Electrical Power and Energy Systems 54 (2014) 123–133

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Electrical Power and Energy Systems

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Optimum network reconfiguration based on maximization of systemloadability using continuation power flow theorem

0142-0615/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.ijepes.2013.06.026

⇑ Corresponding author. Tel.: +60 3 7967 5348; fax: +60 3 7954 7551.E-mail address: mohsinaman@gmail.com (M.M. Aman).

M.M. Aman a,⇑, G.B. Jasmon a, A.H.A. Bakar b, H. Mokhlis a,b

a Department of Electrical Engineering, Faculty of Engineering, University of Malaya, 50603 Kuala Lumpur, Malaysiab UM Power Energy Dedicated Advanced Centre (UMPEDAC) Level 4, Wisma R&D, University of Malaya, Jalan Pantai Baharu, 59990 Kuala Lumpur, Malaysia

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

Article history:Received 9 July 2012Received in revised form 20 June 2013Accepted 29 June 2013

Keywords:Continuation Power Flow (CPF)Discrete Artificial Bee Colony (DABC)Graph theoryLoadability

This paper presents a new algorithm for network reconfiguration based on maximization of system loa-dability. Bifurcation theorem known as Continuation Power Flow (CPF) theorem and radial distributionload flow analysis are used to find the maximum loadability point. Network reconfiguration results arealso compared with existing technique proposed in literature. In the proposed method, to find the opti-mum tie-switch position, a Discrete Artificial Bee Colony (DABC) approach is applied. Graph theory isused to ensure the radiality of the system. The proposed algorithm is tested on 33-bus and 69-bus radialdistribution networks, each having 5-tie switches. The result shows that using the proposed method thekVA margin to maximum loading (KMML) increases, overall voltage profile also improved and the distri-bution system can handle more connected load (kVA) without violating the voltage and line current con-straints. Results further show that the voltage limit is an important factor than the line currentconstraints in adding further load to the buses.

� 2013 Elsevier Ltd. All rights reserved.

1. Introduction

With the ever increasing load demand and the lack of capitalinvestment in the transmission system, the importance of enhanc-ing the existing distribution system capacity has increased. Thesystem capacity is usually limited by two factors, namely thermallimits and voltage limits. Thermal limit or thermal capacity is theampacity or maximum current carrying capacity limit of the con-ductor. The current carrying capacity is limited by the conductor’smaximum design temperature [1]. However the voltage limit is theallowable minimum–maximum voltage variation for safe opera-tion of power system and connected load. The study in [2] has con-cluded that the maximum loadability of the distribution system islimited by the voltage limit rather than the thermal limit.

In literature, minimization of losses in power system was amajor concern for power system researchers. Among differenttechniques for power loss reduction including Distributed Genera-tion (DG) placement and shunt capacitor placement, networkreconfiguration is also utilized. Network reconfiguration is definedas altering the topological structures of the distribution feeders, bychanging the position of tie and sectionalizing switches. Networkreconfiguration is a key tool in operation of medium voltage distri-bution system and in improving the reliability of the system. Thestructure of medium voltage distribution network is designed

mesh, provided with tie and sectionalizing switches. However un-der normal operation, medium voltage distribution networks oper-ates in radial manner [3,4].

Most of the researchers have considered power losses as anobjective function in network reconfiguration. Analytical andheuristic search based optimization techniques have been utilizedby different researchers to perform the network reconfiguration.Authors have formulated the problem in different manners. In[3], Civanlar has analyzed the problem of network reconfigurationconsidering minimization of losses, load flow based approach wasutilized. In [5], Baran and Wu extended the work of [3] and in-cluded a new load balancing index in addition to minimization oflosses, simplified load flow approach is used. In [6], Shirmoham-madi utilized the heuristic approach to find the minimum lossesof the network. The radial system is converted to mesh, later-onoptimum power flow pattern is made and the branch carryingthe minimal current is removed.

Later on, several optimization based algorithms have beendeveloped considering minimization of losses as an objectivefunction. Zhu utilized the refined genetic algorithm [7], Venkateshet al. utilized the Fuzzy adaptation of Evolutionary Programmingtechnique [8], Zhu et al. performed the network reconfigurationbased on modified heuristic solution and experience system oper-ation rules [9]. Srinivasa et al. in [10] used the Harmony SearchAlgorithm, Sathish in [11] solved the problem using BacterialForaging Algorithm, Yuan-Kang et al. [12] utilized the Ant ColonyAlgorithm. de Oliveria et al. [13] mixed the problem of network

Predictor

BAPredictor

124 M.M. Aman et al. / Electrical Power and Energy Systems 54 (2014) 123–133

reconfiguration with capacitor placement considering minimiza-tion of total energy loss as an objective function. Zin et al. in [14]has used the heuristic search algorithm to find the minimumpower losses as an objective function, introduced by the authorin [5]. The update principle of heuristic search is made by findingthe branch having minimal current, till the optimum solution ismade. In the latest research, Rao et al. in [15] has combined thenetwork reconfiguration with distributed generation placement,considering minimization of power losses as fitness function. Mostof the existing research is based on finding optimum tie switchcombinations based on minimization of power losses.

In the present study, a new strategy, based on voltage stabilitycriteria is proposed for solving the reconfiguration problem. Theobjective is to maximize the system loading margin or kVA marginto the point of maximum loadability of the system. Loadability isdefined as the capacity of the system with which the maximumload could be connected without going into the voltage instabilityregion. Voltage stability has been used in solving other power sys-tem problems including optimal power flow solution [16] and opti-mum DG placement [17,18]. The major research consideringmaximum loadability in network reconfiguration is found in [8].In [8], the author has developed the Maximum Loadability Index(MLI) based on the voltage stability criteria and used as a fitnessfunction to solve the network reconfiguration problem. Fuzzy-EPapproach was used by the author to find the optimum tie switchcombinations.

In the proposed method, Continuation Power Flow (CPF) is usedfor finding the maximum loading margin of the system. With CPF,the maximum loadability margin or maximum loadability indexkmax is calculated which corresponds to saddle node bifurcation(SNB) point or point of voltage collapse. The CPF results will alsobe compared with the radial distribution load flow methods. Net-work reconfiguration differs from other optimization problems(e.g. DG sizing, shunt capacitor sizing, unit commitment and oth-ers), the tie switch positions always occur in a discrete manner(e.g. 7, 13, 19, 25, 28) thus a Discrete Artificial Bee Colony (DABC)approach is proposed in finding the optimum tie switch combina-tions. To ensure the radiality of the system for different switchcombinations, Graph Theory (GT) approach is applied.

The paper is organized as follows: In Section 2, the overview ofContinuation Power Flow (CPF) is presented and the mathematicalmodel is given. Section 3 presents the graph theory approach inchecking the radiality of the system for different tie switch combi-nations. Section 4 presents Discrete Artificial Bee Colony (DABC)for finding the optimum switch configuration. Section 5 providesthe definition of Voltage Deviation Index (VDI) for measuringpower quality and kVA Margin to Maximum Loadability (KMML).In Section 6, the proposed algorithm is presented and in the lastsection 7, the proposed algorithm is applied on 33-bus and 69-bus radial distribution test systems. The results are shown and alsodiscussed in detail.

Corrector

Loading parameter λ

Vol

tage

Mag

nitu

de V

C

E

D

GF

Critical Point or

Point of collapse

Exact Solution

λmax

Corrector

Fig. 1. Continuation power flow theorem – solving approach.

2. Continuation Power Flow (CPF) theorem

CPF theorem is commonly used in power system to solve theload flow problem. Most of the theorems get diverges after reach-ing the critical point or point of voltage collapse as in the case ofLimit Induced Bifurcation or Saddle-Node Bifurcation (SNB), andthus the power flow equations have no solution at SNB point. Incomparison to other power flow theorems, CPF has an advantagein terms of complete solution of nose curve even after reachingthe SNB point. CPF theorem is based on bifurcation model. Bifurca-tions occur when the system stability changes due to a change ofsystem parameters [19,20]. In CPF, predictor–corrector approachis used to solve the PV or kV nose curve, as shown in Fig. 1.

In this paper, the parameter that is used to characterize the loa-dability of the system is the maximum loadability margin kmax, asshown in Fig. 1. The loadability factor k is used to modify con-nected load as given by Eq. (1) [21]:

PL1 ¼ PL0 þ k0PD

QL1 ¼ Q L0 þ k0QD

�ð1Þ

where PL0 and QL0 are the initial active and reactive power loadsrespectively.

PG1, PL1 and QL1 are the modified active and reactive power loadsrespectively.

k0 is the initial loadability factor that multiplies variable powersPD and QD, also called power directions.

When power directions PD and QD are in the vector direction de-fined by PL0 and QL0, Eq. (1) changes to Eq. (2):

PL1 ¼ ð1þ k0ÞPL0 ¼ kPL0

QL1 ¼ ð1þ k0ÞQL0 ¼ kQ L0

�ð2Þ

where k = 1 + k0 is the loadability factor.The CPF method utilizes predictor–corrector approach for the

complete solution of PV nose curve. Predictor step is based onthe computation of the tangent vector and a corrector step is ob-tained either by means of a local parameterization or a perpen-dicular intersection [19,20,22]. For mathematical modelling ofCPF, consider a curve AC, shown in Fig. 2, given by the followingmodel

gðy; kÞ ¼ 0 ð3Þ

where y represents the state variables and k represents systemparameter used to drive the system from one state of loading toanother.

2.1. Predictor step

To find the predictor vector, consider an equilibrium point ‘P’ inFig. 2. At equilibrium point ‘P’, the following relation applies:

gðyp; kpÞ ¼ 0 ð4Þdgdk

����p

¼ 0 ¼ ryg��

p

dydk

����p

þ dgdk

����p

ð5Þ

And the tangent vector can be approximated by:

sp ¼dydk

����p

�Dyp

Dkpð6Þ

Fig. 2. Predictor vector computation.

Fig. 4. Corrector vector computation using local parameterization.

M.M. Aman et al. / Electrical Power and Energy Systems 54 (2014) 123–133 125

From Eqs. (5) and (6):

sp ¼ �rygj�1p

dgdk

����p

ð7Þ

Dyp ¼ spDkp ð8Þ

A step size control ‘k’ has to be chosen for the determinant:

Dkp ffikjjspjj

ð9Þ

Dyp ffiksp

jjspjjð10Þ

where k = ±1 and sign determines the increase or the decrease of k.

2.2. Corrector step

In the corrector step, a set of n + 1 equations are solved i.e.

gðy; kÞ ¼ 0 ð11Þqðy; kÞ ¼ 0 ð12Þ

where the solution of g must be in the bifurcation manifold and q isan additional equation to guarantee a non-singular set at the bifur-cation point. The perpendicular intersection and the local parame-terization is used to solve the equation for q.

The illustration of perpendicular intersection corrector methodis shown in Fig. 3, the expression of q is given by Eq. (13):

qðy; kÞ ¼Dyp

Dkp

� �T yc � ðyp þ DypÞkc � ðkp þ DkpÞ

� �¼ 0 ð13Þ

For the local parameterization, one of the parameter i.e. k or avariable y is forced to be a fixed to find the value of q. The choice

Fig. 3. Corrector vector computation using perpendicular intersection.

of the variable to be fixed depends on the bifurcation manifold of g,as shown in Fig. 4. The value of q in case of local parameterizationis given by

qðy; kÞ ¼ yci � ðypi þ DypiÞ ð14Þ

Or

qðy; kÞ ¼ kc � ðkp þ DkpÞ ð15Þ

In the present study, CPF theorem is used to find the fitnessfunction (maximum loadability – kmax) of proposed algorithm.To compare the CPF results, the maximum loadability will alsobe computed using radial load flow analysis. Voltage stabilityand optimization tool will be used to compute the maximumloading of the system [23]. Here it is noted that different tieswitch combinations can results in non-radiality of the system,thus the graph theory will be used to maintain the radiality ofthe system. Section 3 will present a brief overview of graph theoryapproach used in network reconfiguration to ensure the radialityof the system.

3. Graph theory for maintaining the radility of the system

Different tie switch positions in case of solving reconfigurationproblem may results in a mesh circuit. Thus a graph theory will beutilized to ensure the system is always operating in radial mannerand all buses are connected with source node. In general, the graphG (V, E) is a pair of sets mapped by the pair of vertices or nodes (V)through the edges (E). The vertices V are usually labelled asV = {v1,v2, � � � ,vn}.The vertices are said to be adjacent to each otherif they are inter-connected through an edge [24,25]. The exampleof nodes and edges are shown in Fig. 5.

(a)

Fig. 5. (a) A 6-bus radial distribution system, (b) Simplified form of 6-bus systemwith nodes (V) and edges (E).

(b)

Fig. 5 (continued)

126 M.M. Aman et al. / Electrical Power and Energy Systems 54 (2014) 123–133

In the present case, the node or vertices (V) represents thesystem buses and the edge (E) represents the distribution lines(connecting two buses). In graph theory, two different types ofgraphs are normally used i.e. directed graph and undirectedgraph. A directed graph is formed by vertices connected with di-rected edges. In directed graph, there is always a certain directionor flow in the graph between the nodes. While in undirectedgraph, the nodes are connected to each other in a bidirectionalmanner.

In the present problem of checking radiality using graph theory,it is important to create an adjacency matrix which will contain allthe information among connectivity of different nodes or buses. Tocreate the adjacency matrix, a sparse formation will be done usingthe linedata. Eq. (16) represents the adjacency matrix for the direc-ted graph according to Fig. 5. Here it can be seen that each elementin adjacency matrix aij = 1 if (i,k) 2 E and aij = 0 if (i,k) R E, where Eis a set of directed edges {(1,2),(2,3), (3,4),(2,5),(5,6)}.

A ¼

0 1 0 0 0 0

0 0 1 0 1 0

0 0 0 1 0 0

0 0 0 0 0 0

0 0 0 0 0 1

0 0 0 0 0 0

0BBBBBBBBBBBBBBB@

1CCCCCCCCCCCCCCCA

ð16Þ

Eq. (17) represents the adjacency matrix for the undirectedgraph according to Fig. 5. Here it can be seen that each elementin adjacency matrix aij = 1 if (i,k) 2 E and aij = 0 if (i,k) R E, whereE is a set of undirected edges {(1,2),(2,1),(2,3),(2,5),(3,2),(3,4),(4,3),(5,2),(5,6),(6,5)}. For undirected graph, the adjacency matrixis symmetric since the edges are bi-directional i.e. aij = aji.

A ¼

0 1 0 0 0 0

1 0 1 0 1 0

0 1 0 1 0 0

0 0 1 0 0 0

0 1 0 0 0 1

0 0 0 0 1 0

0BBBBBBBBBBBBBBB@

1CCCCCCCCCCCCCCCA

ð17Þ

In the present case of solving network reconfiguration problem,undirected graph is used. Here it can be observed that using undi-

rected graph it is easy to switch of the connection between 4–6 or6–4 (a46 = a64 = 0). However in the case of directed graph, it will beessential to determine either flow of power is 4-to-6 or 6-to-4, thenthe corresponding link can be switched off.

In order to measure the connectivity of the system, two search-ing methods are commonly used, Breadth First Search (BFS) andDepth First Search (DFS) methods [26]. In current application ofnetwork reconfiguration, DFS method is utilized. DFS methodreturns the order of the bus in the system, which is later used torearrange the line-data according to the network flow that ismapped out.

The steps in solving the network reconfiguration problem arebriefly presented here:

� Step 1: Initialize the bus system.� Step 2: Generation of sparse and Adjacency Matrix (A).� Step 3: Generation of random tie switch positions and updating

the Adjacency matrix (A).� Step 4: Checking Radiality of the system. In this step the graph is

traversed in DFS order, starting from source node1 to nth nodein the system [command: graphtraverse ()] and the path ismapped out [command: graphpred2path()]. If the length of thegraphpred2path() is found equal to 2, then the circuit isbelieved to be a radial system (status = 1), otherwise non-radial.In case of non-radiality in the system (status = 0), the programexits and Step 3 is repeated.� Step 5: Checking connectivity among nodes. If status==1, the

DFS order of the radial graph is obtained and stored in variableradial_pathmapped. For example in Fig. 5, the followingradial_pathmapped is obtained, given by Eq. (18). The lengthof radial_pathmapped must be equal to the system total nodes(nbus(traverse) = nbus(system)).

radial pathmapped ¼

1

2

3

4

5

6

0BBBBBBBBBBBBB@

1CCCCCCCCCCCCCA

ð18Þ

� Step 6 Carried out load flow analysis and compute the maxi-mum loadability of the system (kmax).Different tie-switch combinations will result in different maxi-

mum loadability, thus the optimum tie switch configuration willbe found out by using the discrete form of Artificial Bee Colony(ABC) algorithm.

4. Discrete Artificial Bee Colony (DABC)

Artificial bee colony (ABC) is one of the most recently pro-posed algorithm in optimization, introduced by Karaboga andBasturk [27]. ABC is inspired from the foraging behavior ofhoneybees. The bee colony consists of three different groupsof bees including employed bees, onlookers and scouts. Initiallyemployed bees and onlookers are divided into halves. Oneemployed bee is employed for every single food source.Employed bee from their memory determined a food sourcewithin the neighborhood of the food source. Employed beeexchange information with onlookers within the hive and thenthe onlookers select one of the food sources. When employedbee has an abandoned of food source, it becomes a scoutbee and starts to search a new food source randomly. Thusa scout bee is an x-employed bee.

Fig. 6. Effect of network reconfiguration on kVA margin to maximum loadability.

Table 1Proposed Discrete Artificial Bee Colony (DABC) method for optimum tie switch positions.

Parent solution a1 a2 a3 a4 a5

The randomization process is startedFirst run

First tie position is randomly replaced xi1 a2 a3 a4 a5

Second tie position is randomly replaced a1 xi2 a3 a4 a5

Third tie position is randomly replaced a1 a2 xi3 a4 a5

Fourth tie position is randomly replaced a1 a2 a3 xi4 a5

Fifth tie position is randomly replaced a1 a2 a3 a4 xi5

The randomization process is again repeatedSecond run

First tie position is randomly replaced yi1 a2 a3 a4 a5

Second tie position is randomly replaced a1 yi2 a3 a4 a5

Third tie position is randomly replaced a1 a2 yi3 a4 a5

Fourth tie position is randomly replaced a1 a2 a3 yi4 a5

Fifth tie position is randomly replaced a1 a2 a3 a4 yi5

M.M. Aman et al. / Electrical Power and Energy Systems 54 (2014) 123–133 127

The operation of Discrete Artificial Bee Colony (DABC) is nearlysimilar to the original ABC except in terms of searching new foodsearching procedure (mutation). In the DABC, the Employed andOnlooker Bees will search the new food source at the neighborhoodlocation that exists in their memory in greedy manner. The muta-tion process of DABC in case of solving network reconfiguration isshown in Table 1.

Here it can be observed that in DABC certain level of heuristicknowledge is retained based upon last feasible solution to ensurefast convergence in the optimization process. In mutation processof DABC, each parent solution [a1, a2, a3, a4, a5] is mutated in diag-onal manner to obtain the next generation. A single line switch(e.g. a1) is randomly changes at each ith run (a1 ? xi1). Here xi rep-resents the new tie switch for the first run and yi represents thenew tie switch for the second run that is randomly generated.The continuation power flow is run for each successful switch com-bination (radial system only) and maximum loadability margin ismeasured. The process of searching by employed, onlooker andscout bees are continue until it reaches the maximum number ofiteration.

5. Voltage Deviation Index (VDI) and kva margin to maximumloadability (KMML)

In [8], the author has developed the Voltage Deviation Index(VDI) to quantify the power quality of the distribution network.For an N-bus radial network, VDI is defined in:

VDI ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPNVBi¼1 ðVi � VLimitðiÞÞ2

N

sð19Þ

where NVB are the number of buses that violate the voltage limits.VLimit is the upper or lower limit of the ith bus voltage magni-

tude when the respective upper or lower limit violation occurs, isgiven by

Vmin � VLimit � Vmax ð20Þ

In the present case,

0:95 � VLimit � 1:05 ð21Þ

kVA Margin to Maximum Loadability (KMML) is defined in [28] torepresent the additional load from the operating point ‘O’ to thepoint of voltage collapse, as shown in Fig. 6.

From Fig. 6, it can be observed that the curve A (with optimumnetwork reconfiguration) will have a better voltage profile thancurve B at each loading. Further it can also be noted that usingthe optimum network reconfiguration, the operating point of thesystem (kV) can be increased from O1 to O2 (within the allowablebranch current limits (ILimit) and voltage limits VLimits).

6. Proposed algorithm for optimum network reconfiguration

In this section, a new algorithm is proposed for optimum net-work reconfiguration on the basis of maximization of system loa-dability. CPF will be used to find the maximum loading margin.The CPF results will also be compared with radial load flow analy-sis [29]. To find the maximum loadability or loading factor (kmax) ofthe system, the active and reactive load is increased on all buses(using Eq. (22)) with equal loading factor of 0.01, till the divergenceis observed.

Pnew ¼ P0 � Loading FactorðkÞQ new ¼ Q 0 � Loading FactorðkÞ

�ð22Þ

where k is a loading factor, Po and Qo is initial active and reactivepower load, connected with ith bus, and Pnew and Qnew is final activeand reactive power load, connected with ith bus.

128 M.M. Aman et al. / Electrical Power and Energy Systems 54 (2014) 123–133

Maximization of system loadability is considered as fitnessfunction, given by Eq. (23).

f ¼ Maxfkmaxg ð23Þ

where f is a fitness function and kmax is the maximum system load-ing factor or loadability.

Subjected to following line constraints,

Iimin � Ii

Limit � Iimax ð24Þ

where ILimit is a ith branch current limit.

Fig. 7. Flow chart of pr

The additional constraints include, there should be no loopingin the system and all nodes must be connected with the sourcenode.

status ¼¼ 1 ðradial systemÞstatus ¼¼ 0 ðnon-radial systemÞ

�ð25Þ

Different tie switch positions will result in radial as well non-radialsystem, graph theory will select only radial distribution system. TheDABC algorithm is applied on radial distribution test systems to findthe optimum tie switch positions, which will result in maximum

oposed algorithm.

Table 2Proposed method results for optimum network reconfiguration for 33-bus test system.

Test case Base case Method [28] Proposed method using radial load flow Proposed method using CPF

Open tie-switches 33,34,35,36,37 06,14,09,32,37 10,14,32,28,06 10,14,32,28,06System loading margin kMax

kV3.41 5.1 5.52 5.500.5500 0.8700 0.9100 0.90

Power loss (MW) 0.21099 0.12812 0.12952 0.12900Vmax 1 1 1 1Vmin 0.9038 0.9416 0.9445 0.9445KMML 10530.14 17914.34 19749.46 19662.08NBVV 21 4 3 3VDI 0.0245 0.0021 0.0013 0.0013

Fig. 8. Radial distribution test systems with 5 tie switches.

M.M. Aman et al. / Electrical Power and Energy Systems 54 (2014) 123–133 129

130 M.M. Aman et al. / Electrical Power and Energy Systems 54 (2014) 123–133

loadability of the system. The complete flow chart of the proposedalgorithm is shown in Fig. 7.

7. Results and discussion

To test the proposed algorithm 3-phase, 12.66 kV standard 33-bus [28] and 69-bus [30] radial distribution systems are used. Thebase load in 33-bus system is 4369.35 kVA and in 69-bus system is4659.67 kVA. The other system details including bus and line datais given in Appendix A. The single line diagram of the system isshown in Fig. 8.

When the proposed algorithm is tested on 33-bus radial distri-bution system, results presented in Table 2 are obtained. The ob-served results are also compared with existing Venkatesh

Fig. 10. Voltage profile curve of 33-bus test system.

Fig. 9. System loading curve for 33-bus radial distribution system.

method [28]. In [28], the author has implemented the MLI basedalgorithm on 33-bus radial distribution network.

From Table 2, following points are observed:

1. Improving the maximum system loadability has improved theKMML from 10530.14 kVA to 19749.46 kVA (which is higherthan the KMML of existing method [28] by 10.24%).

2. The loading margin factor (k) is also calculated from 0 up tothe voltage limit (kV), satisfying line constraints also. It wasfound that the base case can carry only 2403.14 kVA(kV = 0.55) without violating the voltage and line constraints.However the proposed method can carry up to 3976.10 kVA(kV = 0.91), and the method [28] can sustain only3801.33 kVA (kV = 0.87). Thus the proposed method can carry1572.96 kVA more power than then base case and 175 kVAmore power than the method proposed in [28]. These resultsare also summarized in Fig. 9.

3. The proposed method was also found better than the method[28] in terms of better voltage profile (shown in Fig. 10) andnumber of buses violating voltage limits (NBVV). The VDI incase of method [28] has improved 91.4%, however using theproposed method VDI has improved 94.7% in comparison withbase case.

Fig. 11. System loading curve for 69-bus radial distribution system.

Table 3Proposed method results for optimum network reconfiguration for 69-bus testsystem.

Test case Base case Proposed method(optimum results*)

Open tie-switches 69, 70, 71, 72, 73 69, 14, 70, 55, 61System loading margin kMax

kV3.22 5.50.5800 1

Power loss (MW) 0.22495 0.09859Vmax 1 1Vmin 0.9092 0.9495 (0.95)KMML 10344.47 20968.52NBVV 9 0VDI 0.0119 0

* The optimum results with minimum power losses are presented.

M.M. Aman et al. / Electrical Power and Energy Systems 54 (2014) 123–133 131

The proposed algorithm is also applied on 69-bus radial distri-bution test system and the following results are obtained, tabu-lated in Table 3.

Fig. 13. Bus voltages and available line capacity lim

Fig. 12. Voltage profile curve of 69-bus test system.

From Table 3, following points can be concluded:

1. Improving the system loadability has improved the KMML up to100% from 10530.14 kVA to 19749.46 kVA in comparison withbase case.

2. The loading margin factor (k) is also calculated from 0 up to thevoltage limit (kV). It was found that the base case can carry only2702.61 kVA (kV = 0.58) without violating the voltage and lineconstraints. However the proposed method has improved thesystem loading up to 42% (4659.67 kVA corresponding tokV = 1) without violating the voltage and line constraints. Theseresults are also summarized in Fig. 11.

3. The overall system voltage profile (shown in Fig. 12) andvoltage quality has been improved from VDI equal to0.0119 to 0. The minimum bus voltage in base case wasfound to be 0.9092 V at bus 65, however using the proposedmethod the minimum voltage is found equal to 0.95 V atbus 61.

4. Fig. 13 shows the relationship between bus voltages and avail-able line capacity (ILimit � Iflowing).

From Fig. 13, it can be observed that although all lines can carrymore current, however voltage constraints is limiting the systemoperating point at 2702.61 kVA (kV = 0.58) in case of base caseand 4659.67 kVA (kV = 1) in optimum case respectively. This alsoshows that voltage limits come earlier than the line capacity ofthe system.

it curve at point of allowable voltage limits.

Table A269-Bus test system data.

From bus To bus Ri,i + 1 (X) Xi,i + 1 (X) P (kW) Q (kVAR)

1 2 0.0005 0.0012 0 02 3 0.0005 0.0012 0 03 4 0.0015 0.0036 0 04 5 0.0251 0.0294 0 05 6 0.366 0.1863 2.6 2.26 7 0.381 0.1941 40.4 307 8 0.0922 0.047 75 548 9 0.0493 0.0251 30 229 10 0.819 0.2707 28 19

10 11 0.1872 0.0619 145 10411 12 0.7114 0.2351 145 10412 13 1.03 0.34 8 513 14 1.044 0.345 8 5.514 15 1.058 0.3496 0 015 16 0.1966 0.065 45.5 3016 17 0.3744 0.1238 60 3517 18 0.0047 0.0016 60 35

132 M.M. Aman et al. / Electrical Power and Energy Systems 54 (2014) 123–133

8. Conclusion

This paper has presented a new algorithm for network reconfig-uration based on maximization of system loadability. DiscreteArtificial Bee Colony (DABC) is used here to find the optimumtie-switch combinations and the graph theory is used to maintainthe radiality of the system. The proposed algorithm is tested on a33-bus and 69-bus radial distribution test systems. The proposedalgorithm has also been compared with existing method whichwas based on a voltage stability index. Results have shown thatusing the proposed method kVA margin to maximum loadability(KMML) has been improved by 100% (in comparison with basecase), overall system voltage profile has been improved, numbersof buses violating voltage limits have been reduced significantly,system operating point has been improved by 40% and thus thesystem is able to handle more power system load (kVA) withoutviolating the bus voltages and line current constraints.

18 19 0.3276 0.1083 0 019 20 0.2106 0.069 1 0.620 21 0.3416 0.1129 114 8121 22 0.014 0.0046 5 3.522 23 0.1591 0.0526 0 023 24 0.3463 0.1145 28 2024 25 0.7488 0.2475 0 025 26 0.3089 0.1021 14 10

Acknowledgments

This work was supported by the Bright Spark Programme ofUniversity of Malaya and HIR/MOHE research grant (Grant Code:D000004-16001).

26 27 0.1732 0.0572 14 103 28 0.0044 0.0108 26 18.6

28 29 0.064 0.1565 26 18.629 30 0.3978 0.1315 0 030 31 0.0702 0.0232 0 031 32 0.351 0.116 0 0

Appendix A

See Tables A1 and A2.

32 33 0.839 0.2816 14 1033 34 1.708 0.5646 19.5 1434 35 1.474 0.4873 6 4

3 36 0.0044 0.0108 26 18.5536 37 0.064 0.1565 26 18.5537 38 0.1053 0.123 0 038 39 0.0304 0.0355 24 1739 40 0.0018 0.0021 24 1740 41 0.7283 0.8509 1.2 141 42 0.31 0.3623 0 042 43 0.041 0.0478 6 4.343 44 0.0092 0.0116 0 044 45 0.1089 0.1373 39.22 26.345 46 0.0009 0.0012 39.22 26.3

4 47 0.0034 0.0084 0 047 48 0.0851 0.2083 79 56.448 49 0.2898 0.7091 384.7 274.549 50 0.0822 0.2011 384.7 274.5

8 51 0.0928 0.0473 40.5 28.351 52 0.3319 0.1114 3.6 2.7

9 53 0.174 0.0886 4.35 3.553 54 0.203 0.1034 26.4 1954 55 0.2842 0.1447 24 17.255 56 0.2813 0.1433 0 056 57 1.59 0.5337 0 057 58 0.7837 0.263 0 058 59 0.3042 0.1006 100 7259 60 0.3861 0.1172 0 060 61 0.5075 0.2585 1244 88861 62 0.0974 0.0496 32 2362 63 0.145 0.0738 0 063 64 0.7105 0.3619 227 16264 65 1.041 0.5302 59 4211 66 0.2012 0.0611 18 1366 67 0.0047 0.0014 18 1312 68 0.7394 0.2444 28 2068 69 0.0047 0.0016 28 2011 43 0.5 0.513 21 0.5 0.515 46 1 0.550 59 2 127 65 1 0.5

Other data: Current carrying capacity of branches 1–9 is 400 A, 46–49 and 52–64 is300 A and for all other branches including ties line is 200 A.

Table A133-Bus test system data.

From bus To bus Ri,i + 1 (X) Xi,i + 1(X) P (kW) Q (kVAR)

1 2 0.0922 0.0477 100 602 3 0.493 0.2511 90 403 4 0.366 0.1864 120 804 5 0.3811 0.1941 60 305 6 0.819 0.707 60 206 7 0.1872 0.6188 200 1007 8 1.7114 1.2351 200 1008 9 1.03 0.74 60 209 10 1.04 0.74 60 20

10 11 0.1966 0.065 45 3011 12 0.3744 0.1238 60 3512 13 1.468 1.155 60 3513 14 0.5416 0.7129 120 8014 15 0.591 0.526 60 1015 16 0.7463 0.545 60 2016 17 1.289 1.721 60 2017 18 0.732 0.574 90 40

2 19 0.164 0.1565 90 4019 20 1.5042 1.3554 90 4020 21 0.4095 0.4784 90 4021 22 0.7089 0.9373 90 40

3 23 0.4512 0.3083 90 5023 24 0.898 0.7091 420 20024 25 0.896 0.7011 420 200

6 26 0.203 0.1034 60 2526 27 0.2842 0.1447 60 2527 28 1.059 0.9337 60 2028 29 0.8042 0.7006 120 7029 30 0.5075 0.2585 200 60030 31 0.9744 0.963 150 7031 32 0.3105 0.3619 210 10032 33 0.341 0.5302 60 4021 8 0 2 – –

9 14 0 2 – –12 22 0 2 – –18 33 0 0.5 – –25 29 0 0.5 – –

Other data: Current carrying capacity of branches 1–5 is 400 A, 6–7 and 25–27 is300 A and for all other branches including ties line is 200 A.

M.M. Aman et al. / Electrical Power and Energy Systems 54 (2014) 123–133 133

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