CN109902361B - Logic operator-based power distribution network switch optimal configuration method - Google Patents

Logic operator-based power distribution network switch optimal configuration method Download PDF

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CN109902361B
CN109902361B CN201910106925.7A CN201910106925A CN109902361B CN 109902361 B CN109902361 B CN 109902361B CN 201910106925 A CN201910106925 A CN 201910106925A CN 109902361 B CN109902361 B CN 109902361B
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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 power distribution network switch optimal configuration method based on a logic operator, which comprises the following steps: step 1: providing two mathematical expression forms of logic operators or and if suitable for power distribution network switch optimization configuration; step 2: building a power failure time model of the typical power distribution network about an automatic switch and a manual switch by using the mathematical expression form of the two logic operators provided in the step 1; and step 3: and (3) building a power distribution network switch optimization configuration model by using the power failure time model built in the step (2), and solving by adopting a genetic algorithm.

Description

Logic operator-based power distribution network switch optimal configuration method
Technical Field
The invention relates to the technical field of power distribution automation of a power system, in particular to a power distribution network switch optimal configuration method based on logic operators.
Background
With the development of economic society, the requirements of people on the power supply reliability are increasingly improved. Effective strategies for improving power supply reliability are to improve fault location efficiency, shorten fault isolation time and power supply recovery time. In recent years, automatic switches are deeply applied to power distribution networks, and can remarkably improve the operation reliability of the power distribution networks through information perception and action control of the power distribution networks. However, the investment of the automatic switch is large, and the power grid company faces the contradiction between the power supply reliability and the economy. In addition, the complexity of the topology structure of the power distribution network and the diversity of the operation modes also increase the difficulty of configuration of the automatic switch to a certain extent. As described above, how to optimize the number and the installation position of the automatic switches while considering reliability and economy is an important issue facing the power grid company.
Therefore, a power distribution network switch optimal configuration method based on logic operators is expected to effectively solve the problems in the prior art.
Disclosure of Invention
The invention discloses a power distribution network switch optimal configuration method based on a logic operator, which comprises the following steps:
step 1: providing two mathematical expression forms of logic operators or and if suitable for power distribution network switch optimization configuration;
step 2: building a power failure time model of the typical power distribution network about an automatic switch and a manual switch by using the mathematical expression form of the two logic operators provided in the step 1;
and step 3: and (3) building a power distribution network switch optimization configuration model by using the power failure time model built in the step (2), and solving by adopting a genetic algorithm.
Preferably, the step 1 specifically comprises the following steps:
step 1.1: introducing a mathematical expression (1) of a logic operator or, wherein the mathematical expression of the logic operator or is as follows: if the solution value in the solution set is 1, the expression value is 1, otherwise, the expression value is 0, and the formula (1) is as follows:
Figure GDA0002803432110000021
where X is the set of solutions, ΩXIs the lower corner label of all solutions in the set, xiIs the solution in the set with the lower corner labeled i;
step 1.2: converting the logical operator or of step 1.1 into the mathematical expression (2):
Figure GDA0002803432110000022
step 1.3: introducing a mathematical expression (3) of a logical operator if based on the step 1.1, wherein the mathematical expression of the logical operator if is as follows: if the solution value in the solution set is 1, the expression takes the value a, otherwise, the expression takes the value b, and the formula (3) is as follows:
Figure GDA0002803432110000023
step 1.4: converting the logical operator if of step 1.3 into the mathematical expression (4):
Figure GDA0002803432110000024
preferably, the step 2 specifically includes the following steps:
step 2.1: setting a solution vector for the optimal configuration of the manual switch and the automatic switch of the circuit independently;
step 2.2: according to the radiation type power distribution network, firstly, 3 groups of basic power failure time expressions of formulas (8), (9) and (10) are established:
Figure GDA0002803432110000025
Figure GDA0002803432110000031
Figure GDA0002803432110000032
where equation (8) represents the case: the path between the fault and the load is not switched or the fault is located upstream of the load; when the fault is positioned at the upstream of the load, a switch exists in the path, an interconnection switch does not exist at the tail of the line, and the power failure time is the sum of the fault positioning time, the fault repairing time and the breaker action time;
wherein the case represented by formula (9) is: the fault is at the upstream of the load, a manual switch or an automatic switch is arranged on a path between the fault and the load, and the power failure time is the sum of fault positioning time, corresponding switch action time and breaker action time;
where equation (10) represents the case: the fault is at the downstream of the load, a corresponding switch exists between the fault and the load, and a corresponding switch also exists at the tail of the line, so that 4 different power failure times are corresponded;
wherein t islocFor locating time of failure, tmcsFor manual switching action time, trcsFor automatic switching action time, tcbThe circuit breaker action time;
step 2.3: building a specific power failure time model of the load at the upstream of the fault according to
Figure GDA0002803432110000037
To
Figure GDA0002803432110000038
The power failure time is obtained as shown in formula (11):
Figure GDA0002803432110000033
step 2.4: converting the specific power failure time model of the load upstream of the fault into a power failure time model expressed by a logic operator, wherein the formula (12) is as follows:
Figure GDA0002803432110000034
wherein
Figure GDA0002803432110000035
And
Figure GDA0002803432110000036
a set of all manual switching and automatic switching solutions between the a-th line load I to the fault f;
step 2.5: building a specific power failure time model of the load at the downstream of the fault according to
Figure GDA0002803432110000041
To
Figure GDA0002803432110000042
Ftu and the existence of the last interconnection switch, the power failure time is obtained as the following formula (13):
Figure GDA0002803432110000043
step 2.6: converting the specific power failure time model of the load at the downstream of the fault into a power failure time model expressed by a logic operator as the following formula (14):
Figure GDA0002803432110000044
step 2.7: and (3) constructing a power failure time model of the switch installation candidate position with no load and fault as the formula (15):
Figure GDA0002803432110000045
preferably, the step 2.1 takes a set of a solution vector of the a-th line manual switch and a solution vector of the a-th line automatic switch to represent a solution vector of a line, wherein the solution vector of the a-th line manual switch is formula (5), the solution vector of the a-th line automatic switch is formula (6), and the solution vector of the line is formula (7):
Figure GDA0002803432110000046
Figure GDA0002803432110000047
Xa＝(Xa-mcs，Xa-rcs) (7)
wherein
Figure GDA0002803432110000048
Indicates whether the manual switch is installed at the first switch installation candidate position of the a-th line,
Figure GDA0002803432110000049
and representing whether the automatic switch is installed at the first switch installation candidate position of the a-th line.
Preferably, the step 3 specifically includes the following steps:
step 3.1: a two-level traversal of the traversal load over the fault is used to obtain a power reliability model for the entire distribution system, as shown in equation (16)
Figure GDA0002803432110000051
Wherein omegafeederFor the set of all the feeders of the system,
Figure GDA0002803432110000052
for all the loads on the a-th line,
Figure GDA0002803432110000053
the set of all possible fault points on the a line; n is a radical oflIs the number of users of the system;
step 3.2: and (3) adopting a double-layer traversal to obtain the power failure loss of the whole system caused by power failure, such as formula (17):
Figure GDA0002803432110000054
wherein
Figure GDA0002803432110000055
The fault rate of the f fault on the a line; omegatIs a load type set;
Figure GDA0002803432110000056
the load quantity is the load quantity of the t-th type of the I-th load;
Figure GDA0002803432110000057
a power outage loss function corresponding to the power outage time;
step 3.3: determining the full life cycle cost of the switch, as in equation (18):
Figure GDA0002803432110000058
wherein h isA maintenance cost coefficient; costmcsCost for manual switching; costrcsCost for automatic switching;
step 3.4: building a distribution network switch optimal configuration model, such as a formula (19)
Figure GDA0002803432110000059
Step 3.5: and solving by using a genetic algorithm.
The invention provides a power distribution network switch optimal configuration method based on a logic operator, which accurately builds a power distribution system switch model about power failure time, has high calculation efficiency and is very suitable for practical engineering application.
Drawings
Fig. 1 is a flow chart of a method for optimally configuring a switch of a power distribution network based on a logic operator.
Fig. 2 is a schematic diagram of step 2.3 of building a specific blackout time model of the load upstream of the fault.
Fig. 3 is a schematic diagram of a concrete blackout time model of step 2.4 building load downstream of the fault.
Fig. 4 is a flow chart of the genetic algorithm of step 3.5.
Fig. 5 is a schematic diagram of an optimal switch configuration scheme.
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 of configuring a power distribution system switch includes the steps of:
step A: providing two mathematical expression forms of logic operators or and i f suitable for the switch optimization configuration of the power distribution network;
and B: building a power failure time model of the typical power distribution network about an automatic switch and a manual switch by using the mathematical expression form of the two logic operators provided in the step 1;
and C: and (3) building a power distribution network switch optimization configuration model by using the power failure time model built in the step (2), and solving by adopting a genetic algorithm.
The step A comprises the following steps:
since for a certain fixed position, whether a switch is installed or not can be represented by a1 or a 0, in view of this, a relevant logical operator is introduced
Step A1, introducing a logic operator or, wherein the specific expression is as follows:
Figure GDA0002803432110000061
wherein X is a set of rows of a series, ΩXIs the lower corner label of all solutions in the set, xiIs a solution in the set with the lower corner labeled i. The mathematical meaning is in the set of solutions, but if 1 solution value is 1, the expression takes the value of 1, otherwise, the expression takes the value of 0.
Step A2, converting the logic operator or into a mathematical expression:
Figure GDA0002803432110000071
step A3, introducing a logical operator if based on the step A1, wherein the specific expression is as follows:
Figure GDA0002803432110000072
the mathematical meaning is in the set of solutions, but if 1 solution value is 1, the expression takes the value of a, otherwise, the expression takes the value of b.
Step A5, converting the logical operator if into a mathematical expression
Figure GDA0002803432110000073
In one embodiment of the present invention, the step B includes:
step B1: a solution vector is set separately for the optimal configuration of a line with respect to manual switching and the configuration of automatic switching such as:
Figure GDA0002803432110000074
Figure GDA0002803432110000075
respectively representing the solution vector of the a-th line relative to the manual switch and the solution vector relative to the automatic switch, wherein
Figure GDA0002803432110000076
And
Figure GDA0002803432110000077
whether a manual switch or an automatic switch is installed or not is represented at the first switch installation candidate position of the a-th line, and obviously, the two cannot simultaneously take 1. For convenience of representation, the set of the two is taken as:
Xa＝(Xa-mcs，Xa-rcs) (7)
representing the solution vector for that line.
Step B2: according to the actual situation in the radiation type power distribution network, 3 groups of basic power failure time expressions are firstly established.
Figure GDA0002803432110000078
Figure GDA0002803432110000081
Figure GDA0002803432110000082
The first group of power failure time represents the condition that no switch of any type exists in a path between a fault and a load, or the fault is located at the upstream of the load, any switch exists in the path, but no interconnection switch exists at the tail end of a line, and the power failure time is the sum of fault positioning time, fault repairing time and breaker action time.
The second group of power failure times represents a case where the fault is upstream of the load, and a manual Switch (MCS) or a Remote Controlled Switch (RCS) exists in a path between the fault and the load, and the corresponding power failure time is the sum of the fault location time, the corresponding Switch action time, and the breaker action time.
The third group of power failure time represents the condition that the fault is at the downstream of the load, a corresponding switch is arranged between the fault and the load, and a corresponding switch is arranged at the tail end of the line, so that 4 different power failure times are corresponding. For convenience of expression, it is specified that the lower corner is labeled as a switch that serves to isolate a fault or repair time, and the upper corner is labeled as a switch that serves to restore power.
Wherein T islocFor locating time of failure, tmcsFor manual switching action time, trcsFor automatic switching action time, TcbThe breaker actuation time.
As shown in FIG. 2, step B3 builds a concrete blackout time model of the load upstream of the fault
According to
Figure GDA0002803432110000083
To
Figure GDA0002803432110000084
The power failure time can be obtained as follows
Figure GDA0002803432110000085
Step B3: and converting the specific power failure time model of the load upstream of the fault into a power failure time model expressed by a logic operator.
Figure GDA0002803432110000091
Wherein
Figure GDA0002803432110000092
And
Figure GDA0002803432110000093
is the set of all manual and automatic switching solutions between the a-th line load I to the fault f.
As shown in fig. 3, step B4: building a concrete power failure time model of load at downstream of fault
According to
Figure GDA0002803432110000094
To
Figure GDA0002803432110000095
Ftu and the existence of the last interconnection switch, the power failure time can be obtained as follows
Figure GDA0002803432110000096
Step B5: and converting the specific power failure time model of the load downstream of the fault into a power failure time model expressed by a logic operator.
Figure GDA0002803432110000097
Step B6: building power failure time model of switch installation candidate position without load and fault
Figure GDA0002803432110000098
In one embodiment of the present invention, the step C includes:
step C1: power supply reliability model of whole power distribution system by traversing load-traversing fault through double-layer traversal
Figure GDA0002803432110000099
Wherein omegafeederFor the set of all the feeders of the system,
Figure GDA00028034321100000910
for all the loads on the a-th line,
Figure GDA00028034321100000911
the set of all possible fault points on the a line; n is a radical oflIs the number of users of the system.
Step C2: the power failure loss of the whole system caused by power failure is solved by adopting a double-layer traversal
Figure GDA0002803432110000101
Wherein
Figure GDA0002803432110000102
The fault rate of the f fault on the a line; omegatIs a load type set;
Figure GDA0002803432110000103
the load quantity is the load quantity of the t-th type of the I-th load;
Figure GDA0002803432110000104
as a function of loss of service with respect to time of service
Step C3: determining the full life-cycle cost of the switch
Figure GDA0002803432110000105
Wherein h is a maintenance cost coefficient; costmcsCost for manual switching; costrcsFor automatic opening and closing
Step C4: building optimal configuration model of power distribution network switch
Figure GDA0002803432110000106
As shown in fig. 4, step C5: and solving by using a genetic algorithm.
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 RCS and MCS are $ 3093 and $ 17500, respectively. The annual operation and maintenance cost of the switch is 5 percent of the investment cost, and the service life of the switch is 20 years. The action time of the automatic section switch, the automatic interconnection switch and the manual section switch is respectively 5min, 10min, 60min and 120 min. The mean time to failure maintenance was 240 min. The breaker actuation time was 400 seconds. The default fault location time is 30 min. Reliability indicator threshold ASAIlimIs 99.95 percent
The method proposed by this patent is used to solve the above problem, and the optimal switch configuration scheme is shown in fig. 5, which includes 7 automatic interconnection switches, 7 automatic section switches and 25 manual section switches.
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 (4)

1. A power distribution network switch optimal configuration method based on logic operators is characterized by comprising the following steps:
step 1: providing two mathematical expression forms of logic operators or and if suitable for power distribution network switch optimization configuration;
step 1.1: introducing a mathematical expression (1) of a logic operator or, wherein the mathematical expression of the logic operator or is as follows: if the solution value in the solution set is 1, the expression value is 1, otherwise, the expression value is 0, and the formula (1) is as follows:
Figure FDA0002803432100000011
where X is the set of solutions, ΩXIs the lower corner label of all solutions in the set, xiIs the solution in the set with the lower corner labeled i;
step 1.2: converting the logical operator or of step 1.1 into the mathematical expression (2):
Figure FDA0002803432100000012
step 1.3: introducing a mathematical expression (3) of a logical operator if based on the step 1.1, wherein the mathematical expression of the logical operator if is as follows: if the solution value in the solution set is 1, the expression takes the value a, otherwise, the expression takes the value b, and the formula (3) is as follows:
Figure FDA0002803432100000013
step 1.4: converting the logical operator if of step 1.3 into the mathematical expression (4):
Figure FDA0002803432100000014
step 2: building a power failure time model of the typical power distribution network about an automatic switch and a manual switch by using the mathematical expression form of the two logic operators provided in the step 1;
and step 3: and (3) building a power distribution network switch optimization configuration model by using the power failure time model built in the step (2), and solving by adopting a genetic algorithm.
2. The method for optimally configuring the switches of the power distribution network based on the logic operators according to the claim 1, wherein the method comprises the following steps: the step 2 specifically comprises the following steps:
step 2.1: setting a solution vector for the optimal configuration of the manual switch and the automatic switch of the circuit independently;
step 2.2: according to the radiation type power distribution network, firstly, 3 groups of basic power failure time expressions of formulas (8), (9) and (10) are established:
Figure FDA0002803432100000021
Figure FDA0002803432100000022
Figure FDA0002803432100000023
where equation (8) represents the case: the path between the fault and the load is not switched or the fault is located upstream of the load; when the fault is positioned at the upstream of the load, a switch exists in the path, an interconnection switch does not exist at the tail of the line, and the power failure time is the sum of the fault positioning time, the fault repairing time and the breaker action time;
wherein the case represented by formula (9) is: the fault is at the upstream of the load, a manual switch or an automatic switch is arranged on a path between the fault and the load, and the power failure time is the sum of fault positioning time, corresponding switch action time and breaker action time;
where equation (10) represents the case: the fault is at the downstream of the load, a corresponding switch exists between the fault and the load, and a corresponding switch also exists at the tail of the line, so that 4 different power failure times are corresponded;
wherein t islocFor locating time of failure, tmcsFor manual switching action time, trcsFor automatic switching action time, tcbThe circuit breaker action time;
step 2.3: building a specific power failure time model of the load at the upstream of the fault according to
Figure FDA0002803432100000025
To
Figure FDA0002803432100000024
The power failure time is obtained as shown in formula (11):
Figure FDA0002803432100000031
where Xa represents the solution vector for the line;
and 2.4, converting the specific power failure time model of the load at the upstream of the fault into a power failure time model expressed by a logic operator, such as a formula (12):
Figure FDA0002803432100000032
wherein t islf(Xa) represents the time of the power failure,
Figure FDA0002803432100000033
and
Figure FDA0002803432100000034
the set of all manual switching and automatic switching solutions between the a-th line load l to the fault f;
step 2.5: building a specific power failure time model of the load at the downstream of the fault according to
Figure FDA0002803432100000035
To
Figure FDA0002803432100000036
Ftu and the existence of the last interconnection switch, the power failure time is obtained as the following formula (13):
Figure FDA0002803432100000037
step 2.6: converting the specific power failure time model of the load at the downstream of the fault into a power failure time model expressed by a logic operator as the following formula (14):
Figure FDA0002803432100000038
step 2.7: and (3) constructing a power failure time model of the switch installation candidate position with no load and fault as the formula (15):
Figure FDA0002803432100000041
3. the method for optimally configuring the switches of the power distribution network based on the logic operators according to the claim 2, wherein the method comprises the following steps: the step 2.1 is to take a set of a solution vector of the a-th line manual switch and a solution vector of the a-th line automatic switch to represent a solution vector of the line, wherein the solution vector of the a-th line manual switch is formula (5), the solution vector of the a-th line automatic switch is formula (6), and the solution vector of the line is formula (7):
Figure FDA0002803432100000042
Figure FDA0002803432100000043
Xa＝(Xa-mcs,Xa-rcs) (7)
wherein
Figure FDA0002803432100000044
Indicates whether the manual switch is installed at the first switch installation candidate position of the a-th line,
Figure FDA0002803432100000045
and representing whether the automatic switch is installed at the first switch installation candidate position of the a-th line.
4. The method for optimally configuring the switches of the power distribution network based on the logic operators as claimed in claim 3, wherein the method comprises the following steps: the step 3 specifically comprises the following steps:
step 3.1: a two-level traversal of the traversal load over the fault is used to obtain a power reliability model for the entire distribution system, as shown in equation (16)
Figure FDA0002803432100000046
Wherein omegafeederFor the set of all the feeders of the system,
Figure FDA0002803432100000047
for all the loads on the a-th line,
Figure FDA0002803432100000048
the set of all possible fault points on the a line; n is a radical oflIs the number of users of the system;
step 3.2: and (3) adopting a double-layer traversal to obtain the power failure loss of the whole system caused by power failure, such as formula (17):
Figure FDA0002803432100000049
wherein
Figure FDA00028034321000000410
The fault rate of the f fault on the a line; omegatIs a load type set;
Figure FDA00028034321000000411
the load quantity is the load quantity of the ith load type of the ith load;
Figure FDA00028034321000000412
a power outage loss function corresponding to the power outage time;
and 3.3, obtaining the full life cycle cost of the switch according to a formula (18):
Figure FDA0002803432100000051
wherein h is a maintenance cost coefficient; costmcsCost for manual switching; costrcsCost for automatic switching;
step 3.4, building an optimal configuration model of the power distribution network switch, such as a formula (19)
Figure FDA0002803432100000052
Wherein ASAIlimIs a reliability index threshold;
and 3.5, solving by using a genetic algorithm.
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Feeder-Switch Relocation for Customer Interruption Cost Minimization;Jen-Hao Teng 等;《IEEE Trans on Power Delivery》;20020131;第17卷(第1期);254-259 *

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