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# Graphical Modular Power Technology of Distribution Network Based on Machine Learning Statistical Mathematical Equation

###### Recibido: 15 Feb 2022
Detalles de la revista
Formato
Revista
eISSN
2444-8656
Primera edición
01 Jan 2016
Calendario de la edición
2 veces al año
Idiomas
Inglés
Introduction

Graphical power system analysis software gradually replaces the software that manually generates data files. The power system plant and station wiring diagram is an indispensable module in the graphical power system analysis and calculation software . The process of converting the physical model represented by the system wiring diagram to the logical model of the power system. The process of pattern-to-model conversion can be further refined into three steps. 1) Analysis of connection relationship. The task is to analyze the connection of various power components in the electrical main wiring diagram of the plant. We use this to divide the component number. 2) Analysis of plant and station connection. The task is to analyze how many computing nodes are connected by closed switches to electrical nodes in the plant. We use this to divide the calculation node number. 3) System network analysis. The task is to analyze how many subsystems the computing nodes of the whole system are connected by branches . We use this to divide the system number (island number). Plant-station connection analysis and system network analysis are collectively referred to as power system network topology analysis.

There is no unified and mature algorithm for analyzing connection relationships in academia. At present, the traditional method for analyzing plant and station connections is to rely on the depth search or breadth search strategy. We use the search method to backtrack the frame . At the same time, we use the stack record to divide the process. Since the existence program of backtracking inevitably adopts the form of recursion or recursion, we need to implement programming maintenance. Based on object technology, the author proposes a method of graph-to-mode conversion analysis with the basic idea of set division. This method has the following advantages:

We use a unified thinking model to deal with connection relationship analysis, plant-station connection analysis, and system network analysis. And the system solves the problem of connection relationship analysis well.

The basic idea of this method is simple and simple. At the same time, the algorithm avoids recursive or recursive implementations. The method is easy to maintain and has good space-time efficiency. It has strong practical value.

Set partition method

A set is defined as a cluster of elements. The members of a set can be single elements or sets. The basic idea of set division is to combine elements of the same attribute into the same set. The basic flow of the algorithm is to process the element management set to be divided. The final output of the algorithm is many sets . The elements in each collection have some of the same properties. Suppose there are N (N ≥ 0) sets, and the element to be divided is X. Its relationship with the existing collection can be enumerated in the following three cases:

XINSi, 1 ≤ iN;

X ∈ (Si1,Si2, ⋯, Sim), i1 < i2 < ⋯ < im, 1 ≤ mN;

(NOT (XINSi)) AND (NOT (X ∈ Si)), i 1,2, ⋯, N.

Where IN means that the element hits in the set. ∈ means that the element satisfies the condition to belong to the set, but the element is not hit. The above three cases and the corresponding processing of the partition element X are described as follows:

The element X to be divided is hit by us in the existing set i, and we do not process the element X.

The element X to be divided satisfies the condition of belonging to m(1 ≤ mN) sets Si1,Si2, ⋯, Sim, (i1 < i2 ⋯ < im simultaneously. Si1 = XSi1Si2⋃⋯Sim deletes set. Si2,⋯,Sim; N = Nm + 1 This article calls it the merging of sets. Only Si1 = XSi1 when m = 1 can be regarded as a special case of a set merge.

There is no direct connection between the element X to be divided and the existing set. We dynamically create a collection at this point. We add elements N = N + 1 to this set.

When dividing the first element, there is no set (N = 0) yet, satisfying the situation described above . The following will introduce the method of set division according to the specific problem characteristics and object-oriented idea.

The application of the set partition method in the analysis of the connection relationship
Problem description of connection analysis

The terminals of switches, transformers, generators, loads, etc., and busbars in the primary wiring diagram of the plant, are called components. The purpose of the connection relationship analysis is to assign a uniform number to the components with direct electrical connection on the graph according to the plant-station wiring diagram . Taking the electrical wiring diagram shown in Figure 1 as an example, some results of the connection relationship analysis are as follows.

Electrical junction {busbar segment 1, breaker 1, breaker 4, breaker 7}

Electrical junction {breaker 1, breaker 2}

Dealing with the analysis of the connection relationship by the method of set partitioning
Data structure and data preparation

The power components in the primary wiring diagram are divided into categories according to their electrical characteristics and graphic characteristics . We can roughly divide them into two categories:

Linear components include busbars, connecting wires, and current transformers. The line segment is the element to be analyzed in the connection relationship analysis. This article refers to the device line segment.

Block elements. All power devices except linear components are collectively referred to as bulk components. Each block element has 1~3 connection terminals. This article refers to the device endpoint. The element to be analyzed in the connection relationship analysis of the block component is the device endpoint . We marked the main electrical wiring diagram shown in Figure 1 with the device endpoints and line segments as shown in Figure 2.

The essence of connection relationship analysis is to analyze the connection status between primitives. The objects of analytical processing are points and line segments in graphics. We do element numbering through point, line analysis. The basis for the above division of power devices is as follows: a block element with n electrical terminals simultaneously belongs to n different electrical nodes . It is shown in circuit breaker 1 in Figure 1. It belongs to the electrical node 1 and the electrical node 2 line element simultaneously. It belongs to one and only one electrical junction due to its inherent impedance-free connectivity. The introduction of face technology makes it possible to describe the properties of things and their behaviors as a whole. Construct the electrical node classes shown in Table 1.

Electrical Node Class Data Structure

Electrical Node Class Properties Electrical Junction Class Methods
Device Set C Merge information in electrical nodes
Device Endpoint Collection Determine the relationship between the device endpoint and this electrical node
Device Segment Collection Determine the relationship between the device line segment and this electrical node

The electrical node 1 in Table 1 can be described as: Component set={breaker 1, breaker 4, breaker 7, bus I section}; PointSet= {P1, P5, P9}; Lineset 1 {L1}.

Algorithm Flow

We create a set of electrical nodes.

We sequentially traverse the power devices in the wiring diagram of the plant once. We take out a power device object and set it as a Component. We judge the type of power device corresponding to the component. If it is a block component, go to step c. Otherwise, it is a line element and goes to step d.

We take the j(1 ≤ j ≤ 3) electrical endpoints of the bulk device. We perform the following operations on the device endpoints in turn: Suppose point is one of the device endpoints. 1. We set up a loop and traverse the electrical nodes of the electrical node collection in order. 2. We take an electrical node from the electrical node-set. Let’s make it mode. 3. Call the member function IS Point belongs to this Node of ENode. If the point hits in the ENode’s device endpoint set, we add the component to the ENode’s device set. At this point, we turn to step six. If the point satisfies the condition of falling on a line segment in the ENode device line segment set, we add a point to the ENode device endpoint set. At the same time, we add a component to the device collection of ENode. At this point, we turn to step six. 4. If the traversal of the electrical node-set has not ended, we turn to step 2. 5. We set the newly generated electrical node object as NewENode. We add a point to the NewENode device endpoint collection . We add components to the NewENode device collection. We add NewENode to the electrical node collection. At this point, we turn to step 6. 6. If all device endpoints of the block have been analyzed, then we turn to step e. Otherwise, we take the next device endpoint of the block.

Create a device line segment object according to the specific line type device category. Let’s make it line. 1. K1, K2, ⋯, Km (m ≥ 1, K1 < K2 < ⋯ < Km) collection of electrical nodes along with the calendar. We call the IS Line Belong to This Node function for each electrical node object in the electrical node collection. 2. If there is a device endpoint in the set of device endpoints in electrical node A that satisfies the condition of falling on the line, then electrical node K1 = , electrical node K1 ⋃, electrical node K2 ⋃ ⋯ ⋃, electrical node Km. And we remove K2, K3, ⋯, Km from the electrical node-set. We add the electrical component Component to the component collection of the merged electrical node. We add the segment line to the device segments for this electrical node. 3. Dynamically generate the electrical node object NewENode. We add the power device Component to the NewENode’s device collection. We add the line segment line to the NewENode’s device line segment collection. We add NewENode to the electrical node collection.

If the traversal of the power device ends, the algorithm aborts. Otherwise, it goes to step b.

Example

I was hoping you could assume that the order of power device analysis is circuit breaker 1, circuit breaker 4, busbar section I, circuit breaker 7, circuit breaker 2 ⋯ Initialization: electrical node-set = Ø. The element to be analyzed for circuit breaker 1 is P1, P2. After analyzing P1 P2 in turn, we get the set of electrical nodes = {electrical node 1, electrical node 2}. Its description is shown in Table 2.

Set of electrical nodes after the first connection analysis

Electrical Junction 1 Electrical Junction 2
Component set={circuit breaker 1} Component set={circuit breaker 1}
PointSet={P1} PointSet={P2}
Lineset = Ø Lineset = Ø

The element to be analyzed for circuit breaker 4 is P5, P6. After analyzing P5, P6 in turn, the set of electrical nodes = {electrical node 1, electrical node 2, electrical node 3, electrical node 4}. Its description is shown in Table 3.

Set of electrical nodes after the second connection analysis

Electrical Junction 1 Electrical Junction 2 Electrical Junction 3 Electrical Junction 4
Component Set= {circuit breaker 1} Component Set= {circuit breaker 2} Component Set= {circuit breaker 3} Component Set= {circuit breaker 4}
Point Set={P1} Point Set={P2} Point Set={P5} Point Set={P6}
Lineset = Ø Lineset = Ø Lineset = Ø Lineset = Ø

The element to be analyzed in the I section of the busbar is L1. Because P1, P5 satisfies the condition to fall on L1, there is a merger of electrical junction 1 and electrical junction 3. After we analyze the I section of the busbar. We get the electrical node-set = {electrical node 1, electrical node 2, electrical node 3}. Its description is shown in Table 4.

Set of electrical nodes after the third connection analysis

Electrical Junction 1 Electrical Junction 2 Electrical Junction 3
Component set={circuit breaker 1, circuit breaker 4, Bus I Section} Component Set={circuit breaker 1} Component Set={circuit breaker 2}
PointSet={P1P5} PointSet={P2} PointSet={P6}
Lineset={L1} Lineset = Ø Lineset = Ø

The element to be analyzed for circuit breaker 7 is P9, P10. We analyze P9, P10 in turn where P9 falls on segment L1 in the electrical junction 1 device segment set. After analyzing circuit breaker 7, we get the set of electrical nodes = {electrical node 1, electrical node 2, electrical node 3, electrical node 4}. Its description is shown in Table 5.

Set of electrical nodes after the fourth connection analysis

Electrical Junction 1 Electrical Junction 2 Electrical Junction 3 Electrical Junction 4
Component set={Breaker 1, Breaker 4, Bus Section I, Breaker 7} Component set={circuit breaker 1} Component set={circuit breaker 4} Component set=={circuit breaker 7}
PointSet={P1, P5, P9} PointSet={P2} PointSet={P6} PointSet={P10}
Lineset={L1} Lineset = Ø Lineset = Ø Lineset = Ø

The element to be analyzed for circuit breaker 2 is P2, P3. We analyze P2, P3 in turn. where P2 is hit by us in the electrical junction 2 device endpoint set. After we analyze circuit breaker 2, we get the set of electrical nodes = {electrical node 1, electrical node 2, electrical node 3, electrical node 4, electrical node 5}. Its description is shown in Table 6. According to the above analogy, it is found that after the analysis of the connection relationship, the electrical nodes are divided as follows: electrical node-set = {electrical node 1, electrical node 2, electrical node 3, electrical node 4, electrical node 5, electrical node 6, electrical node 7, electrical node 8}, whose description is shown in Table 7.

Set of electrical nodes after the fifth connection analysis

Electrical Junction 1 Electrical Junction 2 Electrical Junction 3 Electrical Junction 4 Electrical Junction 5
Component set ={Circuit breaker 1, circuit breaker 4, busbar section I, circuit breaker 7} Component set={circuit breaker 1, circuit breaker 2} Component set ={circuit breaker 4} Component set ={circuit breaker 7} Component set ={circuit breaker 2}
Point Set={P1, P5, P9} Point Set ={P2} Point Set ={P6} Point Set ={P10} Point Set ={P3}
LineSet={L1} LineSet = Ø LineSet = Ø LineSet = Ø LineSet = Ø

Final results after connection analysis

Electrical Junction 1 Electrical Junction 2 Electrical Junction 3 Electrical Junction 4
Component set ={Breaker 1, Breaker 4, Breaker 7} Component set ={circuit breaker 1, circuit breaker 2} Component set ={circuit breaker 4, circuit breaker 5} Component set ={circuit breaker 7, circuit breaker 8}
Point Set ={P1,P5,P9} Point Set ={P2} Point Set ={P6} Point Set ={P10}
LineSet={L1} LineSet = Ø LineSet = Ø LineSet = Ø
Electrical Junction 5 Electrical Junction 6 Electrical Junction 7 Electrical Junction 8
Component set={circuit breaker 2, circuit breaker 3} Component set={circuit breaker 5, circuit breaker 6} Component set={circuit breaker 8, circuit breaker 9} Component set={Circuit breaker 3, circuit breaker 6, circuit breaker 9, busbar section II}
PointSet={P3} PointSet={P7} PointSet={P11} PointSet={P4, P8, P12}
LineSet = Ø LineSet = Ø LineSet = Ø LineSet={L2}

The main electrical wiring diagram shown in Figure 1 has undergone connection analysis. We marked the electrical node numbers in the figure as shown in Figure 3.

Application of Set Partitioning Method in Topology Analysis
Problem description of topology analysis

The graph model in graph theory can represent the mathematical model of power system network topology analysis. From graph theory, a graph can be defined as a binary relation. The pair of vertex sets and edge sets is denoted (V, E). Among them, V represents the vertex set, and E represents the connection relationship of the nodes. The topological analysis aims to find all connected components in a graph. This method assigns a uniform identification to the vertices of each connected component in the graph. The purpose is reflected in the plant-station wiring analysis. All electrical nodes are regarded as V, and all closed switching elements can be regarded as E connecting the electrical nodes at both ends. The purpose of the plant-station connection analysis is to merge all the electrical nodes connected by the closed switching devices into the same calculation node by traversing the switching devices . All computing nodes are regarded as V in system network analysis. All transformers and transmission lines are E connecting the calculation nodes at both ends. System network analysis aims to divide all computing nodes connected by transformers and transmission lines into the same system (island). Therefore, only applying set partitioning is described below to deal with plant wiring analysis.

Analysis of plant and station connection employing set division

We use traditional breadth-first search (BFS) or depth-first search (DFS) to process plant-site tie-line analysis. Since the algorithm itself is based on search and backtracking, its implementation must be a recursive or recursive structure. We only need to traverse the switching device information sequentially when we use the method of set division to deal with the wiring of the plant and station. Therefore, we believe that the implementation and maintenance of the process using the sequential loop is relatively simple.

Data Structures and Data Preparation

We build switch info sheets. Each record in the table represents information for one switching device . The information of the switch includes the name of the switch, the on-off state of the switch, and the electrical node numbers corresponding to the two device endpoints of the switch. We construct computational node classes (Table 8).

Compute node data structure

 Calculate node class properties Calculate the node class method Collection of electrical junctions Merge calculation node information
Algorithm Flow

We treat the electrical junctions across the disconnected switching element separately. The electrical nodes at both ends of the closed switching element should be regarded as a whole to apply the method of set division proposed in Section 1.

Establish a set of computing nodes. Initially, the set of computational nodes is empty.

Establish a circular sequence to read the switch information in the switch information table.

We take a switch information record from the switch information table. Assuming that the electrical node number of its two device endpoints is K1, K2, if the switch is closed, go to step d; otherwise, go to step e.

Traverse, the calculation node information, stored in the calculation node-set and analyze the calculation node number corresponding to electrical node K1, K2 : 1. If electrical node A has not been assigned a calculation node number, we create an object dynamically. We add K1 (K2) to the object’s Electric Node Set to the compute node-set. At this point, we go to step f. 2. If electrical node K1 (K2) has been assigned a calculation node number, and electrical node K2 (K1) has not been assigned an electrical node number . We take out the computing node object to which the electrical node K1 (K2) belongs from the computing node-set and add the electrical node K2 (K1) to the object’s Electric Node Set. At this point, we go to step f.

Traverse the computing node objects stored in the computing node-set. We analyze the calculation nodes corresponding to the electrical node K1, K2 separately. If an electrical node K1 (or K2) has not yet been assigned a calculation node number, a calculation node object is dynamically generated. We add K1 (or K2) to the object’s Electric NodeSet and add it to the compute node-set. At this point, we go to step f.

The algorithm aborts if the traversal of the switch information table ends. Otherwise, we go to step c.

Calculation example

The calculation example takes the primary main wiring diagram after the analysis of the connection relationship shown in Figure 3 as an example . The order of the switch information in the switch information table is circuit breaker 7, circuit breaker 4, circuit breaker 6, circuit breaker 5⋯ . The node set is calculated initially, and the node set is calculated after analyzing each switch sequentially as follows. After analyzing circuit breaker 7, the set of calculation nodes = {calculation node 1, calculation node 2}. Calculate node 1, ElectricNodeSet={l}. Calculate node 2, ElectricNodeSet={4}. After analyzing circuit breaker 4, we get: calculation node set = {calculation node 1, calculation node 2}. Computing node 1, ElectricNodeSet={1,3}; computing node 2, ElectricNodeSet={4}. After analyzing circuit breaker 6, the set of calculation nodes = {calculation node 1, calculation node 2, calculation node 3}. Calculate node 1, ElectricNodeSet={1,3}. Calculate node 2, ElectricNodeSet={4}. Calculate node 3, ElectricNodeSet={6,8}.

After analyzing circuit breaker 5, the set of calculation nodes = {calculation node 1, calculation node 2}. Calculate node 1, ElectricNodeSet={1,3,6,8}. Calculate node 2, ElectricNodeSet={4}. The calculation nodes are divided into calculation node sets = {calculation node 1, calculation node 2} after the plant-station connection analysis. For computing node 1, ElectricNodeSet={1,3,6,8,2,5}. For computing node 2, ElectricNodeSet={4,7}.

Algorithm process

We approach the power system graph-mode conversion problem with a set partitioning approach (Fig. 4).

Conclusion

The set partitioning method is simple and easy to implement and has strong operability. We adopt it to deal with the problem of power system graph-mode conversion. This method avoids the problem of stack usage and maintenance that the search algorithm cannot overcome. To speed up the analysis and judgment of the relationship between the elements to be processed and the existing set, we can also use some auxiliary variables to record the current division of the elements. Overall, the algorithm has good space-time efficiency.

#### Set of electrical nodes after the fourth connection analysis

Electrical Junction 1 Electrical Junction 2 Electrical Junction 3 Electrical Junction 4
Component set={Breaker 1, Breaker 4, Bus Section I, Breaker 7} Component set={circuit breaker 1} Component set={circuit breaker 4} Component set=={circuit breaker 7}
PointSet={P1, P5, P9} PointSet={P2} PointSet={P6} PointSet={P10}
Lineset={L1} Lineset = Ø Lineset = Ø Lineset = Ø

#### Electrical Node Class Data Structure

Electrical Node Class Properties Electrical Junction Class Methods
Device Set C Merge information in electrical nodes
Device Endpoint Collection Determine the relationship between the device endpoint and this electrical node
Device Segment Collection Determine the relationship between the device line segment and this electrical node

#### Set of electrical nodes after the second connection analysis

Electrical Junction 1 Electrical Junction 2 Electrical Junction 3 Electrical Junction 4
Component Set= {circuit breaker 1} Component Set= {circuit breaker 2} Component Set= {circuit breaker 3} Component Set= {circuit breaker 4}
Point Set={P1} Point Set={P2} Point Set={P5} Point Set={P6}
Lineset = Ø Lineset = Ø Lineset = Ø Lineset = Ø

#### Set of electrical nodes after the third connection analysis

Electrical Junction 1 Electrical Junction 2 Electrical Junction 3
Component set={circuit breaker 1, circuit breaker 4, Bus I Section} Component Set={circuit breaker 1} Component Set={circuit breaker 2}
PointSet={P1P5} PointSet={P2} PointSet={P6}
Lineset={L1} Lineset = Ø Lineset = Ø

#### Final results after connection analysis

Electrical Junction 1 Electrical Junction 2 Electrical Junction 3 Electrical Junction 4
Component set ={Breaker 1, Breaker 4, Breaker 7} Component set ={circuit breaker 1, circuit breaker 2} Component set ={circuit breaker 4, circuit breaker 5} Component set ={circuit breaker 7, circuit breaker 8}
Point Set ={P1,P5,P9} Point Set ={P2} Point Set ={P6} Point Set ={P10}
LineSet={L1} LineSet = Ø LineSet = Ø LineSet = Ø

#### Set of electrical nodes after the first connection analysis

Electrical Junction 1 Electrical Junction 2
Component set={circuit breaker 1} Component set={circuit breaker 1}
PointSet={P1} PointSet={P2}
Lineset = Ø Lineset = Ø

#### Compute node data structure

 Calculate node class properties Calculate the node class method Collection of electrical junctions Merge calculation node information

#### Set of electrical nodes after the fifth connection analysis

Electrical Junction 1 Electrical Junction 2 Electrical Junction 3 Electrical Junction 4 Electrical Junction 5
Component set ={Circuit breaker 1, circuit breaker 4, busbar section I, circuit breaker 7} Component set={circuit breaker 1, circuit breaker 2} Component set ={circuit breaker 4} Component set ={circuit breaker 7} Component set ={circuit breaker 2}
Point Set={P1, P5, P9} Point Set ={P2} Point Set ={P6} Point Set ={P10} Point Set ={P3}
LineSet={L1} LineSet = Ø LineSet = Ø LineSet = Ø LineSet = Ø

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