CN109768529A - A kind of configuration method of the distribution system switch based on Boolean type variable - Google Patents
A kind of configuration method of the distribution system switch based on Boolean type variable Download PDFInfo
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Abstract
The invention discloses a kind of configuration methods of distribution system switch based on Boolean type variable, the configuration method of the distribution system switch is the following steps are included: step 1: in the case where distribution system switch configuration x is determined, in order to indicate the switch existence above some position or certain sections, introduce Boolean type expression formula, when Boolean type transition formula evaluation is 1, indicating the position or the section, there are corresponding switches, when Boolean type transition formula evaluation is 0, indicate that corresponding switch is not present；Step 2: fault section location accuracy rate is introduced based on step 1；Step 3: the Boolean type expression formula and fault section location accuracy rate introduced by step 1 and 2 builds failure load power off time function；Step 4: with reliability index of powering for constraint, the minimum distribution system switch allocation optimum model with target of the sum of Custom interruption cost and switchgear distribution whole life costing is solved by solver for building.
Description
Technical field
The present invention relates to electric power system power distribution fields of automation technology, more particularly to the power distribution system based on Boolean type variable
The configuration method of system switch.
Background technique
Utilities Electric Co. is higher and higher for the power supply reliability demand of power distribution network.Distribution system is by a series of possible generation
The component of failure forms, how to reduce power off time brought by these component faults and loss of outage be Utilities Electric Co. the most
Concern.Distribution system switch can pass through isolated fault section and section of getting well after determining fault section
Power supply, to effectively improve power supply reliability.More distribution system switches then can more quick positioning failure section
And it is isolated.But as the rising of distribution system switch quantity, cost of investment can also rise with it, how to determine distribution
The switch allocation optimum of system, under the requirement for meeting power supply reliability, so that loss of outage and switchgear distribution Life cycle
Network minimal is the hot subject of power distribution automation (distribution automation, DA) research both at home and abroad at present.
Early stage proposes can be by installing remote control switch (Remote-Controlled Switches, RCS), contracting
Short Fault Isolation time and service restoration time, to improve the power supply reliability of entire power distribution network.Then to manual switch
It is distinguished with automatic switch by capacity, and introduces customer outage hours function, under the constraint for guaranteeing power supply reliability,
It constructs with loss of outage and the smallest switchgear distribution model of configuration expense.It is all meaningful work above, but still can not
Contribution of the accurate allocation position and quantity for measuring distribution system switch to fault section location, is unfavorable for distribution network failure section
Accurate positionin.
Therefore, it is desirable to have a kind of configuration method of distribution system switch based on Boolean type variable effectively to solve existing skill
The problem of art.
Summary of the invention
The invention discloses a kind of configuration method of distribution system switch based on Boolean type variable, the distribution system is opened
The configuration method of pass the following steps are included:
Step 1: in the case where distribution system switch configuration x is determined, in order to indicate on some position or certain sections
The switch existence in face introduces Boolean type expression formula, when Boolean type transition formula evaluation is 1, indicates that the position or the section are deposited
In corresponding switch, when Boolean type transition formula evaluation is 0, indicate that corresponding switch is not present；
Step 2: fault section location accuracy rate is introduced based on step 1；
Step 3: it is negative that the Boolean type expression formula and fault section location accuracy rate introduced by step 1 and 2 builds failure
Lotus power off time function；
Step 4: with reliability index of powering for constraint, Custom interruption cost and switchgear distribution Life cycle are taken for building
With the sum of minimum and target distribution system switch allocation optimum model, solved by solver.
Preferably, the step 1 specifically includes the following steps:
Step 1.1: it is firstly introduced into 4 first kind Boolean type expression formulas:
Wherein 0 and 1 is left and right identifier, and 0 represents left end, and 1 represents right end, two first kind Boolean type expression in formula (1)
Formula respectively indicates the manual switch existence of b sections of feeder line section end left ends and right end on a articles feeder line, two in formula (2)
A kind of Boolean type expression formula, which respectively indicates the automatic switch of b sections of feeder line section end left ends and right end on a articles feeder line, to be existed
Property；
Step 1.2: following 6 the second class Boolean type expression formulas are built by first kind Boolean type expression formula:
In formula (3) two the second class Boolean type expression formulas respectively indicate on a articles feeder line b sections of feeder line section end left ends with
The block switch existence of right end, expression are respectively formula (6) and (7):
Two the second class Boolean type expression formulas respectively indicate the load at b sections of feeder line section ends on a articles feeder line in formula (4)
To the existence of manual segmentation switch and automatic section switch between jth section feeder line section, the expression of manual switch are as follows:
Two the second class Boolean type expression formulas respectively indicate a articles manual interconnection switch of feeder terminal and automatic in formula (5)
The existence of interconnection switch, the expression of manual switch are as follows:
TMa(x)=MCSa,ae,1(x) (9)
Wherein ae represents the final stage of a articles feeder line；
Step 1.3: 2 third class Boolean type expression formulas are built by the second class Boolean type expression formula of step 1.2:
WhereinIndicate the loads of b sections of feeder line section ends on a articles feeder line to point between jth section feeder line section
Duan Kaiguan existence, expression are as follows:
Ta(x) existence of a articles feeder terminal interconnection switch, expression are indicated are as follows:
Step 1.4: the Fault Isolation function of time being built by third class Boolean type expression formula, control centre is in positioning failure
Pass through the corresponding block switch of operation after section and failure is isolated with the load of healthy section, the Fault Isolation time is that segmentation is opened
Actuation time is closed, when there are block switches between failure and load, and at least one automatic section switch, then Fault Isolation time
It is otherwise the manual segmentation switch motion time to be automatically switched actuation time, Fault Isolation function of time formula (13) are as follows:
tisoIt (x) is Fault Isolation time, tisoIt (x) is Fault Isolation time, tSRTo be automatically switched actuation time, tSMFor
Manual segmentation switch motion time, p are that automatic section switch correctly acts probability；
Step 1.5: interconnection switch actuation time correctly acts probability according to the type and automatic interconnection switch of interconnection switch,
Interconnection switch actuation time function, formula are built by third class Boolean type expression formula are as follows:
ttieIt (x) is interconnection switch actuation time, q is that automatic interconnection switch correctly acts probability.
Preferably, the step 2 specifically includes the following steps:
Step 2.1: introducing Boolean type expression formula γa,b(x), it indicates in the case where distribution system switch configuration x is determined,
The distribution system switch existence of the upper b sections of ends two sides feeder line a, γa,b(x) value is 1, indicates that this section of end at least has one
A switch, γa,b(x) value is 0, indicates that switch, Boolean type expression formula γ is all not present in this section of end two sidesa,b(x) it embodies
Formula are as follows:
Step 2.2: using Boolean variable μa,b(x) the fault section localizability of upper b sections of the failure of feeder line a, boolean are indicated
Variable μa,b(x) value is 1, is indicated if faulty occur to pass through the signal framing of block switch to the section, boolean in the section
Variable μa,b(x) value is 0, and expression cannot navigate to the section, using breaker as the 0th section, γa,0(x) be 1, feeder line last
The switch fault electric current of section end two sides does not flow through, Boolean variable μa,b(x) expression are as follows:
Wherein, Ωa,sRepresent the feeder line section set of a articles feeder line；
Step 2.3: defining the fault section location accuracy rate o (x) of a articles feeder line, expression formula are as follows:
Wherein, Na,sFor the quantity of feeder line section on feeder line a；
Step 2.4: failure definition positioning time tins(x) calculation are as follows:
tloc(x)=tbasis+(1-η(x))×tdefult (19)。
Preferably, the step 3 specifically includes the following steps:
Step 3.1: the failure load power off time functionIn the feelings that distribution system switch configuration x is determined
Under condition, whole loads of the c articles branch feeder of b sections of feeder line section ends are because on i-th article of feeder line on a articles feeder line of power distribution network
Power off time caused by the kth of jth section feeder line ' a equivalent position failure, wherein k ' is according to the difference of abort situation, and kth '
The expression formula of a equivalent position are as follows:
Set 9 kinds of scenes:
Step 3.2: the corresponding load power off time of first kind failure is defined, expression formula is formula (21):
Step 3.3: defining the corresponding load power off time of the second class failure is 0, and expression formula is formula (22):
Step 3.4: the corresponding load power off time of third class failure is defined, expression formula is formula (23):
Step 3.5: the corresponding load power off time of the 4th class failure is defined, expression formula is formula (24):
Step 3.6: the corresponding load power off time of the 5th class failure is defined, expression formula is formula (25) and (26):
Preferably, the step 4 specifically includes the following steps:
Step 4.1: building allocation optimum model is averagely stopped with the minimum target of comprehensive cost with average power supply reliability
The scarce power supply volume of electricity and switch installation are limited to constraint condition, construct the allocation optimum model of distribution system switch, the model of building
Are as follows:
Wherein, Cost (x) is comprehensive cost；ASAI (x) is average power supply reliability；AENS (x) is that average have a power failure lacks confession
Electricity, NaFor whole feeder line set, Na,bFor feeder line section set whole on feeder line a；
Step 4.2: building comprehensive cost, the mathematic(al) representation of comprehensive cost Cost (x) are as follows:
Cost (x)=LCC (x)+CIC (x) (28)
Wherein, LCC (x) is switch whole life costing, and CIC (x) is Custom interruption cost expense；
Step 4.3: building constraint function expression formula.
Preferably, the mathematic(al) representation of step 4.2 switch whole life costing LCC (x) are as follows:
LCC (x)=INV (x)+MAI (x) (29)
Wherein, INV (x) is switch investment cost, and MAI (x) is switch maintenance cost.
Preferably, switch investment cost INV (x) includes the buying expenses and mounting cost of switch, formula are as follows:
WhereinInvestment cost is switched for manual segmentation,For automatic section switch capital cost
With,For manual interconnection switch investment cost,For automatic interconnection switch investment cost, divide manually
The expression formula of Duan Kaiguan investment cost and manual interconnection switch investment cost is respectively as follows:
Preferably, the annual operating maintenance expense of switchgear is set as the ratio of investment cost, time limit ΩtIt is opened described in interior
Close the formula of maintenance cost MAI (x) are as follows:
Wherein d is discount rate, and μ is the ratio of maintenance cost and investment cost.
Preferably, in the step 4.2 Custom interruption cost expense CIC (x) formula are as follows:
Wherein ΩiSet for the feeder line that may be broken down；Ωi,jFor the feeder line section collection that may be broken down on feeder line i
It closes；Ωi,j,k′For the position of fault set that i jth section may break down on feeder line；λi,j,k′It breaks down for the place general
Rate；ΩnFor the set of different user types；Represent the n-th class on a articles feeder line, the c articles branch feeder of b sections of feeder line sections
The load of load；M is the annual growth of load；It is negative corresponding to failure for the n-th type load type
Lotus power off timeLoss function.
Preferably, the step 4.3 building constraint function expression formula includes: to construct average power supply reliability constraint expression
Formula, build it is average have a power failure lack power supply volume constraint and build switch installation constraint；
Average power supply reliability constraint expression formula is constructed, the average power supply reliability ASAI (x) of distribution system is not less than it
Threshold value A SAIlim, average power supply reliability constraint mathematic(al) representation are as follows:
ASAI(x)≥ASAIlim
Wherein Na,cFor the number of users on feeder line a, NcFor the number of users of whole system.
It builds average have a power failure and lacks power supply volume constraint, the average power failure of distribution system lacks power supply volume AENS (x) and is not higher than its threshold
Value AENSlim, the average scarce power supply volume constraint mathematic(al) representation that has a power failure are as follows:
AENS(x)≤AENSlim
Switch installation constraint is built, for the switch installation site of each candidate, the switch variety installed cannot be greater than
1, i.e., MCS and RCS, switch installation constraint mathematic(al) representation cannot be installed simultaneously in the same switch installation site are as follows:
MCSa,b,0(x)+RCSa,b,0(x)≤1 (37)。
MCSa,b,1(x)+RCSa,b,1(x)≤1
The present invention proposes a kind of optimal configuration method of distribution system switch based on Boolean type variable.Sample calculation analysis table
Bright, the optimal configuration method of the distribution system switch based on Boolean type variable all has good adaptation to radiation type distribution network
Property, while section locating accuracy is considered, it is more in line with the actual conditions of distribution system.Simulation example demonstrates proposed method
With good solution efficiency and very high computational efficiency, it is suitable for the application of large-scale distribution network network.
Detailed description of the invention
Fig. 1 is a kind of allocation optimum model flow figure of distribution system switch based on Boolean type variable.
Fig. 2 is the structure chart of two sections of distribution feeders.
Fig. 3 is the structure chart of three sections of distribution feeders.
Fig. 4 is failure load relative position relation figure.
Fig. 5 is fault type schematic diagram.
Fig. 6 is switch allocation optimum result schematic diagram.
Fig. 7 is this allocation models cost curve figure.
Fig. 8 is comparison cost curve figure.
Fig. 9 is fault section location accuracy rate curve.
Specific embodiment
To keep the purposes, technical schemes and advantages of the invention implemented clearer, below in conjunction in the embodiment of the present invention
Attached drawing, technical solution in the embodiment of the present invention is further described in more detail.In the accompanying drawings, identical from beginning to end or class
As label indicate same or similar element or element with the same or similar functions.Described embodiment is the present invention
A part of the embodiment, instead of all the embodiments.The embodiments described below with reference to the accompanying drawings are exemplary, it is intended to use
It is of the invention in explaining, and be not considered as limiting the invention.Based on the embodiments of the present invention, ordinary skill people
Member's every other embodiment obtained without creative efforts, shall fall within the protection scope of the present invention.
As shown in Figure 1, a kind of configuration method of the distribution system switch based on Boolean type variable, the distribution system switch
Configuration method the following steps are included:
Step 1: in the case where distribution system switch configuration x is determined, in order to indicate on some position or certain sections
The switch existence in face introduces Boolean type expression formula, when Boolean type transition formula evaluation is 1, indicates that the position or the section are deposited
In corresponding switch, when Boolean type transition formula evaluation is 0, indicate that corresponding switch is not present；
The step 1 specifically includes the following steps:
Step 1.1: it is firstly introduced into 4 first kind Boolean type expression formulas:
Wherein 0 and 1 is left and right identifier, and 0 represents left end, and 1 represents right end, two first kind Boolean type expression in formula (1)
Formula respectively indicates the manual switch existence of b sections of feeder line section end left ends and right end on a articles feeder line, two in formula (2)
A kind of Boolean type expression formula, which respectively indicates the automatic switch of b sections of feeder line section end left ends and right end on a articles feeder line, to be existed
Property；
Step 1.2: following 6 the second class Boolean type expression formulas are built by first kind Boolean type expression formula:
In formula (3) two the second class Boolean type expression formulas respectively indicate on a articles feeder line b sections of feeder line section end left ends with
The block switch existence of right end, expression are respectively formula (6) and (7):
Two the second class Boolean type expression formulas respectively indicate the load at b sections of feeder line section ends on a articles feeder line in formula (4)
To the existence of manual segmentation switch and automatic section switch between jth section feeder line section, the expression of manual switch are as follows:
Two the second class Boolean type expression formulas respectively indicate a articles manual interconnection switch of feeder terminal and automatic in formula (5)
The existence of interconnection switch, the expression of manual switch are as follows:
TMa(x)=MCSa,ae,1(x) (9)
Wherein ae represents the final stage of a articles feeder line；
Step 1.3: 2 third class Boolean type expression formulas are built by the second class Boolean type expression formula of step 1.2:
WhereinIndicate the loads of b sections of feeder line section ends on a articles feeder line to point between jth section feeder line section
Duan Kaiguan existence, expression are as follows:
Ta(x) existence of a articles feeder terminal interconnection switch, expression are indicated are as follows:
Step 1.4: the Fault Isolation function of time being built by third class Boolean type expression formula, control centre is in positioning failure
Pass through the corresponding block switch of operation after section and failure is isolated with the load of healthy section, the Fault Isolation time is that segmentation is opened
Actuation time is closed, when there are block switches between failure and load, and at least one automatic section switch, then Fault Isolation time
It is otherwise the manual segmentation switch motion time to be automatically switched actuation time, Fault Isolation function of time formula (13) are as follows:
tisoIt (x) is Fault Isolation time, tisoIt (x) is Fault Isolation time, tSRTo be automatically switched actuation time, tSMFor
Manual segmentation switch motion time, p are that automatic section switch correctly acts probability；
Step 1.5: interconnection switch actuation time correctly acts probability according to the type and automatic interconnection switch of interconnection switch,
Interconnection switch actuation time function, formula are built by third class Boolean type expression formula are as follows:
ttieIt (x) is interconnection switch actuation time, q is that automatic interconnection switch correctly acts probability.
Step 2: fault section location accuracy rate is introduced based on step 1；
After breaking down in distribution system, for breaker because of fault current tripping, whole system enters power failure.
Fault section is positioned first at this time, automatic section switch can carry out remote control isolation according to fault location information,
But manual switch is due to that can not pass information back, it is therefore desirable to which artificial line walking finds failure physical location, then carries out manual switch
Operation, finally by breaker be overlapped again or the movement of interconnection switch is to realizing restoring electricity for non-faulting section.
The positioning accuracy of fault section can directly influence the power off time of non-faulting section by the line walking time.And pass through installation segmentation
Switch, then can raising positioning accuracy to a certain extent.
As shown in Fig. 2, being the typical structure of distribution feeder in figure, for the convenience of description, the feeder line 1 is set as two
Section.Wherein the leftmost side is breaker.Paragraph 1 feeder line section end two sides have filled manual segmentation switch and automatic section switch respectively,
2nd section of feeder line section end two sides have filled manual segmentation switch and automatic interconnection switch respectively.
Minimum fault section is defined as to the section of the nearest block switch composition in failure two sides first, it can by dividing
The section that Duan Kaiguan is isolated.It is opened according to the characteristic that distribution system is automatically switched if there is fault current flows through automatic switch
Pass will return to fault-signal.For failure in case of in the 2nd feeder line section, No. 2 switches return to fault-signal, 1,3, No. 4 switch
Fault-signal is not returned to, operation center can positioning failure section be in second segment in time, to be rapidly performed by minimum faulty section
The isolation of section reduces the power off time of non-faulting section.
The step 2 specifically includes the following steps:
Step 2.1: introducing Boolean type expression formula γa,b(x), it indicates in the case where distribution system switch configuration x is determined,
The distribution system switch existence of the upper b sections of ends two sides feeder line a, γa,b(x) value is 1, indicates that this section of end at least has one
A switch, γa,b(x) value is 0, indicates that switch, Boolean type expression formula γ is all not present in this section of end two sidesa,b(x) it embodies
Formula are as follows:
Step 2.2: using Boolean variable μa,b(x) the fault section localizability of upper b sections of the failure of feeder line a, boolean are indicated
Variable μa,b(x) value is 1, is indicated if faulty occur to pass through the signal framing of block switch to the section, boolean in the section
Variable μa,b(x) value is 0, and expression cannot navigate to the section, using breaker as the 0th section, γa,0(x) be 1, feeder line last
The switch fault electric current of section end two sides does not flow through, Boolean variable μa,b(x) expression are as follows:
Wherein, Ωa,sRepresent the feeder line section set of a articles feeder line；
Step 2.3: defining the fault section location accuracy rate o (x) of a articles feeder line, expression formula are as follows:
Wherein, Na,sFor the quantity of feeder line section on feeder line a；
Step 2.4: failure definition positioning time tins(x) calculation are as follows:
tloc(x)=tbasis+(1-η(x))×tdefult (19)。
Wherein tbasisIt is related with the average length of the every section feeder line section of power distribution network for the basic line walking time；tdefultFor default event
Hinder the line walking time in section, it is related with the complexity of power distribution network.In the more power distribution network default fault section of feeder line section when line walking
Between it is longer.
The configuring condition of the switch of feeder line 2 is as shown in figure 3, wherein the 2nd section of end two sides are fitted without switch, by Shi Ke get
Fault section location accuracy rate η (x)=66.7% of the feeder line, line walking time t in fault sectionins(x)=tdefault/3.Such as
Fruit installs switch at block switch installation position candidate 3 or 4, can be with fault section location accuracy rate promotion to 1, fault section
Positioning time is reduced to tbasis.Therefore, it can be seen that can be by installing more automatic section switches, to improve faulty section
Section locating accuracy reduces the line walking time in fault section, finally improves power supply reliability.
Step 3: it is negative that the Boolean type expression formula and fault section location accuracy rate introduced by step 1 and 2 builds failure
Lotus power off time function.
After distribution system breaks down, minimum fault section is isolated by positioning failure section in main website, breaker or
The a series of measures such as person's interconnection switch coincidence restore the power supply of non-faulting section.Herein from the relative position of failure and load
Relationship is set out, and fault type is divided into 6 classes, is then discussed one by one, and as shown in figs. 4 and 5, wherein Fig. 5 selectes load to 6 class failures
Feeder line L2,2,1Then failure modes are carried out to the failure of different location, and is marked by arrow and illustrates different fault types.Cause
It can be obviously improved by configuring distribution system switch for load power off time caused by the 3rd class and the 5th class failure, therefore emphatically
These two types of failures are discussed.
The step 3 specifically includes the following steps:
Step 3.1: the failure load power off time functionIn the feelings that distribution system switch configuration x is determined
Under condition, whole loads of the c articles branch feeder of b sections of feeder line section ends are because on i-th article of feeder line on a articles feeder line of power distribution network
Power off time caused by the kth of jth section feeder line ' a equivalent position failure, wherein k ' is according to the difference of abort situation, and kth '
The expression formula of a equivalent position are as follows:
Set 9 kinds of scenes:
Step 3.2: defining the corresponding load power off time of first kind failure, expression formula is formula (21), failure and negative
Lotus is located at same feeder line, and failure occurs on branch feeder, and load and failure are located at same branch feeder.Due to fusing
The presence of device, fault section will be isolated by the fusing of fuse with the load of other branch feeders on the feeder line, will not be right
It is impacted, while obtaining fault section information.Therefore failure-load power off time is fault correction time trepWith open circuit
Device time of coincidence tCBThe sum of:
Step 3.3: defining the corresponding load power off time of the second class failure is 0, and expression formula is formula (22), failure
Be located above same feeder line with load, failure occur on branch feeder, but load from failure in different branch feeders.Due to
The presence of fuse, failure will not impact other loads, while obtain fault section information, therefore failure-load stops
The electric time 0:
Step 3.4: defining the corresponding load power off time of third class failure, expression formula is formula (23), failure and negative
Lotus is located above same feeder line, and failure occurs in feeder line section, and the feeder line section upstream where load occurs for failure.Healthy section
Load after fault section location, if there are any type of block switches between load and failure, and the feeder line end
There are any type of interconnection switches at end, then load can be acted after fault section location by block switch, and contact is opened
Pass movement etc. and replys power supply at a series of measures isolated fault, therefore failure-load power off time is fault section location
Time, the Fault Isolation time, interconnection switch actuation time and.Otherwise failure-load power off time is the fault section location time,
Fault correction time, the sum of breaker actuation time:
Step 3.5: defining the corresponding load power off time of the 4th class failure, expression formula is formula (24), failure and negative
Lotus is located above same feeder line, and failure occurs in feeder line section, and the feeder line section itself where load occurs for failure.Failure can not
It is isolated by block switch, therefore failure-load power off time is fault section location time, fault correction time, breaker
The sum of time of coincidence:
Step 3.6: define the corresponding load power off time of the 5th class failure, expression formula is formula (25) and (26), therefore
Barrier is not with load on same feeder line, and due to the presence of breaker, failure will pass through the tripping of breaker and other feedbacks
The load of line is isolated, and will not be impacted to the load of other feeder lines.Failure-load power off time is 0:
Step 4: with reliability index of powering for constraint, Custom interruption cost and switchgear distribution Life cycle are taken for building
With the sum of minimum and target distribution system switch allocation optimum model, solved by solver.
In power distribution network, the purpose of configuration is optimized generally by determining block switch and connection to distribution system switch
The type of network switch, position and quantity, under the premise of meeting distribution network reliability requirement, so that comprehensive cost is minimum.It is comprehensive
Conjunction expense, that is, distribution system switch life cycle cost and Custom interruption cost expense, wherein distribution system switch life cycle is taken
With the switch maintenance cost being divided into switch investment cost and service life again.
The step 4 specifically includes the following steps:
Step 4.1: building allocation optimum model is averagely stopped with the minimum target of comprehensive cost with average power supply reliability
The scarce power supply volume of electricity and switch installation are limited to constraint condition, construct the allocation optimum model of distribution system switch, the model of building
Are as follows:
Wherein, Cost (x) is comprehensive cost；ASAI (x) is average power supply reliability；AENS (x) is that average have a power failure lacks confession
Electricity, NaFor whole feeder line set, Na,bFor feeder line section set whole on feeder line a；
Step 4.2: building comprehensive cost, the mathematic(al) representation of comprehensive cost Cost (x) are as follows:
Cost (x)=LCC (x)+CIC (x) (28)
Wherein, LCC (x) is switch whole life costing, and CIC (x) is Custom interruption cost expense；
Step 4.3: building constraint function expression formula.
Preferably, the mathematic(al) representation of step 4.2 switch whole life costing LCC (x) are as follows:
LCC (x)=INV (x)+MAI (x) (29)
Wherein, INV (x) is switch investment cost, and MAI (x) is switch maintenance cost.
Preferably, switch investment cost INV (x) includes the buying expenses and mounting cost of switch, formula are as follows:
WhereinInvestment cost is switched for manual segmentation,For automatic section switch capital cost
With,For manual interconnection switch investment cost,For automatic interconnection switch investment cost, divide manually
The expression formula of Duan Kaiguan investment cost and manual interconnection switch investment cost is respectively as follows:
Preferably, the annual operating maintenance expense of switchgear is set as the ratio of investment cost, time limit ΩtIt is opened described in interior
Close the formula of maintenance cost MAI (x) are as follows:
Wherein d is discount rate, and μ is the ratio of maintenance cost and investment cost.
Preferably, in the step 4.2 Custom interruption cost expense CIC (x) formula are as follows:
Wherein ΩiSet for the feeder line that may be broken down；Ωi,jFor the feeder line section collection that may be broken down on feeder line i
It closes；Ωi,j,k′For the position of fault set that i jth section may break down on feeder line；λi,j,k′It breaks down for the place general
Rate；ΩnFor the set of different user types；Represent the n-th class on a articles feeder line, the c articles branch feeder of b sections of feeder line sections
The load of load；M is the annual growth of load；
Correspond to failure load power off time for the n-th type load type's
Loss function.
Preferably, the step 4.3 building constraint function expression formula includes: to construct average power supply reliability constraint expression
Formula, build it is average have a power failure lack power supply volume constraint and build switch installation constraint；
Average power supply reliability constraint expression formula is constructed, the average power supply reliability ASAI (x) of distribution system is not less than it
Threshold value A SAIlim, average power supply reliability constraint mathematic(al) representation are as follows:
ASAI(x)≥ASAIlim
Wherein Na,cFor the number of users on feeder line a, NcFor the number of users of whole system.
It builds average have a power failure and lacks power supply volume constraint, the average power failure of distribution system lacks power supply volume AENS (x) and is not higher than its threshold
Value AENSlim, the average scarce power supply volume constraint mathematic(al) representation that has a power failure are as follows:
AENS(x)≤AENSlim
Switch installation constraint is built, for the switch installation site of each candidate, the switch variety installed cannot be greater than
1, i.e., MCS and RCS, switch installation constraint mathematic(al) representation cannot be installed simultaneously in the same switch installation site are as follows:
MCSa,b,0(x)+RCSa,b,0(x)≤1 (37)。
MCSa,b,1(x)+RCSa,b,1(x)≤1
Solution strategies, the present invention mathematically belong to 0-1 nonlinear programming problem, are suitable for this solution of localsolver
The outstanding mathematical software of large-scale complex mathematical problem is solved using local search algorithm.
In another embodiment: mentioned method being tested on IEEE RBTS-BUS4 power distribution network. IEEE RBTS-
BUS4 power distribution network is an intermediate distribution system, there is 38 load bus, 4779 family users, and overall average load is 24.58MW.It surveys
In examination, parameter setting is as follows: the investment cost of automatic section switch and manual segmentation switch is respectively 3000 dollars, 17000 beauty
The investment cost of member, automatic interconnection switch and manual interconnection switch is respectively 4000 dollars and 18000 dollars.Switch annual fortune
Row maintenance cost is the 5% of investment cost, and research is limited to 5 years in year, Annual Percentage Rate 5%, and load annual growth is 2%.Automatic point
Duan Kaiguan, automatic interconnection switch, manual segmentation switch, the actuation time of manual interconnection switch is 300 seconds respectively, 600 seconds, 3600
Second, 7200 seconds.Mean Time To Repair is 14400 seconds.The breaker actuation time is 300 seconds.Defaulting fault location time is
1800 seconds.The regular event probability 0.999 of automatic section switch, the regular event probability of automatic interconnection switch are 0.99.This is
The reliability index bound of one's last year is respectively as follows: in the research time limit
Select reliability index threshold value A SAIlim,AENSlimRespectively 99.96%, 30 (kWh)/(family a)
Problem above is solved using the second class failure corresponding load power off time of model proposed by the present invention.
Optimal FTU allocation plan is as shown in fig. 6, including 7 automatic interconnection switchs, 11 automatic section switches and 23 hands
Dynamic block switch.
In the above distribution system switch allocation optimum scheme, reliability index ASAI (x) is 99.965%, fault section
The maximum value that registration rate η (x) is 93.10%, AENS (x) is 22.37 (kW h)/(family a).Comprehensive cost Cost
It (x) is 5131446 dollars, wherein switch whole life costing LCC (x) is 529485 dollars, user supply interruption cost CIC (x)
It is 4601961 dollars.
In order to further illustrate the reasonability of the distribution system switch allocation optimum model proposed, construction following two right
Than scheme:
(1) scheme 1, consider fault location accuracy rate, with the allocation plan of the minimum target of comprehensive cost, i.e., set forth herein
Model；
(2) scheme 2 do not consider fault location accuracy rate, with the allocation plan of the minimum target of comprehensive cost；
(3) scheme 3 do not consider fault location accuracy rate, with the allocation plan of the minimum target of Custom interruption cost；
(4) scheme 4 do not consider fault location accuracy rate, to switch the allocation plan of the minimum target of Life cycle.
Constraint condition is identical in 4 schemes.Table 1 gives the corresponding switch number of above 4 kinds of allocation plans, average power supply
Reliability index, average scarce power supply figureofmerit, comprehensive cost, switch life cycle cost and the Custom interruption cost of having a power failure take
With.
The comparison of 1. 4 kinds of table solution schemes
Such as draw a conclusion as can be drawn from Table 1.
(1) scheme 2 is compared to scheme 1, and average power supply reliability few 0.05%, average have a power failure lacks power supply volume more 18%, comprehensive
Conjunction expense increases 6.03%, is inferior to scheme 1 comprehensively.
(2) the Custom interruption cost expense of scheme 3 is minimum.This is because scheme 3 increases largely automatically compared to scheme 1
And block switch；Thus cause scheme 3 bigger by 159.94% than the switch life cycle cost of scheme 1, in terms of comprehensive cost,
Scheme 3 is than scheme 1 big 17.96%.
(3) the switch life cycle cost of scheme 4 is minimum.This is because scheme 4 reduces largely automatically compared to scheme 1
And block switch；Thus cause scheme 4 bigger than the interruption cost of scheme 1 by 51.45%, in terms of comprehensive cost, side 43 compares
Scheme 1 big 28.83%.
(4) scheme 1 has taken into account switch life cycle cost and Custom interruption cost expense, has reached comprehensive cost most
It is small, while the optimization of fault section location time is considered, it is optimal allocation plan.
Further by the way that different average power supply reliability threshold values is arranged, difference is obtained using model solution proposed in this paper
The fault section location accuracy rate of allocation plan, average have a power failure lack power supply volume, number of switches and all kinds of expenses.
Fig. 7 gives average power supply reliability and interruption cost, switchs life cycle cost and comprehensive cost
Relationship.
It can be seen that when section of the average power supply reliability in 99.84%-99.92%, with the increase of number of switches,
Interruption cost is close to a linear downward trend.
When section of the average power supply reliability in 99.92%-99.98%, interruption cost downward trend is gradually
Slow down, then illustrates entirely fewer and fewer by increasing the power off time that the switch of distribution system reduces.
When section of the average power supply reliability in 99.98%-99.99%, although interruption cost still exists at this time
Decline, but the number of switches of entire distribution system installation is close to saturation at this time, by having increased the switch of distribution system on a small quantity
Through power off time cannot be obviously improved, at this time with the growth of average power supply reliability, need that switch is largely installed, so that this
When switch whole life costing and comprehensive cost curve present an ascendant trend.The evidence of Fig. 7 and Fig. 8 also obviously
The situation.
Shown in Fig. 9, can be seen that model proposed in this paper by above simulation analysis can take into account economy and can
While by property, distribution system switch quantity is provided, the configuration scheme of position and type sufficiently improves the use effect of fund
Rate.
Finally it is noted that the above embodiments are merely illustrative of the technical solutions of the present invention, rather than its limitations.To the greatest extent
Present invention has been described in detail with reference to the aforementioned embodiments for pipe, those skilled in the art should understand that: it is still
It is possible to modify the technical solutions described in the foregoing embodiments, or part of technical characteristic is equally replaced
It changes；And these are modified or replaceed, the essence for technical solution of various embodiments of the present invention that it does not separate the essence of the corresponding technical solution
Mind and range.
Claims (10)
1. a kind of configuration method of the distribution system switch based on Boolean type variable, which is characterized in that the distribution system switch
Configuration method the following steps are included:
Step 1: in the case where distribution system switch configuration x is determined, in order to indicate above some position or certain sections
Existence is switched, Boolean type expression formula is introduced, when Boolean type transition formula evaluation is 1, indicates the position or section presence pair
The switch answered when Boolean type transition formula evaluation is 0 indicates that corresponding switch is not present；
Step 2: fault section location accuracy rate is introduced based on step 1；
Step 3: the Boolean type expression formula and fault section location accuracy rate introduced by step 1 and 2 is built failure load and is stopped
The electric function of time；
Step 4: building with reliability index of powering for constraint, Custom interruption cost and switchgear distribution whole life costing it
With minimum and target distribution system switch allocation optimum model, solved by solver.
2. the configuration method of the distribution system switch according to claim 1 based on Boolean type variable, it is characterised in that: institute
State step 1 specifically includes the following steps:
Step 1.1: it is firstly introduced into 4 first kind Boolean type expression formulas:
Wherein 0 and 1 is left and right identifier, and 0 represents left end, and 1 represents right end, two first kind Boolean type expression formulas point in formula (1)
The manual switch existence of b sections of feeder line section end left ends and right end on a articles feeder line, two first kind in formula (2) are not indicated
Boolean type expression formula respectively indicates the automatic switch existence of b sections of feeder line section end left ends and right end on a articles feeder line；
Step 1.2: following 6 the second class Boolean type expression formulas are built by first kind Boolean type expression formula:
Two the second class Boolean type expression formulas respectively indicate b sections of feeder line section end left ends and right end on a articles feeder line in formula (3)
Block switch existence, expression is respectively formula (6) and (7):
Two the second class Boolean type expression formulas respectively indicate the load at b sections of feeder line section ends on a articles feeder line in formula (4)
The existence of manual segmentation switch and automatic section switch, the expression of manual switch between j sections of feeder line sections are as follows:
Two the second class Boolean type expression formulas respectively indicate a articles manual interconnection switch of feeder terminal and automatic contact in formula (5)
The existence of switch, the expression of manual switch are as follows:
TMa(x)=MCSa,ae,1(x) (9)
Wherein ae represents the final stage of a articles feeder line；
Step 1.3: 2 third class Boolean type expression formulas are built by the second class Boolean type expression formula of step 1.2:
WhereinIndicate that the load of b sections of feeder line section ends on a articles feeder line is opened to the segmentation between jth section feeder line section
Close existence, expression are as follows:
Ta(x) existence of a articles feeder terminal interconnection switch, expression are indicated are as follows:
Step 1.4: the Fault Isolation function of time being built by third class Boolean type expression formula, control centre is in positioning failure section
Failure is isolated with the load of healthy section by operating corresponding block switch later, the Fault Isolation time is dynamic for block switch
Make the time, when there are block switches between failure and load, and at least one automatic section switch, then the Fault Isolation time be from
The dynamic switch motion time, is otherwise the manual segmentation switch motion time, Fault Isolation function of time formula (13) are as follows:
tisoIt (x) is Fault Isolation time, tisoIt (x) is Fault Isolation time, tSRTo be automatically switched actuation time, tSMTo divide manually
Section switch motion time, p are that automatic section switch correctly acts probability；
Step 1.5: interconnection switch actuation time correctly acts probability according to the type and automatic interconnection switch of interconnection switch, passes through
Third class Boolean type expression formula builds interconnection switch actuation time function, formula are as follows:
ttieIt (x) is interconnection switch actuation time, q is that automatic interconnection switch correctly acts probability.
3. the configuration method of the distribution system switch according to claim 1 based on Boolean type variable, it is characterised in that: institute
State step 2 specifically includes the following steps:
Step 2.1: introducing Boolean type expression formula γa,b(x), it indicates in the case where distribution system switch configuration x is determined, feeder line a
The distribution system switch existence of upper b sections of ends two sides, γa,b(x) value is 1, indicates that this section of end at least has one and open
It closes, γa,b(x) value is 0, indicates that switch, Boolean type expression formula γ is all not present in this section of end two sidesa,b(x) expression are as follows:
Step 2.2: using Boolean variable μa,b(x) the fault section localizability of upper b sections of the failure of feeder line a, Boolean variable are indicated
μa,b(x) value is 1, is indicated if faulty occur to pass through the signal framing of block switch to the section, Boolean variable in the section
μa,b(x) value is 0, and expression cannot navigate to the section, using breaker as the 0th section, γa,0It (x) is 1, feeder line final stage end
The switch fault electric current of tail two sides does not flow through, Boolean variable μa,b(x) expression are as follows:
Wherein, Ωa,sRepresent the feeder line section set of a articles feeder line；
Step 2.3: defining the fault section location accuracy rate o (x) of a articles feeder line, expression formula are as follows:
Wherein, Na,sFor the quantity of feeder line section on feeder line a；
Step 2.4: failure definition positioning time tins(x) calculation are as follows:
tloc(x)=tbasis+(1-η(x))×tdefult (19)。
4. the configuration method of the distribution system switch according to claim 1 based on Boolean type variable, it is characterised in that: institute
State step 3 specifically includes the following steps:
Step 3.1: the failure load power off time functionIn the case where distribution system switch configuration x is determined,
Whole loads of the c articles branch feeder of b sections of feeder line section ends are because of jth section on i-th article of feeder line on a articles feeder line of power distribution network
Power off time caused by the kth of feeder line ' a equivalent position failure, wherein k ' is according to the difference of abort situation, and kth ' a etc.
Imitate the expression formula of position are as follows:
Step 3.2: the corresponding load power off time of first kind failure is defined, expression formula is formula (21):
Step 3.3: defining the corresponding load power off time of the second class failure is 0, and expression formula is formula (22):
Step 3.4: the corresponding load power off time of third class failure is defined, expression formula is formula (23):
Step 3.5: the corresponding load power off time of the 4th class failure is defined, expression formula is formula (24):
Step 3.6: the corresponding load power off time of the 5th class failure is defined, expression formula is formula (25) and (26):
5. the configuration method of the distribution system switch according to claim 1 based on Boolean type variable, it is characterised in that: institute
State step 4 specifically includes the following steps:
Step 4.1: building allocation optimum model, with the minimum target of comprehensive cost, with average power supply reliability, average have a power failure is lacked
Power supply volume and switch installation are limited to constraint condition, construct the allocation optimum model of distribution system switch, the model of building are as follows:
Wherein, Cost (x) is comprehensive cost；ASAI (x) is average power supply reliability；AENS (x) is that average have a power failure lacks power supply volume,
NaFor whole feeder line set, Na,bFor feeder line section set whole on feeder line a；
Step 4.2: building comprehensive cost, the mathematic(al) representation of comprehensive cost Cost (x) are as follows:
Cost (x)=LCC (x)+CIC (x) (28)
Wherein, LCC (x) is switch whole life costing, and CIC (x) is Custom interruption cost expense；
Step 4.3: building constraint function expression formula.
6. the configuration method of the distribution system switch according to claim 5 based on Boolean type variable, it is characterised in that: institute
State the mathematic(al) representation of step 4.2 switch whole life costing LCC (x) are as follows:
LCC (x)=INV (x)+MAI (x) (29)
Wherein, INV (x) is switch investment cost, and MAI (x) is switch maintenance cost.
7. efficient industrial afterheat recovery varying duty water chiller-heater unit according to claim 6, it is characterised in that: the switch
Investment cost INV (x) includes the buying expenses and mounting cost of switch, formula are as follows:
WhereinInvestment cost is switched for manual segmentation,For automatic section switch investment cost,For manual interconnection switch investment cost,For automatic interconnection switch investment cost, manual segmentation
The expression formula of switch investment cost and manual interconnection switch investment cost is respectively as follows:
8. efficient industrial afterheat recovery varying duty water chiller-heater unit according to claim 6, it is characterised in that: switchgear
Annual operating maintenance expense is set as the ratio of investment cost, time limit ΩtThe formula of interior switch maintenance cost MAI (x)
Are as follows:
Wherein d is discount rate, and μ is the ratio of maintenance cost and investment cost.
9. efficient industrial afterheat recovery varying duty water chiller-heater unit according to claim 5, it is characterised in that: the step
The formula of Custom interruption cost expense CIC (x) in 4.2 are as follows:
Wherein ΩiSet for the feeder line that may be broken down；Ωi,jFor the feeder line section set that may be broken down on feeder line i；
Ωi,j,k′For the position of fault set that i jth section may break down on feeder line；λi,j,k′The probability to break down for the place；
ΩnFor the set of different user types；Represent the n-th type load on a articles feeder line, the c articles branch feeder of b sections of feeder line sections
Load；M is the annual growth of load；
Correspond to failure load power off time for the n-th type load typeLoss
Function.
10. efficient industrial afterheat recovery varying duty water chiller-heater unit according to claim 5, it is characterised in that: the step
Rapid 4.3 building constraint function expression formula includes: to construct average power supply reliability constraint expression formula, build the average scarce power supply volume that has a power failure
Constrain and build switch installation constraint；
Average power supply reliability constraint expression formula is constructed, the average power supply reliability ASAI (x) of distribution system is not less than its threshold value
ASAIlim, average power supply reliability constraint mathematic(al) representation are as follows:
ASAI(x)≥ASAIlim
Wherein Na,cFor the number of users on feeder line a, NcFor the number of users of whole system.
It builds average have a power failure and lacks power supply volume constraint, the average power failure of distribution system lacks power supply volume AENS (x) and is not higher than its threshold value
AENSlim, the average scarce power supply volume constraint mathematic(al) representation that has a power failure are as follows:
AENS(x)≤AENSlim
Switch installation constraint is built, for the switch installation site of each candidate, the switch variety installed cannot be greater than 1, i.e.,
MCS and RCS, switch installation constraint mathematic(al) representation cannot be installed simultaneously in the same switch installation site are as follows:
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| CN104484712A (en) * | 2014-11-24 | 2015-04-01 | 国家电网公司 | Optimization configuration method for three-remote power distribution terminal |
| CN106022971A (en) * | 2016-06-27 | 2016-10-12 | 国网山东省电力公司青岛供电公司 | Method and device for selecting power distribution network power supply reliability enhancement scheme |
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| CN112766738B (en) * | 2021-01-21 | 2022-08-09 | 三峡大学 | Optimal configuration method for distribution network automation terminal |
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