CN104267253A - Power loss calculation method for power cable sheath - Google Patents

Abstract

The invention discloses a power loss calculation method for a power cable sheath. An equivalent admittance matrix of a cable is derived according to basic parameters of the cable and the structure of the cable; the current of a cable sending end is calculated and determined according to the equivalent admittance matrix of the cable and boundary conditions of a cable system; the sheath current of each point of each section along the cable is determined according to the current of the cable sending end, and therefore the loss of the cable sheath is determined. Compared with the prior art, the power loss calculation method is short in consumed time and high in precision, the precise distribution condition of voltage and current along the cable can be calculated, the sheath loss of each section of the cable is determined, and a theoretical basis is provided for subsequent cable loss reducing strategies.

Description

A kind of power attenuation computing method of power cable sheath

Technical field

The invention belongs to power transmission technology field, be specifically related to a kind of power attenuation computing method of power cable sheath.

Background technology

Power cable power transmission mode is being rapidly developed in recent years, and increasing underground transmission system is applied in the expansion of urban distribution network, and reason mainly contains following three: the first, and growing environmental problem limits the application of overhead transmission line in city; The second, in ocean field of power transmission, subsea cable has unrivaled advantage compared with pole line; 3rd, the innovation on cables manufacturing and running technology makes insulated cable more have competitive power.

In single core cable, cable cover(ing) plays protection, in order to avoid single core conductor makes moist and is subject to physical damage; In addition, cable cover(ing) can shield electrostatic field, and as the loop of fault current and capacitive charging current.When flowing through alternating current in cable conductor, cable cover(ing) has induced voltage and produce, if the equal ground connection of the both-end of cable cover(ing), so induced voltage can produce circulation; This circulation then can produce appreciable sheath loss through sheath.For some cable system, circulation flow through sheath produce loss be even comparable to cable conductor produce loss, this will increase the generation of heat and the current-carrying capacity of cable can be made to be restricted.

From the above, cable cover(ing) loss problem can not be ignored, and forefathers mainly concentrate in the mechanism of production of circulating current in sheath and eddy current on the research of this problem and the aspect such as the factor affecting loss size.The Measures compare of systematic study sheath loss is full phase model method effectively, but there are following 2 problems in traditional full phase model method: 1) need all to set up nodal voltage equation at each segmentation segment, if ensure the degree of accuracy of model, overall voltage equation up to several ten thousand rank, may solve and extremely waste time and energy; 2) classic method is when obtaining the transmission matrix of coupling line, and need the characteristic root and the proper vector that solve complex matrix, this is also the link of extremely losing time.On the whole traditional sheath loss computing method for labyrinth cable system the low and time-consuming length of efficiency.

Summary of the invention

For the above-mentioned technical matters existing for prior art, the invention provides a kind of power attenuation computing method of power cable sheath, by solving the Equivalent admittance matrix of power cable and the boundary condition of coupling system, the sheath distribution of current that cable is along the line can be determined, and then solve accurate cable cover(ing) loss.

Power attenuation computing method for power cable sheath, comprise the steps:

(1) basic parameter of cable and the positive order parameter of equivalence of cable two ends electric system is obtained;

Described basic parameter comprises unit length series impedance matrix Z and the unit length shunt admittance matrix Y of cable, and the positive order parameter of described equivalence comprises the equivalent source electromotive force E of the every phase of sending end electric system _swith equiva lent impedance Z _sand the equivalent source electromotive force E of the every phase of receiving end electric system _rwith equiva lent impedance Z _r;

(2) according to the structure of described basic parameter and cable, the Equivalent admittance matrix Ye of cable is determined _q;

(3) according to the Equivalent admittance matrix Ye of cable _qand the boundary conditions of cable, calculate the voltage U of cable sending end _sand electric current I _s;

(4) according to the voltage U of cable sending end _sand electric current I _s, determine the sheath electric current of cable each point along the line;

(5) according to the sheath electric current of cable each point along the line, the power attenuation P of cable cover(ing) is calculated.

Cable Equivalent admittance matrix Y is determined in described step (2) _eqdetailed process as follows:

If cable is not segmental structure, then its Equivalent admittance matrix Y _eqexpression formula as follows:

$Y_{\mathrm{eq}}=\begin{array}{cc}{Y}_s& -Y_m\\ -Y_m& Y_s\end{array}=\begin{array}{cc}{Z}^{-1}\mathrm{\Γ}\coth \left(\mathrm{\Γl}\right)& -Z^{-1}\mathrm{\Γ}\mathrm{csch}\left(\mathrm{\Γl}\right)\\ -Z^{-1}\mathrm{\Γ}\mathrm{csch}\left(\mathrm{\Γl}\right)& Z^{-1}\mathrm{\Γ}\coth \left(\mathrm{\Γl}\right)\end{array}$

Wherein: Y _sand Y _mbe respectively self-admittance matrix and the transadmittance matrix of cable, coth and csch is respectively hyperbolic cotangent and hyperbolic cosecant, and Γ is propagation constant matrix and Γ=(ZY) ^1/2, l is cable length;

If cable be k section cross interconnected type structure or k section circulating picture-changing bit-type structure, then cable comprises k section conductor and k-1 joint, k be greater than 1 natural number;

First, according to the admittance matrix of following formula determination cable every section of conductor:

$Y_i=\begin{array}{cc}{Y}_{\mathrm{si}}& -Y_{\mathrm{mi}}\\ -Y_{\mathrm{mi}}& Y_{\mathrm{si}}\end{array}=\begin{array}{cc}{Z}^{-1}\mathrm{\Γ}\coth \left(\mathrm{\Γ}{l}_i\right)& -Z^{-1}\mathrm{\Γ}\mathrm{csch}\left(\mathrm{\Γ}{l}_i\right)\\ -Z^{-1}\mathrm{\Γ}\mathrm{csch}\left(\mathrm{\Γ}{l}_i\right)& Z^{-1}\mathrm{\Γ}\coth \left(\mathrm{\Γ}{l}_i\right)\end{array}$

Wherein: Y _ibe the admittance matrix of i-th section of conductor, i is natural number and 1≤i≤k, Y _siand Y _mibe respectively self-admittance matrix and the transadmittance matrix of i-th section of conductor, l _ibe the length of i-th section of conductor;

Then, the admittance matrix of each joint of cable is determined;

If the cable cross interconnected type structure that is k section, the admittance matrix of its each joint all adopts following formula:

$Y_c=\begin{array}{cc}{Y}_{\mathrm{sc}}& -Y_{\mathrm{mc}}\\ {Y_{\mathrm{mc}}}^T& Y_{\mathrm{sc}}\end{array}=\begin{array}{cccc}{g}_c{I}_{33}& 0& -g_c{I}_{33}& 0\\ 0& g_s{I}_{3\×3}& 0& -g_s{M}_c\\ -g_c{I}_{33}& 0& g_c{I}_{33}& 0\\ 0& -g_s{M_c}^T& 0& g_s{I}_{3\×3}\end{array}$

If cable is k section circulating picture-changing bit-type structure, the admittance matrix of its each joint all adopts following formula:

$Y_c=\begin{array}{cc}{Y}_{\mathrm{sc}}& -Y_{\mathrm{mc}}\\ {Y_{\mathrm{mc}}}^T& Y_{\mathrm{sc}}\end{array}=\begin{array}{cccc}{g}_c{I}_{3\×3}& 0& -g_c{M}_c& 0\\ 0& g_s{I}_{33\×}& 0& -g_s{I}_{33}\\ -g_c{M_c}^T& 0& g_c{I}_{3\×3}& 0\\ 0& -g_s{I}_{33}& 0& g_s{I}_{33}\end{array}$

Wherein: Y _cfor the admittance matrix of joint, Y _scand Y _mcbe respectively self-admittance matrix and the transadmittance matrix of joint, $M_c=\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 1& 0& 0\end{array},$ ^trepresent transposition, I _{3 × 3}be three rank unit matrixs, g _cfor the admittance of connecting line between conductor, g _sfor the admittance of connecting line between sheath;

Finally, all see conductor and joint as cell block, then cable is made up of 2k-1 cell block cascade; Appoint and get two adjacent cell block p and q and be merged into a new cell block, obtain the admittance matrix Y of new cell block _pqas follows, carry out one by one according to this merging the Equivalent admittance matrix Y namely obtaining cable _eq;

$Y_{\mathrm{pq}}=\begin{array}{cc}{Y}_{\mathrm{sp}}-Y_{\mathrm{mp}}{(Y_{\mathrm{sp}}+Y_{\mathrm{sq}})}^{-1}{Y_{\mathrm{mp}}}^T& -Y_{\mathrm{mp}}{(Y_{\mathrm{sp}}+Y_{\mathrm{sq}})}^{-1}{Y_{\mathrm{mq}}}^T\\ -Y_{\mathrm{mq}}{(Y_{\mathrm{sp}}+Y_{\mathrm{sq}})}^{-1}{Y_{\mathrm{mp}}}^T& Y_{\mathrm{sq}}-Y_{\mathrm{mq}}{(Y_{\mathrm{sp}}+Y_{\mathrm{sq}})}^{-1}{Y_{\mathrm{mq}}}^T\end{array}$

Wherein: Y _spand Y _mpbe respectively self-admittance matrix and the transadmittance matrix of cell block p, Y _sqand Y _mqbe respectively self-admittance matrix and the transadmittance matrix of cell block q.

Described self-admittance matrix Y _sand Y _siand transadmittance matrix Y _mand Y _miemploying Bernoulli's series launches, and expression is as follows:

$Y_s=Z^{-1}\mathrm{\Γ}\coth \left(\mathrm{\Γl}\right)={\left(\mathrm{Zl}\right)}^{-1}[I_{6\×6}+\frac{1}{3}\left({\mathrm{ZYl}}^2\right)-\frac{1}{45}{\left({\mathrm{ZYl}}^2\right)}^2+\frac{2}{945}{\left({\mathrm{ZYl}}^2\right)}^3+...+\frac{2^{2n}{B}_{2n}}{\left(2n\right)!}{\left({\mathrm{ZYl}}^2\right)}^n]$

$Y_{\mathrm{si}}=Z^{-1}\mathrm{\Γ}\coth \left(\mathrm{\Γ}{l}_i\right)={\left(Z{l}_i\right)}^{-1}[I_{6\×6}+\frac{1}{3}\left({\mathrm{ZY}{l}_i}^2\right)-\frac{1}{45}{\left({\mathrm{ZY}{l}_i}^2\right)}^2+\frac{2}{945}{\left({\mathrm{ZY}{l}_i}^2\right)}^3+...+\frac{2^{2n}{B}_{2n}}{\left(2n\right)!}{\left({\mathrm{ZY}{l}_i}^2\right)}^n]$

$Y_{\mathrm{mi}}=Z^{-1}\mathrm{\Γ}\mathrm{csch}\left(\mathrm{\Γl}\right)={\left(\mathrm{Zl}\right)}^{-1}[I_{6\×6}-\frac{1}{6}\left({\mathrm{ZYl}}^2\right)+\frac{7}{360}{\left({\mathrm{ZYl}}^2\right)}^2-\frac{31}{15120}{\left({\mathrm{ZYl}}^2\right)}^3+...+\frac{{1-2}^{2n}{B}_{2n}}{\left(2n\right)!}{\left({\mathrm{ZYl}}^2\right)}^n]$

$Y_{\mathrm{mi}}=Z^{-1}\mathrm{\Γ}\mathrm{csch}\left(\mathrm{\Γ}{l}_i\right)={\left(Z{l}_i\right)}^{-1}[I_{6\×6}-\frac{1}{6}\left({\mathrm{ZY}{l}_i}^2\right)+\frac{7}{360}{\left({\mathrm{ZY}{l}_i}^2\right)}^2-\frac{31}{15120}{\left({\mathrm{ZY}{l}_i}^2\right)}^3+...+\frac{{1-2}^{2n}{B}_{2n}}{\left(2n\right)!}{\left({\mathrm{ZY}{l}_i}^2\right)}^n]$

Wherein: I _{6 × 6}be six rank unit matrixs, n be greater than 9 natural number, B _2nit is 2n item Bernoulli Jacob coefficient.

The voltage U of cable sending end is calculated in described step (3) _sand electric current I _sconcrete grammar as follows:

First, according to the Equivalent admittance matrix Y of cable _eqsetting up cable send the relational expression by both end voltage and electric current as follows:

$\begin{array}{c}{I}_S\\ I_R\end{array}=Y_{\mathrm{eq}}\begin{array}{c}{U}_S\\ U_R\end{array}$

Wherein: U _rand I _rbe respectively the voltage and current of cable receiving end, I _sand I _rbe six-vector and wherein contain the three-phase current of cable core and the three-phase current of cable cover(ing) successively, U _sand U _rbe six-vector and wherein contain the three-phase voltage of cable core and the three-phase voltage of cable cover(ing) successively;

Then, the boundary conditions of simultaneous above formula and cable, can solve the voltage U of cable sending end _sand electric current I _s; If cable is two sides earth system, its boundary conditions is as follows:

$\begin{array}{c}{U}_S^{123}\\ U_S^{456}\end{array}=\begin{array}{c}{E}_S-I_S^{123}{Z}_S\\ 0\end{array}$ $\begin{array}{c}{U}_R^{123}\\ U_R^{456}\end{array}=\begin{array}{c}{E}_R-I_R^{123}{Z}_R\\ 0\end{array}$

If cable is the system single-end earthed without earth lead (being called for short ecc), its boundary conditions is as follows:

$\begin{array}{c}{U}_S^{123}\\ U_S^{456}\end{array}=\begin{array}{c}{E}_S-I_S^{123}{Z}_S\\ 0\end{array}$ $\begin{array}{c}{U}_R^{123}\\ I_R^{456}\end{array}=\begin{array}{c}{E}_R-I_R^{123}{Z}_R\\ 0\end{array}$

If cable is the system single-end earthed with earth lead, its boundary conditions is as follows:

$\begin{array}{c}{U}_S^{123}\\ U_S^{456}\\ U_S^7\end{array}=\begin{array}{c}{E}_S-I_S^{123}{Z}_S\\ 0\\ 0\end{array}$ $\begin{array}{c}{U}_R^{123}\\ I_R^{456}\\ I_R^7\end{array}=\begin{array}{c}{E}_R-I_R^{123}{Z}_R\\ 0\\ 0\end{array}$

Wherein: with be respectively three-phase voltage and the three-phase current of cable sending end core, with be respectively three-phase voltage and the three-phase current of cable receiving end core, with be respectively three-phase voltage and the three-phase current of cable receiving end sheath, with be respectively sending end voltage and the receiving end electric current of earth lead.

Determine in described step (4) that the method for cable each point along the line sheath electric current is as follows:

For some cable i-th section of conductor with this section of conductor initiating terminal apart from length being x, calculate the voltage U of this point according to following formula _xiand electric current I _xi, and then from this electric current I _xiin extract sheath electric current; I is natural number and 1≤i≤k, k is the segmentation number of cable, if cable is not segmental structure, then k=1;

$\begin{array}{c}{I}_{\mathrm{xi}}\\ U_{\mathrm{xi}}\end{array}=\begin{array}{ccc}-Y_{\mathrm{si}}\left(x\right)+Y_{\mathrm{mi}}{\left(x\right)}^{-1}& -Y_{\mathrm{mi}}\left(x\right)+Y_{\mathrm{si}}\left(x\right)Y_{\mathrm{mi}}{\left(x\right)}^{-1}{Y}_{\mathrm{si}}\left(x\right)& I_{\mathrm{Si}}\\ -Y_{\mathrm{mi}}{\left(x\right)}^{-1}& Y_{\mathrm{mi}}{\left(x\right)}^{-1}{Y}_{\mathrm{si}}\left(x\right)& U_{\mathrm{Si}}\end{array}$

Wherein: U _siand I _sibe respectively the voltage and current of cable i-th section of conductor initiating terminal, Y _si(x) and Y _mix () is respectively self-admittance matrix between i-th section of conductor initiating terminal and this point and transadmittance matrix; I _siand I _xibe six-vector and wherein contain the three-phase current of cable core and the three-phase current of cable cover(ing) successively, U _siand U _xibe six-vector and wherein contain the three-phase voltage of cable core and the three-phase voltage of cable cover(ing) successively.

Described self-admittance matrix Y _si(x) and transadmittance matrix Y _mix () adopts Bernoulli's series to launch, expression is as follows:

$\begin{array}{c}{Y}_{\mathrm{si}}\left(x\right)=Z^{-1}\mathrm{\Γ}\coth \left(\mathrm{\Γx}\right)={\left(\mathrm{Zx}\right)}^{-1}[I_{6\×6}+\frac{1}{3}\left({\mathrm{ZYx}}^2\right)-\frac{1}{45}{\left({\mathrm{ZYx}}^2\right)}^2+\frac{2}{945}{\left({\mathrm{ZYx}}^2\right)}^3+...+\frac{2^{2n}{B}_{2n}}{\left(2n\right)!}{\left({\mathrm{ZYx}}^2\right)}^n]\\ ={\left(Z\right)}^{-1}{x}^{-1}+\frac{1}{3}{\mathrm{Yx}}^1-\frac{1}{45}{\mathrm{ZY}}^2{x}^3+\frac{1}{945}{Z}^2{Y}^3{x}^5+...+\frac{2^{2n}{B}_{2n}}{\left(2n\right)!}{Z}^{n-1}{Y}^n{x}^{2n-1}\end{array}$

$\begin{array}{c}{Y}_{\mathrm{mi}}\left(x\right)=Z^{-1}\mathrm{\Γcsth}\left(\mathrm{\Γx}\right)={\left(\mathrm{Zx}\right)}^{-1}[I_{6\×6}-\frac{1}{6}\left({\mathrm{ZYx}}^2\right)+\frac{7}{360}{\left({\mathrm{ZYx}}^2\right)}^2-\frac{31}{15120}{\left({\mathrm{ZYx}}^2\right)}^3+...+\frac{1-2^{2n}{B}_{2n}}{\left(2n\right)!}{\left({\mathrm{ZYx}}^2\right)}^n]\\ ={\left(Z\right)}^{-1}{x}^{-1}-\frac{1}{6}{\mathrm{Yx}}^1+\frac{7}{360}{\mathrm{ZY}}^2{x}^3-\frac{31}{15120}{Z}^2{Y}^3{x}^5+...+\frac{1-2^{2n}{B}_{2n}}{\left(2n\right)!}{Z}^{n-1}{Y}^n{x}^{2n-1}\end{array}$

Wherein: coth and csch is respectively hyperbolic cotangent and hyperbolic cosecant, Γ is propagation constant matrix and Γ=(ZY) ^1/2, I _{6 × 6}be six rank unit matrixs, n be greater than 9 natural number, B2n is 2n item Bernoulli Jacob coefficient.

The voltage U of described cable i-th section of conductor initiating terminal _siand electric current I _simethod for solving as follows: if cable is not segmental structure, then voltage U _siand electric current I _sinamely the voltage U of cable sending end is corresponded to _sand electric current I _s; If cable is segmental structure, then voltage U _siand electric current I _sisolve according to following relational expression:

$\begin{array}{c}{I}_S\\ I_{\mathrm{Si}}\end{array}=Y_{\mathrm{Si}}\begin{array}{c}{U}_S\\ U_{\mathrm{Si}}\end{array}$

Wherein: Y _sifor the admittance matrix between cable sending end and i-th section of conductor initiating terminal, namely between cable sending end and i-th section of conductor initiating terminal all cell blocks merge after admittance matrix.

Calculate the power attenuation P of cable cover(ing) according to following formula in described step (5):

$P=\underset{i=1}{\overset{k}{\mathrm{\Σ}}}{\∫}_0^{l_i}{I}_i^T\left(x\right)I_i\left(x\right)R_c\mathrm{dx}$

Wherein: l _ifor the length of cable i-th section of conductor, I _ix () is for cable i-th section of conductor with this section of conductor initiating terminal distance length being the sheath electric current of the point of x and I _ix () wherein contains the three-phase current of cable cover(ing) for tri-vector, ^trepresent transposition, R _cfor the sheath resistance of cable unit length, k is the segmentation number of cable.

The Advantageous Effects of the inventive method is as follows:

(1) the present invention solves the admittance matrix of coupling line by adopting the method for uncle's series expansion, thus avoids in classic method and solve the eigenwert of complex matrix and the step of proper vector.

(2) invention introduces matrix of coefficients, when calculating the admittance matrix of different length, matrix of coefficients is constant, only different length need be substituted into expression formula and all can; For the admittance matrix solving different length cable saves plenty of time and operand.

(3) the present invention no matter cable be divided into several sections and how little cable step-length dx value have, the exponent number of final nodal voltage equation is 2n*2n, avoids the problem that in classic method, matrix exponent number is excessive.

The present invention can calculate the sheath loss of various structure power cable efficiently, comprising two-terminal-grounding cable, single-end earthed cable, and band ecc cable and cross interconnected cable.While guarantee counting yield, this method also can provide higher precision.In actual cable engineering, this method can be used for comparing and optimizing the construction of cable, seeks the method reducing sheath loss.

Accompanying drawing explanation

Fig. 1 is the schematic flow sheet of the inventive method.

Fig. 2 is the basic block diagram without armored type threephase cable.

Fig. 3 (a) is the cross-over joint schematic diagram of the cross interconnected type construction of cable of n section.

Fig. 3 (b) is the cross-over joint schematic diagram of the n section circulating picture-changing bit-type construction of cable.

The boundary condition schematic diagram that Fig. 4 (a) is two sides earth cable system.

The boundary condition schematic diagram that Fig. 4 (b) is two sides earth cable system.

The boundary condition schematic diagram that Fig. 4 (c) is two sides earth cable system.

Embodiment

In order to more specifically describe the present invention, below in conjunction with the drawings and the specific embodiments, technical scheme of the present invention is described in detail.

As shown in Figure 1, a kind of power attenuation computing method of power cable sheath, comprise the steps:

(1) basic parameter obtaining cable comprises unit length series impedance matrix Z and shunt admittance matrix Y, and the positive order parameter of the equivalence of cable two ends electric system comprises the equivalent source amplitude E of sending end electric system _s, phase theta _swith equiva lent impedance Z _s, the equivalent source amplitude E of receiving end electric system _r, θ _rwith equiva lent impedance Z _r; The method for solving of above parameter is quite ripe, therefore not in the middle of the discussion of the inventive method.

(2) to derive respectively its Equivalent admittance matrix according to the structure of cable:

First the numbering of regulation threephase cable conductor is respectively 1,2,3, and the numbering of three-phase sheath is respectively 4,5,6, as shown in Figure 2, if the construction of cable is the basic structure of not segmentation, then according to the transmission line model of classics, and the Equivalent admittance matrix Y of cable _eqexpression formula as follows:

$Y_{\mathrm{eq}}=\begin{array}{cc}{Y}_s& -Y_m\\ -Y_m& Y_s\end{array}=\begin{array}{cc}{Z}^{-1}\mathrm{\Γ}\coth \left(\mathrm{\Γl}\right)& -Z^{-1}\mathrm{\Γ}\mathrm{csch}\left(\mathrm{\Γl}\right)\\ -Z^{-1}\mathrm{\Γ}\mathrm{csch}\left(\mathrm{\Γl}\right)& Z^{-1}\mathrm{\Γ}\coth \left(\mathrm{\Γl}\right)\end{array}$

Wherein: Y _sfor the self-admittance matrix of cable and Y _s=Z ^-1Γ coth (Γ l), Y _mfor the transadmittance matrix of cable and Y _m=Z ^-1Γ csch (Γ l), coth and csch is respectively coth and hyperbolic cosecant, and Γ is propagation constant matrix and Γ=(ZY) ^1/2, Z is the unit length series impedance matrix of cable, and Y is the unit length shunt admittance matrix of cable, and l is cable length;

If the structure of cable is the cross interconnected type of n section, as shown in Fig. 3 (a), or n section transposition type structure, as shown in Fig. 3 (b), n be greater than 1 natural number, then cable inside is containing n-1 cross-over joint, and the length of known i-th section is l _i, i is natural number and 1<i≤n, so the Equivalent admittance matrix Y of cable _eqderivation as follows:

A1. according to the transmission line model of classics, the admittance matrix Y of i-th section of conductor of the cable of cross interconnected type or transposition type structure can be determined _iexpression formula is as follows:

$Y_i=\begin{array}{cc}{Y}_{\mathrm{si}}& -Y_{\mathrm{mi}}\\ -Y_{\mathrm{mi}}& Y_{\mathrm{si}}\end{array}=\begin{array}{cc}{Z}^{-1}\mathrm{\&Gamma;}\coth \left(\mathrm{\&Gamma;}{l}_i\right)& -Z^{-1}\mathrm{\&Gamma;}\mathrm{csch}\left(\mathrm{\&Gamma;}{l}_i\right)\\ -Z^{-1}\mathrm{\&Gamma;}\mathrm{csch}\left(\mathrm{\&Gamma;}{l}_i\right)& Z^{-1}\mathrm{\&Gamma;}\coth \left(\mathrm{\&Gamma;}{l}_i\right)\end{array}$

Utilize the method for series expansion can in the hope of separating its numerical value:

$\coth \left(\mathrm{\&Gamma;}{l}_i\right)={\left({\mathrm{\&Gamma;l}}_i\right)}^{-1}+\frac{1}{3}\left(\mathrm{\&Gamma;}{l}_i\right)-\frac{1}{45}{\left(\mathrm{\&Gamma;}{l}_i\right)}^3+...+\frac{2^{2n}{B}_{2n}}{\left(2n\right)!}{\left(\mathrm{\&Gamma;}{l}_i\right)}^{2n-1}$

$\mathrm{csth}\left(\mathrm{\&Gamma;}{l}_i\right)={\left({\mathrm{\&Gamma;l}}_i\right)}^{-1}-\frac{1}{6}\left(\mathrm{\&Gamma;}{l}_i\right)+\frac{7}{360}{\left(\mathrm{\&Gamma;}{l}_i\right)}^3+...+\frac{1-2^{2n}{B}_{2n}}{\left(2n\right)!}{\left(\mathrm{\&Gamma;}{l}_i\right)}^{2n-1}$

Wherein: B _2nfor Bernoulli number, Y _si, Y _mibe respectively self-admittance and the transadmittance matrix of i-th section of cable; Then have:

$Y_{\mathrm{si}}=Z^{-1}\mathrm{\&Gamma;}\coth \left(\mathrm{\&Gamma;}{l}_i\right)={\left(Z{l}_i\right)}^{-1}[I+\frac{1}{3}\left({\mathrm{ZY}{l}_i}^2\right)-\frac{1}{45}{\left({\mathrm{ZY}{l}_i}^2\right)}^2+\frac{2}{945}{\left({\mathrm{ZY}{l}_i}^2\right)}^3+...+\frac{2^{2n}{B}_{2n}}{\left(2n\right)!}{\left({\mathrm{ZY}{l}_i}^2\right)}^n]$

$Y_{\mathrm{mi}}=Z^{-1}\mathrm{\&Gamma;}\mathrm{csch}\left(\mathrm{\&Gamma;}{l}_i\right)={\left(Z{l}_i\right)}^{-1}[I-\frac{1}{6}\left({\mathrm{ZY}{l}_i}^2\right)+\frac{7}{360}{\left({\mathrm{ZY}{l}_i}^2\right)}^2-\frac{31}{15120}{\left({\mathrm{ZY}{l}_i}^2\right)}^3+...+\frac{{1-2}^{2n}{B}_{2n}}{\left(2n\right)!}{\left({\mathrm{ZY}{l}_i}^2\right)}^n]$

A2. according to the feature of the cross interconnected type of n section or the transposition type construction of cable, the admittance matrix of n-1 joint of the same construction of cable is consistent, the existing joint admittance matrix Y with regard to the cross interconnected type construction of cable of n section _cexpression formula derive as follows:

As shown in Fig. 3 (a), because the cable of cross interconnected type structure is in joint, its three-phase conductor does not replace, and just threephase cable sheath replaces, successively so joint admittance matrix Y _cself-admittance matrix Y _scexpression formula be:

$Y_{\mathrm{sc}}=\begin{array}{cc}{g}_c{I}_{3\&times;3}& \\ & g_s{I}_{3\&times;3}\end{array}$

Wherein: g _cfor the admittance connected between conductor, g _sfor the admittance connected between sheath, I _{3 × 3}be three rank unit matrixs; Joint admittance matrix Y _ctransadmittance matrix Y _mcexpression formula be:

$Y_{\mathrm{mc}}=\begin{array}{cc}{g}_c{I}_{3\&times;3}& \\ & g_s{M}_c\end{array}$

Wherein: g _cfor the admittance connected between conductor, g _sfor the admittance connected between sheath, I _{3 × 3}be three rank unit matrixs, M _cfor the incidence matrix of joint sheath transposition, and M _cexpression formula is:

$M_c=\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 1& 0& 0\end{array}$

According to joint admittance matrix Y _cself-admittance matrix Y _scwith transadmittance matrix Y _mcexpression formula, the joint admittance matrix Y of the cross interconnected type construction of cable can be determined _cexpression formula is:

$Y_c=\begin{array}{cc}{Y}_{\mathrm{sc}}& -Y_{\mathrm{mc}}\\ {Y_{\mathrm{mc}}}^{\&prime;}& Y_{\mathrm{sc}}\end{array}=\begin{array}{cccc}{g}_c{I}_{33}& 0& -g_c{I}_{33}& 0\\ 0& g_s{I}_{3\&times;3}& 0& -g_s{M}_c\\ -g_c{I}_{33}& 0& g_c{I}_{33}& 0\\ 0& -g_s{M_c}^{\&prime;}& 0& g_s{I}_{3\&times;3}\end{array}$

Wherein: M _c' be M _ctransposed matrix;

In like manner, in joint, its three-phase conductor replaces the cable of transposition type structure successively, and threephase cable sheath does not replace, so joint admittance matrix Y _texpression formula be:

$Y_t=\begin{array}{cccc}{g}_c{I}_{3\&times;3}& 0& -g_c{M}_c& 0\\ 0& g_s{I}_{33}& 0& -g_s{I}_{33}\\ -g_c{M_c}^{\&prime;}& 0& g_c{I}_{3\&times;3}& 0\\ 0& -g_s{I}_{33}& 0& g_s{I}_{33}\end{array}$

A3. for the cross interconnected type of n section or transposition type cable, it comprises n-1 joint, we are referred to as a cell block every section of cable and each joint, so complete cable is equivalent to be composed in series by (n+n-1) individual cell block, as shown in Fig. 3 (a), now get two adjacent cell block p and q carry out abbreviation merging, to obtain its Equivalent admittance matrix to appointing:

Because the Injection Current of any two adjacent cells block junction M is zero, so its nodal voltage equation is:

$\begin{array}{c}{I}_S\\ I_R\\ 0\end{array}=\begin{array}{cccc}{Y}_{\mathrm{sp}}& 0& -Y_{\mathrm{mp}}& U_S\\ 0& Y_{\mathrm{sq}}& -Y_{\mathrm{mq}}& U_R\\ -{Y_{\mathrm{mp}}}^{\&prime;}& -{Y_{\mathrm{mq}}}^{\&prime;}& Y_{\mathrm{sp}}+Y_{\mathrm{sq}}& U_M\end{array}$

Wherein: Y _sp, Y _mpbe respectively self-admittance matrix and the transadmittance matrix of cell block p, Y _sq, Y _mqbe respectively cell block _qself-admittance matrix and transadmittance matrix, Y _mp', Y _mq' be respectively Y _mp, Y _mqtransposed matrix, I _s, U _sbe respectively electric current and the voltage vector of sending end, I _r, U _rbe respectively electric current and the voltage vector of receiving end, U _mfor adjacent two cell block junction voltage vectors;

By cancellation U _m, the Equivalent admittance matrix Y of adjacent cells block p and q can be obtained _eq-2expression formula be:

$Y_{\mathrm{eq}-2}=\begin{array}{cc}{Y}_{\mathrm{sp}}-Y_{\mathrm{mp}}{(Y_{\mathrm{sp}}+Y_{\mathrm{sq}})}^{-1}{Y^{\&prime;}}_{\mathrm{mp}}& -Y_{\mathrm{mp}}{(Y_{\mathrm{sp}}+Y_{\mathrm{sq}})}^{-1}{Y^{\&prime;}}_{\mathrm{mq}}\\ -Y_{\mathrm{mq}}{(Y_{\mathrm{sp}}+Y_{\mathrm{sq}})}^{-1}{Y^{\&prime;}}_{\mathrm{mp}}& Y_{\mathrm{sq}}-Y_{\mathrm{mq}}{(Y_{\mathrm{sp}}+Y_{\mathrm{sq}})}^{-1}{Y^{\&prime;}}_{\mathrm{mq}}\end{array}$

Wherein: the self-admittance matrix of this equivalent admittance matrix is Y _sp-Y _mp(Y _sp+ Y _sq) ^-1y' _mp, transadmittance matrix is-Y _mp(Y _sp+ Y _sq) ^-1y' _mq.

Finally, the Equivalent admittance matrix of being derived the last time is as the known conditions of matrix merging next time, substitute in nodal voltage equation next time, as long as repeat this process 2n-2 time, we can derive the overall Equivalent admittance matrix Y of the cross interconnected type of n section or transposition type cable _eq.

(3) according to the cable Equivalent admittance matrix Y derived in step (2) _eq, determine that the method for cable sending end electric current is as follows:

B1. Fig. 4 (a) ~ (c) represents respectively: two sides earth system, single-end earthed system, system single-end earthed with ecc, and the boundary condition of these three kinds of cable systems is respectively:

Two sides earth system: $\begin{array}{c}{U}_S^{123}\\ U_S^{456}\end{array}=\begin{array}{c}{E}_S-I_S^{123}{Z}_S\\ 0\end{array},$ $\begin{array}{c}{U}_R^{123}\\ U_R^{456}\end{array}=\begin{array}{c}{E}_R-I_R^{123}{Z}_R\\ 0\end{array};$

System single-end earthed: $\begin{array}{c}{U}_S^{123}\\ U_S^{456}\end{array}=\begin{array}{c}{E}_S-I_S^{123}{Z}_S\\ 0\end{array},$ $\begin{array}{c}{U}_R^{123}\\ I_R^{456}\end{array}=\begin{array}{c}{E}_R-I_R^{123}{Z}_R\\ 0\end{array};$

System single-end earthed with ecc: $\begin{array}{c}{U}_S^{123}\\ U_S^{456}\\ U_S^7\end{array}=\begin{array}{c}{E}_S-I_S^{123}{Z}_S\\ 0\\ 0\end{array},$ $\begin{array}{c}{U}_R^{123}\\ I_R^{456}\\ I_R^7\end{array}=\begin{array}{c}{E}_R-I_R^{123}{Z}_R\\ 0\\ 0\end{array};$

Wherein: with represent the voltage and current vector of cable sending end and receiving end conductor respectively, represent the voltage vector of cable sending end sheath, represent the voltage and current vector of cable receiving end sheath respectively, represent sending end voltage and the receiving end electric current of earth lead ecc respectively, E _s, Z _sand E _r, Z _rrepresent equivalent source amplitude and the equiva lent impedance of sending end and receiving end electric system respectively;

B2. according to the numerical solution of the value matrixs such as the cable of trying to achieve in step (2), we can obtain sending the electric current and voltage vector relations of receiving end be:

$\begin{array}{c}{I}_S\\ I_R\end{array}=Y_{\mathrm{eq}}\begin{array}{c}{U}_S\\ U_R\end{array}$

Corresponding cable system boundary condition in simultaneous above formula and B1, can solve the sending end voltage and current vector U of cable _swith I _s.

(4) determine that the process of the cable sheath electric current of every section of each point is along the line as follows:

C1. for i-th section of cable, electric current and the voltage at its arbitrfary point place is solved by following formula:

$\begin{array}{c}{I}_{\mathrm{Si}}\\ I_{\mathrm{xi}}\end{array}=\begin{array}{ccc}{Z}^{-1}\mathrm{\&Gamma;}\coth \left(\mathrm{\&Gamma;x}\right)& -Z^{-1}\mathrm{\&Gamma;}\mathrm{csch}\left(\mathrm{\&Gamma;x}\right)& U_{\mathrm{Si}}\\ -Z^{-1}\mathrm{\&Gamma;}\mathrm{csch}\left(\mathrm{\&Gamma;x}\right)& Z^{-1}\mathrm{\&Gamma;}\coth \left(\mathrm{\&Gamma;x}\right)& U_{\mathrm{xi}}\end{array}=\begin{array}{ccc}{Y}_s\left(x\right)& -Y_m\left(x\right)& U_{\mathrm{Si}}\\ -Y_m\left(x\right)& Y_s\left(x\right)& U_{\mathrm{xi}}\end{array}$

Can obtain further:

$\begin{array}{c}{I}_{\mathrm{xi}}\\ U_{\mathrm{xi}}\end{array}=\begin{array}{ccc}-Y_{\mathrm{si}}\left(x\right)+Y_{\mathrm{mi}}{\left(x\right)}^{-1}& -Y_{\mathrm{mi}}\left(x\right)+Y_{\mathrm{si}}\left(x\right)Y_{\mathrm{mi}}{\left(x\right)}^{-1}{Y}_{\mathrm{si}}\left(x\right)& I_{\mathrm{Si}}\\ -Y_{\mathrm{mi}}{\left(x\right)}^{-1}& Y_{\mathrm{mi}}{\left(x\right)}^{-1}{Y}_{\mathrm{si}}\left(x\right)& U_{\mathrm{Si}}\end{array}$

Wherein: I _si, U _sirepresent electric current and the voltage vector of this section of cable sending end respectively, x represents the distance of this point to this section of cable sending end, I _xi, U _xirepresent electric current and the voltage vector at some x place respectively, Y _si(x), Y _mix () represent respectively apart from this section of sending end to be cable self-admittance and the transadmittance matrix of x;

C2. to Y _si(x), Y _mix () carries out series expansion:

$\begin{array}{c}{Y}_{\mathrm{si}}\left(x\right)=Z^{-1}\mathrm{\&Gamma;}\coth \left(\mathrm{\&Gamma;x}\right)={\left(\mathrm{Zx}\right)}^{-1}[I+\frac{1}{3}\left({\mathrm{ZYx}}^2\right)-\frac{1}{45}{\left({\mathrm{ZYx}}^2\right)}^2+\frac{2}{945}{\left({\mathrm{ZYx}}^2\right)}^3+...+\frac{2^{2n}{B}_{2n}}{\left(2n\right)!}{\left({\mathrm{ZYx}}^2\right)}^n]\\ ={\left(Z\right)}^{-1}{x}^{-1}+\frac{1}{3}{\mathrm{Yx}}^1-\frac{1}{45}{\mathrm{ZY}}^2{x}^3+\frac{1}{945}{Z}^2{Y}^3{x}^5+...+\frac{2^{2n}{B}_{2n}}{\left(2n\right)!}{Z}^{n-1}{Y}^n{x}^{2n-1}\\ =A_{s0}{x}^{-1}+A_{s1}{x}^1+A_{s2}{x}^3+A_{s3}{x}^5+...+A_{\mathrm{sn}}{x}^{2n-1}\end{array}$

$\begin{array}{c}{Y}_{\mathrm{mi}}\left(x\right)=Z^{-1}\mathrm{\&Gamma;}\mathrm{csch}\left(\mathrm{\&Gamma;x}\right)={\left(\mathrm{Zx}\right)}^{-1}[I-\frac{1}{6}\left({\mathrm{ZYx}}^2\right)+\frac{7}{360}{\left({\mathrm{ZYx}}^2\right)}^2-\frac{31}{15120}{\left({\mathrm{ZYx}}^2\right)}^3+...+\frac{1-2^{2n}{B}_{2n}}{\left(2n\right)!}{\left({\mathrm{ZYx}}^2\right)}^n]\\ ={\left(Z\right)}^{-1}{x}^{-1}-\frac{1}{6}{\mathrm{Yx}}^1+\frac{7}{360}{\mathrm{ZY}}^2{x}^3-\frac{31}{15120}{Z}^2{Y}^3{x}^5+...+\frac{1-2^{2n}{B}_{2n}}{\left(2n\right)!}{Z}^{n-1}{Y}^n{x}^{2n-1}\\ =A_{m0}{x}^{-1}+A_{m1}{x}^1+A_{m2}{x}^3+A_{m3}{x}^5+...+A_{\mathrm{mn}}{x}^{2n-1}\end{array}$

Wherein: Y _si(x), Y _mix the multinomial coefficient of () only gets front ten, be respectively:

A _s0＝Z ^-1，A _s1＝(1/3)Y，A _s2＝(-1/45)ZY ²，A _s3＝(2/945)Z ²Y ³，A _s4＝(-1/4725)Z ³Y ⁴，

A _s5＝(2/93555)Z ⁴Y ⁵，A _s6＝(-2.164e-6)Z ⁵Y ⁶，A _s7＝(2.193e-7)Z ⁶Y ⁷，

A _s8＝(-2.221e-8)Z ⁷Y ⁸，A _s9＝(2.251e-9)Z ⁸Y ⁹；

A _m0＝Z ^-1，A _m1＝(-1/6)Y，A _m2＝(7/360)ZY ²，A _m3＝(-31/15120)Z ²Y ³，A _m4＝(2.1e-4)Z ³Y ⁴，

A _m5＝(-2.134e-5)Z ⁴Y ⁵，A _m6＝(2.163e-6)Z ⁵Y ⁶，A _m7＝(-2.192e-7)Z ⁶Y ⁷，

A _m8＝(2.221e-8)Z ⁷Y ⁸，A _m9＝(-2.251e-9)Z ⁸Y ⁹；

When series expansion gets first 10, Y _si(x), Y _mix the precision of () is enough high, we only need by the polynomial coefficient calculations about x once and keep, when i and x gets different value, to solve Y _si(x), Y _mix the efficiency of () will improve greatly, last Y _si(x), Y _mix () substitutes in the formula in C1, can try to achieve the electric current I of i-th section of cable at x place _xi;

C3. the sheath electric current of Integral cable every section of each point is along the line asked:

If the structure of cable is the basic structure of not segmentation, then I in C1 _sinamely equal to solve in step (3) B3 and draw corresponding I _s, the electric current I that cable each point sheath along the line electric current can be tried to achieve by C2 _xiprovide;

If the structure of cable is the cross interconnected type of n section or n section transposition type structure, then i-th section of cable often puts sheath electric current I _i(x) solve the sending end electric current I depending on this section of cable _si, and I _sisolve the Equivalent admittance matrix depending on front i-1 section cable, and the method for solving of this Equivalent admittance matrix has described in detail in step (2) A3;

(5) calculate in step (4) on the basis of the cable sheath electric current of every section of each point along the line, solve cable cover(ing) loss calculation expression formula as follows:

$P_{\mathrm{loss}}=\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{\&Integral;}_0^{l_i}{I}_i^T\left(x\right)I_i\left(x\right)R_c\mathrm{dx}$

Wherein: l _irepresent the length of i-th section of cable, n is total segments of cable, I _ix () represents that i-th section of cable distance this section of sending end is the sheath electric current at x place, R _crepresent the sheath resistance of cable unit length.

Claims (8)

1. power attenuation computing method for power cable sheath, comprise the steps:

(1) basic parameter of cable and the positive order parameter of equivalence of cable two ends electric system is obtained;

Described basic parameter comprises unit length series impedance matrix Z and the unit length shunt admittance matrix Y of cable, and the positive order parameter of described equivalence comprises the equivalent source electromotive force E of the every phase of sending end electric system _swith equiva lent impedance Z _sand the equivalent source electromotive force E of the every phase of receiving end electric system _rwith equiva lent impedance Z _r;

(2) according to the structure of described basic parameter and cable, the Equivalent admittance matrix Y of cable is determined _eq;

(3) according to the Equivalent admittance matrix Ye of cable _qand the boundary conditions of cable, calculate the voltage U of cable sending end _sand electric current I _s;

(4) according to the voltage U of cable sending end _sand electric current I _s, determine the sheath electric current of cable each point along the line;

(5) according to the sheath electric current of cable each point along the line, the power attenuation P of cable cover(ing) is calculated.

2. power attenuation computing method according to claim 1, is characterized in that: determine cable Equivalent admittance matrix Y in described step (2) _eqdetailed process as follows:

If cable is not segmental structure, then its Equivalent admittance matrix Y _eqexpression formula as follows:

$Y_{\mathrm{eq}}=\begin{array}{cc}{Y}_s& -Y_m\\ -Y_m& Y_s\end{array}=\begin{array}{cc}{Z}^{-1}\mathrm{\&Gamma;}\coth \left(\mathrm{\&Gamma;l}\right)& -Z^{-1}\mathrm{\&Gamma;}\mathrm{csch}\left(\mathrm{\&Gamma;l}\right)\\ -Z^{-1}\mathrm{\&Gamma;}\mathrm{csch}\left(\mathrm{\&Gamma;l}\right)& Z^{-1}\mathrm{\&Gamma;}\coth \left(\mathrm{\&Gamma;l}\right)\end{array}$

Wherein: Y _sand Y _mbe respectively self-admittance matrix and the transadmittance matrix of cable, coth and csch is respectively hyperbolic cotangent and hyperbolic cosecant, and Γ is propagation constant matrix and Γ=(ZY) ^1/2, l is cable length;

If cable be k section cross interconnected type structure or k section circulating picture-changing bit-type structure, then cable comprises k section conductor and k-1 joint, k be greater than 1 natural number;

First, according to the admittance matrix of following formula determination cable every section of conductor:

$Y_i=\begin{array}{cc}{Y}_{\mathrm{si}}& -Y_{\mathrm{mi}}\\ -Y_{\mathrm{mi}}& Y_{\mathrm{si}}\end{array}=\begin{array}{cc}{Z}^{-1}\mathrm{\&Gamma;}\coth \left(\mathrm{\&Gamma;}{l}_i\right)& -Z^{-1}\mathrm{\&Gamma;}\mathrm{csch}\left(\mathrm{\&Gamma;}{l}_i\right)\\ -Z^{-1}\mathrm{\&Gamma;}\mathrm{csch}\left(\mathrm{\&Gamma;}{l}_i\right)& Z^{-1}\mathrm{\&Gamma;}\coth \left(\mathrm{\&Gamma;}{l}_i\right)\end{array}$

Wherein: Y _ibe the admittance matrix of i-th section of conductor, i is natural number and 1≤i≤k, Y _siand Y _mibe respectively self-admittance matrix and the transadmittance matrix of i-th section of conductor, l _ibe the length of i-th section of conductor;

Then, the admittance matrix of each joint of cable is determined;

If the cable cross interconnected type structure that is k section, the admittance matrix of its each joint all adopts following formula:

$Y_c=\begin{array}{cc}{Y}_{\mathrm{sc}}& -Y_{\mathrm{mc}}\\ {Y_{\mathrm{mc}}}^T& Y_{\mathrm{sc}}\end{array}=\begin{array}{cccc}{g}_c{I}_{33}& 0& -g_c{I}_{33}& 0\\ 0& g_s{I}_{3\&times;3}& 0& -g_s{M}_c\\ -g_c{I}_{33}& 0& g_c{I}_{33}& 0\\ 0& -g_s{M_c}^T& 0& g_s{I}_{3\&times;3}\end{array}$

If cable is k section circulating picture-changing bit-type structure, the admittance matrix of its each joint all adopts following formula:

$Y_c=\begin{array}{cc}{Y}_{\mathrm{sc}}& -Y_{\mathrm{mc}}\\ {Y_{\mathrm{mc}}}^T& Y_{\mathrm{sc}}\end{array}=\begin{array}{cccc}{g}_c{I}_{3\&times;3}& 0& -g_c{M}_c& 0\\ 0& g_s{I}_{33\&times;}& 0& -g_s{I}_{33}\\ -g_c{M_c}^T& 0& g_c{I}_{3\&times;3}& 0\\ 0& -g_s{I}_{33}& 0& g_s{I}_{33}\end{array}$

Wherein: Y _cfor the admittance matrix of joint, Y _scand Y _mcbe respectively self-admittance matrix and the transadmittance matrix of joint, $M_c=\begin{array}{ccc}0& 1& 0\\ 0& 0& 1\\ 1& 0& 0\end{array},$ ^trepresent transposition, I _{3 × 3}be three rank unit matrixs, g _cfor the admittance of connecting line between conductor, g _sfor the admittance of connecting line between sheath;

Finally, all see conductor and joint as cell block, then cable is made up of 2k-1 cell block cascade; Appoint and get two adjacent cell block p and q and be merged into a new cell block, obtain the admittance matrix Y of new cell block _pqas follows, carry out one by one according to this merging the Equivalent admittance matrix Y namely obtaining cable _eq;

$Y_{\mathrm{pq}}=\begin{array}{cc}{Y}_{\mathrm{sp}}-Y_{\mathrm{mp}}{(Y_{\mathrm{sp}}+Y_{\mathrm{sq}})}^{-1}{Y_{\mathrm{mp}}}^T& -Y_{\mathrm{mp}}{(Y_{\mathrm{sp}}+Y_{\mathrm{sq}})}^{-1}{Y_{\mathrm{mq}}}^T\\ -Y_{\mathrm{mq}}{(Y_{\mathrm{sp}}+Y_{\mathrm{sq}})}^{-1}{Y_{\mathrm{mp}}}^T& Y_{\mathrm{sq}}-Y_{\mathrm{mq}}{(Y_{\mathrm{sp}}+Y_{\mathrm{sq}})}^{-1}{Y_{\mathrm{mq}}}^T\end{array}$

Wherein: Y _spand Y _mpbe respectively self-admittance matrix and the transadmittance matrix of cell block p, Y _sqand Y _mqbe respectively self-admittance matrix and the transadmittance matrix of cell block q.

3. power attenuation computing method according to claim 2, is characterized in that: described self-admittance matrix Y _sand Y _siand transadmittance matrix Y _mand Y _miemploying Bernoulli's series launches, and expression is as follows:

$Y_s=Z^{-1}\mathrm{\&Gamma;}\coth \left(\mathrm{\&Gamma;l}\right)={\left(\mathrm{Zl}\right)}^{-1}[I_{6\&times;6}+\frac{1}{3}\left({\mathrm{ZYl}}^2\right)-\frac{1}{45}{\left({\mathrm{ZYl}}^2\right)}^2+\frac{2}{945}{\left({\mathrm{ZYl}}^2\right)}^3+...+\frac{2^{2n}{B}_{2n}}{\left(2n\right)!}{\left({\mathrm{ZYl}}^2\right)}^n]$

$Y_{\mathrm{si}}=Z^{-1}\mathrm{\&Gamma;}\coth \left(\mathrm{\&Gamma;}{l}_i\right)={\left(Z{l}_i\right)}^{-1}[I_{6\&times;6}+\frac{1}{3}\left({\mathrm{ZY}{l}_i}^2\right)-\frac{1}{45}{\left({\mathrm{ZY}{l}_i}^2\right)}^2+\frac{2}{945}{\left({\mathrm{ZY}{l}_i}^2\right)}^3+...+\frac{2^{2n}{B}_{2n}}{\left(2n\right)!}{\left({\mathrm{ZY}{l}_i}^2\right)}^n]$

$Y_{\mathrm{mi}}=Z^{-1}\mathrm{\&Gamma;}\mathrm{csch}\left(\mathrm{\&Gamma;l}\right)={\left(\mathrm{Zl}\right)}^{-1}[I_{6\&times;6}-\frac{1}{6}\left({\mathrm{ZYl}}^2\right)+\frac{7}{360}{\left({\mathrm{ZYl}}^2\right)}^2-\frac{31}{15120}{\left({\mathrm{ZYl}}^2\right)}^3+...+\frac{{1-2}^{2n}{B}_{2n}}{\left(2n\right)!}{\left({\mathrm{ZYl}}^2\right)}^n]$

$Y_{\mathrm{mi}}=Z^{-1}\mathrm{\&Gamma;}\mathrm{csch}\left(\mathrm{\&Gamma;}{l}_i\right)={\left(Z{l}_i\right)}^{-1}[I_{6\&times;6}-\frac{1}{6}\left({\mathrm{ZY}{l}_i}^2\right)+\frac{7}{360}{\left({\mathrm{ZY}{l}_i}^2\right)}^2-\frac{31}{15120}{\left({\mathrm{ZY}{l}_i}^2\right)}^3+...+\frac{{1-2}^{2n}{B}_{2n}}{\left(2n\right)!}{\left({\mathrm{ZY}{l}_i}^2\right)}^n]$ Wherein: I _{6 × 6}be six rank unit matrixs, n be greater than 9 natural number, B _2nit is 2n item Bernoulli Jacob coefficient.

4. power attenuation computing method according to claim 1, is characterized in that: the voltage U calculating cable sending end in described step (3) _sand electric current I _sconcrete grammar as follows:

First, according to the Equivalent admittance matrix Y of cable _eqsetting up cable send the relational expression by both end voltage and electric current as follows:

$\begin{array}{c}{I}_S\\ I_R\end{array}=Y_{\mathrm{eq}}\begin{array}{c}{U}_S\\ U_R\end{array}$

Wherein: U _rand I _rbe respectively the voltage and current of cable receiving end, I _sand I _rbe six-vector and wherein contain the three-phase current of cable core and the three-phase current of cable cover(ing) successively, U _sand U _rbe six-vector and wherein contain the three-phase voltage of cable core and the three-phase voltage of cable cover(ing) successively;

Then, the boundary conditions of simultaneous above formula and cable, can solve the voltage U of cable sending end _sand electric current I _s; If cable is two sides earth system, its boundary conditions is as follows:

$\begin{array}{c}{U}_S^{123}\\ U_S^{456}\end{array}=\begin{array}{c}{E}_S-I_S^{123}{Z}_S\\ 0\end{array}$ $\begin{array}{c}{U}_R^{123}\\ U_R^{456}\end{array}=\begin{array}{c}{E}_R-I_R^{123}{Z}_R\\ 0\end{array}$

If cable is the system single-end earthed without earth lead, its boundary conditions is as follows:

$\begin{array}{c}{U}_S^{123}\\ U_S^{456}\end{array}=\begin{array}{c}{E}_S-I_S^{123}{Z}_S\\ 0\end{array}$ $\begin{array}{c}{U}_R^{123}\\ I_R^{456}\end{array}=\begin{array}{c}{E}_R-I_R^{123}{Z}_R\\ 0\end{array}$

If cable is the system single-end earthed with earth lead, its boundary conditions is as follows:

$\begin{array}{c}{U}_S^{123}\\ U_S^{456}\\ U_S^7\end{array}=\begin{array}{c}{E}_S-I_S^{123}{Z}_S\\ 0\\ 0\end{array}$ $\begin{array}{c}{U}_R^{123}\\ I_R^{456}\\ I_R^7\end{array}=\begin{array}{c}{E}_R-I_R^{123}{Z}_R\\ 0\\ 0\end{array}$

Wherein: with be respectively three-phase voltage and the three-phase current of cable sending end core, with be respectively three-phase voltage and the three-phase current of cable receiving end core, with be respectively three-phase voltage and the three-phase current of cable receiving end sheath, with be respectively sending end voltage and the receiving end electric current of earth lead.

5. power attenuation computing method according to claim 1, is characterized in that: determine in described step (4) that the method for cable each point along the line sheath electric current is as follows:

For some cable i-th section of conductor with this section of conductor initiating terminal apart from length being x, calculate the voltage U of this point according to following formula _xiand electric current I _xi, and then from this electric current I _xiin extract sheath electric current; I is natural number and 1≤i≤k, k is the segmentation number of cable, if cable is not segmental structure, then k=1;

$\begin{array}{c}{I}_{\mathrm{xi}}\\ U_{\mathrm{xi}}\end{array}=\begin{array}{ccc}-Y_{\mathrm{si}}\left(x\right)+Y_{\mathrm{mi}}{\left(x\right)}^{-1}& -Y_{\mathrm{mi}}\left(x\right)+Y_{\mathrm{si}}\left(x\right)Y_{\mathrm{mi}}{\left(x\right)}^{-1}{Y}_{\mathrm{si}}\left(x\right)& I_{\mathrm{Si}}\\ -Y_{\mathrm{mi}}{\left(x\right)}^{-1}& Y_{\mathrm{mi}}{\left(x\right)}^{-1}{Y}_{\mathrm{si}}\left(x\right)& U_{\mathrm{Si}}\end{array}$

Wherein: U _siand I _sibe respectively the voltage and current of cable i-th section of conductor initiating terminal, Y _si(x) and Y _mix () is respectively self-admittance matrix between i-th section of conductor initiating terminal and this point and transadmittance matrix; I _siand I _xibe six-vector and wherein contain the three-phase current of cable core and the three-phase current of cable cover(ing) successively, U _siand U _xibe six-vector and wherein contain the three-phase voltage of cable core and the three-phase voltage of cable cover(ing) successively.

6. power attenuation computing method according to claim 5, is characterized in that: described self-admittance matrix Y _si(x) and transadmittance matrix Y _mix () adopts Bernoulli's series to launch, expression is as follows:

$\begin{array}{c}{Y}_{\mathrm{si}}\left(x\right)=Z^{-1}\mathrm{\&Gamma;}\coth \left(\mathrm{\&Gamma;x}\right)={\left(\mathrm{Zx}\right)}^{-1}[I_{6\&times;6}+\frac{1}{3}\left({\mathrm{ZYx}}^2\right)-\frac{1}{45}{\left({\mathrm{ZYx}}^2\right)}^2+\frac{2}{945}{\left({\mathrm{ZYx}}^2\right)}^3+...+\frac{2^{2n}{B}_{2n}}{\left(2n\right)!}{\left({\mathrm{ZYx}}^2\right)}^n]\\ ={\left(Z\right)}^{-1}{x}^{-1}+\frac{1}{3}{\mathrm{Yx}}^1-\frac{1}{45}{\mathrm{ZY}}^2{x}^3+\frac{1}{945}{Z}^2{Y}^3{x}^5+...+\frac{2^{2n}{B}_{2n}}{\left(2n\right)!}{Z}^{n-1}{Y}^n{x}^{2n-1}\end{array}$

$\begin{array}{c}{Y}_{\mathrm{mi}}\left(x\right)=Z^{-1}\mathrm{\&Gamma;csth}\left(\mathrm{\&Gamma;x}\right)={\left(\mathrm{Zx}\right)}^{-1}[I_{6\&times;6}-\frac{1}{6}\left({\mathrm{ZYx}}^2\right)+\frac{7}{360}{\left({\mathrm{ZYx}}^2\right)}^2-\frac{31}{15120}{\left({\mathrm{ZYx}}^2\right)}^3+...+\frac{1-2^{2n}{B}_{2n}}{\left(2n\right)!}{\left({\mathrm{ZYx}}^2\right)}^n]\\ ={\left(Z\right)}^{-1}{x}^{-1}-\frac{1}{6}{\mathrm{Yx}}^1+\frac{7}{360}{\mathrm{ZY}}^2{x}^3-\frac{31}{15120}{Z}^2{Y}^3{x}^5+...+\frac{1-2^{2n}{B}_{2n}}{\left(2n\right)!}{Z}^{n-1}{Y}^n{x}^{2n-1}\end{array}$ Wherein: coth and csch is respectively hyperbolic cotangent and hyperbolic cosecant, Γ is propagation constant matrix and Γ=(ZY) ^1/2, I _{6 × 6}be six rank unit matrixs, n be greater than 9 natural number, B _2nit is 2n item Bernoulli Jacob coefficient.

7. power attenuation computing method according to claim 5, is characterized in that: the voltage U of described cable i-th section of conductor initiating terminal _siand electric current I _simethod for solving as follows: if cable is not segmental structure, then voltage U _siand electric current I _sinamely the voltage U of cable sending end is corresponded to _sand electric current I _s; If cable is segmental structure, then voltage U _siand electric current I _sisolve according to following relational expression:

$\begin{array}{c}{I}_S\\ I_{\mathrm{Si}}\end{array}=Y_{\mathrm{Si}}\begin{array}{c}{U}_S\\ U_{\mathrm{Si}}\end{array}$

Wherein: Y _sifor the admittance matrix between cable sending end and i-th section of conductor initiating terminal, namely between cable sending end and i-th section of conductor initiating terminal all cell blocks merge after admittance matrix.

8. power attenuation computing method according to claim 1, is characterized in that: the power attenuation P calculating cable cover(ing) in described step (5) according to following formula:

$P=\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{\&Integral;}_0^{l_i}{I}_i^T\left(x\right)I_i\left(x\right)R_c\mathrm{dx}$

Wherein: l _ifor the length of cable i-th section of conductor, I _ix () is for cable i-th section of conductor with this section of conductor initiating terminal distance length being the sheath electric current of the point of x and I _ix () wherein contains the three-phase current of cable cover(ing) for tri-vector, ^trepresent transposition, R _cfor the sheath resistance of cable unit length, k is the segmentation number of cable.