CN105514997B - The electric energy quality monitoring point collocation method of meter and distributed power source - Google Patents
The electric energy quality monitoring point collocation method of meter and distributed power source Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/08—Locating faults in cables, transmission lines, or networks
- G01R31/081—Locating faults in cables, transmission lines, or networks according to type of conductors
- G01R31/086—Locating faults in cables, transmission lines, or networks according to type of conductors in power transmission or distribution networks, i.e. with interconnected conductors
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
- H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
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Abstract
The electric energy quality monitoring point collocation method of meter and distributed power source, comprises the following steps：Related notion in being distributed rationally to meter and the grid-connected electric energy quality monitoring point of distributed power source is defined；It is defined as meeting the minimum number N of Kirchhoff's current law (KCL) (KCL)KCL；Define voltage Observable region；Binary system particle group optimizing (BPSO) model is improved；Build new evaluation function；Population position and speed are initialized, population is substituted into evaluation function formula calculates adaptive value, and carries out assignment to initial extreme value；According to particle position and iterative, all particles of renewal of speed；All populations are substituted into evaluation function formula again and calculate adaptive value；When reaching maximum iteration, then circulation is jumped out, and export current global extremum as optimum results；Otherwise return to step 7 continues iteration.
Description
Technical field
The present invention relates to it is a kind of it is based on Modified particle swarm optimization, for realize meter and the grid-connected intelligent power distribution of distributed power source
The quality of power supply comprehensive monitoring and disturbance event intelligent diagnostics of net and to electric energy quality monitoring point carry out intelligent optimization configuration side
Method, category electrical engineering and power quality field.
Background technology
With electricity marketization and socio-economic development, power failure and the quality of power supply (Power Quality, PQ) problem
The economic loss caused is continuously increased.Meanwhile, current energy crisis and ecological environment problem so that based on new energy
Distributed power source (Distributed Generator, DG) is more and more paid attention to.However, the grid-connected meeting of distributed power source
Certain influence is produced on the node voltage, power flow and the quality of power supply of power network.Carrying out comprehensive monitoring to power distribution network contributes to soon
Speed excludes power failure and solves the problems, such as PQ, reduction economic loss and clear and definite event responsibility.In view of electric energy quality monitor
The Cost Problems of (Power Quality Monitor, PQM), it is necessary to which installation number and position to PQM are optimized, full
Distributing rationally for financial cost, i.e. electric energy quality monitoring point is reduced under conditions of sufficient global viewable, it has to power supply reliability
Significance.
Existing PQM monitoring points collocation method still suffers from obvious defect and larger limitation, and does not consider that DG is grid-connected
Influence.Some of monitoring point collocation methods only consider kirchhoff electric current criterion KCL, and the overall situation that can only meet electric current can
See, and be unsatisfactory for the global monitoring of voltage；Other monitoring point collocation method only considers voltage sag domain problem, although meet
The global viewable of voltage, can not but meet the completeness of current information.Therefore, existing collocation method can not be met disturbs to PQ
The intelligent diagnostics of event and it is accurately positioned demand.At present, existing related ends are concentrated mainly on the disturbed depth of the quality of power supply, disturbed
In terms of several researchs such as dynamic positioning and on-line monitoring, comprehensive assessment：Application No. CN201510113962.2 proposes a kind of base
In the power disturbance identification and localization method of incomplete S-transformation, CN201510223195.0 proposes a kind of based on evidence theory
Power quality disturbance localization method, CN201510308581.X propose a kind of monitoring of digitalized electric energy quality monitoring terminal
Device and its data transfer device, CN201510313399.3 propose a kind of according to fault resstance matrix elimination voltage dip prison
Survey the monitoring node allocation plan of blind area.These correlative studys fail to take into full account the grid-connected factors of DG and Current Voltage simultaneously
The optimisation strategy of global viewable, and be not directed in these cases with improved Binary Particle Swarm Optimization (Binary
Particle Swarm Optimization, BPSO) realize distributing rationally for electric energy quality monitoring point.
The content of the invention
The present invention will overcome existing Optimal Configuration Method can not be while meeting the shortcoming of the global viewable of voltage x current, simultaneously
The quality of power supply comprehensive monitoring of intelligent distribution network containing distributed power source is realized with relatively low cost and disturbance event intelligence is met
Diagnostic requirements are there is provided a kind of based on Modified particle swarm optimization, meter and distributed power source and meet voltage x current while the overall situation can
The method that the electric energy quality monitoring point of sight is distributed rationally, and with preferable economy and system optimization effect.
The technical solution adopted for the present invention to solve the technical problems is：
It is a kind of based on improve binary system particle group optimizing, meter and distributed power source and meet voltage x current simultaneously the overall situation can
The method that the electric energy quality monitoring point of sight is distributed rationally, the distributed power source is grid-connected to refer to that new energy development is utilized and distributed
Distributed power source access intelligent distribution network under generation technology background, the electric energy quality monitoring point refers to electric energy quality monitor
Potential installation site in power distribution network, the Optimal Configuration Method refers to meet the electricity under the conditions of comprehensive monitoring and intelligent diagnostics
Optimal number and particular location that energy quality monitor PQM is installed.
The electric energy quality monitoring point collocation method of meter and distributed power source of the present invention, comprises the following steps：
1) related notion in being distributed rationally to meter and the grid-connected electric energy quality monitoring point of distributed power source is defined；It is fixed
" comprehensive monitoring of power distribution network " in the case of adopted meter and distributed power source DG, refers to that the intelligence of electrical energy power quality disturbance event can be met
Diagnosis requires and needed the voltage and current information monitoring degree obtained；Define " global viewable of voltage and current ", refer to base
The PQM installed in configuration obtains information, then further obtains other information for not installing circuit and node by state estimation, makes
Obtain the voltage and current information Observable of all circuits of power distribution network the whole network and node." the distribution weight coefficient " of monitoring point is defined,
Refer to that the amount capacity according to some potential monitoring point accounts for a term system obtained from the proportion of all monitoring point rated capacity summations
Number, the order of priority for potential monitoring point；Particularly meter and DG are grid-connected, when direction of tide is inverted so that weight
Coefficient order of priority changes；
2) it is defined as meeting Kirchhoff's current law (KCL) KCL minimum number NKCL, i.e. the configuration quantity of PQM meets electric current
The minimum number of global viewable；Define " feasible zone distributed rationally ", refer to that the installation number for distributing result rationally is no less than
NKCL；KCL principles show the outflow N bar circuits from a bus, and the electric current of a branch road can be calculated by other N-1 bars branch road
Draw, for individual node, N-1 is to avoid the indefinite PQM of branch current from least installing number；And consider that PQM is installed
In the end points of branch road, i.e., just from bus separation point position, PQM monitoring ranges will include whole piece circuit；Therefore, NKCLDefinition
It is as follows
In formula, NaAny bar circuit in the case of potential installation PQM monitorings points, meter and distributed power source in expression system
Two ends are all potential mount points；Bus quantity in β expression systems；I is counting variable；biIt is the determined property value of bus,
When connecting two Above Transmission Lines on bus, biJudge to return to 1, otherwise return to 0；
3) voltage Observable region MRA is defined, when referring to that electrical energy power quality disturbance event occurs for system, certain monitoring point can be seen
Measure the region of the disturbance event；The voltage observability of the whole network is realized, even if the MRA combinations of system monitoring point can cover complete
Net；Failure points use F in systemaRepresent, then the MRA of the whole nodes of system can be N with a dimensiona×FaObservable matrix
MMRARepresent, its element assignment m (di,fj) as follows
In formula, VijRepresent j-th of trouble point fjD during generation short troubleiThe magnitude of voltage of node, VtFor the monitoring electricity of setting
Press threshold value；WithRepresent any i and any j；As m (di,fj) it is equal to 1, represent trouble point fjBelong to node diMRA；Work as m
(di,fj) it is equal to 0, represent trouble point fjIt is not belonging to node diMRA；
4) binary system particle group optimizing BPSO models are improved；In BPSO after improvement, each particle is that have speed
A solution of parameter is spent, its particle position corresponds to NaThe vector of individual potential installation site, 1 × N of vector dimensiona, its element takes
It is worth for 1 or 0, indicates whether that PQM is installed, all feasible solutions constitute the location status in search space；The side of circling in the air of each particle
Determined to distance by velocity amplitude and present position values, carry out adaptive value evaluation by evaluation function, then population is empty in solution
Between in pursue current optimal solution and carry out fast search, find out optimal particle；The iterative process of PSO models includes particle position after improvement
Put the iteration with speed；N-th of particleVelocity amplitudeKth time iteration it is as follows：
In formula, subscript n represents n-th of particle, and subscript k or k+1 represent iterations；ω is inertia weight, representation speed
Inertia coeffeicent；c1And c2For accelerated factor, represent the gap of particle and current more excellent position and produce the coefficient of acceleration；r0、r1
And r2It is [0~+1] interval random real number；Individual extreme valueRepresent n-th particle itself be currently found it is optimal
Position, global extremumRepresent the optimal location that all particles were currently found；OrRepresent vector v or's
I-th of element, any i=1,2 ..., Na；For intermediate variable, iterative it be divided into two by complicated and make statement apparentization；Its
Middle sigmoid () function is defined as follows
In formula (5), z represents aleatory variable；Speed iterative (3) expresses the spy that population follows current more excellent particle
Property, iterative (4) are converted to the span of speed with sigmoid () function the successive value between [- 1~+1]；r0Work
Be prevent speed level off to zero when, search for secular stagnation and be absorbed in local extremum；
N-th of particlePosition iteration, it is as follows with its element representation：
In formula, r3For the random real number between [0~+1]；Subscript k or k+1 represent iterations；Represent n-th of particle
I-th of element value, any i=1,2 ..., Na；Rule of judgment is meant that：If kth time particle position and its speed it
During with more than dynamic threshold, then+1 position value of kth is 1, is otherwise 0, and each element is calculated respectively；The mesh of model refinement
, it is to make algorithm in particle iterative process, keeps the ability to currently more excellent particle direction search, overcome binary arithmetic operation to exist
Applicable sex chromosome mosaicism in optimization process, and its threshold value has dynamic property, prevents from being absorbed in local convergence too early；
5) new evaluation function is built, population is substituted into constructed evaluation function calculates adaptive value, corresponding adaptive value
It is smaller, represent that its solution is more excellent；Evaluation functionIt is made up of 4 subfunctions and its coefficient：
In formula, μ1For single PQM cost factor,For weighting function；μ2Sufficient KCL principles with thumb down and produce
Redundancy factor,For corresponding redundancy functions；λ1Penalty factor during sufficient MRA with thumb down,To be corresponding
Decision function；λ2Represent blanketing fctor,For corresponding coverage function；
Wherein Section 1, weighting functionRepresent to add up to the weight that all installation PQM monitoring points are carried out, if prison
Its fewer value of measuring point number is smaller, and its definition is as follows
In formula, SiFor the rated capacity of i-th of mount point, Σ SNFor all rated capacity summations；ξ (i) is representedIt is right
The distribution weight coefficient answered, its value is the positive number for being slightly less than numerical value 1；Distribution weight coefficient is the amount capacity based on mount point
The ratio of total capacity is accounted for, then obtains its difference with numerical value 1, the smaller weight for representing its priority on the contrary of the coefficient is bigger；
Wherein Section 2, redundancy functionsCalculate the redundancy for being unsatisfactory for N-1 principles and producing；
Wherein Section 3, decision functionFor determining whether to meet voltage global viewable；
In formula, y (j) represents vector y j-th of element；For voltage Observable matrix MMRA1 × FaDimensional vector y
Transition intermediate vector；Formula (12) annotates computing dimension with subscript, ifOperation result y in there is numerical value be 0
, show the current solution trouble point that presence can not be monitored at corresponding ranks, then the continued product condition of formula (11) will be equal to
0 so that judge that return value is equal to 1, and then trigger the penalty factor λ in evaluation function formula (10)1；
Wherein Section 4, coverage functionExpress the utilization ratio of monitoring point；
||y1| |=[y1(1)2+y1(2)2+…y1(Fa)2]1/2 (14)
In formula, | | y1| | vectorial y is sought in expression1Euclidean Norm,Represent 1 × FaComplete 1 vector of dimension, y (j) numerical value
Physical meaning be trouble point by multiple monitoring points while the number monitored；Work as y1Euclidean Norm level off to zero when, show institute
Faulty point can be monitored and only measured by a monitoring point, utilization rate highest；Otherwise its norm is bigger, show exist excessively
Monitoring point is coated over certain block region of power distribution network；
6) initialization population position and speed, substitute into evaluation function formula by population and calculate adaptive value, and to initial
Extreme value carries out assignment；
7) according to particle position and iterative, all particles of renewal of speed；Feedback check is carried out to feasible zone, if discontented
Sufficient feasible zone, then to a random element for the particle1 variation, then feedback check are put, until meeting feasible zone；
8) all populations are substituted into evaluation function formula again and calculates adaptive value；If the adaptive value of particle is better than individual before this
Extreme value, then more new individual extreme value, otherwise constant；If optimal individual extreme value is better than global extremum before this, global pole is updated
Value, it is otherwise constant；
9) when reaching maximum iteration, then circulation is jumped out, and export current global extremum as optimum results；Otherwise
Return to step 7 continues iteration；According to global extremumMiddle value is 1 element, to determine PQM installation site, and is added upAll elements be worth to installation total number.
The present invention is directed to grid-connected distributed power source, power distribution network comprehensive monitoring, disturbance event intelligent diagnostics and is accurately positioned
The influence factor such as integration requirement carry out electric energy intellectual monitoring point distribute research rationally, it is proposed that in the case of meter and DG are grid-connected together
When consider that voltage and current global viewable distributes thinking rationally, the BPSO models improved simultaneously construct new evaluation function,
By the population iterative process with feasible zone feedback check, the optimal solution of PQM allocation plans is found.One kind is realized to be based on changing
Enter BPSO, meter and distributed power source and the side that distributes rationally of electric energy quality monitoring point for meeting voltage x current global viewable simultaneously
Method, and the comprehensive monitoring of power distribution network, disturbance event intelligent diagnostics and pinpoint integration requirement can be met.
Beneficial effects of the present invention are mainly manifested in：1st, the intelligent distribution network in the case of meter and distributed power source is defined
Comprehensive monitoring, voltage and current global viewable, distribution weight coefficient concept；2nd, binary system particle group optimizing BPSO models are improved
And a kind of new evaluation function is constructed, and propose a kind of distributing rationally based on the electric energy quality monitoring point for improving BPSO
Method；3rd, the quality of power supply comprehensive monitoring of the power distribution network containing DG can be realized with relatively low cost by carrying Optimal Configuration Method, and full
Afc voltage and electric current global viewable, meet the intelligent diagnostics of disturbance event and be accurately positioned demand.
Brief description of the drawings
Fig. 1 is the specific implementation flow chart of the inventive method.
Fig. 2 is influence schematic diagrames of the DG to distribution weight.
Fig. 3 is the addition DG node power distribution net topology figures of IEEE 13.
Fig. 4 is the individual extreme value convergence process figure of population.
Fig. 5 is the global extremum convergence process figure of population.
Embodiment
With reference to embodiment and accompanying drawing, the present invention is described in further detail, but embodiments of the present invention are not limited
In this.Embodiment fall into a trap and distributed power source electric energy quality monitoring point configuration scheme the general frame as shown in Figure 1, this
The electric energy quality monitoring point collocation method of the described meter of invention and distributed power source, comprises the following steps：
1) related notion in being distributed rationally to meter and the grid-connected electric energy quality monitoring points of distributed power source DG is defined；
" comprehensive monitoring of power distribution network " in the case of meter and DG is defined, refers to the intelligent diagnostics requirement that can meet electrical energy power quality disturbance event
And need the voltage and current information monitoring degree of acquisition；Define " global viewable of voltage and current ", refer to based on configuration peace
The PQM of dress obtains information, then further obtains by state estimation other information for not installing circuit and node so that power distribution network
The voltage and current information Observable of all circuits of the whole network and node；" the distribution weight coefficient " of monitoring point is defined, refers to foundation
The amount capacity of some potential monitoring point accounts for a term coefficient obtained from the proportion of all monitoring point rated capacity summations, for can
Select the order of priority of monitoring point；As shown in Fig. 2 meter and when DG is grid-connected and direction of tide is inverted so that { S in Fig. 21Extremely
S5Weight coefficient size sequence change；
2) N is definedKCLElectric current is met for the configuration quantity that meets Kirchhoff's current law (KCL) KCL minimum number, i.e. PQM
The minimum number of global viewable；Define " feasible zone distributed rationally ", refer to that the installation number for distributing result rationally is no less than
NKCL；KCL principles show the outflow N bar circuits from a bus, and the electric current of a branch road can be calculated by other N-1 bars branch road
Draw；And considering that PQM is arranged on the end points of branch road, PQM monitoring ranges will include whole piece circuit；Therefore, NKCLDefinition such as formula
(1) shown in；
3) voltage Observable region MRA is defined, when referring to that electrical energy power quality disturbance event occurs for system, certain monitoring point can be seen
Measure the region of the disturbance event；Use FaFailure is counted in expression system, then the MRA of the whole nodes of system is N with a dimensiona
×FaObservable matrix MMRARepresent, its element value m (di,fj) as shown in formula (2)；
4) binary system particle group optimizing BPSO models are improved；In BPSO after improvement, each particle is that have speed
A solution of parameter is spent, its particle position corresponds to NaThe vector of individual potential installation site, 1 × N of vector dimensiona, its element takes
It is worth for 1 or 0 to indicate whether that PQM is installed, all feasible solutions constitute the location status in search space；The side of circling in the air of each particle
Determined to distance by velocity amplitude and present position values, carry out adaptive value evaluation by evaluation function, then population is empty in solution
Between in pursue current optimal solution and carry out fast search, find out optimal particle；The iterative process of PSO models includes particle position after improvement
Put the iteration with speed；N-th of particleVelocity amplitudeKth time iteration such as formula (3-5) shown in；N-th of particlePosition
Iteration is put, with its element representation such as formula (6) Suo Shi；
The purpose of model refinement, is to make algorithm in particle iterative process, is kept to currently more excellent particle direction search
Ability, overcomes applicable sex chromosome mosaicism of the binary arithmetic operation in optimization process, and its threshold value has dynamic property, prevents from falling into too early
Enter local convergence；
5) new evaluation function is built, population is substituted into constructed evaluation function calculates adaptive value, corresponding adaptive value
It is smaller, represent that its solution is more excellent；Evaluation functionIt is made up of 4 subfunctions and its coefficient, as shown in formula (7-14), including
Distribution weight, electric current global viewable, voltage global viewable and covering efficiency four aspects；
6) initialization population position and speed, substitute into evaluation function formula by population and calculate adaptive value, and to initial
Extreme value carries out assignment；
7) according to particle position and iterative, all particles of renewal of speed；Feedback check is carried out to feasible zone, if discontented
Sufficient feasible zone, then to a random element for the particle1 variation, then feedback check are put, until meeting feasible zone；
8) all populations are substituted into evaluation function formula again and calculates adaptive value；If the adaptive value of particle is better than individual before this
Extreme value, then more new individual extreme value, otherwise constant；If optimal individual extreme value is better than global extremum before this, global pole is updated
Value, it is otherwise constant；
9) when reaching maximum iteration, then circulation is jumped out, and export current global extremum as optimum results；Otherwise
Return to step 7 continues iteration；According to global extremumMiddle value is 1 element, to determine PQM installation site, and is added upAll elements be worth to installation total number.
Below using the node power distribution nets of IEEE 13 shown in Fig. 3 as embodiment, the operating process of the present invention is further illustrated,
The DG of addition is grid-connected at Bus 611, and the black box PQM in figure is by information undetermined, it is necessary to by carrying Optimal Configuration Method
Result is obtained to determine later.MATLAB/simulink modeling and simulatings are used, power quality disturbance is located at circuit L6, disturbance event
For the switching in short-term of energy injection type.
Based on fixed wire topologies information, obtained according to formula (1) and meet Kirchhoff's current law (KCL) KCL most
Few number NKCLEqual to 6.And obtain the Observable matrix M of 22 × 12 dimensions that are being made up of 0 or 1MRA, the value of each specific element
Determined according to formula (2), wherein monitoring voltage threshold value is set to 90 the percent of rated value.
Initial parameter in innovatory algorithm is set：Population population quantity is set to 40, and iterations is 300
It is secondary.Other specification sets as follows：Cost factor μ1Take 1.1, redundancy factor μ2Take 0.15, penalty factor λ1Take 2.0, blanketing fctor
λ2Take 0.2.
According to the parameter setting, population is first initialized, 40 particles are taken at random, evaluation function is substituted into and is adapted to
Value, and it is assigned to initial individual extreme value and global extremum.Then population iterative search is carried out, its individual extreme value is obtained
Convergence process as shown in figure 4, being the definition for keeping figure, every 5 iteration mark asterism " * " symbol.From the total of Fig. 4
Body trend obtains the adaptive value of individual extreme value with the rule similar to exponential damping, constantly approaches globally optimal solution.Particle to
Current more excellent position follow effect so that algorithm has faster convergence rate.Such as the 100th~150 iterative process in Fig. 4
In, the poor particle in a part of position can be clearly observed under the effect of following, local convergence region is jumped out, rapidly force
Nearly optimal solution.The convergence process of the global extremum of population is as shown in Figure 5, it is shown that its convergence rate is close to exponential convergence.
The global extremum finally exported according to population iteration, according toMiddle value is 1 element, to determine PQM's
Installation site, and its all elements that add up are worth to installation total number, as shown in table 1, wherein 650-632 is represented from node 650
The outlet position connected to node 632.Optimum results are marked out to the specifying information of PQM configurations, such as Fig. 3 on topology diagram
Shown in middle black box.
The PQM of table 1 optimizes quantity and position
Obtaining optimum results according to table 1 has 73.9% saving rate, i.e., 23 potential installation sites only need to install 6
PQM.Further whether checking computations gained optimum results meet the global viewable of voltage and current：PQM is checked according to formula (1) first
Total number is equal to KCL optimum number NKCL, and verify that any bar does not install PQM circuit and whether meets KCL laws by having installed
PQM, which is calculated, obtains current information；Then according to the MRA matrixes of formula (2), verify that it meets voltage global viewable.Therefore, verify
Institute's extracting method can it is automatic, effectively realize monitoring point optimization configuration, and can be suitably used for the grid-connected situations of DG, and institute's extracting method
The quality of power supply comprehensive monitoring of power distribution network can be realized with relatively low cost, voltage and current global viewable is met, so as to full
The intelligent diagnostics of sufficient disturbance event and it is accurately positioned demand.
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. the electric energy quality monitoring point collocation method of meter and distributed power source, comprises the following steps：
1) related notion in being distributed rationally to meter and the grid-connected electric energy quality monitoring point of distributed power source is defined；Definition meter
And " comprehensive monitoring of power distribution network " in the case of distributed power source DG, refer to that the intelligent diagnostics of electrical energy power quality disturbance event can be met
It is required that and needing the voltage and current information monitoring degree of acquisition；Define " global viewable of voltage and current ", refer to be based on matching somebody with somebody
The electric energy quality monitor PQM acquisition information of installation is put, then other are further obtained by state estimation circuit and section are not installed
The information of point so that the voltage and current information Observable of all circuits of power distribution network the whole network and node；Define " the distribution of monitoring point
Weight coefficient ", refers to that the amount capacity according to some potential monitoring point accounts for the proportion of all monitoring point rated capacity summations and obtained
The term coefficient arrived, the order of priority for potential monitoring point；Particularly meter and DG are grid-connected, when direction of tide is inverted
When so that weight coefficient order of priority changes；
2) it is defined as meeting Kirchhoff's current law (KCL) KCL minimum number NKCL, i.e. it is global that the configuration quantity of PQM meets electric current
Considerable minimum number；Define " feasible zone distributed rationally ", refer to that the installation number for distributing result rationally is no less than NKCL；KCL
Principle shows the outflow N bar circuits from a bus, and the electric current of a branch road can be calculated by other N-1 bars branch road, right
For individual node, N-1 is to avoid the indefinite PQM of branch current from least installing number；And consider that PQM is arranged on branch road
End points, i.e., just from bus separation point position, PQM monitoring ranges will include whole piece circuit；Therefore, NKCLDefinition it is as follows
<mrow>
<msub>
<mi>N</mi>
<mrow>
<mi>K</mi>
<mi>C</mi>
<mi>L</mi>
</mrow>
</msub>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msub>
<mi>N</mi>
<mi>a</mi>
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<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>&beta;</mi>
</munderover>
<msub>
<mi>b</mi>
<mi>i</mi>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, NaPotential installation PQM monitorings are counted in expression system, the two ends of any bar circuit in the case of meter and distributed power source
All it is potential mount point；Bus quantity in β expression systems；I is counting variable；biIt is the determined property value of bus, works as mother
When connecting two Above Transmission Lines on line, biJudge to return to 1, otherwise return to 0；
3) voltage Observable region MRA is defined, when referring to that electrical energy power quality disturbance event occurs for system, certain monitoring point can be observed
The region of the disturbance event；The voltage observability of the whole network is realized, even if the MRA combinations of system monitoring point can cover the whole network；
Failure points use F in systemaRepresent, then the MRA of the whole nodes of system can be N with a dimensiona×FaObservable matrix MMRA
Represent, its element assignment m (di,fj) as follows
<mrow>
<mi>m</mi>
<mrow>
<mo>(</mo>
<msub>
<mi>d</mi>
<mi>i</mi>
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<mi>f</mi>
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<mo>=</mo>
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<mtable>
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</mtd>
<mtd>
<mrow>
<msub>
<mi>V</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>&le;</mo>
<msub>
<mi>V</mi>
<mi>t</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>&ForAll;</mo>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msub>
<mi>N</mi>
<mi>a</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>0</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<msub>
<mi>V</mi>
<mrow>
<mi>i</mi>
<mi>j</mi>
</mrow>
</msub>
<mo>></mo>
<msub>
<mi>V</mi>
<mi>t</mi>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>&ForAll;</mo>
<mi>j</mi>
<mo>=</mo>
<mn>1</mn>
<mo>,</mo>
<mn>2</mn>
<mo>,</mo>
<mo>...</mo>
<mo>,</mo>
<msub>
<mi>F</mi>
<mi>a</mi>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, VijRepresent j-th of trouble point fjNode d during generation short troubleiMagnitude of voltage, VtFor the monitoring voltage threshold of setting
Value；WithRepresent any i and any j；As m (di,fj) it is equal to 1, represent trouble point fjBelong to node diMRA；As m (di,
fj) it is equal to 0, represent trouble point fjIt is not belonging to node diMRA；
4) binary system particle group optimizing BPSO models are improved；In BPSO after improvement, each particle is with speed ginseng
A several solutions, its particle position corresponds to NaThe vector of individual potential installation site, 1 × N of vector dimensiona, its element value is
1 or 0, indicate whether that PQM is installed, all feasible solutions constitute the location status in search space；Each particle circle in the air direction and
Distance is determined by velocity amplitude and present position values, carries out adaptive value evaluation by evaluation function, then population is in solution space
Pursue current optimal solution and carry out fast search, find out optimal particle；The iterative process of particle group optimizing PSO models includes after improvement
The iteration of particle position and speed；N-th of particle of kth time iterationVelocity amplitudeKth time iteration it is as follows：
<mrow>
<msubsup>
<mover>
<mi>v</mi>
<mo>^</mo>
</mover>
<mi>n</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>=</mo>
<msubsup>
<mi>&omega;v</mi>
<mi>n</mi>
<mi>k</mi>
</msubsup>
<mo>+</mo>
<msub>
<mi>c</mi>
<mn>1</mn>
</msub>
<msubsup>
<mi>r</mi>
<mn>1</mn>
<mi>k</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>p</mi>
<mrow>
<mi>b</mi>
<mi>e</mi>
<mi>s</mi>
<mi>t</mi>
<mo>.</mo>
<mi>n</mi>
</mrow>
<mi>k</mi>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>x</mi>
<mi>n</mi>
<mi>k</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>c</mi>
<mn>2</mn>
</msub>
<msubsup>
<mi>r</mi>
<mn>2</mn>
<mi>k</mi>
</msubsup>
<mrow>
<mo>(</mo>
<msubsup>
<mi>g</mi>
<mrow>
<mi>b</mi>
<mi>e</mi>
<mi>s</mi>
<mi>t</mi>
</mrow>
<mi>k</mi>
</msubsup>
<mo>-</mo>
<msubsup>
<mi>x</mi>
<mi>n</mi>
<mi>k</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>3</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msubsup>
<mi>v</mi>
<mi>n</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mn>2</mn>
<mo>&times;</mo>
<mi>s</mi>
<mi>i</mi>
<mi>g</mi>
<mi>m</mi>
<mi>o</mi>
<mi>i</mi>
<mi>d</mi>
<mrow>
<mo>(</mo>
<msubsup>
<mover>
<mi>v</mi>
<mo>^</mo>
</mover>
<mi>n</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mn>1</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>|</mo>
<msubsup>
<mover>
<mi>v</mi>
<mo>^</mo>
</mover>
<mi>n</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
<mo>|</mo>
<mo>></mo>
<mn>0.1</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>2</mn>
<mo>&times;</mo>
<msub>
<mi>r</mi>
<mn>0</mn>
</msub>
<mo>-</mo>
<mn>1</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>|</mo>
<msubsup>
<mover>
<mi>v</mi>
<mo>^</mo>
</mover>
<mi>n</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
<mo>|</mo>
<mo>&le;</mo>
<mn>0.1</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mo>)</mo>
</mrow>
</mrow>
1
In formula, subscript n represents n-th of particle, and subscript k or k+1 represent iterations；ω is inertia weight, representation speed it is used
Property coefficient；c1And c2For accelerated factor, represent the gap of particle and current more excellent position and produce the coefficient of acceleration；r0、r1And r2
It is [0~+1] interval random real number；Individual extreme valueRepresent that n-th of particle itself of kth time iteration was currently found
Optimal location, global extremumRepresent the optimal location that all particles were currently found；OrRepresent vector v
OrI-th of element, any i=1,2 ..., Na；For intermediate variable, iterative it be divided into two by complicated and make statement apparent
Change；Wherein sigmoid () function is defined as follows
<mrow>
<mi>s</mi>
<mi>i</mi>
<mi>g</mi>
<mi>m</mi>
<mi>o</mi>
<mi>i</mi>
<mi>d</mi>
<mrow>
<mo>(</mo>
<mi>z</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>1</mn>
<mo>+</mo>
<msup>
<mi>e</mi>
<mrow>
<mo>-</mo>
<mi>z</mi>
</mrow>
</msup>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>5</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula (5), z represents aleatory variable；Speed iterative (3) expresses the characteristic that population follows current more excellent particle, repeatedly
The span of speed is converted to the successive value between [- 1~+1] with sigmoid () function for formula (4)；r0Effect be anti-
Only speed level off to zero when, search for secular stagnation and be absorbed in local extremum；
N-th of particle of kth time iterationPosition iteration, it is as follows with its element representation：
<mrow>
<msubsup>
<mi>x</mi>
<mi>n</mi>
<mrow>
<mi>k</mi>
<mo>+</mo>
<mn>1</mn>
</mrow>
</msubsup>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mn>0</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>(</mo>
<msubsup>
<mi>x</mi>
<mi>n</mi>
<mi>k</mi>
</msubsup>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
<mo>+</mo>
<msubsup>
<mi>v</mi>
<mi>n</mi>
<mi>k</mi>
</msubsup>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
<mo>)</mo>
<mo>&le;</mo>
<mo>(</mo>
<mfrac>
<msub>
<mi>r</mi>
<mn>3</mn>
</msub>
<mn>2</mn>
</mfrac>
<mo>+</mo>
<mn>0.25</mn>
<mo>)</mo>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>1</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>(</mo>
<msubsup>
<mi>x</mi>
<mi>n</mi>
<mi>k</mi>
</msubsup>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
<mo>+</mo>
<msubsup>
<mi>v</mi>
<mi>n</mi>
<mi>k</mi>
</msubsup>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
<mo>)</mo>
<mo>></mo>
<mo>(</mo>
<mfrac>
<msub>
<mi>r</mi>
<mn>3</mn>
</msub>
<mn>2</mn>
</mfrac>
<mo>+</mo>
<mn>0.25</mn>
<mo>)</mo>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>6</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, r3For the random real number between [0~+1]；Subscript k or k+1 represent iterations；Represent+1 iteration of kth
The value of i-th of element of n-th of particle, any i=1,2 ..., Na；Rule of judgment is meant that：If kth time particle position
When being more than dynamic threshold with its speed sum, then+1 position value of kth is 1, is otherwise 0, and each element is calculated respectively；Mould
The improved purpose of type, is to make algorithm in particle iterative process, keeps the ability to currently more excellent particle direction search, overcomes two
Applicable sex chromosome mosaicism of the system computing in optimization process, and its threshold value has dynamic property, prevents from being absorbed in local convergence too early；
5) new evaluation function is built, population is substituted into constructed evaluation function calculates adaptive value, and corresponding adaptive value is smaller,
Represent that its solution is more excellent；Evaluation functionIt is made up of 4 subfunctions and its coefficient：
<mrow>
<mi>F</mi>
<mrow>
<mo>(</mo>
<msubsup>
<mi>x</mi>
<mi>n</mi>
<mi>k</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>&mu;</mi>
<mn>1</mn>
</msub>
<msub>
<mi>h</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<msubsup>
<mi>x</mi>
<mi>n</mi>
<mi>k</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>&mu;</mi>
<mn>2</mn>
</msub>
<msub>
<mi>h</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<msubsup>
<mi>x</mi>
<mi>n</mi>
<mi>k</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>&lambda;</mi>
<mn>1</mn>
</msub>
<msub>
<mi>g</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<msubsup>
<mi>x</mi>
<mi>n</mi>
<mi>k</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>+</mo>
<msub>
<mi>&lambda;</mi>
<mn>2</mn>
</msub>
<msub>
<mi>g</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<msubsup>
<mi>x</mi>
<mi>n</mi>
<mi>k</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>7</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, μ1For single PQM cost factor,For weighting function；μ2Sufficient KCL principles with thumb down and the redundancy produced
The factor,For corresponding redundancy functions；λ1Penalty factor during sufficient MRA with thumb down,Judge letter to be corresponding
Number；λ2Represent blanketing fctor,For corresponding coverage function；
Wherein Section 1, weighting functionRepresent to add up to the weight that all installation PQM monitoring points are carried out, if monitoring points
Its fewer value is smaller, and its definition is as follows
<mrow>
<msub>
<mi>h</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<msubsup>
<mi>x</mi>
<mi>n</mi>
<mi>k</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<msub>
<mi>N</mi>
<mi>a</mi>
</msub>
</munderover>
<mi>&xi;</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
<mo>&CenterDot;</mo>
<msubsup>
<mi>x</mi>
<mi>n</mi>
<mi>k</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>8</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mi>&xi;</mi>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>1</mn>
<mo>-</mo>
<mfrac>
<msub>
<mi>S</mi>
<mi>i</mi>
</msub>
<mrow>
<msub>
<mi>&Sigma;S</mi>
<mi>N</mi>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>9</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, SiFor the rated capacity of i-th of mount point, Σ SNFor all rated capacity summations；ξ (i) is representedIt is corresponding to match somebody with somebody
Electric weight coefficient, its value is the positive number for being slightly less than numerical value 1；Distribution weight coefficient is that the amount capacity based on mount point accounts for total appearance
The ratio of amount, then its difference with numerical value 1 is obtained, the smaller weight for representing its priority on the contrary of the coefficient is bigger；
Wherein Section 2, redundancy functionsCalculate the redundancy for being unsatisfactory for N-1 principles and producing；
<mrow>
<msub>
<mi>h</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<msubsup>
<mi>x</mi>
<mi>n</mi>
<mi>k</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>|</mo>
<msub>
<mi>N</mi>
<mrow>
<mi>K</mi>
<mi>C</mi>
<mi>L</mi>
</mrow>
</msub>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<msub>
<mi>N</mi>
<mi>a</mi>
</msub>
</munderover>
<msubsup>
<mi>x</mi>
<mi>n</mi>
<mi>k</mi>
</msubsup>
<mrow>
<mo>(</mo>
<mi>i</mi>
<mo>)</mo>
</mrow>
<mo>|</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>10</mn>
<mo>)</mo>
</mrow>
</mrow>
Wherein Section 3, decision functionFor determining whether to meet voltage global viewable；
<mrow>
<msub>
<mi>g</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<msubsup>
<mi>x</mi>
<mi>n</mi>
<mi>k</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = "{" close = "">
<mtable>
<mtr>
<mtd>
<mrow>
<mn>1</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<munderover>
<mo>&Pi;</mo>
<mi>j</mi>
<msub>
<mi>F</mi>
<mi>a</mi>
</msub>
</munderover>
<mi>y</mi>
<mrow>
<mo>(</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mn>0</mn>
<mo>,</mo>
</mrow>
</mtd>
<mtd>
<mrow>
<munderover>
<mo>&Pi;</mo>
<mi>j</mi>
<msub>
<mi>F</mi>
<mi>a</mi>
</msub>
</munderover>
<mi>y</mi>
<mrow>
<mo>(</mo>
<mi>j</mi>
<mo>)</mo>
</mrow>
<mo>&NotEqual;</mo>
<mn>0</mn>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>11</mn>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mrow>
<mo>&lsqb;</mo>
<mi>y</mi>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>&times;</mo>
<msub>
<mi>F</mi>
<mi>a</mi>
</msub>
</mrow>
</msub>
<mo>=</mo>
<msub>
<mrow>
<mo>&lsqb;</mo>
<msubsup>
<mi>x</mi>
<mi>n</mi>
<mi>k</mi>
</msubsup>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>&times;</mo>
<msub>
<mi>N</mi>
<mi>a</mi>
</msub>
</mrow>
</msub>
<mo>&times;</mo>
<msub>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mi>M</mi>
<mrow>
<mi>M</mi>
<mi>R</mi>
<mi>A</mi>
</mrow>
</msub>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<msub>
<mi>N</mi>
<mi>a</mi>
</msub>
<mo>&times;</mo>
<msub>
<mi>F</mi>
<mi>a</mi>
</msub>
</mrow>
</msub>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>12</mn>
<mo>)</mo>
</mrow>
</mrow>
In formula, y (j) represents vector y j-th of element, the physical meaning of y (j) numerical value be trouble point by multiple monitoring points simultaneously
The number monitored；For voltage Observable matrix MMRA1 × FaDimensional vector y transition intermediate vectors；Formula (12) is with lower mark
Computing dimension has been released, ifOperation result y in exist numerical value be 0 item, show current solution at corresponding ranks
In the presence of the trouble point that can not be monitored, then the continued product condition of formula (11) will be equal to 0 so that judges that return value is equal to 1, and then touches
Send out the penalty factor λ in evaluation function formula (10)1；
Wherein Section 4, coverage functionExpress the utilization ratio of monitoring point；
<mrow>
<msub>
<mi>g</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<msubsup>
<mi>x</mi>
<mi>n</mi>
<mi>k</mi>
</msubsup>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mo>|</mo>
<mo>|</mo>
<msub>
<mi>y</mi>
<mn>1</mn>
</msub>
<mo>|</mo>
<mo>|</mo>
<mo>=</mo>
<mo>|</mo>
<mo>|</mo>
<mi>y</mi>
<mo>-</mo>
<msub>
<mrow>
<mo>&lsqb;</mo>
<mn>1</mn>
<mo>&rsqb;</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>&times;</mo>
<msub>
<mi>F</mi>
<mi>a</mi>
</msub>
</mrow>
</msub>
<mo>|</mo>
<mo>|</mo>
<mo>-</mo>
<mo>-</mo>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>13</mn>
<mo>)</mo>
</mrow>
</mrow>
||y1| |=[y1(1)2+y1(2)2+…y1(Fa)2]1/2 (14)
In formula, | | y1| | vectorial y is sought in expression1Euclidean Norm,Represent 1 × FaComplete 1 vector of dimension, works as y1Euclidean Norm become
When being bordering on zero, show that all trouble points can monitor and only be measured by a monitoring point, utilization rate highest；Otherwise the norm is got over
Greatly, show there is certain block region that excessive monitoring point is coated over power distribution network；
6) initialization population position and speed, substitute into evaluation function formula by population and calculate adaptive value, and to initial extreme value
Carry out assignment；
7) according to particle position and iterative, all particles of renewal of speed；Feedback check is carried out to feasible zone, can if being unsatisfactory for
Row domain, then to a random element for the particle1 variation, then feedback check are put, until meeting feasible zone；
8) all populations are substituted into evaluation function formula again and calculates adaptive value；If the adaptive value of particle is better than individual pole before this
Value, then more new individual extreme value, otherwise constant；If optimal individual extreme value updates global extremum better than global extremum before this,
Otherwise it is constant；
9) when reaching maximum iteration, then circulation is jumped out, and export current global extremum as optimum results；Otherwise return
Step 7 continues iteration；According to global extremumMiddle value is 1 element, to determine PQM installation site, and is added up's
All elements are worth to installation total number.
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