CN109768529B - Boolean variable-based configuration method for power distribution system switch - Google Patents

Boolean variable-based configuration method for power distribution system switch Download PDF

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CN109768529B
CN109768529B CN201910085866.XA CN201910085866A CN109768529B CN 109768529 B CN109768529 B CN 109768529B CN 201910085866 A CN201910085866 A CN 201910085866A CN 109768529 B CN109768529 B CN 109768529B
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feeder
fault
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CN109768529A (en
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陈艳波
陈锐智
陈浩
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North China Electric Power University
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Abstract

The invention discloses a method for configuring a power distribution system switch based on Boolean type variables, which comprises the following steps: step 1: in the case of the switch configuration x of the power distribution system, in order to indicate the existence of a switch on a certain position or a certain section, introducing a Boolean expression, when the value of the Boolean expression is 1, indicating that the corresponding switch exists on the position or the section, and when the value of the Boolean expression is 0, indicating that the corresponding switch does not exist; step 2: introducing fault section positioning accuracy based on the step 1; and step 3: establishing a fault load power failure time function through a Boolean expression introduced in the steps 1 and 2 and the fault section positioning accuracy; and 4, step 4: and constructing a power distribution system switch optimal configuration model with the minimum sum of power supply reliability index as constraint, user power failure loss and switch configuration full life cycle cost and a target, and solving through a solver.

Description

Boolean variable-based configuration method for power distribution system switch
Technical Field
The invention relates to the technical field of power distribution automation of a power system, in particular to a method for configuring a power distribution system switch based on a Boolean type variable.
Background
The power supply reliability of the distribution network is increasingly demanded by electric power companies. The power distribution system is composed of a series of components that may fail, and how to reduce the outage time and loss caused by the failure of these components is a major concern for power companies. After the fault section is determined, the power distribution system switch can isolate the fault section and recover the power supply of the healthy section, so that the power supply reliability is effectively improved. The more power distribution system switches, the faster the fault zone can be located and isolated. However, with the increase of the number of switches of the power distribution system, the investment cost also increases, and how to determine the optimal switch configuration of the power distribution system makes the power failure loss and the full life cycle cost of the switch configuration the lowest under the condition of meeting the requirement of power supply reliability is a hot topic of the current domestic and international Distribution Automation (DA) research.
It was proposed earlier that the fault isolation time and the power restoration time can be shortened by installing a Remote-Controlled switch (RCS), thereby improving the power supply reliability of the entire power distribution network. Then, the manual switch and the automatic switch are distinguished through capacity, a user power failure time function is introduced, and a switch configuration model with the minimum power failure loss and configuration cost is constructed under the constraint of ensuring power supply reliability. The above are significant works, but the contribution of the configuration positions and the number of the switches of the power distribution system to the positioning of the fault section cannot be accurately measured, and the accurate positioning of the fault section of the power distribution network is not facilitated.
It is therefore desirable to have a method for configuring a power distribution system switch based on boolean variables that effectively addresses the problems of the prior art.
Disclosure of Invention
The invention discloses a method for configuring a power distribution system switch based on Boolean type variables, which comprises the following steps:
step 1: in the case of the switch configuration x of the power distribution system, in order to indicate the existence of a switch on a certain position or a certain section, introducing a Boolean expression, when the value of the Boolean expression is 1, indicating that the corresponding switch exists on the position or the section, and when the value of the Boolean expression is 0, indicating that the corresponding switch does not exist;
the step 1 specifically comprises the following steps:
step 1.1: first, 4 first-type boolean expressions are introduced:
Figure GDA0002776747200000021
Figure GDA0002776747200000022
wherein 0 and 1 are left and right identifiers, 0 represents a left end, 1 represents a right end, two first-type boolean expressions in formula (1) respectively represent the manual switch existence of the left end and the right end of the tail of the b-th feeder segment on the a-th feeder, and two first-type boolean expressions in formula (2) respectively represent the automatic switch existence of the left end and the right end of the tail of the b-th feeder segment on the a-th feeder;
step 1.2: and building the following 6 second-type Boolean expressions from the first-type Boolean expressions:
Figure GDA0002776747200000023
Figure GDA0002776747200000024
Figure GDA0002776747200000025
two boolean expressions of a second type in the expression (3) respectively represent the existence of the section switches at the left end and the right end of the tail of the section b of the feeder line on the section a, and the specific expressions are respectively the expressions (6) and (7):
Figure GDA0002776747200000026
Figure GDA0002776747200000027
two Boolean-type expressions of a second kind in the expression (4) respectively represent the existence of a manual section switch and an automatic section switch between a load at the end of a b-th section feeder line section and a j-th section feeder line section on an a-th feeder line, and the specific expression of the manual switch is as follows:
Figure GDA0002776747200000031
Figure GDA0002776747200000032
Figure GDA0002776747200000033
in the formula (5), two boolean expressions of a second type respectively represent the existence of a manual interconnection switch and an automatic interconnection switch at the end of the a-th feeder line, and the specific expressions of the manual switch are as follows:
TMa(x)＝MCSa,ae,1(x) (9)
wherein ae represents the last segment of the a-th feeder line;
step 1.3, building 2 third Boolean expressions according to the second Boolean expression in the step 1.2:
Figure GDA0002776747200000034
wherein
Figure GDA0002776747200000041
The presence of a section switch from the load at the tail end of the b-th section feeder line section on the a-th feeder line to the j-th section feeder line section is represented by the following specific expression:
Figure GDA0002776747200000042
Ta(x) The existence of a connection switch at the end of the a-th feeder line is represented by the following specific expression:
Figure GDA0002776747200000043
step 1.4: establishing a fault isolation time function through a third type Boolean expression, isolating the load of the fault section from the load of the healthy section by operating a corresponding section switch by a control center after the fault section is positioned, wherein the fault isolation time is section switch action time, when the section switch exists between the fault section and the load and at least one automatic section switch exists, the fault isolation time is automatic switch action time, otherwise, the fault isolation time is manual section switch action time, and a fault isolation time function formula (13) is as follows:
Figure GDA0002776747200000044
tiso(x) For fault isolation time, tSRWhen actuated by automatic switchM, tSMThe action time of the manual section switch is used, and p is the correct action probability of the automatic section switch;
step 1.5: and establishing an action time function of the interconnection switch through a third type of Boolean expression according to the type of the interconnection switch and the correct action probability of the automatic interconnection switch, wherein the formula is as follows:
Figure GDA0002776747200000045
ttie(x) For connecting the action time of the switch, q for the probability of correct action of the automatic connection switch, tTRFor automatic interconnection of switch actuation time, tTMIs the action time of the manual communication switch;
step 2: introducing fault section positioning accuracy based on the step 1;
and step 3: establishing a fault load power failure time function according to the Boolean expression introduced in the step 1 and the fault section positioning accuracy introduced in the step 2;
and 4, step 4: and constructing a power distribution system switch optimal configuration model with the power supply reliability index as constraint, the minimum sum of the power failure loss of a user and the total life cycle cost of switch configuration and the target, and solving through a solver.
Preferably, the step 2 specifically includes the following steps:
step 2.1: introducing a Boolean expression gammaa，b(x) Denotes the presence of distribution system switches on both sides of the end of the b-th section on the feeder a, gamma, in the case of a defined distribution system switch configuration xa，b(x) A value of 1, indicating the presence of at least one switch at the end of the segment, γa，b(x) A value of 0, indicating that there is no switch on either side of the end of the segment, a Boolean expression γa，b(x) The specific expression is as follows:
Figure GDA0002776747200000051
step 2.2: using the Boolean variable μa，b(x) Presentation feedFault zone location of fault in b-th section on line a, boolean variable mua，b(x) A value of 1, indicating that if a fault occurs in the zone, the boolean variable μ is located in the zone by the signal of the sectionalizera，b(x) A value of 0, indicating that the zone cannot be located, with the circuit breaker as stage 0, γa，0(x) 1, the switch fault current on both sides of the last section of the feeder line does not flow, and the Boolean variable mua，b(x) The specific expression is as follows:
Figure GDA0002776747200000052
Figure GDA0002776747200000053
wherein omegaa，sA set of feeder segments representing an a-th feeder;
step 2.3: defining the fault section positioning accuracy eta (x) of the a-th feeder line, wherein the expression is as follows:
Figure GDA0002776747200000054
wherein eta (x) is the fault section positioning accuracy of the a-th feeder line, Na，bThe number of feeder segments on the feeder a;
step 2.4 defining fault positioning time tloc(x) The calculation method is as follows:
tloc(x)＝tbasis+(1-η(x))×tdefult (19)
wherein t isbasisBased on the time of line patrol, tdefultThe line patrol time in the fault section is the default.
Preferably, the step 3 specifically includes the following steps:
step 3.1: said fault load blackout time function
Figure GDA0002776747200000055
Under the condition that the switch configuration x of the power distribution system is determined, the power failure time of all loads of a c-th branch feeder at the tail end of a b-th feeder section on an a-th feeder of the power distribution network is caused by the fault of a k ' equivalent position of a j-th feeder section on an ith feeder, wherein the k ' is different according to the fault position, and the expression of the k ' equivalent position is as follows:
Figure GDA0002776747200000061
step 3.2: defining the load power failure time corresponding to the first type of fault, wherein trepRepresenting the time of failure recovery, tCBRepresenting the reclosing time of the circuit breaker, the expression of which is formula (21):
Figure GDA0002776747200000062
and 3.3, defining the load power failure time corresponding to the second type of fault as 0, wherein the expression is a formula (22):
Figure GDA0002776747200000063
step 3.4, defining the load power failure time t corresponding to the third type of faultloc(x)、tiso(x)、ttie(x)、trep、tCBRespectively represent fault positioning time, fault isolation time, contact switch action time, fault repair time and circuit breaker coincidence time, and the expression is formula (23):
Figure GDA0002776747200000064
and 3.5, defining the load power failure time corresponding to the fourth type of fault, wherein the expression is a formula (24):
Figure GDA0002776747200000065
and 3.6, defining the load power failure time corresponding to the fifth type of fault, wherein the expressions are shown as formulas (25) and (26):
Figure GDA0002776747200000066
Figure GDA0002776747200000067
preferably, the step 4 specifically includes the following steps:
step 4.1, constructing an optimal configuration model, wherein the optimal configuration model of the switch of the power distribution system is constructed by taking the minimum comprehensive cost as a target and taking the average power supply reliability, the average power failure and power shortage amount and the switch installation limit as constraint conditions, and the constructed model is as follows:
an objective function: the min Cost (x) of the first sequence,
constraint conditions are as follows:
Figure GDA0002776747200000071
wherein cost (x) is the comprehensive cost; ASAI (x) is the average power supply reliability; AENS (x) for average outagelimIs AENS (x) corresponding threshold; ASAIlimRepresents the corresponding threshold value of ASAI (x); omega a is a set of all feeders; omegaa，bAll the feeder lines on the feeder line a are collected;
and 4.2, building comprehensive cost, wherein the mathematical expression of the comprehensive cost (x) is as follows:
Cost(x)＝LCC(x)+CIC(x) (28)
wherein, LCC (x) is the cost of the full life cycle of the switch, CIC (x) is the cost of the power failure loss of the user;
step 4.3: and constructing a constraint function expression.
Preferably, the step 4.2 switch full life cycle cost lcc (x) has the mathematical expression:
LCC(x)＝INV(x)+MAI(x) (29)
wherein INV (x) is the switch investment cost, and MAI (x) is the switch maintenance cost.
Preferably, the switch investment cost inv (x) includes a purchase cost and an installation cost of the switch, and is expressed by the following formula:
Figure GDA0002776747200000072
wherein
Figure GDA0002776747200000073
In order to save the investment cost of the manual section switch,
Figure GDA0002776747200000074
in order to automatically change the investment cost of the section switch,
Figure GDA0002776747200000075
in order to manually communicate the investment cost of the switch,
Figure GDA0002776747200000076
for the investment cost of the automatic interconnection switch, the expressions of the investment cost of the manual section switch and the investment cost of the manual interconnection switch are respectively as follows:
Figure GDA0002776747200000077
Figure GDA0002776747200000078
preferably, the annual operating maintenance costs of the switchgear are set as a ratio of the investment costs, the annual limit ΩtThe formula of the maintenance cost MAI (x) of the switch is as follows:
Figure GDA0002776747200000079
wherein d is the discount rate and mu is the ratio of the maintenance cost to the investment cost.
Preferably, the formula of the user power outage loss cost cic (x) in step 4.2 is as follows:
Figure GDA0002776747200000081
where Ω represents the life cycle of the device, ΩiA set of feeders that are likely to fail; omegai，jThe feeder section set which is possible to have faults on the feeder i; omegai，j，kThe method comprises the steps of collecting fault sites where ith and jth sections on a feeder line can be in fault; lambda [ alpha ]i，j，k′Probability of failure occurring for a location; omeganA set of different user types;
Figure GDA0002776747200000082
representing the load quantity of the nth load on the c-th branch feeder of the b-th feeder section of the a-th feeder; m is the annual growth rate of the load;
Figure GDA0002776747200000083
corresponding to fault load outage time for class n load type
Figure GDA0002776747200000084
A loss function of (d); d is the discount rate.
Preferably, the step 4.3 of constructing the constraint function expression comprises: constructing an average power supply reliability constraint expression, an average power failure and power shortage constraint and a switch installation constraint;
constructing an average power supply reliability constraint expression, wherein the average power supply reliability ASAI (x) of the power distribution system is not lower than the threshold value ASAI (x)limThe average power supply reliability constraint mathematical expression is as follows:
ASAI(x)≥ASAIlim
Figure GDA0002776747200000085
wherein omegaiTo possibly happenA set of feeders of the barriers; omegai，jThe feeder section set which is possible to have faults on the feeder i; lambda [ alpha ]i，j，kProbability of failure occurring for a location; omeganA set of different user types;
Figure GDA0002776747200000086
representing the load quantity of the nth load on the c-th branch feeder of the b-th feeder section of the a-th feeder; m is the annual growth rate of the load;
Figure GDA0002776747200000087
corresponding to fault load outage time for class n load type
Figure GDA0002776747200000088
Loss function of omegaaFor the complete feeder set, Ωa，bAll feeder sections on the feeder a are collected; omegaa，b，cA branch feeder set representing the b-th feeder section of the a-th feeder; omegai，j，kA kth branch feeder representing a jth feeder segment in the ith feeder;
wherein N isa，cNumber of subscribers on feeder a, NcThe number of users of the whole system;
establishing average power failure and shortage power supply amount constraint, wherein the average power failure and shortage power supply amount AENS (x) of the power distribution system is not higher than the threshold value AENS (x)limThe average power failure power shortage constraint mathematical expression is as follows:
AENS(x)≤AENSlim
Figure GDA0002776747200000091
building switch installation constraint, for each candidate switch installation position, the type of the installed switch can not be greater than 1, namely MCS and RCS can not be installed at the same switch installation position at the same time, and the mathematical expression of the switch installation constraint is as follows:
Figure GDA0002776747200000092
the invention provides an optimal configuration method of a power distribution system switch based on Boolean type variables. The example analysis shows that the optimal configuration method of the distribution system switch based on the Boolean type variable has good adaptability to the radiation type distribution network, and simultaneously considers the section positioning accuracy rate, thereby being more in line with the actual situation of the distribution system. The simulation example verifies that the method has good solving efficiency and high calculation efficiency and is suitable for application of a large-scale power distribution network.
Drawings
FIG. 1 is a flow chart of a model for optimal configuration of power distribution system switches based on Boolean-type variables.
Fig. 2 is a block diagram of a two-section distribution feeder.
Figure 3 is a block diagram of a three-segment distribution feeder.
FIG. 4 is a diagram of relative position of fault load.
Fig. 5 is a schematic diagram of the fault type.
Fig. 6 is a diagram showing the result of the optimal configuration of the switches.
FIG. 7 is a graph of the cost of the present configuration model.
Fig. 8 is a graph comparing cost.
FIG. 9 is a fault zone location accuracy curve.
Detailed Description
In order to make the implementation objects, technical solutions and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be described in more detail below with reference to the accompanying drawings in the embodiments of the present invention. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are only some, but not all embodiments of the invention. The embodiments described below with reference to the drawings are illustrative and intended to be illustrative of the invention and are not to be construed as limiting the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, a method for configuring a distribution system switch based on boolean variables includes the following steps:
step 1: in the case of the switch configuration x of the power distribution system, in order to indicate the existence of a switch on a certain position or a certain section, introducing a Boolean expression, when the value of the Boolean expression is 1, indicating that the corresponding switch exists on the position or the section, and when the value of the Boolean expression is 0, indicating that the corresponding switch does not exist;
the step 1 specifically comprises the following steps:
step 1.1: first, 4 first-type boolean expressions are introduced:
Figure GDA0002776747200000101
Figure GDA0002776747200000102
wherein 0 and 1 are left and right identifiers, 0 represents a left end, 1 represents a right end, two first-type boolean expressions in formula (1) respectively represent the manual switch existence of the left end and the right end of the tail of the b-th feeder segment on the a-th feeder, and two first-type boolean expressions in formula (2) respectively represent the automatic switch existence of the left end and the right end of the tail of the b-th feeder segment on the a-th feeder;
step 1.2: and building the following 6 second-type Boolean expressions from the first-type Boolean expressions:
Figure GDA0002776747200000103
Figure GDA0002776747200000111
Figure GDA0002776747200000112
two boolean expressions of a second type in the expression (3) respectively represent the existence of the section switches at the left end and the right end of the tail of the section b of the feeder line on the section a, and the specific expressions are respectively the expressions (6) and (7):
Figure GDA0002776747200000113
Figure GDA0002776747200000114
two Boolean-type expressions of a second kind in the expression (4) respectively represent the existence of a manual section switch and an automatic section switch between a load at the end of a b-th section feeder line section and a j-th section feeder line section on an a-th feeder line, and the specific expression of the manual switch is as follows:
Figure GDA0002776747200000115
Figure GDA0002776747200000116
Figure GDA0002776747200000121
in the formula (5), two boolean expressions of a second type respectively represent the existence of a manual interconnection switch and an automatic interconnection switch at the end of the a-th feeder line, and the specific expressions of the manual switch are as follows:
TMa(x)＝MCSa,ae,1(x) (9)
wherein ae represents the last segment of the a-th feeder line;
step 1.3, building 2 third Boolean expressions according to the second Boolean expression in the step 1.2:
Figure GDA0002776747200000122
wherein
Figure GDA0002776747200000123
The presence of a section switch from the load at the tail end of the b-th section feeder line section on the a-th feeder line to the j-th section feeder line section is represented by the following specific expression:
Figure GDA0002776747200000124
Ta(x) The existence of a connection switch at the end of the a-th feeder line is represented by the following specific expression:
Figure GDA0002776747200000125
step 1.4: establishing a fault isolation time function through a third type Boolean expression, isolating the load of the fault section from the load of the healthy section by operating a corresponding section switch by a control center after the fault section is positioned, wherein the fault isolation time is section switch action time, when the section switch exists between the fault section and the load and at least one automatic section switch exists, the fault isolation time is automatic switch action time, otherwise, the fault isolation time is manual section switch action time, and a fault isolation time function formula (13) is as follows:
Figure GDA0002776747200000131
tiso(x) For fault isolation time, tiso(x) For fault isolation time, tSRThe action time of the automatic section switch is tSM, the action time of the manual section switch is tSM, and p is the probability of the correct action of the automatic section switch;
step 1.5: and establishing an action time function of the interconnection switch through a third type of Boolean expression according to the type of the interconnection switch and the correct action probability of the automatic interconnection switch, wherein the formula is as follows:
Figure GDA0002776747200000132
ttie(x) For connecting the action time of the switch, q for the probability of correct action of the automatic connection switch, tTRFor automatic interconnection of switch actuation time, tTMThe switch actuation time is communicated manually.
Step 2: introducing fault section positioning accuracy based on the step 1;
when a fault occurs in the power distribution system, the circuit breaker is tripped due to fault current, and the whole system enters a power failure state. At this moment, the fault section is firstly positioned, the automatic section switch can carry out remote control and isolation according to fault positioning information, but the manual switch cannot transmit information, so that the manual line patrol is needed to find the actual position of the fault, the manual switch is operated, and finally the power supply recovery of the non-fault section is realized through the reclosing of the circuit breaker or the action of the contact switch. The positioning accuracy of the fault section directly influences the power failure time of the non-fault section through the line patrol time. And by installing the section switch, the positioning precision can be improved to a certain extent.
As shown in fig. 2, which is a typical structure of a feeder for a distribution network, the feeder 1 is set to two stages for convenience of description. With the leftmost breaker. The manual section switch and the automatic section switch are respectively arranged on the two sides of the tail of the 1 st section of feeder line section, and the manual section switch and the automatic interconnection switch are respectively arranged on the two sides of the tail of the 2 nd section of feeder line section.
The minimum fault section is firstly defined as a section formed by the section switches closest to two sides of the fault, namely a section which can be isolated through the section switches. Depending on the nature of the automatic switch of the power distribution system, if a fault current flows through the automatic switch, the switch will return a fault signal. If the fault occurs on the No. 2 feeder line segment, the No. 2 switch returns a fault signal, and the No. 1,3 and 4 switches do not return the fault signal, the operation center can timely position the fault section at the second section, so that the isolation of the minimum fault section is rapidly carried out, and the power failure time of the non-fault section is reduced.
The step 2 specifically comprises the following steps:
step 2.1: introducing a Boolean expression gammaa，b(x) Denotes the presence of distribution system switches on both sides of the end of the b-th section on the feeder a, gamma, in the case of a defined distribution system switch configuration xa，b(x) A value of 1, indicating the presence of at least one switch at the end of the segment, γa，b(x) A value of 0, indicating that there is no switch on either side of the end of the segment, a Boolean expression γa，b(x) The specific expression is as follows:
Figure GDA0002776747200000141
step 2.2: using the Boolean variable μa，b(x) Fault zone location, boolean variable mu, representing fault of b-th section on feeder aa，b(x) A value of 1, indicating that if a fault occurs in the zone, the boolean variable μ is located in the zone by the signal of the sectionalizera，b(x) A value of 0, indicating that the zone cannot be located, with the circuit breaker as stage 0, γa，0(x) 1, the switch fault current on both sides of the last section of the feeder line does not flow, and the Boolean variable mua，b(x) The specific expression is as follows:
Figure GDA0002776747200000142
Figure GDA0002776747200000143
wherein omegaa，sA set of feeder segments representing an a-th feeder;
step 2.3: defining the fault section positioning accuracy o (x) of the a-th feeder line, wherein the expression is as follows:
Figure GDA0002776747200000144
wherein N isa，sThe number of feeder segments on the feeder a;
step 2.4 defining fault positioning time tins(x) The calculation method is as follows:
tloc(x)＝tbasis+(1-η(x))×tdefult (19)。
wherein t isbasisThe basic line patrol time is related to the average length of each feeder line section of the power distribution network; t is tdefultThe default is the line patrol time in the fault section, which is related to the complexity of the power distribution network. The more feeder sections, the longer the line patrol time in the default fault section of the power distribution network.
The switch configuration of the feeder 2 is shown in fig. 3, wherein no switch is installed at the two sides of the end of the 2 nd section, the fault section positioning accuracy η (x) of the feeder is 66.7%, and the line patrol time t in the fault sectionins(x)＝tdefault/3. If the switch is installed at the installation candidate position 3 or 4 of the section switch, the fault section positioning accuracy can be improved to 1, and the fault section positioning time is reduced to tbasis. Therefore, the positioning accuracy of the fault section can be improved, the line patrol time in the fault section is reduced, and the power supply reliability is finally improved by installing more automatic section switches.
And step 3: and (3) building a fault load power failure time function through a Boolean expression introduced in the steps 1 and 2 and the fault section positioning accuracy.
When the power distribution system has a fault, the main station restores the power supply of the non-fault section through a series of measures such as positioning the fault section, isolating the minimum fault section, reclosing a circuit breaker or an interconnection switch and the like. The fault types are divided into 6 types according to the relative position relationship between the fault and the load, and then the fault types are discussed one by one, wherein the 6 types of faults are shown in fig. 4 and fig. 5, wherein fig. 5 selects the load feeder line L2，2，1Then, fault classification is carried out on the faults at different positions, and different fault types are indicated through arrows. Load blackout times due to class 3 and class 5 faults may be opened by configuring the power distribution systemSignificant improvements are concerned and so the discussion is focused on both types of failures.
The step 3 specifically comprises the following steps:
step 3.1: said fault load blackout time function
Figure GDA0002776747200000151
Under the condition that the switch configuration x of the power distribution system is determined, the power failure time of all loads of a c-th branch feeder at the tail end of a b-th feeder section on an a-th feeder of the power distribution network is caused by the fault of a k ' equivalent position of a j-th feeder section on an ith feeder, wherein the k ' is different according to the fault position, and the expression of the k ' equivalent position is as follows:
Figure GDA0002776747200000152
set 9 scenarios:
Figure GDA0002776747200000153
step 3.2: and defining the power failure time of the load corresponding to the first type of fault, wherein the expression is formula (21), the fault and the load are positioned on the same feeder line, the fault occurs on the branch feeder line, and the load and the fault are positioned on the same branch feeder line. Due to the existence of the fuse, the fault section is isolated from the loads of other branch feeder lines on the feeder line by the fusing of the fuse, so that the fault section is not influenced, and meanwhile, the fault section information is obtained. Therefore, the fault-load power failure time is the fault repair time trepTime t of coincidence with circuit breakerCBAnd (3) the sum:
Figure GDA0002776747200000161
and 3.3, defining the power failure time of the load corresponding to the second type of fault as 0, wherein the expression is a formula (22), the fault and the load are positioned on the same feeder line, the fault occurs on a branch feeder line, and the load and the fault are positioned on different branch feeder lines. Due to the existence of the fuse, the fault can not affect other loads, and fault section information is obtained, so that the fault-load power failure time is 0:
Figure GDA0002776747200000162
and 3.4, defining the power failure time of the load corresponding to the third type of fault, wherein the expression is a formula (23), the fault and the load are positioned on the same feeder line, the fault occurs in a feeder line section, and the fault occurs in the upstream of the feeder line section where the load is positioned. After the load of the healthy section is positioned in the fault section, if any type of section switch exists between the load and the fault and any type of interconnection switch exists at the tail end of the feeder line, the load can isolate the fault and recover power supply through a series of measures such as section switch action, interconnection switch action and the like after the fault section is positioned, so that the fault-load power failure time is the sum of the fault section positioning time, the fault isolation time and the interconnection switch action time. Otherwise, the fault-load power failure time is the sum of the fault section positioning time, the fault repairing time and the breaker action time:
Figure GDA0002776747200000163
and 3.5, defining the power failure time of the load corresponding to the fourth type of fault, wherein the expression is a formula (24), the fault and the load are positioned on the same feeder line, the fault occurs in a feeder line section, and the fault occurs in the feeder line section where the load is positioned. The fault can not be isolated by the section switch, so the fault-load power failure time is the sum of the fault section positioning time, the fault repairing time and the circuit breaker reclosing time:
Figure GDA0002776747200000164
and 3.6, defining the load power failure time corresponding to the fifth type of fault, wherein the expressions are formulas (25) and (26), the fault and the load are not on the same feeder line, and due to the existence of the breaker, the fault can be isolated from the loads of other feeder lines through the tripping of the breaker, so that the loads of other feeder lines cannot be influenced. Fault-load outage time is 0:
Figure GDA0002776747200000171
Figure GDA0002776747200000172
and 4, step 4: and constructing a power distribution system switch optimal configuration model with the minimum sum of power supply reliability index as constraint, user power failure loss and switch configuration full life cycle cost and a target, and solving through a solver.
In a power distribution network, the purpose of optimally configuring switches of a power distribution system is to minimize the comprehensive cost on the premise of meeting the reliability requirement of the power distribution network by determining the types, positions and numbers of section switches and interconnection switches. The comprehensive cost is the switch life cycle cost of the power distribution system and the power failure loss cost of a user, wherein the switch life cycle cost of the power distribution system is divided into switch investment cost and switch maintenance cost in a service cycle.
The step 4 specifically comprises the following steps:
step 4.1, constructing an optimal configuration model, wherein the optimal configuration model of the switch of the power distribution system is constructed by taking the minimum comprehensive cost as a target and taking the average power supply reliability, the average power failure and power shortage amount and the switch installation limit as constraint conditions, and the constructed model is as follows:
an objective function: min Cost (x)
Constraint conditions are as follows:
Figure GDA0002776747200000173
wherein cost (x) is the comprehensive cost; ASAI (x) is the average power supply reliability; AENS (x) is average outage power supply, Ω a is total feeder set, Ωa，bIs a feeder linea, all feeder line segment sets;
and 4.2, building comprehensive cost, wherein the mathematical expression of the comprehensive cost (x) is as follows:
Cost(x)＝LCC(x)+CIC(x) (28)
wherein, LCC (x) is the cost of the full life cycle of the switch, CIC (x) is the cost of the power failure loss of the user;
step 4.3: and constructing a constraint function expression.
Preferably, the step 4.2 switch full life cycle cost lcc (x) has the mathematical expression:
LCC(x)＝INV(x)+MAI(x) (29)
wherein INV (x) is the switch investment cost, and MAI (x) is the switch maintenance cost.
Preferably, the switch investment cost inv (x) includes a purchase cost and an installation cost of the switch, and is expressed by the following formula:
Figure GDA0002776747200000181
wherein
Figure GDA0002776747200000182
In order to save the investment cost of the manual section switch,
Figure GDA0002776747200000183
in order to automatically change the investment cost of the section switch,
Figure GDA0002776747200000184
in order to manually communicate the investment cost of the switch,
Figure GDA0002776747200000185
for the investment cost of the automatic interconnection switch, the expressions of the investment cost of the manual section switch and the investment cost of the manual interconnection switch are respectively as follows:
Figure GDA0002776747200000186
Figure GDA0002776747200000187
preferably, the annual operating maintenance costs of the switchgear are set as a ratio of the investment costs, the annual limit ΩtThe formula of the maintenance cost MAI (x) of the switch is as follows:
Figure GDA0002776747200000188
wherein d is the discount rate and mu is the ratio of the maintenance cost to the investment cost.
Preferably, the formula of the user power outage loss cost cic (x) in step 4.2 is as follows:
Figure GDA0002776747200000189
where Ω represents the life cycle of the device, ΩiA set of feeders that are likely to fail; omegai，jThe feeder section set which is possible to have faults on the feeder i; omegai，j，kThe method comprises the steps of collecting fault sites where ith and jth sections on a feeder line can be in fault; lambda [ alpha ]i，j，k′Probability of failure occurring for a location; omeganA set of different user types;
Figure GDA00027767472000001810
representing the load quantity of the nth load on the c-th branch feeder of the b-th feeder section of the a-th feeder; m is the annual growth rate of the load;
Figure GDA00027767472000001811
corresponding to fault load outage time for class n load type
Figure GDA00027767472000001812
Is measured.
Preferably, the step 4.3 of constructing the constraint function expression comprises: constructing an average power supply reliability constraint expression, an average power failure and power shortage constraint and a switch installation constraint;
constructing an average power supply reliability constraint expression, wherein the average power supply reliability ASAI (x) of the power distribution system is not lower than the threshold value ASAI (x)limThe average power supply reliability constraint mathematical expression is as follows:
ASAI(x)≥ASAIlim
Figure GDA0002776747200000191
wherein omegaiA set of feeders that are likely to fail; omegai，jThe feeder section set which is possible to have faults on the feeder i; omegai，j，k′The method comprises the steps of collecting fault sites where ith and jth sections on a feeder line can be in fault; lambda [ alpha ]i，j，kProbability of failure occurring for a location; omeganA set of different user types;
Figure GDA0002776747200000192
representing the load quantity of the nth load on the c-th branch feeder of the b-th feeder section of the a-th feeder; m is the annual growth rate of the load;
Figure GDA0002776747200000193
corresponding to fault load outage time for class n load type
Figure GDA0002776747200000194
Loss function of omegaaFor the complete feeder set, Ωa，bAll feeder sections on the feeder a are collected; omegaa，b，cA branch feeder set representing the b-th feeder section of the a-th feeder; omegai，j，kA kth branch feeder representing a jth feeder segment in the ith feeder;
wherein N isa，cNumber of subscribers on feeder a, NcThe number of users of the whole system.
Establishing average power failure and shortage power supply amount constraint, wherein the average power failure and shortage power supply amount AENS (x) of the power distribution system is not higher than the threshold value AENS (x)limMean power off lack of supplyThe quantity constraint mathematical expression is:
AENS(x)≤AENSlim
Figure GDA0002776747200000195
building switch installation constraint, for each candidate switch installation position, the type of the installed switch can not be greater than 1, namely MCS and RCS can not be installed at the same switch installation position at the same time, and the mathematical expression of the switch installation constraint is as follows:
Figure GDA0002776747200000196
the solving strategy belongs to the nonlinear 0-1 programming problem mathematically, and is suitable for solving the large-scale complex mathematical problem by using excellent mathematical software such as localsolver and adopting a local search method.
In another embodiment: the proposed method was tested on an IEEE RBTS-BUS4 power distribution network. The IEEE RBTS-BUS4 distribution network is a medium voltage distribution system with 38 load nodes, 4779 users, and a total average load of 24.58 MW. In the test, the parameters were set as follows: the investment costs for the automatic section switch and the manual section switch are $ 3000 and $ 17000, respectively, and the investment costs for the automatic tie switch and the manual tie switch are $ 4000 and $ 18000, respectively. The annual operation and maintenance cost of the switch is 5% of the investment cost, the research age limit is 5 years, the annual rate is 5%, and the annual load growth rate is 2%. The action time of the automatic section switch, the automatic interconnection switch and the manual section switch is respectively 300 seconds, 600 seconds, 3600 seconds and 7200 seconds. The mean time to failure service was 14400 seconds. The breaker actuation time was 300 seconds. The default fault location time is 1800 seconds. The normal operation probability of the automatic section switch is 0.999, and the normal operation probability of the automatic contact switch is 0.99. The upper and lower limits of the reliability indexes of the last year in the research period of the system are respectively as follows:
Figure GDA0002776747200000201
Figure GDA0002776747200000202
selecting a reliability index threshold ASAIlim,AENSlimRespectively 99.96%, 30 (kW. h)/(family. a)
The problem is solved by using the load power failure time corresponding to the second type of fault of the model provided by the invention. The preferred FTU configuration is shown in fig. 6, which includes 7 automatic tie switches, 11 automatic section switches and 23 manual section switches.
In the above optimal configuration scheme of the power distribution system switches, the reliability index asai (x) is 99.965%, the fault section positioning accuracy η (x) is 93.10%, and the maximum value of aens (x) is 22.37(kW · h)/(household · a). The combined cost (x) is $ 5131446, where the switch full life cycle cost lcc (x) is $ 529485 and the customer outage cost cic (x) is $ 4601961.
To further illustrate the rationality of the proposed model for optimal configuration of power distribution system switches, the following two comparison schemes are constructed:
(1) in the scheme 1, the fault positioning accuracy is considered, and a configuration scheme with minimum comprehensive cost as a target, namely a model provided by the scheme, is adopted;
(2) the scheme 2 is a configuration scheme which takes the minimum comprehensive cost as a target without considering the fault positioning accuracy;
(3) scheme 3, a configuration scheme which takes the minimum power failure loss of a user as a target without considering the fault positioning accuracy rate;
(4) and 4, a configuration scheme which takes the minimum switch life cycle as a target without considering the fault positioning accuracy.
The constraints are the same in the 4 schemes. Table 1 shows the number of switches, the average power supply reliability index, the average power outage and outage power supply quantity index, the comprehensive cost, the switch life cycle cost and the user power outage loss cost corresponding to the above 4 configuration schemes.
TABLE 1 comparison of the four solutions
Figure GDA0002776747200000211
The following can be concluded from table 1.
(1) Compared with the scheme 1, the scheme 2 has the advantages that the average power supply reliability is less by 0.05%, the average power failure power shortage amount is more than 18%, the comprehensive cost is increased by 6.03%, and the comprehensive cost is comprehensively inferior to the scheme 1.
(2) The cost of power loss for the user of scheme 3 is minimal. This is because scheme 3 adds a large number of automatic and sectionalizing switches compared to scheme 1; this results in a switch life cycle cost of 159.94% greater for scenario 3 than for scenario 1, and 17.96% greater for scenario 3 than for scenario 1 in terms of overall cost.
(3) The switch lifecycle cost of scenario 4 is minimal. This is because scheme 4 reduces the number of automatic and sectionalizing switches compared to scheme 1; this results in a power outage loss cost 51.45% greater for scenario 4 than for scenario 1, and 28.83% greater for scenario 43 than for scenario 1 in terms of overall costs.
(4) The scheme 1 gives consideration to the switch life cycle cost and the user power failure loss cost, achieves the minimum comprehensive cost, simultaneously takes the optimization of the fault section positioning time into consideration, and is the optimal configuration scheme.
And further, by setting different average power supply reliability threshold values, the positioning accuracy of fault sections, average power failure power shortage amount, switch number and various costs of different configuration schemes are obtained by utilizing the model provided by the text to solve.
Fig. 7 shows the average power reliability versus outage loss cost, switch life cycle cost, and total cost.
It can be seen that when the average power reliability is in the region of 99.84% -99.92%, the cost of power loss approaches a linear decrease trend as the number of switches increases.
When the average power supply reliability is in the range of 99.92% -99.98%, the trend of the reduction of the cost of power failure loss is gradually slowed down, and the fact that the power failure time reduced by increasing the switches of the power distribution system is reduced is illustrated.
When the average power supply reliability is in a section of 99.98% -99.99%, although the power failure loss cost is still reduced at the moment, the number of switches installed in the whole power distribution system is close to saturation, the power failure time cannot be obviously improved by slightly increasing the number of switches of the power distribution system, and a large number of switches are needed to be installed along with the increase of the average power supply reliability, so that the whole life cycle cost and the comprehensive cost curve of the switches at the moment show an increasing trend. Fig. 7 and 8 also clearly support this situation.
As shown in fig. 9, it can be seen from the above simulation analysis that the model proposed herein can give an optimal configuration scheme for the number, positions and types of switches of the power distribution system while taking into account economy and reliability, thereby substantially improving the utilization efficiency of capital.
Finally, it should be pointed out that: the above examples are only for illustrating the technical solutions of the present invention, and are not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (9)

1. A method for configuring a power distribution system switch based on a Boolean type variable is characterized by comprising the following steps:
step 1: in the case of the switch configuration x of the power distribution system, in order to indicate the existence of a switch on a certain position or a certain section, introducing a Boolean expression, when the value of the Boolean expression is 1, indicating that the corresponding switch exists on the position or the section, and when the value of the Boolean expression is 0, indicating that the corresponding switch does not exist;
the step 1 specifically comprises the following steps:
step 1.1: first, 4 first-type boolean expressions are introduced:
Figure FDA0002776747190000011
Figure FDA0002776747190000012
wherein 0 and 1 are left and right identifiers, 0 represents a left end, 1 represents a right end, two first-type boolean expressions in formula (1) respectively represent the manual switch existence of the left end and the right end of the tail of the b-th feeder segment on the a-th feeder, and two first-type boolean expressions in formula (2) respectively represent the automatic switch existence of the left end and the right end of the tail of the b-th feeder segment on the a-th feeder;
step 1.2: and building the following 6 second-type Boolean expressions from the first-type Boolean expressions:
Figure FDA0002776747190000013
Figure FDA0002776747190000014
Figure FDA0002776747190000015
two boolean expressions of a second type in the expression (3) respectively represent the existence of the section switches at the left end and the right end of the tail of the section b of the feeder line on the section a, and the specific expressions are respectively the expressions (6) and (7):
Figure FDA0002776747190000016
Figure FDA0002776747190000021
two Boolean-type expressions of a second kind in the expression (4) respectively represent the existence of a manual section switch and an automatic section switch between a load at the end of a b-th section feeder line section and a j-th section feeder line section on an a-th feeder line, and the specific expression of the manual switch is as follows:
Figure FDA0002776747190000022
Figure FDA0002776747190000023
Figure FDA0002776747190000024
in the formula (5), two boolean expressions of a second type respectively represent the existence of a manual interconnection switch and an automatic interconnection switch at the end of the a-th feeder line, and the specific expressions of the manual switch are as follows:
TMa(x)＝MCSa,ae,1(x) (9)
wherein ae represents the last segment of the a-th feeder line;
step 1.3, building 2 third Boolean expressions according to the second Boolean expression in the step 1.2:
Figure FDA0002776747190000031
wherein
Figure FDA0002776747190000032
The presence of a section switch from the load at the tail end of the b-th section feeder line section on the a-th feeder line to the j-th section feeder line section is represented by the following specific expression:
Figure FDA0002776747190000033
Ta(x) The existence of a connection switch at the end of the a-th feeder line is represented by the following specific expression:
Figure FDA0002776747190000034
step 1.4: establishing a fault isolation time function through a third type Boolean expression, isolating the load of the fault section from the load of the healthy section by operating a corresponding section switch by a control center after the fault section is positioned, wherein the fault isolation time is section switch action time, when the section switch exists between the fault section and the load and at least one automatic section switch exists, the fault isolation time is automatic switch action time, otherwise, the fault isolation time is manual section switch action time, and a fault isolation time function formula (13) is as follows:
Figure FDA0002776747190000035
tiso(x) For fault isolation time, tSRFor automatic switching action time, tSMThe action time of the manual section switch is used, and p is the correct action probability of the automatic section switch;
step 1.5: and establishing an action time function of the interconnection switch through a third type of Boolean expression according to the type of the interconnection switch and the correct action probability of the automatic interconnection switch, wherein the formula is as follows:
Figure FDA0002776747190000036
ttie(x) For connecting the action time of the switch, q for the probability of correct action of the automatic connection switch, tTRFor automatic interconnection of switch actuation time, tTMFor manual interconnection of switch actionsTime;
step 2: introducing fault section positioning accuracy based on the step 1;
and step 3: establishing a fault load power failure time function according to the Boolean expression introduced in the step 1 and the fault section positioning accuracy introduced in the step 2;
and 4, step 4: and constructing a power distribution system switch optimal configuration model with the power supply reliability index as constraint, the minimum sum of the power failure loss of a user and the total life cycle cost of switch configuration and the target, and solving through a solver.
2. The method of configuring boolean variable based power distribution system switches as recited in claim 1, further comprising: the step 2 specifically comprises the following steps:
step 2.1: introducing a Boolean expression gammaa，b(x) Denotes the presence of distribution system switches on both sides of the end of the b-th section on the feeder a, gamma, in the case of a defined distribution system switch configuration xa，b(x) A value of 1, indicating the presence of at least one switch at the end of the segment, γa，b(x) A value of 0, indicating that there is no switch on either side of the end of the segment, a Boolean expression γa，b(x) The specific expression is as follows:
Figure FDA0002776747190000041
step 2.2: using the Boolean variable μa，b(x) Fault zone location, boolean variable mu, representing fault of b-th section on feeder aa，b(x) A value of 1, indicating that if a fault occurs in the zone, the boolean variable μ is located in the zone by the signal of the sectionalizera，b(x) A value of 0, indicating that the zone cannot be located, with the circuit breaker as stage 0, γa，0(x) 1, the switch fault current on both sides of the last section of the feeder line does not flow, and the Boolean variable mua，b(x) The specific expression is as follows:
Figure FDA0002776747190000042
Figure FDA0002776747190000043
wherein omegaa，sA set of feeder segments representing an a-th feeder;
step 2.3: defining the fault section positioning accuracy eta (x) of the a-th feeder line, wherein the expression is as follows:
Figure FDA0002776747190000044
wherein eta (x) is the fault section positioning accuracy of the a-th feeder line, Na，bThe number of feeder segments on the feeder a;
step 2.4 defining fault positioning time tloc(x) The calculation method is as follows:
tloc(x)＝tbasis+(1-η(x))×tdefult (19)
wherein t isbasisBased on the time of line patrol, tdefultThe line patrol time in the fault section is the default.
3. The method of configuring boolean variable based power distribution system switches as recited in claim 1, further comprising: the step 3 specifically comprises the following steps:
step 3.1: said fault load blackout time function
Figure FDA0002776747190000051
Under the condition that the switch configuration x of the power distribution system is determined, the power failure time of all loads of a c-th branch feeder at the tail end of a b-th feeder section on an a-th feeder of the power distribution network is caused by the fault of a k ' equivalent position of a j-th feeder section on an ith feeder, wherein the k ' is different according to the fault position, and the expression of the k ' equivalent position is as follows:
Figure FDA0002776747190000052
step 3.2: defining the load power failure time corresponding to the first type of fault, wherein trepRepresenting the time of failure recovery, tCBRepresenting the reclosing time of the circuit breaker, the expression of which is formula (21):
Figure FDA0002776747190000053
and 3.3, defining the load power failure time corresponding to the second type of fault as 0, wherein the expression is a formula (22):
Figure FDA0002776747190000054
step 3.4, defining the load power failure time t corresponding to the third type of faultloc(x)、tiso(x)、ttie(x)、trep、tCBRespectively represent fault positioning time, fault isolation time, contact switch action time, fault repair time and circuit breaker coincidence time, and the expression is formula (23):
Figure FDA0002776747190000055
and 3.5, defining the load power failure time corresponding to the fourth type of fault, wherein the expression is a formula (24):
Figure FDA0002776747190000056
and 3.6, defining the load power failure time corresponding to the fifth type of fault, wherein the expressions are shown as formulas (25) and (26):
Figure FDA0002776747190000061
Figure FDA0002776747190000062
4. the method of configuring boolean variable based power distribution system switches as recited in claim 1, further comprising: the step 4 specifically comprises the following steps:
step 4.1, constructing an optimal configuration model, wherein the optimal configuration model of the switch of the power distribution system is constructed by taking the minimum comprehensive cost as a target and taking the average power supply reliability, the average power failure and power shortage amount and the switch installation limit as constraint conditions, and the constructed model is as follows:
Figure FDA0002776747190000063
wherein cost (x) is the comprehensive cost; ASAI (x) is the average power supply reliability; AENS (x) for average outagelimIs AENS (x) corresponding threshold; ASAIlimRepresents the corresponding threshold value of ASAI (x); omegaaIs a set of all feeders; omegaa，bAll the feeder lines on the feeder line a are collected;
and 4.2, building comprehensive cost, wherein the mathematical expression of the comprehensive cost (x) is as follows:
Cost(x)＝LCC(x)+CIC(x) (28)
wherein, LCC (x) is the cost of the full life cycle of the switch, CIC (x) is the cost of the power failure loss of the user;
step 4.3: and constructing a constraint function expression.
5. The method of configuring boolean variable based power distribution system switches as recited in claim 4, further comprising: the mathematical expression of the step 4.2 switch full life cycle cost lcc (x) is:
LCC(x)＝INV(x)+MAI(x) (29)
wherein INV (x) is the switch investment cost, and MAI (x) is the switch maintenance cost.
6. The method of configuring boolean variable based power distribution system switches as recited in claim 5, further comprising: the switch investment cost INV (x) comprises the purchase cost and the installation cost of the switch, and the formula is as follows:
Figure FDA0002776747190000071
wherein
Figure FDA0002776747190000072
In order to save the investment cost of the manual section switch,
Figure FDA0002776747190000073
in order to automatically change the investment cost of the section switch,
Figure FDA0002776747190000074
in order to manually communicate the investment cost of the switch,
Figure FDA0002776747190000075
for the investment cost of the automatic interconnection switch, the expressions of the investment cost of the manual section switch and the investment cost of the manual interconnection switch are respectively as follows:
Figure FDA0002776747190000076
Figure FDA0002776747190000077
7. the method of configuring boolean variable based power distribution system switches as recited in claim 5, further comprising: the annual operating and maintenance cost of the switch equipment is set as the ratio of the investment costAnnual limit omegatThe formula of the maintenance cost MAI (x) of the switch is as follows:
Figure FDA0002776747190000078
wherein d is the discount rate and mu is the ratio of the maintenance cost to the investment cost.
8. The method of configuring boolean variable based power distribution system switches as recited in claim 4, further comprising: the formula of the user power failure loss cost CIC (x) in the step 4.2 is as follows:
Figure FDA0002776747190000079
where Ω represents the life cycle of the device, ΩiA set of feeders that are likely to fail; omegai，jThe feeder section set which is possible to have faults on the feeder i; omegai，j，kThe method comprises the steps of collecting fault sites where ith and jth sections on a feeder line can be in fault; lambda [ alpha ]i，j，k′Probability of failure occurring for a location; omeganA set of different user types;
Figure FDA00027767471900000710
representing the load quantity of the nth load on the c-th branch feeder of the b-th feeder section of the a-th feeder; m is the annual growth rate of the load;
Figure FDA0002776747190000081
corresponding to fault load outage time for class n load type
Figure FDA0002776747190000082
A loss function of (d); d is the discount rate.
9. The method of configuring boolean variable based power distribution system switches as recited in claim 4, further comprising: the step 4.3 of constructing the constraint function expression comprises the following steps: constructing an average power supply reliability constraint expression, an average power failure and power shortage constraint and a switch installation constraint;
constructing an average power supply reliability constraint expression, wherein the average power supply reliability ASAI (x) of the power distribution system is not lower than the threshold value ASAI (x)limThe average power supply reliability constraint mathematical expression is as follows:
ASAI(x)≥ASAIlim
Figure FDA0002776747190000083
wherein omegaiA set of feeders that are likely to fail; omegai，jThe feeder section set which is possible to have faults on the feeder i; lambda [ alpha ]i，j，kProbability of failure occurring for a location; omeganA set of different user types;
Figure FDA0002776747190000084
representing the load quantity of the nth load on the c-th branch feeder of the b-th feeder section of the a-th feeder; m is the annual growth rate of the load;
Figure FDA0002776747190000085
corresponding to fault load outage time for class n load type
Figure FDA0002776747190000086
Loss function of omegaaFor the complete feeder set, Ωa，bAll feeder sections on the feeder a are collected; omegaa，b，cA branch feeder set representing the b-th feeder section of the a-th feeder; omegai，j，kA kth branch feeder representing a jth feeder segment in the ith feeder;
wherein N isa，cNumber of subscribers on feeder a, NcThe number of users of the whole system;
the average power failure and power supply shortage constraint is built, and the average power failure and power supply shortage of the power distribution system is realizedThe amount of power supplied AENS (x) is not higher than the threshold value AENSlimThe average power failure power shortage constraint mathematical expression is as follows:
AENS(x)≤AENSlim
Figure FDA0002776747190000087
building switch installation constraint, for each candidate switch installation position, the type of the installed switch can not be greater than 1, namely MCS and RCS can not be installed at the same switch installation position at the same time, and the mathematical expression of the switch installation constraint is as follows:
Figure FDA0002776747190000091
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