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Article

# Optimisation Configuration of Overhead-Line Segmentation Switch of a Distribution Network Based on Global Combination Criterion

School of Electrical Engineering, North China University of Water Resources and Electric Power, Zhengzhou 450011, China
*
Author to whom correspondence should be addressed.
Processes 2022, 10(10), 1976; https://doi.org/10.3390/pr10101976
Submission received: 28 August 2022 / Revised: 21 September 2022 / Accepted: 22 September 2022 / Published: 1 October 2022

## Abstract

:
Under certain constraints, the optimisation of the position and number of sectional switches in overhead lines in distribution networks can improve the reliability and economy of the power supply. Therefore, a global combination criterion is proposed to simultaneously evaluate the combination performance of multiple switch positions, which avoids the tedious traditional problem of adjusting only one switch position at a time and that can possibly fall into a local-optimum problem. We directly determine the optimal solution and ensure a global optimum. Firstly, the optimal switching position in each line segment is analysed as an alternative switching position. Subsequently, the optimal installation-position combination that corresponds to a given number of switches is determined according to the global combination criterion. If the constraints are satisfied, the number of switches is increased by one, and the optimal installation-position combination is then determined until the constraints are not satisfied. This process ensures not only the global optimum of the switch position but also the optimum number of switches. Finally, examples are given to demonstrate that the proposed method can further optimise the switch configuration. The utility model effectively improves the device utilisation rate, reduces the influence range of the fault, and improves power supply reliability.

## 1. Introduction

To further optimise the position and number of switches, the first step in the present study adopts the alternative switch positions proposed in [28,29,30]. Thus, the distribution of the switch positions is restricted within a limited range. Then, we individually analyse the presence or absence of contact lines and propose a corresponding global switch-combination criterion. The criterion is used to directly determine the best installation position combination corresponding to a given number of switches, which ensures global optimum. The main contributions of this paper are reflected in the following aspects:
(1)
By comprehensively considering reliability and economy, an optimisation algorithm for the distribution switch of an overhead line segment in a distribution network based on the global combination criterion is proposed, and the switch-configuration scheme is further optimised to effectively improve the utilisation rate of the equipment, reduce the scope of faults, and improve the power supply reliability.
(2)
Simultaneously, we determine multiple switch positions using a global combination criterion. Compared with [28,29] that employed a single-switch criterion to determine one switch at a time, the method of repeated iterative optimisation to determine the switch position is more direct. Further, it does not fall into a local optimum. The calculation speed is also very fast while ensuring global optimum.
(3)
This paper proposes to further optimise the number of switches based on the optimal switch position and reflects the optimisation effect of the method on the number of switches. The use of the optimised optimal switch-position data to determine the number of switches is obviously better than that in [28,29]. The number of switches determined by the switch-position data before optimisation is more accurate and reasonable.

## 2. Relevant Definition and Reliability-Index Selection

#### 2.1. Related Definitions

(1)
Node: connection point of the feeder and distribution transformer. The connection point of the primary branch and trunk is defined as a node.
(2)
Line segment: a line that connects two nodes without a load is defined as a line segment.
(3)
Line power supply end: the end of a line section close to the main power supply (standby power supply) is defined as the main power supply end (backup power supply end) of a line section.

#### 2.2. Power Supply Reliability Index

Currently, the commonly used indicators for evaluating the reliability of a distribution network [14] are the following: system average power outage duration index (SAIDI), system average power outage frequency index, user average power outage frequency index, and system power-shortage indicator [energy not supplied (ENS)], which is characterised by insufficient power supply in the system for a given time. If the aforementioned indicators are evaluated, the workload becomes large and the effect is not good because of the complex relationship among the indicators. This study comprehensively considers the user (the power outage time is shorter) and the power supply company (the lack of power supply is less). Comprehensive evaluations are made using the two indicators: SAIDI and ENS.

#### 2.3. Power Supply Reliability Evaluation Method

The traditional method of distribution network reliability evaluation is adopted, namely, failure mode and effect analysis. This method uses component-reliability data to select the appropriate fault-judgment criteria and then divides the system status into normal operation and fault categories according to the criteria. It then performs reliability calculations. For calculation convenience, the model is simplified, and only the line faults are considered.

## 3. Constructing the Objective Function

#### 3.1. Objective Function

According to SAIDI and ENS, the following multi-objective function is developed:
$minR ( y ) = W 1 × SAIDI ( y ) + W 2 × ENS ( y )$
where,
• y—number of section switches
• R(y)—reliability comprehensive index value
• SAIDI(y)—SAIDI of y switches normalised before multiplying the weights
• ENS(y)—ENS for y switches, which is normalised before multiplying the weights
Weight of W1—SAIDI indicator, which can be changed according to the actual situation. This study considers it in a balanced manner and judged by experts, assumes a value of 0.5.
Weight of W2—ENS index, which can be changed according to the actual situation. This study considers it in a balance manner and assumes a value of 0.5.

#### 3.2. Restrictions

(1)
Power system inequality constraints
The inequality-constraint conditions that ensure normal operation of the power system are expressed by the following formula:
$S K ≤ S K . max U i . min ≤ U i ≤ U i . max I ij ≤ I ij . max f min ≤ f ≤ f max$
S represents the user power, U represents the bus node voltage, I represents the branch current, and f represents the system frequency.
(2)
Power system equality constraints
The equality constraints that ensure normal operation of the power system are expressed by the following formula:
$Σ P Gi - Σ P Li - Σ Δ P s = 0 Σ Q Gi - Σ Q Li - Σ Δ Q s = 0$
$Σ P Gi$,$Σ Δ P s$,$Σ P Li$ represent the power supply, line loss, and active power of the load, respectively, and $Σ Q Gi$,$Σ Δ Q s$,$Σ Q Li$ represent the power supply, line loss, and reactive power of the load, respectively.
(3)
Maximum effective-segment-condition constraints
To allow each additional switch to exert a considerable effect, the set constraint conditions are expressed as follows:
$Δ R ( y ) R ( y ) > ε$
where $Δ R ( y )$ represents the comprehensive-index value, which is reduced by adding one more switch, i.e., $R ( y ) - R ( y - 1 )$. $ε$ is the minimum reduction rate that needs to be satisfied (here, 0.1).
(4)
Economic constraints
$yc ≤ C 0$
Here, c represents the cost of installing a switch, including post-maintenance expenses, and C0 represents the upper limit of the cost of this additional switch project.
(5)
Reliability constraints
$R ( y ) ≤ R 0$
Here, R0 represents the maximum reliability comprehensive-index value R(y). Exceeding this value means that the reliability requirements cannot be met.

## 4. Optimal Switch Configuration Based on Global Combination Criterion

#### 4.1. Definition of Related Quantity

Figure 2 shows that the K1 and K2 switches divide the line into three sections. We let A1 be the length of the trunk line between switch K1 and power point, B1 be the total length of the branch lines in the A1 section trunk line, L1 be the sum of the lengths of A1 and B1, and A2 be the switch between K1 and K2. The length of the trunk line, i.e., B2 represents the sum of the total length of the branch lines in the A2 section of the trunk line, and L2 denotes the sum of the lengths of A2 and B2. A3 represents the length of the trunk line from switch K2 to the end of the line, and B3 denotes the length of the A3 section of the trunk line, i.e., the sum of the total length of the branch lines. L3 denotes the sum of the lengths of A3 and B3. The total number of users in L1 is denoted by N1. The total load is denoted as P1, which are the loads from C1 to C5. The total number of users in L2 is denoted by N2. The total load is denoted as P2, which are the loads from C6 to C10. The total number of users in L3 is denoted as N3, and the total load is represented by P3.
If the number of switches is increased to y, the switches are denoted as K1–Ky from left to right, i.e., the line is divided into y + 1 segments. Then, Li represents the trunk line between the i − 1 and i switches, which represents the total length of the branch line. Ni and Pi denote the number of users and load in Li (i = 1, 2, …, y + 1). When i = 1, Li represents the total length of the main and branch lines between K1 and the power point. When i = y + 1, Li denotes the total length of the main and branch lines from Ky to the end of the line.

#### 4.2. Switch Global Combination Criterion

(1)
Criterion for global switch combination without a tie line
Figure 2 shows that for a single-ray ray path, the installation of switches will present different reliability characteristics at different positions. Here, the effect of the combined installation position of multiple switches on the global reliability is simultaneously investigated. We let L be the sum of L1, L2, and L3, i.e., the total length of the trunk and branch lines. We denote the total number of users in L as N and the total load as P. We also denote the total number of users in L1 as N1 and the total load as P1. The total number of users in L2 is denoted as N2, and the total load is denoted as P2. The total number of users in L3 is listed as N3, and the total load is listed as P3. We assume that two switches K1 and K2 are installed for the preliminary research.
By first considering only one reliability index, i.e., SAIDI, SAIDIbef before the switch installation can be expressed by the following formula:
$SAIDI bef = λ Lt 1 N N = λ Lt 1$
Feeder SAIDIaft after the installation of the segment switch is expressed as
$SAIDI aft = λ [ L 1 t 1 + ( L 2 + L 3 ) t 2 ] N 1 N 1 + N 2 + N 3 + λ [ ( L 1 + L 2 ) t 1 + L 3 t 2 ] N 2 + λ ( L 1 + L 2 + L 3 ) N 3 t 1 N 1 + N 2 + N 3 = λ Lt 1 + [ L 2 N 1 + L 3 ( N 1 + N 2 ) ] λ ( t 2 - t 1 ) N$
where:
• t1—time required for fault repair
• t2—Power-outage time in line B when line A fails. (The value of t2 when a circuit breaker is used as a switch is zero, and that of t2 when a load switch is used is the sum of the time required for the fault location and isolation and the time required for the switch to trip). Line A indicates the part that needs to be isolated and repaired after the fault. Line B indicates the part that can normally supply power after the fault is isolated.
• λ—Line failure rate
After the switch is installed, the reduced value of SAIDI, i.e., ΔSAIDI, is expressed by the following formula:
$Δ SAIDI = [ L 2 N 1 + L 3 ( N 1 + N 2 ) ] λ ( t 1 - t 2 ) N$
We can easily learn that when Equation (9) obtains the maximum value, the best effect and reliability are realised when two switches are installed, and the corresponding switch position at this time is the optimal switch position when two switches are installed.
When y switches are installed, the line is divided into y + 1 segments. Then,
$Δ SAIDI = [ L 2 N 1 + L 3 ( N 1 + N 2 ) + … + L y + 1 ( N 1 + N 2 + … + N y ) ] λ ( t 1 - t 2 ) N$
Similarly, we can observe that when the maximum value is obtained in Equation (10), it indicates the optimal effect when y switches are installed. The reliability reaches the highest value, and the corresponding switch position at this time is the optimal switch position when y switches are installed.
λ, t1, t2, and N in Equations (9) and (10) do not change with the change in the switch position. They are all quantities and do not affect the distribution of the optimal switch position, which can be ignored when the maximum value is sought. We simply calculate the maximum value of
$[ L 2 N 1 + L 3 ( N 1 + N 2 ) + … + L y + 1 ( N 1 + N 2 + … + N y ) ]$
Similarly, if the reliability index considered is ENS, then the corresponding switch position, when
$[ L 2 P 1 + L 3 ( P 1 + P 2 ) + … + L y + 1 ( P 1 + P 2 + … + P y ) ]$
obtains the maximum value is the optimal switch position when y switches are installed.
If the two reliability indexes, namely, SAIDI and ENS, are comprehensively considered, they can be determined using Equation (11). When the value of Equation (11) is the largest, the comprehensive reliability reaches the highest value, and the corresponding switch position represents the comprehensive consideration of SAIDI and ENS, which is the optimal switch position under the two indicators.
$[ L 2 X 1 + L 3 ( X 1 + X 2 ) + … + L y + 1 ( X 1 + X 2 + … + X y ) ]$
In Equation (11), $X i = W 1 N i N + W 2 P i$, (i = 1,2, …, y). Xi can be considered as a comprehensive indicator of the user load. Equation (11) can be used as a global switch-combination criterion for unconnected lines to determine the advantages and disadvantages of the global switch position combination.
(2)
Criterion for global combination of switches with tie lines
Figure 2 shows that, assuming a connection exist at the end of the line, feeder SAIDIaft after the section switch is installed is expressed as
The reduced value of the average power-outage duration of the system after the segment switch is installed, i.e., ΔSAIDI is
$Δ SAIDI = [ ( L - L 1 ) N 1 + ( L - L 2 ) N 2 + ( L - L 3 ) N 3 ] λ ( t 1 - t 2 ) N$
When y switches are installed, the line is divided into y + 1 segments. Then,
$Δ SAIDI = [ ( L - L 1 ) N 1 + ( L - L 2 ) N 2 + … + ( L - L y + 1 ) N y + 1 ] λ ( t 1 - t 2 ) N$
Similar to that without a connection, λ, t1, t2, and N in Equation (14) are all quantities. Then, the corresponding switch position when $[ ( L - L 1 ) N 1 + ( L - L 2 ) N 2 + … + ( L - L y + 1 ) N y + 1 ]$ reaches the maximum value is the optimal switch position for y switches.
Similarly, when the considered reliability index is ENS, the corresponding switch position when $[ ( L - L 1 ) P 1 + ( L - L 2 ) P 2 + … + ( L - L y + 1 ) P y + 1 ]$ achieves the maximum value is the optimal switch position when y switches are installed.
When the two reliability indexes of SAIDI and ENS are comprehensively considered, they can be determined according to the Equation (15). When the value of Equation (15) is the largest, the comprehensive reliability reaches the highest value, and the corresponding switch position denotes the comprehensive consideration of SAIDI and ENS. The optimal switch position under the two indicators is expressed as follows:
$[ ( L - L 1 ) X 1 + ( L - L 2 ) X 2 + … + ( L - L y + 1 ) X y + 1 ]$
Equation (15) can be used as the global switch-combination criterion of the connected circuit to determine the advantages and disadvantages of the global switch-position combination.
(3)
Advantages of the global switch-combination criterion compared with the single-switch criterion
We consider the installation of four switches in a line with 15 alternative switch positions as an example. This condition is compared with the traditional step of selecting the switch positions using the single-switch criterion.
The switch position is traditionally selected using the single-switch criterion:
• All candidate position criteria are first calculated. A switch is then installed at the best point.
• After the installation of the first switch, the criteria for the remaining positions need to be recalculated. The maximum value is then determined, and the second switch is installed.
• Step b is repeated until four switches are installed.
• Due to the installation of the additional switches, the criterion for the position of the previously installed switch also changes and is not optimal. Thus, recalculating the position is necessary to individually find the optimal positions until no change in the switch position occurs. In addition, global optimality is not guaranteed.
We propose to use the switch-combination criterion to select the optimal switch position. We directly calculate the criteria of the C(15,4) combination schemes, determine the optimal value, i.e., the optimal position, and ensure global optimum.
Generally, the overhead lines of a medium-voltage distribution network are limited in terms of capacity, and user access and loads are few. To ensure global optimum, all combination schemes are searched using the enumeration method. A program written in the C language is run in Visual C++ 6.0, and we search for the C(15,4) combination scheme in approximately 2 s, which is relatively fast.

#### 4.3. Alternate Switch Position

The alternative position of the switch is the position where the switch may also be installed. We analyse if the switch is installed in each line section, identify which position is the best in the line section, restrict the distribution of the switch position within a limited range, and significantly reduce the search volume while not reducing the accuracy. In this manner, the problem is transformed into a discrete combination-optimisation problem in which n switch alternative positions are first determined in the line, and y installed switches are then selected at the n positions.
According to the abovementioned analysis, the following alternative switch positions can be obtained with or without a tie switch.
(1)
No contact line section
According to Equation (11) and keeping the other conditions unchanged, when only the switch position in one line segment is used as a variable, the equation solution is the largest when the switch is installed at the power supply end. Therefore, for non-connected lines, the switch alternative position is located at each power end of the line segment, as marked with a solid black dot in Figure 3.
(2)
Similarly, according to Equation (15), this value is the largest when the switch in each line segment is installed at the main power supply terminal or backup power supply terminal. Therefore, for a connected line, the alternative position of the switch is at the main power supply terminal in each line segment, which is marked with a solid black dot in Figure 4.

#### 4.4. Determination of the Installation Position and Number of Switches

• According to whether the line is connected or not, all alternative installation positions are regarded as undetermined positions. The number of switches is denoted as n, and initial switch number y is considered as one.
• We find the most suitable y positions among the n switch positions to install y switches. According to the connection of the line (zero) and the global combination criterion in Equation (15) [Equation (11)], the values of the C(n, y) combination schemes are calculated in sequence. The corresponding switch position is identified when the maximum value is found, which is the optimal switch position when y switches are installed.
• We determine whether the constraint condition is satisfied, i.e., if y = y + 1, step b is repeated; otherwise, step d is performed.
• We output the optimal position and number of y − 1 switches.

#### 4.5. Algorithm Flow

The heuristic algorithm is based on the planning experience of the actual power grid, converts it into a certain logic rule, and then determines whether the segment switch is installed or not based on this logic rule. This paper also belongs to the heuristic algorithm. This paper proposes a global combination criterion to simultaneously judge the pros and cons of the combined effect of multiple switch positions, that is: find the most suitable y positions on the n switch candidate positions to install y switches. According to whether there is a connection or not, according to the global combination criterion of Equation (11) (Equation (15)), the enumeration method is used to calculate the values of C(n, y) combination schemes in turn, and the combination scheme with the maximum value is found, which is the optimal switch position when y switches are installed. This avoids the tediousness of traditionally adjusting only one switch position at a time and the local optimal problem that may fall into, and directly obtains the optimal solution and ensures the global optimality, so that the global optimal position of a given number of switches can be determined.
The number of switches is determined based on the optimal switch position. First, find the best combination of installation positions corresponding to a switch through the global combination criterion. If the constraint conditions (2) to (6) are satisfied, add one to the number of switches, and then find the best combination of installation positions under this number until if the constraints are not met, it is the total number of switches. The flow chart is as follows. This not only ensures the global optimization of the switch position, but also ensures the optimization of the number of switches. Finally, it is verified by two practical examples; the algorithm flow is as shown in Figure 5.

## 5. Calculation Example and Optimisation-Effect Analysis

#### 5.1. Example 1

The method in this study is used to calculate and optimise the actual feeder data in reference [14] listed in Table 1 and to compare the effects. By considering λ as 0.05 times/(year·km), t1 = 3 h and t2 = 0. The considered reliability index is ENS.
Figure 6 shows the alternative positions of the switch without a tie line, and Figure 7 shows those with a tie line. The optimisation results are shown in the switch configuration scheme shown in Figure 8, Figure 9, Figure 10 and Figure 11 in which Figure 9 shows that with no tie. The optimal switch configuration scheme is shown in Figure 11 where contact occurs. Figure 8 shows the optimal switch position when only two switches are installed without a contact. Figure 10 shows the case when only two switches are installed without a contact.
Table 2 lists the comparison between the calculation optimisation results of the method used in the present study and that in [28,29]. Through the calculation, when the line is not connected, we install three switches to optimise the section, i.e., we divide the line into four sections. When four switches are installed, the optimal positions are at the power terminals of 6–10, 10–14, 17–19, and 21–23. The ENS is 3.513 MW·h/year, which is 3% lower than that in the three-switch ENS and satisfy constraint condition number (4). The optimal three switches are located at the power terminals of 6–10, 10–14, and 19–21, and the ENS is 3.593 MW·h/year. The method in [29] also installs three switches, but the positions of the switches are arranged at the power terminals of 4–6, 10–14, and 19–21; the ENS is 3.684 MW·h/year. The method used in the present study is the same as that in [29], i.e., the same number of switches. Thus, investment is the same, which can reduce ENS by 2.47%, and the system reliability is higher. Reference [28] chose to install only two switches for cost considerations, which were arranged at the 6–10 and 14–17 power terminals, and the ENS was 3.900 MW·h/year. However, the position was not optimal. The optimal position of the two switches determined by the method used in the present study is at the 10–14 and 19–21 power terminals, and the ENS is 3.851 MW·h/year. Compared with the switch-layout scheme in [28], the cost remains the same, and the ENS is reduced by 1.26%.
When the line is connected, the calculation reveals that installing five switches is best for segmentation, i.e., we divide the line into six segments. When six switches are installed, the reliability of the upgrade is too low to satisfy constraint condition number (4). The optimal positions of the five switches are at 4–6, 6–10, and 14–17 standby power terminals and 10–14 and 19–21 main power terminals. The ENS is 0.840 MW·h/year. The method employed in [28,29] was to install four switches. The switches in [28] were arranged at the 4–6, 6–10, and 17–19 standby power terminals and 10–14 main power terminal. The ENS was 1.055 MW·h/year. The switches used in [29] were arranged at the 4–6 and 10–14 standby power terminals and 10–14 and 19–21 main power terminals. The ENS was 1.117 MW·h/year. However, the position of the four switches was not optimal. The optimal position of the four switches determined by our study is located at the 4–6, 6–10, and 10–14 standby power terminals and the 19–21 main power terminal. ENS is 1.013 MW·h/year. Under the same number of switches, ENS is reduced by 3.98% compared with that in [28] and by 9.31% compared with that in [29]. The five-switch configuration scheme in the present study is 17.08% lower than the four-switch optimal scheme. Compared with the switch-layout scheme in [28,29], we install one more switch. ENS is reduced by 20.38% compared with that in [28] and by 24.80% compared with that in [29]. We can observe that although one more switch is installed, the ENS is significantly reduced and the reliability is significantly improved, which prove that the proposed scheme can effectively optimise the number of switches.
Table 3 is a chart detailing the various configuration conditions in this paper.
Table 3. Condition and operation table.
Table 3. Condition and operation table.
ExampleContact LineGraphicsConfigure
Example 1 (Actual feeder data in Reference 28)no contact Figure 6Alternative switch-position map
Figure 8Optimal switch-distribution map (two switches)
Figure 9Optimal switch-distribution map (three switches)
with contactFigure 7Alternative switch-position map
Figure 10Optimal switch-distribution map (four switches)
Figure 11Optimal switch-distribution map (five switches)
Example 2 (Actual feeder data in a certain place)with contactFigure 12Alternative switch-position map
Figure 13Optimal switch-distribution map

#### 5.2. Example 2

Table 4 lists the real feeder data of a certain place. The feeder is a connected feeder. The method in this study is used to optimise and compare the effects. The values of λ, t1, and t2 are the same as those in Example 1. The optimisation results are shown in Figure 13.
Table 5 lists the comparison of the results after optimisation of the comprehensive and single indexes after and before optimisation. The feeder is equipped with four segment switches before optimisation, which are arranged at the 2–4 and 11–14 standby power terminals and 7–11 and 16–20 main power supply terminals; ENS is 1.152 MW·h/year, and SAIDI is 0.2349 h/(house·year). The positions obtained by optimising using the comprehensive index by the method employed in the present study are shown in Figure 13, which are at the 4–7, 7–11, 14–16, and 16–20 standby power terminals and the 11–14 main power terminal. ENS is 0.8519 MW·h/year, and SAIDI is 0.1719 h/(household·year). Compared with the values before optimisation, only one more switch is installed, and ENS is reduced by 26.05%, SAIDI is reduced by 26.82%, and the comprehensive reliability index is reduced by 26.42%. We can observe that the reliability-index value is greatly reduced and the reliability is significantly improved.
Compared with the optimisation result under the SAIDI indicator, the optimisation result under the comprehensive indicator has slightly higher SAIDI but lower ENS. The two indicators are normalised and multiplied by their respective weights [W1 (SAIDI) = 0.5; W2 (ENS) = 0.5]. The obtained objective function value is lower, which is better. We can observe that the optimisation results under the comprehensive index are more comprehensive and reliable than that under the single index. Simultaneously, we prove that the method proposed in this paper can effectively optimise the number of switches under the ENS and SAIDI indexes and effectively optimise the number of switches under the comprehensive reliability index, which presents important applicability.

## 6. Conclusions

(1)
Considering the reliability and economy comprehensively, multiple switch positions are judged at the same time through the global combination criterion. Compared with the method of repeatedly iteratively optimizing and determining the switch position using the single switch criterion in literatures [28,29], it is not only more direct, and does not get stuck in a local optimum. When there is no tie switch in the first example, the method in this paper reduces the ENS by 2.47% compared with the literature [29], which effectively improves the utilization rate of the equipment.
(2)
This paper proposes to further optimize the number of switches based on the optimal switch position. In example 1, the ENS of this paper is reduced by 20.38% and 24.80% compared with the literature [28] and literature [29], respectively. In example 2, the comprehensive index of the method in this paper is reduced by 26.05%, SAIDI by 26.82%, and comprehensive reliability index by 26.42% compared with the ENS before optimization. It can be seen that it is obviously more reasonable to use the optimized optimal switch position data to determine the number of switches, which not only ensures the global optimum of the switch position, but also ensures the optimum number of switches, so that the reliability index value is greatly reduced and the reliability is significantly improved.

## Author Contributions

W.C.: project administration, data curation, formal analysis, investigation, methodology; Z.L.: validation, writing—original draft; Y.L.: writing—review and editing. All authors have read and agreed to the published version of the manuscript.

## Funding

This work was supported in part by the Academic Degrees and Graduate Education Reform Project of Henan Province (No.2021SJGLX078Y), the Key Scientific Research Projects Plan of Henan Higher Education Institutions (No.19A470006), and the Cultivation Plan of Young Backbone Teachers in Colleges and Universities of Henan Province (No.2019GGJS104).

## Data Availability Statement

The data used to support the findings of this study are available from the corresponding author upon request.

## Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Optimal number of segments is affected by whether the switch position is optimal or not.
Figure 1. Optimal number of segments is affected by whether the switch position is optimal or not.
Figure 2. Line segmentation diagram.
Figure 2. Line segmentation diagram.
Figure 3. Switch alternative-location diagram (no contact).
Figure 3. Switch alternative-location diagram (no contact).
Figure 4. Switch alternative-location diagram (with contact).
Figure 4. Switch alternative-location diagram (with contact).
Figure 5. Algorithm flowchart.
Figure 5. Algorithm flowchart.
Figure 6. Example 1: alternative switch-position map (no contact).
Figure 6. Example 1: alternative switch-position map (no contact).
Figure 7. Example 1: alternative switch-position map (with contact).
Figure 7. Example 1: alternative switch-position map (with contact).
Figure 8. Example 1: optimal switch-distribution map (no contact, two switches).
Figure 8. Example 1: optimal switch-distribution map (no contact, two switches).
Figure 9. Example 1: optimal switch-distribution map (no contact, three switches).
Figure 9. Example 1: optimal switch-distribution map (no contact, three switches).
Figure 10. Example 1: optimal switch-distribution map (with contact, four switches).
Figure 10. Example 1: optimal switch-distribution map (with contact, four switches).
Figure 11. Example 1: optimal switch-distribution map (with contact, five switches).
Figure 11. Example 1: optimal switch-distribution map (with contact, five switches).
Figure 12. Example 2: alternative switch-position map (with contact).
Figure 12. Example 2: alternative switch-position map (with contact).
Figure 13. Example 2: optimal switch-distribution map (with contact).
Figure 13. Example 2: optimal switch-distribution map (with contact).
Table 1. Piece of the actual feeder data.
Table 1. Piece of the actual feeder data.
120.403
230.120192
240.524
450.480201
460.610
670.000134
680.220201
690.000128
6100.263
10110.000201
10120.936639
10130.815361
10140.583
14150.000658
14160.400201
14170.195
17180.000383
17190.200
19200.200639
19210.204
21220.140255
21230.604
23240.000255
23250.400243
Table 2. Example 1: comparison of the switch position-optimisation result.
Table 2. Example 1: comparison of the switch position-optimisation result.
Wiring ModeMethodSwitch PositionENS (MW·h/Year)
No contactPresent study10–14 Power terminal
19–21 Power terminal
3.851
Reference [14]6–10 Power terminal
14–17 Power terminal
3.900
Present study6–10 Power terminal
10–14 Power terminal
19–21 Power terminal
3.593
Reference [15]4–6 Power terminal
10–14 Power terminal
19–21 Power terminal
3.684
With contactPresent study4–6 Standby power terminal
6–10 Standby power terminal
10–14 Standby power terminal
19–21 Main power terminal
1.013
Reference [14]4–6 Standby power terminal
6–10 Standby power terminal
10–14 Main power terminal
17–19 Standby power terminal
1.055
Reference [15] 4–6 Standby power terminal
10–14 main power terminal
10–14 Standby power terminal
19–21 Main power terminal
1.117
Table 4. Piece of real feeder data in a certain place.
Table 4. Piece of real feeder data in a certain place.
Starting PointEndLine Length (km)Load (kW)Number of Users (Household)
120.604
230.20420453
240.420
450.00014241
460.23124672
470.368
780.000436137
790.27323483
7100.85217466
7110.497
11120.000387132
11130.465589203
11140.373
14150.742628258
14160.405
16170.295291139
16180.000336115
16190.30028393
16200.520
20210.000335102
20220.38027892
20230.434
23240.000377127
Table 5. Example 2: comparison of the switch-position optimisation results.
Table 5. Example 2: comparison of the switch-position optimisation results.
(Household
Year))
ENS (MW·h/
Year)
Value of the Objective Function under the Composite Indicator (Normalised)
Optimal under comprehensive index4–7 Standby power terminal
7–11 Standby power terminal
11–14 Main power terminal
14–16 Standby power terminal
16–20 Standby power terminal
0.17190.85190.155902
Optimal under ENS index4–7 Standby power terminal
7–11 Standby power terminal
11–14 Main power terminal
14–16 Standby power terminal
16–20 Standby power terminal
0.17190.85190.155902
Optimum under SAIDI4–7 Standby power terminal
7–11 Standby power terminal
11–14 Main power terminal
14–16 Standby power terminal
16–20 Power terminal
0.17070.85820.155938
Before optimisation2–4 Standby power terminal
7–11 Main power terminal
11–14 Standby power terminal
16–20 Main power terminal
0.23491.1520.211868
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MDPI and ACS Style

Cao, W.; Li, Z.; Li, Y. Optimisation Configuration of Overhead-Line Segmentation Switch of a Distribution Network Based on Global Combination Criterion. Processes 2022, 10, 1976. https://doi.org/10.3390/pr10101976

AMA Style

Cao W, Li Z, Li Y. Optimisation Configuration of Overhead-Line Segmentation Switch of a Distribution Network Based on Global Combination Criterion. Processes. 2022; 10(10):1976. https://doi.org/10.3390/pr10101976

Chicago/Turabian Style

Cao, Wensi, Zhaohui Li, and Yuxiang Li. 2022. "Optimisation Configuration of Overhead-Line Segmentation Switch of a Distribution Network Based on Global Combination Criterion" Processes 10, no. 10: 1976. https://doi.org/10.3390/pr10101976

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