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The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory

Data publikacji: 15 Jul 2022
Tom & Zeszyt: AHEAD OF PRINT
Zakres stron: -
Otrzymano: 15 Jan 2022
Przyjęty: 23 Mar 2022
Informacje o czasopiśmie
License
Format
Czasopismo
eISSN
2444-8656
Pierwsze wydanie
01 Jan 2016
Częstotliwość wydawania
2 razy w roku
Języki
Angielski
Abstract

This article proposes a fault component location method based on graph theory and analyzes the properties of the elements in the fault judgment matrix. We can use the exclusive OR algorithm to determine the faulty section. On this basis, the realization model and algorithm essence of the optimal test set is given. At the same time, we propose an optimal test set design for circuit fault diagnosis based on graph theory. Finally, the realization of the article verified that the method adapts to the flexible operation mode of the active distribution network structure and can accurately determine the fault section.

Keywords

MSC 2010

Introduction

A process enterprise is a relatively fixed production line established according to process conditions and requirements. The type of equipment structure is complex, and the investment is relatively large. Once the production line of a process enterprise is built, its production capacity largely depends on the operation and use of the equipment. Compared with discrete enterprises, equipment failures and shutdowns cause greater losses to enterprises [1]. This puts forward higher requirements for troubleshooting hidden troubles, finding fault causes, and troubleshooting.

Process companies often rely on various power sources and chemical reactions to perform production operations under high temperature and high-pressure conditions. Among its equipment, electrical energy equipment has an important position. This type of equipment is mostly distributed in two places: one is at the front end of the production line. It plays a role in providing energy, such as substation equipment connected to the high-voltage power grid. The second is interspersed between production equipment. It plays a role in driving and controlling single or multiple production equipment, such as various motors, control cabinets, etc. Due to the distribution and role of electrical equipment in the enterprise, we found that electrical equipment failures have the following characteristics.

1) The scope of influence is large. Once a failure occurs, the entire equipment chain under its control may be shut down, or cascading failures occur. 2) The discovery is difficult. The electrical equipment does not directly perform production operations. Most of them are left unattended, and failures are not easy to detect and manifest in production equipment failure. Equipment management personnel, often only after a lot of investigation work, can eliminate the source of the fault in the production equipment and then turn to the inspection of electrical equipment. 3) Rely on many experiences. The number of electrical equipment is huge, the control relationship is complicated, and it is difficult to locate the fault source. In the past, fault location mostly relied on the experience of managers and familiarity with equipment systems.

These characteristics of electrical equipment make it difficult to quickly locate the source of the fault and delineate the area that may be affected for emergency repair [2]. Quickly finding the equipment and its control equipment to determine the possible impact of the fault has become a difficult problem for process companies in equipment management.

Construction of control relationship matrix for electrical equipment in process enterprises
Analysis of the control relationship of electrical equipment in process enterprises

The simple equipment control network in the process enterprise comprises substation equipment, control equipment, production equipment, etc. The substation equipment is located at the front end of the enterprise's production system, and the electric energy enters the production system through multi-stage voltage reduction [3]. One control device can control multiple lower-level devices, and the lower-level devices can be either control devices or production equipment. This one-way control and the controlled relationship between substation equipment, control equipment, and production equipment can form an equipment network without a closed loop.

The equipment can be decomposed according to its structure to form the equipment BOM, and each part can control a piece of lower-level equipment. For large equipment, different parts of a device are controlled by different control devices [4]. If the equipment BOM is decomposed and added to the control chain, the control chain is more complicated. Since the equipment part can be abstracted into a single piece of equipment, it is not necessary to consider adding parts to the control chain for the time being.

We abstract the device as a node while abstracting the control relationship as a directed edge. The controlling device points to the controlled device, and there is no connected directed edge if there is no control relationship between the devices. In this way, the control network can be abstracted into a directed graph represented by nodes and directed edges, which we also call a control graph. There are two main mathematical representation methods for control charts: arrays and matrices. Array notation builds nodes and processes on a multi-dimensional array to make full use of the adjacency relationship between nodes and edges. The disadvantage is that it occupies a lot of resources, and the operation is complicated. Matrix representation uses the relationship between nodes or between nodes and paths. This way of representation is convenient for the realization of computer algorithms and, at the same time, occupies fewer computer resources. The direction of the arrow along the control edge in the control diagram is called the forward direction, and vice versa. We take any device in the control diagram as a starting point, which is called a reference device [5]. Downward you can find a chain of equipment controlled by it, called the forward control chain. You can find a chain of equipment that controls it upwards, which we call the reverse control chain. The start device has only the forward control chain, and the end has only the reverse control chain.

Construction of control relationship matrix for electrical equipment in process enterprises

We use points ωi(i = 1,2, ⋯, n) to represent equipment. All devices in the control network form a control network device set W01, ω2, ⋯, ωn). Since the control relationship between devices is one-way, the correct control chart is a directed chart without loops [6]. To avoid the formation of loops during the formation of computer algorithms, we sort the equipment according to the control relationship to form an ordered equipment set W1, ω2, ⋯, ωn).

The adjacency matrix is based on the control relationship between devices. The row vector Pi and the column vector Qi together represent the relationship between the control and the controlled device ωi in the control chart. We use aij to represent the control relationship between equipment ωi(i = 1,2, ⋯, n) and ωj(j = 1,2, ⋯, n). aji represents the control relationship of device ωj to device ωi. The formation of the control relationship matrix A is expressed as follows: A=[a11a12a1na21a22a2nan1an2ann]=(P1,P2,,Pn)T=(Q1,Q2,,Qn) A = \left[ {\matrix{ {{a_{11}}} & {{a_{12}}} & \cdots & {{a_{1n}}} \cr {{a_{21}}} & {{a_{22}}} & \cdots & {{a_{2n}}} \cr \cdots & \cdots & \cdots & \cdots \cr {{a_{n1}}} & {{a_{n2}}} & \cdots & {{a_{nn}}} \cr } } \right] = {\left( {{P_1},{P_2}, \cdots ,{P_n}} \right)^T} = \left( {{Q_1},{Q_2}, \cdots ,{Q_n}} \right)

From the one-way nature of the device control relationship, it can be seen that there is no mutual control relationship between devices, that is: aij+aji1andaij×aji=0 {a_{ij}} + {a_{ji}} \le 1\;{\rm{and}}\;{a_{ij}} \times {a_{ji}} = 0

At the same time, the equipment set is ordered, and it can be seen that: wheni>j,aij=0 when\;i > j,{a_{ij}} = 0

From the above characteristics of the control relation matrix, it can be known that the matrix A is an upper triangular sparse matrix. That is, there is no loop in the matrix A. In addition, the matrix A has the following characteristics:

There are y 1s in line i, which means that the device ωi controls the device of y the station. The equipment set composed of the equipment controlled by ωi is called the controlled equipment set Li: Li={ωi|j>i,aij=1,aijPi} {L_i} = \left\{ {{\omega _i}|j > i,{a_{ij}} = 1,{a_{ij}} \subset {P_i}} \right\}

The existence of x 1s in the column i means that the device ωi is controlled by x devices. The equipment set composed of equipment that controls ωi is called control equipment set Fi: Fi={ωi|j<i,aij=1,aijQi} {F_i} = \left\{ {{\omega _i}|j < i,{a_{ij}} = 1,{a_{ij}} \subset {Q_i}} \right\}

There must be at least one start device node and end device node in the device control relationship diagram [7]. We can use the control relationship matrix in this article to quickly determine whether a device is controlled or control other devices. If the column vector Qi = 0, then Fi = ∅. That is, there is no other device control device ωi, ωi is the starting device of the control chart. Row vector Pi = 0, then Li = ∅. The device ωi does not control any device, and device F is the end device of the control chart.

The formation of a logical control chart and control chain
The formation algorithm of the logic control diagram of the equipment control relationship

Informing the control network diagram, we denote the set of devices that have been incorporated into the control network as V. We denote the set of starting device nodes in the control network graph as WB = {ωi | Qi = 0}. The device node controlled by ωi is called the next-neighbor device node. The controlled device set of all the device nodes in WB forms the next-neighbor device set WE = {LiLi+1 | ωiWB, ωi+1WB, aij = 1} after removing the duplicate nodes. The logic control chart formation algorithm idea is as follows:

Step1: Determine the starting device node of the control chart. Determine the starting device node-set WB. We put all the equipment nodes in WB into V, that is, let ωiV and draw the starting equipment node [8]. The search process is to traverse the devices in the ordered device set W. It can be seen that WB obtained by this method is an ordered set of equipment. Find the drawing method as shown in Figure 1.

Figure 1

Finding and drawing the initial device set

Combined with Figure 1, the pseudo-code is implemented as follows:

Function1 finds the starting device node for drawing

Search Begin Equipment (W1, ω2, ⋯, ωn))

For (ωiW = ∅)

Begin

If (Qi 0)

We will include ωi into WB;

Draw the starting device node;

End

Step2: Find the next-neighbor device node from the starting device node. Starting from the starting device node ωi of the control network diagram, use the control relationship matrix to determine ωi the next-neighbor device node-set (WE).

Step3: draw points and draw edges. If the next neighbor device node ωjV, only the control edge needs to be added. On the contrary, if ωjV = ∅, you have to order ωjV and add the control edge simultaneously.

Step4: Iterative drawing. After drawing points and drawing edges of all the next neighbor nodes of the starting device node in Step3 ends, all terminal device nodes in Step2 will be used as the starting device node. Cycle Setp2 and Step3 process. After several loop iterations, the device nodes and control edges are continuously extended to form a control graph. The specific process is shown in Figure 2.

Figure 2

The formation algorithm of the logic control chart

Combined with Figure 2 to achieve pseudo-code as follows:

Function 2 iteratively draw the network diagram

Init Chat (WBi | Qi = 0, i = 1,2, ⋯, n})

For (ωiWB)

Begin

If (Pi ≠ 0)

For (ωiLi)

If (ωjWE = ∅), Incorporate ωj into WE;

Begin

If (ωjV = ∅) ωjV;

Increase the control edge;

Else increases the control edge;

End

Init Chat (WE).

The control diagram can comprehensively reflect the control relationship between the enterprise's electrical equipment and production equipment. It can express the complex control relationship through simple graphics [9]. This is convenient for equipment managers to grasp the overall situation of the enterprise's electrical equipment control network.

In troubleshooting, searching, and controlling the scope of the fault, the control chart has a large range, and the complicated control relationship is displayed on one chart, which also brings certain difficulties to the search. Therefore, we propose two concepts of reverse control chain and forward control chain. The reverse control chain is based on a certain device as the starting point, looking upwards for the superior device that controls it and the superior device of the superior device until a control chain is formed by one or several starting devices in the control chart [10]. The forward control chain is based on a certain device as a starting point to find the lower-level equipment it controls and the lower-level equipment. A controlled chain is formed by equipment until the end of the control chart.

Formation of the reverse control chain

The reverse control chain has only one starting point as the reference device. The formation of the reverse control chain is to find the equipment set that controls the reference equipment after the reference equipment fails. Since the failure of electrical equipment is often manifested as a certain failure phenomenon of the production equipment, after the failure phenomenon occurs, the cause is often not found on the equipment exhibited by the failure phenomenon. We need to quickly show the reverse control chain of the equipment and its control relationship. This is of great help to quickly find the cause of the fault.

The formation of the reverse control chain is similar to the formation of the control chart, but the scope of equipment involved is smaller [11]. The judgment condition of the adjacent device node is the row vector Pi ≠ 0. Just find the equipment set involved in the reverse control chain of the reference equipment, and then add the control edges according to the formation method of the control chart.

Formation of the positive control chain

The forward control chain is to find the set of devices controlled by it after finding the source of the faulty device. Due to the complex situation of equipment failure, there are multiple possible causes. After finding the control device set, these devices can be included in the fault source. After removing the influence of the source of the fault, look for other causes of the fault. This is useful for analyzing complex faults. If the equipment set under its control has not failed, this equipment can also be used as the key preventive object when the equipment failure does not affect the function of the production line at the initial stage. The forward control chain is a special case when the starting device node number of the logical reasoning diagram of the equipment control relationship is “1”. The algorithm and implementation process are the same as drawing the logical reasoning diagram of the equipment control relationship.

Instance verification

To test the validity and correctness of the algorithm proposed in this paper, we select some electrical and mechanical production equipment in a certain cement production line, such as verification. The selected equipment forms ordered equipment set as: W1, ω2, ω3, ω4, ω5, ω6, ω7, ω8, ω9, ω10,). It satisfies that the equipment in the equipment concentration has no independent equipment, and the serial number of the control device is less than the serial number of the controlled device. The relationship between them can be shown in Table 1.

Control relationship table

Equipment wi Set of controlled equipment Li Control equipment set Fi
w1 w3
w2 w3, w4
w3 w5, w6, w7 w1, w2
w4 w5 w2
w5 w7 w3
w6 w9, w10 w3
w7 w10 w3, w5
w8 w9 w4
w9 w6, w8
w10 w6, w7

According to the control relationship between the devices described in Table 1, it can be concluded that the device nodes are taken in order. For ω1, Q1 ≠ 0 is V = ∅ and L = ∅. Include L in V to judge L1 = {ω3} = ∅ and ω3V. We add ω3 to the control chart and add the control edges from ω1 to ω3. Repeat the above process and finally get the control chart shown in Figure 3. The equipment control relationship matrix A is as follows:

Figure 3

Device control diagram

Take the device ω7 as an example to search the device set of the reverse control chain. The first judge knowing Q7 ≠ 0. We put ω7 into V, then V = (ω7). Judge knowing F7 ≠ ∅ = {ω3, ω5}, judge knowing ω3, ω5 all ∈ V. We incorporate ω3 and ω5 into V. The newly incorporated equipment in V repeats the above steps to obtain the reverse control chain equipment set V = {ω1, ω3, ω5, ω7}. After reverse addition, the reverse control chain starting from ω7 is obtained as shown in Figure 4. Take the device ω3 as the starting point and follow the control chart formation method to find the forward control chain (Figure 5).

Figure 4

Reverse control chain starting from w7

Figure 5

The forward control chain starting from w3

Conclusion

This article considers the control relationship between electrical and mechanical equipment in process enterprises as the research object. Based on analyzing the characteristics of electrical equipment faults and control relations, the relevant theories of graph theory are used to construct the electrical equipment control relations matrix of process enterprises. At the same time, the article proposes an algorithm for forming a control relationship control chart and a search algorithm for forward and reverse control chains. It has been verified that the method proposed in this paper can quickly and accurately form the equipment diagram and control chain. This algorithm is of great significance to the dynamic management of the control chain of electrical equipment in process enterprises. This laid the foundation for subsequent computer implementation.

Figure 1

Finding and drawing the initial device set
Finding and drawing the initial device set

Figure 2

The formation algorithm of the logic control chart
The formation algorithm of the logic control chart

Figure 3

Device control diagram
Device control diagram

Figure 4

Reverse control chain starting from w7
Reverse control chain starting from w7

Figure 5

The forward control chain starting from w3
The forward control chain starting from w3

Control relationship table

Equipment wi Set of controlled equipment Li Control equipment set Fi
w1 w3
w2 w3, w4
w3 w5, w6, w7 w1, w2
w4 w5 w2
w5 w7 w3
w6 w9, w10 w3
w7 w10 w3, w5
w8 w9 w4
w9 w6, w8
w10 w6, w7

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