CN112688285A - Fault isolation and load recovery method for optimized scheduling of operators in power distribution network - Google Patents

Fault isolation and load recovery method for optimized scheduling of operators in power distribution network Download PDF

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CN112688285A
CN112688285A CN202011505972.8A CN202011505972A CN112688285A CN 112688285 A CN112688285 A CN 112688285A CN 202011505972 A CN202011505972 A CN 202011505972A CN 112688285 A CN112688285 A CN 112688285A
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operator
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CN112688285B (en
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秦超
刘建存
余贻鑫
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Tianjin University
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    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02B—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO BUILDINGS, e.g. HOUSING, HOUSE APPLIANCES OR RELATED END-USER APPLICATIONS
    • Y02B70/00—Technologies for an efficient end-user side electric power management and consumption
    • Y02B70/30—Systems integrating technologies related to power network operation and communication or information technologies for improving the carbon footprint of the management of residential or tertiary loads, i.e. smart grids as climate change mitigation technology in the buildings sector, including also the last stages of power distribution and the control, monitoring or operating management systems at local level
    • Y02B70/3225—Demand response systems, e.g. load shedding, peak shaving
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y04—INFORMATION OR COMMUNICATION TECHNOLOGIES HAVING AN IMPACT ON OTHER TECHNOLOGY AREAS
    • Y04S—SYSTEMS INTEGRATING TECHNOLOGIES RELATED TO POWER NETWORK OPERATION, COMMUNICATION OR INFORMATION TECHNOLOGIES FOR IMPROVING THE ELECTRICAL POWER GENERATION, TRANSMISSION, DISTRIBUTION, MANAGEMENT OR USAGE, i.e. SMART GRIDS
    • Y04S20/00—Management or operation of end-user stationary applications or the last stages of power distribution; Controlling, monitoring or operating thereof
    • Y04S20/20—End-user application control systems
    • Y04S20/222—Demand response systems, e.g. load shedding, peak shaving

Abstract

The invention discloses a fault isolation and load recovery method for optimal scheduling of operators in a power distribution network, which comprises the steps of establishing a fault isolation and load recovery model considering the optimal scheduling of the operators by taking the minimum system loss load as an objective function, and solving under a given constraint condition to obtain a switching action and operator scheduling scheme for minimizing the system loss load; the constraint conditions comprise power grid operation constraint, operator scheduling constraint and operator and switch action coupling constraint.

Description

Fault isolation and load recovery method for optimized scheduling of operators in power distribution network
Technical Field
The invention belongs to the field of power system analysis, and particularly relates to a fault isolation and load recovery method for optimal scheduling of operators in a power distribution network.
Background
The electric power system is an important infrastructure of modern society, and the safe and reliable operation of the electric power system is an important guarantee for normal proceeding of social life and economic life of people. With the frequent occurrence of extreme weather, the large-scale power failure accidents of the power system caused by the extreme weather are more and more, and the production and the life of people are seriously influenced. When multiple faults in the power distribution system are caused by extreme weather, after the occurrence area of the faults is preliminarily determined through the configured fault indicators, the manual switch and the telemechanical switch can carry out preliminary fault isolation and load recovery. After the patrol personnel patrol and examine the fault area and determine the specific occurrence position of the fault, the manual switch and the telemechanical switch can further complete fault isolation and load recovery. In the fault isolation and load recovery processes, the problems of scheduling and operation of operators and the like need to be considered comprehensively by the action of the manual switch, and the action decision of a plurality of manual switches makes the problems more complicated. Therefore, it is important to comprehensively consider the switching action and the operator scheduling scheme for the operator to optimize the scheduling so as to obtain the minimum system loss load.
Disclosure of Invention
In order to further improve the efficiency of system fault isolation and load recovery after a power distribution system has a fault, particularly after multiple serious faults caused by extreme weather, the invention provides a fault isolation and load recovery method considering the optimized scheduling of an operator, and the efficiency of system fault isolation and load recovery is improved through the optimization of switching action and the scheduling optimization of the operator. The specific scheme comprises the following steps:
a fault isolation and load recovery method for optimized scheduling of operators in a power distribution network comprises a manual switch, a telemechanical switch, a fault indicator and operator position information, and comprises the following steps:
establishing a fault isolation and load recovery model scheduled by an operator according to fault data provided by a fault indicator; wherein
The fault isolation and load recovery model obtains the minimum loss in the power distribution network through the following objective function
The load capacity; the objective function is represented by the form:
Figure BDA0002844956760000011
wherein omegaTRepresenting the time period under consideration; omegaBRepresenting the set of nodes under considerationCombining; omegaiRepresenting the considered node weights; pC,i,tRepresenting the amount of node workload under consideration;
and the fault isolation and load recovery model solves and outputs optimal scheduling data between switching actions and operators in the distribution network for the objective function by setting constraint conditions.
Further, the constraint conditions comprise power distribution network operation constraints, operator scheduling constraints and operator and switch action coupling constraints.
Further, the power distribution network operation constraints include: topology initialization constraints, line on-off state constraints, radial topology constraints, power flow balance constraints, line capacity constraints, voltage amplitude constraints, distributed power supply output constraints, load loss constraints, fault propagation constraints and switch action constraints; wherein:
the topology initialization constraints include:
Figure BDA0002844956760000021
Figure BDA0002844956760000022
wherein the content of the first and second substances,
Figure BDA0002844956760000023
indicating whether the i side of the line ij is closed at the time t, and if so, closing the line ij
Figure BDA0002844956760000024
Otherwise
Figure BDA0002844956760000025
Figure BDA0002844956760000026
Indicates whether the i side of the line ij is closed before the time t is 0, and if the i side is closed, the i side is closed
Figure BDA0002844956760000027
Otherwise
Figure BDA0002844956760000028
ΩLRepresenting the set of lines under consideration.
Constraints (2), (3) limit the initial open and closed state of the line.
The line open-closed state constraint includes:
Figure BDA0002844956760000029
wherein z isij,tIndicating whether the line ij is closed at the time t, if so, zij,t1, otherwise zij,t＝0；fijIndicating whether the line ij is in fault, if so, fij1, otherwise fij＝0；
Constraint (4) indicates that line ij is closed only when both of its side states are closed and not faulty;
equation (4) can be linearized by the following equation:
Figure BDA00028449567600000210
Figure BDA00028449567600000211
the radial topological constraint is expressed as:
Figure BDA0002844956760000031
Figure BDA0002844956760000032
Figure BDA0002844956760000033
wherein N isbusRepresenting the number of considered nodes; gamma rayi,tWhether the node i at the time t is a root node of the island network or not is shown, and if yes, gamma is showni,t1, otherwise γi,t0; m represents a maximum number; chi shapeij,tRepresents the virtual flow size on line ij at time t;
the constraint (7) is a coupling constraint of the number of closed lines and the number of root nodes; constraining (8) the limiting node virtual flow injection; constraints (9) limit the flow of only closed circuits through the virtual stream;
the power flow balance constraint is expressed as:
Figure BDA0002844956760000034
Figure BDA0002844956760000035
Figure BDA0002844956760000036
wherein, PL,iAnd QL,iRespectively representing the active demand and the reactive demand of the node i; pD,i,tAnd QD,i,tRespectively representing the active output quantity and the reactive output quantity of a node i at the time t; pC,i,tAnd QC,i,tRespectively representing the active load loss amount and the reactive load loss amount of a node i at the moment t; pF,ij,tAnd QF,ij,tRespectively representing the active power flow and the reactive power flow of a line ij at the moment t; omegaparent,iRepresenting a node i mother node set; omegachild,iA set of child nodes representing node i;
the line capacity constraint is expressed as:
Figure BDA0002844956760000037
Figure BDA0002844956760000038
wherein the content of the first and second substances,
Figure BDA0002844956760000039
indicating the capacity of line ij.
The voltage magnitude constraint is expressed as:
Figure BDA00028449567600000310
wherein the content of the first and second substances,
Figure BDA00028449567600000311
and
Figure BDA00028449567600000312
respectively representing the minimum and maximum voltages allowed at node i.
The distributed power output constraint is expressed as:
Figure BDA0002844956760000041
Figure BDA0002844956760000042
wherein eta isi,tIndicating whether the node i at the time t is in the fault area, if yes, etai,t1, otherwise ηi,t＝0；
Figure BDA0002844956760000043
And
Figure BDA0002844956760000044
respectively representing the minimum value and the maximum value of the active output of the distributed power supply at the node i;
Figure BDA0002844956760000045
and
Figure BDA0002844956760000046
respectively representing the minimum value and the maximum value of the reactive output of the distributed power supply at the node i.
The loss of load constraint is expressed as:
Figure BDA0002844956760000047
Figure BDA0002844956760000048
the fault propagation constraint is expressed as:
Figure BDA0002844956760000049
Figure BDA00028449567600000410
Figure BDA00028449567600000411
Figure BDA00028449567600000412
constraints (20), (21) represent node faults on both sides of the closed fault line; constraints (22), (23) indicate simultaneous failure or no failure of nodes on both sides of the closed line.
The switching action constraint is expressed as:
Figure BDA00028449567600000413
wherein the content of the first and second substances,
Figure BDA00028449567600000414
indicating whether the i side of the line ij is provided with a telemechanical switch or not, and if so, indicating that the telemechanical switch is arranged on the i side of the line ij
Figure BDA00028449567600000415
Otherwise
Figure BDA00028449567600000416
Figure BDA00028449567600000417
Indicating whether a manual switch is arranged on the i side of the line ij or not, and if so, indicating that the manual switch is arranged on the i side of the line ij
Figure BDA00028449567600000418
Otherwise
Figure BDA00028449567600000419
TMSIndicating the manual switch operation time.
The constraint (24) indicates that the line on-off state can only be changed by the remote switch before the manual switch completes the operation, and the line state can be changed by the manual switch and the remote switch after the manual switch completes the operation.
Further, the operator scheduling constraint is expressed as:
Figure BDA0002844956760000051
Figure BDA0002844956760000052
Figure BDA0002844956760000053
Figure BDA0002844956760000054
wherein phi isk,m,tIndicating whether the kth operator reaches the m position at the time t, if soIs then phik,m,t1, otherwise phik,m,t＝0；ΩCMRepresenting a set of manual switch operators; vS,kIndicating the starting position of the kth operator; t isS,kIndicating a start time when the kth operator can be scheduled; omegaVDRepresenting an initial set of warehouse locations for an operator; t ismnIndicating the time of the operator's transition from the m position to the n position.
The constraint (25) indicates the starting position of the operator at the starting moment; the constraint (26) indicates that the operator is not in any position before the start time at which he can be scheduled, but at most one position at each moment after the start time at which he can be scheduled; the constraint (27) is a transfer constraint of the operator between different positions; the constraint (28) is a transfer constraint for the operator between the initial warehouse and the manual switch position.
Further, the operator and switch action coupling constraint is expressed as:
Figure BDA0002844956760000055
wherein δ () is a mapping function from the position of the line to the line number, and ij ═ δ (m) represents that the position of the line ij is m.
Equation (29) can be linearized by the following equation:
Figure BDA0002844956760000056
Figure BDA0002844956760000057
further, the fault isolation and load recovery model considering the operator optimization scheduling is represented by the following form:
Figure BDA0002844956760000061
advantageous effects
Compared with the prior art, the invention has the beneficial effects that:
in the prior art, when considering the change of the line opening and closing state, only one switch type is generally considered, and the difference between a telecontrol switch and a manual switch in action is ignored. Meanwhile, when considering manual switch action, the scheduling of the switch operator is not usually considered. Compared with the prior art, the method fills the blank, comprehensively considers different characteristics of the telemechanical switch and the manual switch during action, operator scheduling and the coupling relation between the operator scheduling and the manual switch action, and accordingly obtains a fault isolation and load recovery scheme considering the operator optimization scheduling. In conclusion, the method provided by the invention can realize efficient fault isolation and load recovery processes, so that the coping capacity of the power distribution network for multiple serious faults caused by faults, especially extreme weather, is improved.
Drawings
Fig. 1 is a schematic flow chart of a fault isolation and load recovery method for optimal scheduling of an operator in a power distribution network according to the present invention;
fig. 2 is a schematic diagram of an IEEE 123 node power distribution system.
Detailed Description
The technical solution of the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1, the present invention provides a fault isolation and load recovery method for operator optimized scheduling in a power distribution network, which is characterized in that the power distribution network includes a manual switch, a telemechanical switch, a fault indicator and operator position information, and the steps are as follows:
establishing operator scheduled fault isolation and load restoration from fault data provided by a fault indicator
A model; the representation form is:
Figure BDA0002844956760000062
the fault isolation and load recovery model obtains the minimum loss in the power distribution network through the following objective function
The load capacity; the objective function is represented by the form:
Figure BDA0002844956760000063
wherein omegaTRepresenting the time period under consideration; omegaBRepresenting the set of nodes under consideration; omegaiRepresenting the considered node weights; pC,i,tRepresenting the amount of node workload under consideration;
and the fault isolation and load recovery model solves and outputs optimal scheduling data between switching actions and operators in the distribution network for the objective function by setting constraint conditions.
The constraint conditions comprise power distribution network operation constraints, operator scheduling constraints and operator and switch action coupling constraints.
The power distribution network operation constraints include: topology initialization constraints, line on-off state constraints, radial topology constraints, power flow balance constraints, line capacity constraints, voltage amplitude constraints, distributed power supply output constraints, load loss constraints, fault propagation constraints and switch action constraints; wherein:
the topology initialization constraints include:
Figure BDA0002844956760000071
Figure BDA0002844956760000072
wherein the content of the first and second substances,
Figure BDA0002844956760000073
indicating whether the i side of the line ij is closed at the time t, and if so, closing the line ij
Figure BDA0002844956760000074
Otherwise
Figure BDA0002844956760000075
Figure BDA0002844956760000076
Indicates whether the i side of the line ij is closed before the time t is 0, and if the i side is closed, the i side is closed
Figure BDA0002844956760000077
Otherwise
Figure BDA0002844956760000078
ΩLRepresenting the set of lines under consideration.
Constraints (2), (3) limit the initial open and closed state of the line.
The line open-closed state constraint includes:
Figure BDA0002844956760000079
wherein z isij,tIndicating whether the line ij is closed at the time t, if so, zij,t1, otherwise zij,t＝0；fijIndicating whether the line ij is in fault, if so, fij1, otherwise fij＝0；
Constraint (4) indicates that line ij is closed only when both of its side states are closed and not faulty;
equation (4) can be linearized by the following equation:
Figure BDA00028449567600000710
Figure BDA00028449567600000711
the radial topological constraint is expressed as:
Figure BDA0002844956760000081
Figure BDA0002844956760000082
Figure BDA0002844956760000083
wherein N isbusRepresenting the number of considered nodes; gamma rayi,tWhether the node i at the time t is a root node of the island network or not is shown, and if yes, gamma is showni,t1, otherwise γi,t0; m represents a maximum number; chi shapeij,tRepresents the virtual flow size on line ij at time t;
the constraint (7) is a coupling constraint of the number of closed lines and the number of root nodes; constraining (8) the limiting node virtual flow injection; constraints (9) limit the flow of only closed circuits through the virtual stream;
the power flow balance constraint is expressed as:
Figure BDA0002844956760000084
Figure BDA0002844956760000085
Figure BDA0002844956760000086
wherein, PL,iAnd QL,iRespectively representing the active demand and the reactive demand of the node i; pD,i,tAnd QD,i,tRespectively representing the active output quantity and the reactive output quantity of a node i at the time t; pC,i,tAnd QC,i,tRespectively representing the active load loss amount and the reactive load loss amount of a node i at the moment t; pF,ij,tAnd QF,ij,tRespectively representing active tide of line ij at time tFlow and reactive power flow; omegaparent,iRepresenting a node i mother node set; omegachild,iA set of child nodes representing node i;
the line capacity constraint is expressed as:
Figure BDA0002844956760000087
Figure BDA0002844956760000088
wherein the content of the first and second substances,
Figure BDA0002844956760000089
indicating the capacity of line ij.
The voltage magnitude constraint is expressed as:
Figure BDA00028449567600000810
wherein the content of the first and second substances,
Figure BDA00028449567600000811
and
Figure BDA00028449567600000812
respectively representing the minimum and maximum voltages allowed at node i.
The distributed power output constraint is expressed as:
Figure BDA0002844956760000091
Figure BDA0002844956760000092
wherein eta isi,tIndicating whether the node i at the time t is in the fault area, if yes, etai,t1, otherwise ηi,t＝0；
Figure BDA0002844956760000093
And
Figure BDA0002844956760000094
respectively representing the minimum value and the maximum value of the active output of the distributed power supply at the node i;
Figure BDA0002844956760000095
and
Figure BDA0002844956760000096
respectively representing the minimum value and the maximum value of the reactive output of the distributed power supply at the node i.
The loss of load constraint is expressed as:
Figure BDA0002844956760000097
Figure BDA0002844956760000098
the fault propagation constraint is expressed as:
Figure BDA0002844956760000099
Figure BDA00028449567600000910
Figure BDA00028449567600000911
Figure BDA00028449567600000912
constraints (20), (21) represent node faults on both sides of the closed fault line; constraints (22), (23) indicate simultaneous failure or no failure of nodes on both sides of the closed line.
The switching action constraint is expressed as:
Figure BDA00028449567600000913
wherein the content of the first and second substances,
Figure BDA00028449567600000914
indicating whether the i side of the line ij is provided with a telemechanical switch or not, and if so, indicating that the telemechanical switch is arranged on the i side of the line ij
Figure BDA00028449567600000915
Otherwise
Figure BDA00028449567600000916
Figure BDA00028449567600000917
Indicating whether a manual switch is arranged on the i side of the line ij or not, and if so, indicating that the manual switch is arranged on the i side of the line ij
Figure BDA00028449567600000918
Otherwise
Figure BDA00028449567600000919
TMSIndicating the manual switch operation time.
The constraint (24) indicates that the line on-off state can only be changed by the remote switch before the manual switch completes the operation, and the line state can be changed by the manual switch and the remote switch after the manual switch completes the operation.
The operator scheduling constraint is expressed as:
Figure BDA0002844956760000101
Figure BDA0002844956760000102
Figure BDA0002844956760000103
Figure BDA0002844956760000104
wherein phi isk,m,tIndicating whether the kth operator reaches the position m at the moment t, if so, phik,m,t1, otherwise phik,m,t＝0；ΩCMRepresenting a set of manual switch operators; vS,kIndicating the starting position of the kth operator; t isS,kIndicating a start time when the kth operator can be scheduled; omegaVDRepresenting an initial set of warehouse locations for an operator; t ismnIndicating the time of the operator's transition from the m position to the n position.
The constraint (25) indicates the starting position of the operator at the starting moment; the constraint (26) indicates that the operator is not in any position before the start time at which he can be scheduled, but at most one position at each moment after the start time at which he can be scheduled; the constraint (27) is a transfer constraint of the operator between different positions; the constraint (28) is a transfer constraint for the operator between the initial warehouse and the manual switch position.
The operator and switch action coupling constraint is expressed as:
Figure BDA0002844956760000105
wherein δ (·) is a mapping function from the location of the line to the line number, and ij δ (m) represents that the location of the line ij is m.
Equation (29) can be linearized by the following equation:
Figure BDA0002844956760000106
Figure BDA0002844956760000107
the invention is applied in practice:
step 1: the validity and correctness of the method provided by the invention are verified by adopting an IEEE 123 node power distribution system as shown in figure 2. Based on the line fault information, the operators 1, 2, 5, 6 reach the positions 28-34, 32-33, 113 and 114 and 115 respectively at the time t-13 to start the operation tasks, and the operators 3, 4 reach the positions 59-60 and 74-75 respectively at the time t-19 to start the operation tasks.
Step 2:
and establishing a fault isolation and load recovery model considering the optimal scheduling of the operators by taking the minimum system loss load as an objective function, and solving under a given constraint condition to obtain a switching action and operator scheduling scheme for minimizing the system loss load. The constraint conditions include grid operation constraints, operator scheduling constraints, and operator and switch action coupling constraints.
And step 3:
the optimal switching action and personnel scheduling scheme results obtained by solving the fault isolation and load recovery model considering the operator optimal scheduling are shown in table 1. Wherein, the elements in the table represent that the operator arrives at a certain position at a certain time or the telemechanical switch at a certain position acts at a certain time, such as: operator 1 arrives at lines 28-34 at time t-13, lines 26-29 at time t-16, and lines 22-24 at time t-19; at time t 15, the telemechanical switch at line 115 and 116 is actuated, at time t 17, the telemechanical switch at line 49-121, at time t 20, the telemechanical switch at line 14-19, at time t 21, the telemechanical switch at line 102 and 122, at time t 22, the telemechanical switch at line 53-119, and at time t 23, the telemechanical switches at lines 55-95 and 79-81. As shown in table 1:
TABLE 1 optimal scheme for switching actions and operator scheduling
Figure BDA0002844956760000111

Claims (6)

1. A fault isolation and load recovery method for optimized scheduling of operators in a power distribution network is characterized in that the power distribution network comprises a manual switch, a telemechanical switch, a fault indicator and position information of the operators, and the method comprises the following steps:
establishing a fault isolation and load recovery model scheduled by an operator according to fault data provided by a fault indicator; wherein
The fault isolation and load recovery model obtains the minimum loss load in the power distribution network through the following objective function; the objective function is represented by the form:
Figure FDA0002844956750000011
wherein omegaTRepresenting the time period under consideration; omegaBRepresenting the set of nodes under consideration; omegaiRepresenting the considered node weights; pC,i,tRepresenting the amount of node workload under consideration;
and the fault isolation and load recovery model solves and outputs optimal scheduling data between switching actions and operators in the distribution network for the objective function by setting constraint conditions.
2. The method for fault isolation and load restoration for operator optimized scheduling in a power distribution network of claim 1, wherein: the constraint conditions include: distribution network operation constraints, operator scheduling constraints, and operator and switch action coupling constraints.
3. The method for fault isolation and load restoration for operator optimized scheduling in an electrical distribution network of claim 2, wherein: the power distribution network operation constraints include: topology initialization constraints, line on-off state constraints, radial topology constraints, power flow balance constraints, line capacity constraints, voltage amplitude constraints, distributed power supply output constraints, load loss constraints, fault propagation constraints and switch action constraints; wherein:
the topology initialization constraints include:
Figure FDA0002844956750000012
Figure FDA0002844956750000013
wherein the content of the first and second substances,
Figure FDA0002844956750000014
indicating whether the i side of the line ij is closed at the time t, and if so, closing the line ij
Figure FDA0002844956750000015
Otherwise
Figure FDA0002844956750000016
Figure FDA0002844956750000017
Indicates whether the i side of the line ij is closed before the time t is 0, and if the i side is closed, the i side is closed
Figure FDA0002844956750000018
Otherwise
Figure FDA0002844956750000019
ΩLRepresenting the set of lines under consideration.
Constraints (2), (3) limit the initial open and closed state of the line.
The line open-closed state constraint includes:
Figure FDA0002844956750000021
wherein z isij,tIndicating whether the line ij is closed at the time t, if so, zij,t1, otherwise zij,t＝0；fijIndicating whether the line ij is in fault, if so, fij1, otherwise fij＝0；
Constraint (4) indicates that line ij is closed only when both of its side states are closed and not faulty;
equation (4) can be linearized by the following equation:
Figure FDA0002844956750000022
Figure FDA0002844956750000023
the radial topological constraint is expressed as:
Figure FDA0002844956750000024
Figure FDA0002844956750000025
Figure FDA0002844956750000026
wherein N isbusRepresenting the number of considered nodes; gamma rayi,tWhether the node i at the time t is a root node of the island network or not is shown, and if yes, gamma is showni,t1, otherwise γi,t0; m represents a maximum number; chi shapeij,tRepresents the virtual flow size on line ij at time t;
the constraint (7) is a coupling constraint of the number of closed lines and the number of root nodes; constraining (8) the limiting node virtual flow injection; constraints (9) limit the flow of only closed circuits through the virtual stream;
the power flow balance constraint is expressed as:
Figure FDA0002844956750000027
Figure FDA0002844956750000028
Figure FDA0002844956750000029
wherein, PL,iAnd QL,iRespectively representing the active demand and the reactive demand of the node i; pD,i,tAnd QD,i,tRespectively representing the active output quantity and the reactive output quantity of a node i at the time t; pC,i,tAnd QC,i,tRespectively representing the active load loss amount and the reactive load loss amount of a node i at the moment t; pF,ij,tAnd QF,ij,tRespectively representing the active power flow and the reactive power flow of a line ij at the moment t; omegaparent,iRepresenting a node i mother node set; omegachild,iA set of child nodes representing node i;
the line capacity constraint is expressed as:
Figure FDA0002844956750000031
Figure FDA0002844956750000032
wherein the content of the first and second substances,
Figure FDA0002844956750000033
indicating the capacity of line ij.
The voltage magnitude constraint is expressed as:
Figure FDA0002844956750000034
wherein the content of the first and second substances,
Figure FDA0002844956750000035
and
Figure FDA0002844956750000036
respectively representing the minimum and maximum voltages allowed at node i.
The distributed power output constraint is expressed as:
Figure FDA0002844956750000037
Figure FDA0002844956750000038
wherein eta isi,tIndicating whether the node i at the time t is in the fault area, if yes, etai,t1, otherwise ηi,t＝0；
Figure FDA0002844956750000039
And
Figure FDA00028449567500000310
respectively representing the minimum value and the maximum value of the active output of the distributed power supply at the node i;
Figure FDA00028449567500000311
and
Figure FDA00028449567500000312
respectively representing the minimum value and the maximum value of the reactive output of the distributed power supply at the node i.
The loss of load constraint is expressed as:
Figure FDA00028449567500000313
Figure FDA00028449567500000314
the fault propagation constraint is expressed as:
Figure FDA00028449567500000315
Figure FDA00028449567500000316
Figure FDA00028449567500000317
Figure FDA00028449567500000318
constraints (20), (21) represent node faults on both sides of the closed fault line; constraints (22), (23) indicate simultaneous failure or no failure of nodes on both sides of the closed line.
The switching action constraint is expressed as:
Figure FDA0002844956750000041
wherein the content of the first and second substances,
Figure FDA0002844956750000042
indicating whether the i side of the line ij is provided with a telemechanical switch or not, and if so, indicating that the telemechanical switch is arranged on the i side of the line ij
Figure FDA0002844956750000043
Otherwise
Figure FDA0002844956750000044
Figure FDA0002844956750000045
Indicating whether a manual switch is arranged on the i side of the line ij or not, and if so, indicating that the manual switch is arranged on the i side of the line ij
Figure FDA0002844956750000046
Otherwise
Figure FDA0002844956750000047
TMSIndicating the manual switch operation time.
The constraint (24) indicates that the line on-off state can only be changed by the remote switch before the manual switch completes the operation, and the line state can be changed by the manual switch and the remote switch after the manual switch completes the operation.
4. The method for fault isolation and load restoration for operator optimized scheduling in an electrical distribution network of claim 2, wherein the operator scheduling constraint is expressed as:
Figure FDA0002844956750000048
Figure FDA0002844956750000049
Figure FDA00028449567500000410
Figure FDA00028449567500000411
wherein phi isk,m,tIndicating whether the kth operator reaches the position m at the moment t, if so, phik,m,t1, otherwise phik,m,t＝0；ΩCMRepresenting a set of manual switch operators; vS,kIndicating the starting position of the kth operator; t isS,kIndicating a start time when the kth operator can be scheduled; omegaVDRepresenting an initial set of warehouse locations for an operator; t ismnIndicating the time of the operator's transition from the m position to the n position.
The constraint (25) indicates the starting position of the operator at the starting moment; the constraint (26) indicates that the operator is not in any position before the start time at which he can be scheduled, but at most one position at each moment after the start time at which he can be scheduled; the constraint (27) is a transfer constraint of the operator between different positions; the constraint (28) is a transfer constraint for the operator between the initial warehouse and the manual switch position.
5. The method for fault isolation and load restoration for operator optimized scheduling in an electric power distribution network according to claim 2, wherein the operator and switch action coupling constraints are expressed as:
Figure FDA0002844956750000051
wherein δ (·) is a mapping function from the location of the line to the line number, and ij δ (m) represents that the location of the line ij is m.
Equation (29) can be linearized by the following equation:
Figure FDA0002844956750000052
Figure FDA0002844956750000053
。
6. the method for fault isolation and load restoration according to any one of claims 1-5, wherein the model for fault isolation and load restoration considering the operator optimization scheduling is represented by:
Figure FDA0002844956750000054
。
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