Electrical Power and Energy Systems 57 (2014) 404–413

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Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

Optimal power quality monitor placement in power systems usingan adaptive quantum-inspired binary gravitational search algorithm

0142-0615/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.ijepes.2013.12.019

⇑ Corresponding author.E-mail addresses: asrul@eng.ukm.my (A.A. Ibrahim), azah@eng.ukm.my

(A. Mohamed), shareef@eng.ukm.my (H. Shareef).

Ahmad Asrul Ibrahim, Azah Mohamed, Hussain Shareef ⇑Department of Electrical, Electronic and Systems Engineering, Universiti Kebangsaan Malaysia, Bangi, 43600 Selangor, Malaysia

a r t i c l e i n f o

Article history:Received 27 April 2012Received in revised form 20 December 2013Accepted 23 December 2013

Keywords:Quantum-inspired binary gravitationalsearch algorithmPower quality monitorVoltage sag assessmentTopological monitor reach areaArtificial immune system

a b s t r a c t

This paper presents a novel adaptive quantum-inspired binary gravitational search algorithm (QBGSA)to solve the optimal power quality monitor (PQM) placement problem in power systems. In thisalgorithm, the standard binary gravitational search algorithm is modified by applying the conceptsand principles of quantum behavior to improve the search capability with a fast convergence rate.QBGSA is integrated with an artificial immune system, which acts as an adaptive element to improvethe flexibility of the algorithm toward economic capability while maintaining the quality of thesolution and speed. The optimization involves multi-objective functions and handles the observabilityconstraints determined by the concept of the topological monitor reach area. The objective functionsare based on the number of required PQM, monitor overlapping index, and sag severity index. Theproposed adaptive QBGSA is applied on several test systems, which include both transmission anddistribution systems. To evaluate the effectiveness of the proposed adaptive QBGSA method, itsperformance is compared with that of the conventional binary gravitational search algorithm, binaryparticle swarm optimization, quantum-inspired binary particle swarm optimization, and geneticalgorithm.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

In conventional power quality monitoring practice, powerquality monitors (PQMs) are usually installed in locations wherethe utility or customer wishes to measure the power quality ofthe system by detecting and analyzing power quality events [1].Voltage sag is the most frequent type of event captured amongall power quality events [2]. Voltage sag is defined by the Instituteof Electrical and Electronics Engineers (IEEE) standard 1159-1995as a voltage reduction in the root mean square (RMS) voltage from0.1 to 0.9 per unit for a duration of between half of a cycle and<1 min. Voltage sag has become a significant concern because itcreates huge economic losses resulting from the failure or malfunc-tion of sensitive equipment in industries. The installation of PQMsat selected buses in a power system is important to monitor anddetect the occurrence of voltage sags.

In a distributed power quality monitoring scheme, selecting thenumber and location of PQMs is a critical problem because it is di-rectly related to the efficiency of the monitoring system. InstallingPQMs at all buses in a power distribution network to monitor volt-age sags is uneconomical and inefficient. Thus, the number of

PQMs must be decreased to reduce the total cost of the powerquality monitoring system and the redundancy of the data beingmeasured by monitors [3]. In the past, the procedure for selectingthe minimum number and best locations for PQM installation isusually performed manually by power quality experts throughtheir experience and knowledge on power quality and systemtopology. However, such a procedure is unreliable and inconsis-tent. Therefore, an automated approach to determine the optimalnumber and location of PQMs is necessary to establish how manyPQMs are required to monitor the entire power network with thelowest possible redundancy. Each possible voltage sag that may oc-cur in the power network can be observed by at least one of the in-stalled monitors. The minimum number and optimal location ofPQMs are often linked together because the number of monitorsrequired is reduced by installing the monitors in strategic networkbuses with the highest observability capacities. The concept ofmonitor observability based on the monitor reach area (MRA)has been utilized to determine the optimal placement of PQMs intransmission networks [3–9]. In other applications similar toPQM placement, deciding where to place the optimal phasor mea-surement unit only applies to transmission networks [10–12]. Notenough evidence has been provided to prove that the concept isapplicable to radial distribution networks. Therefore, a new opti-mal PQM placement method that is applicable for both transmis-sion and distribution networks and caters to the system topologyissue must be developed.

A.A. Ibrahim et al. / Electrical Power and Energy Systems 57 (2014) 404–413 405

A few optimization techniques have been utilized in the last fewyears to solve the optimal PQM placement problem. In [3], a PQMplacement method based on covering and packing was developedwith the GAMS software as an integer linear program. In [4–6],the branch and bound algorithm was applied by dividing the solu-tion space into small spaces for easy solving. However, this algo-rithm may provide an incorrect solution when a branch isincorrectly selected in the earlier stages. In [7–9], the genetic algo-rithm (GA) was used to solve the optimal PQM placement problem.GA is commonly utilized to solve the optimization problem; how-ever, the disadvantage of GA is its slow convergence rate. Thus, analternative optimization technique with a faster convergence rate,such as particle swarm optimization (PSO), is recommended [13]. Arelatively new heuristic optimization technique known as thegravitational search algorithm (GSA) is gaining popularity becauseit has been reported to provide a solution better than that of PSO insolving certain problems [14]. Therefore, GSA is examined in thisstudy to evaluate its performance in solving the optimal PQMplacement problem.

The main aim of this study is to develop a new method to solvethe optimal PQM placement problem in both transmission and dis-tribution networks through a new heuristic optimization tech-nique that considers three concepts, namely, quantum behavior,binary gravitational search algorithm (BGSA), and artificial im-mune system (AIS). The observability concept based on the topo-logical monitor reach area (TMRA) is introduced in the proposedoptimal PQM placement method to allow for the application ofobservability to both transmission and distribution systems [15].In addition, the monitor coverage control parameter is employedto provide flexibility to the search algorithms in complying withsensitivity and economic capability. Control parameter a is definedas a voltage threshold level in p.u. at a monitored bus to indicatewhether a fault occurs inside or outside the monitor’s coveragearea. A PQM usually detects and captures voltage variations whenthe measured RMS voltage reaches 0.9 p.u. [16]. In this study, themaximum a value is set at 0.85 p.u. to allow some overlapping ofthe monitor coverage area at the boundary. This approach will helpovercome the boundary issues and non-monitored fault on the linesegment at the boundary.

This paper is organized as follows. The core subject, which re-fers to the monitor coverage concept in the PQM placement meth-od, is explained in Section 2. The existing MRA concept is brieflyreviewed, and then the proposed TMRA concept is described. Theproblem formulation for optimal PQM placement is discussed inSection 3. The overview and procedures of BGSA, quantum-in-spired binary gravitational search algorithm (QBGSA), and AIS arepresented in Section 4. The test results on the power systems un-der study and the optimal solutions are provided and discussedin Section 5.

2. Monitor coverage concept

Monitor coverage is the most important entity in the determi-nation of PQM placement. This concept is employed to evaluatethe placement and guarantee the observability of the entire powernetwork. The monitoring coverage concept is called MRA [4].Residual voltages at each bus for all fault cases are required inthe formation of MRA. Therefore, residual voltages should be savedin the form of the fault voltage (FV) matrix where the matrix col-umns (j) represent the bus numbers of residual voltage readingsand the matrix rows (k) relate to the specific type of fault position[7]. The MRA matrix can be obtained by comparing all the FV ma-trix elements for each phase with the threshold value, a. Each ele-ment of the MRA matrix is given the value of 1 when the voltage is

less than or equal to a p.u. in any phase and given the value of 0otherwise as provided by the following equation.

MRAðj; kÞ ¼1; if FVðj; kÞ 6 a p:u: at any phase0; if FVðj; kÞ > a p:u: at all phases

8j; k�

ð1Þ

TMRA is introduced in this study and applied to both distribu-tion and transmission systems. The TMRA matrix is a combinationof the MRA matrix and the topology (T) matrix by using the oper-ator ‘‘AND’’ as expressed in Eq. (2). Similar to MRA and FV matrices,the T matrix columns represent the bus number and its rows arecorrelated to fault location and type of fault. The T matrix is con-structed based on the concept of paths as in graph theory. Duringthe occurrence of a fault, the faulted bus voltage level drops tonearly ground level and becomes a cut vertex. At this moment,the faulted bus can be separated into several independent verticesthat correspond to the number of branches connected to the bus.Thus, a path is considered when at least one route from start vertexto end vertex, which does not go through the cut vertex, is avail-able. In this case, each generating station can be a start vertex,and a bus under consideration for PQM placement can be an endvertex. Based on the condition, the T matrix is given the value of1 when a path from any generating bus to a particular bus underconsideration exists and given the value of 0 otherwise. As a result,all downstream PQMs from the faulted location require anotherupstream PQM for effective event recording.

TMRAðj; kÞ ¼MRAðj; kÞ � Tðj; kÞ ð2Þ

Fig. 1 shows examples of a particular row in a T matrix for a ra-dial system with a single power source, a radial system with twopower sources, and a ring system with a single power source.When a fault occurs at bus 3, the system can be represented in agraph with bus 3 separated into several numbers depending onthe number of branches connected to the bus. The T matrix columnis then given the value of 1 or 0 by checking the connectivity be-tween the generator bus and the other bus based on the criteriamentioned previously. The system in Fig. 1(a) has only one gener-ator located at bus 1. Obviously, a path from the generator bus (bus1) to buses 1, 2, and 3 exists in this system, but not for the rest.Therefore, the T matrix column is given the value of 1 up to column3 and 0 for the rest. A different situation is observed when anothergenerator is added to the system at bus 5 as shown in Fig. 1(b). Inthis case, buses 4 and 5 have a link to the second generator. Thus,the T matrix is given the value of 1 up to column 5. The ring systemshown in Fig. 1(c) provides a value of 1 to all columns of the T ma-trix because a path connects the generator bus (bus 1) to the otherbuses. As a result, this T matrix provides information on systemtopology. These examples are considered only for a fault at bus 3and must be implemented at all buses in the system to obtain acomplete T matrix.

3. Optimal PQM placement problem formulation

The three common elements required in the binary optimiza-tion technique are decision vectors, objective functions, and opti-mization constraints. Each element is formulated and explainedto obtain the optimal solution of PQM placement. The optimizationtechnique explores the optimal solution as defined in the objectivefunction through the manipulation of the bits of the decision vec-tor subject to the constraints in each generation. The process isiterated for a fixed number of times or until a convergence crite-rion is achieved.

(a) A radial 7-bus system with a single power (b) A system in a) with two power sources

(c) A ring 6-bus system with a single source

Fig. 1. Example of row 3 in the T matrix for different system topologies.

406 A.A. Ibrahim et al. / Electrical Power and Energy Systems 57 (2014) 404–413

3.1. Decision vector

The position of PQMs in a power system is estimated to providea solution from the optimization process and is called the monitorplacement (MP) vector. This vector is required to evaluate the per-formance of the installed monitor in terms of its system observ-ability. MP is defined as a binary decision vector (xij) in whichthe bits of this vector indicate the positions of monitors that are re-quired or not in the power system network. The dimension of thevector should correspond to the number of buses in the system. Avalue of 0 in MP (n) indicates that no monitor should be installed atbus n, whereas a value of 1 indicates that a monitor should be in-stalled at bus n. The MP vector can be described by the expressionbelow.

MPðnÞ ¼1; if monitor is required at bus n

0; if monitor is not required at bus n8n

�ð3Þ

3.2. Objective functions

As stated previously, optimization is utilized to determine theminimum number of monitors with the best placements in apower network capable of observing any fault that may cause avoltage sag in the system. Thus, the objective function is formu-lated to solve two objectives, namely, the optimal number of re-quired monitors (NRM) and the optimal locations to install themonitors. NRM, which needs to be minimized, can be expressed as

NRM ¼XN

n¼1

MPðnÞ ð4Þ

where N is the total number of buses in a power system.Additional parameters are required to determine the best place-

ment to install the monitors. The placement of monitors in a powersystem results in different overlaps of monitor coverage areas fordifferent arrangements. These overlaps indicate the number ofmonitors that record the same fault occurrence in a power system;

therefore, these overlaps should be minimized. The overlaps can becalculated by multiplying the TMRA matrix and the transposed MPvector. If all the elements in the obtained results have a value of 1,then no overlap of the monitors’ coverage occurs. A monitor over-lapping index (MOI) is introduced to evaluate the best monitorarrangement in a power system. MOI is provided by

MOI ¼R TMRA �MPT� �

NFLTð5Þ

where NFLT is the total number of fault locations considering alltypes of faults.

A low MOI value indicates a good arrangement of PQMs in apower system. However, MOI alone is not enough to provide agood solution in determining the best placement of monitors. Asa result, another index, which is called the sag severity index(SSI), is considered. This index defines the severity level (SL) of aspecific bus toward a voltage sag, where any fault occurrencecauses a big drop in voltage magnitudes for most of the buses inthe system. SSI is dependent on SL, which should be initially deter-mined, and is provided by

SLðtÞ ¼ NSPB

NTPBð6Þ

where NSPB is the number of phases experiencing a voltage sag withmagnitudes less than t p.u. and NTPB is the number of total phases inthe system.

SSI is then obtained by applying weighting factors for differentSL values. The SL value with the lowest threshold t value is as-signed the highest weighting factor and vice versa. In this case, fivethresholds are considered (0.1, 0.3, 0.5, 0.7, and 0.9) per unit. SSI isexpressed as

SSIF ¼ 115

X5

k¼1

k � SL 1�2k�110ð Þ ð7Þ

where the number 5 refers to the weighting factor levels and the va-lue 15 corresponds to the total weight.

A.A. Ibrahim et al. / Electrical Power and Energy Systems 57 (2014) 404–413 407

The calculated SSI value must be stored in matrix form, wherethe matrix columns correlate to the bus number and the matrixrows correlate to the type of fault (F). A high value of SSI indicatesa good MP.

To combine the MOI and SSI indices, both of these indicesshould have similar maximum or minimum optimal criteria. TheSSI matrix should be modified to provide the minimum criteriain optimization and to make it similar to the case of MOI minimi-zation. The maximum value of SSI elements is equal to 1. By using acomplementary matrix of SSI, a negative severity sag index (NSSI)is introduced to evaluate the best placement of monitors in thesystem. A low NSSI value indicates a good arrangement of PQMsin the system. NSSI is expressed as

NSSI ¼R ð1� SSIÞ �MPTj k

NFTð8Þ

where NFT is the number of fault types.All the functions above can be combined in a single objective

function through summation method because all the functionsnow have similar optimal criteria. However, the objective func-tions should be independent and should not influence one anotherin determining the optimal solution. The single multi-objectivefunction to solve the optimization problem in this study is ex-pressed as Eq. (9).

f ¼ ðNRM�MOIÞ þ NSSI ð9Þ

In this equation, the value of the product of NRM and MOI willnever be less than the value of NSSI. Inherently, MOI is given higherpriority in determining optimal MP compared with the NSSI value.The concept is based on weighted sum method, which has beenused extensively to solve multi-objective problems [17]. However,the concept is not exactly similar because the relative weight ofNRM automatically increases when NSSI increases because morePQMs are placed in the system to maintain the selection priority.

3.3. Optimization constraints

The optimization algorithm must be implemented while satis-fying all constraints used to determine the optimal allocation num-ber of PQMs for the system. Multiplication of the TMRA matrix bythe transposed MP matrix provides the number of monitors thatcan detect voltage sags because of a fault at a specific bus. If oneof the resulting matrix elements has a value of 0, then no monitoris capable of detecting a sag caused by faults at a particular bus; ifthe value is greater than 1, then one monitor detected a fault at thesame bus. For this reason, the following restriction must be ful-filled to ensure that each fault is observed by at least one monitor.

XK

i¼1

TMRAðk; iÞ �MPðiÞP 1 8k ð10Þ

4. Adaptive QBGSA

This section provides a brief overview of BGSA, QBGSA, andadaptive QBGSA using AIS. The implementation of the proposedadaptive QBGSA to solve the optimal PQM placement problem isalso described.

4.1. BGSA

BGSA is a probabilistic optimization algorithm introduced anddeveloped by [18]. Similar to PSO, this algorithm was originally de-signed to solve problems in continuous valued space. The searchalgorithm is based on the metaphor of gravitational interaction

between masses in Newton’s theory. A jth bit of the ith agent(xij) in a system is represented as bit 0 or 1, where a combinationof bits provides the ith agent position. The GSA operators calculatethe agent’s acceleration (aij) based on gravitational force and theagent’s mass in each iteration with the following equations.

GðtÞ ¼ G0 1� tT

� �ð11Þ

FkijðtÞ ¼ GðtÞMiðtÞ �MkðtÞ

RikðtÞ þ eðxkjðtÞ � xijðtÞÞ ð12Þ

FijðtÞ ¼X

k2Kbest;k–i

r � FkijðtÞ ð13Þ

aijðtÞ ¼FijðtÞMiðtÞ

ð14Þ

where G0 is the initial gravitational constant; T is the total numberof iterations; F is the gravitational force action; M is the agent grav-itational mass; Rik is the Hamming distance between ith agent andkth agent; e is the small positive coefficient, 2�52; and Kbest is theselection number of the best agent applying force to a system. Kbestdecreases monotonously in percentage from Kbestmax to Kbestmin asthe iteration progresses.

The next agent’s velocity (vij) is calculated based on its currentvelocity and acceleration as expressed in Eq. (15). Then, a newagent’s position (xij) is updated using the condition shown in Eq.(16). However, the velocity is limited within interval [�6,6] toachieve a good convergence rate.

mijðt þ 1Þ ¼ r � mijðtÞ þ aijðtÞ ð15Þ

xijðt þ 1Þ ¼ xijðtÞ; if r < j tanhðmijðt þ 1ÞÞjxijðtÞ; otherwise

(ð16Þ

4.2. QBGSA

The first quantum-inspired computing method was introducedby [19]. This method is a numerical computational technique thatemploys the principle of quantum mechanics. The smallest unit forquantum computing, which is known as quantum bit (Q-bit), maybe in the ‘‘1’’ state, in the ‘‘0’’ state, or superposition of the two cor-responding to the weighting factors of a complex number (a,b) asrepresented in Eq. (17). The |a|2 and |b|2 in the representation pro-vide a probability that the Q-bit is in the ‘‘0’’ state and ‘‘1’’ state,respectively. Thus, the state probability can be normalized to unityas |a|2 + |b|2 = 1.

jWi ¼ aj0i þ bj1i ð17Þ

Similar to the particle’s position in BGSA, all the decision vari-ables (xij) can be represented by a string of Q-bits as a single rep-resentation called as the Q-bit individual. In quantum computing,the Q-bit individual is updated with a quantum gate (Q-gate),which is basically a unitary operator, U. The quantum gate canbe in the form of a rotation gate, an NOT gate, a controlled NOTgate, or a Hadamard gate [20]; it is used to change the probabilityof the Q-bit state to achieve a reversible formation. The rotationgate is considered in this study because it has been applied withthe search algorithm as performed in [21–23]. The rotation gateis expressed as follows:

UðDhÞ ¼cosðDhÞ � sinðDhÞsinðDhÞ cosðDhÞ

� �ð18Þ

In the proposed QBGSA, a rotation angle (Dh) is utilized todetermine the new agent’s position, xij. Therefore, the concept ofacceleration updating procedure (aij) in BGSA is applied to obtainthe rotation angle. The magnitude of the rotation angle (h) is uti-lized to replace the gravitational mass. To reduce exploration that

non-self antigens

self antigens

T cellsfrom

Infected cell

Fig. 2. Neutralization of the pathogenic effect process in immune system response.

1- for j = 1 to maximum population 2- for k = 1 to maximum TMRA row, do3- constraint = TMRA(k,:)*MP(j,:)T

4- if constraint < 1, do5- NS = {location of entry ‘1’ in TMRA(k,:)} 6- rd = Randomly select the location in NS 7- MP(j,rd) = 1 8- end if9- end for10- end for

Fig. 3. Pseudo algorithm in the adaptive process to meet the optimizationconstraints.

408 A.A. Ibrahim et al. / Electrical Power and Energy Systems 57 (2014) 404–413

depends largely on a randomized process, the random variables inEqs. (13) and (15) are removed. As a result, the agent’s acceleration,aij, is the total gravitational force action from the other agents anddepends on their mass and distance to a particular agent. Thesetwo elements are provided by a decision parameter, c, in QBGSA.In this study, similar variation operators as those in [23], whichare called the coordinate rotation gate and dynamic magnituderotation angle, are employed. The rotation angle is provided bythe following expression.

DhijðtÞ ¼X

k2Kbest;k–i

h� cki � ðxkjðtÞ � xijðtÞÞ

ð19Þ

where h is the magnitude of the rotation angle; it monotonously de-creases from hmax to hmin during the iteration. ck

i is obtained withthe following conditions.

kki ¼

1; if MðkÞ > MðiÞ and Rik 6 s0; if elsewhere

�ð20Þ

cki ¼

kki þ 1; if f ðXkÞ ¼ f ðXbestÞ

kki ; otherwise

(ð21Þ

where s is the maximum number of different bits between the ithagent and the kth agent from the percentage of total bits regardedas effective force action on the ith agent.

The attraction force by a far agent is considered very small andcan be neglected. However, the best fitness agent with the highestmass can provide an effective force on the agent even if its positionis far from the ith agent and will provide a twice effective forcethan the other forces when its position is near the ith agent. Forthis reason, only the heavy kth agent can provide effective acceler-ation on the ith agent. Meanwhile, a light agent can move easilycompared with a heavy agent because of its inertia mass actionagainst motion [18].

The QBGSA operators update the Q-bit individual string basedon the obtained rotation angle using the rotation gate providedin Eq. (22). The agent’s position (xij) is updated based on the prob-ability of |b|2 stored in the Q-bit individual using the criteria pro-vided in Eq. (23).

aijðt þ 1Þbijðt þ 1Þ

� �¼ UðDhijðtÞÞ �

aijðtÞbijðtÞ

" #ð22Þ

xijðt þ 1Þ ¼ 1; if r < jbijðt þ 1Þj2

0; otherwise

(ð23Þ

where r is a random variable in interval [0,1].

4.3. QBGSA with adaptive concept using AIS

In the optimization procedure described in the previous section,rejection may occur in the algorithm when the suggested solutiondoes not fulfill the optimization constraints; thus, another feasiblesolution must be established. In addition, a randomized initial pop-ulation is required in the beginning of the optimization process;this condition requires much time to search for a solution whenlimited feasible solutions exist. To overcome this problem, param-eter a is increased to increase the sensitivity of the monitoringscheme and reduce the number of feasible solutions. An adaptiveprocess is required to make the algorithm flexible while maintain-ing the computational speed.

In this study, the proposed adaptive process is based on the im-mune system response of T cells against foreign pathogens in theAIS concept [24]. The immune system, which is illustrated inFig. 2, is responsible for neutralizing all pathogenic effects ordestroying infected cells that are classified as ‘‘non-self’’ cells.

However, the neutralization mechanism appears to be a more suit-able and appropriate concept for the problem in this study. In thismechanism, the infected cell produces non-self-antigens, whichare fragmented pathogen proteins, and self-antigens, which arefragmented self-proteins, and then displays the antigens on its sur-face. Simultaneously, the T cells with a specific receptor are sto-chastically produced in the thymus, which is an immune organ.Only the T cells whose receptor matches the non-self-antigensare released to the bloodstream after going through the negativeselection process in the thymus. Each T cell binds with the recog-nized non-self-antigens and becomes inactivated non-toxic anti-gens. These T cells cannot bind with self-antigens because theirreceptors do not match. Finally, the infected cell is completely neu-tralized when all the non-self-antigens on the infected cell’s sur-face are bonded; the infected cell is then recognized as a ‘‘self’’ cell.

In applying AIS to solve the optimal PQM placement problem,the MP vectors produced in the optimization algorithm are recog-nized as non-self cells when they do not fulfill the constraints inEq. (10) and are recognized as self-cells otherwise. Instead ofchanging the entire string of the MP vector, bits manipulationcan be performed to adapt to the aforementioned constraints.The manipulation can be performed by randomly replacing ‘‘1’’ inthe non-self MP vector, which represents the binding mechanismbetween the T cells and the non-self-antigens. The replacementis specified to locations of entries ‘‘1’’ in a particular row of TMRAthat does not fulfill the constraints. The determination is based onthe condition where the constraint is not fulfilled only if mismatchexists between entry ‘‘1’’ in the particular TMRA row and the MPvector. This determination process follows negative selection inthe thymus to produce specific T cells to attack the target antigens.Thus, the particular constraint is fulfilled after entry ‘‘1’’ is placedat one of the locations. The process ceases when the MP vector isfully adapted to the optimization constraints and can be utilizedin the next process. A pseudo code of the process is shown in Fig. 3.

4.4. Implementation of adaptive QBGSA to solve the optimal PQMplacement problem

Optimization explores the optimal solution as defined in theobjective function by manipulating the bits of the decision vector

Start

Develop T matrix Obtain MRA matrix

Conduct the power flow and short circuit analysis

Generate initial population of agent (MP vector)

Construct TMRA matrix

Calculate SL and SSI

Evaluate fitness of each agent

Obtain NRM, MOI and NSSI

Update θ, the best and worst agent (PQM placement) in the population

Calculate mass (M) and rotation angle (Δθ) for each agent

Update Q-bit individual and the agent’s position (New MP vector)

Are all agents fulfill the

constraints

Optimal PQM Placement

Are best and worst fitness

equal?

Manipulate agent’s position using artificial immune system

as to fulfill the constraints

NO

YES

YES

NO

Fig. 4. Implementation of adaptive QBGSA for optimal PQM placement.

A.A. Ibrahim et al. / Electrical Power and Energy Systems 57 (2014) 404–413 409

subject to the optimization constraints in each generation. The pro-cess is iterated for a fixed number of times or until a convergencecriterion is achieved. The following are the steps in implementingthe adaptive QBGSA to determine the optimal PQM placement inthe power system.

Step 1: Power flow and short circuit analyses are implemented.Step 2: SL is calculated, and an SSI matrix is formed. The MRAmatrix is constructed simultaneously based on the short circuitresults.

Table 1Parameter settings used in GA, BPSO, BGSA, QPSO, and QBGSA.

Parameter GA BPSO BGSA QBPSO QBGSA

Population size 40 40 40 40 40Max. iteration 150 150 150 150 150c1 and c2 – 2 – – –G0 – – 100 – 100wmin/hmin – 0.4 – 0.001p 0.001pwmax/hmax – 0.9 – 0.050p 0.050pCrossover rate 0.95 – – – –Mutation rate 0.05 – – – –Kbestmin – – 2.5% – 2.5%Kbestmax – – 100% – 100%Effective distance (s) – – – – 8%

Step 3: The T matrix is developed from the network configura-tion, and the TMRA matrix is constructed.Step 4: All entries of the MP vectors (agent’s positions, xij) in thesystem are randomly initialized. The Q-bit individual values areset as 1=

ffiffiffi2pþ j1=

ffiffiffi2p

for all entries.Step 5: If the MP vectors do not fulfill the mentioned constraints,the entries of each MP vectors are manipulated with AIS to ful-fill the constraints.Step 6: All the PQM placement evaluation indices, namely, NRM,MOI, and NSSI, are obtained.Step 7: The performance of each MP vector is evaluated with theformulated objective function (f) based on the obtained indices.The fitness values for each agent, fi(t), are recorded.Step 8: The magnitude of the rotation angle, h, and the best andworst fitness values are updated with the following equations.

hðtÞ ¼ hmax þ hmin 1� tT

� �ð24Þ

bestðtÞ ¼ mini2f1;...;Ng

fiðtÞ ð25Þ

worstðtÞ ¼ maxi2f1;...;Ng

fiðtÞ ð26Þ

Step 9: Each agent’s mass (Mi) is calculated with the equation

MiðtÞ ¼miðtÞPNi¼1miðtÞ

ð27Þ

where

miðtÞ ¼fiðtÞ �worstðtÞ

bestðtÞ �worstðtÞ ð28Þ

Step 10: The rotation angle of each agent, Dhij(t + 1), is updatedwith

DhijðtÞ ¼X

k2Kbest;k–i

h� cki � ðxkjðtÞ � xijðtÞÞ

ð29Þ

where

kki ¼

1; if Mk > Mi and Rik 6 s0; if elsewhere

�ð30Þ

cki ¼

kki þ 1; if f ðXkÞ ¼ f ðXbestÞ

kki ; otherwise

(ð31Þ

Step 11: The new pair a(t + 1), b(t + 1) of each Q-bit individual,Q-bit(t + 1), is obtained as follows:aijðt þ 1Þbijðt þ 1Þ

" #¼

cosðDhijðt þ 1ÞÞ � sinðDhijðt þ 1ÞÞsinðDhijðt þ 1ÞÞ cosðDhijðt þ 1ÞÞ

� ��

aijðtÞbijðtÞ

" #:

ð32Þ

Step 12: Each MP vector to a new position, xij(t + 1), is updatedwith the following criteria.

xijðt þ 1Þ ¼ 1; if r < jbijðt þ 1Þj2

0; otherwise

(ð33Þ

Step 13: Steps 5–12 are repeated until convergence is obtained,where the best fitness value is equal to the worst fitness value.Upon convergence, the optimal PQM placement is obtained.The overall procedure in the optimal PQM placement method

using adaptive QBGSA is shown in a flowchart in Fig. 4.

5. Test results and discussion

The performance of QBGSA is compared with that of other heu-ristic optimization techniques, namely, GA [15], BPSO [25], QBPSO[26], and BGSA [27], to demonstrate the effectiveness of QBGSA insolving the optimal PQM placement problem. Two test systems,

Table 2Performance of GA, BPSO, BGSA, QBPSO, and QBGSA in obtaining the optimal PQM placement solution for the 69-bus system.

Technique Convergence rate (iterations) Fitness value

Best Average Worst r Best Average Worst r

GA 73 124.1 149 21.67 20.06 24.72 32.33 4.11BPSO 11 25.8 55 11.51 35.89 47.65 62.32 6.07BGSA 137 143.8 149 3.91 19.85 23.95 35.53 3.81QBPSO 30 84.3 145 39.64 18.37 20.44 23.32 1.54QBGSA 48 111.2 150 30.33 18.28 19.94 23.03 0.77

Fig. 5. Convergence characteristics of GA, BPSO, BGSA, QBPSO, and QBGSA for the69-bus system.

Fig. 6. Convergence characteristics of GA, BPSO, BGSA, QPSO, and QBGSA for the118-bus system.

410 A.A. Ibrahim et al. / Electrical Power and Energy Systems 57 (2014) 404–413

namely, the 69-bus distribution system and the IEEE 118-bustransmission system, are utilized in the case study. The new adap-tive QBGSA technique is then compared with the original QBGSA toevaluate its performance in terms of computation time and mini-mum number of PQMs at different a values. Three-phase faults,double-line to ground faults, and single-phase to ground faultswere simulated at each bus in the test systems with 0 O faultimpedance. The FV matrix is obtained with the DIgSILENTsoftware.

Table 3Optimal placement of PQM for the 69-bus system identified by GA, BPSO, BGSA, QBPSO, a

Technique Fitness value Numbe

GA 20.06 8BPSO 35.89 12BGSA 19.85 8QBPSO 18.37 8QBGSA 18.28 8

Table 4Performance of GA, BPSO, BGSA, QPSO, and QBGSA in obtaining the optimal PQM placeme

Technique Convergence rate (iterations)

Best Average Worst r

GA 114 139.3 150 9.4BPSO 13 34.2 92 20.7BGSA 114 135.4 148 9.1QBPSO 75 119.7 149 22.4QBGSA 78 128.4 150 21.5

5.1. Comparative study of optimization techniques

As mentioned previously, the QBGSA optimization technique iscompared with GA, BPSO, BGSA, and QBPSO to compare theeffectiveness of the techniques in solving the same problem. Theobjective of this comparison is to select the most appropriate opti-mization technique for solving the optimal PQM placement prob-lem. To ensure a fair comparison, all the optimization parametersare standardized as shown in Table 1. The table shows the required

nd QBGSA for a = 0.85 p.u.

r of PQMs PQM placement location (bus)

1, 6, 26, 30, 33, 38, 49 and 631, 5, 6, 29, 31, 35, 38, 44, 48, 49, 64 and 691, 6, 26, 30, 34, 38, 49 and 641, 6, 29, 32, 37, 41, 48 and 571, 6, 29, 32, 36, 38, 48 and 57

nt solution for the 118-bus system.

Fitness value

Best Average Worst r

6 40.73 63.97 106.12 14.061 108.68 149.7 181.96 16.382 77.31 101.8 135.40 16.574 30.06 36.65 45.70 5.160 26.22 30.58 39.92 3.27

Table 5Optimal placement of PQM for the 69 bus system identified by GA, BPSO, BGSA, QBPSO and QBGSA for a = 0.85 p.u.

Technique Fitness value Number of PQMs PQM placement location (bus)

GA 40.73 13 11, 22, 39, 45, 53, 62, 71, 83, 86, 89, 98, 101 and 104BPSO 108.68 23 7, 17, 18, 19, 32, 36, 46, 47, 54, 55, 61, 73, 79, 81, 85, 86, 90, 92, 98, 104, 106, 110 and 118BGSA 77.31 19 9, 11, 15, 23, 37, 43, 45, 58, 67, 69, 75, 80, 82, 85, 88, 98, 100, 103 and 106QBPSO 30.06 11 6, 22, 43, 52, 60, 71, 80, 87, 92, 98 and 105QBGSA 26.22 10 6, 22, 43, 56, 62, 71, 87, 93, 98 and 108

Table 6Performance of QBGSA with and without adaptive element on the 69-bus system atdifferent a values.

a Value (p.u.) QBGSA Adaptive QBGSA

Fitness value Time (s) Fitness value Time (s)

0.85 18.281 40.19 18.281 15.450.75 27.813 243.73 27.813 16.210.65 26.006 565.76 26.006 16.280.55 40.774 30354.85 40.732 16.43

Table 8Performance of QBGSA with and without adaptive element on the 118-bus system.

a Value (p.u.) QBGSA Adaptive QBGSA

Fitness value Time (s) Fitness value Time (s)

0.85 26.217 345.87 26.217 28.220.75 53.414 6958.69 53.379 29.56

A.A. Ibrahim et al. / Electrical Power and Energy Systems 57 (2014) 404–413 411

parameter settings for all the optimization techniques utilized inthis study.

5.1.1. Case study I: 69-bus systemThe 69-bus test system has a balanced radial distribution and is

fed by an external grid to a feeder nominal voltage at 12.66 kV. Thesystem consists of 69 buses interconnected by 73 lines, including 5tie lines. The system data are provided in [28]. Table 2 shows theworst, average, best, and standard deviation (r) values obtainedfrom the performances of the various optimization techniques interms of convergence rate and quality of the optimal solution afterperforming 25 runs at a = 0.85 p.u.. Fig. 5 shows the convergencecharacteristics of the techniques in obtaining the best optimalsolution for the test system. As indicated by the results shown inTable 2, QBGSA provides the most accurate optimal solution com-pared with the other optimization techniques because it has thelowest fitness function value of 18.28 and the lowest standarddeviation value of 0.77. QBPSO provides the second-best optimalsolution. The difference in the best fitness value of these two tech-niques is very small, that is, 0.09. QBPSO is then followed by BGSAand GA with best fitness function values of 19.85 and 20.06,respectively. BPSO provides the worst performance with the high-est fitness function value of 35.89. The results shown in Fig. 5 indi-cate that QBPSO exhibits the fastest convergence compared withthe other techniques. Initially, BPSO exhibits an almost similar con-vergence rate to that of QBPSO. However, BPSO exhibits prematureconvergence after some time. In terms of overcoming the problemof premature convergence and providing an improved optimalsolution, QBPSO and QBGSA exhibit a significant improvementcompared with BPSO, BGSA, and GA. The figure also shows thatBGSA exhibits the slowest convergence compared with the othertechniques. However, in terms of accuracy, BGSA is better thanBPSO as indicated by the standard deviation results shown in Table2. Comparing all the optimization techniques, QBGSA provides thebest optimal solution because of its accuracy and lowest standard

Table 7Number and placement of PQM with different a values in the 69-bus system.

a Value (p.u.) Fitness value Number of PQMs

0.85 18.281 80.75 27.813 110.65 26.006 110.55 40.732 150.45 51.614 18

deviation. Although QBGSA’s convergence rate is slightly slowerthan that of QBPSO, we conclude that QBGSA is the most effectivetechnique. Table 3 shows the number and optimal location ofPQMs for the 69-bus system. QBGSA identifies eight PQMs to be in-stalled at buses 1, 6, 29, 32, 36, 38, 48, and 57 for the 69-bus sys-tem based on the lowest best fitness value.

5.1.2. Case study II:IEEE 118-bus systemThe IEEE 118-bus test system is a balanced transmission system

that consists of two voltage levels, namely, 138 and 345 kV. Thissystem has 34 generating stations, 20 sychronous condensers,and 9 transformers. The test system consists of 118 buses intercon-nected by 177 lines. The IEEE 118-bus test system data are pro-vided in [29]. Table 4 shows the performances of the techniquesin terms of convergence rate and quality of the solution after per-forming 50 runs. As shown in the table, QBGSA is the most accurateoptimization technique because it provides the lowest best fitnessvalue (26.22) and lowest standard deviation value (3.27). QBPSOprovides the second-best accurate solution with its best fitness va-lue of 36.65 and standard deviation value of 5.16. The other opti-mization techniques produce high best fitness and standarddeviation values and are considered inaccurate.

Fig. 6 shows the best convergence characteristic of each tech-nique in obtaining the optimal solution for the 118-bus system.BGSA provides the slowest convergence rate, and GA has a betterconvergence rate compared with BGSA. The use of quantum com-puting in BGSA and BPSO enabled QBGSA and QBPSO to improvethe convergence rate in obtaining the optimum solution. The con-vergence rates of QBPSO and QBGSA are almost similar; however,QBGSA provides the best optimal solution because it is the mostaccurate as it provides the lowest standard deviation value. Table5 shows the number and location of PQMs for the IEEE 118-bussystem based on the best fitness values calculated by the variousoptimization techniques. As shown in the table, QBGSA providesthe lowest number of PQMs, in which only 10 PQMs are requiredto be installed at buses 6, 22, 43, 56, 62, 71, 87, 93, 98, and 108of the 118-bus system. Hence, we conclude that QBGSA is the most

PQM placement at bus

1, 6, 29, 32, 36, 38, 48 and 571, 6, 15, 29, 31, 34, 37, 41, 48, 50 and 581, 6, 13, 29, 30, 33, 37, 41, 48, 49 and 571, 5, 6, 14, 29, 30, 33, 35, 37, 41, 48, 49, 52, 57 and 671, 5, 6, 7, 10, 15, 29, 30, 33, 34, 37, 38, 41, 48, 49, 56, 58 and 69

Table 9Number and placement of PQM with different a values on the IEEE 118-bus system.

a Value(p.u.)

Fitnessvalue

Number ofPQMs

PQM placement at bus

0.85 26.217 10 6, 22, 43, 56, 62, 71, 87, 93, 98 and 1080.75 53.379 20 8, 22, 27, 37, 42, 45, 45, 50, 52, 62, 69,71, 74, 82, 86, 91, 98, 99, 102, 109 and 1170.65 83.017 30 3, 10, 13, 16, 22, 26, 31, 33, 42, 44, 46, 50, 52, 59, 67, 72, 73, 75, 79, 81, 86, 90, 93, 96, 98, 99, 102, 105, 112 and 1170.55 95.418 37 1, 10, 13, 14, 16, 17, 22, 25, 28, 33, 34, 40, 44, 47, 48, 52, 57, 59, 61, 67, 71, 72, 78, 85, 87, 91, 93, 96, 97, 98, 99, 101, 107, 110,

116, 117 and 118

Table 10Voltage sag monitored by PQM on the 69-bus system considering 100 faults and different a values.

a Value (p.u.) Number of faults

Voltage sag wrongly monitored Voltage sag monitored by 1 PQM (no repetition) Voltage sag monitored by P2 PQM (with repetition)

0.85 0 66 340.90 5 83 12

Table 11Voltage sag monitored by PQM on the IEEE 118-bus system considering 100 faults and different a values.

a Value (p.u.) Number of faults

Voltage sag wrongly monitored Voltage sag monitored by 1 PQM (no repetition) Voltage sag monitored by P2 PQM (with repetition)

0.85 0 31 690.90 3 53 44

412 A.A. Ibrahim et al. / Electrical Power and Energy Systems 57 (2014) 404–413

suitable optimization technique to be applied to solve the optimalPQM placement problem.

5.2. Implementation of adaptive element

Adaptive QBGSA is tested on the studied test systems and com-pared with the standard QBGSA to verify the former’s effectiveness.Table 6 shows the comparison of the results of QBGSA and adaptiveQBGSA in terms of fitness value and computation time at differenta values for the optimal placement of PQM in the 69-bus test sys-tem. The results indicate that the fitness function values of the twotechniques are similar at various a values except at a = 0.55 p.u., inwhich adaptive QBGSA has a lower fitness value of 40.732 com-pared with the standard QBGSA with a fitness value of 40.774. Interms of computation time, adaptive QBGSA provides a much fas-ter solution compared with standard QBGSA. At different computa-tion times and a values, both of these techniques provide the sameoptimal number of PQM as shown in Table 7. The table shows thatthe fitness value decreases from 27.813 (a = 0.75 p.u.) to 26.006(a = 0.65 p.u.). This decrease may be due to the fact that at thesetwo a values, the number of PQM is similar, that is, 11. By decreas-ing the a value, the number of PQM increases and each PQM cov-erage area becomes small.

Table 8 shows the results of QBGSA and adaptive QBGSA interms of fitness function values and computation times at differenta values for the IEEE 118-bus system. As shown in the table, adap-tive QBGSA requires much less computation time in obtaining theoptimal solution compared with QBGSA. Hence, the adaptive ele-ment helps the algorithm speed up its computation. Table 9 showsthe optimal number of PQM and the locations of PQMs at differenta values in the IEEE 118-bus system.

5.3. Optimal placement of PQM by adaptive QBGSA

The adaptive QBGSA is applied to the aforementioned test sys-tems to determine whether the PQMs placed at the optimal loca-tions are able to monitor the voltage sags in the systems. One

hundred fault simulations that produce voltage sags are conductedat various bus and line locations in the 69-bus and 118-bus testsystems. Tables 10 and 11 provide a summary of the results forthe two test systems, respectively, in terms of voltage sags incor-rectly monitored by PQM and voltage sags monitored by onePQM and more than two PQMs at different a values. Referring tothe results in Table 10, for a = 0.90 p.u., five voltage sags wereincorrectly monitored by PQM. However, for a = 0.85 p.u., no volt-age sag was incorrectly monitored. For the voltage sags monitoredby more than two PQMs, 34 faults that resulted in voltage sagswere monitored more than once at a = 0.85 p.u., whereas 12 faultswere monitored at a = 0.90 p.u. This condition caused overlappingin the monitor coverage area.

Referring to the results in Table 11, for a = 0.85 p.u., no voltagesag was incorrectly monitored. However, for a = 0.90 p.u., threevoltage sags were incorrectly monitored by PQM. For the voltagesags monitored by more than two PQMs, 69 faults that resultedin voltage sags were monitored more than once at a = 0.85 p.u.,whereas 44 faults were monitored at a = 0.90 p.u. However, a moreaccurate PQM monitoring of voltage sags is achieved ata = 0.85 p.u. compared with a = 0.9 p.u.

6. Conclusions

The performances of GA, BPSO, BGSA, QBPSO, QBGSA, and a no-vel adaptive QBGSA in solving the multi-objective optimizationproblem for optimal PQM placement were compared in this study.The optimization problem formulation was mainly based on theuse of TMRA and two placement evaluation indices, namely, SSIand MOI. Five different optimal PQM placement programs wereimplemented on the 69-bus and IEEE 118-bus test systems to re-veal the most suitable optimization techniques. QBGSA providesthe best optimal PQM placement results in terms of computationspeed and accuracy compared with GA, BPSO, BGSA, and QBPSO.QBGSA was also compared with adaptive QBGSA in terms of accu-racy in determining the optimal PQM placement and computationtime required to obtain the solution at different voltage threshold

A.A. Ibrahim et al. / Electrical Power and Energy Systems 57 (2014) 404–413 413

levels or a values. The comparison results reveal that adaptiveQGBSA provides better optimal PQM placement in terms of compu-tational speed than the standard QGBSA. Thus, adaptive QBGSA isthe most effective and accurate approach among GA, BPSO, BGSA,QBPSO, and standard QBGSA.

Acknowledgment

The authors are grateful to Universiti Kebangsaan Malaysia(UKM) for supporting this study under grants DIP-2012-30 andETP-2013-044.

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