Optimal electric distribution network configuration using adaptive sunflower optimization

Bulletin of Electrical Engineering and Informatics
Vol. 10, No. 4, August 2021, pp. 1777~1784
ISSN: 2302-9285, DOI: 10.11591/eei.v10i4.2588 1777
Journal homepage: http://beei.org
Optimal electric distribution network configuration using
adaptive sunflower optimization
Thuan Thanh Nguyen, Ngoc Thiem Nguyen, Trung Dung Nguyen
Faculty of Electrical Engineering Technology, Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam
Article Info ABSTRACT
Article history:
Received May 1, 2020
Revised Mar 25, 2021
Accepted Jun 1, 2021
Network reconfiguration (NR) is a powerful approach for power loss
reduction in the distribution system. This paper presents a method of network
reconfiguration using adaptive sunflower optimization (ASFO) to minimize
power loss of the distribution system. ASFO is developed based on the
original sunflower optimization (SFO) that is inspired from moving of
sunflower to the sun. In ASFO, the mechanisms including pollination,
survival and mortality mechanisms have been adjusted compared to the
original SFO to fit with the network reconfiguration problem. The numerical
results on the 14-node and 33-node systems have shown that ASFO
outperforms to SFO for finding the optimal network configuration with
greater success rate and better obtained solution quality. The comparison
results with other previous approaches also indicate that ASFO has better
performance than other methods in term of optimal network configuration.
Thus, ASFO is a powerful method for the NR.
Keywords:
Adaptive sunflower
optimization
Distribution system
Network reconfiguration
Power loss
Sunflower optimization
This is an open access article under the CC BY-SA license.
Corresponding Author:
Thuan Thanh Nguyen
Faculty of Electrical Engineering Technology
Industrial University of Ho Chi Minh City
No. 12 Nguyen Van Bao, Ward 4, Go Vap District, Ho Chi Minh City, Vietnam
Email: nguyenthanhthuan@iuh.edu.vn
1. INTRODUCTION
Electric distribution network (EDN) transfers electricity from the transmission system to customers.
Because of operating at low voltage level, the EDN’s power loss often takes high part with about 70% in the
total losses of distribution and transmission networks [1]. Thus, power loss reduction of distribution network
is one of important missions in operating distribution network. There are a lot of techniques for power loss
reduction such as capacitor placement, distributed generation installation, increasing cross-section of
conductor and operating at high voltage level and network reconfiguration. Whereas, NR is one of the most
powerful approaches for decreasing power loss of distribution network. The network reconfiguration
approach is achieved by opening and closing switches located in the system. By changing network
configuration, load from heavy branches will be transferred to other branches, as a result, and total losses of
the system are reduced.
The network reconfiguration has been first solved Merlin and Back in [2] by a branch-and-bound
approach. Then several approaches have been demonstrated for the NR problem. Civanlar et al. in [3], a
heuristic technique has been used to find the optimal network configuration. The idea of this approach is that
an open switch is replaced by other one to decrease power loss. Shirmohammadi and Hong in [4], another
heuristic technique has proposed for the network reconfiguration problem, wherein, the branch-and-bound
method Merlin and Back in [2] has been improved to determine optimal configuration. Later on, there are a
lot of techniques that are inspired from ideals of nature or society phenomena have been proposed for the NR

 ISSN: 2302-9285
Bulletin of Electr Eng & Inf, Vol. 10, No. 4, August 2021 : 1777 – 1784
1778
problem. The common feature of these methods is that they yield more positive results than heuristic
methods. Typical of the above methods must be mentioned to genetic algorithm (GA) [5], [6], particle swarm
optimization (PSO) [7]-[9], grey wolf optimization [10], [11], backtracking search algorithm [12], tabu
search algorithm (TS) [13], runner root (RRA) [14], symbiotic organisms search (SOS) [15], adaptive
shuffled frogs leaping algorithm (ASFLA) [16], improved shuffled frogs leaping algorithm (ISFLA) [17],
improved elitist-jaya algorithm (IEJAYA) [18], improved cuckoo search algorithm (ICSA) [19], binary
particle swarm gravity search algorithm (BPSO-GSA) [20], and biogeography based optimization (BBO) [21].
Sunflower optimization (SFO) is a new metaheuristic algorithm is first proposed by Gomes et al.
[22]. Wherein, SFO is inspired from an idea of moving of sunflower plant to the sun. To solve the
optimization problem, a sunflower plant is a candidate solution for the optimization problem and a radiation
intensity that the sunflower plant received from the sun is considered as the quality of the candidate solution.
Furthermore, a best sunflower plant is considered as the sun and other ones will move to the sun. Gomes et
al. in [22], SFO is applied for the problem of damage detection for the composite plate and its performance
has been shown to be better than GA. However, the effectiveness of SFO for another problem is still needed
to evaluate.
This paper presents a method for optimal network reconfiguration (NR) to minimize power loss
using adaptive sunflower optimization (ASFO). In which, ASFO is adjusted from the SFO for adapting to the
NR problem. To generate better solution for the NR problem, the all of mechanisms of creating of new
sunflower plants such as pollination, survival and mortality mechanisms have been modified. The proposed
ASFO has been applied to determine the optimal NR for the 14-node and 33-node distribution systems. The
numerical result compared to SFO have shown the outstanding efficiency of the proposed ASFO. Based on
the contents of the paper, the highlights of this work can be emphasized is being as:
− SFO is adapted to ASFO for solving the network reconfiguration problem.
− All of mechanisms of creating of new sunflower plants consisting of pollination, survival, and mortality
mechanisms have been modified to generate better candidate solutions for the NR problem.
− The performance of ASFO is validated on the 14-node and 33-node systems.
− ASFO is outstanding to SFO for searching optimal NR.
The rest of paper is organized is being as. The problem of network reconfiguration is shown in the
below section. The network reconfiguration using adaptive sunflower optimization is shown in section 3.
Section 4 shows the results and discussion. Section 5 presents the main conclusion.
2. PROBLEM OF NETWORK RECONFIGURATION
There are many benefits of network reconfiguration such as reduction of power loss, over load and
improvement of voltage, and load balance. Wherein, due to high power loss character of distribution level,
power loss reduction is considered as one of important goals of network reconfiguration. It is calculated is
being as:
𝑃𝑙𝑜𝑠𝑠 = ∑ 𝑝𝑙𝑜𝑠𝑠,𝑖
𝑛𝑏𝑟
𝑖=1 (1)
Where 𝑃𝑙𝑜𝑠𝑠 and 𝑝𝑙𝑜𝑠𝑠,𝑖 are the power loss of the system and the branch 𝑖, respectively. 𝑛𝑏𝑟 is number of
branches. Changing the network configuration of distribution system should ensure the following constraints:
The radial network configuration: In order to maintain the constraint, (2) should be ensured [13]:
|𝑑𝑒𝑡⁡(𝐶)| = 1 (2)
Where, 𝑑𝑒𝑡⁡(𝐶) is the 𝐶 matrix’s determinant. 𝐶 is a connected matrix among branches and nodes of the
distribution system. In addition, the obtained network configuration by reconfiguration should not negatively
affect to voltage and current profile:
{
𝑉
𝑗 ≥ 𝑉𝑙𝑜,𝑙𝑖𝑚𝑖𝑡⁡; 𝑗 = 1, … , 𝑛𝑛𝑜
𝐼𝑖 ≤ 𝐼𝑖,𝑚𝑎𝑥⁡; 𝑖 = 1, … , 𝑛𝑏𝑟⁡
(3)
Where, 𝑉
𝑗 is the voltage amplitude of the node 𝑗. 𝑉𝑙𝑜,𝑙𝑖𝑚𝑖𝑡 is allowed minimum voltage amplitude which is
often set to 0.95 in per unit. 𝑛𝑛𝑜 is number of nodes. 𝐼𝑖 and 𝐼𝑖,ℎ𝑖,𝑙𝑖𝑚𝑖𝑡 are the current of the branch 𝑖 and its
rated current.

Bulletin of Electr Eng & Inf ISSN: 2302-9285 
Optimal electric distribution network configuration using adaptive sunflower … (Thuan Thanh Nguyen)
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3. NETWORK RECONFIGURATION USING ADAPTIVE SUNFLOWER OPTIMIZATION
In this section, a method of network reconfiguration using ASFO is presented. Wherein, the original
SFO is adjusted to ASFO for generating better solution for the network reconfiguration problem. Details of
ASFO for searching the optimal NR are described is being as:
Step 1: generate randomly the population of sunflower plants
𝑆𝐹𝑖 = 𝑢𝑝 + 𝑟𝑎𝑛𝑑(1, 𝑑). (𝑢𝑝 − 𝑙𝑜)⁡; 𝑖 = 1 ÷ 𝑛⁡ (4)
Where 𝑆𝐹𝑖 is the sunflower plant 𝑖.⁡𝑑 is dimension of the network reconfiguration problem. 𝑢𝑝 and 𝑙𝑜 are the
upper and lower boundaries of the control variables. 𝑛 is number of sunflowers in the population. The control
variables of the network reconfiguration problem present for open switches of the distribution system. Thus,
their values are rounded to integer. Then, their adaptive function (𝐴𝐹𝑖) value consisting of the objective
function value and the penalty value of violating constraints is calculated is being as:
𝐴𝐹𝑖 = 𝑃𝑙𝑜𝑠𝑠 + 𝐾𝑃. [𝑚𝑎𝑥(𝑉𝑙𝑜,𝑙𝑖𝑚𝑖𝑡 − 𝑉𝑚𝑖𝑛, 0) + 𝑚𝑎𝑥(𝐾𝐼𝑚𝑎𝑥 −⁡𝐾𝐼ℎ𝑖,𝑙𝑖𝑚𝑖𝑡, 0)] (5)
Where, 𝐾𝑃 is penalty factor that is set to 1000 in this work. 𝑉𝑚𝑖𝑛 is minimum voltage of the obtained network
configuration. 𝐾𝐼𝑚𝑎𝑥 is maximum load carrying factor of the obtained network configuration. 𝐾𝐼ℎ𝑖,𝑙𝑖𝑚𝑖𝑡 is the
permitted load carrying factor that is set to 1.
Step 2: generate new sunflower plants using the pollination mechanism
In the original SFO, the new solutions are generated by using the pollination mechanism is being as:
𝑆𝐹𝑖,𝑛𝑒𝑤 = 𝑟𝑎𝑛𝑑(0,1). (𝑆𝐹𝑖 − 𝑆𝐹𝑖+1) + 𝑆𝐹𝑖+1⁡; 𝑖 = 1 ÷ 𝑅𝑝. 𝑛⁡ (6)
Where 𝑅𝑝 is the pollination rate which is set to 0.6 [22]. It can be seen that all sunflowers in the population
will tend to move to the sun. The component of difference of the two solutions in the above equation will not
produce significant increments to create an entirely new solutions for exploring the search space.
Furthermore, to increase the diversity of the control variables, a vector of random numbers are used instead
of the random number only. Therefore, in order to create a new solutions for the network reconfiguration
problem, the above equation is adjusted is being as:
𝑆𝐹𝑖,𝑛𝑒𝑤 = 𝑟𝑎𝑛𝑑(1, 𝑑). 𝛽. (𝑆𝐹𝑖 − 𝑆𝐹𝑖+1) + 𝑆𝐹𝑖+1⁡; 𝑖 = 1 ÷ 𝑅𝑝. 𝑛⁡ (7)
Where, 𝛽 is a gain coefficient. Its value depends on the space search of variables. Depending on the scale of
the distribution system, the space search of each variable can range from some switches to several dozen
switches. So, in this work it is chosen to 4.
Step 3: generate new sunflower plants using the survival mechanism
In this mechanism of SFO, new sunflower plants are created based on distance between itself to the best
sunflower plant (𝑆𝐹𝑏𝑒𝑠𝑡) is being as:
𝑆𝐹𝑖,𝑛𝑒𝑤 = 𝑆𝐹𝑖 + 𝑟𝑎𝑛𝑑(0,1). ((𝑆𝐹𝑏𝑒𝑠𝑡 − 𝑆𝐹𝑖)/(‖𝑆𝐹𝑏𝑒𝑠𝑡 − 𝑆𝐹𝑖‖))⁡; 𝑖 = 𝑅𝑝. 𝑛 ÷ 𝑛. (1 − 𝑅𝑑)⁡ (8)
Where, 𝑆𝐹𝑏𝑒𝑠𝑡 is the best sunflower plant. ‖𝑆𝐹𝑏𝑒𝑠𝑡 − 𝑆𝐹𝑖‖ is the Euclidean length between plant 𝑖 and the best
plant. 𝑅𝑑 is a death rate which is set to 0.1 [22]. Similarly to the pollination mechanism, the survival
mechanism is adjusted is being as:
𝑆𝐹𝑖,𝑛𝑒𝑤 = 𝑆𝐹𝑖 + 𝑟𝑎𝑛𝑑(1, 𝑑). 𝛽. ((𝑆𝐹𝑏𝑒𝑠𝑡 − 𝑆𝐹𝑖)/(‖𝑆𝐹𝑏𝑒𝑠𝑡 − 𝑆𝐹𝑖‖))⁡;𝑖 = 𝑅𝑝. 𝑛 ÷ 𝑛. (1 − 𝑅𝑑)⁡ (9)
Step 4: generate new sunflower plants using the mortality mechanism
The rest sunflower plants are renewed by using random initialization. In ASFO the vector of random
numbers are used instead of the random number only in the original SFO is being as:
𝑆𝐹𝑖,𝑛𝑒𝑤 = 𝑢𝑝 + 𝑟𝑎𝑛𝑑(1, 𝑑). (𝑢𝑝 − 𝑙𝑜)⁡; ⁡𝑛. (1 − 𝑟𝑑) ÷ 𝑛⁡ (10)
Step 5: Selection new population of sunflower plants for next generation
All of new sunflower plants are evaluated the adaptive function by using in (5) to obtain the
adaptive function value (𝐴𝐹𝑖,𝑛𝑒𝑤). Then, if new plants have the better quality than the corresponding ones,
they will substitute for current sunflower plants is being as:

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𝑆𝐹𝑖 =⁡{
𝑆𝐹𝑖,𝑛𝑒𝑤⁡; 𝑖𝑓⁡𝐴𝐹𝑖,𝑛𝑒𝑤 < 𝐴𝐹𝑖
𝑆𝐹𝑖⁡; ⁡𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
⁡ (11)
𝐴𝐹𝑖 =⁡{
𝐴𝐹𝑖,𝑛𝑒𝑤⁡; 𝑖𝑓⁡𝐴𝐹𝑖,𝑛𝑒𝑤 < 𝐴𝐹𝑖
𝐴𝐹𝑖⁡; ⁡𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
⁡ (12)
Step 6: stop searching the optimal solution
The searching process from step 2 to step 5 will be performance until the maximum number of
generations (𝑀𝐺𝑚𝑎𝑥) reaches. The flowchart of ASFO for finding the optimal network configuration is
shown in Figure 1.
Begin
- Set parameters: n, d, Rp, Rd and MGmax
- Initialize the whole ecosystem by using (4)
- Evaluate quality of sunflower plants using (5)
- Identify the best sunflower plant
- Set current generation (G) to 1
Generate new sunflower plants based on the pollination mechanism by (7)
G < MGmax ?
No
Output: the best sunflower plant
Finish
Yes
G = G + 1
Generate new sunflower plants based on the survival mechanism by (9)
Generate new sunflower plants based on the mortality mechanism by (10)
Evaluate quality of sunflower plants by (5)
Select new population of sunflower plants by (11) and (12)
Figure 1. Flowchart of ASFO for network reconfiguration
4. RESULTS AND DISCUSSION
To demonstrate effectiveness of ASFO, two distribution systems consisting of 14-node and 33-node
networks are used to find the optimal NR. The performance of ASFO is compared to the SFO in criteria such
as maximum (𝐴𝐹𝑚𝑎𝑥), minimum (𝐴𝐹𝑚𝑖𝑛), mean (𝐴𝐹𝑚𝑒𝑎𝑛) and standard deviation (𝑆𝑇𝐷) values of the
adaptive function gained in 50 runs as well as the mean run times (𝑇𝑟𝑢𝑛) [23]. Both of these methods have
coded in Matlab 2016a and run on the same personal computer of 4 G random access memory (RAM) and
intel core i5, 2.4 Gh. In addition, the obtained results from ASFO are also compared with other methods in
literature to show the reliability of the proposed method. The parameters of ASFO and SFO consisting of 𝑛
and 𝑀𝐺𝑚𝑎𝑥 are chosen to {10, 100} for the 14-node system and {20, 150} for the 33-node system.
4.1. The 14-node network
The system consists of three open switches as shown in Figure 2 [5]. The initial power loss of the
system is 511.4356 kW. The optimal network configuration obtained by the proposed ASFO method are
shown in Table 1. The switches (SW) consisting of {6-12-14} are opened substituting for {14-15-16} in the
optimal network configuration. This changing has caused power loss (𝑃𝑙𝑜𝑠𝑠) of 466.1267 kW and minimum
voltage (𝑉𝑚𝑖𝑛) of 0.9716 p.u. Both of these indicators are better than those of the initial network configuration.
Wherein, the former is 45.3089 kW lower and the latter is 0.0023 higher than those of the initial network
configuration. Furthermore, the voltage amplitude of nodes shown in Figure 3 sends a message that voltage
improvement gained by network reconfiguration is remarkable with most of node voltages have been
increased. The optimal network configuration gained by ASFO is identical to that of GA [5], BPSO-GSA
[20] and TS [13]. These comparisons demonstrate the reliability of the ASFO for the network reconfiguration
problem.

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F1 F2 F3
4 5 13
14
2
3 9
7
6
8 12
11
10
1
7
4
3
14
11 10
9
8
16
6
5
13
12
15
2
Figure 2. The first test 14-node system
Table 1. The obtained results of ASFO, SFO, and previous methods for the 14-node network
Item None ASFO SFO GA [5] BPSO-GSA [20] TS [13]
𝑆𝑊 14-15-16 6-12-14 6-12-14 6-12-14 6-12-14 6-12-14
𝑃𝑙𝑜𝑠𝑠 (kW) 511.4356 466.1267 466.1267 466.1267 466.1267 466.1267
𝑉𝑚𝑖𝑛 (p.u.) 0.9693 0.9716 0.9716 0.9716 0.9716 0.9716
𝐴𝐹𝑚𝑎𝑥 - 466.1267 511.44 - - -
𝐴𝐹𝑚𝑖𝑛 - 466.1267 466.1267 - - -
𝐴𝐹𝑚𝑒𝑎𝑛 - 466.1267 475.7757 - - -
𝑆𝑇𝐷 - 0 10.7152 - - -
𝑇𝑟𝑢𝑛 (s) - 2.9475 2.6288 - - -
Figure 3. The voltages of the initial and optimal configurations of the 14-node network
In comparison with SFO, the indicators such as 𝐴𝐹𝑚𝑎𝑥, 𝐴𝐹𝑚𝑖𝑛, 𝐴𝐹𝑚𝑒𝑎𝑛 and 𝑆𝑇𝐷 values of the
adaptive function gained in 50 runs show that ASFO outperforms to SFO. Although both of ASFO and SFO
have searched out the optimal network configuration (shown by the same 𝐴𝐹𝑚𝑖𝑛 value), the 𝐴𝐹𝑚𝑎𝑥, and
𝐴𝐹𝑚𝑒𝑎𝑛 values of ASFO are much lower compared to SFO. In which, the 𝐴𝐹𝑚𝑎𝑥 and 𝐴𝐹𝑚𝑒𝑎𝑛 values of ASFO
are 45.3133 and 9.649 lower compared to those of SFO. In addition, STD value of ASFO is much lower
compared to that of SFO. Figure 4 (a) shows that ASFO has achieved the optimal NR in all of 50 runs with
STD of 0 while SFO has found the optimal solution in 21 per 50 runs with STD of 10.7152. The maximum,
mean and minimum convergence characters of both methods are shown in Figure 4 (b). Figure shows that
ASFO converges to lower value and lower convergence generations compared to SFO. The run times of
ASFO is 0.3187 seconds (s) higher than that of SFO. These results show that the improvement of ASFO is
remarkable to the NR problem.
(a) (b)
Figure 4. The performance of ASFO and SFO for the 14-node network, (a) obtained adaptive function value,
(b) convergence curves

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4.2. The 33-node network
The EDN in Figure 5 consists of five open switches of {33-34-35-36-37} [24]. The maximum
branch current limit is set to 255 A [25], [26]. The power loss, maximum load carrying factor and minimum
voltage of the system in case of none reconfiguration are 202.6863 kW, 0.8250 and 0.9131 p.u.
The optimal network configuration achieved by the ASFO method are shown in Table 2. The
switches (SW) consisting of {7-9-14-28-32} are opened substituting for {33-34-35-36-37} in the optimal
network configuration. This changing has caused 𝑃𝑙𝑜𝑠𝑠 of 139.9823 kW and 𝑉𝑚𝑖𝑛 of 0.9412. Both of these
indicators are better than those of the initial network configuration. Wherein, the former is 62.704 kW lower
and the latter is 0.0281 greater than those of the initial network configuration. In addition, the voltage
amplitude of nodes and current of branches shown in Figure 6 show that voltage and current improvements
gained by network reconfiguration are remarkable with increasing of most of node voltages and decreasing of
most of branch currents.
The optimal network configuration gained by ASFO is identical to that of ASFLA [16], SOS [15]
and IEJAYA [18]. The result of ASFO is better than that of BPSO-GSA [20] and GA [27]. Wherein, 𝑃𝑙𝑜𝑠𝑠
value obtained by ASFO is 1.2248 and 23.1648 lower than that of BPSO-GSA [20] and GA [27]. The 𝑉𝑚𝑖𝑛
value of ASFO is also 0.0034 and 0.0333 higher than that of BPSO-GSA [20] and GA [27]. Compared with
ISFLA [17], PSO [7], and BBO [21], the 𝑃𝑙𝑜𝑠𝑠 value obtained by ASFO is 0.428, 0.0223 and 0.428 higher
than that of above methods but the 𝑉𝑚𝑖𝑛 value of ASFO is 0.0034, 0.0117 and 0.0034 higher than that of the
ISFLA [17], PSO [7], and BBO [21] methods. These comparisons have demonstrated once again that the
reliability of the ASFO for the network reconfiguration problem.
5
4 6 8
2 3 7
19
9 12
11 14
13 16
15 18
17
26 27 28 29 30 31 32 33
23 24 25
20 21 22
10
2 3 5
4 6 7
18
19 20
33
1 9 10 11 12 13 14
34
8
21 35
15 16 17
25
26 27 28 29 30 31 32 36
37
22
23 24
1
Figure 5. The second test 33-node network
Table 2. The obtained results of ASFO, SFO, and other methods for the 33-node network
Method 𝑆𝑊 𝑃𝑙𝑜𝑠𝑠 (kW) 𝑉𝑚𝑖𝑛(p.) 𝐾𝐼𝑚𝑎𝑥 𝐴𝐹𝑚𝑎𝑥 𝐴𝐹𝑚𝑖𝑛 𝐴𝐹𝑚𝑒𝑎𝑛 𝑆𝑇𝐷 𝑇𝑟𝑢𝑛 (s)
None rec. 33-34-35-36-37 202.6863 0.9131 0.8250 - - - - -
ASFO 7-9-14-28-32 139.9823 0.9412 0.8126 164.309 148.7392 153.6637 4.0604 7.6666
SFO 7-10-14-27-32 144.0295 0.9398 0.8135 197.927 154.2448 174.6159 9.3234 5.7231
ASFLA [16] 7-9-14-28-32 139.9823 0.9412 0.8126 - - - - -
BPSO-GSA [20] 7-11-14-32-37 141.2071 0.9378 - - - - - -
SOS [15] 7-9-14-28-32 139.9823 0.9412 - - - - - -
ISFLA [17] 7-9-14-32-37 139.5543 0.9378 - - - - - -
IEJAYA [18] 7-9-14-28-32 139.9823 0.9412 - - - - - -
PSO [7] 7-14-32-35-37 139.9600 0.92946 - - - - - -
BBO [21] 7-9-14-32-37 139.5543 0.9378 - - - - - -
GA [27] 7-12-31-35-37 163.1471 0.9079 - - - - - -
(a) (b)
Figure 6. The voltages and currents achieved by ASFO and SFO for the 33-node network, (a) voltage profile,
(b) current profile

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In comparison with SFO, in 50 runs, SFO has only searched the network configuration with power
loss of 144.0295 kW that is 4.0472 kw higher than that of ASFO and the 𝑉𝑚𝑖𝑛 value is 0.0014 higher than
that of ASFO. In addition, the indicators consisting of 𝐴𝐹𝑚𝑎𝑥, 𝐴𝐹𝑚𝑖𝑛, 𝐴𝐹𝑚𝑒𝑎𝑛 and 𝑆𝑇𝐷 values of ASFO are
much lower compared to SFO. In which, these values of ASFO are 33.618, 5.5056, 20.9522 and 5.263 lower
compared to those of SFO. Figure 7 (a) shows that ASFO has gained lower adaptive function value than that
of SFO in most of runs. The maximum, mean and minimum convergence characters of both methods are
shown in Figure 7 (b). Figure 7 shows that ASFO converges to lower value and lower convergence
generations compared to SFO. The 𝑇𝑟𝑢𝑛 value of ASFO is 1.9435s higher than that of SFO. These achieved
results presents that ASFO is better than SFO for the NR problem.
(a) (b)
Figure 7. The performance of ASFO and SFO for the 33-node network, (a) obtained adaptive function value,
(b) convergence curves
5. CONCLUSION
In this work, the network reconfiguration problem for power loss reduction has been successfully
solved by using the proposed ASFO method. Wherein, to increase the efficiency of ASFO for the NR
problem, the ASFO search mechanisms including pollination, survival, and mortality mechanisms have been
adjusted compared to the original SFO. In which, the pollination and survival mechanisms has been added
gain factors and all of three mechanisms vector of random numbers have been used to replace for a random
number. The performance of ASFO has been validated on the 14-node and 33-node systems. The obtained
results compared to SFO show that ASFO has better performance than SFO in terms of the optimal network
configuration and maximum, minimum, mean and STD values of the adaptive function in several runs. The
compared results to other techniques have also shown that ASFO is in one of the effective approach for the
network reconfiguration problem. Future work may consider the performance of AFO for the NR for other
purposes or other optimization problems in power systems.
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