CN105911429A - Particle swarm optimization based aerial conductor's double end out-synchronization fault location method - Google Patents

Abstract

The invention relates to particle swarm optimization based aerial conductor's double end out-synchronization fault location method with the object to solving a fault location observing equation set and the method comprises the following steps: extracting the three phases of voltage and current power frequency components at the starting end and the finishing end of a line after an aerial conductor breaks down; performing symmetrical component transformation to the work frequency components to obtain corresponding zero sequence component, positive sequence component and negative sequence component; building fault point voltage equations by considering the impact of the out-synchronization of data; decoupling the fault point voltage equations to obtain the fault location observing equation set; and based on the particle swarm optimization, solving the fault location observing equation set and determining the fault location. Compared to the prior art, the method is capable of effectively and accurately finding the location of a fault with limited calculations. With the prospects for wide use, the method is also convenient to calculate.

Description

A kind of aerial line unsynchronized two-terminal fault distance-finding method based on particle cluster algorithm

Technical field

The present invention relates to a kind of relay protecting method, especially relate to a kind of aerial line unsynchronized two-terminal fault localization side Method.

Background technology

The fast development of national economy and the growing of electricity needs make the structure of power system the most complicated, transmission of electricity Circuit carries transmission electric energy, connects electrical network and the important task of electrical equipment, is the basis of whole power system safety and stability operation. But, transmission line of electricity is also one of the most part that breaks down in power transmission network, owing to transmission line of electricity distribution distance is wide, and mostly The natural environment area that approach is the most severe, it is short out that the reason such as windage yaw, thunderbolt, icing and branch short circuit is all likely to result in power transmission line Road fault.Above-mentioned area generally has inconvenient traffic, and line walking exists bigger difficulty；And existing circuit rapid protecting device generally therefore Barrier expands front action, and the vestige that circuit is destroyed by fault is inconspicuous, and abort situation is the most hidden, is not easy to naked eyes inspection equally. Determine Location rapidly and accurately, effectively can not only work by guide field line walking, repair power supply recovered from failure in time, and And weak link and the potential risk of circuit can be found in time, improve transmission line of electricity operational reliability.Therefore, the event of transmission line of electricity Barrier location technology can improve line walking work efficiency, reduces the economic loss that line fault causes to greatest extent, has important warp Ji and social benefit.

At present, transmission open acess research method can be divided into two kinds according to data type classifications, and one is based on fault The travelling wave positioning method of transient, trouble point is positioned by the time difference arriving circuit two ends by calculating fault traveling wave, But it is relatively big that the method needs to develop Special Equipment, technical sophistication and investment, and in engineer applied, difficulty is bigger；Two is based on fault The fault analytical method of steady-state quantity, by utilizing the fault message of circuit both sides to construct the range equation of redundancy, thus was reducing In the case of crossing Resistance Influence, trouble point is positioned, but the method needs to realize the synchronization of circuit two end data, and calculate Result there may be pseudo-root.

Summary of the invention

It is an object of the invention to for the problems referred to above provide a kind of efficiently, be accurately positioned calculating based on population of abort situation The aerial line unsynchronized two-terminal fault distance-finding method of method.

For realizing purpose of the present invention, the present invention provides the event of a kind of aerial line unsynchronized two-terminal based on particle cluster algorithm Barrier distance-finding method, the method utilize particle cluster algorithm to solve fault localization observational equation group, described distance-finding method, including with Lower step:

(1) by the three-phase voltage power frequency component of circuit head end after difference fourier algorithm extraction aerial line faultCircuit head end three-phase current power frequency componentThe three-phase voltage power frequency component of line endAnd the three-phase current power frequency component of line end

(2) above-mentioned power frequency component is carried out respectively symmetrical component transformation, obtain zero sequence, positive sequence and the negative sequence component of correspondence；

(3) the fault point voltage equation of the consideration asynchronous impact of data is set up；

(4) decouple described fault point voltage equation, obtain fault localization observational equation group；

(5) based on fault localization observational equation group described in PSO Algorithm, localization of faults position.

In described step (2), symmetrical component transformation is:

$\left[\begin{array}{c}{\stackrel{\·}{U}}_{M0}\\ {\stackrel{\·}{U}}_{M1}\\ {\stackrel{\·}{U}}_{M2}\end{array}\right]=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& \mathrm{\α}& {\mathrm{\α}}^2\\ 1& {\mathrm{\α}}^2& \mathrm{\α}\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{U}}_{MA}\\ {\stackrel{\·}{U}}_{MB}\\ {\stackrel{\·}{U}}_{MC}\end{array}\right]$

In formula: For circuit head end three-phase voltage zero sequence, Positive sequence and negative sequence component；

In like manner, it is thus achieved that circuit head end three-phase current zero sequence, positive sequence and negative sequence component after aerial line asymmetry short circuit faultLine end three-phase voltage zero sequence, positive sequence and negative sequence componentAnd circuit End three-phase current zero sequence, positive sequence and negative sequence component

The fault point voltage equation set up in described step (3) is:

${\stackrel{\·}{U}}_{M1}\cosh \mathrm{\γ}x-Z_L{\stackrel{\·}{I}}_{M1}\sinh \mathrm{\γ}x=\[{\stackrel{\·}{U}}_{N1}\cosh \mathrm{\γ}(L-x)+Z_L{\stackrel{\·}{I}}_{N1}\sinh \mathrm{\γ}(L-x)\]e^{j\mathrm{\δ}}$

In formula: x is the distance of trouble point distance aerial line head end；γ is aerial line propagation constant；δ is aerial line first and last two The asynchronous angle of terminal voltage；L is the length of overhead transmission line；Z_LFor aerial line natural impedance；For circuit head end three-phase voltage just Order components,For the positive-sequence component of line end three-phase voltage,For circuit head end three-phase current positive-sequence component；For line Road end three-phase current positive-sequence component.

In described step (4), fault localization observational equation group is:

$\left\{\begin{array}{c}(U_{MR}-B_3\cos \mathrm{\δ}+B_4\sin \mathrm{\δ})\cosh R_{1}x\cosh R_{2}x-(U_{MI}-B_3\sin \mathrm{\δ}-B_4\cos \mathrm{\δ})\sinh R_{1}x\sinh R_{2}x+\\ (B_5\cos \mathrm{\δ}-B_6\sin \mathrm{\δ}-B_1)\sinh R_{1}x\cosh R_{2}x-(B_5\sin \mathrm{\δ}+B_6\sin \mathrm{\δ}-B_2)\cosh R_{1}x\sinh R_{2}x=0\\ (U_{MI}-B_3\sin \mathrm{\δ}-B_4\cos \mathrm{\δ})\cosh R_{1}x\cosh R_{2}x+(U_{MR}-B_{3}cos\mathrm{\δ}+B_4\sin \mathrm{\δ})\sinh R_{1}x{\mathrm{sinhR}}_{2}x+\\ (B_5\sin \mathrm{\δ}+B_6\cos \mathrm{\δ}-B_2)\sinh R_{1}x\cosh R_{2}x+(B_5\cos \mathrm{\δ}-B_6\sin \mathrm{\δ}-B_1)\cosh R_{1}x\sinh R_{2}x=0\end{array}\right.$

$U_{MR}=\mathrm{Re}\left({\stackrel{\·}{U}}_M\right);U_{MI}=\mathrm{Im}\left({\stackrel{\·}{U}}_M\right);B_1=\mathrm{Re}\left(Z_L{\stackrel{\·}{I}}_{M1}\right);B_2=\mathrm{Im}\left(Z_L{\stackrel{\·}{I}}_{M1}\right);$

$B_3=\mathrm{Re}({\stackrel{\·}{U}}_{N1}\cosh \mathrm{\γ}L+Z_L{\stackrel{\·}{I}}_{N1}\sinh \mathrm{\γ}L);B_4=\mathrm{Im}({\stackrel{\·}{U}}_{N1}\cosh \mathrm{\γ}L+Z_L{\stackrel{\·}{I}}_{N1}\sinh \mathrm{\γ}L);$

$B_5=\mathrm{Re}({\stackrel{\·}{U}}_{N1}\sinh \mathrm{\γ}L+Z_L{\stackrel{\·}{I}}_{N1}\cosh \mathrm{\γ}L);B_6=\mathrm{Im}({\stackrel{\·}{U}}_{N1}\sinh \mathrm{\γ}L+Z_L{\stackrel{\·}{I}}_{N1}\cosh \mathrm{\γ}L);$

R₁=Re (γ)；R₂=Im (γ)

In formula: x is the distance of trouble point distance aerial line head end；γ is aerial line propagation constant；δ is aerial line first and last two The asynchronous angle of terminal voltage；L is the length of overhead transmission line；Z_LFor aerial line natural impedance；For circuit head end three-phase voltage just Order components,For the positive-sequence component of line end three-phase voltage,For circuit head end three-phase after overhead transmission line unbalanced fault Electric current positive-sequence component；For line end three-phase current positive-sequence component.

In described step (5), detailed process based on PSO Algorithm fault localization observational equation group includes:

(501) fitness function of particle cluster algorithm is set up:

F (x, δ)=f₁ ²(x,δ)+f₂ ²(x,δ)

f₁(x, δ)=(U_MR-B₃cosδ+B₄sinδ)coshR₁xcoshR₂x-(U_MI-B₃sinδ-B₄cosδ) sinhR₁xsinhR₂x+

(B₅cosδ-B₆sinδ-B₁)sinhR₁xcoshR₂x-(B₅sinδ+B₆sinδ-B₂)coshR₁xsinhR₂x

f₂(x, δ)=(U_MI-B₃sinδ-B₄cosδ)coshR₁xcoshR₂x+(U_MR-B₃cosδ+B₄sinδ) sinhR₁xsinhR₂x+

(B₅sinδ+B₆cosδ-B₂)sinhR₁xcoshR₂x+(B₅cosδ-B₆sinδ-B₁)coshR₁xsinhR₂x

(502) n particle S of random initializtion_i, i=0,1 ..., n-1, wherein, the position p of each particle_i(0)= [x_i(0),δ₍₀₎], the maximum evolutionary generation N and the computational accuracy that set particle require ε；

(503) position of current each particle is substituted into described fitness function respectively to calculate, and by result of calculation It is designated as optimal function value F that each particle is currently available respectively_i, each particle position is designated as current optimal particle position P_i, its In, i=0,1 ..., n-1；

(504) all described optimal function values F are compared_i, minima therein is designated as the current optimum letter of whole population Numerical value F_g, remember the current optimal location P that corresponding particle position is whole population_g, make particle algebraically k=0；

(505) updating search speed and the position of each particle, more new formula is:

$\left\{\begin{array}{c}{V}_{i(k+1)}={\mathrm{wV}}_{i\left(k\right)}+c_1{r}_1(P_i-p_{i\left(k\right)})+c_2{r}_2(P_g-p_{i\left(k\right)})\\ p_{i(k+1)}=p_{i\left(k\right)}+V_{i(k+1)}\end{array}\right.$

Wherein, V_i(k)For particle i in the speed in kth generation；W is inertia weight；c₁Lean on to self desired positions for regulation particle Near weight constant, c₂For regulation particle to the overall situation close weight constant of desired positions；r₁And r₂Be 2 separate with Machine number；p_i(k)For particle i in the position in kth generation；

(506) the renewal position of each particle is substituted into described fitness function respectively to calculate, and by result of calculation With F_iCompare, if result of calculation is less than F_i, then by F_iReplace with described result of calculation, and to corresponding P_iIt is replaced；

(507) relatively all F_i, choose minima therein, by this minima and F_gCompare, if this value is less than F_g, Then by F_gReplace with this minima, and by P_gReplace with corresponding particle position；

(508) judge whether particle algebraically reaches maximum evolutionary generation N, the most then perform step (509)；If it is not, then k =k+1, returns step (505)；

(509) F is judged_gWhether meet F_g＜ ε, the most then calculate and terminate, current P_gFault the most required for corresponding x away from From；If it is not, then return step (502).

Compared with prior art, the present invention utilizes and surveys the asynchronous voltage of aerial line both-end and current data arrived, and passes through Set up the fault localization equation containing two unknown quantitys of position of failure point and the asynchronous angle of data, and apply particle cluster algorithm to it Solve, it is achieved to aerial line abort situation efficient, be accurately positioned, have the advantages that

(1) present invention application difference fourier algorithm power frequency component of false voltage and electric current is carried out extract can eliminate decay The DC component impact on result of calculation, and amount of calculation is less；

(2) asynchronous for data angle is introduced fault localization equation and can measure the circuit two end data difference obtained by the present invention Still obtaining accurate fault distance in the case of step, application is wide；

(3) complex number voltage equation decoupling is that fault localization observational equation group solves by the present invention, it is to avoid directly ask Solving complex number equation and solve the problem of difficulty, amount of calculation is little；

(4) present invention application particle cluster algorithm solves energy simple and Convenient Calculation further to fault localization equation group, is carrying Improve while high solution efficiency and solve accuracy；

(5) present invention can realize aerial line localization of fault, calculates fault distance efficiently and accurately；By by number Introduce fault localization equation according to asynchronous angle, the asynchronous impact on positioning result of line double-end data can be eliminated；Meanwhile, should With particle cluster algorithm, range equation group is solved, calculating can be simplified, improve accuracy in computation and efficiency.

Accompanying drawing explanation

Fig. 1 is the flow chart of aerial line Two-terminal Fault Location of the present invention；

Fig. 2 is the calculating convergence applying particle cluster algorithm to obtain when solving fault localization equation group in the present embodiment Curve.

Detailed description of the invention

The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.The present embodiment is with technical solution of the present invention Premised on implement, give detailed embodiment and concrete operating process, but protection scope of the present invention be not limited to Following embodiment.

As it is shown in figure 1, the present embodiment carries out Two-terminal Fault Location with a single-line to ground fault aerial line for object of study, press According to the following step fault point:

Step 1: apply difference fourier algorithm, calculating support ceases to be busy respectively to measuring the circuit both end voltage current data obtained The power frequency component of circuit head end three-phase voltage during asymmetry short circuit faultThe power frequency of head end three-phase current is divided AmountThe power frequency component of line end three-phase voltageThe power frequency component of end three-phase currentDifference fourier algorithm described in this step is mathematical method conventional in this area, and therefore inventor is at this No longer it is described in detail.

Step 2: respectively the power frequency component of aerial line head and end three-phase voltage and electric current is carried out symmetrical component transformation, To head and end three-phase voltage during circuit asymmetry short circuit fault and the zero sequence of electric current power frequency component, positive sequence and negative sequence component, and It is designated asWherein, i=0,1,2, represent zero sequence, positive sequence and negative sequence component respectively.With circuit head end three-phase electricity Illustrating as a example by pressure, described transformation for mula is:

$\left[\begin{array}{c}{\stackrel{\·}{U}}_{M0}\\ {\stackrel{\·}{U}}_{M1}\\ {\stackrel{\·}{U}}_{M2}\end{array}\right]=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& \mathrm{\α}& {\mathrm{\α}}^2\\ 1& {\mathrm{\α}}^2& \mathrm{\α}\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{U}}_{MA}\\ {\stackrel{\·}{U}}_{MB}\\ {\stackrel{\·}{U}}_{MC}\end{array}\right]$

In formula:

Step 3: setting up the fault point voltage equation considering the asynchronous impact of data, described voltage equation is:

${\stackrel{\·}{U}}_{M1}\cosh \mathrm{\γ}x-Z_L{\stackrel{\·}{I}}_{M1}\sinh \mathrm{\γ}x=\[{\stackrel{\·}{U}}_{N1}\cosh \mathrm{\γ}(L-x)+Z_L{\stackrel{\·}{I}}_{N1}\sinh \mathrm{\γ}(L-x)\]e^{j\mathrm{\δ}}$

In formula: γ is aerial line propagation constant；X is that trouble point to be asked is to aerial line head end distance；Z_LFor aerial line ripple Impedance；L is aerial line length；δ is the asynchronous angle of unknown aerial line both end voltage；Herein, γ=0.0002+j0.0011, Z_L=(343.14-j62.971) Ω/km, L=50km.

Step 4: decouple described fault point voltage equation, obtains fault localization observational equation group, described observation Equation group is:

$\left\{\begin{array}{c}(U_{MR}-B_3\cos \mathrm{\δ}+B_4\sin \mathrm{\δ})\cosh R_{1}x\cosh R_{2}x-(U_{MI}-B_3\sin \mathrm{\δ}-B_4\cos \mathrm{\δ})\sinh R_{1}x\sinh R_{2}x+\\ (B_5\cos \mathrm{\δ}-B_6\sin \mathrm{\δ}-B_1)\sinh R_{1}x\cosh R_{2}x-(B_5\sin \mathrm{\δ}+B_6\sin \mathrm{\δ}-B_2)\cosh R_{1}x\sinh R_{2}x=0\\ (U_{MI}-B_3\sin \mathrm{\δ}-B_4\cos \mathrm{\δ})\cosh R_{1}x\cosh R_{2}x+(U_{MR}-B_{3}cos\mathrm{\δ}+B_4\sin \mathrm{\δ})\sinh R_{1}x{\mathrm{sinhR}}_{2}x+\\ (B_5\sin \mathrm{\δ}+B_6\cos \mathrm{\δ}-B_2)\sinh R_{1}x\cosh R_{2}x+(B_5\cos \mathrm{\δ}-B_6\sin \mathrm{\δ}-B_1)\cosh R_{1}x\sinh R_{2}x=0\end{array}\right.$

In formula:

$B_3=\mathrm{Re}({\stackrel{\·}{U}}_{N1}\cosh \mathrm{\γ}L+Z_L{\stackrel{\·}{I}}_{N1}\sinh \mathrm{\γ}L);B_4=\mathrm{Im}({\stackrel{\·}{U}}_{N1}\cosh \mathrm{\γ}L+Z_L{\stackrel{\·}{I}}_{N1}\sinh \mathrm{\γ}L);$

$B_5=\mathrm{Re}({\stackrel{\·}{U}}_{N1}\sinh \mathrm{\γ}L+Z_L{\stackrel{\·}{I}}_{N1}\cosh \mathrm{\γ}L);B_6=\mathrm{Im}({\stackrel{\·}{U}}_{N1}\sinh \mathrm{\γ}L+Z_L{\stackrel{\·}{I}}_{N1}\cosh \mathrm{\γ}L);$

R₁=Re (γ)；R₂=Im (γ).

Step 5: application PSO Algorithm fault localization observational equation group, calculates position of failure point, described fault The calculating process of some position is:

Step 501: determine that the fitness function of particle cluster algorithm, described fitness function are:

F (x, δ)=f₁ ²(x,δ)+f₂ ²(x,δ)

f₁(x, δ)=(U_MR-B₃cosδ+B₄sinδ)coshR₁xcoshR₂x-(U_MI-B₃sinδ-B₄cosδ) sinhR₁xsinhR₂x+

(B₅cosδ-B₆sinδ-B₁)sinhR₁xcoshR₂x-(B₅sinδ+B₆sinδ-B₂)coshR₁xsinhR₂x

f₂(x, δ)=(U_MI-B₃sinδ-B₄cosδ)coshR₁xcoshR₂x+(U_MR-B₃cosδ+B₄sinδ) sinhR₁xsinhR₂x+

(B₅sinδ+B₆cosδ-B₂)sinhR₁xcoshR₂x+(B₅cosδ-B₆sinδ-B₁)coshR₁xsinhR₂x

Step 502: n particle S of random initializtion_i, i=0,1 ..., n-1, wherein, the position p of each particle_i(0)= [x_i(0),δ_i(0)]；Set the maximum evolutionary generation N of particle；Setup algorithm required precision ε；Herein, n=10, N=30, ε=0.1；

Step 503: the position of current each particle is substituted into described fitness function respectively and calculates, and will calculate Result is designated as optimal function value F that each particle is currently available respectively_i, each particle position is designated as current optimal particle position P_i, Wherein, i=0,1 ..., n-1；

Step 504: the most all described current particle optimal function values F_i, minima therein is designated as whole population Current optimal function value F_g, remember the current optimal location P that corresponding particle position is whole population_g, make particle algebraically k= 0；

Step 505: update search speed and the position of each particle, described more new formula is:

$\left\{\begin{array}{c}{V}_{i(k+1)}={\mathrm{wV}}_{i\left(k\right)}+c_1{r}_1(P_i-p_{i\left(k\right)})+c_2{r}_2(P_g-p_{i\left(k\right)})\\ p_{i(k+1)}=p_{i\left(k\right)}+V_{i(k+1)}\end{array}\right.$

In formula: V_i(k)For particle i in the speed in kth generation；W is inertia weight；c₁Lean on to self desired positions for regulation particle Near weight constant, c₂For regulation particle to the overall situation close weight constant of desired positions, c₁And c₂Generally value between 0-2；r₁ And r₂It is 2 separate randoms number；p_i(k)For particle i in the position in kth generation；Herein, w=0.8, c₁=2, c₂=2；

Step 506: the renewal position of each particle is substituted into described fitness function respectively and calculates, and will calculate Result and F_iCompare, if result of calculation is less than F_i, then by F_iReplace with this result of calculation, and to corresponding P_iIt is replaced；

Step 507: to all F_iCompare, choose minima therein, by this minima and F_gCompare, if should Value is less than F_g, then by F_gReplace with this minima, and by P_gReplace with corresponding particle position；

Step 508: judge whether particle algebraically reaches maximum evolutionary generation N, if reaching, performs step 509；If not reaching Arrive, then k=k+1, perform step 505；

The most whether step 509: judge whether result of calculation meets required precision, meet F_g＜ ε, if meeting, calculates knot Bundle, current P_gThe fault distance that corresponding x is the most required；If being unsatisfactory for, perform step 502.

Herein, F_gIterative process as in figure 2 it is shown, final calculated F_g=0.035, less than required precision 0.1, corresponding x=13.00, i.e. failure judgement point position are 13.0km away from aerial line head end distance.By aerial line is entered Find after the actual line walking of row that position of failure point distance line head end 12.5km demonstrates effectiveness and the accuracy of this method.

The present invention counts when fault location calculates and affects produced by dual ended data asynchronism, then when circuit two ends When data synchronization unit is by Hardware Response Delay or software algorithm delay, can not be by asynchronous the caused calculating deviation shadow of data Ring.The present invention is when utilizing circuit distributed parameter model to set up fault localization equation, if it is different to introduce a unknown quantity in equation Step angle, then can click on fault by solving the complex coefficient equation containing two unknown quantitys of abort situation and asynchronous angle simultaneously Row location.Compared with existing fault distance-finding method, whether the data no matter line double-end records synchronize, can be relatively accurately Obtain position of failure point, thus substantially increase the accuracy of location.

Claims (5)

1. an aerial line unsynchronized two-terminal fault distance-finding method based on particle cluster algorithm, it is characterised in that the method utilizes Particle cluster algorithm solves fault localization observational equation group, described distance-finding method, comprises the following steps:

(1) by the three-phase voltage power frequency component of circuit head end after difference fourier algorithm extraction aerial line fault Circuit head end three-phase current power frequency componentThe three-phase voltage power frequency component of line endAnd The three-phase current power frequency component of line end

(2) above-mentioned power frequency component is carried out respectively symmetrical component transformation, obtain zero sequence, positive sequence and the negative sequence component of correspondence；

(3) the fault point voltage equation of the consideration asynchronous impact of data is set up；

(4) decouple described fault point voltage equation, obtain fault localization observational equation group；

(5) based on fault localization observational equation group described in PSO Algorithm, localization of faults position.

A kind of aerial line unsynchronized two-terminal fault distance-finding method based on particle cluster algorithm, it is special Levying and be, in described step (2), symmetrical component transformation is:

$\left[\begin{array}{c}{\stackrel{\·}{U}}_{M0}\\ {\stackrel{\·}{U}}_{M1}\\ {\stackrel{\·}{U}}_{M2}\end{array}\right]=\frac{1}{3}\left[\begin{array}{ccc}1& 1& 1\\ 1& \mathrm{\α}& {\mathrm{\α}}^2\\ 1& {\mathrm{\α}}^2& \mathrm{\α}\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{U}}_{MA}\\ {\stackrel{\·}{U}}_{MB}\\ {\stackrel{\·}{U}}_{MC}\end{array}\right]$

In formula: Zero sequence, positive sequence for circuit head end three-phase voltage And negative sequence component；

In like manner, it is thus achieved that circuit head end three-phase current zero sequence, positive sequence and negative sequence component after aerial line asymmetry short circuit faultLine end three-phase voltage zero sequence, positive sequence and negative sequence componentAnd circuit End three-phase current zero sequence, positive sequence and negative sequence component

A kind of aerial line unsynchronized two-terminal fault distance-finding method based on particle cluster algorithm, it is special Levying and be, the fault point voltage equation set up in described step (3) is:

${\stackrel{\·}{U}}_{M1}\cosh \mathrm{\γ}x-Z_L{\stackrel{\·}{I}}_{M1}\sinh \mathrm{\γ}x=\[{\stackrel{\·}{U}}_{N1}\cosh \mathrm{\γ}(L-x)+Z_L{\stackrel{\·}{I}}_{N1}\sinh \mathrm{\γ}(L-x)\]e^{j\mathrm{\δ}}$

In formula: x is the distance of trouble point distance aerial line head end；γ is aerial line propagation constant；δ is aerial line head and end electricity The asynchronous angle of pressure；L is the length of overhead transmission line；Z_LFor aerial line natural impedance；Positive sequence for circuit head end three-phase voltage Component,For the positive-sequence component of line end three-phase voltage,For circuit head end three-phase current positive-sequence component；For circuit End three-phase current positive-sequence component.

A kind of aerial line unsynchronized two-terminal fault distance-finding method based on particle cluster algorithm, it is special Levying and be, in described step (4), fault localization observational equation group is:

$\left\{\begin{array}{c}(U_{MR}-B_3\cos \mathrm{\δ}+B_4\sin \mathrm{\δ})\cosh R_{1}x\cosh R_{2}x-(U_{MI}-B_3\sin \mathrm{\δ}-B_4\cos \mathrm{\δ})\sinh R_{1}x\sinh R_{2}x+\\ (B_5\cos \mathrm{\δ}-B_6\sin \mathrm{\δ}-B_1)\sinh R_{1}x\cosh R_{2}x-(B_5\sin \mathrm{\δ}+B_6\sin \mathrm{\δ}-B_2)\cosh R_{1}x\sinh R_{2}x=0\\ (U_{MI}-B_3\sin \mathrm{\δ}-B_4\cos \mathrm{\δ})\cosh R_{1}x\cosh R_{2}x+(U_{MR}-B_3\cos \mathrm{\δ}+B_4\sin \mathrm{\δ})\sinh R_{1}x{\mathrm{sinhR}}_{2}x+\\ (B_5\sin \mathrm{\δ}+B_6\cos \mathrm{\δ}-B_2)\sinh R_{1}x\cosh R_{2}x+(B_5\cos \mathrm{\δ}-B_6\sin \mathrm{\δ}-B_1)\cosh R_{1}x\sinh R_{2}x=0\end{array}\right.$

$U_{MR}=\mathrm{Re}\left({\stackrel{\·}{U}}_M\right);U_{MI}=\mathrm{Im}\left({\stackrel{\·}{U}}_M\right);B_1=\mathrm{Re}\left(Z_L{\stackrel{\·}{I}}_{M1}\right);B_2=\mathrm{Im}\left(Z_L{\stackrel{\·}{I}}_{M1}\right);$

$B_3=\mathrm{Re}({\stackrel{\·}{U}}_{N1}\cosh \mathrm{\γ}L+Z_L{\stackrel{\·}{I}}_{N1}\sinh \mathrm{\γ}L);B_4=\mathrm{Im}({\stackrel{\·}{U}}_{N1}\cosh \mathrm{\γ}L+Z_L{\stackrel{\·}{I}}_{N1}\sinh \mathrm{\γ}L);$

$B_5=\mathrm{Re}({\stackrel{\·}{U}}_{N1}\sinh \mathrm{\γ}L+Z_L{\stackrel{\·}{I}}_{N1}\cosh \mathrm{\γ}L);B_6=\mathrm{Im}({\stackrel{\·}{U}}_{N1}\sinh \mathrm{\γ}L+Z_L{\stackrel{\·}{I}}_{N1}\cosh \mathrm{\γ}L);$

R₁=Re (γ)；R₂=Im (γ)

In formula: x is the distance of trouble point distance aerial line head end；γ is aerial line propagation constant；δ is aerial line head and end electricity The asynchronous angle of pressure；L is the length of overhead transmission line；Z_LFor aerial line natural impedance；Positive sequence for circuit head end three-phase voltage Component,For the positive-sequence component of line end three-phase voltage,For circuit head end three-phase electricity after overhead transmission line unbalanced fault Stream positive-sequence component；For line end three-phase current positive-sequence component.

A kind of aerial line unsynchronized two-terminal fault distance-finding method based on particle cluster algorithm, it is special Levying and be, in described step (5), detailed process based on PSO Algorithm fault localization observational equation group includes:

(501) fitness function of particle cluster algorithm is set up:

$f(x,\mathrm{\δ})=f_1^2(x,\mathrm{\δ})+f_2^2(x,\mathrm{\δ})$

f₁(x, δ)=(U_MR-B₃cosδ+B₄sinδ)coshR₁xcoshR₂x-(U_MI-B₃sinδ-B₄cosδ)sinhR₁xsinhR₂x+ (B₅cosδ-B₆sinδ-B₁)sinhR₁xcoshR₂x-(B₅sinδ+B₆sinδ-B₂)coshR₁xsinhR₂x

f₂(x, δ)=(U_MI-B₃sinδ-B₄cosδ)coshR₁xcoshR₂x+(U_MR-B₃cosδ+B₄sinδ)sinhR₁xsinhR₂x+ (B₅sinδ+B₆cosδ-B₂)sinhR₁xcoshR₂x+(B₅cosδ-B₆sinδ-B₁)coshR₁xsinhR₂x

(502) n particle S of random initializtion_i, i=0,1 ..., n-1, wherein, the position p of each particle_i(0)=[x_i(0), δ_i(0)], the maximum evolutionary generation N and the computational accuracy that set particle require ε；

(503) position of current each particle is substituted into described fitness function respectively to calculate, and by result of calculation respectively It is designated as optimal function value F that each particle is currently available_i, each particle position is designated as current optimal particle position P_i, wherein, i= 0,1,...,n-1；

(504) all described optimal function values F are compared_i, minima therein is designated as the current optimal function value of whole population F_g, remember the current optimal location P that corresponding particle position is whole population_g, make particle algebraically k=0；

(505) updating search speed and the position of each particle, more new formula is:

$\left\{\begin{array}{c}{V}_{i(k+1)}={\mathrm{wV}}_{i\left(k\right)}+c_1{r}_1(P_i-p_{i\left(k\right)})+c_2{r}_2(P_g-p_{i\left(k\right)})\\ p_{i(k+1)}=p_{i\left(k\right)}+V_{i(k+1)}\end{array}\right.$

Wherein, V_i(k)For particle i in the speed in kth generation；W is inertia weight；c₁Close to self desired positions for regulation particle Weight constant, c₂For regulation particle to the overall situation close weight constant of desired positions；r₁And r₂It is 2 separate randoms number； p_i(k)For particle i in the position in kth generation；

(506) the renewal position of each particle is substituted into described fitness function respectively to calculate, and by result of calculation and F_iEnter Row compares, if result of calculation is less than F_i, then by F_iReplace with described result of calculation, and to corresponding P_iIt is replaced；

(507) relatively all F_i, choose minima therein, by this minima and F_gCompare, if this value is less than F_g, then by F_g Replace with this minima, and by P_gReplace with corresponding particle position；

(508) judge whether particle algebraically reaches maximum evolutionary generation N, the most then perform step (509)；If it is not, then k=k+ 1, return step (505)；

(509) F is judged_gWhether meet F_g＜ ε, the most then calculate and terminate, current P_gThe fault distance that corresponding x is the most required； If it is not, then return step (502).