CN103413047A - Determining method of single-core cable metal layer overvoltage - Google Patents

Abstract

The invention provides a determining method of single-core cable metal layer overvoltage. The method includes the following steps: (1) building a following matrix equation according to an electric power lead system where a single-core cable is located; (2) building a current equation of the single-core cable requiring determining of an overvoltage value according to the Kirchhoffs current law; (3) building a characteristic equation under a short circuit pattern according to the Kirchhoffs voltage law; (4) building simultaneous equations of the three equations, solving to obtain voltage difference between two ends of the single-core cable metal layer, and determining the single-core cable metal layer overvoltage according to the voltage difference between the two ends of the single-core cable metal layer. The determining method has the advantages of facilitating design of the most reasonable single-core cable, greatly saving project cost and having good economical benefit.

Description

A kind of superpotential definite method of single core cable metal level

Technical field

The present invention relates to technical field of electricity, especially relate to a kind of superpotential definite method of single core cable metal level.

Background technology

In electric system, when electric pressure surpassed 35kV, the power cable great majority adopted single core cable, and the single core cable metal level is superpotential determines it is an important content of single core cable design.

Main calculating single core cable metal level superpotential has two kinds of methods at present: first method is to adopt robot calculator to calculate, and this method needs positive sequence, negative phase-sequence, the zero sequence impedance of counting circuit, utilizes circuit theory to solve various parameters.Because the short circuit pattern is a lot, calculation and programming is difficult to all short circuit patterns are all taken into account but in fact.Second method is to adopt analytical algorithm, but this method can only be calculated simple short circuit pattern, as single-phase, three-phase shortcircuit, be difficult to calculate for comparatively complicated two phase ground short circuit, and the computation process more complicated.

Summary of the invention

The object of the invention is to: the problem for prior art exists, provide a kind of single core cable metal level superpotential definite method, can help to design the most rational single core cable, greatly save construction costs, have good economic benefit.

Goal of the invention of the present invention is achieved through the following technical solutions:

A kind of superpotential definite method of single core cable metal level, is characterized in that, the method comprises the following steps:

(1) according to the electrical lead system at single core cable place, set up following matrix equation:

Wherein

$Z_{\mathrm{Ln}}=R_n+j\frac{{\mathrm{\μ}}_0}{2\mathrm{\π}}\left(\ln \frac{1}{r_n}\right),$ $Z_{\mathrm{Mki}}=j\frac{{\mathrm{\μ}}_0}{2\mathrm{\π}}\left(\ln \frac{1}{E_{\mathrm{ki}}}\right),$ Z in formula _LnBe n root wire self-impedance, Z _MkiBe that k, the mutual inductance of i root wire are anti-, R _nBe n root conductor resistance, r _nBe n root wire equivalent redius, D _KiBe k, i root wire pitch,

For the electric current that flows through wire,

Voltage difference for the wire two ends;

(2) according to Kirchhoff's current law (KCL), set up the current equation of the single core cable that needs definite overvoltage value;

(3) according to Kirchhoff's second law, set up the secular equation under the short circuit pattern;

(4) aforementioned three equations of simultaneous, and solve that to obtain single core cable metal level both end voltage poor, then according to the poor definite single core cable metal level superpotential of single core cable metal level both end voltage.

Preferably, in step (1), the electrical lead system at single core cable place comprises three-phase conducting wire, three-phase conducting wire metal level, return wire and the earth wire that the earth equivalence is become separately.

Preferably, the self-induction of described the earth wire is

With any other wire mutual inductances, be The equivalent degree of depth and equivalent radius are D _g.

Preferably, when for A phase single-phase short circuit single-end earthed, the current equation of A phase single core cable is For the A phase current,

For the electric current in the earth wire,

For the electric current in return wire.

Preferably, when for A phase single-phase short circuit single-end earthed, its secular equation is

For the return wire both end voltage,

For the electric current in the earth wire, R ₁And R ₂Stake resistance, R for the wire two ends _gFor ground resistance,

Voltage for the earth wire.

Preferably, be specially according to the poor definite single core cable metal level superpotential of single core cable metal level both end voltage, first poor to deduct the return wire both end voltage poor by single core cable metal level both end voltage, can draw the return wire current potential; Be superimposed with again the earth mat potential rise, can draw the metal level voltage-to-ground, be i.e. the metal level superpotential.

Compared with prior art, the present invention replaces the earth with a hypothetically middle wire parallel with wire, and imaginary wire simultaneous together with the electric system circuit is formed to matrix equation, then set up electric current and the voltage equation of wire, finally, by some current known or the magnitude of voltage that record, calculate the superpotential of wire metal level.The inventive method is than traditional metal level superpotential computing method, can greatly reduce and measure the spent time of required physical quantity, and computational accuracy is high, the inventive method not only can be calculated simple short circuit form in addition, can also be applicable to different wire short circuit forms, thereby can design the most rational single core cable, greatly save construction costs, have good economic benefit.

The accompanying drawing explanation

Fig. 1 is n root wire loop magnetic linkage schematic diagram;

Fig. 2 is many wiring systems schematic diagram;

Fig. 3 is the circuit diagram of A phase cable metal sheath one end ground connection (return wire is arranged).

Embodiment

The present invention is described in detail below in conjunction with the drawings and specific embodiments.

Embodiment

Through test of many times research, find in n root wiring system as shown in Figure 1 i ₁+ i ₂+ ... i _nMany wiring systems of=0 have following magnetic linkage relation:

Between P point and n root wire, the magnetic linkage of interlinkage is:

${\mathrm{\ψ}}_{\mathrm{ap}}=\frac{{\mathrm{\μ}}_0}{2\mathrm{\π}}[i_1\left(\ln \frac{D_{\∞}}{D_{1p}}\right)+......+i_n\left(\ln \frac{D_{\∞}}{D_{\mathrm{np}}}\right)]$

Work as i ₁+ i ₂+ ... i _n=0 o'clock, following formula is got the limit to infinite distance to be had:

${\mathrm{\ψ}}_{\mathrm{ap}}=\frac{{\mathrm{\μ}}_0}{2\mathrm{\π}}[i_1\left(\ln \frac{1}{D_{1p}}\right)+......+i_n\left(\ln \frac{1}{D_{\mathrm{np}}}\right)]$

Be that P point place's wire and i root Mutual Inductances are desirable

Special, (r when the P wire overlaps with i root conductor _pR _i), mutual inductance is got

When P is i root conductor, this Xiang Ze is the self-induction of i root conductor

When wherein a conductor was the earth imagination wire, its mutual inductance was got

Wherein: r _P-wire P radius, r _i'-i root wire equivalent redius, D _gThe equivalent degree of depth of-earth current.

The cable self-induction is calculated " wire-ground " loop self-induction situation that often can run into, and Carlson, Evans Fordyce (J.R.Carson) proposed in nineteen twenty-six, can replace the earth with a hypothetically middle wire parallel with wire, and earth current concentrates in imaginary wire and flows through.The equivalent radius of imagination wire is R _g, the equivalent radius of wire is r', wire and imaginary conductor spacing D _Ag, the total self-induction of loop unit length is:

$L=\frac{{\mathrm{\μ}}_0}{2\mathrm{\π}}\left[\ln \frac{D_{\mathrm{ag}}}{r^{\′}}\right]+\frac{{\mathrm{\μ}}_0}{2\mathrm{\π}}\left[\ln \frac{D_{\mathrm{ag}}}{R_g}\right]=\frac{{\mathrm{\μ}}_0}{2\mathrm{\π}}\left[\ln \frac{D_g}{r^{\′}}\right]$

$D_g=D_{\mathrm{ag}}^2/R_g=660/{\sqrt{\mathrm{f\γ}}}^m$

Wherein: D _gThe equivalent degree of depth of-imaginary wire, f-power frequency (Hz), γ-ground conductivity (S/m).

Visible, the earth being equivalent to a radius herein is D _gWire.

In old place, can be equivalent to radius be equivalent depth D to electric current _gWire, self-induction is

With any other wire mutual inductances, also be

According to top analysis, can be just like the superpotential general definite method of the core cable metal layer that places an order:

As shown in Figure 2, more than one in wiring system, i ₁+ i ₂+ ... i _n=0.If three-phase electricity separately metal level of its many wiring systems of electric power three-phase conducting wire, three-phase conducting wire, return wire and the earth wire that the earth equivalence is become; As be other forms, according to circumstances determine the element that need to list equation in.When every of three-phase electricity wire and metal level are all considered, so can obtain following matrix equation:

$Z_{\mathrm{Ln}}=R_n+j\frac{{\mathrm{\μ}}_0}{2\mathrm{\π}}\left(\ln \frac{1}{r_n}\right)$

$Z_{\mathrm{Mki}}=j\frac{{\mathrm{\μ}}_0}{2\mathrm{\π}}\left(\ln \frac{1}{D_{\mathrm{ki}}}\right)$

Wherein: Z _LnThe-the n root wire self-impedance, Z _MkiThe-the k, the mutual inductance of i root wire resist, R _nThe-the n root conductor resistance, r _nThe-the n root wire equivalent redius, D _KiThe-the k, i root wire pitch.

To different short circuit patterns, Z _LMAll the same, only need be on as above matrix basis, according to Kirchhoff's law, list different characteristic formula (listing characteristic formula is that those skilled in the art can implement), simultaneous solution, can obtain under different short-circuit conditions every wire both end voltage poor, then according to the poor definite single core cable metal level superpotential of single core cable metal level both end voltage.Short-circuit conditions while single-end earthed return wire being arranged as following single core cable.

As shown in Figure 3, a phase single-phase short circuit single-end earthed, a short-circuit current part be by return wire, and a part during by the earth, can be listed following formula: $Z_{\mathrm{LM}}\·\left[\begin{array}{c}{\stackrel{\·}{I}}_a\\ 0\\ 0\\ 0\\ 0\\ 0\\ {\stackrel{\·}{I}}_p\\ {\stackrel{\·}{I}}_g\end{array}\right]=\left[\begin{array}{c}{\stackrel{\·}{U}}_a\\ {\stackrel{\·}{U}}_b\\ {\stackrel{\·}{U}}_c\\ {\stackrel{\·}{U}}_{a^{\′}}\\ {\stackrel{\·}{U}}_{b^{\′}}\\ {\stackrel{\·}{U}}_{c^{\′}}\\ {\stackrel{\·}{U}}_p\\ {\stackrel{\·}{U}}_g\end{array}\right];$ For the A phase current, For the electric current in the earth wire,

For the electric current in return wire;

Be respectively a, b, c three-phase conducting wire both end voltage is poor;

Be respectively a, b, c three-phase phase conductor metal level both end voltage is poor; For the return wire both end voltage;

Voltage for the earth wire.

By Kirchhoff's second law must this short circuit pattern under characteristic formula:

For the return wire both end voltage; For the electric current in the earth wire, comprise return wire induced potential generation current and short-circuit current partial current; R ₁And R ₂Stake resistance for the wire two ends; R _gFor ground resistance,

Voltage for the earth wire.

Solve above variously, can show that each phase metal level both end voltage is poor; Deduct the return wire both end voltage poor, can draw the return wire current potential; Be superimposed with again the earth mat potential rise, can draw the metal level voltage-to-ground.The earth mat potential rise calculates, and can calculate by GB/T50065-2011 appendix B.

Because the various superpotential for cable and calculation of circulating current all can be used same cable conductor system impedance matrix, while adopting the instrument such as Mathcad, Matlab, calculating is easier.Be below certain cable power supply loop, referring to Fig. 3, single-end earthed, during A phase single-phase short circuit, its superpotential is determined calculating process to metal level:

At first determine known parameters: I _a=1000A, metal level mean radius r _s=22.07mm, the return wire radius r _P=10mm, return wire resistance R=0.015 Ω, cable length L=1km(can calculate conductor resistance according to cable radius, length and resistivity, this is prior art), each wire pitch: D _Ab==D _Bc=200mm, D _Ac=400mm, D _Ag=600mm, D _Bg=400mm, Dc _g=200mm, D _g=1000m, ground resistance R _G=0.2 Ω etc., then ask the metal level induced voltage with general shortcut calculation.

Solution, according to general calculation method, solves as follows with Mathcad:

f:=50

ω＝2·π·f

k:＝i·2·10 ^-7·ω R1:＝0.1 R2：＝0.1

$\mathrm{rs}:=\frac{22.07}{1000}$ $\mathrm{rp}:=\frac{10}{1000}$ Ia：＝1000

Dab：＝0.2 Dbc：＝0.2 Dac：＝0.4 Dag:＝0.6 Dbg:=0.4 Dcg:＝0.2 Dg:＝1000

The metal level both end voltage is:

$\mathrm{ff}:=\left(\begin{array}{cccccccc}R+k\·l\·\ln \left(\frac{1}{\mathrm{rs}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dab}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dac}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dag}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dg}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{rs}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dab}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dac}}\right)\\ k\·l\·\ln \left(\frac{1}{\mathrm{Dab}}\right)& R+k\·l\·\ln \left(\frac{1}{\mathrm{rs}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dbc}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dbg}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dg}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dab}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{rs}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dbc}}\right)\\ k\·l\·\ln \left(\frac{1}{\mathrm{Dac}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dbc}}\right)& R+k\·l\·\ln \left(\frac{1}{\mathrm{rs}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dcg}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dac}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dac}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dbc}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{rs}}\right)\\ k\·l\·\ln \left(\frac{1}{\mathrm{Dag}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dbg}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dcg}}\right)& 0.015+k\·l\·\ln \left(\frac{1}{\mathrm{rp}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dag}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dac}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dbg}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dcg}}\right)\\ k\·l\·\ln \left(\frac{1}{\mathrm{Dg}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dg}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dg}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dg}}\right)& 0.2+k\·l\·\ln \left(\frac{1}{\mathrm{Dg}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dg}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dg}}\right)& k\·l\·\ln \left(\frac{1}{\mathrm{Dg}}\right)\end{array}\right)\left(\begin{array}{c}0\\ 0\\ 0\\ -I0p\\ I0p-\mathrm{Ia}\\ \mathrm{Ia}\\ 0\\ 0\end{array}\right)$

ff3＝ff4+(I0p-Ia)·R1+(I0p)·R2solve，I0p→522.22000677120313202-323.72010002109839887i

ff substitute， $I0p=522.22000677120313202-323.72010002109839887i\→\left(\begin{array}{c}-150.89344416186897774+430.21974909546257276i\\ -159.14057760315035468+278.42803651345192044i\\ -14.098567739152693839-22.74358045646449719i\\ -91.111997291518747193-129.48804000843935955i\\ -95.555998645759373595-64.744020004219679776i\end{array}\right)$

The foregoing is only preferred embodiment of the present invention, not in order to limit the present invention, it should be pointed out that all any modifications of doing within the spirit and principles in the present invention, be equal to replacement and improvement etc., within all should being included in protection scope of the present invention.

Claims (6)

1. the superpotential definite method of single core cable metal level, is characterized in that, the method comprises the following steps:

(1) according to the electrical lead system at single core cable place, set up following matrix equation:

Wherein $Z_{\mathrm{Ln}}=R_n+j\frac{{\mathrm{\μ}}_0}{2\mathrm{\π}}\left(\ln \frac{1}{r_n}\right),$ $Z_{\mathrm{Mki}}=j\frac{{\mathrm{\μ}}_0}{2\mathrm{\π}}\left(\ln \frac{1}{E_{\mathrm{ki}}}\right),$ Z in formula _LnBe n root wire self-impedance, Z _MkiBe that k, the mutual inductance of i root wire are anti-, R _nBe n root conductor resistance, r _nBe n root wire equivalent redius, D _KiBe k, i root wire pitch,

For the electric current that flows through wire,

Voltage difference for the wire two ends;

(2) according to Kirchhoff's current law (KCL), set up the current equation of the single core cable that needs definite overvoltage value;

(3) according to Kirchhoff's second law, set up the secular equation under the short circuit pattern;

(4) aforementioned three equations of simultaneous, and solve that to obtain single core cable metal level both end voltage poor, then according to the poor definite single core cable metal level superpotential of single core cable metal level both end voltage.

2. the superpotential definite method of a kind of single core cable metal level according to claim 1, it is characterized in that, in step (1), the electrical lead system at single core cable place comprises three-phase conducting wire, three-phase conducting wire metal level, return wire and the earth wire that the earth equivalence is become separately.

3. the superpotential definite method of a kind of single core cable metal level according to claim 2, is characterized in that, the self-induction of described the earth wire is With any other wire mutual inductances, be

The equivalent degree of depth and equivalent radius are D _g.

4. the superpotential definite method of a kind of single core cable metal level according to claim 2, is characterized in that, when for A phase single-phase short circuit single-end earthed, the current equation of A phase single core cable is

For the A phase current,

For the electric current in the earth wire,

For the electric current in return wire.

5. the superpotential definite method of a kind of single core cable metal level according to claim 2, is characterized in that, when for A phase single-phase short circuit single-end earthed, its secular equation is

For the return wire both end voltage,

For the electric current in the earth wire, R ₁And R ₂Stake resistance, R for the wire two ends _gFor ground resistance,

Voltage for the earth wire.

6. the superpotential definite method of a kind of single core cable metal level according to claim 1, it is characterized in that, according to the poor definite single core cable metal level superpotential of single core cable metal level both end voltage, be specially, first poor to deduct the return wire both end voltage poor by single core cable metal level both end voltage, can draw the return wire current potential; Be superimposed with again the earth mat potential rise, can draw the metal level voltage-to-ground, be i.e. the metal level superpotential.

Images