CN115470602B - Power supply network topology optimization method considering node differentiation and destruction resistance requirements - Google Patents

Power supply network topology optimization method considering node differentiation and destruction resistance requirements Download PDF

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CN115470602B
CN115470602B CN202211167753.2A CN202211167753A CN115470602B CN 115470602 B CN115470602 B CN 115470602B CN 202211167753 A CN202211167753 A CN 202211167753A CN 115470602 B CN115470602 B CN 115470602B
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nodes
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CN115470602A (en
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黄生俊
焦鹏
王锐
张涛
刘亚杰
史志超
黄旭程
江波
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National University of Defense Technology
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/10—Geometric CAD
    • G06F30/18—Network design, e.g. design based on topological or interconnect aspects of utility systems, piping, heating ventilation air conditioning [HVAC] or cabling
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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    • G06Q10/0631—Resource planning, allocation, distributing or scheduling for enterprises or organisations
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    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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    • G06Q50/06—Electricity, gas or water supply
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
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    • G—PHYSICS
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    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/04—Power grid distribution networks
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Abstract

The invention discloses a power supply network topology optimization method considering node differentiation and destruction resistance requirements, which comprises the following steps: s1, collecting node information of a distributed autonomous power supply network; s2, adding line length constraint L between network nodes 1 The method comprises the steps of carrying out a first treatment on the surface of the S3, judging the type of the network node, if the network node is the I-type node, constructing a fault scene and generating corresponding constraint conditions; if the node is a class II node, adding a selection range constraint L between two network nodes 2 When constructing a fault scene, only considering that the distance between two fault nodes is less than or equal to L 2 Generating corresponding constraint conditions; s4, taking the minimum line total length as an optimization target, taking an adjacency matrix of network nodes as a decision variable, and solving an optimal topological structure of the mixed integer linear programming model through a YALMIP linear solver under the constraint condition obtained in the step S3. The invention can reduce the size of decision space, reduce the number of constraint conditions and remarkably improve the calculation efficiency.

Description

Power supply network topology optimization method considering node differentiation and destruction resistance requirements
Technical Field
The invention relates to the technical field of power supply network topology optimization design, in particular to a power supply network topology optimization method considering node differentiation and destruction resistance requirements.
Background
Compared with the traditional centralized power supply, the distributed power supply has various advantages: high-voltage power transmission is not needed, and the line loss is low; the construction of a power distribution station is not needed, and the additional increase of the construction cost, the power transmission cost and the power distribution cost can be avoided; the initial construction and installation cost is low, the use, the expansion and the transformation are easy, and the flexibility is high; the distributed power stations are mutually independent and can be controlled by themselves, so that the occurrence probability of large-area power supply accidents is greatly reduced, and the power supply reliability is high; renewable energy sources can be used for supplying power on a large scale, and the environment-friendly effect is promoted; suitable for remote areas, islands and other areas where a centralized power supply station cannot be or is difficult to build. Particularly, in the context of the urgent need to optimize energy structure, improve energy utilization efficiency, enhance safety and reliability of energy industry, and solve environmental pollution, distributed power supply networks have gained widespread attention in industrial, commercial, and academic fields with their unique advantages. The topology structure can have great influence on the aspects of construction, operation, control, performance and the like of the distributed power supply network, so that the topology structure is also one of main research directions in the research of the distributed power supply network.
The distributed power supply network needs to perform networking connection on each distributed power supply, which needs to be applied to micro-grid technology. The micro-grid technology is an effective way for realizing local source load balance and improving the distributed energy permeability and the utilization rate. However, a single micro-grid is limited by locality, so that the power generation capacity of the single micro-grid is limited, and due to fluctuation and uncertainty of renewable energy sources, events such as abrupt change of output power and the like can occur in the operation process, so that the reliability of the independent micro-grid is insufficient. Therefore, the reliability and the elasticity of the power system can be improved by the mode of jointly operating a plurality of micro-grids, the further efficient utilization of renewable energy sources is promoted, and the method also receives more and more attention.
However, the current research on the survivability of the network topology structure is only considered from the system perspective, but ignores the difference of survivability requirements of different nodes, and does not consider the energy complementation among the nodes of the distributed power supply network in combination with the differentiated survivability requirements, so that the system energy is not beneficial to fully, efficiently and accurately utilizing the system energy. Therefore, it is necessary to develop a power supply network topology optimization method considering the node differentiation and destruction resistance requirements.
Disclosure of Invention
The invention aims to provide a power supply network topology optimization method considering node differentiation and destruction resistance requirements, so as to overcome the defects of the prior art.
In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
a power supply network topology optimization method considering node differentiation and destruction resistance requirements comprises the following steps:
s1, collecting distributed autonomous power supply network node information, wherein the distributed autonomous power supply network node information at least comprises node power generation capacity, load demand, position coordinates and type of survivability demand;
s2, adding line length constraint L between network nodes 1 And only for pitches less than or equal to L 1 Considering whether to lay a line or not;
s3, judging the type of the network node according to the type of the survivability requirement, if the network node is the I-type node, constructing a fault scene and generating corresponding constraint conditions; if the node is II-type node, adding a selection range constraint L between two network nodes 2 When constructing a fault scene, only considering that the distance between two fault nodes is less than or equal to L 2 Generating corresponding constraint conditions;
s4, taking the minimum total length of the line as an optimization target, taking whether any two nodes in the network are connected as an adjacent matrix or not, taking the adjacent matrix as a decision variable, and solving an optimal topological structure of a mixed integer linear programming model through a YALMIP linear solver under the constraint condition obtained in the step S3, wherein the mixed integer linear programming model is formed based on node information.
Further, in the step S1, the power generation capacity of each network node in a normal state is greater than the load requirement, the class i node and the class II node respectively meet constraint conditions under different fault scenes, the class i node needs to meet simpler constraint conditions, and the class II node needs to meet complex constraint conditions.
Further, in the step S2, the pitch is only L or less 1 The step of considering whether to lay a line is specifically: traversing the distance matrix of the network node, if the element in the distance matrix is greater than L 1 The element at the position corresponding to the adjacent matrix is fixed to 0.
Further, in the step S3:
if the type of the network node is I-type node, constructing a fault scene to be a fault scene which only needs to consider that the network node loses the power generation capacity, and generating corresponding constraint conditions to be that each I-type node only needs to meet the load recovery requirement when the network node fails to generate power;
if the type of the network node is a class II node, the fault scene is that the class II node and another network node lose the power generation capacity, and each class II node and the class II node are in L 2 Any network node in the range forms a fault scene, and the load recovery requirements of two fault nodes in each fault scene need to be met.
Further, in the step S4, the obtained constraint condition is added to the mixed integer linear programming model, and the optimal topology structure is solved.
Further, the optimization objective function of the mixed integer linear programming model is:
Figure BDA0003862063770000021
l ij ＝|x i -x j |+|y i -y j | (2)
equation (1) represents an objective function to be minimized, in which
Figure BDA0003862063770000022
Representing the total length of the line to be laid between the nodes, +.>
Figure BDA0003862063770000023
A penalty value representing when the constraint cannot be fully satisfied; formula (2) represents the distance between two nodes, wherein i and j represent any two nodes, x i ，y i And x j ，y j Representing the abscissa, l, and the ordinate of i and j, respectively ij Representing the Manhattan distance between i and j; s is(s) ij Decision variables 0-1, indicating whether a tie line is to be set between i and j, all s ij A symmetrical decision variable matrix can be formed, and i is greater than j to avoid repetition when calculating the target value; delta k Is a relaxation variable; m is a constant large enough to represent penalty ratio;
constraint conditions of the mixed integer linear programming model are as follows:
Figure BDA0003862063770000031
Figure BDA0003862063770000032
Figure BDA0003862063770000033
r ij ＝s ij ·(g i -d i +g j -d j ) (6)
Figure BDA0003862063770000034
Figure BDA0003862063770000035
Figure BDA0003862063770000036
Figure BDA0003862063770000037
Figure BDA0003862063770000038
Figure BDA0003862063770000039
equation (3) represents a line length constraint; equation (4) represents the energy supply of all nodes connected to node i; the formula (5) shows that the energy support obtained by all neighbor nodes can meet the self-load recovery requirement when the class I node fails; equation (6) represents the mutual energization between two failed nodes; equation (7) represents the energy supply of the public neighbor nodes of the two fault nodes to the two fault nodes; formulas (8) - (11) represent linearization operations of the variables; the formula (12) represents that the load can be recovered through the energy supply of all neighbors of two failed nodes when the class II node fails, if the two nodes are connected with the line between the respective neighboring nodes and can be communicated, the load needs of the two nodes need to be met at the same time, otherwise, the class II node load needs to be met only through the neighbors of the two nodes, wherein i and j represent the failed nodes; n represents the number of network nodes; g m Representing the power generation capacity of node m; d, d m Representing the load demand of node m; x is x ij,t Indicating whether node t is connected to both i and j, for s it ·s jt Is a linearization operation of x ij,t E {0,1}, if and only if s it ＝s jt X when=1 ij,t ＝1；mdt ij Indicating whether or not the faulty nodes i and j are indirectly connected, mdt ij E {0,1}, if i and j have common neighbor nodes, mdt ij ＝1If and only if
Figure BDA0003862063770000041
When mdt ij ＝0；y ij Indicating whether i and j are connected, including direct and indirect, y ij E {0,1}, if and only if s ij ＝mdt ij When=0, y ij ＝0；yp j Indicating the energy support, yp, that j can provide in the network formed by connecting the connecting lines between the faulty node and its neighboring nodes after the fault occurs j ∈{0,p j -if and only if y ij Yp when=0 j ＝0；/>
Figure BDA0003862063770000042
Representing class II node L from current failure 2 A set of nodes within range.
Compared with the prior art, the invention has the advantages that: according to the power supply network topology optimization method considering the node differential destruction-resistant requirements, on a model level, a modeling angle of the destruction-resistant requirements is changed from a system level to a node level, and the destruction-resistant requirements are different by combining the functions and characteristics of different nodes in an actual scene, so that the nodes are divided into two types, the load recovery requirements under fault scenes with different degrees are required to be met, on the node level, two constraint reduction decision variables and constraint quantity are added, first heavy line length constraint is added, and the neighbor selection range of the nodes is limited; and adding a second fault node selection range constraint, limiting fault scene combinations which can be generated by the class II nodes, and further solving the model to obtain an optimized topological structure. The method can reduce the size of the decision space, reduce the number of constraint conditions and remarkably improve the calculation efficiency.
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In order to more clearly illustrate the embodiments of the invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, it being obvious that the drawings in the following description are only some embodiments of the invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a schematic diagram of the present invention with link length constraints and node selection range constraints.
Fig. 2 is a flow chart of a power supply network topology optimization method taking into account node differentiation and destruction resistance requirements.
Detailed Description
The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby making clear and defining the scope of the present invention.
Referring to fig. 1 and 2, the embodiment discloses a power supply network topology optimization method considering node differentiation and destruction resistance requirements, which comprises the following steps:
step S1, collecting distributed autonomous power supply network node information which at least comprises node power generation capacity, load demand, position coordinates and type of survivability demand.
Specifically, each network node can be self-sufficient in a normal state, namely, the power generation capacity of the node is larger than the load demand of the node, the node is divided into two types of I type and II type according to the different types of the survivability demand, constraint conditions under different fault scenes are respectively met, the I type node needs to meet simpler constraint conditions, and the II type node needs to meet complex constraint conditions.
Step S2, adding line length constraint L between network nodes 1 And only for pitches less than or equal to L 1 Is considered whether or not to lay a line.
Specifically, only for pitches less than or equal to L 1 The step of considering whether to lay a line is specifically: traversing the distance matrix of the network node, if the element in the distance matrix is greater than L 1 I.e. the distance between two corresponding nodes is greater than L 1 The element at the corresponding position of the adjacency matrix is fixed to 0, i.e. the setting of this part of the line is not considered. Line length constraint L 1 Meaning as in figure 1As shown.
Wherein each value of the distance matrix X is an element, for example x_ij, representing the distance between the nodes i and j; the adjacency matrix M, each of which is also an element, e.g. m_ij, indicates whether there is a connection between node i and node j, if so m_ij=1, and if not m_ij=0.
S3, judging the type of the network node, if the network node is the I-type node, constructing a fault scene and generating corresponding constraint conditions; if the node is II-type node, adding a selection range constraint L between two network nodes 2 When constructing a fault scene, only considering that the distance between two fault nodes is less than or equal to L 2 Is a scene of (a).
Specifically, if the type of the network node is a class I node, constructing a fault scene to be a fault scene which only needs to consider that the network node loses the power generation capacity, and generating corresponding constraint conditions to be that each class I node only needs to meet the load recovery requirement when the network node fails to generate power;
if the type of the network node is a class II node, the fault scene is that the class II node and the other network node lose the power generation capacity, and the distance between the network node and the class II node is larger than L 2 And have weak or even no contact with each other, so these fault scenarios are cut down to reduce the number of constraints. Selection range constraint L 2 The meaning is shown in figure 1. Each class II node is connected with the node at L 2 Any network node in the range forms a fault scene, the load recovery requirements of two fault nodes in each fault scene need to be met, and corresponding constraint conditions are generated.
And S4, taking the minimum total length of the line as an optimization target, taking whether any two nodes in the network are connected (namely an adjacent matrix) as a decision variable, and solving an optimal topological structure of the mixed integer linear programming model through a YALMIP linear solver under the constraint condition obtained in the step S3.
Specifically, the obtained survivability constraint and constraint (constraint condition) are added into the model, the optimal node connection relation (adjacent matrix) is solved, and the topological structure can meet survivability requirements under all fault scenes meeting requirements, and meanwhile, the total length of lines among nodes is shortest, and the structure is concise.
According to the method provided by the embodiment, after the information of the power generation capacity, the load demand, the position coordinates, the destruction-resistant demand types and the like of each node is obtained, the line length constraint is firstly added, the neighbor selection range of the node is limited, and lines exceeding the length constraint are not considered, namely, the elements are limited to be 0 in the decision variable matrix, so that most decision variables can be reduced; and then, on the basis of the first heavy limitation, adding a fault scene node selection range constraint, limiting the selection range of another fault node according to the scene when each class II node fails, and not considering the fault scene formed by the node exceeding the selection range and the current class II node, so that the fault scene with smaller influence can be reduced to a great extent, and the added constraint quantity is greatly reduced. At this time, the minimum line total length is taken as an optimization target; taking an adjacency matrix representing line connection in a network as a decision variable; and taking a constraint set formed by line length constraint, fault scene construction constraint and node survivability requirement constraint under different fault scenes as constraint conditions, and further solving the topological structure of the network.
In this embodiment, the optimization objective function of the mixed integer linear programming model is:
Figure BDA0003862063770000061
l ij ＝|x i -x j |+|y i -y j | (2)
equation (1) represents an objective function to be minimized, in which
Figure BDA0003862063770000062
Representing the total length of the line to be laid between the nodes, +.>
Figure BDA0003862063770000063
A penalty value representing when the constraint cannot be fully satisfied; equation (2) represents the distance between two nodes, wherein,i and j represent any two nodes, x i ，y i And x j ，y j Representing the abscissa, l, and the ordinate of i and j, respectively ij Representing the Manhattan distance between i and j; s is(s) ij Decision variables 0-1, indicating whether a tie line is to be set between i and j, all s ij A symmetrical decision variable matrix can be formed, and i is greater than j to avoid repetition when calculating the target value; delta k To relax variables, ensure that the problem has a solution; m is a constant large enough to represent penalty ratio;
constraint conditions of the mixed integer linear programming model are as follows:
Figure BDA0003862063770000064
Figure BDA0003862063770000065
Figure BDA0003862063770000066
r ij ＝s ij ·(g i -d i +g j -d j ) (6)
Figure BDA0003862063770000071
Figure BDA0003862063770000072
Figure BDA0003862063770000073
Figure BDA0003862063770000074
Figure BDA0003862063770000075
Figure BDA0003862063770000076
equation (3) represents a line length constraint; equation (4) represents the energy supply of all nodes connected to node i; the formula (5) shows that the energy support obtained by all neighbor nodes can meet the self-load recovery requirement when the class I node fails; equation (6) represents the mutual energization between two failed nodes; equation (7) represents the energy supply of the public neighbor nodes of the two fault nodes to the two fault nodes; formulas (8) - (11) represent linearization operations of the variables; the formula (12) represents that the load can be recovered through the energy supply of all neighbors of two failed nodes when the class II node fails, if the two nodes are connected with the line between the respective neighboring nodes and can be communicated, the load needs of the two nodes need to be met at the same time, otherwise, the class II node load needs to be met only through the neighbors of the two nodes, wherein i and j represent the failed nodes; n represents the number of network nodes; g m Representing the power generation capacity of node m; d, d m Representing the load demand of node m; x is x ij,t Indicating whether node t is connected to both i and j, for s it ·s jt Is a linearization operation of x ij,t E {0,1}, if and only if s it ＝s jt X when=1 ij,t ＝1；mdt ij Indicating whether or not the faulty nodes i and j are indirectly connected, mdt ij E {0,1}, if i and j have common neighbor nodes, mdt ij =1 if and only if
Figure BDA0003862063770000077
When mdt ij ＝0；y ij Indicating whether i and j are connected, including direct and indirect, y ij E {0,1}, if and only if s ij ＝mdt ij When=0, y ij ＝0；yp j Indicating the energy which j can provide in the network formed by connecting the connecting line between the faulty node and its neighbor nodeQuantity support yp j ∈{0,p j -if and only if y ij Yp when=0 j ＝0；/>
Figure BDA0003862063770000081
Representing class II node L from current failure 2 A set of nodes within range.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, the patentees may make various modifications or alterations within the scope of the appended claims, and are intended to be within the scope of the invention as described in the claims.

Claims (4)

1. The power supply network topology optimization method considering node differentiation and destruction resistance requirements is characterized by comprising the following steps of:
s1, collecting distributed autonomous power supply network node information, wherein the distributed autonomous power supply network node information at least comprises node power generation capacity, load demand, position coordinates and type of survivability demand;
s2, adding line length constraint L between network nodes 1 And only for pitches less than or equal to L 1 Considering whether to lay a line or not;
s3, judging the type of the network node according to the type of the survivability requirement, if the network node is the I-type node, constructing a fault scene and generating corresponding constraint conditions; if the node is a class II node, adding a selection range constraint L between two network nodes 2 When constructing a fault scene, only considering that the distance between two fault nodes is less than or equal to L 2 Generating corresponding constraint conditions;
s4, taking the minimum total length of the line as an optimization target, taking whether any two nodes in the network are connected as an adjacent matrix or not, taking the adjacent matrix as a decision variable, and solving an optimal topological structure of a mixed integer linear programming model through a YALMIP linear solver under the constraint condition obtained in the step S3, wherein the mixed integer linear programming model is formed based on node information;
the power generation capacity of each network node in the step S1 in a normal state is larger than the load demand of the network node, the class I node and the class II node respectively meet constraint conditions in different fault scenes, the class I node needs to meet simpler constraint conditions, and the class II node needs to meet complex constraint conditions;
in the step S3:
if the type of the network node is I-type node, constructing a fault scene to be a fault scene which only needs to consider that the network node loses the power generation capacity, and generating corresponding constraint conditions to be that each I-type node only needs to meet the load recovery requirement when the network node fails to generate power;
if the type of the network node is a class II node, the fault scene is that the class II node and another network node lose the power generation capacity, and each class II node and the network node are in L 2 Any network node in the range forms a fault scene, and the load recovery requirements of two fault nodes in each fault scene need to be met.
2. The power supply network topology optimization method considering node differentiation and destruction tolerance requirements according to claim 1, wherein in the step S2, the distance is L or less 1 The step of considering whether to lay a line is specifically: traversing the distance matrix of the network node, if the element in the distance matrix is greater than L 1 The element at the position corresponding to the adjacent matrix is fixed to 0.
3. The power supply network topology optimization method considering node differentiation and destruction resistance requirements according to claim 1, wherein the constraint conditions obtained in the step S4 are added to a mixed integer linear programming model, and an optimal topology structure is solved.
4. The power supply network topology optimization method considering node differential survivability requirements as claimed in claim 1, wherein the optimization objective function of the mixed integer linear programming model is:
Figure FDA0004228400820000011
l ij ＝|x i -x j |+|y i -y j | (2)
equation (1) represents an objective function to be minimized, in which
Figure FDA0004228400820000021
Indicating the total length of the line to be laid between the nodes,
Figure FDA0004228400820000022
a penalty value representing when the constraint cannot be fully satisfied; formula (2) represents the distance between two nodes, wherein i and j represent any two nodes, x i ，y i And x j ，y j Representing the abscissa, l, and the ordinate of i and j, respectively ij Representing the Manhattan distance between i and j; s is(s) ij Decision variables 0-1, indicating whether a tie line is to be set between i and j, all s ij A symmetrical decision variable matrix can be formed, and i is greater than j to avoid repetition when calculating the target value; delta k Is a relaxation variable; m is a constant large enough to represent penalty ratio;
constraint conditions of the mixed integer linear programming model are as follows:
Figure FDA0004228400820000023
Figure FDA0004228400820000024
Figure FDA0004228400820000025
r ij ＝s ij ·(g i -d i +g j -d j ) (6)
Figure FDA0004228400820000026
Figure FDA0004228400820000027
Figure FDA0004228400820000028
Figure FDA0004228400820000029
Figure FDA0004228400820000031
Figure FDA0004228400820000032
equation (3) represents a line length constraint; equation (4) represents the energy supply of all nodes connected to node i; the formula (5) shows that the energy support obtained by all neighbor nodes can meet the self-load recovery requirement when the class I node fails; equation (6) represents the mutual energization between two failed nodes; equation (7) represents the energy supply of the public neighbor nodes of the two fault nodes to the two fault nodes; formulas (8) - (11) represent linearization operations of the variables; the formula (12) represents that the load can be recovered through the energy supply of all neighbors of two failed nodes when the class II node fails, if the two nodes are connected with the line between the respective neighboring nodes and can be communicated, the load needs of the two nodes need to be met at the same time, otherwise, the load of the class II node needs to be met only through the neighbors of the two nodes, wherein i and j represent the failed nodes; n represents the number of network nodes; g m Representing the power generation capacity of node m; d, d m Representing the load demand of node m; x is x ij,t Indicating whether node t is connected to both i and j, for s it ·s jt Is a linearization operation of x ij,t E {0,1}, if and only if s it ＝s jt X when=1 ij,t ＝1；mdt ij Indicating whether or not the faulty nodes i and j are indirectly connected, mdt ij E {0,1}, if i and j have common neighbor nodes, mdt ij =1 if and only if
Figure FDA0004228400820000033
When mdt ij ＝0；y ij Indicating whether i and j are connected, including direct and indirect, y ij E {0,1}, if and only if s ij ＝mdt ij When=0, y ij ＝0；yp j Indicating the energy support, yp, that j can provide in the network formed by connecting the connecting lines between the faulty node and its neighboring nodes after the fault occurs j ∈{0,p j -if and only if y ij Yp when=0 j ＝0；/>
Figure FDA0004228400820000034
Representing class II node L from current failure 2 A set of nodes within range.
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