Power quality and reliability enhancement in distribution systems viaoptimum network reconfiguration by using quantum firefly algorithm

⇑ Corresponding author. Tel.: +60 389216591; fax: +60 389118359.E-mail addresses: shareef@eng.ukm.my (H. Shareef), asrul@eng.ukm.my

(A.A. Ibrahim), nesrullahsalman@yahoo.com (N. Salman), azah@eng.ukm.my(A. Mohamed), ling_ai89@hotmail.com (W. Ling Ai).

H. Shareef a, A.A. Ibrahim a,⇑, N. Salman b, A. Mohamed a, W. Ling Ai a

a Department of Electrical, Electronic and Systems Engineering, University Kebangsaan Malaysia, Bangi, 43600 Selangor, Malaysiab Department of Electrical Power and Machines Engineering, College of Engineering, Diyala University, 32001 Baqubah, Iraq

a r t i c l e i n f o a b s t r a c t

Article history:Received 2 July 2013Received in revised form 7 January 2014Accepted 18 January 2014

Keywords:Voltage sagReliabilityNetwork reconfigurationFirefly algorithmOptimization

Network reconfiguration (NR) is the process of varying the topological arrangement of distribution feed-ers by changing the open/closed status of sectionalizing and tie switches. This paper presents a method toimprove the power quality (PQ) and reliability of distribution systems by employing optimal NR. OptimalNR is applied independently to a system in a specified period to minimize the number of propagatedvoltage sags (Nsag) and other reliability indexes such as the average system interruption frequency index,sustained average interruption frequency index, and momentary average interruption frequency index.The quantum-inspired binary firefly algorithm (QBFA) is used to find the optimal NR. The QBFA perfor-mance for the application of optimal NR to minimize Nsag is first compared with other establishedoptimization methods such as the standard binary firefly algorithm and gravitational search algorithm.Case studies are conducted by using other objective functions, and reliability assessment is performedto observe the reliability improvement caused by the new network topology. Simulation results showthat the proposed optimum NR effectively enhances system reliability level and PQ.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

A modern electric power system must be designed to supplyacceptable levels of electrical energy to customers. Simple powerquality (PQ) disturbance events, such as voltage sags, may causeconsiderable economic losses because industrial processes relyon electronic power-control devices. Thus, the power supplied toutilities must be reliable and of good quality. Electrical PQ isdefined as the degree in which electrical power deployment anddelivery affect equipment functions [19]. Reliability denotes thecapability of a system to perform its required functions underdeclared conditions in a specified period. Available reliabilityassessment indexes are categorized into three clusters, namely,load-related indexes, continued interruption indexes, and short-term indexes [11]. Load-related indexes, such as the averagesystem interruption frequency index (ASIFI), and continued inter-ruption indexes, such as the sustained average interruption fre-quency index (SAIFI), are the most common reliabilityassessment indexes in addressing voltage sag.

Voltage sags, which are normally caused by system faults thatlast over 0.01 s, may induce the breakdown of sensitive equipmentand process downtime. A disrupted process may require several

hours before resuming operations even though the power supplyhas been restored. Thus, the reliability level may be affected byvoltage sag propagation in distribution systems. Voltage sag is de-fined as a reduction in root-mean-square (RMS) voltage magnitudebetween 0.1 and 0.9 pu at durations of 0.01 s to 60 s [10]. Chenet al. [3] used a series of strategies based on network reconfigura-tion (NR) to mitigate voltage sags and improve system reliability.Yun et al. [29] applied a feeder transfer scheme to alleviate voltagesag propagation in power distribution systems. GA was recentlyimproved by using the edge-window-decoder encoding techniquein NR to identify new network topologies with minimal powerlosses [26]. Jazebi et al. [14] the applied differential evolution algo-rithms for optimal NR and DSTATCOM allocations to mitigatepower losses and improve voltage profiles in power distributionnetworks. They also indicated that PQ improvement, voltage stabil-ity, system loadability, and reconfiguration management stabilityshould be considered in future. [22–24] adopted an integratedmethod by combining NR and DSTATCOM placement to mitigatethe voltage sag problem. Jazebi and Vahidi [12] used the differen-tial evolution algorithm to address the ability of NR to enhance PQissues such as harmonics and voltage sags while mitigating powerlosses.

Studies have focused on system reliability assessment andimprovement instead of PQ mitigation. Mohammadi and AkbariNasab [19] developed a reliability enhancement algorithm by usinga static series voltage regulator. Mohammadi and Akbari Nasab[19] considered the effects of distributed generation units, system

reconfiguration, load shedding, and load addition were consideredin the assessment of distribution system reliability. Skoonpong andSirisumrannukul [25] considered the use of NR to minimize cus-tomer interruption costs and enhance the reliability of electricpower supplies. The aforementioned studies recommended GAfor optimal reconfiguration. Monte Carlo simulations and historicaldata were used for reliability assessment in a related research [27].Zhang et al. [30] considered uncertainties in loads, power genera-tion, and electrical and reliability parameters to improve systemreliability and reduce losses. They used a neighborhood searchalgorithm to obtain the optimal solution. Kumar and Jayabarathi[15] used the bacterial foraging optimization algorithm in distribu-tion NR to minimize system losses. Kavousi-Fard et al. [16] recentlyproposed an NR strategy to overcome the uncertainty problem inwind-turbine output power variations and forecasting errors withregard to system voltage profile, power loss, and total cost. Theyused self-adaptive modified teacher learning optimization (MTLO)to address the multi-objective optimization problem concurrently.Niknam et al. [20] used MTLO and NR to obtain the optimal powerloss, total cost, and total emission of a fuel cell power plant and ex-tended the optimal NR concept in terms of reliability. Kavousi-Fardand Niknam [17] investigated the role of the NR problem as a reli-ability reinforcement strategy in reliability indexes such as SAIFI,average energy not supplied (AENS), and utility-oriented objectivefunctions such as the MW power production cost and active powerloss. To solve the uncertainty problem in wind turbines, they pro-posed an adaptive bat algorithm to explore the total search spaceglobally. Their results showed that the adoptive bat algorithm isthe most suitable algorithm for finding the optimal NR. A similarwork can be found in the study of Kavousi-Fard and Akbari-Zadeh[18], who applied an improved shuffled frog leaping algorithm tosolve NR problems with the multi-objective function including SAI-FI, AENS, system average interruption duration index, and powerlosses. However, all of these previous works do not consider volt-age sag propagation and voltage-sag-related reliability indicators,such as the system average RMS variation frequency index (SARFI),for a costless NR solution to the reliability problem.

Load outages are often caused by voltage sag; thus, the reliabil-ity levels of the distribution systems are adversely affected by volt-age sag propagation. In this paper, a method for reducing thenumber of voltage sags experienced at each load point in a distri-bution system is developed by using optimal NR. The quantum bin-ary firefly algorithm (QBFA) is proposed in the current study todetermine the optimal solutions [28]. The QBFA algorithm is vali-dated by using proven heuristic computational optimization toolssuch as the standard binary firefly algorithm (BFA) and binarygravitational search algorithm (BGSA) [21]. After the effectivenessof QBFA for optimal NR and for minimizing voltage sags is verified,other reliability indexes, such as SAIFI, ASIFI, and MAIFI, are used asobjective functions in optimal NR with QBFA. The effect of optimalNR on various objective functions is assessed by using the voltagesag index SARFI [2]. Reliability assessment is conducted by usingSAIFI, ASIFI, and MAIFI.

2. PQ and reliability assessment indices

System PQ performance is often specified by using SARFI, whichrepresents the average number of RMS variations over the assess-ment period per customer served. SARFI-90 calculates all voltagesags with remaining voltages of less than 90% regardless of sagduration. Therefore, the sum of the expected number of sags Nsag

caused by every registered fault event can be used to obtain theSARFI of the entire system [2]. Nsag represents the number of cus-tomers affected by all possible fault events during the assessmentperiod. The customers served in the assessment area are consid-

ered the customers supplied by all system buses Nbus. SARFI canbe defined as follows:

SARFI ¼ number of sags ðNsagÞtotal number of customers servedðNTÞ ð1Þ

The number of sags in SARFI can be transformed into continuedinterruptions, short-term interruptions, and load outages to accesssystem reliability. The reliability assessment indexes of distributionsystems can be grouped into three categories, namely, load-relatedindexes, continued interruption indexes, and short-term indexes[11]. ASIFI, MAIFI, and SAIFI can indicate load-related, continuedinterruption, and short-term indexes, respectively, in reliabilityassessment [11]. These indexes are defined in the following equa-tions [11]:

ASIFI ¼ sum of total connected kVA of load interruptedðLiÞtotal connected kVA servedðLTÞ ð2Þ

MAIFI ¼ sum of customer short-term interruptionstotal number of customers servedðNTÞ ð3Þ

SAIFI¼ sum of all customer continued interruptions due to each eventtotal number of customers servedðNTÞ

ð4Þ

ASIFI can be used to indicate the financial losses caused by load out-ages, whereas MAIFI can be used to represent customer disruptionbecause of protection-device operations. SAIFI can be used toindicate sustained customer interruptions.

3. Materials and methods

This section describes the necessary components required toperform NR for the improvement of system PQ and reliability.These components include the system sag calculation, problem for-mulation for optimization, proposed optimization method, andprocedure.

3.1. Determining the number of voltage sags and interruptions

Voltage sag propagation is dependent on the fault position in asystem, and buses that are far from faults have low severity [9].The sag-exposed area of each fault point can be identified by faultanalysis. However, identifying the system component that causesconsiderable voltage sag propagation during a fault is importantin PQ and reliability improvement and in the determination of faultoccurrence probability. Line faults are frequent and are the maincause of voltage sags. Therefore, fault analysis can determine thesystem branches inducing great sag exposure. Possible fault com-ponents, such as bus and transformer faults, can also beinvestigated.

If the fault rate of a faulted line with length L is kL, the estimatednumber of line faults per year fL can be defined as follows [1,9]:

fL ¼X4

k¼1

XNL

i¼1

LikLi ð5Þ

where k represents the three-phase, line-to-ground, line-to-line,and line-to-line-to-ground faults; NL is the total number of linesin the system. The annual number of transformer faults (fT) andbus faults (fB) can be obtained via the fault rates. The total numberof faults can then be obtained by using all of these faults [1,9]:

ftotal ¼ fL þ fT þ fB ð6Þ

Nsag and the total number of interruptions (Nint) can be determinedby monitoring the individual bus voltage magnitude (Vi) in the

Fig. 1. Flowchart of the proposed optimal NR algorithm by QBFA.

system and identifying the type and location of load bus i. AnnualNsag can be obtained as follows [2,10]:

Nsag ¼XNbus

i¼1

Xftotal

f¼1

1 if 0:1 p:u < Vi < 0:9 p:u

0 otherwise

�ð7Þ

The portion of Nsag corresponding to sensitive buses is equal to thetotal number of continued interruptions because most processesinvolving sensitive equipment experience long downtimes. The to-tal number of interruptions per year for non-sensitive loads can beobtained as follows [2,10]:

Nint ¼XNbus

i¼1

Xftotal

f¼1

1 if Vi � 0:1p:u

0 otherwise

�ð8Þ

The interruptions highlighted in Eq. (8) can be divided further intocontinued interruptions if the non-sensitive load bus is the fault busor if the non-sensitive load bus is located downstream from thefault because all of these buses are isolated when opening the cir-cuit breaker to clear the fault. Otherwise, such interruptions canbe registered as short term or momentary interruptions becausethe fault will be cleared by the protection system after service res-toration. By using Eqs. (7) and (8), the above mentioned categoriesof interruptions can be used to calculate the PQ index SARFI peryear and reliability indexes (e.g., ASIFI, MAIFI and SAIFI) per yearcaused by NR.

3.2. Distribution NR

NR alters the topological arrangement of distribution feeders byaltering the open/closed status of tie and sectionalizing switches. Afeeder may either be partially or fully fed by an alternate feeder byactivating a tie switch that connects both feeders. The appropriatesectionalizing switch must be deactivated to preserve radial struc-tures [4]. NR is commonly used to reduce system losses, balanceloads, and enhance voltage fluctuation in power distribution net-works. NR can also be used to alleviate voltage sag propagationin the system by escalating line impedance in the fault current dur-ing faults. Several system buses occasionally encounter voltage sagwhen the fault occurs at certain buses. Thus, system PQ and reli-ability may be affected by faults in the weak area. NR is mainlyused to reduce Nsag and reliability indexes, such as ASIFI, MAIFI,and SAIFI, by distancing the weak area from the main powersource. However, NR must be restrained to avoid increasing the to-tal system line losses. A balance between the increase of line lossesand the enhancement of system PQ and reliability must be made.Therefore, optimization methods are necessary to determine asuitable configuration that can achieve both low voltage sag countand low or acceptable power loss.

3.3. Proposed QBFA for optimum NR

A binary version of the firefly algorithm (FA), that is, QBFA, isdeveloped and used to optimize the NR problem. This techniqueavoids the drawbacks of conventional BFA.

FA is based on the social activities of fireflies. Standard FA con-siders two important parameters, namely, variation in light inten-sity I and the formulation of attractiveness b. When b isproportionate to I, b, which varies with distance r, can be expressedas follows [28]:

bðrÞ ¼ boe�crm; ðm � 1Þ ð9Þ

where bo is the attractiveness at r = 0, c is the light absorption coef-ficient, and r is the distance between two fireflies.

The distance between any two fireflies, i and j, at xi and xj can beexpressed as the Cartesian distance rij:

rij ¼ jjxi � xjjj ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXd

k¼1

xi;k � xj;k

� �vuut ð10Þ

where xi,k is the k-th component of the spatial coordinate xi of thei-th firefly. A firefly i is attracted to a brighter firefly j; thismovement is expressed as follows:

xi ¼ xi þ boe�cr2ij ðxj � xiÞ þ alpha rand� 1

2

� �ð11Þ

alphaðt � 1Þ ¼ alphaðtÞ � 0:99 ð12Þ

where the second term represents the attraction, and the third termcorresponds to the randomization of the randomization parameter.alpha and the uniformly distributed random number generator randchanges in value with each iteration.

The position of firefly i(xi) changes from a binary number to areal number when firefly i becomes attracted to firefly j in discreteFA. Therefore, the sigmoid function S(xi) shown in Eq. (13) limitsthe continuous output between zero and one. The value of S(xi)determines the probability that the value of bit xi is ‘‘1’’ as shownin Eq. (14).

SðxiÞ ¼1

1þ expð�xiÞð13Þ

xi ¼1; if SðxiÞ > r

0; otherwise

�ð14Þ

where r is a uniform random variable between ‘‘0’’ and ‘‘1.’’The distance between fireflies may increase when the algorithm

iterates further with Eq. (13). The probability that the value of xi is

26

27

28

2930

31

39

40

7143

41

42

43

35

38

44

45

46

47

36

37

32

33

Gr

SWT

SW

G

Fig. 2. Actual 47-bus test

Table 1Details of the 47-bus test system.

Bus no. kV Load Load type No. of customers

P MW Q Mvar

1 132 0 0 0 02 11 0 0 0 03 11 0.85 0.527 1 14 11 0.342 0.194 4 15 11 0.244 0.145 3 246 11 0.244 0.177 3 247 11 0 0 0 08 3.3 0 0 0 09 3.3 1.275 0.513 1 1

10 0.433 1.594 0.641 1 111 11 0.146 0.098 3 1412 11 0.294 0.143 3 2913 11 0.488 0.341 2 414 11 0.437 0.199 2 415 11 1.776 1.006 2 816 11 0.297 0.098 3 3017 11 0 0 0 018 11 0.616 0.43 3 6119 11 0.388 0.23 3 3920 11 0.732 0.354 1 121 3.3 1.063 0.427 1 122 11 0.925 0.549 2 523 11 0.582 0.345 2 324 11 0.504 0.23 4 100

‘‘0’’ or ‘‘1’’ is 0.5 regardless of the previous position xi�1. This prob-ability may worsen the convergence of the algorithm.

The use of quantum computing theory easily solves the BFA-re-lated problem mentioned above. A quantum bit (Q-bit) is thesmallest unit in quantum computing and can be either ‘‘1,’’ ‘‘0,’’or in a linear superposition of the two [6]:

1

2

9

18

22

23

24

25

15

16

19

20

12

13

14

3

4

11

5

6

7

8

21

10

id

SWT

SWT

SWT

SWT

T

G

M

M

M

SWT

distribution system.

Bus no. kV Load Load type No. of customers

P MW Q Mvar

25 11 1.25 0.605 3 12526 11 0.351 0.149 6 127 11 0.276 0.118 3 2828 11 0.314 0.134 4 6329 11 0.613 0.261 2 330 11 0.592 0.252 3 5931 11 0 0 0 032 6.6 0 0 0 033 11 0.032 0.024 6 134 33 0 0 0 035 33 0 0 0 036 33 0 0 0 037 11 8 6 5 838 11 7.65 4.741 5 739 33 0 0 0 040 33 0 0 0 041 33 0 0 0 042 33 0 0 0 043 33 0 0 0 044 11 12.75 7.902 5 2645 11 12.75 7.902 5 2646 11 6.8 4.214 5 1447 11 4.8 3.6 5 10

0 5 10 15 20 25 30 35 40 45 500

0.2

0.4

0.6

0.8

1

System Buses

Volta

ge m

agni

tude

pu.

Load FlowLLL Faut at bus 22

Fig. 4. Pre- and post-bus voltage magnitudes in Bus 22 given the LLL fault.

wj i ¼ a 0j i þ b 1j i ð15Þ

where a and b are complex numbers that specify the probabilityamplitudes of the corresponding states. |a|2 and |b|2 show the prob-ability for a Q-bit to be in the ‘‘0’’ or ‘‘1’’ state, respectively. There-fore, the states can be normalized to unity as follows:

ajj 2 þ bjj 2 ¼ 1 ð16Þ

The Q-bit state is updated by using a quantum gate and can be rep-resented as a unitary operator U. The types of quantum gates in-clude NOT, controlled NOT, rotation, and Hadamard gates [7]. Therotation gate is used (Eq. (17)) in the current study because severalheuristic search algorithms have applied this gate [6,13,5,8].

UðDhiÞ ¼cosðDhiÞ � sinðDhiÞsinðDhiÞ cosðDhiÞ

� ð17Þ

where Dhi, i = 1, 2, 3. . ., n denotes the rotation angle of each Q-bittoward either the ‘‘0’’ or ‘‘1’’ state depending on the Q-bit sign.

This proposed rotation gate involves two techniques, namely,the coordinate rotation gate approach and the dynamic rotationangle approach; these methods are used to update Q-bits anddetermine the rotation angle magnitude, respectively. Therefore,pre-specified lookup tables are not required and the rotation anglecan be formulated as follows:

Dhi ¼ h� xi þ boe�cr2ij ðxj � xiÞ þ alpha rand� 1

2

� �� �ð18Þ

where h is the rotation angle magnitude along the iteration anddecreases monotonously from hmax to hmin. The Q-bit individualstring is then updated based on the rotation angle and rotation gate

Table 2Percentage of fault occurrence according to fault type.

Fault type L-G-fault LL-G-fault LL-fault LLL-fault

Occurrence percentage 73% 17% 6% 4%

Table 3Fault rates of various system elements.

System element Bus fault/year Line fault/km/year Transformer fault/year

Fault rate 0.08 4.5 0.015

4 6 8 10 12 14 16 18 201

5

9

13

17

21

25

29

33

37

41

4547

Fault loca

Num

ber o

f sys

tem

bus

es

Fig. 3. System voltage levels at individ

(Eq. (19)). Finally, the firefly’s position is updated based on theprobability of |b|2 by using Eq. (20).

aiðt þ 1Þbiðt þ 1Þ

� ¼ UðDhiÞ �

aiðtÞbiðtÞ

� ð19Þ

xi ¼1; if jbiðt þ 1Þj2 > r

0; otherwise

(ð20Þ

3.4. Objective functions and constraints

The purpose of the optimization is to determine a suitable NRthat can reduce Nsag and reliability indexes and improve system

22 24 26 28 30 38 45 47tions

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ual buses attributed to LLL faults.

Table 4BFA, BGSA, and QBFA parameter settings.

Parameter BFA BGSA QBFA

Population size 30 30 30Max. iteration 30 30 30G0 – 100 –Q0 – – 1=

ffiffiffi2pþ j1=

ffiffiffi2p

Kbestmin/hmin – 2.5% 0.001pKbestmax/hmax – 100% 0.05pLight absorption coefficient (c) 100 – 100Initial randomization parameter

(alpha, at t = 1)1 – 1

4750

4800

4850

4900

4950

5000

BGSA QBFA BFA

Algorithm

Fitn

ess

1200

1400

1600

1800

2000

2200

2400

2600

2800

BGSA QBFA BFA

AlgorithmC

ompu

tatio

n tim

e (s

ec)

5

10

15

20

25

30

BGSA QBFA BFA

Algorithm

Itera

tion

coun

t

Fig. 5. Performance of QBFA, BGSA, and BFA in obtaining an optimal NR solution and minimizing Nsag in a 47-bus system.

0 5 10 15 20 25 304000

4500

5000

5500

6000

6500

7000

No of Generations

Fitn

ess

valu

e

QBFABGSABFA

Fig. 6. QBFA, BGSA, and BFA convergence characteristics for minimizing Nsag in a47-bus system.

PQ and reliability without increasing the total line losses. Objectivefunctions can be formulated to minimize the following: (i) Nsag

(Eq. (21)), (ii) Nsag and total power loss (Ploss) (Eq. (22)), (iii) ASIFI(Eq. (23)), (iv) MAIFI (Eq. (24)), and (v) SAIFI (Eq. (25)) via optimi-zation. These objective functions are expressed as follows:

Fitness ¼minðNsagÞ ð21Þ

Fitness ¼minNsag

Nsag maxþ Ploss

Ploss max

� �ð22Þ

Fitness ¼minðASIFIÞ ð23Þ

Fitness ¼minðMAIFIÞ ð24Þ

Fitness ¼minðSAIFIÞ ð25Þ

Table 5Summarized PQ and reliability improvements after NR when Nsag is the objective function

System status Due to weak area fault System lossesMW

Healthy busesV < 0.9 pu

Sag exposed area%

Without NR 19 61.70 2.09After Optimal NR 42 10.77 2.33Overall

performanceImproved 121.1% Reduced 82.5% Raised 11.5%

where Nsag_max and Ploss_max in Eq. (22) are the maximum number ofsags and maximum power loss in the system, respectively. Nsag_max

and Ploss_max are used to normalize individual objectives in thefunction.

In evaluating all the above objective functions, the optimizationsolution is subjected to the operation constraints of the distribu-tion system; that is, the network structure must be radial, thenominal bus voltages must remain within standard limits, all ofthe network nodes and loads must be connected, and the powerflows must be within the thermal limits of the lines. Ploss must alsobe within acceptable limits in all cases except in Eq. (22).

3.5. QBFA implemention for optimal NR

On the basis of the objective functions and constraints indicatedin Section 3.4, reconfiguration can be performed by changing thepredefined status of the tie and sectionalizing switches in thedistribution network. Nsag, SARFI, ASIFI, MAIFI, SAIFI, and Ploss arecalculated by using the short circuit analysis and steady state loadflow algorithm in Matlab environment for every modification innetwork configuration.

An encoding and decoding technique presented by Salman et al.[23] is used to avoid generating unfeasible solutions as a result ofsystem constraints on the initial random population during opti-mization. Only feasible configurations are generated by radialstructures in the encoding technique. The main binary string isdeconstructed into the original substrings in the decoding tech-nique, and the binary number of each substring is changed to adecimal number that represents the open switch location in thecorresponding loop [23]. Additional details regarding the encodingand decoding process are provided in the study of Salman et al.[23]. The implementation of the overall optimum NR algorithm isdetailed in the flowchart shown in Fig. 1.

in the optimization.

System sag index System reliability indices

Nsag Sag IndexSARFI

SAIFI ASIFI MAIFI

11577 2.97 18.88 55.07 4.334752 1.22 17.45 23.45 2.32Reduced143.6%

Reduced143.4%

Reduced8.19%

Reduced134.8%

Reduced86.6%

4. Results and discussions

A practical 47-bus distribution network is shown in Fig. 2 and isused to validate the proposed technique. The system consists of 47buses and 42 branches supplied by a 132 kV transmission system.Four major substations are connected at Buses 2, 17, 34, and 39.Substation Buses 2 and 17 are fed by 132/11 kV and 30 MVA trans-formers, whereas Substation Buses 34 and 39 are fed by 132/33 kVand 45 MVA transformers. Bus 1 is the swing bus. The seven tieswitches between Buses 25 and 38, 29 and 38, 24 and 29, 16 and18, 4 and 19, 20 and 23, and 4 and 14 may be used to change thesystem topology in case of unexpected events or contingencies.The details of the system bus are given in Table 1.

The fault distributions and fault rates of the system elementsare obtained from Zhang [31] and Aung et al. [1]. These data arelisted in Tables 2 and 3.

All loads and voltages are assumed to be balanced in the opti-mal NR simulations. Faults do not occur in the main substations,and each load point is considered a group of customers in the reli-ability evaluation. All industrial loads are sensitive to the voltagesag problem in the reliability evaluation.

Table 6Open switches attributed to different optimal NRs with various objective functions.

System status Open switches

Before NR 19–4, 14–4, 16–18, 20–23, 24–29,25–38, 17–3, 2–18, 29–38

After NR with objective function Nsag 2–18, 3–4, 15–16, 17–26, 17–33,18–19, 20–23, 22–23, 24–29

After NR with objective functionNsag + Ploss

2–18, 3–4, 16–18, 17–26, 17–33,18–19, 20–23, 24–25, 24–29

After NR with objective function ASIFI 2–15, 2–18, 3–4, 17–26, 17–33,18–19, 20–23, 24–25, 24–29

After NR with objective function MAIFI 2–18, 3–4, 15–16, 17–26, 17–33,18–19, 20–23, 22–24, 24–29

After NR with objective function SAIFI 2–18, 3–4, 15–16, 17–33,18–19, 20–23, 24–25, 24–29, 28–29

4.1. Base case test results

Base case analyses, such as load flow and fault analyses, areconducted to assess the performance of the 47-bus distributionsystem prior to the optimum NR. Fault analysis simulations areconducted on all buses, except for major substations. Ploss, Nsag,SARFI, SAIFI, ASIFI, and MAIFI are 2.09, 11577, 2.97, 18.88, 55.07,and 4.33, respectively (Table 5).

All four types of fault simulations are conducted on all buseswith voltage levels below 33 kV, except for the main substationsand buses supplied by more than one feeder, to determine theweak area or the bus that causes sag propagation in the system.The voltage levels at all system buses given by the LLL fault withzero fault resistance are shown in Fig. 3. Sensitive buses (weakareas) that may affect PQ and reliability can be determined byobserving the dark points and the color bar representing the volt-age magnitude. Buses 19, 20, 22, 23, and 24 are the most sensitiveto voltage sag propagation throughout the system, and Bus 22influences most system buses. Fig. 4 shows the system voltage pro-file during normal condition and the LLL fault at Bus 22.

4 6 8 10 12 14 16 18 201

5

9

13

17

21

25

29

33

37

41

4547

Fault locati

Num

ber o

f sys

tem

bus

es

Fig. 7. Voltage sag distribution of system buses attributed to the LLL fault in all f

4.2. NR optimization results

Optimal NR is conducted to improve PQ and reliability by usingthe new QBFA. QBFA is validated by standard BFA and BGSA, whichis another commonly used algorithm. All optimization parametersare standardized (Table 4) to compare the algorithms fairly. Thetable below displays the necessary parameter settings for alloptimization techniques used in this study.

4.2.1. Analysis with Nsag as the objective functionThree optimization algorithms, namely, QBFA, BGSA, and stan-

dard BFA, are used to formulate a unique optimal NR solution.These algorithms possess different searching patterns and conver-gence characteristics. Optimum NR with QBFA, BGSA, and BFA isrepeated 30 times by using Eq. (21) to determine the effectivenessof the proposed QBFA. The capabilities of QBFA, BGSA, and standardBFA to generate an optimal NR solution for the 47-bus system after30 iterations are shown in Fig. 5. QBFA, BGSA, and standard BFA arecompared in terms of convergence rate (the number of iterationsrequired to converge), quality of the optimal solution (fitness va-lue), and the time consumed by optimization. The box plot corre-sponding to the fitness values shows that QBFA performs betterthan other algorithms because the 25th and 75th percentiles ofthe QBFA samples lean toward the minimum solution with a nar-row interquartile range. The mean and median values of the QBFAare ideal, as indicated by the red line in Fig. 5, thus indicating thatthe probability of obtaining the ideal solution is high in QBFA

22 24 26 28 30 38 45 47

ons

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ault locations after optimal NR by QBFA when Nsag is the objective function.

compared with other algorithms. QBFA evidently outperformsstandard BFA in terms of computation time, with outliers close tothe interquartile range. QBFA is also consistent in terms of conver-gence rate, with whiskers close to the interquartile range. The

Fig. 8. Performance indicators of optimal NRs given various objective functions: (a) he(h) SAIFI.

whiskers of the other algorithms extend to the maximum genera-tion criterion of 30 sets in the simulation.

The best convergence characteristics in the three optimizationalgorithms are depicted in Fig. 6. QBFA converges quickly with

althy buses, (b) Nsag, (c) sag-exposed areas, (d) Ploss, (e) ASIFI, (f) MAIFI, (g) SARFI,

minimum fitness value. BGSA and BFA are slightly slower thanQBFA in finding the optimal solution.

The best Nsag minimization results obtained by using the threesimulated optimization methods are summarized in Table 5.System PQ and reliability can be improved by applying any ofthe optimization methods proposed in this study because eachalgorithm generates similar ideal solutions after several simulationiterations (30 iterations in this study). However, QBFA generatesthe ideal fitness value 70% of the time, whereas BGSA and BFA onlygenerates the ideal fitness value 30% of the time in 30 runs. SystemPQ and reliability are enhanced without NR by reducing Nsag to143.6%, whereas SARFI is improved by 143.4% without NR. Net-work reliability is also optimized when SAIFI, ASIFI, and MAIFIare reduced to 8.19%, 134.80%, and 86.60%, respectively. Systemlosses increase by only 11.50% with the increase in PQ and reliabil-ity. The outage of heavy loads as a result of poor system PQ andreliability may induce considerable financial losses compared withthe slight increment in line losses.

QBFA efficiently generates the optimal NR solution based on theresults. PQ and system reliability are considerably improved de-spite the slight increase in system loss caused by NR. Fig. 7 showsthe voltage distribution of all system buses attributed to the LLLfault in various fault locations after optimal NR by QBFA when Nsag

is the objective function. The voltage sag performances of mostsystem buses are significantly improved compared with the basecase in Fig. 3, as shown in the dark points and the color bar repre-senting the voltage magnitude. Table 6 depicts various reconfig-ured systems represented by sets of open switches locatedbetween two nodes. Considering the effectiveness of QBFA, onlythis algorithm is used to evaluate the performance of the reconfig-ured network with the objective functions.

4.2.2. Analysis with the other objective functionThe QBFA procedure shown in Fig. 1 is executed 30 times for

each of the objective functions provided in Eqs. (22)–(25) to eval-uate the optimal NR performance. The best results are summarizedin Fig. 8. Nsag is the most appropriate objective function for PQ(Fig. 8). However, the multi-objective function in Eq. (22), whichincludes Nsag and Ploss, is ideal if PQ, power loss, and reliabilityare equally important. The use of the multi-objective function(Eq. (22)) in NR can reasonably increase the number of healthybuses to 40, decrease Nsag to 4906, and reduce the number ofsag-exposed areas, ASIFI, MAIFI, SARFI, and SAIFI to 14.89%,33.73%, 1.89%, 1.26%, and 17.21%, respectively. The power lossesincurred at 2.25 MW are higher than the base case loss at2.09 MW; however, the loss incurred by the multi-objective func-tion is less than the 2.33 MW lost when Nsag is the objective func-tion. SAIFI is unsuitable for PQ improvement compared with theperformances of other objective functions. Fig. 8 shows that mostPQ indicators, such as Nsag, exposed sag areas, ASIFI, and SARFI,are high when SAIFI is the objective function compared with otherobjective functions. Table 6 shows the open switches attributed todifferent optimal NRs of the 47-bus system when various objectivefunctions are considered.

5. Conclusion

A novel optimal NR method with various objective functions ispresented in this study to enhance the PQ and reliability of electricpower distribution systems. FA is greatly improved by quantumtheory integration and is used as an optimization tool during NR.The results obtained by using the proposed method are comparedwith other well-known optimization algorithms for validation. Theproposed QBFA is more effective than BGSA and standard BFA. Nsag

is the most suitable objective function for PQ. However, the

multi-objective function, including Nsag and Ploss, is more appropri-ate than other objective functions if both PQ and reliability areequally important. System PQ index, SARFI, and reliability indexes(e.g., SAIFI, ASIFI, and MAIFI) can be significantly reduced by apply-ing the proposed method with the objective functions and QBFA.

Acknowledgement

The authors are grateful to Universiti Kebangsaan Malaysia(UKM) for supporting this study under Grants DIP-2013-30 andETP-2013-044.

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