in the layer i and the layer j respectively, r.sub.i is the distance from the center of circle of a single conductor in the layer i to the center of the wire, r.sub.j is the distance from the center of circle of the single conductor in the layer j to the center of the wire, and .sub.ik.sub.j1 is an opening angle between the center of circle of the k.sup.th conductor in the layer i and the center of circle of the 1.sup.st conductor in the layer j, relative to the center of circle of the wire.

5. The method for determining the amplitude and phase of a stratified current of an overhead wire of claim 1, characterized in that the calculation formula for the self-inductance L.sub.aiai in step S202 is specifically as follows: $L_{\mathrm{aiaj}}=\frac{{}_0}{2.Math.}\left[\mathrm{Ln}\left(\frac{2.Math.l}{D_{\mathrm{ij}}}-1\right)\right],.Math.\mathrm{wherein},D_{\mathrm{ii}}=\sqrt[m]{r_{\mathrm{eq}}.Math.\underset{k=2}{\overset{m}{.Math.}}.Math.\left[r_i^2+r_1^2-2.Math.r_i.Math.r_1.Math.\cos \left({}_{\mathrm{ik}}-{}_{i.Math..Math.1}\right)\right]}$ where m is the number of conductors in the layer i, D.sub.ii is a geometric mean of distances between conductors in the layer i, r.sub.i is the distance from the center of circle of a single conductor in the layer i to the center of the wire, .sub.ik.sub.i1 is an opening angle between the center of circle of the k.sup.th conductor in the layer i and the center of circle of the 1.sup.st conductor in the layer i, relative to the total center of circle of the wire, and r.sub.eq is an equivalent radius of the first conductor in the layer i.

6. The method for determining the amplitude and phase of a stratified current of an overhead wire of claim 1, characterized in that step S301 is specifically as follows: assuming that the system is in three-phase current symmetry, that is
i.sub.ai+i.sub.bi+i.sub.ci=0 the wire is in three-phase symmetry after alternation and the equivalent distance between wires is D.sub.eq, and the distance between the wires is much greater than the distance between each strand within a one-phase wire, then for the conductor layer i within an A phase wire, a magnetic flux linkage generated by the current in the conductor layer j is: $\begin{array}{c}{}_{\mathrm{aij}}=.Math.M_{\mathrm{aiaj}}.Math.i_{\mathrm{aj}}+M_{\mathrm{aibj}}.Math.i_{\mathrm{bj}}+M_{\mathrm{aicj}}.Math.i_{\mathrm{cj}}\\ =.Math.\frac{{}_0}{2.Math.}\left[\mathrm{Ln}\left(\frac{2.Math.l}{D_{\mathrm{ij}}}-1\right)\right].Math.i_{\mathrm{aj}}+\frac{{}_0}{2.Math.}\left[\mathrm{Ln}\left(\frac{2.Math.l}{D_{\mathrm{eq}}}-1\right)\right].Math.i_{\mathrm{bj}}+\frac{{}_0}{2.Math.}\left[\mathrm{Ln}\left(\frac{2.Math.l}{D_{\mathrm{eq}}}-1\right)\right].Math.i_{\mathrm{cj}}\\ =.Math.\frac{{}_0}{2.Math.}\left[\mathrm{Ln}\left(\frac{2.Math.l}{D_{\mathrm{ij}}}-1\right)\right].Math.i_{\mathrm{aj}}+\frac{{}_0}{2.Math.}\left[\mathrm{Ln}\left(\frac{2.Math.l}{D_{\mathrm{eq}}}-1\right)\right].Math.\left(i_{\mathrm{bj}}+i_{\mathrm{cj}}\right)\\ =.Math.\frac{{}_0}{2.Math.}.Math.\mathrm{Ln}\left(\frac{D_{\mathrm{eq}}}{D_{\mathrm{ij}}}\right).Math.i_{\mathrm{aj}}\end{array}$ then, in a three-phase symmetric system, the total mutual inductance between the conductor layer i within an A-phase wire and the conductor layer j within the A-phase wire is: $M_{\mathrm{aiaj}}=\frac{{}_0}{2.Math.}\left[\mathrm{Ln}\left(\frac{2.Math.l}{D_{\mathrm{ij}}}-1\right)\right]$ and in the three-phase symmetric system, the total mutual inductance reactance between the conductor layer i within the A-phase wire and the conductor layer j within the A-phase wire is: $X_{\mathrm{aij}}={}_0.Math.f.Math..Math.\mathrm{Ln}\left(\frac{D_{\mathrm{eq}}}{D_{\mathrm{ij}}}\right).$

7. The method for determining the amplitude and phase of a stratified current of an overhead wire of claim 6, characterized in that step S302 is specifically as follows: in the mutual inductance reactance $X_{\mathrm{aij}}={}_0.Math.f.Math..Math.\mathrm{Ln}\left(\frac{D_{\mathrm{eq}}}{D_{\mathrm{ij}}}\right)$ making i=j to obtain the self-inductance reactance of the conductor layer i $X_{\mathrm{aii}}={}_0.Math.f.Math..Math.\mathrm{Ln}\left(\frac{D_{\mathrm{eq}}}{D_{\mathrm{ii}}}\right).$

8. The method for determining the amplitude and phase of a stratified current of an overhead wire of claim 1, characterized in that step S4 is specifically as follows: assuming that in one phase the resistances of each layer from inside to outside is r.sub.1, r.sub.2, r.sub.3 . . . r.sub.m respectively, and taking a wire segment of unit length, wherein the voltage drops between each layer on the wire segment should be equal, denoted as V, then there is $V=r_1.Math.i_1+j\left(X_{11}.Math.i_1+X_{12}.Math.i_2+X_{13}.Math.i_3+\mathrm{.Math.}.Math..Math.X_{1.Math.m}.Math.i_m\right)$ $V=r_2.Math.i_2+j\left(X_{21}.Math.i_1+X_{22}.Math.i_2+X_{23}.Math.i_3+\mathrm{.Math.}.Math..Math.X_{2.Math.m}.Math.i_m\right)$ $V=r_3.Math.i_1+j\left(X_{31}.Math.i_1+X_{32}.Math.i_2+X_{33}.Math.i_3+\mathrm{.Math.}.Math..Math.X_{3.Math.m}.Math.i_m\right)$ $\mathrm{.Math.}$ $V=r_m.Math.i_1+j\left(X_{m.Math..Math.1}.Math.i_1+X_{m.Math..Math.2}.Math.i_2+X_{m.Math..Math.3}.Math.i_3+\mathrm{.Math.}.Math..Math.X_{.Math.m.Math..Math.m}.Math.i_m\right),$ combining the above formulas and eliminating V and D.sub.eq to obtain $\left[\begin{array}{c}{r}_1-j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{11}}{D_{12}}\\ r_1-j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{11}}{D_{13}}\\ \mathrm{.Math.}\\ r_1-j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{11}}{D_{1.Math.m}}\end{array}\right]\left[\begin{array}{ccccc}{i}_1& 0& 0& \mathrm{.Math.}& 0\\ 0& i_1& 0& \mathrm{.Math.}& 0\\ 0& 0& i_1& \mathrm{.Math.}& 0\\ \mathrm{.Math.}& & & & \\ 0& 0& 0& \mathrm{.Math.}& i_1\end{array}\right]=\left[\begin{array}{cccc}{r}_2+j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{12}}{D_{22}}& j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{13}}{D_{23}}& \mathrm{.Math.}& j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{1.Math.m}}{D_{2.Math.m}}\\ j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{12}}{D_{23}}& r_3+j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{13}}{D_{23}}& \mathrm{.Math.}& j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{12}}{D_{3.Math.m}}\\ \mathrm{.Math.}& & & \\ j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{12}}{D_{2.Math.m}}& j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{13}}{D_{3.Math.m}}& \mathrm{.Math.}& r_4+j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{1.Math.m}}{D_{m.Math..Math.m}}\end{array}\right]\left[\begin{array}{c}{i}_2\\ i_3\\ \mathrm{.Math.}\\ i_m\end{array}\right],.Math..Math.T={\left[r_1-j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{11}}{D_{12}}.Math..Math.r_1-j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{11}}{D_{13}}.Math..Math.\mathrm{.Math.}.Math..Math.r_1-j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{11}}{D_{1.Math.m}}\right]}^T.Math..Math..Math.\mathrm{denoting}.Math..Math.X=[.Math.\begin{array}{cccc}{r}_2+j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{12}}{D_{22}}& j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{13}}{D_{23}}& \mathrm{.Math.}& j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{1.Math.m}}{D_{2.Math.m}}\\ j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{12}}{D_{23}}& r_3+j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{13}}{D_{23}}& \mathrm{.Math.}& j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{12}}{D_{3.Math.m}}\\ \mathrm{.Math.}& & & \\ j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{12}}{D_{2.Math.m}}& j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{13}}{D_{3.Math.m}}& \mathrm{.Math.}& r_4+j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{1.Math.m}}{D_{m.Math..Math.m}}\end{array}].Math..Math..Math.\mathrm{then}.Math.\left[\begin{array}{c}{i}_2\\ i_3\\ \mathrm{.Math.}\\ i_4\end{array}\right]=X^{-1}.Math.T\left[\begin{array}{ccccc}{i}_1& 0& 0& \mathrm{.Math.}& 0\\ 0& i_1& 0& \mathrm{.Math.}& 0\\ 0& 0& i_1& \mathrm{.Math.}& 0\\ \mathrm{.Math.}& & & & \\ 0& 0& 0& \mathrm{.Math.}& i_1\end{array}\right],$ when vectors are used for representation $\left[\begin{array}{c}{\stackrel{.}{I}}_2\\ {\stackrel{.}{I}}_3\\ \mathrm{.Math.}\\ {\stackrel{.}{I}}_4\end{array}\right]=X^{-1}.Math.T\left[\begin{array}{ccccc}{\stackrel{.}{I}}_1& 0& 0& \mathrm{.Math.}& 0\\ 0& {\stackrel{.}{I}}_1& 0& \mathrm{.Math.}& 0\\ 0& 0& {\stackrel{.}{I}}_1& \mathrm{.Math.}& 0\\ \mathrm{.Math.}& & & & \\ 0& 0& 0& \mathrm{.Math.}& {\stackrel{.}{I}}_1\end{array}\right],$ by means of the solution described above, the ratio distribution between currents of each layer is obtained, and by adding the formula
.sub.1+.sub.2+.sub.3+ . . . .sub.m=.sub. the current distribution in each layer is calculated.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0043] FIG. 1 is a flowchart of a method for determining the amplitude and phase of a stratified current of an overhead wire disclosed in the present invention.

DETAILED DESCRIPTION OF EMBODIMENTS

[0044] In order to make the objectives, technical solutions and advantages of embodiments of the present invention clearer, the technical solutions in embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Apparently, the described embodiments are a part, but not all of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without any creative effort shall fall within the protection scope of the present invention. On the basis of the embodiments of the present invention, all the other embodiments obtained by a person skilled in the art without any inventive effort shall fall within the scope of protection of the present invention.

Embodiment

[0045] In this embodiment, in combination with an LGJ300/40 type A phase wire being used as an object to be calculated, a method for calculating a stratified current of an overhead wire is proposed, however, the method is not limited to the LGJ300/40 type wire, wherein the 2D cross-section view of the LGJ 300/40 type wire consists of four layers, which are, from the inside to the outside, a steel core having a radius of 1.33 mm of which a center of circle is the center of the wire, six steel cores having a radius of 1.33 mm of which the centers of circle are uniformly spaced and distributed in a circle with a radius of 2.66 mm, nine aluminum cores having a radius of 1.995 mm of which the centers of circle are uniformly spaced and distributed in a circle with a radius of 5.985 mm, and fifteen aluminum cores having a radius of 1.995 mm of which the centers of circle are uniformly spaced and distributed in a circle with a radius of 9.975 mm, respectively.

[0046] As in FIG. 1, a flowchart of a method for determining the amplitude and phase of a stratified current of an overhead wire is disclosed, the method specifically comprising the following steps:

[0047] S1, determining the specification, the size and main technical parameters of a wire, the step specifically further comprising the following sub-steps:

[0048] S101, determining the number of layers of the overhead wire and the number of conductors in each layer and the planned size thereof;

[0049] In a specific embodiment, the 2D cross-section view of the LGJ 300/40 type wire consists of four layers, which are, from the inside to the outside, a steel core having a radius of 1.33 mm of which a center of circle is the center of the wire, six steel cores having a radius of 1.33 mm of which the centers of circle are uniformly spaced and distributed in a circle with a radius of 2.66 mm, nine aluminum cores having a radius of 1.995 mm of which the centers of circle are uniformly spaced and distributed in a circle with a radius of 5.985 mm, and fifteen aluminum cores having a radius of 1.995 mm of which the centers of circle are uniformly spaced and distributed in a circle with a radius of 9.975 mm, respectively.

[0050] in terms of current, using .sub.i to indicate the total current of the layer i, and using .sub.i to indicate the current on a wire inside the layer i, that is

.sub.i=n.sub.i,

[0051] where n is the number of conductors in the layer i, and .sub.i appears only in the result analysis to compare effects of a skin effect.

[0052] S102, determining the material of the conductors in each layer and the corresponding resistivity and magnetic permeability;

[0053] In a specific embodiment, the material of the conductors in the first and second layers within an overhead wire is steel with a resistivity of 510-7 m. Since the metal steel is a ferromagnetic material which will change as the current changes, and the value of relative magnetic permeability varies from 1 to 2000. The material of the conductors in the third and fourth layers is aluminum with a resistivity of 2.8310-8 m, which is a non-ferromagnetic material, and the value of the relative magnetic permeability is 1.0.

[0054] S2, calculating mutual inductances between conductors within an A-phase wire and the self-inductance thereof, the step specifically comprising the following sub-steps:

[0055] S201, calculating the mutual inductance between a conductor layer i and a conductor layer j within an A-phase wire;

[00011]$M_{\mathrm{aiaj}}=\frac{{}_0}{2.Math.}\left[\mathrm{Ln}\left(\frac{2.Math.l}{D_{\mathrm{ij}}}-1\right)\right],.Math.\mathrm{wherein}.Math..Math.D_{\mathrm{ij}}=\sqrt[\mathrm{mn}]{\underset{k=1}{\overset{m}{.Math.}}.Math..Math.\underset{i=1}{\overset{n}{.Math.}}.Math..Math.\left[r_i^2+r_j^2-2.Math.r_i.Math.r_j.Math.\cos \left({}_{\mathrm{ik}}-{}_{j.Math..Math.1}\right)\right]},$

[0056] where m is the number of conductors in the layer i, n is the number of conductors in the layer j, D.sub.ij is a geometric mean of distances between conductors between the layer i and the layer j, r.sub.i is the distance from the center of circle of a single conductor in the layer i to the center of the wire, r.sub.j is the distance from the center of circle of the single conductor in the layer j to the center of the wire, and .sub.jk.sub.j1 is an opening angle between the center of circle of the k.sup.th conductor in the layer i and the center of circle of the 1.sup.st conductor in the layer j, relative to the total center of circle of the wire.

[0057] S202, calculating the self-inductance of the conductor layer i within the A-phase wire;

[00012]$L_{\mathrm{aiaj}}=\frac{{}_0}{2.Math.}\left[\mathrm{Ln}\left(\frac{2.Math.l}{D_{\mathrm{ij}}}-1\right)\right],.Math.\mathrm{wherein},D_{\mathrm{ii}}=\sqrt[m]{r_{\mathrm{eq}}.Math.\underset{k=2}{\overset{m}{.Math.}}.Math..Math.\left[r_i^2+r_1^2-2.Math.r_i.Math.r_1.Math.\cos \left({}_{\mathrm{ik}}-{}_{i.Math..Math.1}\right)\right]},$

[0058] where m is the number of conductors in the layer i, D.sub.ii is a geometric mean of distances between conductors in the layer i, r.sub.i is the distance from the center of circle of a single conductor in the layer i to the center of the wire, .sub.ik.sub.i1 is an opening angle between the center of circle of the k.sup.th conductor in the layer i and the center of circle of the 1.sup.st conductor in the layer i, relative to the total center of circle of the wire, and r.sub.eq is an equivalent radius of the first conductor in the layer i.

[0059] S3, calculating mutual inductance reactance between conductors within each single-phase wire of a three-phase system and the self-inductance reactance thereof, the step specifically comprising the following sub-steps:

[0060] S301, calculating the total mutual inductance reactance between the conductor layer i and the conductor layer j within an A-phase wire in a three-phase system.

[0061] assuming that the system is in three-phase current symmetry, that is

.sub.1+.sub.2+.sub.3+ . . . .sub.m=.sub.,

[0062] the wire is in three-phase symmetry after alternation and the equivalent distance between wires is D.sub.eq, and the distance between the wires is considered to be much greater than the distance between each strand within a one-phase wire, then for the conductor layer i within an A phase wire, a magnetic flux linkage generated by the current in the conductor layer j is:

[00013]$\begin{array}{c}{}_{\mathrm{aij}}=M_{\mathrm{aiaj}}.Math.i_{\mathrm{aj}}+M_{\mathrm{aibj}}.Math.i_{\mathrm{bj}}+M_{\mathrm{aicj}}.Math.i_{\mathrm{cj}}\\ =\frac{{}_0}{2.Math.}\left[\mathrm{Ln}\left(\frac{2.Math.l}{D_{\mathrm{ij}}}-1\right)\right].Math.i_{\mathrm{aj}}+\frac{{}_0}{2.Math.}\left[\mathrm{Ln}\left(\frac{2.Math.l}{D_{\mathrm{eq}}}-1\right)\right].Math.i_{\mathrm{bj}}+\frac{{}_0}{2.Math.}\left[\mathrm{Ln}\left(\frac{2.Math.l}{D_{\mathrm{eq}}}-1\right)\right].Math.i_{\mathrm{cj}}\\ =\frac{{}_0}{2.Math.}\left[\mathrm{Ln}\left(\frac{2.Math.l}{D_{\mathrm{ij}}}-1\right)\right].Math.i_{\mathrm{aj}}+\frac{{}_0}{2.Math.}\left[\mathrm{Ln}\left(\frac{2.Math.l}{D_{\mathrm{eq}}}-1\right)\right].Math.\left(i_{\mathrm{bj}}+i_{\mathrm{cj}}\right)\\ =\frac{{}_0}{2.Math.}.Math.\mathrm{Ln}\left(\frac{D_{\mathrm{eq}}}{D_{\mathrm{ij}}}\right).Math.i_{\mathrm{aj}}\end{array}$

[0063] in a three-phase symmetric system, the total mutual inductance between the conductor layer i within an A-phase wire and the conductor layer j within the A-phase wire is

[00014]$M_{\mathrm{aiaj}}=\frac{{}_0}{2.Math.}\left[\mathrm{Ln}\left(\frac{2.Math.l}{D_{\mathrm{ij}}}-1\right)\right]$

[0064] and in the three-phase symmetric system, the total mutual inductance reactance between the conductor layer i within the A-phase wire and the conductor layer j within the A-phase wire is

[00015]$X_{\mathrm{aij}}={}_0.Math.f.Math..Math.\mathrm{Ln}\left(\frac{D_{\mathrm{eq}}}{D_{\mathrm{ij}}}\right),$

[0065] where f is the grid frequency, and since the system is in three-phase symmetry, X.sub.ij is used afterwards to represent the mutual inductance reactance between a layer i and a layer j of a certain phase, that is

[00016]$X_{\mathrm{aij}}={}_0.Math.f.Math..Math.\mathrm{Ln}\left(\frac{D_{\mathrm{eq}}}{D_{\mathrm{ij}}}\right).$

[0066] S302, calculating the self-inductance reactance of the conductor layer i within the A-phase wire in the three-phase system; and

[0067] In the above formula, by making i=j, the self-inductance reactance of the conductor layer i can be obtained

[00017]$X_{\mathrm{aii}}={}_0.Math.f.Math..Math.\mathrm{Ln}\left(\frac{D_{\mathrm{eq}}}{D_{\mathrm{ii}}}\right).$

[0068] S4, calculating the distribution of currents in each layer.

[0069] assuming that in one phase the resistances of each layer from inside to outside is r.sub.1, r.sub.2, r.sub.3 . . . r.sub.4 respectively, and taking a wire segment of unit length, wherein the voltage drops between each layer on the wire segment should be equal, denoted as V, then there is

V=r.sub.1i.sub.1+j(X.sub.11i.sub.1+X.sub.12i.sub.2+X.sub.13i.sub.3+X.sub.14i.sub.4)

V=r.sub.2i.sub.2+j(X.sub.21i.sub.1+X.sub.22i.sub.2+X.sub.23i.sub.3+X.sub.24i.sub.4)

V=r.sub.3i.sub.3+j(X.sub.31i.sub.1+X.sub.32i.sub.2+X.sub.33i.sub.3+X.sub.34i.sub.4)

V=r.sub.4i.sub.4+j(X.sub.41i.sub.1+X.sub.42i.sub.2+X.sub.43i.sub.3+X.sub.44i.sub.4),

[0070] combining the above formulas and eliminating V and D.sub.eq to obtain

[00018]$\left[\begin{array}{c}{r}_1-j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{11}}{D_{12}}\\ r_1-j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{11}}{D_{13}}\\ .r_1-j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{11}}{D_{14}}\end{array}\right]\left[\begin{array}{ccc}{i}_1& 0& 0\\ 0& i_1& 0\\ 0& 0& i_1\end{array}\right]=\left[\begin{array}{ccc}{r}_2+j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{12}}{D_{22}}& j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{13}}{D_{23}}& j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{14}}{D_{24}}\\ j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{12}}{D_{23}}& r_3+j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{13}}{D_{23}}& j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{12}}{D_{34}}\\ j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{12}}{D_{24}}& j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{13}}{D_{34}}& r_4+j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{14}}{D_{44}}\end{array}\right]\left[\begin{array}{c}{i}_2\\ i_3\\ i_4\end{array}\right],.Math..Math.\mathrm{denoting}.Math..Math..Math.T={\left[r_1-j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{11}}{D_{12}}.Math..Math.r_1-j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{11}}{D_{13}}.Math..Math.r_1-j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{11}}{D_{14}}\right]}^T,.Math..Math.X=\left[\begin{array}{ccc}{r}_2+j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{12}}{D_{22}}& j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{13}}{D_{23}}& j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{14}}{D_{24}}\\ j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{12}}{D_{23}}& r_3+j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{13}}{D_{23}}& j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{12}}{D_{34}}\\ j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{12}}{D_{24}}& j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{13}}{D_{34}}& r_4+j.Math..Math.{}_0.Math.f.Math..Math.\mathrm{Ln}.Math.\frac{D_{14}}{D_{44}}\end{array}\right],.Math..Math.\mathrm{then}.Math..Math.\left[\begin{array}{c}{i}_2\\ i_3\\ i_4\end{array}\right]=X^{-1}.Math.T\left[\begin{array}{ccc}{i}_1& 0& 0\\ 0& i_1& 0\\ 0& 0& i_1\end{array}\right],$

[0071] when vectors are used for representation

[00019]$\left[\begin{array}{c}{\stackrel{.}{I}}_2\\ {\stackrel{.}{I}}_3\\ {\stackrel{.}{I}}_4\end{array}\right]=X^{-1}.Math.T\left[\begin{array}{ccc}{\stackrel{.}{I}}_1& 0& 0\\ 0& {\stackrel{.}{I}}_1& 0\\ 0& 0& {\stackrel{.}{I}}_1\end{array}\right],$

[0072] by means of the solution described above, the ratio between currents of various layers is obtained, and by adding the formula

.sub.1+.sub.2+.sub.3+.sub.4=.sub.

[0073] the current distribution in each layer is calculated.

[0074] Model Effect Analysis:

[0075] Using the model calculation process described above, the current of each layer within the LGJ300/40 type wire is calculated, and the total effective value of the applied current is 700 A, and the phase angle is 0. Comparing the calculated results with the finite element calculation results, the comparison results are shown in Table 1:

TABLE-US-00001 TABLE 1 Comparison table of calculation results the first layer the second layer the third layer the fourth layer finite .sub.1 = 0.65 29.0 .sub.2 = 0.67 20.9 .sub.3 = 28.91 5.0 .sub.4 = 29.17 +4.0 element .sub.r = 1000 .sub.1 = 0.74 16.3 .sub.2 = 0.74 16.2 .sub.3 = 28.93 4.5 .sub.4 = 29.12 +2.9 error % 13.31 10.51 0.08 0.19 .sub.r = 2000 .sub.1 = 0.70 25.8 .sub.2 = 0.70 25.7 .sub.3 = 28.95 4.5 .sub.4 = 29.14 +2.9 error % 8.32 5.67 0.12 0.11

[0076] Considering that the steel-cored aluminum stranded wire has a non-uniform current distribution at the power frequency, and the current mainly flows through the aluminum conductor layer, so that the heat generation inside the conductors mainly occurs in the aluminum conductor layer. Although the calculation result of the patent of the present invention differs greatly in the simulation results of the steel-cored conductor and the finite element, for the aluminum conductor layer having a large heat generation rate, by correcting the relative magnetic permeability, the error can be reduced to 0.125%. In addition, the method can reflect the phase difference between the conductors in each layer. Therefore, when calculating the internal radial temperature distribution of an overhead wire or calculating the temperature of a steel core, the calculation method in this patent can be used to calculate the current distribution and the heat generation rate of each layer.

[0077] The above-described embodiments are preferred embodiments of the present invention; however, the embodiments of the present invention are not limited to the above-described embodiments, and any other change, modification, replacement, combination, and simplification made without departing from the spirit, essence, and principle of the present invention should be an equivalent replacement and should be included within the scope of protection of the present invention.