CN104809096B - A kind of transmission system short circuit current in single phase grounding distribution calculation method based on phase component model - Google Patents
A kind of transmission system short circuit current in single phase grounding distribution calculation method based on phase component model Download PDFInfo
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Abstract
A kind of transmission system short circuit current in single phase grounding distribution calculation method based on phase component model, pass through the improvement to phase component model, transmission system after failure the independent network in left and right two has been divided into, the row of the equation based on phase component model are carried out respectively to write, form corresponding matrix, further to matrix optimizing, after can accurately calculating typical transmission system single-line to ground fault, the detailed distribution situation of upper short circuit current along aerial earth wire and phase line.The application is applied to the transmission system of single ended power supply and two kinds of different situations of transmission system of Double-End Source；Also the mode for having two aerial earth wires while operation in transmission system is included；Also include two aerial earth wires whether graded insulation and whether the complex modes of operation being grounded by tower；Further include the regularity of distribution of short circuit current on the aerial earth wire calculated by new algorithm.Present techniques are ripe, reliability is high.
Description
Technical field
The application belongs to transmission system field, and in particular to a kind of transmission system single-phase earthing based on phase component model is short
Road CURRENT DISTRIBUTION new algorithm, suitable for the complicated transmission of electricity system of double aerial earth wires of 110~500kV bilateral sources or single-side power
System, aerial earth wire therein include OPGW and common aerial earth wire.The method of operation of aerial earth wire more connects
The actual operating state of modern times transmission system, including whether graded insulation operation connects aerial earth wire with aerial earth wire by tower
Run on ground.When the application can accurately analyze transmission line of electricity single phase ground fault, short-circuit current value and aerial in phase line
The distribution of short circuit current on ground wire, there is fine application value, to the short circuit after transmission system single phase ground fault
CURRENT DISTRIBUTION has great meaning.
Background technology
Because transmission line of electricity can be decomposed into the large-scale electric power networks formed by span for unit, it is directed to
The transposition of circuit, the model of shaft tower, the series of shaft tower, the parameter etc. of pole tower ground resistance and the side system of circuit two, pass through these
Parametric solution equivalent circuit.Transmission line of electricity operation is complicated, and the pass that these parameters are also quantitative analysis is handled using suitable method
Key.Computational methods based on phase component then can fully reflect the complicated operation conditions of transmission line of electricity, to three-phase system parameter
Symmetry do not require, the factor such as different running method of mutual inductance, aerial earth wire between wire can in phase components method body
It is existing.Therefore, in face of the circuit method of operation complicated with aerial ground, based on phase components method, short circuit current divides on aerial earth wire is calculated
The application of cloth is more and more extensive.
Based on the double-sided elimination method of phase component model in terms of theoretical and research, there is researcher to do substantial amounts of work.Add
The scholar F.Dawalibi that puts on airs proposes the calculating prototype of phase components method, and considerable work has all been done in practice in theoretical and engineering
Make, some scholars are introduced and studied to the algorithm at home.It is worth noting that, its research does not have to the number of phase line
Limitation, has carried out generalized extended, but it is targeted in analyzing all be the situation of single aerial earth wire, and do not account for defeated
The situation of electric line both ends power supply.Improvement of the application to single-phase short circuit current algorithm on aerial earth wire in transmission system, at it
The situation of bilateral source is considered in theoretical foundation, while the transmission system of the double aerial earth wires of the typical triple line being directed to, fully
Consider the graded insulation on the every span of aerial earth wire and the situation of operation whether is grounded by tower, more conform to modern overhead power transmission
Actual operating.
In all kinds of failures, the occurrence frequency highest of single-phase short circuit.Short circuit current is on transmission line of electricity and aerial earth wire line
Distribution situation also directly influence the safe operation of system, while be also to realize the Selection and Design of aerial earth wire line and progress
Ensureing that gap is breakdown in short trouble when clearance for insulation is adjusted has great significance.
The distribution new algorithm of the transmission system short circuit current in single phase grounding based on phase component model illustrated in this application, energy
It is enough when accurately analyzing transmission line of electricity single phase ground fault, short circuit current on short-circuit current value and aerial earth wire in phase line
Distribution.
The content of the invention
The purpose of the application is overcome the shortcomings of in prior art, is proposed that the transmission system based on phase component model is single-phase and is connect
Ground short circuit CURRENT DISTRIBUTION new algorithm.This research method be innovatively put forward it is short in transmission line of electricity single-phase grounding fault
The new method of the processing of road CURRENT DISTRIBUTION.The application is applied to double aerial earth wires of 110~500kV bilateral sources or single-side power
Complicated transmission system, aerial earth wire therein includes OPGW and common aerial earth wire.Aerial earth wire
The method of operation closer to modern transmission system actual operating state, including aerial earth wire whether graded insulation operation and aerial ground
Whether line is grounded by tower is run.It is short-circuit in phase line when the application can accurately analyze transmission line of electricity single phase ground fault
The distribution of short circuit current on current value and aerial earth wire, there is fine application value, single-phase earthing is occurred to transmission system
Great meaning is distributed with short circuit current after short circuit.
The technical scheme of the application is as follows：
A kind of transmission system short circuit current in single phase grounding distribution calculation method based on phase component model, it is characterised in that：
Transmission system after failure has been divided into the independent network in left and right two, the row of the equation based on phase component model has been carried out respectively and writes,
Corresponding matrix is formed, further to matrix optimizing, after calculating typical transmission system short circuit current in single phase grounding, is maked somebody a mere figurehead
The detailed distribution situation of upper short circuit current along ground wire and phase line.
A kind of transmission system short circuit current in single phase grounding distribution calculation method based on phase component model, suitable for single-ended or
The transmission system of double aerial earth wires of person's Double-End Source, it is characterised in that the described method comprises the following steps：
(1) tower number of the shaft tower of single phase ground fault failure in transmission system is determined；
(2) using the shaft tower of single phase ground fault failure as boundary, whole overhead power transmission network is divided into left and right sides net
Network；
(3) the mesh series for determining two networks in left and right respectively is respectively m levels and n levels；
(4) mesh of two networks in left and right is numbered respectively；
(5) according to Kirchhoff's second law, voltage circuit equation, described net are write to all mesh row of the left and right sides
Hole includes all mesh of phase line and each self-forming of aerial earth wire, and all mesh row in the left and right sides write voltage circuit equation；
(6) respectively to the mesh equation matrixing of the left and right sides, and it is iterated respectively in the network of left and right two；
(7) determine at failure shaft tower, the current boundary condition of the mesh of the left and right sides, the mesh electricity of the described left and right sides
Stream boundary condition refers to that according to Kirchhoff's law the 1st grade of the left and right sides mesh in the step of obtaining (6) is i.e. single-phase from generation
The nearest cyclic currents of the left and right sides of the shaft tower of ground short circuit and the relational expression of short circuit current in single phase grounding；
(8) all mesh equations after Joint iteration and current boundary condition carry out the solution of equation, solve phase line and every
Short circuit current on each span of bar aerial earth wire；
(9) resulting short circuit current is drawn, the regularity of distribution and feature of obtained electric current.
In step (2), the network of the described left and right sides specifically refers to, left side network：From generation ground short circuit failure
Shaft tower to the phase line between all shaft towers and shaft tower of transmission line of electricity head end, aerial earth wire formed all mesh；Right web
Network：From the shaft tower of generation ground short circuit failure to the phase line all shaft towers and shaft tower of transmission line of electricity end, aerial earth wire
All mesh formed.
In step (3), all mesh share n levels in the network of left side, and all mesh share m levels in the network of right side；
The series of these mesh is determined jointly by the shaft tower of single phase ground fault failure and the shaft tower series of whole transmission system
, after failure occurs, m and n value are just corresponding to be determined, wherein m+n value is equal to the shaft tower series of whole transmission system.
In step (4), described specific coding rule is：From the shaft tower of single phase ground fault to transmission line of electricity
Head end direction, all mesh number consecutivelies in left side arrive n for 1；From the shaft tower of single phase ground fault to the end of transmission line of electricity
Direction, all mesh number consecutivelies in right side arrive m for 1；
In step (5), the voltage circuit equation write listed by the described left and right sides, every grade of mesh of every aerial earth wire
In, induced voltage includes the aerial to its induced voltage and another of the failure phase line current that single-phase earthing occurs in the span
Induced voltage of the ground wire to it.
In step (6), the iteration specific method of the mesh voltage equation to matrixing is：To the net in left side
Network, it is respectively 1 to n progress an iteration from mesh numbering, is further that n to 1 carries out second of iteration from mesh numbering；To the right side
The network of side, it is respectively 1 to m progress an iteration from mesh numbering, is further that m to 1 carries out second repeatedly from mesh numbering
Generation, the final purpose of iteration are that No. 1 mesh of the short circuit current and left and right sides network allowed on spans at different levels has and pushed away accordingly
Lead relation；
Wherein, the alternative manner in described left side network refers to first obtain from left side network electric power to trouble point direction
The relational expression of front and back stages cyclic currents, then from trouble point network electric power direction to the left, obtain front and back stages cyclic currents
Relational expression, two relational expressions described in simultaneous give expression to No. 1 mesh of arbitrary cyclic currents and left side network in the network of left side
The relational expression of electric current；Alternative manner in described right side network refers to first obtain from right side network electric power to trouble point direction
The relational expression of front and back stages cyclic currents, then from trouble point network electric power direction to the right, obtain front and back stages cyclic currents
Relational expression, two relational expressions described in simultaneous give expression to No. 1 mesh of arbitrary cyclic currents and right side network in the network of right side
The relational expression of electric current.
In step (7), at described determination breakdown stick tower, the current boundary condition of the mesh of the left and right sides, specific side
Method is：According to Kirchhoff's current law (KCL), the loop current for finding the 1st mesh of short dot left network and right network meets
Relational expression.
Described that resulting short circuit current is drawn in step (9), specific method is：Will be from transmission line of electricity
The value of top to short circuit current in single phase grounding all on two aerial earth wires of transmission line of electricity end is drawn, and is drawn in close hair
The distribution scenario of short circuit current at raw singlephase earth fault shaft tower and at remote failure shaft tower.
The application's has the beneficial effect that：
1st, during transmission system single phase ground fault failure, the independent network in the left and right sides, structure are divided into transmission system
Mesh equation is made, and obtained matrix is iterated respectively, obtains the relation between clearly electrical quantity.
When the 2nd, to transmission system single phase ground fault failure, the short circuit current on transmission line of electricity, on aerial earth wire
Short circuit current is analyzed and studied.
3rd, reliability is high, suitable for the complicated transmission of electricity system of double aerial earth wires of 110~500kV bilateral sources or single-side power
System, aerial earth wire therein include OPGW and common aerial earth wire.
Brief description of the drawings
Fig. 1 is the flow of the transmission system short circuit current in single phase grounding distribution calculation method of the invention based on phase component model
Schematic diagram；
Fig. 2 transmission line of electricity operation schematic diagrams；
The equivalent circuit diagram of double aerial earth wire transmission systems during Fig. 3 single phase ground faults.
Embodiment
With reference to Figure of description, the technical scheme of the application is described in further detail by specific embodiment.
It is as shown in Figure 1 the transmission system short circuit current in single phase grounding distribution disclosed by the invention based on phase component model
The schematic flow sheet of computational methods, the electric system short circuit current in single phase grounding distribution calculation method comprise the following steps：
(1) tower number of the shaft tower of single phase ground fault failure in transmission system is determined；
(2) using the shaft tower of single phase ground fault failure as boundary, whole overhead power transmission network is divided into left and right sides net
Network；The network of the described left and right sides specifically refers to, left side network：It is first to transmission line of electricity from the shaft tower that ground short circuit failure occurs
All mesh that phase line, aerial earth wire between all shaft towers and shaft tower at end are formed；Right side network：From generation ground short circuit event
All mesh that the shaft tower of barrier is formed to the phase line between all shaft towers and shaft tower of transmission line of electricity end, aerial earth wire.
(3) the mesh series for determining two networks in left and right respectively is respectively n levels and m levels；All mesh in the network of left side
Shared n levels, all mesh share m levels in the network of right side；The series of these mesh is by single phase ground fault failure
What shaft tower and the shaft tower series of whole transmission system determined jointly, after failure occurs, m and n value are just corresponding to be determined, wherein
M+n value is equal to the shaft tower series of whole transmission system.
(4) mesh of two networks in left and right is numbered respectively；Specifically coding rule is：From single phase ground fault
Shaft tower to the head end direction of transmission line of electricity, all mesh number consecutivelies in left side are 1 to arrive n；From the bar of single phase ground fault
For tower to the end direction of transmission line of electricity, all mesh number consecutivelies in right side are 1 to arrive m；
(5) according to Kirchhoff's second law, voltage circuit equation is write to all mesh row of the left and right sides；Described net
Hole includes all mesh of phase line and each self-forming of aerial earth wire, the voltage circuit equation write listed by the described left and right sides, often
In every grade of mesh of bar aerial earth wire, induced voltage include the span in occur single-phase earthing failure phase line current to its
Induced voltage and another aerial earth wire include the net to its induced voltage in the voltage circuit equation of the described left and right sides
The electric current on electric current and mesh adjacent thereto on hole, described voltage circuit equation is it can be shown that electricity on described mesh
The relational expression of stream.
(6) respectively to the mesh equation matrixing of the left and right sides, and it is iterated；Iteration side in described left side network
Method refers to first from left side network electric power to trouble point direction, is 1 to n progress an iteration to mesh numbering, obtains front and back stages
The relational expression of cyclic currents, then be that n to 1 carries out second of iteration to mesh numbering from trouble point network electric power direction to the left,
The relational expression of front and back stages cyclic currents is obtained, two relational expressions described in simultaneous give expression to arbitrary mesh electricity in the network of left side
The relational expression of No. 1 cyclic currents of stream and left side network；；Alternative manner in described right side network refers to first from right side network
Power supply is 1 to m to carry out an iteration to trouble point direction, to mesh numbering, obtains the relational expression of front and back stages cyclic currents, then
From trouble point network electric power direction to the right, it is that m to 1 carries out second of iteration to mesh numbering, obtains front and back stages mesh electricity
The relational expression of stream, two relational expressions described in simultaneous give expression to No. 1 of arbitrary cyclic currents and right side network in the network of right side
The relational expression of cyclic currents.
(7) determine at failure shaft tower, the current boundary condition of the mesh of the left and right sides, the mesh electricity of the described left and right sides
Stream boundary condition refers to according to Kirchhoff's law, the 1st grade of left and right sides cyclic currents in the step of obtaining (6) and single-phase connects
The relational expression of ground short circuit electric current；
(8) all mesh equations after Joint iteration and current boundary condition carry out the solution of equation, solve phase line and every
Short circuit current on each span of bar aerial earth wire；
(9) resulting short circuit current is drawn, the regularity of distribution and feature of obtained electric current are described to gained
To short circuit current drawn, specific method is：By two aerial earth wires from transmission line of electricity top to transmission line of electricity end
The value of upper all short circuit current in single phase grounding is drawn, and is drawn close at generation singlephase earth fault shaft tower and away from breakdown stick
The distribution scenario of short circuit current at tower, described short circuit current are drawn and illustrated below in connection with accompanying drawing 3.
The transmission line of electricity schematic diagram shown further below by Figure of description 2 is used as technology of the embodiment to the present invention
Scheme is described in further detail.
Overhead power transmission system operation model is as shown in Fig. 2 aerial earth wire-X and aerial ground-Y form aerial double earth wire in figure
System, parameter meaning are as follows：Zx(n) self-impedance of the n-th speed position away from internal frame vacant lot-X, Z are representedy(n) represent n-th speed position away from internal frame vacant lot-
Y self-impedance；Zm-xpi(n) represent n-th speed position away from the aerial ground-X mutual impedance relatively of interior transmission pressure i-th, Zm-ypi(n) n-th is represented
Aerial ground-the Y relatively of transmission pressure i-th mutual impedance in span (i therein represents A, B and C phase)；Zm-xy(n) represent n-th speed position away from
Mutual impedance between internal frame vacant lot-X and aerial ground-Y；Rx (n) and Ry (n) represents respectively n-th speed position away from interior simulation aerial ground-X with
The resistance of aerial ground-Y graded insulations operation, resistance closure are then to be run without graded insulation, and the resistance disconnects then exhausted for segmentation
Edge is run, and this set can effectively show the electrical connection situation of aerial ground in the horizontal direction；KxAnd K (n)y(n) divide
Not Biao Shi n-th speed position the resistance of operation whether is grounded at shaft tower away from interior simulation aerial ground-X and aerial ground-Y, the resistance closes then
Operation is grounded at this grade of tower, the resistance disconnects the then ungrounded operation at this grade of tower, and this set can effectively be shown
Electrical connection situation in vertical direction aerially；RgRepresent the equivalent pole tower ground resistance at every grade of shaft tower.
When accompanying drawing 3 represents single phase ground fault, the equivalent circuit diagram of double aerial earth wire transmission systems.It is noticeable
It is, in order to distinguish the network at left and right sides of trouble point, to be identified in the upper left corner of each variable, l represents trouble point left net
Network, r represent trouble point right network.Mesh in Fig. 2 is renumberd, a left side is followed successively by from trouble point to circuit head end
M levels are arrived in the 1 of side, and the 1 of right side is followed successively by from trouble point to line end to n levels；Wherein Eas, Ebs, EcsAnd Eam, Ebm, EcmRespectively
It is the side system three-phase equivalent power supply of circuit road two.Il As、Il BsAnd Il CsWhen ground short circuit respectively occurs, transmission line of electricity head end arrives
The electric current of short dot, Ir Am, Ir BmAnd Ir CmWhen ground short circuit respectively occurs, the electric current of transmission line of electricity end to short dot；
Zl m_pxARepresent the mutual induction reactance in every span between phase line A and ground wire X, Z on the left of trouble pointr m_pxARepresent on the right side of trouble point in every span
Mutual induction reactance between phase line A and ground wire X；Zl m_pyAThe mutual induction reactance in every span between phase line A and ground wire Y on the left of trouble point is represented,
Zr m_pyARepresent the mutual induction reactance in every span between phase line A and ground wire Y on the right side of trouble point；Zl m_xyRepresent on the left of trouble point in every span
Mutual induction reactance between ground wire X and ground wire Y, Zr m_xyRepresent the mutual induction reactance in every span between ground wire X and ground wire Y on the right side of trouble point；Il xWith
Il yThe loop current in every span in aerial earth wire-X and aerial earth wire-Y complete loops, I on the left of trouble point are represented respectivelyr xWith
Ir yThe loop current in every span in aerial earth wire-X and aerial earth wire-Y complete loops on the right side of trouble point is represented respectively；RfaTable
When showing single phase ground fault, the arc light resistance of failure phase；R0When representing single phase ground fault, the ground connection electricity of trouble point
Resistance；For more convenient analysis, the structure of phase line is made some adjustment by us, it is assumed that on the position of every grade of span, phase line
Structure be by a resistance rlOr rrGround connection (actual value of this resistance is infinitely great).The resistance Z of every grade of upper phase linel pAnd Zr p
Still with every grade of electric current distance and the product of the impedance value of unit length.NM parameter meaning and parameter in Fig. 2 in Fig. 3
It is corresponding consistent.
Using failure shaft tower as separation, the shared m section spans in its left side, the shared n section spans in its right side；Meanwhile failure shaft tower
Two adjacent spans be span that left and right sides numbering is 1 respectively, span series is incremented by successively to both sides.According to kirchhoff
Voltage law, voltage circuit equation is write to n levels mesh row to the 1 of left side.
The equation of left side fault point (span numbering now is 1)：
Failure phase line equation：
Il x(1)×Zl m_pxA(1)+Iy l(1)×Zl m_pyA(i)+Il bs(1)×Zl m_ppAB(1)+Il Cs(1)×Zl m_ppAC(1)+
Il As(1)×Zl p(1)-Il As(2)×rl(1)+Idk×Rfa=0
Two aerial earth wire equations are respectively such as following formula：
Three equations above can be write as matrix reduction form：
S1 lIl 1=Bl 1I2 l-HlIl 0
Wherein：
I1 l=[Ix l(1),Iy l(1),Il As(1),Il Bs(1),Il Cs(1)]T
I2 l=[Ix l(2),Iy l(2),Il As(2),Il Bs(2),Il Cs(2)]T
I0=Idk
S1 lRepresent equivalent impedance matrix.
Equation at sinistral power (span numbering now is n)：
Failure phase line equation：
Ix l(n)×Zl m_pxA(n)+Il y(n)×Zl m_pyA(n)+Il bs(n)×Zl m_ppAB(n)+Il Cs(n)×Zl m_ppAC(n)
+Il As(n)×Zl p(n)-Il As(n-1)×rl(n)-Eas=0
Two aerial earth wire equations are respectively such as following formula：
Three above equation can be write as matrix reduction form：
Sl nIl n=Al nIl n-1+El
Wherein：
In l=[Il x(n),Il y(n),Il As(n),Il Bs(n),Il Cs(n)]T
Il n-1=[Il x(n-1),Il y(n-1),Il As(n-1),Il Bs(n-1),Il Cs(n-1)]T
El=Eas
Sl nRepresent the equivalent impedance matrix of sinistral power point.
The equation (span numbering now is k) in left side stage casing somewhere：
Failure phase line equation：
Ix l(k)×Zl m_pxA(k)+Il y(k)×Zl m_pyA(k)+Il bs(k)×Zl m_ppAB(k)+Il Cs(k)×Zl m_ppAC(k)
+Il As(k)×Zl p(k)-Il As(k-1)×rl(k)=0
Two aerial earth wire equations are respectively such as following formula：
Three above equation can be write as matrix reduction form：
Sk lIk l=Al kIl k-1+Bk lIl k+1
Wherein：
Il k=[Ix l(k),Iy l(k),IAs l(k),Il Bs(k),Il Cs(k)]T
Il k-1=[Ix l(k-1),Iy l(k-1),Il As(k-1),Il Bs(k-1),Il Cs(k-1)]T
Il k+1=[Il x(k+1),Il y(k+1),Il As(k+1),Il Bs(k+1),Il Cs(k+1)]T
Sk lIt is the equiva lent impedance matrix at k to represent span numbering.
Alternative manner in left side network described herein is described in detail as follows：
First from left side network electric power to trouble point direction, the cyclic currents of -1 section of front and back stages mesh kth and kth section are obtained
Relation it is as follows：
Ik l=αl kIl k-1+λl k
In above formula：
αl k=(Sl k-Bl kαl k+1)-1Al k
λl k=(Sk l-Bl kαl k+1)-1Bl kλl k+1
From trouble point network electric power direction to the left, the cyclic currents of+1 section of front and back stages mesh kth section and kth are obtained
Relation it is as follows：
Ik l=ηk lIl k+1+δl kI0 l
In above formula：
ηk l=(Sl k-Al kηl k-1)-1Bl k
δl k=(Sk l-Al kηl k-1)-1Al kδl k-1
Recurrence equation that simultaneous obtains from from left side network electric power to trouble point direction and from trouble point network electric power to the left
The recurrence equation that direction obtains, obtains following formula：
Ik l=Ul k+Vl kI0
In above formula：
Uk l=(1- ηl kαl k+1)-1ηl kλl k+1
Vl k=(1- ηk lαl k+1)-1δl k
Similarly, network can arrange that to write out similar equation as follows on the right side of trouble point.
According to Kirchhoff's second law, voltage circuit equation is write to m levels mesh row to the 1 of right side.
The equation of right side fault point (span numbering now is 1)：
Failure phase line equation：
Ir x(1)×Zr m_pxA(1)+Iy r(1)×Zr m_pyA(i)+Ir bs(1)×Zr m_ppAB(1)+Ir Cs(1)×Zr m_ppAC(1)+
Ir As(1)×Zr p(1)-Ir As(2)×rr(1)+Idk×Rfa=0
Two aerial earth wire equations are respectively such as following formula：
Three equations above can be write as matrix reduction form：
S1 rIr 1=Br 1I2 r-HrIr 0
Wherein：
I1 r=[Ix r(1),Iy r(1),Ir As(1),Ir Bs(1),Ir Cs(1)]T
I2 r=[Ix r(2),Iy r(2),Ir As(2),Ir Bs(2),Ir Cs(2)]T
I0=Idk
S1 rRepresent equivalent impedance matrix.
Equation at east power (span numbering now is m)：
Failure phase line equation：
Ix r(m)×Zr m_pxA(m)+Ir y(m)×Zr m_pyA(m)+Ir bs(m)×Zr m_ppAB(m)+Ir Cs(m)×Zr m_ppAC(m)
+Ir As(m)×Zr p(m)-Ir As(m-1)×rr(m)-Eas=0
Two aerial earth wire equations are respectively such as following formula：
Three above equation can be write as matrix reduction form：
Sr mIr m=Ar mIr m-1+Er
Wherein：
Im r=[Ir x(m),Ir y(m),Ir As(m),Ir Bs(m),Ir Cs(m)]T
Ir m-1=[Ir x(m-1),Ir y(m-1),Ir As(m-1),Ir Bs(m-1),Ir Cs(m-1)]T
Er=Eam
Sr mRepresent the equivalent impedance matrix of sinistral power point.
The equation (span numbering now is k) in right side stage casing somewhere：
Failure phase line equation：
Ix r(k)×Zr m_pxA(k)+Ir y(k)×Zr m_pyA(k)+Ir bs(k)×Zr m_ppAB(k)+Ir Cs(k)×Zr m_ppAC(k)
+Ir As(k)×Zr p(k)-Ir As(k-1)×rr(k)=0
Two aerial earth wire equations are respectively such as following formula：
Three above equation can be write as matrix reduction form：
Sk rIk r=Ar kIr k-1+Bk rIr k+1
Wherein：
Ir k=[Ix r(k),Iy r(k),IAs r(k),Ir Bs(k),Ir Cs(k)]T
Ir k-1=[Ix r(k-1),Iy r(k-1),Ir As(k-1),Ir Bs(k-1),Ir Cs(k-1)]T
Ir k+1=[Ir x(k+1),Ir y(k+1),Ir As(k+1),Ir Bs(k+1),Ir Cs(k+1)]T
Sr kIt is the equiva lent impedance matrix at k to represent span numbering.
Alternative manner in right side network described herein is described in detail as follows：
First from right side network electric power to trouble point direction, the cyclic currents of -1 section of front and back stages mesh kth and kth section are obtained
Relation it is as follows：
Ik r=αr kIr k-1+λr k
In above formula：
αr k=(Sr k-Br kαr k+1)-1Ar k
λr k=(Sk r-Br kαr k+1)-1Br kλr k+1
From trouble point network electric power direction to the right, the cyclic currents of+1 section of front and back stages mesh kth section and kth are obtained
Relation it is as follows：
Ik r=ηk rIr k+1+δr kI0 r
In above formula：
ηk r=(Sr k-Ar kηr k-1)-1Br k
δr k=(Sk r-Ar kηr k-1)-1Ar kδr k-1
Recurrence equation that simultaneous obtains from from right side network electric power to trouble point direction and from trouble point network electric power to the right
The recurrence equation that direction obtains, obtains following formula：
Ik r=Ur k+Vr kI0
In above formula：
Uk r=(1- ηr kαr k+1)-1ηr kλr k+1
Vr k=(1- ηk rαr k+1)-1δr k
In short-circuit point, the electric current of each bar circuit first section can be obtained using KCL.Using the recurrence formula of each section of electric current,
Can solves the electric current on each bar circuit.If it is known that power supply, directly can be set to current source by faulty line electric current.Can profit
The complicated electric power networks containing double aerial earth wires, the especially various overhead transmission line of connection are solved in aforementioned manners.
Above formula shows arbitrary IkIt can represent that power supply component is known quantity by the boundary value of its both sides, still need and determine border
Electric current Io.According to KCL laws, the first paragraph electric current of short dot left network and right network meets following formula：
I0=Il 1+I1 r
For the first paragraph of the right and left network of short dot, following formula can be obtained by above formula：
I1 l=U1 l+Vl 1I0
I1 r=U1 r+Vr 1I0
Simultaneous above formula solves, and the boundary condition of two mesh in left and right described herein is shown below：
I0=(1-V1 r-V1 l)-1(Ur 1+Ul 1)
The distribution situation of each section of electric current just can be obtained according to above formula, i.e. on each span of every phase line and every aerial earth wire
Short circuit current.
Likewise, for other current circuits near faulty line, the application is first counted using the method calculated paragraph by paragraph
Faulty line is calculated, then calculates All other routes.
It is described drawing is carried out to resulting short circuit current to refer to, it is abscissa with the span numbering of overhead power transmission network
Value, the short circuit current in single phase grounding being distributed on every overhead line are drawn for ordinate value, in figure it can be clearly seen that
On every one-level span, the size of short circuit current in single phase grounding value on aerial earth wire, and according to described short-circuit current value
Size analyzes the distance range that single-line to ground fault has a great influence.
Claims (8)
1. a kind of transmission system short circuit current in single phase grounding distribution calculation method based on phase component model, suitable for single-ended or
The transmission system of double aerial earth wires of Double-End Source, it is characterised in that the described method comprises the following steps：
(1) tower number of the shaft tower of single phase ground fault failure in transmission system is determined；
(2) using the shaft tower of single phase ground fault failure as boundary, whole overhead power transmission network is divided into left and right sides network；
(3) the mesh series for determining two networks in left and right respectively is respectively m levels and n levels；
(4) mesh of two networks in left and right is numbered respectively；
(5) according to Kirchhoff's second law, voltage circuit equation, described mesh bag are write to all mesh row of the left and right sides
All mesh of phase line and each self-forming of aerial earth wire are included, all mesh row in the left and right sides write voltage circuit equation；
(6) respectively to the mesh equation matrixing of the left and right sides, and it is iterated respectively in the network of left and right two；
(7) determine at failure shaft tower, the current boundary condition of the mesh of the left and right sides, the cyclic currents side of the described left and right sides
Boundary's condition refers to according to Kirchhoff's law, and the 1st grade of the left and right sides mesh in the step of obtaining (6) is i.e. from occurring single-phase earthing
The nearest cyclic currents of the left and right sides of short-circuit shaft tower and the relational expression of short circuit current in single phase grounding；
(8) all mesh equations after Joint iteration and current boundary condition carry out the solution of equation, solve phase line and every frame
Short circuit current on each span of vacant lot line；
(9) resulting short circuit current is drawn, the regularity of distribution and feature of obtained electric current.
2. the transmission system short circuit current in single phase grounding distribution calculating side according to claim 1 based on phase component model
Method, it is characterised in that：
In step (2), the network of the described left and right sides specifically refers to, left side network：From the bar that ground short circuit failure occurs
All mesh that tower is formed to the phase line between all shaft towers and shaft tower of transmission line of electricity head end, aerial earth wire；Right side network：From
The shaft tower that ground short circuit failure occurs is formed to the phase line between all shaft towers and shaft tower of transmission line of electricity end, aerial earth wire
All mesh.
3. the transmission system short circuit current in single phase grounding distribution according to claim 1 or 2 based on phase component model calculates
Method, it is characterised in that：
In step (3), all mesh share n levels in the network of left side, and all mesh share m levels in the network of right side；These
The series of mesh is determined jointly by the shaft tower of single phase ground fault failure and the shaft tower series of whole transmission system, when
After failure occurs, m and n value are just corresponding to be determined, wherein m+n value is equal to the shaft tower series of whole transmission system.
4. the transmission system short circuit current in single phase grounding distribution calculating side according to claim 1 based on phase component model
Method, it is characterised in that：
In step (4), rule, which is numbered, to mesh is：From the shaft tower of single phase ground fault to the head end of transmission line of electricity
Direction, all mesh number consecutivelies in left side arrive n for 1；From the shaft tower of single phase ground fault to the end direction of transmission line of electricity,
All mesh number consecutivelies in right side arrive m for 1.
5. the transmission system short circuit current in single phase grounding distribution calculating side according to claim 1 based on phase component model
Method, it is characterized in that：
In step (5), the voltage circuit equation write listed by the described left and right sides, in every grade of mesh of every aerial earth wire,
Induced voltage is including the interior failure phase line current that single-phase earthing occurs of the span to its induced voltage and another aerial earth wire
To its induced voltage.
6. the transmission system short circuit current in single phase grounding distribution calculating side according to claim 1 based on phase component model
Method, it is characterized in that：
In step (6), the iteration specific method of the mesh voltage equation to matrixing is：To the network in left side, divide
It is 1 to n progress an iteration not from mesh numbering, is further that n to 1 carries out second of iteration from mesh numbering；To right side
Network, it is respectively 1 to m progress an iteration from mesh numbering, is further that m to 1 carries out second of iteration from mesh numbering, repeatedly
The final purpose in generation is that there is No. 1 mesh of the short circuit current and left and right sides network allowed on spans at different levels corresponding derive to close
System；
Wherein, the alternative manner in described left side network refers to before and after first being obtained from left side network electric power to trouble point direction
The relational expression of two-stage cyclic currents, then from trouble point network electric power direction to the left, obtain the relation of front and back stages cyclic currents
Formula, two relational expressions described in simultaneous give expression to No. 1 cyclic currents of arbitrary cyclic currents and left side network in the network of left side
Relational expression；Alternative manner in described right side network refers to before and after first being obtained from right side network electric power to trouble point direction
The relational expression of two-stage cyclic currents, then from trouble point network electric power direction to the right, obtain the relation of front and back stages cyclic currents
Formula, two relational expressions described in simultaneous give expression to No. 1 cyclic currents of arbitrary cyclic currents and right side network in the network of right side
Relational expression.
7. the transmission system short circuit current in single phase grounding distribution calculation method based on phase component model according to claim 1,
It is characterized in that：
In step (7), at described determination breakdown stick tower, the current boundary condition of the mesh of the left and right sides, specific method is：
According to Kirchhoff's current law (KCL), the pass that the loop current of the 1st mesh of short dot left network and right network meets is found
It is formula.
8. the transmission system short circuit current in single phase grounding distribution calculating side based on phase component model according to claim 1 or 7
Method, it is characterized in that：
Described that resulting short circuit current is drawn in step (9), specific method is：Will be from transmission line of electricity top
The value of all short circuit current in single phase grounding is drawn on to two aerial earth wires of transmission line of electricity end, is drawn single close to occurring
The distribution scenario of short circuit current at phase earth fault shaft tower and at remote failure shaft tower.
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