CN104899353B - A kind of power quality disturbance localization method based on evidence theory - Google Patents
A kind of power quality disturbance localization method based on evidence theory Download PDFInfo
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Abstract
A kind of power quality disturbance localization method theoretical based on evidence fusion, including:Determine system set covering theory AL×NAnd the direction determining matrix B realized according to two kinds of criterions of power of disturbance and disturbance energyv,N×1;Structure characterizes the reliability function of each influence factor of perturbation direction result of determination;Fusion treatment is carried out based on the uncertain disturbance direction determining information that D S evidence theories each obtain to two kinds of different criterions;Power quality disturbance locational decision is carried out based on the perturbation direction trip current after fusion and matrix algorithm;The reliability assessment of power quality disturbance positioning result is carried out based on the coincident indicator between more evidence sources.
Description
Technical field
The present invention relates to a kind of power quality disturbance localization method based on evidence theory and meter and monitoring availability, category
Electrical engineering and power quality field.
Background technology
In recent years, as sensitive equipment increases sharply in power network and electricity marketization process constantly promotes, electrical energy power quality disturbance is made
Into economic loss increase sharply, the demand that people determine to responsibility is increasingly strong.Power quality disturbance (Power
Quality Disturbance Source, PQDS) positioning, refer to work as generation electrical energy power quality disturbance event in target grid region
When, pass through the equipment for monitoring power quality (Power Quality Monitor, PQM) and electric energy quality monitoring arranged in system
Center is acquired to disturbing signal, calculates, analyzes and handled, and then realizes the definite circuits of PQDS or the intelligent diagnostics of position.
PQDS it is quick, be accurately positioned, be electric administrative department find out as early as possible disturbing cause, clearly defining responsibilities, exclude disturbing source, take conjunction
Improving Measurements are managed, so as to ensure that the quality of power supply meets premise and the basis of user's request, and network in following intelligent distribution network
Change the advanced work(of core of electric energy quality monitoring system (Network Power Quality Monitoring System, NPQMS)
One of can.
Currently, the related study hotspot of the quality of power supply is concentrated mainly on the identification processing of electric energy quality signal, the quality of power supply
The directions such as evaluation index, the structure of equipment for monitoring power quality and system, electric energy quality optimizing and control, on PQDS positioning sides
The achievement in research of method is less.The patent of invention of Application No. 2013104676593 and 2014101006927 proposes a kind of base respectively
In the voltage sag source localization method of limited electric energy quality monitoring point and by calculating faulty line both ends electric energy quality monitoring section
Point monitors the time difference of problem and localization method is carried out to the source of trouble, but its main thought is the side based on fault distance measure
Formula solves the determination of specific abort situation on a small amount of circuit;The patent of invention of Application No. 2008100612549 proposes a kind of base
In the power distribution network PQDS automatic positioning methods of matrix algorithm principle, but its positioning accuracy depends on each measuring point PQM disturbance unduly
The reliability of discriminating direction result and the completeness of information;The patent of invention of Application No. 2014105375263 proposes a kind of base
Innovatory algorithm is positioned in the meter of particle swarm optimization algorithm and the matrix of monitoring availability.Patent of the present invention is directed to various influence PQM
Factor, the influence degree of perturbation direction result of determination reliability characterize function, the PQDS intelligent locating methods based on more evidence sources
Studied, establish a variety of sign direction determining information credibility functions, based on two kinds of different disturbance sides of evidence theory fusion
The automatic and accurate positioning of PQDS to criterion information realization in the case of part monitoring information is wrong, and propose with evidence
Source uniformity structure evaluation function realizes the reliability evaluation of positioning result.
The content of the invention
The present invention will overcome each monitoring point PQM perturbation directions in existing PQDS location algorithms accuracy heavy dependence NPQMS
The problem of result of determination reliability and direction determining information completeness, consider disturbing signal power, current perturbation feature,
The factor such as distributed power source access and state estimation error judges perturbation direction the influence of reliability, there is provided one kind is based on card
According to the PQDS automatic positioning methods of blending theory, realize that part monitoring information missing, wrong or perturbation direction are sentenced in NPQMS
Determine result it is undesirable in the case of, can still realize being accurately positioned for PQDS, and the confidence level of its positioning result can be assessed.
The present invention is to achieve the above object, it is proposed that a kind of PQDS localization method theoretical based on evidence fusion, such as accompanying drawing 1
Shown, its process comprises the following steps:
1st, system set covering theory A is determinedL×NAnd direction determining matrix Bv,N×1.In the power distribution network containing L bars line segment, N number of PQM
In network, it can build to characterize the set covering theory A of all circuits and PQM position relationships respectivelyL×N, and in sign system
All monitoring point PQM foundation power of disturbance (Disturbance Power, DP) and disturbance energy during disturbance event occur for certain position
The direction matrix for the perturbation direction result of determination that (Disturbance Energy, DE) both different perturbation direction criterions are realized
Bv,N×1.Wherein, v=1 is represented according to power of disturbance criterion;V=2 is represented according to disturbance energy criterion.AL×NAnd Bv,N×1In each member
Plain ajiAnd bv,iAssignment principle such as formula (1), shown in (2).
2nd, structure characterizes the reliability function of each influence factor of perturbation direction result of determination.Define PQM direction determining information
" confidence level " concept, build characterize a variety of confidence levels subitem function indexs respectively, to describe disturbing signal power, current perturbation
The various factors such as feature, distributed power source access and virtual PQM state estimation errors are sentenced under different scenes to perturbation direction
The influence degree of credible result degree is determined, so as to realize the fuzzy quantization of each monitoring point direction determining process and result.
Step 201, structure characterizes the strong and weak direction determining reliability function of disturbing signal.The power of disturbing signal characteristic quantity
Degree, it can be embodied by the relative ratio of the disturbing signal characteristic quantity measured by monitoring point and system signal characteristic quantity when stable.
Accordingly, structure characterizes the strong and weak direction determining confidence level γ of disturbancei:
In formula, Ev(i) signal characteristic quantity of i-th of monitoring point when system is stable is represented;Δev(i) PQM is representediDisturbance letter
Number characteristic quantity;V=1 represents that it is power of disturbance DP to take characteristic quantity;V=2 represents that it is disturbance energy DE to take characteristic quantity.
Step 202, structure characterizes the direction determining reliability function of current perturbation feature.Disturbed caused by uneven disturbing source
Move while influenceing system three-phase equilibrium and spending, can also there is certain zero-sequence current, its amplitude size and the PQM are relative to disturbing
The position of dynamic point is closely related:If disturbance point is located at PQM backward region, the zero-sequence current amplitude detected is larger;If disturb
Dynamic point is located at PQM forward region, then zero-sequence current is smaller.Accordingly, current perturbation feature when structure characterizes uneven disturbance
Direction determining confidence level Si:
Wherein,
In formula, I0(i) the zero-sequence current root-mean-square value for being monitoring point i;biRepresent PQMiThe perturbation direction result of determination at place;
βiFor I0(i) with system in all monitoring point I0(i) ratio of average value;A is constant, to cause SiIn [1~0.9] section
Typically take 2.2~2.5.
Step 203, structure characterizes the direction determining reliability function of disturbance energy fluctuation characteristic.During disturbance source locating, DE
Fluctuation characteristic reflects the possibility of perturbation direction erroneous judgement indirectly to a certain extent.Draft following perturbation direction and judge original
Then:If DE waveforms initial spike is different from end value symbol or the DE symbol moment changes, the monitoring point perturbation direction judges
Credible result degree reduces.Accordingly, structure characterizes the direction determining credible result degree θ of disturbance energy fluctuation characteristici:
In formula, σ is confidence value, and span is 0.5~0.75;DE0(i) it is theiIndividual monitoring point DE waveform initial peaks
Value;DER(i) it is i-th of monitoring point DE final value;Sgn is sign function.
Step 204, structure characterizes the direction determining reliability function of virtual PQM dotted states evaluated error.Because state is estimated
Count error to introduce, the perturbation direction of virtual PQM points judges that confidence level may reduce.Accordingly, structure characterizes the direction of virtual PQM points
Result of determination confidence level ξi:
Wherein,
In formula, UiFor uncertainty corresponding to confidence level u;x1、x2It is virtual PQM measuring points i foundation measuring points z1、z2State estimate
Count result;Function is measured corresponding to it;diFor its relative displacement;f(di) construction letter corresponding to it
Number.
3rd, it is automatically positioned based on the theoretical PQDS of evidence fusion.D-S evidence theory has the ability of processing uncertain information,
PQDS positioning based on D-S evidence theory, combination each obtain according to power of disturbance and disturbance energy both different criterions
Uncertain disturbance direction determining information so that disturbance source locating is more accurate, credible.
Step 301, target identification framework is built.If target power distribution network has N number of PQM, a numbering shape is configured to each PQM
Into by array giThe identification framework Θ of composition:
Θ={ gi| i=1,2,3 ..., N } (7)
Step 302, basic brief inference function is built.From γi、Si、θiAnd ξiMultiple angles consider, structure synthesis
Reliability function.Consider at 2 points:S when being disturbed caused by positioning by uneven disturbing sourceiReliability configuration could be participated in,
Now Si、θiThe probability for causing to repeat that occurs simultaneously is likely to occur to decline, therefore to Si、θiAverage probability processing is carried out, to avoid reliability
Rapidly reduce;To avoid the occurrence of γiSituation more than 1, using minimum value function processing mode.Accordingly, synthetic reliability is built
Function W (i):
In formula, min is minimum value function;μ is voltage unbalance factor coefficient, because system normal voltage degree of unbalancedness scope is
2%~4%, it is boundary's point to take μ=0.04.
Defined according to basic brief inference function, new reliability function w (i) is obtained after W (i) is normalized.It is then basic
Brief inference function m (gi):
Step 303, perturbation direction judges confidence level combination.Using two kinds of direction criterions of power of disturbance and disturbance energy, one
The basic belief function distribution of corresponding one of kind direction determining criterion, can define the basic brief inference function under two kinds of scenes respectively
mv, and two prescriptions are corresponded to matrix Bv,N×1.So, two groups of basic brief inferences of perturbation direction with symbol characteristic be can obtain
Value m1(O)、m2(Γ):
m1(O):m1(g1)b1,1,m1(g2)b1,2,...,m1(gN)b1,N (10)
m2(Γ):m2(g1)b2,1,m2(g2)b2,2,...,m2(gN)b2,N
In formula, burnt first O, Γ ∈ Θ;bv,iIt is two prescriptions to matrix Bv,N×1Component;mv(gi) represent two kinds of scenes
Lower PQMiDirection determining confidence level.
Because fused data carries symbol characteristic, traditional D-S evidences failure.According to classical combinatorial formula, change
Rule of combination after entering follows following relation:
Wherein,
In formula, m (P) is the basic brief inference function after fusion, its burnt first P ∈ Θ;KτFor the factor that conflicts.
4th, disturbance source locating decision-making.Perturbation direction trip current after definition fusion is MN×1, its component is m (P),
The disturbance positional matrix C ' based on evidence fusion is obtained by matrix multiplication operationL×1:
C’L×1=AL×N*MN×1 (12)
Matrix C 'L×1In each element value c 'jContain system PQDS positional informations, its unique maximum element c 'Jm=max
{c’j, j=1,2 ..., L corresponding to circuit L where PQMjmLine segment where PQDS as in target power distribution network.
5th, the reliability assessment of disturbance source locating result.To assess the credibility of disturbance source locating result, propose to be based on
Coincident indicator between more evidence sources carries out the reliability evaluation of certain positioning result.If { y1,y2,...,yNIt is that O, Γ are identical
The set of burnt member composition, O (yk)、Γ(yk) for basic certainty value corresponding to it, then evaluation function Hi,j:
According to evaluation function Hi,j, can be according to the reliability assessment of following rule progress disturbance source locating result:Hi,jIt is bigger,
Then represent that this disturbance source locating credible result degree is high;On the contrary, Hi,jSmaller, then positioning result confidence level is lower, and works as Hi,j≤
When 0.7, then it is assumed that positioning result confidence level is not high.
Beneficial effects of the present invention are mainly manifested in:1st, construct characterize influence perturbation direction differentiate reliability it is a variety of because
The reliability function of element;2nd, the perturbation direction that different evidence sources acquisitions are merged using D-S rules of combination differentiates reliability matrix, most
Comprehensive perturbation direction is obtained afterwards differentiates result;3rd, commenting for disturbance source locating result accuracy is realized based on evidence conformance criteria
Estimate.4th, to realize that disturbing source in the case of part monitoring information is wrong is accurately positioned, it is proposed that a kind of based on evidence theory
Power quality disturbance localization method.
Brief description of the drawings
Fig. 1 is the specific implementation flow chart of the inventive method.
Fig. 2 is the topology diagram of a 9 node radiation type distribution networks.
Fig. 3 is PQM forward regions and backward zoning plan.
Embodiment
With reference to embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention are unlimited
In this.The general frame based on the theoretical PQDS targeting schemes of evidence fusion in embodiment as shown in Figure 1, including following step
Suddenly:
1st, system set covering theory A is determinedL×NAnd direction determining matrix Bv,N×1.In the power distribution network containing L bars line segment, N number of PQM
In network, it can build to characterize the set covering theory A of all circuits and PQM position relationships respectivelyL×N, and in sign system
All monitoring point PQM occur during disturbance event for certain position according to power of disturbance and disturbance energy both different perturbation direction criterions
The direction matrix B of the perturbation direction result of determination of realizationv,N×1。AL×NAnd Bv,N×1Middle each element ajiAnd bv,iAssignment principle such as formula
(1), shown in (2).
2nd, structure characterizes the reliability function of each influence factor of perturbation direction result of determination.Define PQM direction determining information
" confidence level " concept, build characterize a variety of confidence levels subitem function indexs respectively, to describe disturbing signal power, current perturbation
The various factors such as feature, distributed power source access and virtual PQM state estimation errors are sentenced under different scenes to perturbation direction
The influence degree of credible result degree is determined, so as to realize the fuzzy quantization of each monitoring point direction determining process and result.
Step 201, structure characterizes the strong and weak direction determining reliability function of disturbing signal.The power of disturbing signal characteristic quantity
Degree, it can be embodied by the relative ratio of the disturbing signal characteristic quantity measured by monitoring point and system signal characteristic quantity when stable.
Accordingly, the structure as shown in formula (3) characterizes the strong and weak direction determining confidence level γ of disturbancei。
Step 202, structure characterizes the direction determining reliability function of current perturbation feature.Disturbed caused by uneven disturbing source
Move while influenceing system three-phase equilibrium and spending, can also there is certain zero-sequence current, its amplitude size and the PQM are relative to disturbing
The position of dynamic point is closely related:If disturbance point is located at PQM backward region, the zero-sequence current amplitude detected is larger;If disturb
Dynamic point is located at PQM forward region, then zero-sequence current is smaller.Accordingly, disturbed when structure characterizes uneven disturbance as shown in formula (4)
The direction determining confidence level S of current characteristici。
Step 203, structure characterizes the direction determining reliability function of disturbance energy fluctuation characteristic.During disturbance source locating, DE
Fluctuation characteristic reflects the possibility of perturbation direction erroneous judgement indirectly to a certain extent.Draft following perturbation direction and judge original
Then:If DE waveforms initial spike is different from end value symbol or the DE symbol moment changes, the monitoring point perturbation direction judges
Credible result degree reduces.Accordingly, structure characterizes the direction determining credible result degree of disturbance energy fluctuation characteristic as shown in formula (5)
θi。
Step 204, structure characterizes the direction determining reliability function of virtual PQM dotted states evaluated error.Because state is estimated
Count error to introduce, the perturbation direction of virtual PQM points judges that confidence level may reduce.Accordingly, the structure as shown in formula (6) characterizes virtual
The direction determining credible result degree ξ of PQM pointsi。
3rd, it is automatically positioned based on the theoretical PQDS of evidence fusion.D-S evidence theory has the ability of processing uncertain information,
PQDS positioning based on D-S evidence theory, combination each obtain according to power of disturbance and disturbance energy both different criterions
Uncertain disturbance direction determining information so that disturbance source locating is more accurate, credible.
Step 301, target identification framework is built.If target power distribution network has N number of PQM, a numbering shape is configured to each PQM
Into by array giThe identification framework Θ of composition, as shown in formula (7).
Step 302, basic brief inference function is built.From γi、Si、θiAnd ξiMultiple angles consider, structure synthesis
Reliability function.Consider at 2 points:S when being disturbed caused by positioning by uneven disturbing sourceiReliability configuration could be participated in,
Now Si、θiThe probability for causing to repeat that occurs simultaneously is likely to occur to decline, therefore to Si、θiAverage probability processing is carried out, to avoid reliability
Rapidly reduce;To avoid the occurrence of γiSituation more than 1, using minimum value function processing mode.Accordingly, the structure as shown in formula (8)
Synthetic reliability function W (i).
Defined according to basic brief inference function, obtain new reliability function w (i) after W (i) is normalized, then such as formula
(9) basic brief inference function m (g can be obtained shown ini)。
Step 303, perturbation direction judges confidence level combination.Using two kinds of direction criterions of power of disturbance and disturbance energy, one
The basic belief function distribution of corresponding one of kind direction determining criterion, can define the basic brief inference function under two kinds of scenes respectively
mv, and two prescriptions are corresponded to matrix Bv,N×1.So, two groups of perturbation directions with symbol characteristic are can obtain as shown in formula (10)
Basic brief inference value m1(O)、m2(Γ)。
Because fused data carries symbol characteristic, traditional D-S evidences failure.According to classical combinatorial formula, change
Shown in rule of combination such as formula (11) after entering.
4th, disturbance source locating decision-making.Perturbation direction trip current after definition fusion is MN×1, its component is m (P),
The disturbance positional matrix C ' based on evidence fusion is obtained by the matrix multiplication operation as shown in formula (12)L×1。C’L×1In each member
Plain value c 'jContain system PQDS positional informations, its unique maximum element c 'Jm=max{c’j, j=1,2 ..., L } corresponding to
Circuit L where PQMjmLine segment where PQDS as in target power distribution network.
5th, the reliability assessment of disturbance source locating result.To assess the credibility of disturbance source locating result, propose to be based on
Coincident indicator between more evidence sources carries out the reliability evaluation of certain positioning result.If { y1,y2,...,yNIt is that O, Γ are identical
The set of burnt member composition, O (yk)、Γ(yk) basic certainty value corresponding to it, then it can build the evaluation function as shown in formula (13)
Hi,j。
Accordingly, the reliability assessment of PQDS positioning results can be carried out according to following rule:Hi,jIt is bigger, then it represents that this time is disturbed
Dynamic source positioning result is with a high credibility;On the contrary, Hi,jSmaller, then positioning result confidence level is lower, and works as Hi,jWhen≤0.7, then it is assumed that
Positioning result confidence level is not high.
Emulated by taking topological structure 9 node 10.5KV distribution network systems as shown in Figure 2 as an example, further illustrate this hair
Bright implementation process.Match somebody with somebody 7 PQM, 2 virtual PQM in system in fact, and access a distributed power source DG.Pass through MATLAB/
Simulink simulation softwares power system blockset, builds system simulation model.Circuit L is set7For disturbance point, simulate respectively single-phase
Ground short circuit, induction machine starts and three kinds of typical voltage Sag Disturbances of capacitor switching.
By step 2, single-phase earthing, capacitor switching, the γ of the different disturbances of three kinds of induction machine are calculated respectivelyi、Si、θi、ξi
And reliability m (P) value after fusion, as shown in table 1.
1 all kinds of confidence values of table
It is balance disturbing source because capacitor switching and induction machine start, therefore, is opened by capacitor switching and induction machine
Disturbed caused by dynamic, without calculating SiNumerical value.
The structural information of power distribution network and PQM placement informations as shown in accompanying drawing 2, system set covering theory can be obtained such as according to step 1
Under:
In formula, numerical value ± 1 corresponds to each PQM backward region and forward region respectively.With PQM3Exemplified by, displaying basis is matched somebody with somebody
Electric network swim direction is by the method that whole network region division is forward region and backward region, as shown in Figure 3.
Disturbance source locating decision-making is carried out according to step 4,5 and assesses the degree of reliability of positioning result, what reliability m (P) was formed
Direction determining matrix MN×1With set covering theory AL×NIt is multiplied, and Calculation Estimation function Hi,jObtain the PQDS positioning based on evidence fusion
The positioning result of method is as shown in table 2.
The positioning result of PQDS localization method of the table 2 based on evidence fusion
Take evaluation function Hi,j=0.7 is separation, if Hi,j< 0.7 then thinks that positioning result confidence level is not high.Table 2 emulates
As a result show, in the case where many places erroneous judgement be present, institute's extracting method of the present invention remains to make accurately different type PQDS positions
Judgement, and the credibility of positioning result is very high.In some cases, though erroneous judgement number is more, uniformity between evidence compared with
It is high so that Hi,jNumerical value is higher.
As described above, the present invention can be better realized, above-described embodiment is only the exemplary embodiments of the present invention, is not used
To limit the practical range of the present invention, i.e., all equivalent changes and modifications made according to present invention all will for right of the present invention
Scope claimed is asked to be covered.
Claims (1)
1. a kind of power quality disturbance localization method theoretical based on evidence fusion, power quality disturbance abbreviation PQDS, bag
Include following steps:
Step 1, determine system set covering theory AL×NAnd direction determining matrix Bv,N×1;Containing L bars line segment, N number of quality of power supply prison
Survey in the distribution network of device, equipment for monitoring power quality abbreviation PQM, build to characterize all circuits and PQM positions respectively
The set covering theory A of relationL×N, and to all monitoring point PQM foundations disturbances during certain position generation disturbance event in sign system
The direction matrix B of the perturbation direction result of determination of both different perturbation direction criterions realizations of power and disturbance energyv,N×1, disturb
Dynamic power abbreviation DP, disturbance energy vehicle economy;Wherein, v=1 is represented according to power of disturbance criterion;V=2 is represented according to disturbance energy
Measure criterion;AL×NAnd Bv,N×1Middle each element ajiAnd bv,iAssignment principle such as formula (1), shown in (2);
Step 2, structure characterize the reliability function of each influence factor of perturbation direction result of determination;Define PQM direction determining information
" confidence level " concept, build characterize a variety of confidence levels subitem function indexs respectively, to describe disturbing signal power, current perturbation
Feature, distributed power source access and virtual PQM state estimation error various factors are judged perturbation direction under different scenes
The influence degree of credible result degree, so as to realize the fuzzy quantization of each monitoring point direction determining process and result;
Step 201, structure characterizes the strong and weak direction determining reliability function of disturbing signal;The strong and weak journey of disturbing signal characteristic quantity
Degree, can by the disturbing signal characteristic quantity measured by monitoring point and system stably when signal characteristic quantity relative ratio embody;According to
This, structure characterizes the strong and weak direction determining confidence level γ of disturbancei:
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In formula, Ev(i) signal characteristic quantity of i-th of monitoring point when system is stable is represented;Δev(i) PQM is representediDisturbing signal is special
Sign amount;V=1 represents that it is power of disturbance DP to take characteristic quantity;V=2 represents that it is disturbance energy DE to take characteristic quantity;
Step 202, structure characterizes the direction determining reliability function of current perturbation feature;Disturbance exists caused by uneven disturbing source
While influence system three-phase equilibrium is spent, can also there is certain zero-sequence current, its amplitude size is with the PQM relative to disturbance point
Position it is closely related:If disturbance point is located at PQM backward region, the zero-sequence current amplitude detected is larger;If disturbance point
Positioned at PQM forward region, then zero-sequence current is smaller;Accordingly, the direction of current perturbation feature when structure characterizes uneven disturbance
Judge confidence level Si:
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<mn>2</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>b</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mo>-</mo>
<mn>1</mn>
<mo>,</mo>
<msub>
<mi>&beta;</mi>
<mi>i</mi>
</msub>
<mo>></mo>
<mn>0.01</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>1</mn>
<mo>~</mo>
<mn>0.9</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>b</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mo>-</mo>
<mn>1</mn>
<mo>,</mo>
<mn>0</mn>
<mo><</mo>
<msub>
<mi>&beta;</mi>
<mi>i</mi>
</msub>
<mo>&le;</mo>
<mn>0.01</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein,
In formula, I0(i) the zero-sequence current root-mean-square value for being monitoring point i;biRepresent PQMiThe perturbation direction result of determination at place;βiFor I0
(i) with system in all monitoring point I0(i) ratio of average value;A is constant, to cause SiTake 2.2 in [1~0.9] section~
2.5;
Step 203, structure characterizes the direction determining reliability function of disturbance energy fluctuation characteristic;During disturbance source locating, DE fluctuations
Feature reflects the possibility of perturbation direction erroneous judgement indirectly to a certain extent;Draft following perturbation direction decision principle:
If DE waveforms initial spike is different from end value symbol or the DE symbol moment changes, the monitoring point perturbation direction result of determination
Confidence level reduces;Accordingly, structure characterizes the direction determining credible result degree θ of disturbance energy fluctuation characteristici:
<mrow>
<msub>
<mi>&theta;</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mn>1</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>sgn</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>DE</mi>
<mn>0</mn>
</msub>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mi>sgn</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>DE</mi>
<mi>R</mi>
</msub>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mi>&sigma;</mi>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>sgn</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>DE</mi>
<mn>0</mn>
</msub>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mi>sgn</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>DE</mi>
<mi>R</mi>
</msub>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>-</mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, σ is confidence value, and span is 0.5~0.75;DE0(i) it is i-th of monitoring point DE waveform initial spike;DER
(i) it is i-th of monitoring point DE final value;Sgn is sign function;
Step 204, structure characterizes the direction determining reliability function of virtual PQM dotted states evaluated error;Because state estimation is missed
Difference introduces, and the perturbation direction of virtual PQM points judges that confidence level may reduce;Accordingly, structure characterizes the direction determining of virtual PQM points
Credible result degree ξi:
<mrow>
<msub>
<mi>&xi;</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mn>1</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mn>0</mn>
<mo><</mo>
<msub>
<mi>d</mi>
<mi>i</mi>
</msub>
<mo>&le;</mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>1</mn>
<mo>-</mo>
<mo>&lsqb;</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>d</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>+</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mo>-</mo>
<msub>
<mi>d</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>d</mi>
<mi>i</mi>
</msub>
<mo>></mo>
<mn>1</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein,
In formula, UiFor uncertainty corresponding to confidence level u;x1、x2It is virtual PQM measuring points i foundation measuring points z1、z2State estimation knot
Fruit;Function is measured corresponding to it;diFor its relative displacement;f(di) it is its corresponding constructed fuction;
Step 3, the PQDS based on evidence fusion theory are automatically positioned;D-S evidence theory has the ability of processing uncertain information,
PQDS positioning based on D-S evidence theory, combination each obtain according to power of disturbance and disturbance energy both different criterions
Uncertain disturbance direction determining information so that disturbance source locating is more accurate, credible;
Step 301, target identification framework is built;If target power distribution network has N number of PQM, to each PQM configure one numbering formed by
Array giThe identification framework Θ of composition:
Θ={ gi| i=1,2,3 ..., N } (7)
Step 302, basic brief inference function is built;From γi、Si、θiAnd ξiMultiple angles consider, and build comprehensive credible
Spend function;Consider at 2 points:S when being disturbed caused by positioning by uneven disturbing sourceiReliability configuration could be participated in, now Si、
θiThe probability for causing to repeat that occurs simultaneously is likely to occur to decline, therefore to Si、θiAverage probability processing is carried out, to avoid reliability from rapidly subtracting
It is small;To avoid the occurrence of γiSituation more than 1, using minimum value function processing mode;Accordingly, synthetic reliability function W is built
(i):
<mrow>
<mi>W</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mfrac>
<mrow>
<msub>
<mi>S</mi>
<mi>i</mi>
</msub>
<mo>+</mo>
<msub>
<mi>&theta;</mi>
<mi>i</mi>
</msub>
</mrow>
<mn>2</mn>
</mfrac>
<msub>
<mi>&xi;</mi>
<mi>i</mi>
</msub>
<mo>*</mo>
<mi>min</mi>
<mo>{</mo>
<msub>
<mi>&gamma;</mi>
<mi>i</mi>
</msub>
<mo>,</mo>
<mn>1</mn>
<mo>}</mo>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>&mu;</mi>
<mo>&GreaterEqual;</mo>
<mn>0.04</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&theta;</mi>
<mi>i</mi>
</msub>
<msub>
<mi>&xi;</mi>
<mi>i</mi>
</msub>
<mo>*</mo>
<mi>min</mi>
<mo>{</mo>
<msub>
<mi>&gamma;</mi>
<mi>i</mi>
</msub>
<mo>,</mo>
<mn>1</mn>
<mo>}</mo>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>&mu;</mi>
<mo><</mo>
<mn>0.04</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, min is minimum value function;μ is voltage unbalance factor coefficient, because system normal voltage degree of unbalancedness scope is 2%
~4%, it is boundary's point to take μ=0.04;
Defined according to basic brief inference function, new reliability function w (i) is obtained after W (i) is normalized;Then basic reliability
Partition function m (gi):
Step 303, perturbation direction judges confidence level combination;Using two kinds of direction criterions of power of disturbance and disturbance energy, Yi Zhongfang
To the basic belief function distribution of corresponding one of criterion is judged, the basic brief inference function m under two kinds of scenes is defined respectivelyv, with
And two prescriptions are corresponded to matrix Bv,N×1;So, two groups of basic brief inference value m of perturbation direction with symbol characteristic are obtained1
(O)、m2(Γ):
<mrow>
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>m</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>O</mi>
<mo>)</mo>
</mrow>
<mo>:</mo>
<msub>
<mi>m</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>g</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>b</mi>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>m</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>g</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>b</mi>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
</mrow>
</msub>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msub>
<mi>m</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>g</mi>
<mi>N</mi>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>b</mi>
<mrow>
<mn>1</mn>
<mo>,</mo>
<mi>N</mi>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>m</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>&Gamma;</mi>
<mo>)</mo>
</mrow>
<mo>:</mo>
<msub>
<mi>m</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>g</mi>
<mn>1</mn>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>b</mi>
<mrow>
<mn>2</mn>
<mo>,</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>,</mo>
<msub>
<mi>m</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>g</mi>
<mn>2</mn>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>b</mi>
<mrow>
<mn>2</mn>
<mo>,</mo>
<mn>2</mn>
</mrow>
</msub>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msub>
<mi>m</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>g</mi>
<mi>N</mi>
</msub>
<mo>)</mo>
</mrow>
<msub>
<mi>b</mi>
<mrow>
<mn>2</mn>
<mo>,</mo>
<mi>N</mi>
</mrow>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, burnt first O, Γ ∈ Θ;bv,iIt is two prescriptions to matrix Bv,N×1Component;mv(gi) represent PQM under two kinds of scenesi
Direction determining confidence level;
Because fused data carries symbol characteristic, traditional D-S evidences failure;According to classical combinatorial formula, after improvement
Rule of combination follow following relation:
Wherein,
In formula, m (P) is the basic brief inference function after fusion, its burnt first P ∈ Θ;KτFor the factor that conflicts;
Step 4, disturbance source locating decision-making;Perturbation direction trip current after definition fusion is MN×1, its component is m (P),
The disturbance positional matrix C ' based on evidence fusion is obtained by matrix multiplication operationL×1:
C’L×1=AL×N*MN×1 (12)
Matrix C 'L×1In each element value c 'jContain system PQDS positional informations, its unique maximum element c 'jm=max
{c’j, j=1,2 ..., L corresponding to circuit L where PQMjmLine segment where PQDS as in target power distribution network;
The reliability assessment of step 5, disturbance source locating result;To assess the credibility of disturbance source locating result, propose to be based on
Coincident indicator between more evidence sources carries out the reliability evaluation of certain positioning result;If { y1,y2,...,yNIt is that O, Γ are identical
The set of burnt member composition, O (yk)、Γ(yk) for basic certainty value corresponding to it, then evaluation function Hi,j:
<mrow>
<msub>
<mi>H</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>j</mi>
</mrow>
</msub>
<mo>=</mo>
<mi>exp</mi>
<mo>{</mo>
<mrow>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>k</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<mo>&lsqb;</mo>
<mo>-</mo>
<msup>
<mrow>
<mo>(</mo>
<mi>O</mi>
<mo>(</mo>
<msub>
<mi>y</mi>
<mi>k</mi>
</msub>
<mo>)</mo>
<mo>-</mo>
<mi>&Gamma;</mi>
<mo>(</mo>
<msub>
<mi>y</mi>
<mi>k</mi>
</msub>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
<mo>&rsqb;</mo>
</mrow>
<mo>}</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>13</mn>
<mo>)</mo>
</mrow>
</mrow>
According to evaluation function Hi,j, can be according to the reliability assessment of following rule progress disturbance source locating result:Hi,jIt is bigger, then table
Show that this disturbance source locating credible result degree is high;On the contrary, Hi,jSmaller, then positioning result confidence level is lower, and works as Hi,j≤0.7
When, then it is assumed that positioning result confidence level is not high.
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