CN104135019B - A kind of multiple-loop line transmission line three-phase imbalance suppressing method - Google Patents

Abstract

The present invention relates to a kind of multiple-loop line transmission line three-phase imbalance suppressing method, calculate line impedance matrix according to wire type, wire divisional mode, shaft tower type and lightning conducter connected mode; List transmission line electric current, voltage equation according to transmission line condition, often returned negative phase-sequence, zero-sequence current expression formula by matrixing and symmetrical component transformation; According to obtained negative phase-sequence, zero-sequence current expression formula, find the impedance parameter of negative phase-sequence, zero-sequence current sensitivity; According to obtained responsive impedance parameter configuration building-out capacitor, sensitive parameter is compensated to minimum with limiting circuitry negative phase-sequence, zero-sequence current.By compensating negative phase-sequence, the responsive impedance parameter of zero-sequence current, realize the adjustment to line parameter circuit value, effectively can suppress the imbalance problem of multiple-loop line transmission line, for safe, stable, the economical operation of multiple-loop line transmission line provide theoretical foundation and guidance.

Description

A kind of multiple-loop line transmission line three-phase imbalance suppressing method

Technical field

The present invention relates to a kind of multiple-loop line technical field of electric power transmission, particularly a kind of multiple-loop line transmission line three-phase imbalance suppressing method.

Background technology

Multiple-loop line technology of transmission of electricity refers to the New Technologies of Electric Power Transmission utilizing same tower erection twice or many back transmission lines to carry out electric power transfer, there is many advantages such as saving line corridor, increase transmission line capability, minimizing power construction cost, can adapt to well cause the problems such as power transmission line corridor anxiety, power demand increase due to rapid economic development, be widely used in China, and achieve significant economic benefit.

Multiple-loop line transmission line is due to transmission of electricity compact conformation, and line arrangement is complicated, and between circuit and line-to-ground position is asymmetric, causes producing very strong asymmetric coupling between circuit, thus causes line parameter circuit value asymmetrical three-phase.The asymmetric meeting of Three-phase Power Systems causes adverse effect to electric equipments such as generator, relaying protection, transformers, and line loss is increased, and the user side quality of power supply reduces.Therefore, the braking measure of analysis and research multiple-loop line transmission line three-phase imbalance, to ensureing that safe, reliable, the economical operation of multiple-loop line transmission line have direct realistic meaning.

The degree of unbalance of transmission line, depends on forward-order current scale shared by circuit negative-sequence current, zero-sequence current.The suppressing method of current multiple-loop line transmission line three-phase imbalance, is mainly limited to and optimizes phase sequence layout, adopts the phase sequence that between circuit, degree of coupling is minimum to arrange, makes degree of unbalance reach requirement.But when multiple-loop line transmission line sets up, due to factor impacts such as landform, tower structure, lightning protection properties, optimum phase sequence usually cannot be adopted to arrange; Along with putting into operation of same tower six back transmission line, circuit degree of coupling increases further, and circuit adopts optimum phase sequence layout that degree of unbalance also cannot be made to reach requirement.

Summary of the invention

The present invention be directed to and arrange that the degree of unbalance overcoming transmission line can not meet the requirements of problem by the optimum phase sequence of circuit, propose a kind of multiple-loop line transmission line three-phase imbalance suppressing method, by reasonable disposition building-out capacitor, circuit asymmetry parameter is compensated, realize the adjustment to line parameter circuit value, make circuit negative phase-sequence, zero-sequence current reaches minimum, fundamentally suppress imbalance problem, guarantee multiple-loop line transmission line safety, stable, economical operation.

Technical scheme of the present invention is: a kind of multiple-loop line transmission line three-phase imbalance suppressing method, specifically comprises the steps:

1) multiple-loop line transmission line impedance matrix is calculated according to wire type, wire divisional mode, shaft tower type and lightning conducter connected mode;

2) according to step 1) impedance matrix that calculates, list transmission line electric current, voltage equation, often returned negative phase-sequence, zero-sequence current expression formula by impedance matrix conversion with symmetrical component transformation;

3) according to step 2) negative phase-sequence, the zero-sequence current expression formula that obtain, find the impedance parameter of negative phase-sequence, zero-sequence current sensitivity, responsive impedance parameter is the impedance parameter had a direct impact circuit negative phase-sequence and zero-sequence current size;

4) according to step 3) the responsive impedance parameter configuration building-out capacitor that obtains, sensitive parameter is compensated to minimum with limiting circuitry negative phase-sequence, zero-sequence current, thus suppress multiple-loop line transmission line imbalance problem.

Described step 2) in often return negative phase-sequence in two loop line roads, zero-sequence current expression formula is as follows:

$\left\{\begin{array}{c}\left|I_{1-2}\right|={\left\{\frac{1}{3}\right[{(X-Y+2(C-B))}^2+{(Y-Z+2(B-A))}^2+{(X-Z+2(C-A))}^2\left]\right\}}^{1/2}\\ \left|I_{1-0}\right|={\left\{{\frac{1}{6}[((X-Y)-(C-B))}^2+{((Y-Z)-(B-A))}^2+{((X-Z))-(C-A)}^2]\right\}}^{1/2}+S_0\end{array}\right.$

$\left\{\begin{array}{c}\left|I_{2-2}\right|={\left\{\frac{1}{3}\right[{(x-y+2(c-b))}^2+{(y-z+2(b-a))}^2+{(x-z+2(c-a))}^2\left]\right\}}^{1/2}\\ \left|I_{2-0}\right|={\left\{{\frac{1}{6}[((x-y)-(c-b))}^2+{((y-z)-(b-a))}^2+{\left((x-z)\right)(c-a)}^2]\right\}}^{1/2}+S_0\end{array}\right.$

I _1-2, I _1-0be first time negative phase-sequence, zero-sequence current, I _2-2, I _2-0be second time negative phase-sequence, zero-sequence current,

$X=x=X_{\mathrm{aa}}^{\′2}-X_{\mathrm{bc}}^{\′2},$

$Y=y=X_{\mathrm{bb}}^{\′2}-X_{\mathrm{ac}}^{\′2},$

$Z=z=X_{\mathrm{cc}}^{\′2}-X_{\mathrm{ab}}^{\′2},$

A＝a＝X′ ₁，

B＝b＝X′ ₂，

C＝c＝X′ ₃，

Two loop line road self-impedances are respectively X _aa, X _bb, X _cc, in loop, mutual impedance is respectively X _ab, X _ac, X _bc, S ₀for containing X _mcomplicated multinomial;

Step 3) as A=B=C, X=Y=Z, a=b=c, x=y=z, negative-sequence current, zero-sequence current will reach minimum, and (X-Y), (B-A), (C-B), (Y-Z), (C-A), (X-Z) are negative phase-sequence, the responsive impedance parameter of zero-sequence current.

Described when meeting following condition, circuit negative phase-sequence, zero-sequence current will reach minimum, C ₁~ C ₆be respectively the capacitor electrode capacitance in two loops, 6 branch roads compensated,

$\left\{\begin{array}{c}X-\mathrm{\ω}(C_1+C_2)=Y-\mathrm{\ω}(C_1+C_3)=Z-\mathrm{\ω}(C_2+C_3)\\ A+\mathrm{\ω}{C}_1=B+\mathrm{\ω}{C}_2=C+\mathrm{\ω}{C}_3\\ x-\mathrm{\ω}(C_4+C_5)=y-\mathrm{\ω}(C_4+C_6)=z-\mathrm{\ω}(C_5+C_6)\\ a+\mathrm{\ω}{C}_4=b+\mathrm{\ω}{C}_5=c+\mathrm{\ω}{C}_6\end{array}\right..$

Beneficial effect of the present invention is: multiple-loop line transmission line three-phase imbalance suppressing method of the present invention, by compensating negative phase-sequence, the responsive impedance parameter of zero-sequence current, realize the adjustment to line parameter circuit value, effectively can suppress the imbalance problem of multiple-loop line transmission line, guarantee safe, stable, the economical operation of multiple-loop line transmission line.

Accompanying drawing explanation

Fig. 1 is that multiple-circuit on same tower of the present invention compensates asymmetry parameter schematic diagram.

Embodiment

A kind of multiple-loop line transmission line three-phase imbalance suppressing method, comprises the steps:

S1) multiple-circuit on same tower compensates asymmetry parameter schematic diagram as shown in Figure 1, according to transmission line wire model, wire divisional mode, shaft tower type etc., with reference to following formula, calculates circuit initial impedance matrix,

$\left\{\begin{array}{c}{Z}_{\mathrm{nn}}=R+0.05+j0.145(\lg \frac{2l}{r_e}-1)\mathrm{\Ω}/\mathrm{km}\\ Z_{\mathrm{mn}}=0.05+j0.0145(\lg \frac{2l}{d_{\mathrm{mn}}}-1)\mathrm{\Ω}/\mathrm{km}\end{array}\right.$

In formula, Z _nnfor circuit n self-impedance, Z _mnfor mutual impedance between circuit m and n, l is conductor length; R is the resistance of wire that circuit n is corresponding or lightning conducter; r _ethe wire corresponding for circuit n or the effective radius of lightning conducter; d _mnbe two wire m and n geometric center spacing;

S2) step S1 is established) calculate gained two loop line road self-impedance and be respectively X _aA, X _bB, X _cC, X _aa, X _bb, X _cc, in loop, mutual impedance is respectively X _aB, X _aC, X _bC, X _ab, X _ac, X _bc, between loop, mutual impedance is respectively X _aa, X _ab, X _ac, X _ba, X _bb, X _bc, X _ca, X _cb, X _cc, according to step S1 gained impedance matrix, multiple-circuit on same tower electric current and voltage equation can be write out as follows:

$\left[\begin{array}{c}{U}_A\\ U_B\\ U_C\\ U_a\\ U_b\\ U_c\end{array}\right]=\left[\begin{array}{cccccc}{X}_{\mathrm{AA}}& X_{\mathrm{AB}}& X_{\mathrm{AC}}& X_{\mathrm{Aa}}& X_{\mathrm{Ab}}& X_{\mathrm{Ac}}\\ X_{\mathrm{BA}}& X_{\mathrm{BB}}& B_{\mathrm{BC}}& X_{\mathrm{Ba}}& X_{\mathrm{Bb}}& X_{\mathrm{Bc}}\\ X_{\mathrm{CA}}& X_{\mathrm{CB}}& X_{\mathrm{CC}}& X_{\mathrm{Ca}}& X_{\mathrm{Cb}}& X_{\mathrm{Cc}}\\ X_{\mathrm{aA}}& X_{\mathrm{aB}}& X_{\mathrm{aC}}& X_{\mathrm{aa}}& X_{\mathrm{ab}}& X_{\mathrm{ac}}\\ X_{\mathrm{bA}}& B_{\mathrm{bA}}& X_{\mathrm{bC}}& X_{\mathrm{ba}}& X_{\mathrm{bb}}& X_{\mathrm{bc}}\\ X_{\mathrm{cA}}& X_{\mathrm{cB}}& X_{\mathrm{cC}}& X_{\mathrm{ca}}& X_{\mathrm{cb}}& X_{\mathrm{cc}}\end{array}\right]\left[\begin{array}{c}{I}_A\\ I_B\\ I_C\\ I_a\\ I_b\\ I_c\end{array}\right]$

Wherein, U is made ₁=[U _au _bu _c] ^t=[U _a1-U _a0u _b1-U _b0u _c1-U _c0] ^tfor loop one line voltage distribution phasor, U _a0, U _b0, U _c0three-phase input voltage in loop one respectively, U _a1, U _b1, U _c1three-phase output voltage in loop one respectively;

U ₂=[U _au _bu _c] ^t=[U _a1-U _a0u _b1-U _b0u _c1-U _c0] ^tfor loop two circuit voltage phasor, U _a0, U _b0, U _c0three-phase input voltage in loop two respectively, U _a1, U _b1, U _c1three-phase output voltage in loop two respectively; I ₁=[I _ai _bi _c] ^t, I ₂=[I _ai _bi _c] ^tbeing two loop line road electric current phasors, is simplified operation, to suppose between twice that mutual impedance is equal and averages as X _m, loop internal impedance matrix is X _s, then have:

$X_s=\left[\begin{array}{ccc}{X}_{\mathrm{aa}}& X_{\mathrm{ab}}& X_{\mathrm{ac}}\\ X_{\mathrm{ba}}& X_{\mathrm{bb}}& X_{\mathrm{bc}}\\ X_{\mathrm{ca}}& X_{\mathrm{cb}}& X_{\mathrm{cc}}\end{array}\right],X_m=\left[\begin{array}{ccc}{X}_m& X_m& X_m\\ X_m& X_m& X_m\\ X_m& X_m& X_m\end{array}\right]$

Then line voltage distribution current equation can be written as:

$\left[\begin{array}{c}{U}_1\\ U_2\end{array}\right]={\left[\begin{array}{cc}{X}_s& X_m\\ X_m& X_s\end{array}\right]}^{-1}\left[\begin{array}{c}{I}_1\\ I_2\end{array}\right]$

Impedance matrix is inverted and obtains admittance matrix form electric current and voltage equation:

$\left[\begin{array}{c}{I}_1\\ I_2\end{array}\right]={\left[\begin{array}{cc}{X}_s& X_m\\ X_m& X_s\end{array}\right]}^{-1}\left[\begin{array}{c}{U}_1\\ U_2\end{array}\right]$

By symmetrical component transformation, often returned sequence current expression:

$\left[\begin{array}{c}{I}_{1-120}\\ I_{2-120}\end{array}\right]=\left[\begin{array}{cc}S& \\ & S\end{array}\right]{\left[\begin{array}{cc}{X}_s& X_m\\ X_m& X_s\end{array}\right]}^{-1}\left[\begin{array}{c}{U}_1\\ U_2\end{array}\right]$

In above formula, I _1-120be the first positive and negative zero-sequence current in loop, I _2-120for the positive and negative zero-sequence current of second servo loop, S is 3 rank symmetrical component transformation matrixes, and admittance matrix can be written as:

$\mathrm{\Ω}={\left[\begin{array}{cc}{X}_s& X_m\\ X_m& X_s\end{array}\right]}^{-1}=\begin{array}{c}\left[\begin{array}{cc}{(X_s-X_m{X}_s^{-1}{X}_m)}^{-1}& -X_s^{-1}{X}_m{(X_s-X_m{X}_s^{-1}{X}_m)}^{-1}\\ -X_s^{-1}{X}_m{(X_s-X_m{X}_s^{-1}{X}_m}^{-1}& (X_s-X_m{X}_s^{-1}{X}_m{)}^{-1}\end{array}\right]\end{array}$

Above-mentioned admittance matrix abbreviation computational process is as follows:

${X_s}^{-1}{\left[\begin{array}{ccc}{X}_{\mathrm{aa}}& X_{\mathrm{ab}}& X_{\mathrm{ac}}\\ X_{\mathrm{ba}}& X_{\mathrm{bb}}& X_{\mathrm{bc}}\\ X_{\mathrm{ca}}& X_{\mathrm{cb}}& X_{\mathrm{cc}}\end{array}\right]}^{-1}=\frac{1}{\mathrm{\Δ}}\left[\begin{array}{ccc}{X}_{\mathrm{aa}}^2-X_{\mathrm{bc}}^2& X_1& X_2\\ X_1& X_{\mathrm{bb}}^2-X_{\mathrm{ac}}^2& X_3\\ X_2& X_3& X_{\mathrm{cc}}^2-X_{\mathrm{ab}}^2\end{array}\right]$

Wherein, $\mathrm{\Δ}=X_{\mathrm{aa}}^3-X_{\mathrm{aa}}(X_{\mathrm{bc}}^2+X_{\mathrm{ac}}^2+X_{\mathrm{ab}}^2)+2X_{\mathrm{ab}}{X}_{\mathrm{ac}}{X}_{\mathrm{bc}};$

X ₁＝X _bcX _ac-X _aaX _ab；

X ₂＝X _abX _bc-X _aaX _ac；

X ₃＝X _abX _ac-X _aaX _bc；

By can be calculated expression formula:

$X_m{X}_s^{-1}{X}_m=\frac{X_m^2}{\mathrm{\Δ}}({2X}_1+2X_2+{2X}_3+X_{\mathrm{aa}}^2+X_{\mathrm{bb}}^2+X_{\mathrm{cc}}^2-X_{\mathrm{bc}}^2-X_{\mathrm{ac}}^2-X_{\mathrm{ab}}^2)\left[\begin{array}{ccc}1& 1& 1\\ 1& 1& 1\\ 1& 1& 1\end{array}\right]$

Order $Z=\frac{X_m^2}{\mathrm{\Δ}}(2X_1+2X_2+2X_3+X_{\mathrm{aa}}^2+X_{\mathrm{bb}}^2+X_{\mathrm{cc}}^2-X_{\mathrm{bc}}^2-X_{\mathrm{ac}}^2-X_{\mathrm{ab}}^2),$

Then can be expressed as:

$X_m{X}_s^{-1}{X}_m=\left[\begin{array}{ccc}Z& Z& Z\\ Z& Z& Z\\ Z& Z& Z\end{array}\right]$

Therefore, matrix be equivalent to X _smiddle element all deducts Z, Ke Yishe:

$X_s^{\′}=X_s-X_m{X}_s^{-1}{X}_m=\left[\begin{array}{ccc}{X}_{\mathrm{aa}}& X_{\mathrm{ab}}& X_{\mathrm{ac}}\\ X_{\mathrm{ba}}& X_{\mathrm{bb}}& X_{\mathrm{bc}}\\ X_{\mathrm{ca}}& X_{\mathrm{cb}}& X_{\mathrm{cc}}\end{array}\right]-\left[\begin{array}{ccc}Z& Z& Z\\ Z& Z& Z\\ Z& Z& Z\end{array}\right]=\left[\begin{array}{ccc}{X}_{\mathrm{aa}}^{\′}& X_{\mathrm{ab}}^{\′}& X_{\mathrm{ac}}^{\′}\\ X_{\mathrm{ba}}^{\′}& X_{\mathrm{bb}}^{\′}& X_{\mathrm{bc}}^{\′}\\ X_{\mathrm{ca}}^{\′}& X_{\mathrm{cb}}^{\′}& X_{\mathrm{cc}}^{\′}\end{array}\right]$

Wherein, X ' _ij=X _ij-Z, i, j are in a, b or c any two.

According to above-mentioned X _sto invert result, in like manner obtain:

$X_s^{\′-1}={\left[\begin{array}{ccc}{X}_{\mathrm{aa}}^{\′}& X_{\mathrm{ab}}^{\′}& X_{\mathrm{ac}}^{\′}\\ X_{\mathrm{ba}}^{\′}& X_{\mathrm{bb}}^{\′}& X_{\mathrm{bc}}^{\′}\\ X_{\mathrm{ca}}^{\′}& X_{\mathrm{cb}}^{\′}& X_{\mathrm{cc}}^{\′}\end{array}\right]}^{-1}=\frac{1}{{\mathrm{\Δ}}^{\′}}\left[\begin{array}{ccc}{X}_{\mathrm{aa}}^{\′2}-X_{\mathrm{bc}}^{\′2}& X_1^{\′}& X_2^{\′}\\ X_1^{\′}& X_{\mathrm{bb}}^{\′2}& X_3^{\′}\\ X_2^{\′}& X_3^{\′}& X_{\mathrm{cc}}^{\′2}-X_{\mathrm{ab}}^{\′2}\end{array}\right]$

Wherein, ${\mathrm{\Δ}}^{\′}=X_{\mathrm{aa}}^{\′3}-{X^{\′}}_{\mathrm{aa}}(x_{\mathrm{bc}}^{\′2}+X_{\mathrm{ac}}^{\′2}+X_{\mathrm{ab}}^{\′2})+{{2X}^{\′}}_{\mathrm{ab}}{X^{\′}}_{\mathrm{ab}}{X^{\′}}_{\mathrm{bc}};$

X′ ₁＝X′ _bcX′ _ac-X′ _aaX′ _ab；

X′ ₂＝X′ _abX′ _bc-X′ _aaX′ _ac；

X′ ₃＝X′ _abX′ _ac-X′ _aaX′ _bc；

X′ _ij＝X _ij-Z；

I, j are in a, b or c any two.For expressing conveniently, if: a=a=X ' ₁, B=b=X ' ₂, C=c=X ' ₃.

Admittance matrix is obtained as follows after abbreviation:

$\mathrm{\Ω}=\left[\begin{array}{cccccc}X& A& B& & & \\ A& Y& C& & -X_s^{-1}{X}_m{(X_s-X_m{X}_s^{-1}{X}_m)}^{-1}& \\ B& C& Z& & & \\ & & & x& a& b\\ & -X_s^{-1}{X}_m{(X_s-X_m{X}_s^{-1}{X}_m)}^{-1}& & a& y& c\\ & & & b& c& z\end{array}\right]$

In above formula, A, B, C, a, b, c and X, Y, Z, x, y, z are the complicated multinomial that in impedance matrix, parameter forms, and line impedance parameter is constant after determining.

Calculate every loop line road negative phase-sequence further, zero-sequence current expression formula be as follows:

$\left\{\begin{array}{c}\left|I_{1-2}\right|={\left\{\frac{1}{3}\right[{(X-Y+2(C-B))}^2+{(Y-Z+2(B-A))}^2+{(X-Z+2(C-A))}^2\left]\right\}}^{1/2}\\ \left|I_{1-0}\right|={\left\{{\frac{1}{6}[((X-Y)-(C-B))}^2+{((Y-Z)-(B-A))}^2+{((X-Z))-(C-A)}^2]\right\}}^{1/2}+S_0\end{array}\right.$

$\left\{\begin{array}{c}\left|I_{2-2}\right|={\left\{\frac{1}{3}\right[{(x-y+2(c-b))}^2+{(y-z+2(b-a))}^2+{(x-z+2(c-a))}^2\left]\right\}}^{1/2}\\ \left|I_{2-0}\right|={\left\{{\frac{1}{6}[((x-y)-(c-b))}^2+{((y-z)-(b-a))}^2+{\left((x-z)\right)(c-a)}^2]\right\}}^{1/2}+S_0\end{array}\right.$

In above formula, I _1-2, I _1-0be first time negative phase-sequence, zero-sequence current, I _2-2, I _2-0be second time negative phase-sequence, zero-sequence current, S ₀for containing X _mcomplicated multinomial.

S3) the every loop line road negative phase-sequence obtained according to step S2, zero-sequence current expression formula can obtain, as X, Y, Z, A, B, C, x, y, z, when the value of a, b, c is close respectively, circuit negative phase-sequence, zero-sequence current will reduce, and as A=B=C, X=Y=Z, a=b=c, x=y=z, negative-sequence current, zero-sequence current will reach minimum.Therefore, (X-Y), (B-A), (C-B), (Y-Z), (C-A), (X-Z) be negative phase-sequence, the responsive impedance parameter of zero-sequence current.

S4) according to the responsive impedance parameter of circuit that step S3 obtains, configuration building-out capacitor compensates the uneven parameter of circuit, and as shown in Figure 1, after compensating, admittance matrix is as follows, C ₁~ C ₆be respectively the capacitor electrode capacitance in two loops, six branch roads compensated:

${\mathrm{\Ω}}^{\′}=\frac{1}{\mathrm{\Δ}}\left[\begin{array}{cccccc}X-\mathrm{\ω}(C_1+C_2)& A+\mathrm{\ω}{C}_1& B+\mathrm{\ω}{C}_2& & & \\ A+\mathrm{\ω}{C}_1& Y-\mathrm{\ω}(C_1+C_3)& C+\mathrm{\ω}\left(C_3\right)& & -X_s^{-1}{X}_m{(X_s-X_m{X}_s^{-1}{X}_m)}^{-1}& \\ B+\mathrm{\ω}{C}_2& C+\mathrm{\ω}{C}_3& Z-\mathrm{\ω}(C_2+C_3)& & & \\ & & & x-\mathrm{\ω}(C_4+C_5)& a+\mathrm{\ω}{C}_4& b+\mathrm{\ω}{C}_5\\ & -X_s^{-1}{X}_m{(X_x-X_m{X}_s^{-1}{X}_m)}^{-1}& & a+\mathrm{\ω}{C}_4& y-\mathrm{\ω}(C_4+C_6)& c+\mathrm{\ω}{C}_6\\ & & & b+\mathrm{\ω}{C}_5& c+\mathrm{\ω}{C}_6& z-\mathrm{\ω}(C_5-C_6)\end{array}\right]$

According to the conclusion that S3 obtains, when meeting following condition, circuit negative phase-sequence, zero-sequence current will reach minimum:

$\left\{\begin{array}{c}X-\mathrm{\ω}(C_1+C_2)=Y-\mathrm{\ω}(C_1+C_3)=Z-\mathrm{\ω}(C_2+C_3)\\ A+\mathrm{\ω}{C}_1=B+\mathrm{\ω}{C}_2=C+\mathrm{\ω}{C}_3\\ x-\mathrm{\ω}(C_4+C_5)=y-\mathrm{\ω}(C_4+C_6)=z-\mathrm{\ω}(C_5+C_6)\\ a+\mathrm{\ω}{C}_4=b+\mathrm{\ω}{C}_5=c+\mathrm{\ω}{C}_6\end{array}\right.$

In concrete configuration process, generally cannot meet above four conditions simultaneously, therefore when calculation compensation capacitance, three should be met as far as possible and be worth close to each other.

For same tower more than three times and three times transmission lines, analytical method is the same, is namely reduced negative phase-sequence, zero-sequence current by compensation negative phase-sequence, the responsive impedance parameter of zero sequence, and is all obtained similar conclusion, do not do it state at this.

Claims (3)

1. a multiple-loop line transmission line three-phase imbalance suppressing method, is characterized in that, specifically comprise the steps:

1) multiple-loop line transmission line impedance matrix is calculated according to wire type, wire divisional mode, shaft tower type and lightning conducter connected mode;

2) according to step 1) impedance matrix that calculates, list transmission line electric current, voltage equation, often returned negative phase-sequence, zero-sequence current expression formula by impedance matrix conversion with symmetrical component transformation;

3) according to step 2) negative phase-sequence, the zero-sequence current expression formula that obtain, find the responsive impedance parameter of negative phase-sequence, zero-sequence current, responsive impedance parameter is the impedance parameter had a direct impact circuit negative phase-sequence and zero-sequence current size;

4) according to step 3) the responsive impedance parameter configuration building-out capacitor that obtains, configuration building-out capacitor compensates the uneven parameter of circuit, makes described negative phase-sequence and zero-sequence current reach minimum, thus suppresses multiple-loop line transmission line imbalance problem.

2. multiple-loop line transmission line three-phase imbalance suppressing method according to claim 1, is characterized in that, when multiple-loop line transmission line is two loop line road, described step 2) in often return negative phase-sequence, zero-sequence current expression formula is as follows:

$\left\{\begin{array}{c}\left|I_{1-2}\right|={\left\{\frac{1}{3}\[{(X-Y+2(C-B\left)\right)}^2+{(Y-Z+2(B-A\left)\right)}^2+{(X-Z+2(C-A\left)\right)}^2\]\right\}}^{1/2}\\ \left|I_{1-0}\right|={\{\frac{1}{6}\[{\left(\right(X-Y)-(C-B\left)\right)}^2+{\left(\right(Y-Z)-(B-A\left)\right)}^2+{\left(\right(X-Z)-(C-A\left)\right)}^2\]\}}^{1/2}+S_0\end{array}\right.$

$\left\{\begin{array}{c}\left|I_{2-2}\right|={\left\{\frac{1}{3}\[{(x-y+2(c-b\left)\right)}^2+{(y-z+2(b-a\left)\right)}^2+{(x-z+2(c-a\left)\right)}^2\]\right\}}^{1/2}\\ \left|I_{2-0}\right|={\{\frac{1}{6}\[{\left(\right(x-y)-(c-b\left)\right)}^2+{\left(\right(y-z)-(b-a\left)\right)}^2+{\left(\right(x-z)-(c-a\left)\right)}^2\]\}}^{1/2}+S_0\end{array}\right.$

I _1-2, I _1-0be first time negative phase-sequence, zero-sequence current, I _2-2, I _2-0be second time negative phase-sequence, zero-sequence current,

$X=x=X_{aa}^{\′2}-X_{bc}^{\′2},$

$Y=y=X_{bb}^{\′2}-X_{ac}^{\′2},$

$Z=z=X_{cc}^{\′2}-X_{ab}^{\′2},$

A＝a＝X′ ₁，

B＝b＝X′ ₂，

C＝c＝X′ ₃，

X′ ₁＝X′ _bcX′ _ac-X′ _aaX′ _ab；

X′ ₂＝X′ _abX′ _bc-X′ _aaX′ _ac；

X′ ₃＝X′ _abX′ _ac-X′ _aaX′ _bc；

$X_{ij}^{\′}=X_{ij}-\frac{X_m^2}{\mathrm{\Δ}}(2X_1+2X_2+2X_3+X_{aa}^2+X_{bb}^2+X_{cc}^2-X_{bc}^2-X_{ac}^2-X_{ab}^2),$

$X_{ij}^{\′}=\left[\begin{array}{ccc}{X}_{aa}^{\′}& X_{ab}^{\′}& X_{ac}^{\′}\\ X_{ba}^{\′}& X_{bb}^{\′}& X_{bc}^{\′}\\ X_{ca}^{\′}& X_{cb}^{\′}& X_{cc}^{\′}\end{array}\right],X_{ij}=\left[\begin{array}{ccc}{X}_{aa}& X_{ab}& X_{ac}\\ X_{ba}& X_{bb}& X_{bc}\\ X_{ca}& X_{cb}& X_{cc}\end{array}\right],$

X ₁＝X _bcX _ac-X _aaX _ab；

X ₂＝X _abX _bc-X _aaX _ac；

X ₃＝X _abX _ac-X _aaX _bc；

$\mathrm{\Δ}=X_{aa}^3-X_{aa}(X_{bc}^2+X_{ac}^2+X_{ab}^2)+2X_{ab}{X}_{ac}{X}_{bc},$

Two loop line road self-impedances are respectively X _aa, X _bb, X _cc, in loop, mutual impedance is respectively X _ab, X _ac, X _bc, S ₀for containing X _mcomplicated multinomial, between twice, mutual impedance is equal and average as X _m;

Step 3) as A=B=C, X=Y=Z, a=b=c, x=y=z, negative-sequence current, zero-sequence current will reach minimum, and (X-Y), (B-A), (C-B), (Y-Z), (C-A), (X-Z) are negative phase-sequence, the responsive impedance parameter of zero-sequence current.

3. multiple-loop line transmission line three-phase imbalance suppressing method according to claim 2, it is characterized in that, when meeting following condition, circuit negative phase-sequence, zero-sequence current will reach minimum, C ₁~ C ₆be respectively the capacitor electrode capacitance in two loops, 6 branch roads compensated,

$\left\{\begin{array}{c}X-\mathrm{\ω}(C_1+C_2)=Y-\mathrm{\ω}(C_1+C_3)=Z-\mathrm{\ω}(C_2+C_3)\\ A+{\mathrm{\ωC}}_1=B+{\mathrm{\ωC}}_2=C+{\mathrm{\ωC}}_3\\ x-\mathrm{\ω}(C_4+C_5)=y-\mathrm{\ω}(C_4+C_6)=z-\mathrm{\ω}(C_5+C_6)\\ a+{\mathrm{\ωC}}_4=b+{\mathrm{\ωC}}_5=c+{\mathrm{\ωC}}_6\end{array}\right..$