Optimal Capacitor Placement in Radial Distribution System Using Moth Flame Optimization Algorithm

ISSN -

0258-2724 DOI：

10.35741/issn.0258-2724.54.3.21

Research article

O

PTIMAL

C

APACITOR

P

LACEMENT IN

R

ADIAL

D

ISTRIBUTION

S

YSTEM

U

SING

M

OTH

F

LAME

O

PTIMIZATION

A

LGORITHM

Ihsan Salman 1, Khalid Mohammed 2, Khalid Shaker3, Hothefa Shaker 4 1

Computer Department, College of Basic Education, University of Diyala, Iraq,[email protected]

2 _{Computer Department, College of Science, University of Diyala, Diyala, Iraq,}

[email protected]

3 _{College of Computer Science and Information Technology, University of Anbar, Ramadi, Iraq,}

[email protected]

4

Modern College of Business & Science, Al-Khuwair Oman, [email protected]

Abstract

The environment friendly designing and running of electricity distribution structures are becoming vaster with the conjunction of renewable electricity options into power distribution systems. This study presents Moth Flame Optimization (MFO) approach to minimize total losses kW and energy cost and maximize net savings with solving the voltage deviation problem through optimal site and size of capacitor banks in electrical radial distribution networks. Two various load profiles are utilized to take a look at the modified algorithm on IEEE 123-, and 13-bus check networks. The OpenDSS software is utilized to resolve the power flowing via MATLAB programming interface. The results obtained are compared with IEEE normal state and other two heuristic approaches in same study, namely, imperialist competitive algorithm and particle swarm optimization. The proposed algorithm is more effective to minimise the total power losses and total cost and maximise net savings and to enhance the voltage profile for various distribution systems.

Keywords: Distribution Systems; Smart Grids; Voltage Optimization; Total Power Losses.

摘要 : 隨著可再生電力選擇與配電系統的結合，配電結構的環境友好設計和運行變得越來越大。本研究提 出了蛾火焰優化（MFO）方法，通過電氣徑向分佈網絡中電容器組的最佳位置和尺寸解決電壓偏差問題，最 大限度地降低總損耗 kW 和能量成本，並最大化淨節省。利用兩種不同的負載配置文件來查看 IEEE 123 和 13 總線檢查網絡上的修改算法。 OpenDSS 軟件用於通過 MATLAB 編程接口解決功率流。將得到的結果與同 一研究中的 IEEE 正態和其他兩種啟發式方法進行了比較，即帝國主義競爭算法和粒子群優化算法。所提出 的算法更有效地最小化總功率損耗和總成本並最大化淨節省並且增強各種配電系統的電壓分佈。 关键词: 配電系統; 智能電網; 電壓優化; 總功率損耗。

I. INTRODUCTION

Last few years, electricity systems have been growing, exhibiting these modifications as cancel

regulation and integrating of new energy sources into the planning and working mentalities. Through the view of operational point, control

means which include the coordinated technique of tap changeable transformers, like capacitors, are wanted due to the fact masses fee are not fixed via time and the production of new energy capacity sources are sporadic. Optimization of Voltage (VO) is a tremendous technological know-how that has been rescuing a lot of money in lost electrical power since the commencing of the new millenary [1]. Rise request utilized to be administer by voltage decrease [2]. The capacitors are using as another way to helping system operation for get better power factor, minimize power losses and improve voltage profile [3]. The capacitors are usually utilized to supply imaginary power kVAr reparation in power distribution systems. The installation of capacitors bank includes definition of size kVAr and capacitors location. Selecting better site of the capacitor will minimize the demand of the imaginary power, which therefore increase the pure savings and utilized to keep voltage profile values within allowable limits. For example, in an algorithm that rely on genetic algorithm, Fuzzy Logic and Dynamic Programming techniques are utilized for best capacitor allocation in distribution network. Flower pollination optimization algorithm and power loss index was used for best sizing and locations of capacitors in power radial distribution networks in [4]. Gravitational search algorithm was used for optimal capacitor placement in [5], whereas a teaching–learning-based optimization was used for the same aim in [6]. Capacitors can as well be utilized to reduce the effects of harmonics in distribution networks; the harmony search algorithm was utilized for this aim in [7]. Capacitor size and site problem have been resolved through other heuristics, for example ant colony algorithm [8], clonal selection algorithm [8], and particle swarm optimization [9].

Making the better potential results with the ready resources are constantly an objective in scientific and problems of engineering. Generally two approaches are utilizing to solve problems of optimization. The first method is depend on arithmetic analysis, whereas the second method is depend on numerical computations. Numeral optimization procedures can be classified into derivative and non-derivative. The non-derivative process are applied when the derivatives of the performed sample are difficult to discover or not exist a numerical task connected to the sample. These techniques are generally enthused through nature. The greatest public sample is GA, which reverses the development operation in the natural world [10]. Afterward, approaches motivated through the attitude of fish and birds (particle swarm optimization [PSO]) [11] improvised

operation of musical group (harmony search) [12], and the direction finding method of moths in nature, which is called transverse direction (moth flame optimization [MFO]) [13] were developed. As shown in the literature summary, the application of MFO has not been discussed so far to solve for capacitor size and placement in radial distribution system. Therefore, this motivates to utilize MFO to find best place and size of capacitor in power distribution system to reduce total power loss and total cost and maximize net savings and to enhance the voltage profile. OpenDSS software is applied to implement power influx and load influx to discovery the parameters of power system such as voltage profile, power factor, power losses , real and imaginary power flow in every line, and etc. [14], [15]. Two test systems IEEE 13-, and 123-node are applied in this work. Results acquired from the suggested algorithm has been compared with those gained from IEEE standard case, PSO and ICA. MATLAB and an open power distribution system simulation gadget OpenDSS [14], [15] are utilized in the emulations.

The remnant of the paper is orderlies as follows. Section II suggested the mathematical problem formulation. Section III briefly dissect MFO, ICA, and PSO and modified algorithms for solving the optimal capacitor placement problem. Section IV presents the experiments and the simulation results. Finally, Section V presents the conclusions, followed by the References used in this paper.

1.

MATHEMATICAL PROBLEM FORMULATION

A. Objective function

The capacitors costs and the power losses cost represent the total cost in power system. The aim of best capacitor placement and size of distribution network is to improvement a specific aim function such minimize losses and cost and enhance the voltage values and maximize annual savings. The aim function in this work can be written as follows:

Minimize x = P

cost

. P

iloss Nb

i=1

+ Cap

j_cost

. Cap

j Nc

j=1

+ |V

k

− 1|

Nb

Minimize x =

P

_cost

. P

i_loss Nb i=1

+

Cap

j cost

. Cap

j Nc j=1

+

|V

_k

− 1|

Nb k=1 (1)

Where, x denotes the aim of better capacitor placement and size, Nb indicate the number of buses,

P

_cost represents cost of real power losses [168 $/kW],

P

i_lossrepresents real power losses on bus i [kW], Nc represents number of capacitors.

Cap

j_cost is the cost of capacitor j [$/kVAr],

Cap

j is the size of capacitor j [kVAr], and Vk is the voltage magnitude of bus k.The capacitors size and cost as shown in Table 1.

Table 1: Possible choice of capacitor size in kVAr and cost in $/kVAr

Q kVAr $/kVAR Q kVAr $/kVAR Q kVAr $/kVAR

50 0.5 1350 0.207 2850 0.183 100 0.5 1500 0.201 3000 0.180 150 0.5 1650 0.193 3150 0.195 300 0.35 1800 0.187 3300 0.174 450 0.253 1950 0.211 3450 0.188 600 0.220 2100 0.176 3600 0.170 750 0.276 2250 0.197 3750 0.183 900 0.183 2400 0.170 3900 0.182 1050 0.228 2550 0.189 4050 0.179 1200 0.170 2700 0.187 B. Constraints

The best capacitor siting of distribution network problem has the following constraints:  The voltage volume on the bus is the initial

constraint in optimal capacitor placement and sizing problem. It is necessary preserved within the specific limits :

0.95 ≤ Vi ≤ 1.05 (2)

Where, Vi is the voltage size on bus i.

 The installed capacitors size at each bus must be less than the total effective reactive power kVAr in the test system as follows:

Cap

i

<

Nc

𝑖=1

Q

j

Nb

j=1 (3)

Where, Nc indicate to the number of capacitors,

Cap

i show the size of capacitor i, Nb indicate the number of buses, and

Q

j is the reactive power kVAr in bus j.

 The optimal capacitor location between bus number two and number of buses in simulation system. The bus number one is represent substation.

2 ≤ li ≤ Lmax (4)

Where, li indicate the site of the capacitor in bus i,

and Lmax indicate the maximum bus location.

2.

HEURISTICALGORITHMS

A. Moth Flame Optimization (MFO)

Public method: MFO is a meta-heuristics algorithm sophisticated by means of Mirjalili in 2015; the optimization of this method reflects transversal direction, which is the style of move of moths in the natural world at night [13]. Nearly 160,000 various groups of insects, include moths, are present in nature. Moths have two life phases: maggot and mature phase. These insects are a lot like to the family of butterflies only possess a specific function when shifting at night-time [16]. Moths go lengthy spaces and rectum lines through way of preserve a fixed perspective together with the moonlight. This method is so nice for touring these insects specifically while the lighting supply is far from them. When the lighting source is near, the moths flies round it with a spiral direction, and collect with it in last. The moths appear the nominee resolutions and moth’s site in examine space appear problem’s directions. So, the moths have the ability to fly in one dimensions area or more with replace the site vectors. Figure 1 illustrates a MFO algorithm flowchart. This optimization algorithm is executed as follows:

1.

Set the fixed parameters: size of dimensions, size of moths, higher number of repetitions, and maximum and minimum boundaries.

2.

Randomly be the initial population depending on the population size, size of dimensions, maximum and minimum bounds as follow: Mo =

Mo

11

⋯ Mo

1d

Mo

₂₁

… Mo

_2d

⋮

⋱

⋮

Mo

_n1

⋯ Mo

_nd (5)

where n denotes size of moths, and d represent size of dimensions.

3.

Compute and order the identical cost values for each an individual's.

OMo =

OMo

₁

OMo

₂

⋮

OMo

_n (6)

Where n indicate to number of moths

4.

Initialize inhabitance of flames and flames efficiency that is evenness sort population of moths, and sort moth’s cost values, respectively. F =

F

11

⋯ F

1d

F

₂₁

… F

_2d

⋮

⋱

⋮

F

n1

⋯ F

nd (7) OF =

OF

₁

OF

₂

⋮

OF

_n (8)

Where n indicate to size of moths, and d indicate to size of dimensions.

5.

Reiterate until the stopping state is met.

6.

Compute the space of the ith moth for the jth flame through neutralization:

Di = |Fj-Moi| (9)

7.

Modernize moths site utilizing spiral task as follow:

Moi =Di . e bt

. cos(2ℼt)+Fj (10)

Where, Di space, b is a fixed number (b=1), and t is a random number in [-1, 1].

8.

Modernize flames site that is the same better former and actual moth’s site, identical as with flames efficiency.

Repetition = 1

Sort the population of moths and save as an initial flames population

Modernize flames site that is equal better previous and current site of moths

Sort moth’s efficiency and save as an initial flames efficiency

Update flames efficiency that is equal better previous and current efficiency values of moths

Initialize initial populations utilize specified limits

Compute the aim function to all moths in population

Update moth’s site

Achieve the stop state? Yes No End Yes No

Modernize flames size

Begin

Initialize parameters values

Figure 2. Flowchart of modified MFO algorithm.

F = Sort (Moi-1, Moi) (11)

OF = Sort (OMoi-1, OMoi) (12)

Where, i indicate to actual repetition.  MFO for resolve optimal capacitor

site problem: Figure 2 shows the modify MFO algorithm flowchart, and the proceedings as follows:

Step 1: Initialize set fixed variables such as: size of moths N, size of

dimensions D, maximum repetitions Maxit, lower bound value lb, and upper bound value ub. Set voltage size, and capacitor sites and size limits.

Step 2: At random generate the site and size of the capacitors, then form the initial moth site as in Equation (5).

Step 3: Utilize the particular load profile and solution candidates to implement a load and power flux , then compute the moth efficiency of the trial system use Equations (1) as in Equation (6).

Step 4: Choice the better moth site as flame site and the better moth cost value as the flame cost value using Equations (11) and (12), as shown in Equations (7) and (8), respectively.

Step 5: Compute the space among flames and moths, then compute different moth site by Equations (9) and (10).

 Step 6: Reiterate procedures 3–5 till the ending case is seen.

Begin

Initialize parameters values

At random generate the site and size of the capacitors by fixed lower and upper limits as in Eq. (5)

Implement a load and power flow utilize the identified load profile

Choice better moth’s site and efficiency as a flames site and efficiency utilize Eqs. (11) and (12).

Modernize moths site (capacitors site and size) using Eqs. (9) and (10)

Achieve the stop state?

End Yes No

B. Imperialist Competitive Algorithm (ICA) General approach: ICA is a new meta-heuristic algorithm suggested for continuous optimization issues. This algorithm stimulated by means of the imperialistic competition process. It is

brought with the aid of Esmaeil Atashpaz-Gargari and Lucas in 2007 [17]. This algorithm

is a new socio-politically motivated global search strategy

that has been added for dealing with various optimization tasks. Figure.3 presents a flowchart of ICA [17].

Begin

Setting the empires

Transfer the colonies to their pertinent imperialist

A colony in empire has been cost less of imperialist?

Exchange site of colony and imperialist

Calculate the full all empires cost

Choice the feeblest colony from the frailest empire then give it to the empire which owns the best probability to possess it

Achieve the stop state?

End

There an empire without colonies?

Remove this empire Y es N o N o Y es Y es N o

Figure 4. Modified ICA The method is conducted as follows:

1- Generating initial Empires. For the Dn-dimensional optimization problem a 1 x Dn dimensional vector regarded as a solution that is named country as shown:

countryi = [P1, P2, P3, … , PDN] (13)

Where, DN denotes dimensions of problem. Unplanned for Pi values must be within the upper and lower domain for every variable.

2- The cost of every country is calculated through the function f as shown:

f (countryi) = f (P1, P2, P3,…, PDN) (14)

3- Divided the countries into imperialists, which represents the most powerful countries, and colonies, which represents the others left. To distribute the colonies between imperialists proportionally, the following normalized cost

of each imperialist is described as shown: Cn = cn - max (ci) (15)

Where, cn represent cost of n th

imperialist, and Cn represents normalized value.

4- The colonies are shift to the site of the imperialist through X units to start the process of optimization. The DN country of population is generated, and Nimp represents

the most powerful population, whose members have been selected as imperialists (the controller coefficients sets with same cost function). The remaining Ncol countries are

the colonies (the controller coefficients sets with a high cost function), each of which is a part of one of the abovementioned empires. the colonies move toward the imperialists with the attraction policy, along Mx units and are situated in a new position. Mx is a random variable with regular distribution and can be expressed as follows:

Mx ~ U (0, β. ds) (16)

Where, β is a digit bigger than 1 (β = 2) and ds is the space between colony and

imperialist.

Compute the aim function for all the inhabitants as in Eq. (1) Begin

Initialize variables value

At random generate the country as in Eq. (17)

Implement a load and power flow utilize the identified load profile

Choice the colonized countries and imperialist as in Eqs. (14) and (15)

Modernize capacitors site and size as in Eq. (16)

Achieve the stop state?

End Yes No

Figure 5. PSO algorithm ICA for resolve optimal capacitor site

problem: Figure 4 shows a flowchart of the modify ICA algorithm, and the proceedings as follows:

Step 1: Initialize set fixed variables such as: inhabitance size Npop, maximum repetition

number Maxit, number of imperialist

countries Nimp, and number of colony

countries Ncol. Set voltage size, and capacitor

sites and size limits.

Step 2: Create randomly the site and size of capacitors, then form the first country as follows:

countryi = [l1, . . . , lm, Cap1, . . . , Capm] (17)

Where, m is the amounts of capacitors bank.

Step 3: Utilize the particular load profile and solution candidates to implement a load and power flux of the exam system as in Equations (1).

Step 4: Define the colonized countries and imperialist depend on cost values as in Equations (14) and (15).

Step 5: Modernize the site and size of the capacitors for wholly empires as in Equation (16).

Step 6: Reiterate procedures 3–5 till the ending case is seen.

C.

Particle Swarm Optimization (PSO)

General approach: PSO is initially developed by Eberhart and Kennedy in 1995, and was once stimulated by way of the public conduct of birds clustering and fishes education [18]. The birds in a herd are described as particles in the PSO method. These particles can be flying over a examine space. A particle’s site in the examine space look as one answer for the issue. New various answer is created when a particle shift to a new site in the examine space. Each answer can be examine by the usage of an aim function that affords a value of the advantage of the answer. The path and speed of every element can be transferring alongside every dimension of the examine space; so, will be shifting with each generation of motion. PSO is typically viewed to be an evolutionary computation (EC) model.

Begin

At random generate velocities and individual sites utilize specific upper and lower limits

Compute the aim purpose for all particle in the inhabitants

Locate the global and local better site

Modernize particle velocity and site

Achieve the stop state?

End Yes No

Other EC samples consist of evolutionary strategies (ES), evolutionary programming (EP), genetic programming (GP), and Genetic Algorithms (GA) [19]. Every particle (i) preserve the following data [20]:

 Xi = The actual site of the particle.  Vi = The actual speed of the particle.

 Yi = The personal better site of the particle

(pbest); the better site visited until now by the particle.

 Ŷ = The global better site of the swarm (gbest); the better site visited until now by the entire swarm.

Figure 5 shows a flowchart of the PSO algorithm.

By utilize the above note, the method is execute as follows:

1. Initialize a set of fixed parameters such as: size of the swarm, variable of the problem, high quantity of iterations, maximum and minimum bounds and etc.

2. At random initialization of particle locations depending on the fixed parameters.

3. Randomly initialization of particle speeds depending on the fixed parameters.

4. Reiterate till the ending case is seen. 5. Estimate the cost values utilize the

aim function.

6. Locate gbest and pbest value.

7. Locate the change element speed vector as follows:

Vi (t+1) = W.Vi(t)+c1.r1(t).(Yi

(t)-Xi(t))+c2.r2(t).(Ŷ(t)-Xi(t)) (18)

Begin

Set variables value

At random generate velocities and individual sites utilize specific upper and lower limits

Implement a load and power flow utilize the identified load profile

Choice global and local best [(gb) , (lb)]

Modernize particle velocity, capacitors site and size utilize Eqs. (18)- (20)

Achieve the stop state?

End Yes No

Compute the aim function for all particle in the inhabitants as in Eq. (1)

where, t represents actual repetition, r1(t) and r2(t) denote regular random

numbers among 0 and 1, and W represents the inertia weight, which is calculated as follows:

W = (Maxit-t)/Maxit (19)

8. Locate the change element site vector as follows:

Xi (t+1) = Xi (t) +Vi (t+1) (20)

 PSO for resolve optimal capacitor site problem: Figure 6 shows a flowchart of the modify PSO algorithm, and the proceedings as follows:

 Step 1: Initialize set fixed variables such as: group size Psize, element of

the problem Npar, high number of

repetitions Maxit, cognitive parameter

c1, public parameter c2, high bound

value ub, lesser bound value lb, and

high speed value Vmax. Set the

voltage size, possible capacitor sites, and size limits.

 Step 2: Create randomly initial particle speed, define the site and size of the capacitors, then form particle site as follows:

particlei = [l1, . . . , lm, Cap1, . . . ,

Capm] (21)

Where, m denote the numbers of capacitors bank.

 Step 3: Utilize the particular load profile and solution candidates to implement a load and power flux of the exam system as in Equations (1).

 Step 4: Select local and global best, then locate change particle speed and sites as in Equations (18)–(20).

 Step 5: Reiterate procedures 3 and 4 till the ending case is seen.

Figure 9: Simulation I voltage values on IEEE 13-node trial system, MFO optimal capacitors placement with standard case and without capacitor.

3.

SIMULATION RESULTS

The suggested optimization sample for placement of capacitor and size kVAr has been experimented on IEEE 13- and 123-node trial

system. The node maps of the trial system are be seen in Figures 7, and 8, respectively. The sum of population and iteration are taken 30 and 1000, respectively for all simulation in this study.

Table 3: Simulation II, performance of MFO over without control, standard case, PSO method, ICA method on 13 bus RDN. Title Witho ut contro l Standa rd case

PSO ICA MFO

Total losses (kW) 130.3 110.8 107.7 107.9 107.5 % Loss reduction - 15% 17.3% 17.2% 17.5 % Candidate buses - 675 611 675 633 634 652 675 684 634 633 675 652 634 645 Optimal capacitor size (kVAr) - 600

100 50 50 1500 50 50 600 1050 50 50 50 1500 50 Total kVAr - 700 1650 1750 1650

Annual cost for kW loss ($168/kW) 21890 .4 18614 .4 18093 .6 18127 .2 18060 Annual capacitor cost ($/kVAr) - 182 376.5 421.4 376.5 Total annual cost ($) 21890

.4 18796 .4 18470 .1 18548 .6 18436 .5 Net savings ($) 0 3094 3419. 9 3341. 8 3453. 9 % Savings 0.0% 14.1% 15.6% 15.3% 15.8 %

Minimum voltage (p.u.) 0.892 0.973 0.967 0.966 0.968 Maximum voltage (p.u.) 0.999 1.047 1.05 1.048 1.048 Mean voltage (p.u.) 0.946 1.004 1.010 1.009 1.01 Standard deviation voltage (p.u.) 0.035 0.021 0.024 0.024 0.023 A. IEEE 13-node trial system

The all information around this test system such as line and bus data have been explain in [21]. The gross active power load kW and reactive power load kVAr of this trial system in simulation I is 2364 kW and 2102 kVAr

respectively, and in simulation II is 3463 kW and 2102 kVAr respectively. The MFO optimal outcomes are matched with the standard IEEE state, without capacitors installation case and other methods which is shown in Table 2 for simulation I and Table 3 for simulation II.

Figure 11: MFO iteration versus total power losses (kW) on 13-node trial system in simulation I

Figure 12: MFO iteration versus total power losses (kW) on 13-node trial system in simulation II. Figure 10: Simulation II voltage values on IEEE 13-node trial system, MFO optimal capacitors placement with standard case and without capacitor

The results of the proposed algorithm in Tables 2 and 3 are better than those of other

algorithms, without control, and standard case. Figures 9 and 10 shows the voltage profile for

Table 4: Simulation I, performance of MFO over without control, standard case, PSO and ICA on 123 bus RDN. Title Witho ut contro l Standa rd case

PSO ICA MFO

Total losses (kW) 63 47.5 44.5 43.9 43.1 % Loss reduction - 24.6% 29.4% 30.3% 31.6% Candidate buses - 83 88 90 92 76 49 114 15 72 47 114 160 76 70 114 44 Optimal capacitor size (kVAr) - 600

50 50 50 50 50 50 1650 50 50 50 100 50 100 50 150 Total kVAr - 750 1800 250 350

Annual cost for kW loss ($168/kW) 10584 7980 7476 7375.2 7240.8 Annual capacitor cost ($/kVAr) - 207 393.45 125 175 Total annual cost ($) 10584 8187 7869.45 7500.2 7415.8

Net savings ($) 0 2397 2714.55 3083.8 3168.2

% Savings 0.0% 22.7% 25.6% 29.1% 29.9%

Minimum voltage (p.u.) 0.933 0.996 0.997 0.999 0.99 Maximum voltage (p.u.) 0.999 1.048 1.04 1.039 1.045 Mean voltage (p.u.) 0.964 1.024 1.023 1.019 1.019 Standard deviation voltage (p.u.) 0.016 0.015 0.013 0.014 0.014 standard case, without capacitors case and MFO

optimal capacitors placement on IEEE 13-node trial system in simulation I and simulation II respectively. The propose algorithm iteration versus total active power losses (kW) of simulation I and II on 13-node trial system shown in Figures 11 and 12 respectively.

B. IEEE 123 bus exam system

The information around this test system like line and bus data have been explain in [22]. The gross active power load kW and reactive power load kVAr of this trial system in simulation I is 2305 kW and 1920 kVAr respectively, and in simulation II is 3435 kW and 1920 kVAr

respectively. The MFO best outcomes are

matched with the standard IEEE state, without capacitors installation case and other methods which is shown in Table 4 for simulation I and Table 5 for simulation II.

The results of the proposed algorithm in Tables 4 and 5 are better than those of other algorithms, without control, and standard case. Figures 13 and 14 shows the voltage profile for standard case, without capacitors case and MFO optimal capacitors placement on IEEE 123-node trial system in simulation I and simulation II respectively. The proposed algorithm iteration versus total active power losses (kW) of simulation I, and II on 123-node trial system be seen in Figures 15, and 16 respectively.

Figure 13: Simulation I voltage values on IEEE 123-node trial system, MFO optimal capacitors placement with standard case and without capacitor.

4.

CONCLUSION

A newly meta-heuristics Moth Flame optimization algorithm for optimum capacitor size and site on radial distribution system resulted the total power losses (kW) reduction,

enhance the voltage profile, cost minimization, and maximize net savings. The proposed MFO algorithm and open source OpenDSS software through MATLAB coding interface are applied to resolve the power inflow and optimization issues. To prove the implementation of the suggested approach, the test system IEEE 13, and 123-bus are executed. Moreover, the Figure 14: Simulation II voltage values on IEEE 123-node trial system, MFO optimal capacitors placement with standard case and without capacitor.

Figure 15: MFO iteration versus total power losses (kW) on 123 bus system in simulation I

outcomes of proposed MFO are compared together with standard state, without capacitor placement, PSO, and ICA as in Tables 2-5. The comparison affirm the effectiveness and surpass of the proposed MFO algorithm over the other techniques.

REFERENCES

[1] L. M. Rios and N. V. Sahinidis, "Derivative-free optimization: a review of algorithms and comparison of software implementations," Journal of Global Optimization, vol. 56, pp. 1247-1293, 2013.

[2] R. Uluski and M. Mcgranaghan, "Load models for voltage optimization," in

Proceedings of the International Conference on Electricity Distribution,

2011, p. 1312.

[3] A. Elsheikh, Y. Helmy, Y. Abouelseoud, and A. Elsherif, "Optimal capacitor placement and sizing in radial electric power systems," Alexandria Engineering

Journal, vol. 53, pp. 809-816, 2014.

http://dx.doi.org/10.1016/j.aej.2014.09.012.

[4] A. Abdelaziz, E. Ali, and S. A. Elazim, "Optimal sizing and locations of capacitors in radial distribution systems via flower pollination optimization algorithm and power loss index," Engineering Science and

Technology, an International Journal, vol.

19, pp. 610-618, 2016.

http://dx.doi.org/10.1016/ j.jestch.2015.09.002.

[5] Y. M. Shuaib, M. S. Kalavathi, and C. C. A. Rajan, "Optimal capacitor placement in radial distribution system using gravitational search algorithm,"

International Journal of Electrical Power & Energy Systems, vol. 64, 2015.

http://dx.doi.org/10.1016/j.ijepes.2014.07.0 41

[6] S. Sultana and P. K. Roy, "Optimal capacitor placement in radial distribution systems using teaching learning based optimization,"International Journal of Electrical Power & Energy Systems, vol.

54, pp. 387-398, 2014.

http://dx.doi.org/10.1016/j.ijepes.2013.07.0 11.

[7] K. Muthukumar and S. Jayalalitha, "Harmony search approach for optimal capacitor placement and sizing in unbalanced distribution systems with harmonics consideration," in Advances in

Engineering, Science and Management (ICAESM), 2012 International Conference on, 2012, pp. 393-398.

[8] D. Kaur and J. Sharma, "Multiperiod shunt capacitor allocation in radial distribution systems," International Journal of Electrical Power & Energy Systems, vol.

52, pp. 247-253, 2013.

http://dx.doi.org/10.1016/j.ijepes.2013.03.0 26.

[9] K. Prakash and M. Sydulu, "Particle swarm optimization based capacitor placement on radial distribution systems," in Power

Engineering Society General Meeting, 2007. IEEE, 2007, pp. 1-5.

[10] D. E. Goldberg and J. H. Holland, "Genetic algorithms and machine learning," Machine

learning, vol. 3, pp. 95-99, 1988.

[11] R. Eberhart and J. Kennedy, "A new optimizer using particle swarm theory," in

Micro Machine and Human Science, 1995. MHS'95., Proceedings of the Sixth International Symposium on, 1995.

[12] Z. W. Geem, J. H. Kim, and G. V. Loganathan, "A new heuristic optimization algorithm: harmony search," simulation, vol. 76, pp. 60-68, 2001.

[13] S. Mirjalili, "Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm," Knowledge-Based Systems, vol. 89, pp. 228-249, 2015.

http://dx.doi.org/10.1016/j.knosys.2015.07. 006.

[14] R. Dugan, "Open distribution simulations system workshop: Using open dss for smart distribution simulations," in EPRI PQ

Smart Distribution 2010 Conference and Exhibition, Québec, 2010, pp. 14-17.

[15] P. Anbarasan and T. Jayabarathi, "Optimal Reactive Power Dispatch Using Moth-Flame Optimization Algorithm,"

International Journal of Applied Engineering Research, vol. 12, pp.

3690-3701, 2017.

[16] Benjamin Durakovic, Muris Torlak, "Simulation and experimental validation of phase change material and water used as

heat storage medium in window

applications", J. of Mater. and Environ. Sci., Vol. 8, No. 5, (2017), ISSN: 2028-2508, pp 1837-1846..

[17] Kennedy J, Eberhart R , “Particle swarm optimization”, Proceedings of the 1995 IEEE International Conference on Neural Networks, pp. 1942-1948, IEEE Press. [18] Ogudo, K.A.; Muwawa Jean Nestor, D.;

Ibrahim Khalaf, O.; Daei Kasmaei, H. A Device Performance and Data Analytics Concept for Smartphones’ IoT Services and

Machine-Type Communication in Cellular Networks. Symmetry 2019, 11, 593

[19] D. Van der Merwe and A. P. Engelbrecht, "Data clustering using particle swarm optimization," in Evolutionary Computation, 2003. CEC'03. The 2003 Congress on, 2003, pp. 215-220.

[20] W. H. Kersting, "Radial distribution test feeders," in 2001 IEEE Power Engineering

Society Winter Meeting. Conference Proceedings (Cat. No. 01CH37194), 2001,

pp. 908-912.

[21] Radial Distribution Test Feeders. [Online]. Available:ttps://ewh.ieee.org/soc/pes/dsaco m/testfeeders/testfeeders.pdf .

参考文:

[1] L. M. Rios 和 N. V. Sahinidis，“無衍生優 化：算法評估和軟件實施比較”，全球優 化 雜 誌 ， 第 一 卷 。 56 ， pp.1247-1293, 2013。 [2] R. Uluski 和 M. Mcgranaghan，“用於電壓 優化的負載模型”，載於“國際電力分配 會議論文集”，2011 年，第 7 頁。 1312。 [3] A. Elsheikh，Y。Helmy，Y。Abouelseoud 和 A. Elsherif，“徑向電力系統中的最佳 電 容 器 放 置 和 尺 寸 ” ， Alexandria Engineering Journal，vol。 53，pp.809-816, 2014。 http://dx.doi.org/10.1016/j.aej.2014.09.012。 [4] A. Abdelaziz，E。Ali 和 S. A. Elazim，“通 過花授粉優化算法和功率損耗指數在徑 向分佈系統中優化尺寸和電容器位置”， “工程科學與技術”，國際期刊，第一卷。 19，pp.610-618, 2016。 http://dx.doi.org/10.1016/j.jestch.2015.09.002。 [5] Y. M. Shuaib，M。S. Kalavathi 和 C. C. A. Rajan，“使用重力搜索算法的徑向分佈 系統中的最佳電容器放置”，國際電力和 能源系統期刊，第一卷。 64，2015。 http://dx.doi.org/10.1016/j.ijepes.2014.07.041 [6] S. Sultana 和 P. K. Roy，“使用基於教學學 習的優化的徑向分佈系統中的最佳電容 器放置”，國際電力與能源系統雜誌，第 一卷。 54，第 387-398 頁，2014 年。 http://dx.doi.org/10.1016/j.ijepes.2013.07.011。 [7] K. Muthukumar 和 S. Jayalalitha，“在諧波 考慮的非平衡配電系統中優化電容器放 置和尺寸的和諧搜索方法”，“工程，科 學和管理進展”（ICAESM），2012 年國 際會議，2012 年，pp 393-398 [8] D. Kaur 和 J. Sharma，“徑向分佈系統中的 多周期並聯電容器分配”，“國際電力與 能源系統雜誌”，第一卷。 52，pp.247-253, 2013。 http://dx.doi.org/10.1016/j.ijepes.2013.03.026。 [9] K. Prakash 和 M. Sydulu，“基於粒子群優 化的徑向分佈系統電容放置”，電力工程 學會大會，2007 年.IEEE，2007，pp.1-5。 [10] D. E. Goldberg 和 J. H. Holland，“遺傳算 法和機器學習”，機器學習，第一卷。 3， pp.95-99, 1988。 [11] R. Eberhart 和 J. Kennedy，“使用粒子群 理論的新優化器”，“微機械和人類科學”， 1995 年.MHS'95。，第六屆國際研討會 論文集，1995 年。 [12] Z. W. Geem ， J 。 H. Kim 和 G. V. Loganathan ， “ 一 種 新 的 啟 發 式 優 化 算 法：和諧搜索”，模擬，第一卷。 76， pp.60-68, 2001。 [13] S. Mirjalili，“蛾火焰優化算法：一種新 穎的自然啟發式啟發式範例”，“知識系 統”，第一卷。 89，pp.228-249, 2015。 http://dx.doi.org/10.1016/j.knosys.2015.07.006 。 [14] R. Dugan，“開放分佈模擬系統研討會： 使用開放式 dss 進行智能分佈模擬”，在

EPRI PQ Smart Distribution 2010 會議和 展覽中，魁北克，2010 年，第 14-17 頁。 [15] P. Anbarasan 和 T. Jayabarathi，“使用蛾

火焰優化算法的最佳無功功率調度”，國

際應用工程研究期刊，第一卷。 12，

pp.3690-3701, 2017。

[16] Benjamin Durakovic，Muris Torlak，“用 於窗戶應用中作為儲熱介質的相變材料 和水的模擬和實驗驗證”，J.of Mater。和 環 境 。 Sci 。 ， Vol 。 8 ， No 。 5 ， （2017），ISSN：2028-2508，pp 1837-1846 ..

[17] Kennedy J，Eberhart R，“Particle swarm optimization” ， Proceedings of the 1995 IEEE International Conference on Neural Networks，pp.1942-1948，IEEE Press。 [18] Ogudo，K.A。; Muwawa Jean Nestor，

D。; Ibrahim Khalaf，O。; Daei Kasmaei， H。智能手機在蜂窩網絡中的物聯網服 務和機器類通信的設備性能和數據分析 概念。 Symmetry 2019, 11, 593

[19] D. Van der Merwe 和 A. P. Engelbrecht， “ 使 用 粒 子 群 優 化 的 數 據 聚 類 ” ， 在 Evolutionary Computation ， 2003 中.CEC'03。 2003 年大會，2003 年，第 215-220 頁。 [20] W. H. Kersting，“徑向分佈測試饋線”， 2001 年 IEEE 電力工程學會冬季會議。 會 議 論 文 集 （ 目 錄 號 01CH37194 ）， 2001 年，第 908-912 頁。 [21] 徑向分佈測試饋線。 [線上]。可用： ttps ： //ewh.ieee.org/soc/pes/dsacom/testfeeders/t estfeeders.pdf 。