CN107423478A - A kind of computational methods of supergrid fault current limiter Optimizing - Google Patents

A kind of computational methods of supergrid fault current limiter Optimizing Download PDF

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Publication number
CN107423478A
CN107423478A CN201710347998.6A CN201710347998A CN107423478A CN 107423478 A CN107423478 A CN 107423478A CN 201710347998 A CN201710347998 A CN 201710347998A CN 107423478 A CN107423478 A CN 107423478A
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mrow
msub
fault current
current limiter
msubsup
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刘民伟
钱纹
郭洪芹
胡凯
赵爽
张秀钊
刘娟
赵庆丽
陈瑾
钱卫华
吴政声
彭俊春
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Energy China Ynpd
Yunnan Power Grid Co Ltd
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Energy China Ynpd
Yunnan Power Grid Co Ltd
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G06F30/36—Circuit design at the analogue level
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E60/00—Enabling technologies; Technologies with a potential or indirect contribution to GHG emissions mitigation

Abstract

The present invention provides a kind of computational methods of supergrid fault current limiter Optimizing, and step is：Calculation of short-circuit current is carried out to target grid, filters out the exceeded super-pressure node set of short circuit current；The mathematical modeling of fault current limiter Optimizing problem is established, solution draws fault current limiter Optimizing result；To the grid short circuit electric current and the satisfaction of security and stability analysis Judging fault demand limiter Optimizing number after execution fault current limiter Optimizing, and introduce and cut-off circuit reduction short circuit current measure, continue Optimization Solution, the Optimizing result and cut-off circuit result that output increase fault current limiter number constrains.The present invention is applied in supergrid fault current limiter Optimizing, small to power network scale-dependent, can be applied to the optimization problem of layouting for solving large scale electric network fault current limiter.

Description

A kind of computational methods of supergrid fault current limiter Optimizing
Technical field
The present invention relates to a kind of short circuit current method for limiting, and in particular to a kind of supergrid fault current limiter is excellent Change the computational methods layouted.
Background technology
With power network development, power supply installation is continuously increased, and electric network composition constantly strengthens, and electrical link is close in net, electric power System short circuit currents level increases year by year, the major issue that oneself faces in terms of turning into Power System Planning, operation at present.
Short-circuit current limiting measure mainly by terms of operation untie electromagnetic looped network, bus fanout operation, broken string, jump pass to And use high-impedance transformer, the transformer neutral point of equipment aspect install low reactance additional, install fault current limiter etc. additional.
Various current limiting measures applicable situations are different, need, according to actual conditions reasonable disposition, such as to untie electromagnetic looped network to 220kV Side is single-phase and three short circuit current has obvious reduction to act on, and also has certain reduction effect to 500kV sides short circuit current, and Transformer neutral point low reactance is installed additional only to limiting 500kV transformer station 220kV side single-phase short circuit current positive effects.And transformer station 500kV short circuit currents excessive problem should be addressed mainly from 500kV power networks, because 500kV sides self-impedance depends primarily on 500kV electric network compositions, measure have：Change rupturing capacity deficiency breaker, 500kV circuits jump switching line, install current-limiting reactor additional Device, install fault current limiter additional, jump switching line due to 500kV circuits has an impact to grid structure, current-limiting reactor access Increase system operation is lost, reduces economy, three of the above measure can bring certain negative effect to operation of power networks, more Change breaker and be then related to construction power failure, cost issues, and as power network development short circuit current outstanding problem needs to change more Equipment, and fault current limiter only plays a role when short circuit current flows through, therefore fault current limiter is that reply is super A kind of important technical of high-voltage fence fault current rapid growth.
Fault current limiter is a kind of electrical equipment of limiting short-circuit current.FCL is mainly made up of following four part, such as Shown in figure：Fast failure gallon element, switch, current-limiting reactor and overvoltage protection element are switched fast, in system During normal operation, switching device is in closure state, and FCL is put into without reactance；And quick disconnect only is switched in the system failure and is thrown Enter reactor and carry out current limliting, i.e.,：When short trouble occurs, current-limiting impedance is automatically engaged, plays a part of limiting short-circuit current.
Fault current limiter species mainly by：Superconductive current limiter, solid-state current limiter, magnetic current limiter, series resonance limit Flow device.The existing Practical Project of 500kV fault current limiters is gone into operation, and as East China Power Grid gone into operation in the end of the year 2009 is arranged on bottle 8 ohm, the fault current limiter that rated current is 2kA on kiln~Hangzhoupro north single line, equipment are arranged in 500kV bottle transmutation, For series resonance-type.
With the development of Power Electronic Technique, superconductor technology, computer technology and new material, fault current limiter is ground System and exploitation are quickly propelled, and its equipment manufacturing cost can be reduced, and performance is improved, and limiting short-circuit current is to mitigate cut-offfing for breaker Burden is possibly realized, therefore for supergrid limiting short-circuit current, install additional fault current limiter be it is a kind of more Preferable, effective solution.
Fault current limiter layouting in supergrid belongs to optimization problem, and the principle of its Optimizing is to meet Fault current limiter cloth is minimized on the premise of each node circuit breaker interrupting capacity to count out and total current-limiting reactor, can also be same When consider config failure demand limiter caused by income problem.
When the exceeded node of power network short circuit currents is less, layouting for fault current limiter can be drawn using enumerative technique Scheme, but when power network has the exceeded point of multiple short circuit currents and distributing position difference, using enumerating, rule is cumbersome and more difficult acquisition Optimum organization, consider from Electric Power Network Planning and economy point how to determine the optimal installation site of fault current limiter, impedance Value turns into difficult point, and this is a large-scale discontinuous, nonlinear multi-objective optimization question, currently used optimized algorithm master If various intelligent algorithms, such as simulated annealing, tabu search algorithm, genetic algorithm, swarm intelligence algorithm etc., these Algorithm is mainly used in academic research, is mostly the less modular system of node using example, and when actual electric network scale is big, constraint is many When more, solving speed is very slow, and adaptability is poor.
This patent initially sets up the mathematical modulo of fault current limiter Optimizing mainly from Practical angle Type, then solved using heuristic value, finally carry out result verification and evaluation, draw Optimizing scheme, form one The algorithm of set system.
The content of the invention
In view of above-mentioned analysis, the present invention is intended to provide a kind of calculating of supergrid fault current limiter Optimizing Method, for solving the above problems.
The purpose of the present invention is mainly achieved through the following technical solutions：
A kind of computational methods of supergrid fault current limiter Optimizing, it is characterised in that：Methods described bag Include following steps：
Step 1：Calculation of short-circuit current is carried out to target grid, filters out the exceeded super-pressure node set of short circuit current；
Step 2：The mathematical modeling of fault current limiter Optimizing is established, interior point method is used to the mathematical modeling of foundation Solve, draw Optimizing result；
Step 3：To the grid short circuit electric current and security and stability analysis after execution fault current limiter Optimizing；
Step 4：The satisfaction of Judging fault demand limiter Optimizing number, if satisfied, output fault current limit Device Optimizing result processed, otherwise increase fault current limiter cloth and count out limitation, and introduce and cut-off circuit to reduce short circuit electric Stream measure, continue Optimization Solution, the Optimizing result and cut-off circuit knot that output increase fault current limiter number constrains Fruit.
In the step 1, calculation of short-circuit current is carried out to target grid, filters out the exceeded super-pressure node of short circuit current Set；Calculation of short-circuit current is carried out by using the power system analysis software PSD-BPA of maturation, and filters out short circuit current and surpasses Target super-pressure node set, super-pressure node refer generally to 500kV and above exchange node.
Step 2：The mathematical modeling of fault current limiter Optimizing is established, interior point method is used to the mathematical modeling of foundation Solve, draw Optimizing result；Concretely comprise the following steps：
Step 2-1：The mathematical modeling of fault current limiter Optimizing is established, expression formula is as follows：
(XF, k-XF, 1) (XF, k-XF, 2）...（XF, k-XF, i)=0 (3)
Wherein variable is XF, k, represent the fault current limiter resistance that kth bar branch road is installed；
Object function (1) is that the total cost of expression installation fault current limiter is minimum, wherein The total number of power network installation fault current limiter is expressed, adds 10 in denominator-6Be in order to impedance be 0 when the formula it is significant, and Impedance value is not counted to set for 0 number；wFCLFor the weight coefficient of current limiter total amount, new 1 fault current limit of installation is represented Device investment processed and the ratio of reactor specific investment cost；
Constraints (2) is the breaker breaking current level that expression node short circuit current should be no more than corresponding transformer station, Represent that the breaker breaking current of transformer station is horizontal, f ∈ TF, TFRepresent the exceeded node set of short circuit current, k ∈ SF, SFRepresent event Hinder demand limiter installation set of fingers, NFFor set SFMiddle branch road total number；zff 0F before fault current limiter is installed in expression additional The self-impedance of node；d0, k、d3, k、d4, kFor the constant parameter corresponding with kth bar branch road, Respectively install fault current limiter front nodal point i and j system equivalent impedance additional,To install failure electricity additional The mutual impedance of system before stream limiter；
zffFor the self-impedance of f points, VfFor node perunit threshold voltage, reference voltage is typically taken, then VfFor 1, short circuit is represented with f Point, then f points three short circuit current be：
After circuit branch road installation fault current limiter, trouble point f three short circuit current is If, i.e.,：
In formula：ΔIfFor f point short circuit current variable quantities.If only installing current-limiting reactor in kth branch road, cause f point three-phases The variable quantity of short circuit current is designated as Δ Ifk, ignore in different branch fault current limiter to IfJoint effect, Δ IfRepresent For Δ IfkLinear superposition, i.e.,：
When only 1 fault current limiter, during installed in kth bar branch road, to a certain node f short circuit current variable quantity ΔIfkInfluence derive it is as follows：Note impedance value is XF,kFault current limiter be installed in series on kth bar branch road, branch road k two End node is i and j, installs the branch impedance before fault current limiterSubscript L represents branch road constant, installs failure It is z that branch road, which has been equivalent to size in parallel, after demand limiterpImpedance, schematic diagram below figure, shown in expression formula such as formula (7), The fault current limiter impedance X of series connectionF,kWith zpRelation be：
The fault current limiter of configuration passes through equivalent parallel impedance zpInfluence Δ Ifk, Δ IfkWith network node impedance matrix The relation of element such as formula (8), (9).
Additional parallel branch z in electric power networksp, to the diagonal element z of nodal impedance matrixff、Influence such as formula (9)：
Formula (9) is substituted into formula (8), obtains formula (10), it is seen that Δ IfkIt is XF,kInverse proportion function.
Therefore, formula (6) can be expressed as formula (11)：
According to formula (5), then node short circuit current constraints expression formula is derived as formula (2)；
Step 2-2：Using Sensitivity Method, candidate's set of fingers of installation fault current limiter is formed, it is specific as follows：
For actual bulk power grid, if candidate branch road of all branch roads as installation fault current limiter, formula (2) conduct Constraint equation, then the openness difference of coefficient matrix, optimization efficiency is low, therefore candidate's branch road can be screened according to sensitivity, reduces Candidate's set of fingers scope of fault current limiter is installed, improves optimization efficiency.For short dot f, by the change of branch impedance Change influences descending sequence, the i.e. descending sequence of sensitivity factor, by preceding N to trouble point f three short circuit currentSIndividual peace Fill candidate's branch road sequence number deposit set S of fault current limiterf, NFFor each set SfNumber, NFTake the corresponding electricity of node f The total outlet of grade is pressed to return number；
Node short circuit current is as follows to the Calculation of Sensitivity of branch impedance, according to formula (10), obtains working as XFΔ I when=0fkIt is right XF, kDerivative Δ I 'fk。
For f points, to select and which branch road fault current limiter to be installed to I atfHave a great influence, then need more each Δ I′fk, k=1 ..., NF, take the Δ I ' of negativefk, compare the preceding N of maximum absolute valueFIndividual (NF<), N the sequence number k of candidate's branch road is counted Enter set SfIn, applied to constraints (2)；
Step 2-3：Fault current limiter resistance sequence is set, it is specific as follows：
Constraints (3) is the impedance value constraint of expression fault current limiter；The 1 ohm of resistance of 500kV fault current limiters It is worth equivalent to 4 × 400mm that length is 3.4 kms2500kV circuits, line length corresponding to 6 ohm are 20.4km, 20 ohm Corresponding line length is 68km, due to equipment manufacturing cost, apparatus insulated requirement, place limitation etc., fault current limiter resistance Should not be too big, too small then current limitation effect unobvious, are not any for the reactance value with engineering practicability, fault current limiter Value, it is more reasonable using the serializing value with Practical significance, such as use XF=[0,6,7,8,9,10,11,12,13,14,15, 16,17,18,19,20], Z is usedF, iRepresent i-th of impedance value to be selected of fault current limiter, i=1 ..., NFCL, NFCLFor impedance Impedance value number to be selected, works as X in value sequenceF, iFor 0 when, represent that the branch road does not install fault current limiter.Using Practical After serializing resistance, fault current limiter resistance constraint expression is formula (3)；
Step 2-4：The step 2-1 fault current limiter Optimizing mathematical modelings established are solved；By formula (3) As can be seen that fault current limiter reactance value is the multinomial with sequential value number identical exponent number, direct solution is very multiple It is miscellaneous and difficult, therefore pre-process very practical.It is currently the research of optimization problem using the Non-Linear Programming containing Constraints Focus, therefore the key that the Constraints condition that need to construct fault current limiter resistance discrete variable is to solve for；
In order to seek two boundaries of discrete variable, Constraints condition is constructed, discrete variable can be worked as to continuous variable, serialization Carry out precomputation.Mathematical modeling is as follows：
Modern interior point method comparative maturity at present, its calculating speed is fast, convergence is good, strong robustness, initial value is chosen not The features such as sensitivity, strong processing inequality constraints, powerful vitality is shown in Optimization Problems In Power Systems；
If optimal solution be present in problem, the optimal solution for the discrete magnitude serialization being calculated, it is however generally that, although the solution For feasible solution, but there is any discrepancy with engineered sequences value, and the value that simply rounds up is more coarse, therefore constructs fault current The Constraints condition of limiter resistance is as follows：
(XF, k-XF, i)(XF, k-XF, i+1)=0 (14)
Using the solution that precomputation is drawn as initial value, the Constraints condition of discrete variable is added, tectonic model is as follows：
(XF, k-XF, i)(XF, k-XF, i+1)=0 (15)
Using modern interior point method solving model (15), optimal solution is drawn.
In order to ensure convergence, method of relaxation is selected, (15) can be converted into (16), as follows：
ε≤(XF, k-XF, i) (XF, k-XF, i+1)≤ε (16)
Relaxation parameter ε is introduced, is updated after each iteration, with (XF, k-XF, i)(XF, k-XF, i+1) diminish and gradually tend to 0, ε Renewal presses shaping variable serialization, when it is close to integer solution according to the deflation of variable bound bound that is, during calculating When the bound of constraint is tightened centered on close integer solution according to given strategy, its acceleration is approached integer solution.
Step 3：To the grid short circuit electric current and security and stability analysis after execution fault current limiter Optimizing；Specifically For：
Step 3-1：Short circuit current meter is carried out to the power network after performing fault current limiter Optimizing using PSD-BPA Calculate, verify current limitation effect；
Step 3-2：Safety and stability point is carried out to the power network after performing fault current limiter Optimizing using PSD-BPA Analysis, because fault current limiter does not influence normal condition trend, therefore Main Analysis influences on Power Network Transient Stability.
Step 4：The satisfaction of Judging fault demand limiter Optimizing number, if satisfied, output fault current limit Device Optimizing result processed, otherwise increase fault current limiter cloth and count out limitation, and introduce and cut-off circuit to reduce short circuit electric Stream measure, continue Optimization Solution, the Optimizing result and cut-off circuit knot that output increase fault current limiter number constrains Fruit.Specially：
Step 4-1：The satisfaction of Judging fault demand limiter Optimizing number, if satisfied, calculating terminates, and exports Fault current limiter Optimizing result；Otherwise setting fault current limiter cloth, which counts out to limit, enters step 4-2；
Step 4-2：Circuit is cut-off in introducing reduces short circuit current measure, corrects mathematical modeling, is superimposed in object function (1) The corresponding expense of circuit is cut-off, is superimposed in constraints (2) and cut-offs influence of the circuit to node short circuit current；
The sensitivity that circuit uses node short circuit current to break branch road is cut-off, refers to that kth bar branch breaking causes failure The numerical value of point f three short circuit currents change.Branch road breaks, XF, k=∞, according to formula (7), equivalent to parallel impedance；
The changing value to break to node f three short circuit currents, such as formula (18), as node f three short circuit current is to kth The sensitivity of bar branch road broken string.
Take the Δ I of negativefk, compare the preceding N of maximum absolute valueSIndividual (Ns<), N the sequence number k of candidate's branch road is included in set Sf In, applied to constraints.
Step 4-3：Step 4-2 mathematical modeling is solved using interior point method, method is the same as step 2；
Step 4-4：To the grid short circuit electric current and safety and stability after execution step 4-3 fault current limiter Optimizings Analysis, the Optimizing result and cut-off circuit result that output increase fault current limiter number constrains.
Compared with immediate prior art, the beneficial effects of the invention are as follows：
The present invention is by fault current limiter Optimizing problem, including installation site and impedance value, only with one group of variable Represent, mathematical modeling is clear, and optimizes solution with modern interior point method, and solving speed is fast, small to power network scale-dependent, can Optimization problem of layouting applied to the fault current limiter of large-scale electrical power system.
The present invention is further described below in conjunction with the accompanying drawings.
Brief description of the drawings
Fig. 1 is：A kind of computational methods of supergrid fault current limiter Optimizing in the embodiment of the present invention Flow chart；
Fig. 2 is existing fault current limiter theory diagram；
Fig. 3 is existing fault current limiter illustraton of model；
Fig. 4 is the isoboles of fault current limiter installation branch road.
Embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present application, the technical scheme in the embodiment of the present application is carried out clear, complete Site preparation describes.Accompanying drawing forms the part of the application, and is used for the principle for explaining the present invention together with embodiments of the present invention.
The invention provides the computational methods of supergrid fault current limiter Optimizing, Fig. 1 shows the party The method flow diagram of method；Methods described concretely comprises the following steps：
Step 1：Calculation of short-circuit current is carried out to target grid, filters out the exceeded super-pressure node set of short circuit current； Calculation of short-circuit current is carried out by using the power system analysis software PSD-BPA of maturation, and it is exceeded to filter out short circuit current Super-pressure node set, super-pressure node refer generally to 500kV and above exchange node；
Step 2：The mathematical modeling of fault current limiter Optimizing is established, interior point method is used to the mathematical modeling of foundation Solve, draw Optimizing result；
Step 2-1：The mathematical modeling of fault current limiter Optimizing is established, expression formula is as follows：
(XF, k-XF, 1)(XF, k-XF, 2)...(XF, k-XF, i)=0 (3)
Wherein variable is XF, k, represent the fault current limiter resistance that kth bar branch road is installed.
Object function (1) is that the total cost of expression installation fault current limiter is minimum, wherein The total number of power network installation fault current limiter is expressed, adds 10 in denominator-6Be in order to impedance be 0 when the formula it is significant, and Impedance value is not counted to set for 0 number；wFCLFor the weight coefficient of current limiter total amount, new 1 fault current limit of installation is represented Device investment processed and the ratio of reactor specific investment cost；
Constraints (2) is the breaker breaking current level that expression node short circuit current should be no more than corresponding transformer station, Represent that the breaker breaking current of transformer station is horizontal, f ∈ TF, TFRepresent the exceeded node set of short circuit current, k ∈ SF, SFRepresent event Hinder demand limiter installation set of fingers, NFFor set SFMiddle branch road total number；zff 0F before fault current limiter is installed in expression additional The self-impedance of node；d0, k、d3, k、d4, kFor the constant parameter corresponding with kth bar branch road, Respectively install fault current limiter front nodal point i and j system equivalent impedance additional,To install failure electricity additional The mutual impedance of system before stream limiter.
Step 2-2：Using Sensitivity Method, candidate's set of fingers of installation fault current limiter is formed, it is specific as follows：
For actual bulk power grid, if candidate branch road of all branch roads as installation fault current limiter, formula (2) conduct Constraint equation, then the openness difference of coefficient matrix, optimization efficiency is low, therefore candidate's branch road can be screened according to sensitivity, reduces Candidate's set of fingers scope of fault current limiter is installed, improves optimization efficiency.For short dot f, by the change of branch impedance Change influences descending sequence, the i.e. descending sequence of sensitivity factor, by preceding N to trouble point f three short circuit currentSIndividual peace Fill candidate's branch road sequence number deposit set S of fault current limiterf, NFFor each set SfNumber, NFTake the corresponding electricity of node f The total outlet of grade is pressed to return number.
For f points, to select and which branch road fault current limiter to be installed to I atfHave a great influence, then need more eachK=1 ..., NF, take the Δ I ' of negativefk, compare the preceding N of maximum absolute valueFIndividual (NF<), N by candidate's branch road Sequence number k be included in set SfIn, applied to constraints (2).
Step 2-3：Fault current limiter resistance sequence is set, it is specific as follows：
Constraints (3) is the impedance value constraint of expression fault current limiter；The 1 ohm of resistance of 500kV fault current limiters It is worth equivalent to 4 × 400mm that length is 3.4 kms2500kV circuits, line length corresponding to 6 ohm are 20.4km, 20 ohm Corresponding line length is 68km, due to equipment manufacturing cost, apparatus insulated requirement, place limitation etc., fault current limiter resistance Should not be too big, too small then current limitation effect unobvious, are not any for the reactance value with engineering practicability, fault current limiter Value, it is more reasonable using the serializing value with Practical significance, such as use XF=[0,6,7,8,9,10,11,12,13,14,15, 16,17,18,19,20], Z is usedF, iRepresent i-th of impedance value to be selected of fault current limiter, i=1 ..., NFCL, NFCLFor impedance Impedance value number to be selected, works as X in value sequenceF, iFor 0 when, represent that the branch road does not install fault current limiter.Using Practical After serializing resistance, fault current limiter resistance constraint expression is formula (3).
Step 2-2：The step 2-1 fault current limiter Optimizing mathematical modelings established are solved；By formula (3) As can be seen that fault current limiter reactance value is the multinomial with sequential value number identical exponent number, direct solution is very multiple It is miscellaneous and difficult, therefore pre-process very practical.It is currently the research of optimization problem using the Non-Linear Programming containing Constraints Focus, therefore the key that the Constraints condition that need to construct fault current limiter resistance discrete variable is to solve for.
In order to seek two boundaries of discrete variable, Constraints condition is constructed, discrete variable can be worked as to continuous variable, serialization Carry out precomputation.Mathematical modeling is as follows：
Modern interior point method comparative maturity at present, its calculating speed is fast, convergence is good, strong robustness, initial value is chosen not The features such as sensitivity, strong processing inequality constraints, powerful vitality is shown in Optimization Problems In Power Systems.
If optimal solution be present in problem, the optimal solution for the discrete magnitude serialization being calculated, it is however generally that, although the solution For feasible solution, but there is any discrepancy with engineered sequences value, and the value that simply rounds up is more coarse, therefore constructs fault current The Constraints condition of limiter resistance is as follows：
(XF, k-XF, i)(XF, k-XF, i+1)=0 (14)
Using the solution that precomputation is drawn as initial value, the Constraints condition of discrete variable is added, tectonic model is as follows：
(XF, k-XF, i)(XF, k-XF, i+1)=0 (15)
Using modern interior point method solving model (15), optimal solution is drawn.
In order to ensure convergence, method of relaxation is selected, (15) can be converted into (16), as follows：
ε≤(XF, k-XF, i)(XF, k-XF, i+1)≤ε (16)
Relaxation parameter ε is introduced, is updated after each iteration, with (XF, k-XF, i)(XF, k-XF, i+1) diminish and gradually tend to 0, ε Renewal presses shaping variable serialization, when it is close to integer solution according to the deflation of variable bound bound that is, during calculating When the bound of constraint is tightened centered on close integer solution according to given strategy, its acceleration is approached integer solution.
Step 3：To the grid short circuit electric current and security and stability analysis after execution fault current limiter Optimizing；Specifically Including：
Step 3-1：Short circuit current meter is carried out to the power network after performing fault current limiter Optimizing using PSD-BPA Calculate, verify current limitation effect；
Step 3-2：Safety and stability point is carried out to the power network after performing fault current limiter Optimizing using PSD-BPA Analysis, because fault current limiter does not influence normal condition trend, therefore Main Analysis influences on Power Network Transient Stability；
Step 4：The satisfaction of Judging fault demand limiter Optimizing number, if satisfied, output fault current limit Device Optimizing result processed, otherwise increase fault current limiter cloth and count out limitation, and introduce and cut-off circuit to reduce short circuit electric Stream measure, continue Optimization Solution, the Optimizing result and cut-off circuit knot that output increase fault current limiter number constrains Fruit.Specifically include：
Step 4-1：The satisfaction of Judging fault demand limiter Optimizing number, if satisfied, calculating terminates, and exports Fault current limiter Optimizing result；Otherwise setting fault current limiter cloth, which counts out to limit, enters step 4-2；
Step 4-2：Circuit is cut-off in introducing reduces short circuit current measure, corrects mathematical modeling, is superimposed in object function (1) The corresponding expense of circuit is cut-off, is superimposed in constraints (2) and cut-offs influence of the circuit to node short circuit current；
The sensitivity that circuit uses node short circuit current to break branch road is cut-off, refers to that kth bar branch breaking causes failure The numerical value of point f three short circuit currents change.Branch road breaks, XF, k=∞, according to formula (7), equivalent to parallel impedance.
The changing value to break to node f three short circuit currents, such as formula (18), as node f three short circuit current is to kth The sensitivity of bar branch road broken string.
Take the Δ I of negativefk, compare the preceding N of maximum absolute valueSIndividual (Ns<), N the sequence number k of candidate's branch road is included in set Sf In, applied to constraints.
Step 4-3：Step 4-2 mathematical modeling is solved using interior point method, method is the same as step 2；
Step 4-4：To the grid short circuit electric current and safety and stability after execution step 4-3 fault current limiter Optimizings Analysis, the Optimizing result and cut-off circuit result that output increase fault current limiter number constrains.
Finally it should be noted that：Described embodiment is only some embodiments of the present application, rather than whole realities Apply example.Based on the embodiment in the application, those of ordinary skill in the art are obtained under the premise of not making creative work again Every other embodiment, belong to the application protection scope.

Claims (5)

  1. A kind of 1. computational methods of supergrid fault current limiter Optimizing, it is characterised in that this method include with Lower step：
    Step 1：Calculation of short-circuit current is carried out to target grid, filters out the exceeded super-pressure node set of short circuit current；
    Step 2：The mathematical modeling of fault current limiter Optimizing is established, the mathematical modeling of foundation is asked using interior point method Solution, draws Optimizing result；
    Step 3：To the grid short circuit electric current and security and stability analysis after execution fault current limiter Optimizing；
    Step 4：The satisfaction of Judging fault demand limiter Optimizing number, if satisfied, export fault current limiter Optimizing result, otherwise increase fault current limiter cloth and count out limitation, and introduce and cut-off circuit reduction short circuit current and arrange Apply, continue Optimization Solution, the Optimizing result and cut-off circuit result that output increase fault current limiter number constrains.
  2. 2. according to a kind of computational methods of supergrid fault current limiter Optimizing described in claim 1, its It is characterised by, calculation of short-circuit current is carried out to target grid in the step 1, filters out the exceeded super-pressure node of short circuit current Set, calculation of short-circuit current is carried out by using the power system analysis software PSD-BPA of maturation, and filter out short circuit current and surpass Target super-pressure node set, super-pressure node refer generally to 500kV and above exchange node.
  3. 3. according to a kind of computational methods of supergrid fault current limiter Optimizing described in claim 1, its It is characterised by, the step 2 establishes the mathematical modeling of fault current limiter Optimizing, in the mathematical modeling use of foundation Point method solves, and draws Optimizing result, specific steps include：
    Step 2-1：The mathematical modeling of fault current limiter Optimizing is established, expression formula is as follows：
    <mrow> <mi>M</mi> <mi>I</mi> <mi>N</mi> <mi> </mi> <mi>F</mi> <mo>=</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>F</mi> </msub> </munderover> <msub> <mi>X</mi> <mrow> <mi>F</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>w</mi> <mrow> <mi>F</mi> <mi>C</mi> <mi>L</mi> </mrow> </msub> <mo>&amp;times;</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>F</mi> </msub> </munderover> <msub> <mi>X</mi> <mrow> <mi>F</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>/</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>X</mi> <mrow> <mi>F</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mi>S</mi> <mi>T</mi> <mo>:</mo> <mfrac> <mn>1</mn> <msubsup> <mi>z</mi> <mrow> <mi>f</mi> <mi>f</mi> </mrow> <mn>0</mn> </msubsup> </mfrac> <mo>+</mo> <msubsup> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>F</mi> </msub> </msubsup> <mrow> <mo>(</mo> <mfrac> <msub> <mi>d</mi> <mrow> <mn>3</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mrow> <msub> <mi>X</mi> <mrow> <mi>F</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>d</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> </mrow> </mfrac> <mo>+</mo> <msub> <mi>d</mi> <mrow> <mn>4</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>-</mo> <mfrac> <mn>1</mn> <msubsup> <mi>z</mi> <mrow> <mi>f</mi> <mi>f</mi> </mrow> <mn>0</mn> </msubsup> </mfrac> <mo>)</mo> </mrow> <mo>&amp;le;</mo> <msub> <mover> <mi>I</mi> <mo>&amp;OverBar;</mo> </mover> <mi>f</mi> </msub> <mo>,</mo> <mi>f</mi> <mo>&amp;Element;</mo> <msub> <mi>T</mi> <mi>F</mi> </msub> <mo>,</mo> <mi>k</mi> <mo>&amp;Element;</mo> <msub> <mi>S</mi> <mi>F</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
    (XF, k-XF, 1)(XF, k-XF, 2)...(XF, k-XF, i)=0 (3)
    Wherein variable is XF, k, represent the fault current limiter resistance that kth bar branch road is installed；
    Object function (1) is that the total cost of expression installation fault current limiter is minimum, wherein The total number of power network installation fault current limiter is expressed, adds 10 in denominator-6Be in order to impedance be 0 when the formula it is significant, and Impedance value is not counted to set for 0 number；wFCLFor the weight coefficient of current limiter total amount, new 1 fault current limit of installation is represented Device investment processed and the ratio of reactor specific investment cost；
    Constraints (2) is the breaker breaking current level that expression node short circuit current should be no more than corresponding transformer station, is represented The breaker breaking current of transformer station is horizontal, and f ∈ TF, TF represent the exceeded node set of short circuit current, and k ∈ SF, SF represent failure electricity Limiter installation set of fingers is flowed, NF is branch road total number in set SF；Zff0 represents f nodes before installation fault current limiter Self-impedance；D0, k, d3, k, d4, k are the constant parameter corresponding with kth bar branch road, <mrow> <msub> <mi>d</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>z</mi> <mrow> <mi>f</mi> <mi>f</mi> </mrow> <mn>0</mn> </msubsup> <msup> <mrow> <mo>(</mo> <msubsup> <mi>z</mi> <mrow> <mi>L</mi> <mo>,</mo> <mi>k</mi> </mrow> <mn>0</mn> </msubsup> <mo>)</mo> </mrow> <mi>z</mi> </msup> </mrow> <mrow> <msubsup> <mi>z</mi> <mrow> <mi>f</mi> <mi>f</mi> </mrow> <mn>0</mn> </msubsup> <mrow> <mo>(</mo> <mrow> <msub> <mi>D</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>-</mo> <msubsup> <mi>z</mi> <mrow> <mi>L</mi> <mo>,</mo> <mi>k</mi> </mrow> <mn>0</mn> </msubsup> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>D</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> </mrow> </mfrac> <mo>,</mo> <msub> <mi>d</mi> <mrow> <mn>3</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <msub> <mi>D</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <msubsup> <mi>z</mi> <mrow> <mi>L</mi> <mo>,</mo> <mi>k</mi> </mrow> <mn>0</mn> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> <msup> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>z</mi> <mrow> <mi>f</mi> <mi>f</mi> </mrow> <mn>0</mn> </msubsup> <mrow> <mo>(</mo> <mrow> <msub> <mi>D</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>-</mo> <msubsup> <mi>z</mi> <mrow> <mi>L</mi> <mo>,</mo> <mi>k</mi> </mrow> <mn>0</mn> </msubsup> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>D</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mfrac> <mo>,</mo> <msub> <mi>d</mi> <mrow> <mn>4</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>D</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>-</mo> <msubsup> <mi>z</mi> <mrow> <mi>L</mi> <mo>,</mo> <mi>k</mi> </mrow> <mn>0</mn> </msubsup> </mrow> <mrow> <msubsup> <mi>z</mi> <mrow> <mi>f</mi> <mi>f</mi> </mrow> <mn>0</mn> </msubsup> <mrow> <mo>(</mo> <mrow> <msub> <mi>D</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>-</mo> <msubsup> <mi>z</mi> <mrow> <mi>L</mi> <mo>,</mo> <mi>k</mi> </mrow> <mn>0</mn> </msubsup> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>D</mi> <mrow> <mi>z</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> </mrow> </mfrac> <mo>,</mo> </mrow> Fault current limiter front nodal point i and j system equivalent impedance are respectively installed additional, to install failure electricity additional The mutual impedance of system before stream limiter；
    Step 2-2：Using Sensitivity Method, candidate's set of fingers of installation fault current limiter is formed, it is specific as follows：
    For actual bulk power grid, if candidate branch road of all branch roads as installation fault current limiter, formula (2) is as constraint Equation, then the openness difference of coefficient matrix, optimization efficiency is low, therefore candidate's branch road can be screened according to sensitivity, reduces installation Candidate's set of fingers scope of fault current limiter, improve optimization efficiency.For short dot f, by the change pair of branch impedance Trouble point f three short circuit current influences descending sequence, the i.e. descending sequence of sensitivity factor, by preceding NSIndividual installation event Hinder candidate's branch road sequence number deposit set S of demand limiterf, NFFor each set SfNumber, NFTake node f corresponding voltages etc. Number is returned in the total outlet of level；
    For f points, to select and which branch road fault current limiter to be installed to I atfHave a great influence, then need more eachK=1 ..., NF, take the Δ I ' of negativefk, compare the preceding N of maximum absolute valueFIndividual (NF<), N by candidate's branch road Sequence number k be included in set SfIn, applied to constraints (2)；
    Step 2-3：Fault current limiter resistance sequence is set, it is specific as follows：
    Constraints (3) is the impedance value constraint of expression fault current limiter；The ohmic resistance phase of 500kV fault current limiters 1 When in 4 × 400mm that length is 3.4 kms2500kV circuits, line length corresponding to 6 ohm are 20.4km, 20 ohm of correspondences Line length be 68km, due to equipment manufacturing cost, it is apparatus insulated require, place limitation etc., fault current limiter resistance is unsuitable Too big, too small then current limitation effect unobvious, are not arbitrary values for the reactance value with engineering practicability, fault current limiter, It is more reasonable using the serializing value with Practical significance, such as use XF=[0,6,7,8,9,10,11,12,13,14,15,16, 17,18,19,20], Z is usedF, iRepresent i-th of impedance value to be selected of fault current limiter, i=1 ..., NFCL, NFCLFor impedance value Impedance value number to be selected, works as X in sequenceF, iFor 0 when, represent that the branch road does not install fault current limiter.Using Practical sequence After rowization resistance, fault current limiter resistance constraint expression is formula (3)；
    Step 2-4：The step 2-1 fault current limiter Optimizing mathematical modelings established are solved；Can be with by formula (3) Find out, fault current limiter reactance value is the multinomial with sequential value number identical exponent number, direct solution it is extremely complex and Difficulty, therefore pre-process very practical.It is currently the study hotspot of optimization problem using the Non-Linear Programming containing Constraints, Therefore the key that the Constraints condition of fault current limiter resistance discrete variable is to solve for need to be constructed；
    In order to seek two boundaries of discrete variable, Constraints condition is constructed, discrete variable can be worked as to continuous variable, serialization is carried out Precomputation；Mathematical modeling is as follows：
    <mrow> <mi>M</mi> <mi>I</mi> <mi>N</mi> <mi> </mi> <mi>F</mi> <mo>=</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>F</mi> </msub> </munderover> <msub> <mi>X</mi> <mrow> <mi>F</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>w</mi> <mrow> <mi>F</mi> <mi>C</mi> <mi>L</mi> </mrow> </msub> <mo>&amp;times;</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>F</mi> </msub> </munderover> <msub> <mi>X</mi> <mrow> <mi>F</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>/</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>X</mi> <mrow> <mi>F</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mrow>
    <mrow> <mi>S</mi> <mi>T</mi> <mo>:</mo> <mfrac> <mn>1</mn> <msubsup> <mi>z</mi> <mrow> <mi>f</mi> <mi>f</mi> </mrow> <mn>0</mn> </msubsup> </mfrac> <mo>+</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>F</mi> </msub> </munderover> <mrow> <mo>(</mo> <mfrac> <msub> <mi>d</mi> <mrow> <mn>3</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mrow> <msub> <mi>X</mi> <mrow> <mi>F</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>d</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> </mrow> </mfrac> <mo>+</mo> <msub> <mi>d</mi> <mrow> <mn>4</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>-</mo> <mfrac> <mn>1</mn> <msubsup> <mi>z</mi> <mrow> <mi>f</mi> <mi>f</mi> </mrow> <mn>0</mn> </msubsup> </mfrac> <mo>)</mo> </mrow> <mo>&amp;le;</mo> <msub> <mover> <mi>I</mi> <mo>&amp;OverBar;</mo> </mover> <mi>f</mi> </msub> <mo>,</mo> </mrow>
    <mrow> <msubsup> <mi>X</mi> <mi>F</mi> <mi>min</mi> </msubsup> <mo>&amp;le;</mo> <msub> <mi>X</mi> <mrow> <mi>F</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>&amp;le;</mo> <msubsup> <mi>X</mi> <mi>F</mi> <mi>max</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>
    Modern interior point method comparative maturity at present, its calculating speed is fast, convergence is good, strong robustness, initial value is chosen it is insensitive, The features such as inequality constraints is strong is handled, powerful vitality is shown in Optimization Problems In Power Systems；
    If optimal solution be present in problem, the optimal solution for the discrete magnitude serialization being calculated, it is however generally that, although the solution is can Row solution, but there is any discrepancy with engineered sequences value, and the value that simply rounds up is more coarse, therefore construct fault current limitation The Constraints condition of device resistance is as follows：
    (XF, k-XF, i)(XF, k-XF, i+1)=0 (14)
    Using the solution that precomputation is drawn as initial value, the Constraints condition of discrete variable is added, tectonic model is as follows：
    <mrow> <mi>M</mi> <mi>I</mi> <mi>N</mi> <mi> </mi> <mi>F</mi> <mo>=</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>F</mi> </msub> </munderover> <msub> <mi>X</mi> <mrow> <mi>F</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>w</mi> <mrow> <mi>F</mi> <mi>C</mi> <mi>L</mi> </mrow> </msub> <mo>&amp;times;</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>F</mi> </msub> </munderover> <msub> <mi>X</mi> <mrow> <mi>F</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>/</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>X</mi> <mrow> <mi>F</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mrow>
    <mrow> <mi>S</mi> <mi>T</mi> <mo>:</mo> <mfrac> <mn>1</mn> <msubsup> <mi>z</mi> <mrow> <mi>f</mi> <mi>f</mi> </mrow> <mn>0</mn> </msubsup> </mfrac> <mo>+</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>F</mi> </msub> </munderover> <mrow> <mo>(</mo> <mfrac> <msub> <mi>d</mi> <mrow> <mn>3</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mrow> <msub> <mi>X</mi> <mrow> <mi>F</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>d</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> </mrow> </mfrac> <mo>+</mo> <msub> <mi>d</mi> <mrow> <mn>4</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>-</mo> <mfrac> <mn>1</mn> <msubsup> <mi>z</mi> <mrow> <mi>f</mi> <mi>f</mi> </mrow> <mn>0</mn> </msubsup> </mfrac> <mo>)</mo> </mrow> <mo>&amp;le;</mo> <msub> <mover> <mi>I</mi> <mo>&amp;OverBar;</mo> </mover> <mi>f</mi> </msub> <mo>,</mo> </mrow>
    (XF, k-XF, i)(XF, k-XF, i+1)=0 (15)
    Using modern interior point method solving model (15), optimal solution is drawn；
    In order to ensure convergence, method of relaxation is selected, (15) can be converted into (16), as follows：
    <mrow> <mi>M</mi> <mi>I</mi> <mi>N</mi> <mi> </mi> <mi>F</mi> <mo>=</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>F</mi> </msub> </munderover> <msub> <mi>X</mi> <mrow> <mi>F</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>w</mi> <mrow> <mi>F</mi> <mi>C</mi> <mi>L</mi> </mrow> </msub> <mo>&amp;times;</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>F</mi> </msub> </munderover> <msub> <mi>X</mi> <mrow> <mi>F</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>/</mo> <mrow> <mo>(</mo> <mrow> <msub> <mi>X</mi> <mrow> <mi>F</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>+</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>6</mn> </mrow> </msup> </mrow> <mo>)</mo> </mrow> </mrow>
    <mrow> <mi>S</mi> <mi>T</mi> <mo>:</mo> <mfrac> <mn>1</mn> <msubsup> <mi>z</mi> <mrow> <mi>f</mi> <mi>f</mi> </mrow> <mn>0</mn> </msubsup> </mfrac> <mo>+</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>N</mi> <mi>F</mi> </msub> </munderover> <mrow> <mo>(</mo> <mfrac> <msub> <mi>d</mi> <mrow> <mn>3</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mrow> <msub> <mi>X</mi> <mrow> <mi>F</mi> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>d</mi> <mrow> <mn>0</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> </mrow> </mfrac> <mo>+</mo> <msub> <mi>d</mi> <mrow> <mn>4</mn> <mo>,</mo> <mi>k</mi> </mrow> </msub> <mo>-</mo> <mfrac> <mn>1</mn> <msubsup> <mi>z</mi> <mrow> <mi>f</mi> <mi>f</mi> </mrow> <mn>0</mn> </msubsup> </mfrac> <mo>)</mo> </mrow> <mo>&amp;le;</mo> <msub> <mover> <mi>I</mi> <mo>&amp;OverBar;</mo> </mover> <mi>f</mi> </msub> <mo>,</mo> </mrow>
    ε≤(XF, k-XF, i)(XF, k-XF, i+1)≤ε (16)
    Relaxation parameter ε is introduced, is updated after each iteration, with (XF, k-XF, i)(XF, k-XF, i+1) diminish and gradually tend to 0, ε renewals According to the deflation of variable bound bound, i.e., shaping variable serialization is pressed during calculating, is pressed when it is close to integer solution The bound of constraint is tightened centered on close integer solution according to given strategy, its acceleration is approached integer solution.
  4. 4. according to a kind of computational methods of supergrid fault current limiter Optimizing described in claim 1, its It is characterised by, to the grid short circuit electric current and safety and stability point after execution fault current limiter Optimizing in the step 3 Analysis, specific steps include：
    Step 3-1：Calculation of short-circuit current is carried out to the power network after performing fault current limiter Optimizing using PSD-BPA, Verify current limitation effect；
    Step 3-2：Security and stability analysis is carried out to the power network after performing fault current limiter Optimizing using PSD-BPA, Because fault current limiter does not influence normal condition trend, therefore Main Analysis influences on Power Network Transient Stability.
  5. 5. according to a kind of computational methods of supergrid fault current limiter Optimizing described in claim 1, its It is characterised by, the satisfaction of Judging fault demand limiter Optimizing number in the step 4, if satisfied, exports failure Demand limiter Optimizing result, otherwise increase fault current limiter cloth and count out limitation, and introduce and cut-off circuit and reduce Short circuit current measure, continue Optimization Solution, the Optimizing result and cut-off that output increase fault current limiter number constrains Circuit result.Specific steps include：
    Step 4-1：The satisfaction of Judging fault demand limiter Optimizing number, if satisfied, calculating terminates, and exports failure Demand limiter Optimizing result；Otherwise setting fault current limiter cloth, which counts out to limit, enters step 4-2；
    Step 4-2：Circuit is cut-off in introducing reduces short circuit current measure, corrects mathematical modeling, is superimposed and cut-offs in object function (1) The corresponding expense of circuit, it is superimposed in constraints (2) and cut-offs influence of the circuit to node short circuit current；
    Step 4-3：Step 4-2 mathematical modeling is solved using interior point method, method is the same as step 2；
    Step 4-4：To the grid short circuit electric current and safety and stability point after execution step 4-3 fault current limiter Optimizings Analysis, the Optimizing result and cut-off circuit result that output increase fault current limiter number constrains.
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CN109031041A (en) * 2018-07-06 2018-12-18 广州供电局有限公司 Distribution network voltage monitoring device points distributing method and system
CN109031041B (en) * 2018-07-06 2023-10-20 广东电网有限责任公司广州供电局 Distribution network voltage monitoring device point distribution method and system
CN109066623A (en) * 2018-07-27 2018-12-21 国电南瑞科技股份有限公司 Fault current limiter universal model construction method and system
CN109858662A (en) * 2018-10-12 2019-06-07 国网江西省电力有限公司电力科学研究院 A kind of differential evolution method of fault current limiter Optimizing in bulk power grid
CN109446608A (en) * 2018-10-16 2019-03-08 广东电网有限责任公司 A kind of Short-circuit Current of Power Network calculation method containing high tc superconducting fault current limiter
CN109446608B (en) * 2018-10-16 2023-04-28 广东电网有限责任公司 Power grid short-circuit current calculation method containing high-temperature superconducting current limiter
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CN109888755A (en) * 2019-03-22 2019-06-14 广东电网有限责任公司 A kind of power grid superconductive current limiter optimal configuration method, device and equipment
CN112260243A (en) * 2019-12-18 2021-01-22 国网宁夏电力有限公司经济技术研究院 Method for reducing short-circuit current of transformer substation by using fault current limiter
CN112260243B (en) * 2019-12-18 2023-04-18 国网宁夏电力有限公司经济技术研究院 Method for reducing short-circuit current of transformer substation by using fault current limiter
CN111209663A (en) * 2019-12-31 2020-05-29 华中科技大学 Modeling analysis method and system for equivalent ultra-long wave antenna array of high-voltage power grid

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