Electric distribution network reconfiguration for power loss reduction based on runner root algorithm

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 10, No. 5, October 2020, pp. 5016~5024
ISSN: 2088-8708, DOI: 10.11591/ijece.v10i5.pp5016-5024  5016
Journal homepage: http://ijece.iaescore.com/index.php/IJECE
Electric distribution network reconfiguration for power loss
reduction based on runner root algorithm
Thuan Thanh Nguyen
Faculty of Electrical Engineering Technology, Industrial University of Ho Chi Minh City, Viet Nam
Article Info ABSTRACT
Article history:
Received Oct 27, 2019
Revised Apr 8, 2020
Accepted Apr 23, 2020
This paper proposes a method for solving the distribution network
reconfiguration (NR) problem based on runner root algorithm (RRA) for
reducing active power loss. The RRA is a recent developed metaheuristic
algorithm inspired from runners and roots of plants to search water and
minerals. RRA is equipped with four tools for searching the optimal solution.
In which, the random jumps and the restart of population are used for
exploring and the elite selection and random jumps around the current best
solution are used for exploiting. The effectiveness of the RRA is evaluated
on the 16 and 69-node system. The obtained results are compared with
particle swarm optimization and other methods. The numerical results show
that the RRA is the potential method for the NR problem.
Keywords:
Distribution network
Network reconfiguration
Power loss
Radial topology
Runner root Copyright © 2020 Institute of Advanced Engineering and Science.
All rights reserved.
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, Viet Nam.
Email: nguyenthanhthuan@iuh.edu.vn
1. INTRODUCTION
Electric distribution system (EDS) has mesh topology but it is usually operated in radial topology
due some advantages such as reduction of short-circuit current and installation of protect devices. However,
radial operation takes more power loss compared with mesh operation. Therefore, reduction of power loss in
EDS takes a high role in operating EDS. In among methods of reduction power loss, network reconfiguration
(NR) is the most efficient technique because of no costs. It is performed by changing the status of opened and
closed switches in EDS.
The NR problem is first proposed in [1]. In this study, the NR problem is formulated by a mixed
integer non-linear problem and solved by a discrete branch-and-bound technique. Then, Civanlar et al., [2]
solved the NR problem based on exchanging switches to reduce power loss. After almost four decades,
the NR problem has solved by many modern methods stimulated from phenomena of nature or society such
as genetic algorithm (GA), particle swarm optimization (PSO), fireworks algorithm (FWA) and cuckoo
search algorithm (CSA), biogeography based optimization (BBO), grey wolf optimization (GWO). In [3-5],
GA has been used to solve the NR problem for minimizing power loss. In [6-8], PSO is proposed for solving
the NR problem to reduce power loss. In [9, 10] FWA is proposed for the NR problem to reduce power loss
and improve the node voltage. In [11-13], CSA has been successful solved the NR problem for reducing
power loss and improving node voltage. In [14] modified BBO is successful applied for finding the optimal
configuration for power loss reduction. The GWO is also successful applied for the NR problem to reduce
power loss [15, 16]. In comparison with the heuristic methods which are based on the knowledge of electric
power system such as [1, 2], the modern methods have more advantages. While the heuristic methods are
only usually to optimize the radial topology for power loss reduction, the modern methods called
metaheuristic methods are easy used to optimize the radial topology for different type of objective such as

Int J Elec & Comp Eng ISSN: 2088-8708 
Electric distribution network reconfiguration for power loss reduction … (Thuan Thanh Nguyen)
5017
power loss reduction, voltage improving, reliability improving or multi-objective. Furthermore, the obtained
result of the heuristic methods is usually local extremes but the meta-heuristic methods have ability to
provide good solution for the NR problem. In recent years, many algorithms belonging to this method group
are being developed. Therefore, the study of applying new algorithms to the NR problem is also a matter of
great concern to find out and contribute more effective methods for the NR problem.
Runner root algorithm (RRA) is a recent meta-heuristic method inspired from runners and roots of
plants to search water and minerals [17]. To explore the search space, RRA uses random jumps technique
with high steps to generate the new solutions far from current solutions and the re-initialization technique to
restart the current population. To exploit the search space, RRA uses random jumps technique with small
steps to generate new solutions around the current best solution and the elite selection technique to save
the current best solution for next generation. For solving twenty-five benchmark functions, RRA has
demonstrated advantages compared to others methods [17]. For application of RRA for the problems of
the power system, RRA have been successful applied for the NR problem with multi-objective function [18]
and the placement of DG in the EDS [19]. In this paper, RRA is adapted to solve the NR problem for power
loss reduction. The performance of RRA is tested in different EDS and compared with the well-known PSO
that has been successful applied for the NR problem [8, 20]. In addition, the calculated results obtained by
RRA are also compared to other methods in literature. The highlights of the paper is summarized as follows:
- RRA is adapted for solve the NR problem for power loss reduction;
- RRA outperforms PSO and other methods in literature in terms of successful rate and the quality of
the obtained optimal solution.
In the bellowing section, the problem formulation is presented. The application of RRA for the NR
problem is presented in section 3. Section 4 shows the results and analysis and finally conclusions are listed
in section 5.
2. PROBLEM FORMULATION
The purpose of the NR is transferring a part of loads from the heavy branches to light branches by
changing the opened/closed status of switches located on each branch. Power loss of EDS is calculated by
sum of power loss of each branch of the system. However, there are closed branches carrying current and
opened branches not carrying current in the EDS. Therefore power loss of the EDS is calculated by
as follows:
∆𝑃 = ∑ 𝑘𝑖 𝑅𝑖
𝑃𝑖
2
+𝑄𝑖
2
𝑉𝑖
2
𝑁𝑏𝑟
𝑖=1
(1)
In which, 𝑁𝑏𝑟 is a number of branches of EDS, 𝑅𝑖 is the ith branch’s resistance. Pi and Qi are the active and
reactive power flow on the ith branch. 𝑘𝑖 stands for the status of the branch ith in the EDS which is equal to 1
for closed status and 0 for vice versa.
The results of NR problem is a radial topology of EDS that satisfy following constraints:
- Radial topology constraint: To satisfy this constraint, the empirical formula [21] is proposed to check
candidate solutions.
𝑑𝑒𝑡(𝐴) = {
−1 𝑜𝑟 1, 𝑟𝑎𝑑𝑖𝑎𝑙
0, 𝑛𝑜𝑡 𝑟𝑎𝑑𝑖𝑎𝑙
(2)
In which, det(A) is determinant of matrix A. A is the branch by node matrix built by connection of EDS.
- Node voltage constraint: node voltage magnitude must lie in permissible ranges [𝑉 𝑚𝑖𝑛, 𝑉𝑚𝑎𝑥]. They are
respectively set equal to [0.95, 1] in per unit.
𝑉 𝑚𝑖𝑛 ≤ 𝑉𝑗 ≤ 𝑉𝑚𝑎𝑥 𝑤𝑖𝑡ℎ 𝑗 = 1, 2, . . 𝑁𝑏𝑢𝑠 (3)
where 𝑁𝑏𝑢𝑠 is the number of nodes in the EDS.
- Branch current constraint: For avoiding over load, the branches’ current magnitude must lie in their
permissible range.
𝐼𝑖 ≤ 𝐼 𝑚𝑎𝑥,𝑖 𝑤𝑖𝑡ℎ 𝑖 = 1, 2, . . 𝑁𝑏𝑟 (4)

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 10, No. 5, October 2020 : 5016 - 5024
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3. RRA FOR THE NR PROBLEM WITH POWER LOSS REDUCTION
RRA is inspired from the plants propagated through runners and roots. To apply this as an
optimization tool, Merrikh-Bayat used three idealized rules [17]:
- The mother plant is generated the daughter plant through its runner for exploring resources.
- The plants produce roots and root hairs to exploit resources around its position.
- The daughter plants will grow faster and become the mother plant at new position with rich resources.
Otherwise, they will be die at new position with poor resources.
In this study, the implementation of RRA for the NR problem is summarized as follows:
- Step 1: Initialization
For solving the NR problem, each mother plant is considered as radial topology of the distribution
system. In the first step, the population of the problem is generated as (5). In which, each radial topology is
presented as (6) and each variable of candidate solution which is an open switch is generated randomly as (7).
𝑝𝑜𝑝𝑢𝑙𝑎𝑡𝑖𝑜𝑛 = {
𝑋 𝑚𝑜𝑡ℎ𝑒𝑟,1
𝑋 𝑚𝑜𝑡ℎ𝑒𝑟,2
…
𝑋 𝑚𝑜𝑡ℎ𝑒𝑟,𝑁
(5)
𝑋 𝑚𝑜𝑡ℎ𝑒𝑟(𝑘) = [𝑋1, 𝑋2, … , 𝑋 𝑑, … , 𝑋 𝑑𝑖𝑚] (6)
𝑋 𝑑(𝑘) = 𝑟𝑜𝑢𝑛𝑑[𝑋𝑙𝑜𝑤,𝑑 + 𝑟𝑎𝑛𝑑 × (𝑋ℎ𝑖𝑔ℎ,𝑑 − 𝑋𝑙𝑜𝑤,𝑑)] (7)
where, k = 1, 2, …, N and d = 1, 2, …, dim with N and dim are respectively population size and the number
of variables. 𝑋𝑙𝑜𝑤,𝑑 and 𝑋ℎ𝑖𝑔ℎ,𝑑 are respectively low and high limit of tie-switch Xd. Based on the initialized
population of the mother plants, each mother plan is evaluated by the fitness function and the plant with
the best fitness function is saved to the best daughter plant 𝑋 𝑑𝑎𝑢𝑔ℎ𝑡𝑒𝑟,𝑏𝑒𝑠𝑡. Noted that, to calculate the fitness
function value, the power flow is performed and the value of the (1) is obtained.
- Step 2: Global search with generation of daughter plants
To explore search space, a new population of daughter plants is generated to replace the population
of mother plants.
𝑋 𝑑𝑎𝑢𝑔ℎ𝑡𝑒𝑟(𝑘) = {
𝑋 𝑑𝑎𝑢𝑔ℎ𝑡𝑒𝑟,𝑏𝑒𝑠𝑡,𝑘 , 𝑘 = 1
𝑟𝑜𝑢𝑛𝑑[𝑋 𝑚𝑜𝑡ℎ𝑒𝑟,𝑘(𝑘) + 𝑑 𝑟𝑢𝑛𝑛𝑒𝑟 × 𝑟𝑎𝑛𝑑], 𝑘 = 2, … , 𝑁
(8)
where, the constant parameter drunner is a large distance between the mother and daughter plant. Then, the fitness
function of each daughter plant is evaluated and a best daughter plant (𝑋 𝑑𝑎𝑢𝑔ℎ𝑡𝑒𝑟,𝑏𝑒𝑠𝑡) is updated.
- Step 3: Local search with large and small distances
To exploit search space, this step is performed as the value of the best daughter plant in two
generations is not improved considerably. The best daughter plant will generate dim new plants by modifying
one by one element in the best daughter plant. The first dim new plants are generated around the best
daughter plant with large distances as follows:
𝑋 𝑝𝑒𝑟𝑡𝑢𝑟𝑏𝑒𝑑,𝑑 = 𝑟𝑜𝑢𝑛𝑑[𝑣𝑒𝑐{1,1 … ,1,1,1 + 𝑑 𝑟𝑢𝑛𝑛𝑒𝑟 × 𝑟𝑎𝑛𝑑 𝑑, 1, … ,1} × 𝑋 𝑑𝑎𝑢𝑔ℎ𝑡𝑒𝑟,𝑏𝑒𝑠𝑡(𝑖)] (9)
where 𝑣𝑒𝑐{1,1 … ,1,1,1 + 𝑑 𝑟𝑢𝑛𝑛𝑒𝑟 × 𝑟𝑎𝑛𝑑, 1, … ,1} is a vector with all elements are equal to 1 except for
the d-th one, which is equal to 1 + 𝑑 𝑟𝑢𝑛𝑛𝑒𝑟 × 𝑟𝑎𝑛𝑑 𝑑. The second dim new plants are generated by replacing
𝑑 𝑟𝑢𝑛𝑛𝑒𝑟 with 𝑑 𝑟𝑜𝑜𝑡, which is much smaller than 𝑑 𝑟𝑢𝑛𝑛𝑒𝑟. The new daughter plants are evaluated the fitness
function and the best daughter plant is updated again.
- Step 4: Generation of new mother plants and escaping the local optimal
At the final stage of each iteration, based on the fitness of the daughter plants, the roulette wheel
selection method [22] is used to selection the daughter plants as the mother plants for the next generation.
Noted that the best daughter plant will has large probability selected for the next generation. In addition,
to escape local optimal solution, a re-initialization strategy is used to restart the algorithm. If after Stallmax
generations that the value of the best daughter plant still no considerable improvement, the population of
mother plants will be randomly generated similar to step 1. The pseudo code of the RRA for the NR to
minimize power is given in Figure 1.

5019
Figure 1. Pseudo code of the RRA for the NR problem for power loss reduction
4. RESULTS AND ANALYSIS
To show the efficient of RRA, the application of RRA for the NR problem is implemented in
platform Matlab 2016a, executed on a personal computer Intel(R) Core(TM) i5-2430 CPU@2.4GHz with
4GB RAM. The performance of RRA is evaluated in two EDS consisting of 14-node and 69-node system.
In addition, the application of PSO for the NR problem is also implemented and run on the same computer
for comparing with RRA besides comparing RRA with other methods in literature.
4.1. The 16-node system
The 23kV 16-node test system shown in Figure 2 contains 3 feeders and 13 load nodes. The data of
the system is referenced from [3]. The three initially-open switches are {S14, S15 and S16}. The total load of
the system is 28.7 MW, while the initial total power loss is 511.4356 kW. The minimal voltage amplitude
(Vmin) of the system is 0.9693 p.u. The calculated time of the algorithm usually depends on the mechanism of
operation of the algorithm. While some algorithms create new solutions using simple procedures, others
produce new solutions using more complex and time-consuming procedures. But overall, increasing
the population size (N) the maximum number of iterations (itermax) and the maximum number of fitness
Input: Line and load data of the EDS.
Output: Optimal configuration with minimum power loss
Step 1: Generate randomly initial population of N mother plants 𝑋 𝑚𝑜𝑡ℎ𝑒𝑟(𝑘) =
[𝑋1, 𝑋2, … , 𝑋 𝑑, … , 𝑋 𝑑𝑖𝑚] with k = 1, 2… N.
Check radially condition of each plant by Equation (2)
If 𝑋 𝑚𝑜𝑡ℎ𝑒𝑟(𝑘) is radial configuration then
Calculate the fitness function of 𝑋 𝑚𝑜𝑡ℎ𝑒𝑟(𝑘) to find the best plant 𝑋 𝑑𝑎𝑢𝑔ℎ𝑡𝑒𝑟,𝑏𝑒𝑠𝑡
Else
Fitness function of 𝑋 𝑚𝑜𝑡ℎ𝑒𝑟(𝑘) = inf
End if
While (Maximum evaluation fitness function not reach or current iteration (i) < maximum
iteration 𝑖𝑡𝑒𝑟 𝑚𝑎𝑥) do
Step 2: Global search with generation of daughter plants
Generate the new population of daughter plants from the population of mother
plants by Equation (8)
If 𝑋 𝑑𝑎𝑢𝑔ℎ𝑡𝑒𝑟(𝑘) is radial configuration then
Evaluate fitness function and update the best plant
Else
Fitness function of 𝑋 𝑑𝑎𝑢𝑔ℎ𝑡𝑒𝑟(𝑘) = inf
End if
Step 3: Local search with large and small distances
Generate the number of dim new plants 𝑋 𝑝𝑒𝑟𝑡𝑢𝑟𝑏𝑒𝑑,𝑑 by modifying the best plant through
Equation (9) and dim new plants based on replacing 𝑑 𝑟𝑢𝑛𝑛𝑒𝑟 by 𝑑 𝑟𝑜𝑜𝑡
If the each new plant is radial configuration then
Evaluate fitness function
Else
Fitness function of Xi = inf
End if
If fitness (𝑋 𝑝𝑒𝑟𝑡𝑢𝑟𝑏𝑒𝑑,𝑑) < fitness (𝑋 𝑑𝑎𝑢𝑔ℎ𝑡𝑒𝑟,𝑏𝑒𝑠𝑡) then
𝑋 𝑑𝑎𝑢𝑔ℎ𝑡𝑒𝑟,𝑏𝑒𝑠𝑡= 𝑋 𝑝𝑒𝑟𝑡𝑢𝑟𝑏𝑒𝑑,𝑑
End if
Save the fitness of 𝑋 𝑑𝑎𝑢𝑔ℎ𝑡𝑒𝑟,𝑏𝑒𝑠𝑡 called the best fitness for current iteration
Step 4: Generation of new mother plants and escaping the local optimal
Selection daughter plants to become the next mother plants based on the roulette
wheel selection
If the best fitness (i) = the best fitness (i-1) then
Counter = Counter + 1
Else
Counter = 0
End if
If Counter = Stallmax then
Generate randomly population of mother plants similar to Step 1.
End if
End While
Post process result: best fitness value and the plant 𝑋 𝑑𝑎𝑢𝑔ℎ𝑡𝑒𝑟,𝑏𝑒𝑠𝑡

 ISSN: 2088-8708
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evaluation (MFE) to high values can help the algorithms to produce the higher number of new solutions in
the searching space but it will take a long time for searching optimal solutions. Therefore, in this study based
on the scale and complexity of the test system, the control parameters of RRA and PSO consisting of N,
itermax and MFE are experimented several times and chosen to 10, 50 and 500 respectively. For RRA,
the drunner and droot are set to 4 and 2 respectively [18]. For PSO, two constants C1 and C2 in the velocity
equation of particles to control the position of particle learn from its own and the best so far particle
experience are set to 2 [8, 20].
The obtained results on the 16-node test system is presented in Table 1. The power loss of
the 16-node system has been decreased from 511.4356 kW to 466.1267 kW corresponding to 8.9% by using
the RRA method. This power loss value is reached by opening the switches {S6, S12 and S14} replacing for
the switches {S14, S15 and S16}. The minimal voltage amplitude has been increased from 0.9693 p.u. at
the node 10 before reconfiguration to 0.97158 p.u. after performing reconfiguration. This results is identical
to the results obtained by the genetic algorithm [3], modified tabu search algorithm (MTS) [21] and binary
particle swarm gravity search algorithm (BPSOGSA) [23]. Noted that, although BPSOGSA has found out
the optimal configuration but the average value of the fitness function (Fitaverge) and the standard deviation
(STD) of the fitness function are 479.2 and 28.9 which are 9.5083 and 21.0377 higher compared with those
of RRA. The voltage of nodes in the 16-node test system after reconfiguration shown in Figure 3
demonstrates that most of voltage of nodes has been improved after opening the switches {S6, S12 and S14}
and no node violates the voltage constraints.
Similar to RRA, PSO has also determined the optimal configuration { s6, s12 and s14} but in 50 runs
PSO has only achieved the optimal solution in 12 runs corresponding to 24% while RRA has reached
the optimal configuration in 41 runs corresponding to 82% which is 58% higher than PSO. In 50 runs,
the maximal (Fitmax), Fitaverge and STD of the fitness function values of RRA are lower than those of PSO.
Their values of RRA are respectively 493.1542, 469.6917 and 7.8623 for RRA while for PSO they are
511.4356, 495.4369 and 18.6443 respectively. In addition, the executed times for RRA solving the16-node
system reconfiguration is also faster than that of PSO. The mean, minimum and maximum convergence curves
of proposed RRA and PSO in 50 runs are presented in Figure 4. As presented from the figure, RRA has better
performance compared with PSO in terms of the optimal convergence value for 50 runs. These results
demonstrate that RRA outperforms to PSO for the NR problem.
F1 F2 F3
4 5 1314
2
3 9
7
6
8 12
11
10
s1
s7s4
s3
s14s11 s10
s9
s8
s16
s6s5
s13
s12
s15
s2
Figure 2. 16-node test system
Table 1. The comparisons among RRA with PSO and other methods for the 16-node system
Item Initial RRA PSO GA [3] MTS [21] BPSOGSA [23]
Optimal opened switches 14, 15, 16 6, 12, 14 6, 12, 14 6, 12, 14 6, 12, 14 6, 12, 14
∆P(kW) 511.4356 466.1267 466.1267 466.1267 466.1267 466.1267
Vmin (p.u.) (bus) 0.9693 (10) 0.97158 (10) 0.97158 (10) 0.97158 (10) 0.97158 (10) 0.97158 (10)
Fitmax - 493.1542 511.4356 - - -
Fitmin - 466.1267 466.1267 - - -
Fitaverage - 469.6917 495.4369 - - 479.2
STD of fit. - 7.8623 18.6443 - - 28.9
Found out runs/ total runs 41 12 - -
Successful rate (%) - 82 24 - - -
Average convergence
iterations
- 20 3 - - -
Run time (sec) - 1.4891 1.7559 - - -

5021
Figure 3. The voltage of nodes in the 16-
node test system after reconfiguration
Figure 4. The convergence curves of RRA and PSO for
16-node test system
4.2. The 69-node system
The 12.66kV 16-node system shown in Figure 5 contains 1 feeders and 68 load nodes. The data of
the system is referenced from [24]. The five initially-open switches are {S69, S70, S71, S72 and S73}.
The total load of the system is 3.8015 MW, while the initial total power loss is 224.8871 kW. The minimal
voltage amplitude (Vmin) of the system is 0.9092 p.u. at the node 65. The control parameters for both of RRA
and PSO consisting of N, itermax and MFE are set to 20, 150 and 3000 respectively. The values of the drunner,
droot for RRA and C1, C2 for PSO are set similar to those in the 16-node system.
1
54 6 82
3
7 199 1211 1413 1615 1817 27
66 67
23 24 2520 21 22 26
68 69
10
36 37 3938 40 41 4342 44 45 46
5853 5554 56 59 6560 6261 6463
47 4948 50
3328 3029 3231 34 35
1 2 54 6 7 8 9 1211 141310 191615 1817
27
23 24 2520 21 22 26
3328 3029 3231 34
35
37 3938 40 41 4342 44 45
46
36
47 4948
5152
50
51
52
57
5853 5554 56 59
65
60 6261 646357
66
67
68
69
70
71
72
73
Figure 5. The 69-node test system
The obtained results on the 69-node test system is presented in Table 2. The power loss of
the 69-node system has been decreased from 224.8871 kW to 98.5875 kW corresponding to 56.16% by using
the RRA method. This power loss value is reached by opening the switches {S69, S70, S14, S57 and S61}
replacing for the switches {S69, S70, S71, S72 and S73}. The minimal voltage amplitude has been increased
from 0.9092 p.u. at the node 65 before reconfiguration to 0.9495 p.u. at the node 61 after performing
reconfiguration. This results is identical to the results obtained by the cuckoo search (CSA) [13], adaptive
shuffled frogs leaping algorithm (ASFLA) [25] and BPSOGSA [23] and better than harmony search
algorithm (HSA) [26] and GWO [15]. Similar to the 16-node system, the values of the Fitaverge and the STD
of BPSOGSA are 171.5 and 168.1 which are much higher compared with those of RRA. The voltage of
nodes in the 69-node test system after reconfiguration shown in Figure 6 shows that most of voltage of nodes
has been improved after opening the switches { S69, S70, S71, S72 and S73}.

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Table 2. The comparisons among RRA with PSO and other methods for the 69-node system
Item Initial RRA PSO CSA
[13]
ASFLA
[25]
HAS
[26]
BPSOGSA
[23]
GWO
[15]
Optimal
opened
switches
69, 70,
71, 72, 73
69, 70, 14,
57, 61
69, 70,
14, 57, 61
69, 70, 14,
57, 61
69, 70, 14,
56, 61
13, 18,
56, 61, 69
69, 70, 14,
56, 61
58, 12,
61, 69, 70
∆P(kW) 224.8871 98.5875 98.5875 98.5875 98.5875 105.19 98.5875 99.8206
Vmin (p.u.)
(bus)
0.9092
(65)
0.9495
(61)
0.9495
(61)
0.9495
(61)
0.9495 (61) 0.9495
(61)
0.9495 (61) -
Fitmax - 116.3852 140.7413 - - - - -
Fitmin - 99.11695 99.11695 - - - - -
Fitaverage - 102.7848 114.1333 - - - 171.5 -
STD of fit. - 5.3052 15.1119 - - - 168.1 -
Found out
runs/ total runs
29 12 - - - -
Successful rate
(%)
- 58 24 - - - - -
Average
convergence
iterations
- 87 35 - - - - -
Run time (sec) - 24.21 28.4922 - - - - -
In comparison between RRA with PSO, for the 69-node system PSO has also obtained the optimal
configuration {S69, S70, S14, S57 and S61} but in 50 runs PSO has only returned the optimal solution in 12
runs corresponding to 24% while RRA has returned the optimal configuration in 29 runs corresponding to
58% which is 34% higher than PSO. In 50 runs, the values of Fitmax, Fitaverge and STD of RRA are much
lower than those of PSO. Their values of RRA are respectively 116.3852, 102.7848 and 5.3052 for RRA
while for PSO they are 140.7413, 114.1333 and 15.1119 respectively. In term of the number of average
convergence iterations, although PSO has converged early than RRA but PSO converges usually to local
solution. In addition, the executed times for PSO solving the 69-node system reconfiguration is also slower
than that of RRA. The mean, minimum and maximum convergence curves of RRA and PSO in 50 runs are
presented in Figure 7. As presented from the figure, RRA has better performance compared with PSO in
terms of the optimal convergence value for 50 runs and the mean convergence curve of RRA is very closed
to the minimum convergence curve and much lower than that or PSO. These results once again confirm that
RRA is better than PSO and is the potential tool for the NR problem.
Figure 1. The voltage of nodes in the 69-
node test system after reconfiguration
Figure 2. The convergence curves of RRA and PSO for
69-node test system
5. CONCLUSION
The paper demonstrates the NR method based on RRA to optimize the network configuration.
The objective function of the NR problem is minimizing of power loss. The effectiveness of the RRA is
evaluated on the 16 and 69-node EDS system. The obtained results are compared with PSO and other
methods in literature. The obtained results in 50 runs have shown that RRA is outperformed PSO in terms of
quality of the obtained optimal solution and the successful rates and the executed times. The success rate of

5023
RRA on 16-node and 69-node systems are respectively up to 82% and 58% while those of PSO is only 24%
for both system. The simulated results are also shown that RRA is better than some others in literature.
In addition, successful applying of RRA for the NR problem to decrease power loss in the 16 and 69-node
system has shown that RRA is the potential method for the NR problem of reducing power loss and other
objective functions.
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