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systems. Dynamic control of congestion as reported in [16] may be too expensive and also require precisemonitoring.

In the present work, the congestion zones in a power network are first identified using a line loading indexmethod described in section II. The computed line loading indices further assists to develop the ranking tablewhere most congested (heavily loaded) lines can be easily identified. Tripping of one or more of these lines leadto even greater level of congestion in the remaining lines. The objective of the present work is to relievecongestion in these lines by formulating a penalty based congestion constrained OPF problem and solving thesame using Particle Swarm Optimization (PSO) technique as described in section II. The OPF solution attemptsto reschedule the generators in such a way that the individual line flows are brought down to a desired level, notexceeding their loadability limits. The effectiveness of the proposed algorithm has been demonstrated on themodified IEEE 30 bus system under contingencies. The results indicate that the method proposed in this paper isefficient in limiting line congestion at the cost of a nominal congestion management charge without any loadcurtailment and installation of FACTS devices. The proposed method also provides better management of busvoltage profile, reduces the total line loss and improves the security of the system in the event of contingencies.

The work in this paper has been divided into two sections. The first section is the theory containing problemformulation, implementation of the proposed methodology with PSO and the formulation of the proposed lineloading index. Simulation and results to depict the applicability of the proposed methodology to minimizecongestion, operating cost and to offer a net saving in respect of congestion management cost have been

presented in the second part of the paper.

II. Theory:The proposed methodology rests on proper formulation of the objective functions along with the constraints.The methodology has been primarily used with voltage security and line loss penalty based optimization alongwith conventional cost optimization and then it has been applied with the proposed congestion constrained costoptimization problem using PSO. The equality, inequality and security constraints , however remains same forthe all the two algorithms and the proposed algorithm.

A. Problem formulation:

Objective function for conventional cost optimization:Minimize

1

G

T

N

n

F C=

= $/hr (1)2

i gi giC AP BP C = + + (2)

GN =No of generators

A, B, C = cost co-efficient of generators

giP = generation of ith generator in MW.

Objective function for voltage and line loss penalty based optimization:Minimize

min max

1

1 2G

T

N

l

n

F C p xV p xP=

= + + $/hr (3)

1p =Penalty for voltage

minV = Minimum bus voltage in p.u. to be allowed.

2p =Penalty for line loss

maxlP =Maximum limit of line loss to be allowed

Objective function for the proposed voltage , line loss and congestion penalty based optimization

Minimize

Sandip Chanda et al. / International Journal of Engineering Science and Technology (IJEST)

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min max max1

1 2 3G

T

N

l ij

n

F C p xV p xP p xP=

= + + + $/hr (4)

3p =Penalty for congestion

maxijP =Maximum line flow to be allowed between ith and jth bus.

The penalties are added only when the constrains violate their limit as in case of static penalty optimization.The constraints are common for all the above objective functions and are as follows:

1. Equality or power balance constraints:

1

( cos sin ) 0n

Gi Di i j ij ij ij ij

i

P P V V G B =

+ = (5)

1

( sin cos ) 0n

Gi Di i j ij ij ij ij

i

Q Q V V G B =

= (6)

GiP =Active power injected in bus i

DiP =Active power demand on bus i

iV =magnitude of voltage of buse i

jV = magnitude of voltage of buse j

ijG =Conductance of transmission line from bus i to j

ijB = Susceptance of transmission line from bus i to j

n = no of buses

2. Inequality or generator output constraints:min max

gi gi giP P P (7)

min max

gi gi giQ Q Q (8)

giP ,

giQ = Active and reactive power of generator i respectively

min

giP , min

giQ =Upper limit of active and reactive power of the generators

max

giP ,

max

giQ =lower limit of active and reactive power of the generators

3.Voltage constraint:min max

i i iV V V (9)max

iV ,min

iV are upper and lower limit of iV

4. Transmission constraint:

max minij ij i jP P P (10)

maxijP , minijP are the max and minimum line flow limits of Pij

B. Line loading index :The loadability limit of transmission lines are restricted by several constraints. In many cases the transmissioncapacity is limited by thermal capacity of the lines . However, it has been established in [17] [18] that in case oflong EHVAC lines the synchronous (Angular) and static voltage stability limits play more predominant role inrestricting the power flow through long lines . For such lines , the surge impedance loading (SIL) level can beconsidered as sufficiently accurate loadability limit. The SIL level for such lines is generally lower than thethermal capacity of the lines . SIL level of typical uncompensated 400KV line is in the range of 550-625 MWdepending upon number of sub-conductors, bundle conductor configuration, tower structure etc., whereas

thermal limit is of the order of 800-900MW.Hence in the present paper a line loading indexing method has beenproposed to identify the congested lines in the system , which have power in the vicinity of SIL limit. Theproposed method is more practical than the earlier security sensitivity indices method [3] which rely on the


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thermal limits of lines. The lines having high value of loading index represent the most congested lines in asystem, and outage or further loading of these lines will lead to the worst possible contingencies of the system.The congestion level of a line can be judged by an index proposed as

Line loading index= ijPSIL

(11)

ijP = Line flow between ith and jth bus

SIL= surge impedance loading of the line

It is quite imperative that the higher the value of this index, the higher is the congestion level and lower is itssecurity level of that line.

C. Methodology implementation with PSO :

PSO is a population based optimization method first proposed by Kennedy and Eberhart in 1995.[19]-[20]. Thisalgorithm is motivated by social behavior of organisms, such as bird flocking. In PSO, a number of particles

constitute a swarm, and each particle is a solution of the optimization problem. The position of each particle inrepresented by XY axis position and also velocity is expressed by Vx (velocity in x axis ) and Vy( velocity in Yaxis).

1

1 1 2 2. (....) ( ) (....) ( )k k k k

i i i i iv wV c xrand x pbest x c xrand x gbest x

+= + + (12)

1 1k k k

i i i x x v+ += + (13)

Each particle knows its best value so far (pbest) and its XY position. This information is analogy of personalexperience of each agent. Moreover each agent knows its best value so far in the group (gbest) among pbests.

1

1

1 1

if (

if ( ) pbest

t t t

i i it

i t t t

i i i

pbest f x pbest pbest

x f x

+

+

+ +

) >=

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Fig.2 The standard IEEE 30 bus system

TABLE IA: SYSTEM DESCRIPTION FOR CASE STUDIES

Sl.No

Variables 30 bus system

1 Buses 30

2 Branches 41

3 Generators 6

4 Generator buses 6

5 Total demand(MW)

283.6

TABLE IB: GENERATOR COST CO-EFFICIENT OF IEEE 30 BUS SYSTEM

Busno

Real Power outputlimit in MW

Cost Co-efficient

Min Max a(US$/MW2)

b(US$/MW)

c(US$)

1 50 200 0.00375 2.00 5000

2 20 80 0.01750 1.75 1000

5 15 50 0.06250 1.00 600

8 10 35 0.00834 3.25 300

11 10 30 0.02500 3.00 350

13 12 40 0.02500 3.00 400

A. The step by step procedure followed in the present study are as follows :1. For a given generation and load pattern, ac load flow analysis in the IEEE 30 bus system under study has beencarried out using Newton-Raphson load flow method and overloaded lines have been selected using theproposed Line Loading index method described in Section II.

2. Six most congested lines were identified based upon their loading indices presented in Table II. It is obviousthat tripping of one of these lines would lead to worst possible scenario in respect of congestion.3. A multiobjective congestion constrained cost optimization algorithm has been developed using particleswarm optimization.4.For outage of each of the six congested lines , according to the ranking table ac load flow has been carriedout to determine the degree of congestion.5. The constraints are set in PSO based OPF , each for maximum line flows ,line losses and minimum busvoltage amplitudes.6. The results of PSO are evaluated to determine constraint violation. The penalties are applied for violation ofmaximum line flow limits , minimum value of p.u. bus voltage and on actual value of the line losses.7. PSO search algorithm now looks for the optimal generation pattern which minimizes the overall operationalcost including cost of generation , power loss charges , penalty charges for congestion and poor voltage profiles.8.The search procedure repeats the following steps for a given number of iterations. The parameter setting of

PSO based search is given in the appendix.i) velocity of the particles with inertia weight have been found according to equation[12]


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ii) The velocity is added with the previous iteration solution to obtain the new set of population following theequation [13]

iii) Ac power flow has been carried out and the fitness function is calculated as stated in step5.iv) Compare fitness values and find the best possible solution.

B. The detailed flow chart of the proposed algorithm is given in fig.2

Fig 2. Flowchart of the Proposed methodology

C. Identification of most vulnerable lines in terms of congestion by Line Loading Index :For proper identification and assessment of the congestion zone in the system, at the outset, the studyconcentrates on the determination of most congested lines using the proposed line loading index developed insection II. The ranking table (Table II) represents 38 lines with their respective line loading indices. With thehelp of this table, congested lines of the system can be identified and proper congestion relief can beimplemented.


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TABLE II: SELECTION OF VULNERABLE LINES BY LINE LOADING INDEX

line no power(MW) LineLoading

index

1-2 117.7962 0.818029

1-3 59.44315 0.41282-4 34.07481 0.236631

2-5 63.01612 0.437612

2-6 45.4126 0.315365

3-4 55.59228 0.386058

4-6 50.85563 0.353164

4-12 30.17419 0.209543

6-7 34.65778 0.240679

6-8 10.09864 0.070129

6-9 24.83771 0.172484

6-10 12.25928 0.085134

7-5 11.53319 0.0800929-10 18.50686 0.12852

10-20 10.04907 0.069785

10-17 6.59687 0.045812

10-21 17.84925 0.123953

10-22 8.9778 0.062346

11-9 12.176 0.084556

12-14 7.60297 0.052798

12-15 17.39429 0.120794

12-16 5.97692 0.041506

13-12 12 0.083333

14-15 1.33518 0.009272

15-18 5.02098 0.034868

15-23 5.31357 0.0369

16-17 2.44593 0.016986

18-19 1.79543 0.012468

20-19 7.73483 0.053714

21-22 0.2059 0.00143

22-24 9.10916 0.063258

23-24 2.08428 0.014474

25-26 3.54677 0.02463

27-25 1.32728 0.009217

27-29 6.20025 0.043057

27-30 7.10515 0.049341

28-27 14.63268 0.101616

29-30 3.70687 0.025742

D. Determination of line flow limit:It is evident from the ranking Table II, 6 lines namely 1-2,2-5, 1-3, 3-4, 4-6 and 2-6 are most congested and it isquite apparent that their exclusion form the system would represent worst possible single line contingencies. Itmay be noted that with the increase of congestion, the security level of the lines decreases and at the same timethe penalty cost associated with congestion level goes up. On the contrary relieving congestion in the lines willdemand rescheduling of generation and increased generation cost, commonly termed as congestion relief cost.Thus the particular level of congestion relief to be adopted is an important area of study.Table III presents the cost of congestion relief (increased generation cost due to rescheduling) against variousallowable levels of line congestion. In standard IEEE 30 bus system most of the line flows remain below 50%

of their SIL limits (below the congestion threshold point). However in contingent condition, the line flowsexceed this congestion threshold, and some relief measures have to be adopted. The example case presented inTable III, thus corresponds to one such contingency condition, with line 1-2 tripped. It is evident that the line


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flow limit can be restricted to any arbitrary value but only at the cost of rescheduling .The maximum line flowlimit, in practice should be chosen at such a value that it can cater possible new transactions and increase in loaddemand in future without exceeding SIL as well . Henceforth the line limit has been set at 50% of SIL.

TABLEIII: VARIATION OF CONGESTION RELIEF COST (RESCHEDULLING COST) FOR DIFFERENT ALLOWABLE LEVELSOF CONGESTION WITH 1-2 LINE TRIP

Line flow as apercentage of SIL Rescheduling cost$/hr

40% 1171.108

50% 59.85

70% 16.12

100% 5.8

110% 0.28

E. Relieving congestion by imposing Penalty :A practical approach for relieving congestion in the power lines would be to impose penalty for line flows

exceeding the preset threshold limit for congestion. (50% of respective line SIL limits). Under this proposedcongestion penalty regime, the system operator will be forced to reschedule the generation and transmissionof power to avoid paying high penalty charges for routing power through already congested lines. The

rescheduling of generation would generally mean an increase in generation cost above the optimumgeneration cost based upon cost co-efficients of generators alone . The objective should now be to optimizethe overall operational cost of the power generating system including the cost of generation as well as thepenalty cost due to congestion. The line losses under rescheduled power flow condition must be taken intoconsideration in the optimization problem. Further the voltage profile of the buses have to be maintainedwithin the stipulated limits(5%) of the nominal values . This can be ensured by imposing additional penaltyfor any deviation of load bus voltages beyond these stipulated limits. Thus the present problem reduces to amulti objective optimization problem described in section. The case study on IEEE 30 bus system undervarious contingent conditions demonstrate that the proposed multi-objective optimization will lead tominimization of overall operational cost of the system ( cost of generation plus various penalty charges ) atthe same time relieving congestion on power lines and thereby enhancing the securityThe present case study deals with n-1 contingency(1 from n elements to be contingent) of the system . Everytime, the proposed algorithm reschedules the generators to achieve a feasible solution maintaining the voltage

, power loss and congestion constraints. The table VI depicts the results of the case study where a comparisonof line flows between the conventional method and the proposed method. In deregulated environment, the ISOcan use this algorithm to re-schedule the GENCOS for required level of congestion management duringcontingency..

TABLE IV: COMPARISON OF LINE FLOW WITH CONVENTIONAL, AND PROPOSED PENALTY BASED OPTIMISATIONS

Tripped

lines

Conventional Optimizationwithout any Penalty

Optimization with voltage andpower loss Penalty

Optimization with voltage ,powerloss and congestion Penalty

Genera-

tioncost

($/hr)

Lineloss(MW)

minvolta

ge(pu)

Maxlineflow(MW

)

Genera-

tioncost

($/hr)

Lineloss(MW)

Minvolta

ge(PU)

Maxlineflow(MW

)

Generation

cost($)

Lineloss(MW)

Minvolta

ge(PU)

Maxlineflow(MW)

1-2 849016.2

90.991

7151.3

08600 8.43

0.9947

101.05

8560 5.730.994

471.9

9

2-5 849018.3

20.990

4103.4

99250 6.58

0.9932

41.44 8910 6.810.993

450.5

9

1-3 847012.3

20.992

8169.4

78520 5.99

0.9926

98.01 8560 5.180.992

471.9

8

3-4 846012.1

40.993

167.29

8520 5.990.992

698.01 8550 5.26

0.9926

71.99

4-6 846010.3

50.991

3129.2

68490 5.99

0.9925

84.34 8510 5.980.992

171.9

4

2-6 846010.2

60.992

104.43

8490 5.990.992

569.68 8490 5.99

0.9924

69.66


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It is observed that the proposed multi-objective OPF algorithm can effectively reduce line flows only by re-scheduling of generation and without any load curtailment or installation of FACTS devices. As expected, thegeneration cost increases due to the change in individual contribution of the generators but overall savings inoperational cost shall be achieved due to reduction in the penalty charges on congestion, voltage and power loss.The comparison of overall operating cost has been depicted in table V.

TABLE V: COMPARISON OF OPERATING COSTS

Trippedlines

OPF without penaltiesOPF with voltage constraint

and power loss charges

OPF with voltage constraint,power loss charges and

congestion penalty

Cost

ofgene-

ration

($/h

r)

Penaltycostfor

conges-tion

($/hr)

Pen-altyForPower

loss($/hr

)

Totalopera

tingcost

($/hr)

Costof

genera-

tion($/Hr

)

Penalty

costfor

conges

tion($/hr

)

Pen-altyForPower

Loss($,hr

)

TotalOperat-ingcost

($/hr)

Costof

genera-

tion($/hr

)

Penalty

costfor

conges-tion

($/hr)

Penalty

ForPowe

rLoss($/hr

)

Totaloperati

ngcost

($/hr)

1-2849

0317.23

316.29

9120 8600116.2

381.9

78800 8560 NIL NIL 8560

2-5849

0211.58

344.86

9040 9250-

36.61-

7.369200 8910 NIL NIL 8910

1-3847

0389.95

213.31

9070 8520104.1

124.5

78650 8560 NIL NIL 8560

3-4846

0381.16

205.55

9050 8520104.0

622.1

78650 8550 NIL NIL 8550

4-6846

0229.23

130.31

8820 8490 49.58 0.40 8540 8510 NIL NIL 8510

2-6846

0139.06

127.30

8720 8490 0.07-

0.058490 8490 NIL NIL 8490

The net saving in operational cost can now be defined as the difference between un-constrained operation(simply based on optimal generation schedules) and constrained based optimal operation (including variouspenalty charges). Table VI demonstrates the net savings achieved by i) voltage and power loss constrained OPFii) congestion, voltage and power loss constrained OPF.

TABLE VI: SAVING WITH RE-SCHEDULLING

Tripped lines net savings for OPF with voltageconstraint and power loss charges

($/hr)

net savings for OPF with voltageconstraint, power loss charges and

congestion penalty($/hr)

1-2 560 2392-5 130 292

1-3 510 891

3-4 500 966

4-6 310 334

2-6 230 92

Congestion Management Cost :The congestion management cost can be defined as the difference between the generation cost of theconventional method and generation as in the multi-objective multi-constraint OPF obtained from the proposedalgorithm. The power loss management cost and voltage profile management cost are defined in similar mannerand the same has been calculated .Table VII shows the variation of congestion management cost as well as

voltage and power loss management cost in the proposed OPF under various contingent operation of the system.The ISO may recover this excess charge from the market participants.


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Table VII: VARIATION OF CONGESTION MANAGEMENT COST WITH CONTINGENCIES

Trippedlines

Voltage and power lossmanagement cost for OPF with

voltage constraint and power losscharges($/hr)

congestion management charge forOPF with voltage constraint, powerloss charges and congestion penalty

($/hr)

1-2 110 71.32-5 760 42.7

1-3 55.2 92.3

3-4 56 87.7

4-6 36.1 49.1`

2-6 35 34.9

OPERATIONAL ISSUES :A. Generation Shift:As mentioned earlier , the multi-objective OPF algorithm leads to wide generation shift from theconventional generation cost coefficient based optimal generation scheduling .Further this generation willbe variable depending upon the operating conditions and contingencies making it even more difficult for the

GENCOs to pre-plan their generation schedule. In real time operation, the ISO has to negotiate with theGENCOs to realize this in practice. Sometimes the GENCOs may charge this additional amount for thisgeneration shift which may further be incorporated in congestion management cost. [5]Fig. 3 depicts the shift in generation under voltage and line loss constrained OPF and under congestionvoltage and power loss constrained OPF from the base case (unconstrained optimal generation schedule) fornormal operating condition of the system.

Fig3. Comparison of generation Shift

B. Improvement in Voltage Profile :Another important feature of the proposed algorithms is the improvement in voltage profiles .Fig. 4 showsthe comparison of voltage profiles between the two algorithms and the conventional cost optimization .The voltage profile with penalty algorithms is better than the conventional cost optimization method. Hence

it can be inferred that the congestion management cost not only relieves congestion but also improve thevoltage profile. Improvement in voltage profile suggests an improvement in power transfer capability of theline.


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Fig.4 Comparison of voltage profile

C. Reduction in Power Loss:

Improvement of performance of a power system network depends on line loss minimization. Along withcongestion management, the proposed algorithm can cause a considerable reduction in total line loss . Fig 5shows the comparison of total line losses of the network with the conventional and proposed algorithms. Duringthe consideration of the generation shift, the cost of power losses and the corresponding saving need also to becalculated.

Fig 5. Comparison of total line losses

Conclusion:A PSO based methodology has been proposed in this paper for congestion management in a contingent systemat a minimum cost of management but without any load curtailment. On violation of a stipulated line flow , anadditional penalty has been added to the objective function to direct the PSO based search process to the mostfeasible optimal solution considering the constraints . In doing so , line congestion has been limited to aspecified value by generation re-scheduling. It has been also been observed that the bus voltage profile of thesystem has improved and total system loss has decreased appreciably with the application of the proposedalgorithm. The net increase in cost in the proposed method is contributed due to generation rescheduling tomaintain limited congestion and net decrease in cost is due to voltage improvement and reduced loss. It has alsobeen shown that in the present deregulated power market scenario, the proposed methodology can offer a netsaving of congestion cost to the market participants and can thus contribute to social welfare without affectingthe sustainability of power supply. For proper assessment of congestion and security an index being referred asline loading index has also been proposed in this paper to assist proper selection of contingency. The IEEE30bus system is analyzed to establish the technique. The results show that the proposed algorithm develops a costeffective congestion management technique in a restructured contingent power system which can be used byeffectively used by ISO.


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References:

[1] Ye Peng , Yao Bing , Song Jiahua, Comparison study of Spot Price under Transmission Congestion with Different ControlMechanism, IEEE/PES Transmission and Distribution Conference & Exhibition : Asia and Pacific Dalian, China

[2] K. Selvi, T.Meena , Dr.N.Ramaraj ,A generation Rescheduling Method to Alleviate Line Overloads using PSO, IE(I) Journal-EL,2005[3] Yu Xiaodan, Jia Hongjie, Zhao Jing, Wei Wei, Li Yan , Zeng Yuan, Interface Control Based on Power Flow Tracing and Generator

Re-redispatching, Automation of Electric Power Systems IEEE,2008

[4] G.Baskar, M.R. Mohan, Contingency constrained economic load dispatch using improved particle swarm optimization for securityenhancement, Electric Power System Research Elsevier ,2008[5] E.Muneender, M.D. Vinod Kumar,Optimal Rescheduling of real and reactive powers of generators for zonal Congestion Management

Based on FDR PSO, IEEE T&D Asia, 2009

[6] Sujatha Balaraman, K.Kamaraj , Congestion management in Deregulated power system using real coded genetic algorithm,International Journal of Engineering Science and Technology , Vol2(11),2010,6681-6690

[7] Sujatha Balaraman , K. Kamaraj, Application of Diffrential Evolution for Congeation management in power system, Modern AppliedScience ,Vol 4, No 8, August 2010

[8] Zhao Jinli, Jia Hongjie, Yu Xiaodan, Voltage Stability Control Based on real power flow tracing ,Proceedings of CSEE, IEEE,2009[9] Xiaosong Zou, Xianjue Luo, Zhiwei Peng ,Congestion Management Ensuing Voltage Stability under Multicontingency with

preventive and Corrective Controls, IEEE,2009

[10] Hwa-Sik Choi, Seung II Moon ,A new Operation of series compensating device under Line Flow Congestion using the Linear zedLine Flow sensitivity, Power Engineering Society winter meeting IEEE,2001

[11] E.M. Yap, M.Al-Dabbagh, P.C. Thum ,UPFC Controller in Mitigating Line Congestion for Cost-Efficient Power Delivery, PowerEngineering Conference IPEC, IEEE,2006

[12] Xiao-Ping Zhang , Liangzhong Yao, A Vision of Electricity network Congestion Management with FACTS and HVDC,DRPT2008,6-9 April, 2008 Nanjing China

[13] Garng.M.Huang, Nirmal Kumar , C Nair ,An OPF based Algorithm to Evaluate Load Curtailment Incorporating Voltage StabilityMargin Criteria, Power Engineering Society Winter Meeting ,IEEE, 2002

[14] Fei HE, Yihong WANG, Ka Wing CHAN, Yutong ZHANG, Shengwei MEI ,Optimal Load Shedding Stategy Based on ParticleSwarm Optimisation, 8th international conference on Advances in Power System Control operation and Management .APSCOM 2009

[15] Igor Kopcak , Luiz C.P. da Silva , Vivaldo F. Da Costa, Jim S. Naturesa,Transmission Systems Congestion Management By UsingModal Participation Factors, IEEE Bologna Power Tech Conference , June 23-24, Bologna ,Italy,2003

[16] J.Ma, Y.H.Song,Q.Lu, S.Mei , Framework for dynamic congestion Management in open power markets, IEE Proc.Gener.Transm.Distrib. Vol.149,No.2 March 2002

[17] R.N.Nayak, Y.K. Sehgal, Subir Sen ,EHV Transmission Line Capacity Enhancement through Increase in Surge Impedance LoadingLevel, Power India Conference ,2006

[18] K.P. Basu , Power transfer Capability of Transmission Line Limited by voltage Stability : Simple Analytical Expressions, IEEEPower Engineering Review, September 2000

[19] Kennedy, J, and Eberhart.R , Particle Swarm Optimisation,. Proc. IEEE Int. Conf. Neural Netw. 1995, Vol 4, pp. 1942-1948[20] Kennedy, J, and Eberhart.R , A New Optimiser using particle swarm theory,. Proc6th Int Symp on Micro Machine and Human science

, Nagoya, IEEE Service Center, October 1995, pp. 39-43


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Appendix

BUSDATA OF IEEE30 BUS SYSTEM


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LINE DATA OF IEEE30 BUS SYSTEM

| From | To | R | X | B/2 | X'mer |

| Bus | Bus | pu | pu | pu | TAP (a) |

1 2 0.0192 0.0575 0.0264 1

1 3 0.0452 0.1652 0.0204 1

2 4 0.0570 0.1737 0.0184 1

3 4 0.0132 0.0379 0.0042 1

2 5 0.0472 0.1983 0.0209 1

2 6 0.0581 0.1763 0.0187 1

4 6 0.0119 0.0414 0.0045 1

5 7 0.0460 0.1160 0.0102 1

6 7 0.0267 0.0820 0.0085 1

6 8 0.0120 0.0420 0.0045 1

6 9 0.0 0.2080 0.0 0.978

6 10 0.0 0.5560 0.0 0.969

9 11 0.0 0.2080 0.0 1

9 10 0.0 0.1100 0.0 1

4 12 0.0 0.2560 0.0 0.932

12 13 0.0 0.1400 0.0 1

12 14 0.1231 0.2559 0.0 1

12 15 0.0662 0.1304 0.0 1

12 16 0.0945 0.1987 0.0 1

14 15 0.2210 0.1997 0.0 1

16 17 0.0824 0.1923 0.0 1

15 18 0.1073 0.2185 0.0 1

18 19 0.0639 0.1292 0.0 1

19 20 0.0340 0.0680 0.0 1

10 20 0.0936 0.2090 0.0 1

10 17 0.0324 0.0845 0.0 1

10 21 0.0348 0.0749 0.0 1

10 22 0.0727 0.1499 0.0 1

21 23 0.0116 0.0236 0.0 1

15 23 0.1000 0.2020 0.0 1

22 24 0.1150 0.1790 0.0 1


ISSN : 0975-5462 Vol. 3 No. 5 May 2011 4447

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